Facilitating the integration of renewable energy through ......No te rindas que la vida es eso, Continuar el viaje, Perseguir tus sueños, Destrabar el tiempo, Correr los escombros,

Facilitating the integration of renewable energy

through combined-heat-and-power flexibility

Juliana Victoria ZAPATA RIVEROS

Examination committee: Prof. dr. ir. Hugo Hens, chair Prof. dr. ir. William D’haeseleer, supervisor Prof. dr. ir. Ronnie Belmans Prof. dr. ir. Lieve Helsen Prof. dr. ir Geert Deconinck dr. ir. Erik Delarue Prof. Maurizio Sasso, PhD (University of Sannio, Italy)

Dissertation presented in partial fulfilment of the requirements for the degree of PhD in Engineering Science

May 2015

© 2015 KU Leuven – Faculty of Engineering Science

Uitgegeven in eigen beheer, Juliana Victoria Zapata Riveros, Celestijnenlaan 300A box 2421, B-3001 Heverlee (Belgium)

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No te rindas que la vida es eso, Continuar el viaje,

Perseguir tus sueños, Destrabar el tiempo,

Correr los escombros, Y destapar el cielo

-Mario Benedetti

To my parents

I

Acknowledgements

¿Cuatro años, chiquita? Four years, my little one? A bit more than four years have already passed since the moment when my father asked me if I was seriously thinking about spending four years more of my life studying at the university… four years.

Now four years later, I would like to thank my promoter professor D’haeseleer for giving me the opportunity to start and successfully finish an important step of my career, and for all the patience and time he invested in this work. I also appreciate the constructive comments of my jury members. Thanks to their feedback, my work has been largely improved.

I do not know who invented the motto of “TME colors your life”, but it truly reflects my experience in this division: during my time here not every day had a blue sky (figuratively speaking), but my colleagues were there to make me smile and I am sincerely thankful for that. After all, who can resist the contagious laughter of Dieter, or the funny anecdotes of Ruben’s time in Colombia. I will not forget his “flattering” comments that Dries tried hard to continue (with no real success). Among all the hard work, lunch was always a moment to look forward to: Joris and his strange conversations, Geert describing my food as baby vomit and Kris’ appropriate comments at the appropriate moment.

I would also like to thank all the colleagues who in one way or another helped me through these four years: Jeroen and Kenneth for the interesting discussions; Kenneth VdB who was always ready to help with a big smile and a funny comment; Nico for being our first reference of rectitude; Tijs for fighting for our “rights”; Cornelia for our short conversations in the hall; Sepideh for carrying always a big smile; Annouk for reminding the TME group that “girls have the power”; Emre for explaining me that I should not drink 8 liters of water a day; Marteen for reminding me that we are in Belgium and I should have learnt more Dutch than “Dank u well en graag gedaan”; and Damian for being kind and patient explaining me the principles of heat pumps.

I owe special thanks to my office colleagues for all the jokes and conversations: Daniel for being like the older brother in the office helping me to find my way in Belgium; Stefan for his infinite kindness and for cheering me up these last months; Wouter for keeping the seriousness at work and for finishing the chocolates I could not finish myself; Mats for his funny and cheeky comments; Roel for his ecological principles;

II Acknowledgments

Andreas for bringing some fresh air to the office (not only literally by opening the windows).

Next to our office there were always Valerie and Kathleen ready to help with visas, tickets, hotel bookings, and asking about my health. I really appreciate all your patience and your work.

For all those colleagues that I forgot to mention: enjoy your time in TME. One day you will be writing this and thinking “Oh my god! How much I am going to miss this group!”.

I would like to specially thank my group of friends. Natalia’s way to see the life challenged my white and black version of life and I am grateful for that. For most of my PhD, I counted on Elena’s practical advice which helped me see that life situations were not as complicated as I had thought. Laura, my favorite “costeña”, thanks for all the enthusiasm and party spirit that you and Oonagh have brought to my life. Thanks for being a fantastic football fan – without you and Andrea the World Cup would not have been as fun as it was and thanks for being always ready to celebrate my small victories. And my dear Heidi, who has become like a sister, thank you for letting me get involved in your wedding arrangements, for cheering me up with your logical (and not so logical) explanations, for forcing me to go to the gym and entertaining me in those hours of pain.

My sincere thanks go to my Colombian supporting group without whom my European adventure would not have worked so well: Carito, Willie y Hector gracias por estar siempre ahí, reírse conmigo, reírse de mí y enseñarme a no tomar la vida tan en serio. Gracias por probar que la amistad no tiene fronteras ni visas que la detengan.

I would like to express my gratitude to my family. Cómo no darle las gracias a mi tío Jhon por esperarnos cada año con la comida más deliciosa del mundo; a mi tío Jorge por tenernos siempre en sus oraciones y ser el vivo recuerdo de mi padre; a mi hermana por poner sus metas muy altas y mostrarme que es posible alcanzarlas, por ayudarme y preocuparse por mí; y a mi mamá a ella se lo debo todo. Su fortaleza, su ternura y su lucha cada día por salir adelante han sido la más grande motivación para cumplir mis sueños.

Außerdem möchte ich mich bei meinem Freund Micha dafür bedanken, dass er immer an mich geglaubt und mir Mut gemacht hat meine Ziele zu erreichen. Er hat mich zum Lachen gebracht und mein Leben mit Freude erfüllt. Darum freue ich mich auf zukünftige Abenteuer.

Four years later, I do not regret this fantastic experience and I am sure my father agrees with me. Now he would be proudly saying “esa es mi chiquita”.

III

Abstract

The liberalization of the electricity markets as well as the growing environmental concerns have triggered the widespread use of distributed generation technologies, especially renewable energy resources and combined heat and power generation (CHP). Nevertheless, the intermittency of some of these technologies such as photovoltaic installations and wind turbines, yields an important challenge to the electric grid operator.

In this context it is proposed to group controllable and intermittent generation devices in what is known as a virtual power plant (VPP). This kind of aggregation will facilitate not only the participation of distributed generators in the electricity market but it also might help to compensate the forecast errors of renewables by using the flexibility of controllable devices.

The aim of this work is to develop several control strategies for the economic optimal operation of distributed generation devices that are aggregated into a virtual power plant incorporating thermal-demand aspects. The main focus is on the role that cogeneration can play in increasing the flexibility of the system and the profits of the virtual power plant operator. In this respect, three main research questions are assessed: the ability to reduce the imbalance volume and the associated costs using residential micro-CHPs, the opportunity to provide passive balancing with an aggregation of micro-CHPs and the ability of cogeneration district heating to compensate for the uncertainty in the system.

It is shown that micro-CHPs are able to partially compensate for the deviations between local electric power demand and local power generation. Nevertheless, this imbalance volume reduction does not always lead to a reduction of the imbalance cost. It is demonstrated that a control strategy aiming to minimize imbalance volumes disregarding the imbalance tariffs can lead to an increase in operational costs, especially during spring and summer. Furthermore, the results indicate that even in the best case scenario, the level of savings are not to be sufficiently high to motivate CHP owners to join a VPP.

The possibility to provide real-time balancing services or passive balancing is assessed for an aggregation of micro-CHP devices installed in different households and service buildings. The results give a clear indication that providing passive balancing leads to

IV Abstract

a total cost decrease in all the seasons compared to a case in which the electricity is traded only in the day-ahead market.

Finally, the added value of using CHP linked to a district heating network (CHP-DH) to compensate for the uncertainties regarding electricity generation and market prices development is investigated. Stochastic programming is used to explicitly model the uncertainties in the system. It is shown that using the flexibility of the CHP-DH together with a thermal-storage unit results in an increase in profits during spring and summer. However, due to the high demand for heat during the winter, the CHP-DH can offer less flexibility during these months resulting in a lower added value. In addition, if the VPP is allowed to react in real time to the current imbalance prices the profit increase is even larger.

To a large extent, the research work presented in the thesis was supported by the LINEAR project1.

1 http://www.linear-smartgrid.be/en/research-smart-grids

V

Beknopte samenvatting

Zowel de liberalisering van de elektriciteitsmarkten als de toenemende aandacht voor de klimaatsverandering zorgden voor een toename in het gebruik van decentrale energieopwekking, voornamelijk in hernieuwbare energie en warmte-krachtkoppeling (WKK). De variabiliteit en moeilijke voorspelbaarheid van sommige van deze technologieën, zoals zonnepanelen en windturbines, zorgen voor grote uitdagingen voor de operatoren van het elektrisch net.

In deze context wordt er voorgesteld om de controleerbare en oncontroleerbare elektriciteitsproductie te groeperen in een zogenaamde virtuele elektriciteitcentrale. Deze aggregatie laat de participanten van decentrale energieopwekking niet alleen toe om deel te nemen aan de elektriciteitsmarkt, deze kan ook helpen om de voorspellingsfouten van hernieuwbare energie te compenseren.

De bedoeling van dit werk is om verschillende regelestrategieën te ontwikkelen voor optimale techno-economische regeling van virtuele elektriciteitscentrales van decentrale energieopwekking. De klemtoon ligt op de rol die cogeneratie kan spelen in een verhoging van de flexibiliteit in het systeem en de opbrengsten voor de operator van de virtuele elektriciteitscentrale. Hierin worden voornamelijk drie mogelijkheden geëvalueerd: de mogelijkheid om de hoeveelheid onbalans en de geassocieerde kost te verminderen door slimme aansturing van micro-WKK’s, de mogelijkheid tot het leveren van passieve balancering met een aggregatie van micro-WKK’s en de mogelijkheid om onzekerheid in het systeem te compenseren door gebruik te maken van een warmtenet met warmte-krachtkoppeling.

Er werd aangetoond dat micro-WKK’s de afwijkingen tussen lokale elektrische vraag en productie gedeeltelijk kunnen compenseren. Desondanks is de vermindering in de hoeveelheid onbalans niet altijd in overeenstemming met de reductie in onbalanskost. Verder werd ook aangetoond dat een regelestrategie, gericht op het minimaliseren van de onbalans, kan leiden tot een stijging in de operationele kost, voornamelijk tijdens de lente en de zomer. Verder tonen de resultaten aan dat zelfs in het beste scenario, de kostvermindering niet genoeg lijkt om eigenaars van een WKK aan te moedigen om in een virtuele energiecentrale te stappen.

De resultaten voor passieve balancering van de aggregatie van micro-WKK’s in zowel residentiële als commerciële gebouwen zijn beter. Deze resultaten geven aan dat

VI Beknopte samenvatting

passieve balancering in staat is om de totale kost te reduceren gedurende alle seizoenen, in vergelijking met het geval waarin de elektriciteit op de day-ahead markt wordt verhandeld.

Ten slotte werd de toegevoegde waarde onderzocht van het gebruik van warmte-krachtkoppeling met een warmtenet om de onzekerheden inzake elektriciteitsproductie en marktprijzen te compenseren. Het gebruik van stochastisch programmeren liet toe om de onzekerheden in het systeem expliciet te modelleren. De flexibiliteit in de combinatie van warmte-krachtkoppeling met warmteopslag en warmtenet, liet toe om de winst te verhogen in het tussenseizoen en de zomer. In de winter is dit systeem minder flexibel en zijn de resultaten conservatiever. Ten slotte, wanneer de virtuele energiecentrale toegelaten wordt om op elk ogenblik op de actuele onbalansprijzen te reageren, kan deze zijn winsten verder verhogen.

Een groot deel van het onderzoek dat in deze thesis wordt gerapporteerd werd gefinancierd door het LINEAR-project2.

2 http://www.linear-smartgrid.be/en/research-smart-grids

VII

Abbreviations

ACF Auto Correlation Function

ADR Active Demand Response

ARIMA Autoregressive Integrative Moving Average

BRP Balance Responsible Party

CCGT Combined Cycle Gas Turbine

CDF Cumulative Distribution Function

CHP Combined Heat and Power

CPP Conventional Power Plant

DA Day-ahead

DG Distributed Generation

DH District Heating

DSO Distribution System Operator

ECDF Empirical cumulative distribution function

EU European union

EV Electric Vehicle

FCR Frequency Containment Reserves

FUR Fuel Utilization Ratio

FRR Frequency Replacement Reserves

GA Genetic Algorithms

HHV Higher Heating Value

HP Heat Pumps

ICE Internal Combustion Engine

ICT Information and Communication Technology

IEA International Energy Agency

LHV Lower Heating Value

VIII Abbreviations

LP Linear Programming

LT Life time of a project

MAS Multi-agent system

MDP Marginal Decremental Price

MILP Mixed Integer Linear Programming

MINLP Mixed Integer non-Linear Programming

MIP Marginal Incremental Price

MPC Model Predictive Control

NLP Nonlinear Programming

NPV Net Present Value

NRV Net Regulation Volume

OTC Over the counter

PACF Partial Auto Correlation Function

PHS Pumped-hydro Storage

PV Photovoltaic

RES Renewable Energy Sources

RES-E Renewable Energy Sources of Electricity

RR Replacement Reserves

RSC Relative Storage Capacity

RT Real Time

SARIMA Seasonal ARIMA

SDP Stochastic Dynamic Programming

SI System Imbalance

SOC State of Charge of the Storage Tank

TSO Transmission System Operator

VPP Virtual Power Plant

WPP Wind Power Plant

IX

List of Symbols

Additional incentive applied on top of the regulation costs in cases of major positive system imbalances [€/MWh]

Electrical efficiency of the CHP [%]

Thermal efficiency of the CHP [%]

Additional incentive applied on top of the regulation costs in cases of major negative system imbalances [€/MWh]

On/off status of the CHP device [-]

∆ Difference between the actual and planned operational cost [€/MWh]

∆ Difference between the electric power generated by the CHP and planned electric power [MW]

∆ Difference between the actual and forecasted electric power demand [MW]

∆ Total imbalance error of the VPP [MW]

∆ Negative imbalance volume [MW]

∆ Positive imbalance volume [MW]

∆ Imbalance caused by the photovoltaic installation [MW]

∆ Difference between RES electric power dispatched and scheduled [MW]

∆ Difference between the actual and scheduled fuel consumption of the boiler [MW]

X List of Symbols

∆ Difference between the actual and scheduled fuel consumption of the CHP [MW]

∆! Difference between the delivered and planned thermal power of the boiler [MW]

∆! Difference between the delivered and planned thermal power of the CHP [MW]

∆" Revenues obtained from selling the flexibility in the balancing market [€]

∆"# Extra gain or loss of green certificates [€]

∆$ Simulation time step [h]

∆% Temperature difference of the storage tank [K]

&'()*+ Thermal efficiency of the boiler [%]

& Electrical efficiency of the reference system [%]

& Thermal efficiency of the reference system [%]

&,- Storage tank loss factor [%]

. Probability of occurrence of a scenario [%]

/0 Day-ahead market prices [€/MWh]

/12 Gas prices [€/MWh]

/# Price to buy electricity from the grid [€/MWh]

/ Imbalance market prices [€/MWh]

/ Negative imbalance prices [€/MWh]

/ Positive imbalance prices [€/MWh]

/ 0 Local price of the electricity [€/MWh]

34 Slope of the electric power to prime energy curve of the CHP [-]

3-5 Slope of the electric power to thermal power of the CHP [-]

List of Symbols XI

67 Banding factor [-]

64 Intercept of the electric power to prime energy curve of the CHP [MW]

6-5 Intercept of the electric power to thermal power output curve of the CHP [MW]

8 Initial investment cost [€]

94 Specific heat [J/kg∙K]

Operational cost of the boiler [€]

Operational cost of the CHP [€]

Cost of producing electricity with the CHP [€]

; Deviation penalty [€]

# Cost of the electricity bought from the grid [€]

Imbalance cost [€/MWh]

Operational cost of the CHP system (boiler and prime mover) [€]

,-<+-_>4 Start-up cost [€]

?1 First component of the piecewise penalty function [MW]

?2 Second component of the piecewise penalty function [MW]

?3 Third component of the piecewise penalty function [MW]

?CD Limits of the piecewise deviation function

E%F Minimum down time of each CHP unit [h]

Electric power generated by the CHP [MW]

GHIJK Scheduled electric power output of the CHP [MW]

HLM Electric power generated by the CHP exported to the grid [MW]

NIJN Electric power generated by the CHP used locally [MW]

XII List of Symbols

O<P Maximum electric power output of the CHP [MW]

O(F Minimum electric power output of the CHP [MW]

JIKQJN Electric power output delivered by the CHP [MW]

0 Electric power traded in the day-ahead market [MW]

0 Day-ahead market bid [MWh]

Electric power demand [MW]

1 0R Forecasted electric power output of the VPP [MW]

; Electric power generated by the PV installation [MW]

;GHIJK Forecasted electric power output of the PV installation [MW]

;JIKQJN Actual electric power output of the PV installation [MW]

0 R20 Actual electric power output of the VPP [MW]

Expected electric power generated by the RES [MW]

R Electric power generated on real time [MW]

R Real time energy generation [MWh]

O<P; Total installed capacity of the VPP [MW]

ST Energy generated by the wind power plant [MWh]

Primary fuel consumption of the CHP [MW]

Primary fuel consumption of the boiler [MW]

U Mass of water in the storage tank [Kg]

V Net cash flow [€]

! Thermal power generated by the auxiliary boiler [MW]

!O(F Minimum thermal power output of the auxiliary boiler [MW]

!O<P Maximum thermal power output of the auxiliary boiler [MW]

! Thermal (dis)charging power from/to the storage tank [MW]

List of Symbols XIII

! Thermal power generated by the CHP [MW]

!O<P Maximum thermal power output of the CHP [MW]

!O(F Minimum thermal power output of the CHP [MW]

! Thermal power demand [MW]

! State of charge of the thermal-storage tank [MWh]

!O<P Maximum capacity of the thermal-storage tank [MWh]

W3$C Discount rate [%]

"0 Day-ahead market profits [€]

"# Profits obtained from selling the electricity to the grid [€]

" Imbalance market profits [€]

" 0 Savings due to the self-consumption of the electricity [€]

X%F Minimum up time of each CHP unit [h]

Subscripts

Y Scenarios

Z Imbalance prices scenario

[ Number of CHP units

W Renewable energy scenarios

\ Day-ahead prices scenarios

$ Time

XV

Contents

Abstract ............................................................................... III

Beknopte samenvatting ........................................................ V

Contents .............................................................................. XV

1. Introduction ................................................................... 1

1.1 General Context.....................................................................................1

1.2 Research Questions ...............................................................................3

1.3 Assumptions and Delimitation of this Work ...............................................4 1.4 Overview of this Work ............................................................................4

2. Background on VPPs, the Belgian Electricity Market, DG and CHPs ........................................................................ 7

2.1 Definition ..............................................................................................7 2.2 The Belgian Electricity Market .................................................................9

2.2.1 Trading ....................................................................................................... 10 2.2.2 Balancing .................................................................................................... 12 2.2.3 Reserve Power ............................................................................................. 14

2.3 Virtual Power Plants in the Electricity Market .......................................... 15 2.3.1 Active Participation in the Balancing Market ................................................... 16 2.3.2 Self-Balancing .............................................................................................. 20 2.3.3 Passive Balancing ......................................................................................... 22

2.4 Cogeneration Concept .......................................................................... 23 2.4.1 Micro-CHPs .................................................................................................. 24 2.4.2 District Heating Cogeneration ....................................................................... 26

2.5 Summary and Conclusions .................................................................... 27

3. Preliminary Concepts ...................................................29

3.1 Heat-Driven Operation ......................................................................... 29

3.2 Electricity-Driven Operation .................................................................. 30

3.3 Economic-Optimization Model ............................................................... 32

3.4 Application to a Case Study .................................................................. 35 3.4.1 CHP Sizing ................................................................................................... 36 3.4.2 Gas and Electricity Prices .............................................................................. 38 3.4.3 Sizing of the Thermal-Storage Tank .............................................................. 39 3.4.4 Reference Case ............................................................................................ 40

3.5 Results and Discussion ......................................................................... 40 3.5.1 Electricity and Heat Generation ..................................................................... 40 3.5.2 Cost Savings ................................................................................................ 45 3.5.3 Influence of the Storage Capacity ................................................................. 46

XVI Contents

3.5.4 Net Present Value ........................................................................................ 47

3.6 Conclusions ......................................................................................... 52

4. Self-Balancing Using Virtual Power Plants ...................53

4.1 Introduction ........................................................................................ 53

4.2 Problem Description ............................................................................. 54

4.3 Optimization Algorithm ......................................................................... 56 4.3.1 Day-Ahead Optimization Algorithm ................................................................ 58 4.3.2 Actual Day Optimization - ‘Forced Self-Balancing’ ........................................... 59 4.3.3 Actual Day Optimization - ‘Economic Self-Balancing’ ....................................... 59

4.4 Assumptions ........................................................................................ 60 4.4.1 Cogeneration System ................................................................................... 60 4.4.2 Electricity and Gas Prices .............................................................................. 61

4.5 Forecasting ......................................................................................... 61 4.5.1 Forecasted and Measured Photovoltaic Data .................................................. 61 4.5.2 Imbalance Price Forecast .............................................................................. 62

4.6 Results and Discussion ......................................................................... 63 4.6.1 Day-Ahead Schedule Compliance .................................................................. 64 4.6.2 Total Operational Cost .................................................................................. 66


5. Passive Balancing Using Micro-CHPs ............................75

5.1 Introduction ........................................................................................ 75

5.2 Methodology ....................................................................................... 76

5.3 Optimization Algorithm ......................................................................... 78 5.3.1 Day-Ahead Optimal Nomination .................................................................... 78 5.3.2 Near Real Time Balancing Optimization ......................................................... 79

5.4 Application to a Belgian case study ........................................................ 81 5.4.1 Description of the Case Study ....................................................................... 81 5.4.2 Auxiliary Boiler and Thermal-Storage Tank .................................................... 82 5.4.3 Gas and Electricity Prices .............................................................................. 83

5.5 Results from the Case Study ................................................................. 83 5.5.1 Results from the Day-Ahead Optimization ...................................................... 84 5.5.2 Results from the Near Real Time Balancing Optimization ................................ 86

5.6 Sensitivity Assessment ......................................................................... 91 5.6.1 Boiler Efficiency ........................................................................................... 91 5.6.2 Sensitivity on the Gas Price ........................................................................... 91 5.6.3 CHP Certificates ........................................................................................... 93


6. Bidding of a VPP in the Day-Ahead Market under Uncertainty...................................................................97

6.1 Introduction ........................................................................................ 97

6.2 Introduction to Stochastic Optimization .................................................. 98

6.3 Methodology ..................................................................................... 103 6.3.1 Stochastic Optimization Model .................................................................... 107 6.3.2 Application to a Case Study ........................................................................ 112 6.3.3 Scenario Generation and Reduction ............................................................. 113

Contents XVII

6.3.4 Limiting the Imbalance Volume ................................................................... 113 6.4 Results and Discussion ....................................................................... 117

6.5 Conclusions and Further Work ............................................................ 122

7. Summary and Conclusions .........................................125

7.1 Self-Balancing Using Residential micro-CHPs ........................................ 125

7.2 Passive Balancing with an Aggregation of micro-CHPs ........................... 127

7.3 Bidding of a VPP under Uncertainty ..................................................... 128

7.4 General conclusions ........................................................................... 130

7.5 Recommendation for Further Work ...................................................... 130

References ..........................................................................151

List of Publications .............................................................163

Short Curriculum ................................................................165

1

1. Introduction

1.1 General Context

The traditional electric power system is evolving from a centralized system largely based on fossil-fuels and nuclear energy, towards a more decentralized electric power system with high penetration of combined heat and power (CHP) generation and electricity from renewable energy sources (RES-E).

According to [1], decentralized or distributed generation (DG) can be defined as an electric power generation source connected directly to the distribution network grid or on the customer side of the meter, independent of the size, fuel or technology used.

Decentralized generation is not a new concept. The first power plants generated electricity locally to meet the demand of the neighboring customers. The economies of scale and technological advances paved the way for a centralized generation system [2]. However, during the last decades, the interest for distributed generators has been rising in Europe.

One of the most important aspects that triggered the renewed interest in DG is the increase of environmental awareness. In line with the environmental concerns, several governments have launched incentives to promote the use of RES-E and energy-efficient technologies. In this context, cogeneration3 can play an important role due to its ability to efficiently use the waste heat and thus reduce primary energy consumption [2].

As a consequence of these support mechanisms, in the coming years, distributed and RES generation will play an important role for the electricity generation. This fact is already visible in the European electric system. According to the statistics given by ENTSO-E, between 2012 and 2013, the increase of the share of RES-E (excluding hydro) was 12%. This then results in a total share of renewables (excluding hydro) of 13% of the electric energy generated by ENTSO-E members [3].

Aside from all expected benefits resulting from the connection of decentralized resources, several concerns arise due to the variable and unpredictable nature of some

3 The terms ‘cogeneration’ and combined heat and power (CHP) are used as synonyms.

2 Introduction

RES-E such as wind and solar generation. The intermittency of RES-E has to be compensated in order to keep the optimal operation of the electricity system.

Traditionally, conventional power plants have been used as operational reserves to satisfy the electric power balance on the short time scale. In general terms, the task of the reserve power is to deal with unforeseen occurrences on the supply side and deviations from the expected demand.

However, the large penetration of intermittent (i.e., largely variable and to some extent uncertain) RES-E, requires an adaptation of the electric power system. The impact of large amounts of intermittent RES-E, especially wind power, in the electric power system has been extensively studied ([4], [5], [6], [7], [8], [9], [10]). In the PhD dissertation of De Vos [9] it is stated that increasing operation reserves in order to accommodate the intermittency of RES-E, can impact the electricity generation cost. Holttinen, et al., [5] conclude that with a penetration of 10% (of gross electric energy demand) of wind energy the reserve cost could increase between 1 and 15%. Milligan, et al., [10] highlight that: “flexibility is the key to successfully and efficiently integrating wind energy”‘.

In this PhD thesis flexibility is understood as “the ability to quickly and inexpensively adapt […] own power generation and demand in response to varying electricity prices, electricity market conditions, transmission and distribution system conditions, and of regulation [11]”.

According to EURELECTRIC several measures can be taken to backup renewables and increase the system flexibility [12]. In addition to the already mentioned dispatch of flexible and back-up generation such as combined cycle gas turbines and hydro power plants, other measures are: interconnection with neighboring zones, applying curtailment and increasing the energy storage capacity. Concerning the last one, this is not limited to large electricity storages such as pumping hydro plants but also to domestic/distributed electric and thermal-storage devices.

Furthermore, flexibility can also be achieved by incentivizing the end users to play an active role in the energy market. This can be done by stimulating active demand response (ADR). This mechanism has been extensively studied in the LINEAR project [13]. The results of this project demonstrate not only the technical feasibility of ADR but also the large potential of using ADR to mitigate the difficulties faced in a deregulated electricity market.

In the same spirit as the LINEAR project, this thesis focuses on consumers who act as small electricity generators, also called prosumers, and provide flexibility by means of

Research Questions 3

energy storage. The aim is to study several measures that can be implemented by these small market players to increase their flexibility. Additionally, the economic benefits obtained by exploiting this flexibility are evaluated.

1.2 Research Questions

The objective of this thesis is to design and develop different control strategies for the optimal techno-economic operation of a group of DG devices incorporating thermal-demand aspects. The main focus is on the role that cogeneration can play to increase the flexibility of the system. In addition, the economic benefits associated with using this flexibility are estimated. The studied cogeneration system includes not only the prime mover but also a backup boiler and a thermal-storage tank that help to decouple the heat demand from electricity generation. This analysis concerns not only small scale micro-cogeneration but also larger units used for district-heating (CHP-DH) applications.

In this context, three different strategies have been identified. They assess the new opportunities that cogeneration units have to exploit their flexibility in the framework of the actual energy market. The three studied strategies build on each other in a complementary manner.

The first, or ‘self-balancing’ strategy, starts from the assumption that the market players have enough motivation to keep their portfolio balanced in real time. Thus, the ability of residential micro-CHPs to reduce imbalance volumes due to forecast errors of RES-E is assessed.

Nevertheless, keeping the own balance is not always convenient for the system operator. In fact, the actual design of the Belgian balancing market allows the participants to react on imbalance tariffs modifying their physical position in real-time, thereby helping to reduce the residual system imbalance. The second strategy, or ‘passive balancing’, investigates the possibility to provide near-real-time electrical balancing services, making use of an aggregation of micro-CHPs.

Finally, the last strategy tackles the problem of ‘bidding under uncertainty’. In the previous strategies, the decisions where taken under a particular level of uncertainty. In this last strategy, the uncertainty is explicitly modeled using stochastic programming and the ability of cogeneration to cope with this uncertainty is evaluated.

In summary, this research seeks to address the following questions:

4 Introduction

What is the potential of using micro-CHP to reduce the local imbalance volume between local electric power demand and local power generation? Can this operation reduce the imbalance cost and increase the total income of the micro-CHP operator?

Which control scheme can be used to provide near real time electrical balancing services aggregating several micro-CHP devices? Which are the economic benefits for the aggregator?

What is the added value of using CHP-DH to compensate for the uncertainties regarding electric power generation and market prices development?

1.3 Assumptions and Delimitation of this Work

One of the most important assumptions in this work is that cogeneration devices are able to participate in the electricity market for energy and reserve power. Currently, this assumption is true for large cogeneration units. In this PhD thesis it is assumed that micro-CHPs interact with the electricity market only via an aggregator.

This work does not aim to be a reference for deciding whether certain investments on DG are profitable or not. For this reason, the capital cost is generally disregarded. Only Chapter 3 considers the investment cost of micro-CHP. The other chapters aim at analyzing the potential operational cost savings and revenues that can be obtained by the optimal operation of CHP devices.

Additionally, the characteristics of the building where the CHPs are installed are a boundary condition. They are represented by given heat demands. These heat demands are obtained from measurements performed on real buildings located in central-western-Europe.

Finally it is important to remark that this thesis is not intended to analyze the integration of the DG technology into the electrical grid, their impact on the power quality, cables and conductors, nor on any other criteria that utilities may require in order to guarantee the operation of their grids.

1.4 Overview of this Work

Besides this introduction, this work is structured into six additional chapters.

Chapter 2 provides the necessary background for understanding this work. It gives a definition of the virtual power plant concept and a description of the Belgian electricity

Overview of this Work 5

market. Additionally, it provides a detailed literature review concerning the use of DG flexibility. Afterwards it gives a description of the principles of cogeneration and the characteristics of the most important prime movers.

Chapter 3 serves as a reference for the development of the following chapters. It compares the traditional operation strategies employed for micro-CHP units, namely: ‘heat-driven’, ‘electrically-driven’ and ‘economic optimization’. Within this framework it explains several concepts that are repeatedly applied in the following chapters, such as: the methodology employed to size (or dimension) the cogeneration device and the thermal-storage tank. In addition, it states the principles behind the linear programming developed in this dissertation and the advantages of using this technique.

In chapter 4, the first research question is addressed. This chapter investigates the possibilities to reduce imbalance errors making use of micro-CHPs. The imbalance stems from the forecast deviation of a photovoltaic facility. The conclusion shows that it is technically possible to reduce large amounts of imbalance volume by using a micro-CHP. Nevertheless, it is important to weight the imbalance reduction cost against the avoided imbalance penalties, in order to evaluate the profitability and avoided economic losses.

Chapter 5 presents a methodology to provide near real time balancing of the electrical power grid using an aggregation of micro-CHP units. The methodology is based on two mixed integer linear optimizations. The first optimization aims to find the optimal electrical-generation day-ahead schedule of the micro-CHP aggregation. The objective of the second optimization is to provide real-time balancing services. The latter is performed each time step in a rolling-horizon approach. The results show that the developed methodology leads to a positive economic impact for the aggregator.

Chapter 6 assesses the third research question. The study aggregates a CHP connected to a district heating system (CHP-DH) together with intermittent renewables. The aim is to estimate the added value of using CHP-DH to compensate the uncertainties of the electric power system. In order to explicitly account for the uncertainties stochastic programming is used. The results indicate that the aggregation of RES and CHP-DH can result in a decrease of the total operational cost. Additional larger advantages can be obtained when using the flexibility of CHP-DH in near real time.

Finally, Chapter 7 presents the summary and conclusions of this work and recommendations for future research.

7

2. Background on VPPs, the Belgian

Electricity Market, DG and CHPs

This chapter outlines the fundamental concepts related to the operation of a virtual power plant (VPP) in the electricity market. The chapter begins with a definition of the term “virtual power plant” in Section 2.1. Next, a comprehensive description of the operation of the Belgian electricity market is given in Section 2.2. Section 2.3 explains three possible approaches to operate a VPP that participates in both the day-ahead and imbalance market. An extensive literature review on this topic is given in Sections 2.3.1, 2.3.2 and 2.3.3. As the focus of this thesis is on cogeneration or combined heat and power (CHP) devices, Section 2.4 elaborates on the cogeneration concept. This chapter ends with a summary presented in Section 2.5.

2.1 Definition

The concept of a virtual electric power plant has been investigated extensively ([14]-[19]). According to these works, a virtual electric power plant is defined as an aggregation of distributed electricity generators, controllable electrical loads and electrical energy storage devices that emulates the operation of a single electric power plant [15], [19]. This aggregation enables the participation of distributed devices in the power exchange market ([16], [20]).

In other words, the function of a VPP operator is not limited to aggregate several distributed electricity generation devices in terms of capacity,he also coordinates them to obtain a single operating profile in order to resemble a conventional generation power plant ([17], [18], [21]). As a result, a VPP operator is in charge of forecasting the electric power generation and demand of his participants. Based on this information, he nominates optimal bids in the electricity market. Afterwards, he monitors the actual electric power generation and demand in order to calculate the possible deviations from the day-ahead (DA) schedule. Finally, he takes optimal decisions regarding the actual dispatch of electric power [22]. Figure 1 illustrates the concept of a VPP.

8 Background on VPPs, the Belgian Electricity Market, DG and CHPs

Figure 1: Definition of a VPP. A VPP operator is in charge of forecasting, monitoring and optimizing the operation of the aggregated devices that belong to his portfolio, to resemble a single electrical power plant.

The benefits of using VPPs has been addressed in several studies ([14], [20], [23]). According to Asmus [20], the use of a VPP could bring several benefits, such as increasing the flexibility of the electric grid without a large investment in infrastructure. Braun [23] states that the VPP concept brings along several benefits not only for the DG owner but also for the system operators. Additionally, Dulau, et al., [14] claim that VPPs can play an important role in facilitating the integration of small-scale RES-E in the electricity system whilst reducing the CO2 emissions.

Whether the expected benefits of VPP can be substantiated depends on several circumstantial factors. For instance the nature and geographical location of distributed RES-E: e.g., in north-western Europe, there are several moments without direct solar radiation and/or substantial wind speed. In those cases, limited local electricity storage may be insufficient.

To better exploit the idea of a VPP, this PhD research has broaden the scope of a VPP to incorporate and take advantage of the heat-demand side. Indeed through the use of CHP devices, assisted by thermal-storage tanks and back-up boilers, the overall energy system (electricity, heat and gas) can be better optimized4. The key point is that CHPs run efficiently only if no heat is disposed; by using thermal-storage, electricity generation and heat ‘delivery’ of a CHP system can be decoupled, as such

4 The effects of CHP with thermal-storage tank on the gas-distribution system have been investigated by Vandewalle [124]. The current thesis concentrates on the integration of CHP and thermal-storage in a VPP through electricity markets.

The Belgian Electricity Market 9

allowing the CHP to respond to electricity market signals and terms providing more flexibility on the electric side.

The financial benefits expected from using VPPs depend largely on the interaction with the exchange power market. The next Section 2.2 describes the functioning of the Belgian electricity market.

2.2 The Belgian Electricity Market

The liberalization of the electricity market in Europe started in the early 1990s. The objective was to increase the efficiency and competitiveness of the electricity market. The most important actors of the liberalized market are shown in Figure 2.

The generators are in charge of converting primary energy into electricity. The electricity in Belgium is generated using different kinds of power plants, with currently effectively only nuclear power stations, combined cycle gas turbines5, cogeneration units6, pumped hydro plants7 and electrical energy harvested from renewable resources (e.g., solar and wind energy) [24]. The additional electric demand is covered via imports8.

The generated electricity is transmitted to the consumers using extensive transmission and distribution networks. The high and very high voltage networks are controlled by the transmission system operator (TSO). The TSO guaranties the reliable operation of the grid. Elia is the Belgian TSO. Similarly, medium and low voltage distribution systems are operated by Distribution System Operators (DSO) [25].

The consumers are the end users; this group includes anyone who uses electricity, ranging from large industrial players, usually connected to the high voltage grid, to residential users that are connected to the distribution grid.

5 At the time of writing, there is still one coal-fired plant active and two smaller biomass plants. The coal-fired plant will be shut down in the near future; the long term future of biomass plants is uncertain. 6 During the year 2013, cogeneration accounted for almost 12 % of the total installed capacity [125]. 7 During the year 2013, pumped-hydro plants (in discharge mode) accounted for almost 8 %of the total installed capacity [125]. 8 During the year 2013, the net import balance was 9.64 TWh [125].


Figure 2: Main actors of the traditional electricity market. Traditionally, the electricity is generated in central power plants and transmitted to the end user using the transmission and distribution networks.

2.2.1 Trading

Electricity is typically traded either over the counter (OTC), establishing bilateral agreements, or through the power exchange market, which is a standardized market ([26], [27]). Table 1 summarizes the most important characteristics of these markets, the details are explained in the following sections.

Table 1: Main characteristics of the day-ahead and intraday electricity market in Belgium [28].

Bilateral

Agreements

Day-Ahead

Market

Continuous

Intraday

Market

Price tick value [€/MWh] FREE 0.01 0.10

Minimum contract volume [MWh] FREE 0.10 0.10

Minimum order price [€/MWh] FREE -500.00 -99999.90

Maximum order price [€/MWh] FREE 3000.00 99999.90

Closing gate [h] FREE 12:00 (D-1) 12:00 (D+1)

2.2.1.1 Bilateral Agreements

OTC trading usually results in Agreements between two parties to exchange a certain amount of electricity at a determined price during a specific period in time. These agreements are usually non-regulated contracts and in most of the cases they are made for the long term, e.g., one to several years in advance [29].


2.2.1.2 Day-Ahead Electricity Market

The day before delivery (D-1) market participants possess actualized information regarding their generation and consumption portfolio. Day-ahead markets are short-term markets that enable the participants to adjust their contracted positions on an hour-by-hour basis [30].

In the day-ahead market, the participants can place bids for selling and buying electricity the following day. In Belgium, the transactions are made via the organized power market Belpex. The deadline for submitting the bids at the Belpex is 12:00 CET. After the closure, the market price for each hour is cleared by matching the supply and demand curve as illustrated in Figure 3.

Figure 3: Market clearing price. The market price is determined by matching supply and demand curves.

Once the prices are calculated, trades are settled. The electricity is physically delivered every hour of the next day following the agreed contracts.

Note that since February 2014 the day-ahead market of the North-Western European region is coupled. This interconnection includes the following countries: Belgium, Denmark, Estonia, Finland, France, Germany/Austria, Great Britain, Latvia, Lithuania, Luxembourg, the Netherlands, Norway, Poland (via the SwePol Link) and Sweden [31].

2.2.1.3 Intraday Electricity Market

This market enables to trade electricity closer to real time to react to short-term modifications of supply or demand. Since the majority of the electricity that is handled on the power-exchange markets is traded in the day-ahead market, intraday markets


have lower liquidity. Nevertheless, this market is acquiring importance with the increasing share of unpredictable generation such as solar and wind energy.

According to Vandezande [30], the importance of a well-functioning intraday market is twofold: it can help to adjust possible infeasible schedules that result from the day-ahead operation and it can accommodate forecast errors of RES-E generation [30].

2.2.2 Balancing

The fact that the electrical energy cannot be stored in large amounts in an economical manner requires that the balance between power injected into the grid (generation and imports) and power taken from it, should be kept at all time.

A deviation between electric power supply and demand is reflected in a deviation of the grid frequency from the ideal value of 50 Hz (in Europe). As explained by Vandezande [30], if generation exceeds demand, the frequency increases; if generation is lower than demand, the frequency drops [30]. A stable frequency is important for the optimal operation of several electrical appliances; large deviations may result in the disconnection of generation units and load and eventually lead to a system black-out [30].

The TSO is responsible for keeping the balance between generation and demand. This responsibility is shared with Balance Responsible Parties (BRP). Each BRP is responsible for ensuring the balance between the total amount of injection and offtake it committed to at its access points on a quarter-hourly basis ([30], [32]).

The day before the actual delivery, the BRP must provide the TSO with a schedule of its nominations. The TSO checks on the actual day whether the nominations are consistent with the physical real time transmission. If this is not the case and an imbalance is found, the TSO takes action to reduce the imbalance and the BRP is charged an imbalance tariff. These imbalance tariffs depend on the Marginal Incremental Price (MIP) and the Marginal Decremental Price (MDP) corresponding to the largest and lowest prices the TSO has paid to reduce the imbalance in the 15 minute frame, respectively. The Net Regulation Volume (NRV) is the reserve power the TSO has to activate in the specified 15 minutes to preserve the balance in the system. If the grid has a surplus of power and downward regulation is need, the NRV is negative. On the contrary, if the grid has a deficit of power, upward regulation is necessary and the NRV is positive.


The imbalance tariffs are calculated taking into account several factors such as:

• The nature of the imbalance with regards to the BRP commitments (positive or negative).

• The cost that the TSO has to pay to settle the total system imbalance (SI)9. • The position of the TSO (surplus or deficit of energy).

The mechanisms for imbalance pricing are summarized in Table 2. As shown in the table, four different cases can occur (called A, B, C and D).

Table 2: Belgian balancing pricing depending on the position of the TSO and the BRP [33].

Situation of the TSO

Surplus Deficit

Imbalance of the BRP Positive CASE A CASE B

POS TARIFF=MDP-α POS TARIFF =MIP-β

Negative CASE C CASE D

NEG TARIFF =MDP+β NEG TARIFF =MIP+α

NEG TARIFF = Negative Imbalance Tariff; POS TARIFF = Positive Imbalance Tariff; MIP = Marginal Incremental Price; MDP = Marginal Decremental Price.

In the cases B and C of Table 2 the position of the BRP helps the TSO to reduce the general imbalance. As a consequence, in case B, the TSO pays to the BRP the MIP and in case C, the BRP pays for the lack of energy to the Belgian TSO at a price equal to MDP (The MDP might become negative at some moments and the BRP gets paid for not generating enough power). In the contrary cases (A and D) the BRP position increases the total imbalance; thus it will receive the MDP or pay the MIP in case of positive or negative imbalance, respectively.

If the total system imbalance is larger than 140 MW, the variables α and β shown in Table 2 are activated. The activation of β is only “in principle” since, according to Elia, β is usually set equal to zero. On the other hand, α is estimated based on the average of the 8 previous values of the system imbalance as shown in Equation (2-1):

^$_ = a18∑ def^$ − Z_hij(k81500 (2-1)

9 The system imbalance is the difference between the scheduled and measured values of the Belgian control area considering the amount of reserve power activated. In other words, it is the remaining imbalance after the Net Regulating Volume has been activated.


^$_ = 0 (2-2)

Finally, it is important to highlight that in the cases when α and β are not activated, the positive and negative imbalance tariffs are the same [34].

2.2.3 Reserve Power

In order to correct the imbalance, the TSO can use either active or passive balancing. The first one entails contracting of reserve capacity and energy that can be activated in case of imbalance. The second one, on the other hand, allows the market participants to contribute to maintain the system balance by changing their physical position close to real time. The contracted products by the TSO are described in what follows:

2.2.3.1 Frequency Containment Reserves

Frequency Containment Reserve (FCR; formerly called “primary reserves”) is activated automatically by measuring the deviation of the grid frequency. The provider should be able to deliver half of the contractual FCR within 15 seconds. The whole amount should be supplied after 30 seconds and should stay activated for at least 15 consecutive minutes [33].

2.2.3.2 Frequency Restoration Reserves

Once the FCR have stabilized the grid frequency, Frequency Restoration Reserves (FRR, formerly called “secondary reserves”) are triggered to bring the frequency back from the quasi steady state to the nominal 50 Hz within 15 minutes.

In Belgium the FRR consist of two elements: contracted reserves and free bids. The contracted reserves are required by Elia in order to keep a total capacity of 140 MW upwards and downwards available at every time [32].

On the other hand, free bids can be offered by all market participants that sign a contract to provide FRR, even when the reserved capacity is equal to 0 MW. Free bids are voluntary and the tendering process occurs the day before the actual delivery [32].

The activation of FRR is selected separately for upward and downward reserve. The selection is performed following an economic ranking as shown in Figure 4. The lowest prices for up-regulation are activated first; in contrast, the largest prices for down-regulation have priority.

Virtual Power Plants in the Electricity Market 15

Figure 4: Merit-order mechanism for the selection of upward and downward bids. The lowest prices for upward regulation and the highest prices for down regulation are selected first.

The remuneration for providing secondary control power is divide in two parts: those participants that offered contracted reserves, receive a fee per MW per hour for the capacity reservation. Additionally, all the participants (i.e., free bids and contracted capacity) that are selected are paid for the energy provided. The remuneration is equal to their own bidding price (i.e., the energy provided is paid as bid) [32].

2.2.3.3 Replacement Reserves

Replacement Reserves (RR, formerly called “tertiary reserves”) is the mechanism used to relieve FRR when the grid frequency deviation lasts for longer than 15 minutes. This kind of reserve is activated manually by the operator. Similarly to the FRR a generator providing RR gets paid for the reserved capacity and for the energy delivered in case of activation [33].

2.3 Virtual Power Plants in the Electricity Market

As explained in the previous Section 2.2, a traditional power plant has several opportunities to participate in the electricity market. For instance, it can bid electricity on the day-ahead market or provide control reserves. Similarly, it is expected that a VPP composed by controllable or programmable devices (e.g., CHP and heat pumps) can also offer considerable flexibility to these markets. Hence, it is instructive to study and evaluate several options to offer this flexibility in the electricity market. This section provides a literature survey regarding three different operation strategies that enable the participation of a VPP, directly or indirectly, in the day-ahead and reserve market.


The first concept is the ‘active participation in the balancing markets’. This implies that the VPP operator contracts with the TSO to reserve some capacity with the conditions explained in Section 2.2.3. The second strategy, or ‘self-balancing’, aims to minimize the total imbalance error of the VPP portfolio. It indirectly affects the reserve market by reducing the amount of reserves needed to balance the grid. The final concept analyzes the possibility to provide ‘passive balancing’. This implies changing the position of the VPP at near real time with the goal to reduce the total system imbalance.

2.3.1 Active Participation in the Balancing Market

In the literature, several studies assess the possibility of offering ancillary services to the electric grid using DG devices. These services range from providing reserves to balancing the grid or enhancing the voltage stability. Wang, et al., [35] investigate the possibility to provide ancillary services with an aggregation of individual heat pumps (HP). The conclusions indicate that HP aggregation can help to improve the stability of the power grid.

Providing spinning reserves using Active Demand Response (ADR) is a common topic of study since it is believed that there is a large potential of using flexible loads to support the reserve power system [36]. Weckx, et al., [37] have implemented a control algorithm that enables a cluster of loads to provide primary control. Ioakimidis and Oliveira [38] have developed a stochastic dynamic programming (SDP) tool that enables an aggregator of distributed generators and controllable loads to offer tertiary reserve power. Ruthe, et al., [39] have evaluated the potential of VPP to participate in frequency control stabilization. Molina-Garcia, et al., [40] have analyzed the contribution of ADR to primary frequency control in isolated power systems.

Nevertheless, there are still major barriers that hinder the incorporation of ADR in the reserve power market. Biegel, et al., [41] mention that both the minimum-energy requirement to enter the balancing market and the uncertainty regarding the own generation hamper the penetration of ADR into the reserve market. Koliou, et al., [42] also highlight the minimum bidding volume as one of the factors that undermine the penetration of DG in the German balancing market. Van Dievel, et al., [43] remark that the regulatory framework regarding demand response in distribution grids is incomplete. This hinders the participation of this technologies in the energy market.

A different promising technology that can improve grid stability is the electric vehicle (EV). In the PhD dissertation of Vandael [44] several control strategies for EVs that provide ancillary services to the grid have been developed and validated. Andersson, et al., [45] have calculated that the maximum profits that can be obtained by offering secondary reserve power with EVs are in the range of 30-80 € in the German case.


Dallinger, et al., [46] estimate profits of around 180 € per car and per year. Druitt and Früh [47] show that a fleet of EVs can help balancing the grid. Nevertheless, they also mention that the economic benefits for the car owner are limited in the studied market environment. Similar results are reported by Jargstorf and Wickert [48]. According to them, electric vehicles are not suitable to offer reserve power.

Mashhour and Moghaddas-Tafreshi ([49], [50]) develop a nonlinear mixed-integer program that enables the participation of a VPP in the energy and reserve market. The problem is solved using genetic algorithms (GA). It includes several DG devices, electrochemical storage and load shedding options. Niese, et al., [51] give a conceptual description of a VPP operated with a multi-agent system (MAS). The VPP is controlled not only to provide energy but also ancillary services. Furthermore, Varkani, et al., [52] show that combining the operation of a wind power plant (WPP) with a pumped-hydro storage (PHS) can significantly increase the added value of the portfolio.

Finally, von Roon [53] and Steck [54] focus their research on micro-CHPs. In [53], the technical feasibility of providing FCR and RR making use of micro-CHPs is analyzed. Steck [54] develops and compares several algorithms to provide reserve power using an aggregation of micro-CHP. A summary of the more relevant works regarding active participation of DG devices in the balancing market is provided in Table 3.

As the active participation of micro-CHPs in the balancing markets has been already assessed in previous works, this PhD thesis focuses more on other market opportunities such as the self-balancing and passive balancing explained in the following sections.


Table 3: Literature review: VPP to provide grid services.

Publication

Service VPP components

Technique Main findings

[35] Voltage stability

ADR: HP Two step multi-objective optimization

Distributed HPs can be aggregated to increase the stability of the grid.

[36] Reserve power

ADR: HP,

EV,

Electrolyzer

NLP Responsive loads can increase flexibility of the grid.

[37] Reserve power

EV

Water heater

MAS Clustered loads can emulate primary frequency control provided by conventional generation.

[38] RR ADR

Storage

EV

Micro-wind turbine

PV

SDP Providing tertiary reserve power with an aggregation of small generators and controllable loads can lead to profits for both the micro grid and the clients.

[39] FRR Flexible energy devices

Simulation Flexible energy devices can be controlled to provide FRR.

[40] Reserve power

ADR

Steam

HP

Wind power

Simulation ADR can substantially contribute to improve frequency stability and relieve FRR.

[41] Reserve power

ADR:

HP

Refrigerator

EV

Using intra-day markets to adjust the operation of flexible loads increases the feasibility to provide reserve bids.

[42] Reserve power

ADR The minimum bidding volume, the minimum bid duration and the binding up and down bids are the most important mechanism that limit the penetration of DG in the German balancing system.

[43] ADR The current regulatory framework concerning demand response in distribution systems is inadequate or incomplete.


[44] Reserve

power EV MAS Centralized coordination of

EV can provide larger amounts of power for ancillary services. Decentralized control facilitates large scale integration.

[45] Reserve power

EV Providing regulating power in the German market can lead to maximum profits up to 80 € per vehicle and month.

[46] Reserve power

EV Providing negative secondary regulation capacity is the most profitable way in which EV can participate in the German regulation markets.

[47] Grid balancing

EV MAS Optimal EV charging can help to reduce impact of variability of large amount of wind.

[48] Reserve power

EV Simulations Analyzes a business case of providing reserve power with EVs and concludes that these vehicles are not suitable to offer reserve power.

[49][50] Reserve power

Storage load

NLP solved with genetic algorithms

A VPP can provide spinning reserve regardless of its main role (Consumer or producer).

[51] Reserve power

- MAS Concept overview: Trading active power and ancillary services, including reactive scheduling in case of activation

[52] Reserve power

WPP

PHS

MINLP Integrating WPP and PHS increase the added value of the portfolio.

[53] Reserve power

micro-CHP It is technically possible to provide tertiary reserve power using micro-CHPs

[54] Reserve power

micro-CHP LP

MILP

Heuristic

Development of several strategies to plan optimal energy and reserve power bid.


2.3.2 Self-Balancing

The strategy of self-balancing consist of aggregating diverse DG devices in a portfolio and minimize the schedule deviation of the whole VPP portfolio. Thus, the VPP is not actively providing services to the grid but indirectly reducing the residual imbalance volume that needs to be compensated by the system operator.

Kok, et al., [55] and Bliek, et al., [56] introduce a demonstration case of the self-balancing. Several DG technologies are aggregated and coordinated to reduce the WPP imbalance. The measurements demonstrate that, in practice, using MAS allows achieving a reduction of 40 % of the total imbalance volume. Additionally, Bliek, et al., [56] demonstrate that using CHPs and HP to reduce imbalance, the user’s comfort is not foregone.

This practical experience tests the technical feasibility of a VPP to reduce imbalance volumes however, Kok, et al., [55] and Bliek, et al., [56] do not evaluate the economic impact thoughtfully. In other words, the possibility that at some point it might be more expensive to correct the imbalance internally than to pay for the imbalance tariff was not taken into account. This case was reported in [57]. Angarita and Usaola [57] study the joint operation of a WPP and a hydro power plant. The results show that, rescheduling the hydro power plant only make sense when the imbalance penalties are very large. Larger benefits can be obtained improving the quality of the WPP forecast.

Houwing ([58] [59]) investigates the idea of balancing a wind turbine making use of a micro-CHP aggregation. In [58] it is reported that it is possible to reduce 73 % of the wind forecast error using micro-CHP and 38 % of the associated imbalance cost. However, though the cost reduction as a whole is significant, the total savings per individual unit are very low.

Other technologies such as EVs and ADR seem to give better economic benefits when used for self-balancing ([60], [61]). Mohammadi, et al., [61] conclude that ADR is not only capable of decreasing the imbalance volume when operating together with a wind power plant but also of reducing the imbalance penalties. Mekonnen, et al., [62] and Kessels, et al., [63] have investigated the use of ADR for balancing wind. The results show large economic benefits of using ADR. Leterme, et al., [64] have developed an algorithm that control EV for the purpose of balance wind-power.

With respect to wind power balancing, Scharf and Amelin [65] have investigated the value of self-balancing in the light of higher wind power penetration. Vogstad [66] hase assessed the possibility to minimize imbalance volume coordinating different


generation units with complementary characteristics such as wind power and hydropower.

Finally, Pandžić, et al., [67] describe the stochastic optimization of a VPP that consist of a WPP, a conventional power plant (CPP) and a pumped hydro storage basin. According to Pandžić, et al., [67] large profits can be expected from the aggregation of these plants. This can be achieved without larger disturbance from the individual operation. To summarize, Table 4 gives an overview of the consulted literature on VPPs and self-balancing.

Table 4: Literature review: self-balancing using VPPs.

VPP Components Technique Main Findings

[55] WPP

CHP

Cold storage

Emergency generator

HP

MAS Coordinating the operation of different DG an imbalance volume reduction of 40 % can be reached.

[56] HP

CHP

PV

MAS Intermittency of photovoltaics (PV) resources can be balanced using DG appliance without sacrificing users comfort.

[57] PHS

WPP

MILP Only under large imbalance penalties it is economically profitable to compensate the WPP imbalances changing the hydro schedule. The best option is to improve accuracy of the WPP predictions.

[58][59] WPP

CHP

MILP Clustering micro-CHP can reduce the imbalance volume by 73 % and the cost associated to this imbalance can decrease by 38 %.

[60] WPP

CP

EV

Simulates a Danish island as a VPP. The results show that the schedule deviation can be compensated using EV.

[61] ADR

WPP

LP Flexible load can balance uncertainty of RES and reduce imbalance penalties.

[62] ADR

Thermal

WPP

Develop an optimization model that aims to minimize wind imbalance using ADR.


[63] ADR

Thermal

WPP

Large profits can be achieved by using ADR to minimize wind imbalance. This profits depends largely on the imbalance settlement.

[64] EV SDP Dynamic programming enables the coordination of EV to balance wind power errors.

[65] Hydro

WPP

CPP

LP Develop an algorithm to evaluate self-balancing in the light of higher wind power penetration.

[66] Hydro

WPP

CPP

LP To profit from self-balancing it is necessary to have a portfolio with many different power plants.

[67] WPP

CPP

PHS

Stochastic MILP

Large profits can be expected from VPP setup without large disturbance in the operation of the individual plants

Even though self-balancing strategy has been broadly studied in the literature, some research gaps can be identified. From the reviewed literature, Kok, et al., [55] and Bliek, et al., [56] do not consider the economic benefits of providing self-balancing. Other studies deal with large power plants or ADR ([57], [60], [61], [62], [63], [65], [66], [67]) that are not influenced by the demand constraints as in the case of cogeneration. Only Houwing ([58], [59]) focuses on micro-CHPs. However, these studies are evaluated during one month in winter only. Thus the seasonal effect on the heat demand is neglected.

2.3.3 Passive Balancing

As mentioned in Section 2.2.3, in Belgium a BRP is allowed to contribute passively to restore the system imbalance. In other words, a BRP can participate in balancing the system even when it is not actively selected in the merit-order mechanism explained in Section 2.2.3. This occurs when the internal imbalance of the BRP has the opposite direction of the total system imbalance.

As shown in Table 2, if the position of the BRP contributes to restoring the system balance, it receives an economic reward equal to the marginal incremental or decremental price for up and down regulation.

Cogeneration Concept 23

Passive balancing, however, entails a larger risk for the BRP than the active participation in the balancing market. This risk stems from the uncertainty regarding the direction of the imbalance and the evolution of the imbalance prices. Nevertheless, passive balancing is seen as an alternative to integrate DG in the balancing system [68].

Additionally, a comparison between countries with and without passive contributions indicates that the use of passive balancing leads to a reduction in the total balance management cost [69]. However, to benefit from passive balancing, there is not only a need for an adequate design of the imbalance tariffs, but also a frequent (almost real time) publication of the information regarding the imbalance prices [68].

In the reviewed literature, only three studies explicitly consider passive balancing ([70], [71], [72]). Abdisalaam, et al., [70] have shown that potential economic benefits can be achieved by providing real-time balancing services with an aggregation of flexible residential loads. Lampropoulos [71] has assessed the economic benefits of a battery energy storage system that provides passive balancing. Chaves-Avila, et al., [72] have considered the case of a wind power producer who bids his electricity in the day-ahead market and who can adjust his output in real time.

This PhD thesis contributes to the passive balancing literature by assessing the possibility of real-time balancing making use of micro-CHPs.

2.4 Cogeneration Concept

“Combined heat and power” (CHP) plants are generation units that produce simultaneously thermal and electrical power10. The advantage of CHP in comparison with other DG technologies such as PV and wind turbines is its controllable output. Additionally, when operated together with a thermal-storage tank, it is possible to detach the heat delivery from the electricity generation, increasing the operational flexibility.

Compared to conventional power plants, CHP units can achieve higher fuel utilization, as is illustrated in Figure 5. This figure compares separated generation of heat and power against the operation of a CHP unit. In the former case, the electricity is

10 Although CHP units deliver both thermal power and electrical power, the former is usually referred as “heat” and the latter as “power”. One should, however, always be careful to distinguish between thermal and electrical output products, with can be “power” (in the physical sense as rate of change of “energy”) and “energy” (in the physical sense as the time integral of power, = n o^$_?$R8 ).


provided by a combined cycle gas turbine (CCGT) with an electric efficiency of 55 % and the heat by a boiler with a thermal efficiency of 90 %. The efficiencies of separate production are denoted by &(. The electric and thermal efficiencies of the CHP are respectively, 35 % and 50 %. The efficiencies of the CHP are denoted by ( . Looking at the figure it is clear that the separated generation requires larger amounts of primary energy (1.2 instead of 1.0) to generate the same amount of electricity and heat [73].

Figure 5: Comparison of CHP against separated generation for a fuel input (in terms of primary

fuel “power”) F=1 for the CHP, and both delivering the same output, E and Q . &Z. and Z are

the efficiencies for separate production and CHP, respectively. The use of cogeneration leads to significant fuel savings [73].

Thus considerable primary energy savings are one of the benefits that can be achieved from the installation of CHPs. In line with the energy savings, a reduction on greenhouse gases emissions is also expected, although this largely depends on the ‘fuel mix’ of the local electricity system. This PhD thesis focuses mainly on micro-CHPs technology and on CHPs connected to district heating (DH) systems. The next sections give an overview of the characteristics of these technologies.

2.4.1 Micro-CHPs

According to the European directive on the promotion of cogeneration (Directive 2004/8/EC) the term micro-CHP concerns all cogeneration devices with a maximum electrical output of 50kWe. The main prime movers for micro-CHP systems are: internal combustion engines (ICEs), Stirling engines, micro-turbines and fuel cells.

Internal combustion micro-CHPs are widely available in the market. They are usually based on spark ignition engines [74]. The electric efficiency of these engines is in the range of 25-35 %, whereas the thermal efficiency ranges from 50 to 65 % [75], [76]. ICEs are able to operate at part load though with a slight decrease in electrical efficiency. The major advantages of ICEs over other CHP technologies are the low

Cogeneration Concept 25

capital cost, low maintenance cost and long service life. Some disadvantages are the level of noise and relatively high NOx emissions [59], [74].

Stirling engines are based on external combustion engines that work on a closed regenerative thermodynamic cycle. In the Stirling cycle a working gas is continually compressed and expanded by repeatedly heating and cooling it. This causes the movement of a piston [76].

The major advantages of Stirling engines are fuel flexibility, low emissions, few vibrations and noise. On the other hand, the most important disadvantage is the low electric efficiency (in the range of 10 to 20 %). Furthermore, though their performance at part load is good, their start up time is long [74], [76].

Micro-turbines are small versions of their large-scale counterparts. Their electric efficiency is around 30% and the fuel utilization ratio (FUR)11 in CHP operation is approximately 80 %. In comparison with ICE, micro-turbines are more compact, lighter and have a lower number of moving parts. In addition, micro-turbines have a high outlet temperature that can be used in several applications. The downside of micro-turbines is the low efficiency at part load operation and the need for skilled personnel for maintenance.

Fuel cells represent an emerging technology that generates electricity and heat by means of an electrochemical reaction between fuel and oxygen. The most common fuel is hydrogen, natural gas can be used, although a reformer is needed for low temperature fuel cells.

Fuel cells can achieve larger electrical efficiencies than other micro-CHP units [74]. The advantages of fuel cell micro-CHP are low noise level, potential low maintenance, due to fewer moving parts and good part load operation. Nevertheless, it is recommended to operate fuel cells at nominal output due to life time considerations. The major drawbacks of fuel cells are the large investment cost and the short life time. Table 5 summarizes the most important aspects of the previously explained CHP technologies.

11 The fuel utilization ratio is the ratio of the useful energy—both electric and thermal—to the primary energy, FUR= + .


Table 5: Characteristics of CHP prime movers [74], [75], [76].

Technology ICE Stirling Engines

Micro-gas turbines

Micro-Fuel cell

Typical range (kWe)

5 – 6000 3 - 1500 35 - 300 0.7 - 400

Electric efficiency () (%)

25 – 35 10 - 20 25 - 30 35 - 40

Fuel utilization ratio (%)

65 – 90 75 - 90 65 - 90 85 - 90

Part load operation ok ok low excellent

2.4.2 District Heating Cogeneration

Under appropriate circumstances, district heating may be an important technology that is able to provide cost-effective, environmentally friendly heat [77]. Cogeneration has been widely applied as a heat source for DH. Typical prime movers used for DH applications are steam turbines, gas turbines and internal combustion engines (otherwise called, reciprocating engines).

Steam turbines are extensively used in classical power plants; their operation is based on the Rankine cycle. The heat generated from the combustion of the fuel is used to pressurize steam. This steam is expanded in a turbine to create mechanical rotation [78]. The remaining heat in the steam can be extracted to be used in several applications.

CHP with steam turbines can achieve large FUR (of the order of 80 %). Nevertheless, their electric efficiency tends to be low (in the range of 14-35 %). Additionally, their part load performance is poor [79].

Gas turbines are the most widely spread prime movers used for DH. The operation of a gas turbine starts by compressing the air and heating it in a combustion chamber. The hot combustion gas mixture is expanded in a turbine generating mechanical energy. The remaining hot exhaust gases are recovered to generate useful heat [78], [79]. Electrical efficiencies are in the range of 25-40 % at full load, during part load operation the efficiency decreases significantly.

Reciprocating engines are internal combustion engines that operate with the same principles as automotive engines. There are two main types of reciprocating engines:

Summary and Conclusions 27

compression ignition (diesel engines) and spark ignition (Otto cycle) engines (usually fuelled with natural gas, although gasoline (petrol) would be also possible. The electrical efficiencies of diesel engines range from 35-55 %, while gas or Otto engines have lower efficiencies (30 % to 50 %) and are also smaller in size. The major advantage of reciprocating engines over other technologies is their low investment cost and their good performance record. Table 6 gives an overview of the characteristics of the most important CHP technologies used for DH [79].

Table 6: Characteristics of CHP-DH prime movers [80].

Output range [MW]

αe [%] for loads FUR E /Q 100 % 50 %

Steam turbine 0.5-100 14-35 12-28 60-85 1:2 → 1:10

Gas turbine 0.1-100 25-40 18-30 60-80 1:1 → 1:3

Diesel engine 0.07-50 35-45 32-40 60-85 1:1 → 1:1.2

Otto engine 0.05-20 27-40 22-35 60-85 1:1 → 1:3

FUR=fuel utilization ratio

2.5 Summary and Conclusions

A virtual power plant can be defined as an aggregation of several distributed generation devices that operate together in order to participate in the electricity market. In this market, electricity is traded on the long term using bilateral contracts. These contractual agreements can be adjusted in the day-ahead market. Afterwards, during the actual day of the delivery, the difference between the contractual position and the physical output can be traded in the intraday market or settled in the balancing market.

There are several possibilities for a VPP to participate in both the day-ahead and the balancing market. A first approach is to actively offer reserve capacity. This possibility is usually limited to FRR and RR due to the strict technical constraints necessary to provide FCR. The second possibility in fact tries to minimize the interaction of a VPP with the reserve market by accommodating the imbalance errors within the portfolio. This possibility will be evaluated in Chapter 4. A last approach is to indirectly help the grid by modifying the dispatch in real time and creating imbalance in the opposite direction of the system imbalance. This strategy will be analyzed in Chapters 5 and 6.

Nevertheless, in order to be able to provide services to the grid, some degree of flexibility is needed. This flexibility largely depends on the kind of devices that compose


the VPP. This PhD thesis focuses on the role of cogeneration devices in a VPP, specifically micro-CHP and district heating cogeneration are considered.

29

3. Preliminary Concepts

This chapter compares three different strategies to control CHP devices, namely: heat-driven, electricity-driven and economic-optimization. The first one is the traditional way to operate a CHP unit. It assumes that the CHP should follow the heat demand and the electricity is taken as a by-product. In contrast, the second strategy tries to follow the local electrical power demand. The last approach takes into account the electricity and gas prices and aims to find the schedule that leads to the minimal operational cost.

Sections 3.1, 3.2 and 3.3 outline the control strategies. Next, Section 3.4 describes the case study and explains the assumptions made. Section 3.5 provides an extensive discussion of the results. Section 3.5.1 compares the different strategies in terms of the amount of thermal and electric power generated. The cost reduction is estimated in Section 3.5.2; Section 3.5.3 analyzes the influence of the storage capacity and Section 3.5.4 calculates the net present value (NPV) for the different strategies. Finally, Section 3.6 summarizes the most important conclusions.

3.1 Heat-Driven Operation

The heat-driven operation seeks to meet as much thermal energy demand as possible making use of the CHP device. This kind of control does not take into account the electricity demand. The electricity generated is considered as a by-product that can be used on site or fed into the electric grid. Furthermore, this algorithm disregards the actual prices of electricity and gas.

This control strategy is justified by the assumption that a cogeneration device should operate only when the heat generated can be directly used. This is due to the fact that the electric efficiency of most of the commercial micro-CHP devices is low. As a consequence, using the CHP to generate electricity at moments when the heat cannot be used is inefficient. This situation changes slightly when a thermal-storage tank is installed in the system, increasing the flexibility.

The heat-driven operation is implemented using heuristic rules as shown in Figure 6. At each time step the algorithm checks whether the heat demand is greater than the maximum thermal output that can be delivered by the micro-CHP. If this is the case,

30 Preliminary Concepts

the CHP operates at maximum thermal output. The remaining heat demand is covered either discharging the thermal-storage12 or using the auxiliary boiler.

If the heat demand is lower than the maximum possible thermal output of the CHP but still larger than the minimum thermal power output, the thermal output of the CHP is equal to the heat demand. Finally, if the thermal load is lower than the lowest thermal output limit of the CHP and there is no space left in the thermal buffer to store heat, the heat demand is met by discharging the storage tank.

3.2 Electricity-Driven Operation

The electricity-driven control strategy aims to cover as much as possible electric power demand while at the same time reducing the amount of energy that is fed into the grid. Similar to the heat-driven strategy, this algorithm is based on heuristic rules.

The operation of the CHP depends mainly on the instantaneous electric power demand. However, in this PhD thesis it is assumed that dumping excess heat is not allowed, the status of the thermal-storage tank is also an important parameter that has to be checked during every time step.

The algorithm is visualized in Figure 7. It can be summarized as follows. If the electric power demand is higher than the maximum electric capacity of the CHP, the CHP dispatches at maximum output level (i.e., it generates electricity at its rated capacity). However, if excess heat cannot be stored in the thermal storage tank, the CHP modulates down in order to reduce or avoid the excess heat.

As long as the electric power demand is higher than the minimum electric output level of the CHP but below the rated capacity, the CHP follows the electric power demand. This is possible only if the excess heat can be accommodated in the buffer; otherwise, the CHP decreases its output until the excess heat can be stored in the thermal buffer.

In Figure 7, the heat demand is not mentioned since the heat generated by the CHP is considered a by-product. Nevertheless, the implemented algorithm ensures that the heat demand is always met by using the heat generated by the CHP, the auxiliary boiler or by discharging the storage tank. In the figure, the excess heat refers to the thermal power that remains after the heat demand is met.

12 In this work the words “thermal-storage buffer” and “thermal-storage tank” are used as synonyms.

Electricity-Driven Operation 31

Figure 6: Heat-driven operation of a CHP system that consists of a prime mover, a thermal-storage tank and an auxiliary boiler. The CHP tries to meet as much heat demand as possible. The excess heat is stored in the thermal-storage buffer and used in future time steps.


Figure 7: Electricity-driven operation. The CHP tries to follow the instantaneous electric power demand. The heat generated is used to meet the heat demand. Excess heat is stored in the buffer.

3.3 Economic-Optimization Model

The economic-optimization model uses a linear program to find the optimal schedule of a cogeneration device that minimizes the total cost. A linear programming is a group of (linear) equations that minimizes or maximizes an objective function as shown in Equation (3-1):

UZ[t u7Rtv (3-1)

Economic-Optimization Model 33

Linear programs are subject to several constraints such as inequalities (Equation (3-2)), equalities (Equation (3-3)) and bounding constraints (Equation (3-4)):

wt ≤ 6

(3-2)

w*yt = 6*y

(3-3)

z6 ≤ t ≤ 6 (3-4)

In these equations t represents the vector of variables to be determined, w and w*y

are matrices of known coefficients associated with t through a linear relationship while, 6 and 6*y are vectors of known parameters and z6 and 6 represent respectively, the

lower and upper bounds of t.

This thesis uses the commercial software GAMS to formulate the linear program and the solver CPLEX to solve the equations. At this point, it is important to remark that the following equations will be repeatedly used in the next chapters with small modifications.

In general terms, the objective function aims to maximize profits or minimize cost. In this specific case the objective function aims to minimize the total operational cost of the cogeneration system. This is explained in Equation (3-5):

min 6 = ^- + - + -# − "-#_R-k

(3-5)

The operational cost is equal to the sum of the fuel cost of the CHPs and the boilers- , - plus the cost of the electricity that has to be bought from the grid to meet the remaining electricity demand -# minus the revenues due to the

electricity that is sold to the grid "-+(.

Additionally, several technical constraints control the operation of the CHP unit:

!- = 3-5 ∙ - + 6-5 ∙ - (3-6)

- = 34 ∙ - + 64 ∙ - (3-7)


Equation (3-6) relates the electric - and the thermal power output !- of the CHP. In a similar way, equation (3-7) describes the relationship between the electric power - and the primary fuel consumption - of the CHP unit.

This CHP model is used in chapters 4 and 5. Both equations represent linear regressions calculated from measured data of commercial CHP devices provided by the IEA annex 54 and reported in [76] the characteristics are illustrated in Figure 10. The coefficients ath, ap are the slopes of the lines and bth, bp are the intercepts. These parameters depend on the characteristics of each unit. The binary variable - represent the on/off status of the CHP device.

The thermal energy balance is given in Equation (3-8):

!- = !- + !- − !- (3-8)

Equation (3-8) ensures that the heat demand !- is met at any time instant using the CHP!- , the boiler !- or the heat stored in the thermal-storage tank. The variable !- represents the average thermal power charged to or discharged from the heat storage tank.

The thermal buffer used in the research reported in this thesis assumes perfect stratification of the storage tank. The thermal energy content of the storage tank is calculated using Equation (3-9):

!- = &,- ∙ !- + !- ∙ ∆$ (3-9)

Where !- is the state of charge of the storage at each time instant. The time step ∆t considered in this chapter is 1 hour. The efficiency of the storage tank13 &,- is assumed to be constant. Recall that in this thesis it is assumed that excess heat cannot be dumped.

The primary energy consumption of the boiler can be estimated as in Equation (3-10):

- = !- &'()*+ (3-10)

In this equation, - corresponds to the fuel consumption of the boiler and ηboileris the efficiency of the boiler and it is assumed to be constant. The fuel cost of the CHP system (boiler and primary mover) can be calculated as stated in Equation (3-11):

13 The efficiency of the storage tank represents the percentage of thermal energy that is preserved by the storage after it has been stored during one time step of 1 hour.

Application to a Case Study 35

- + - = d- + - h ∙ /12 ∙ ∆$ (3-11)

The primary-fuel (usually natural-gas) price is represented by /X. On the other

hand, it is assumed that, the electric output of the CHP can be used locally or sold in the electricity market as expressed in Equation (3-12):

- =- NIJN + - HLM (3-12)

In this equation, - is the total electric power delivered by the CHP, - NIJN is the

part that can be used internally in the house and - HLM is the electricity fed back

into the grid.

Consequently, the revenues obtained from selling or using locally the electricity generated are estimated in Equation (3-13):

"-# = /-0 ∙ - HLM ∙ ∆$ (3-13)

Where, /-0 represents the DA market price. The cost to buy the remaining electricity from the grid can be estimated as:

-# = d-0T − - NIJNh ∙ /-)<) ∙ ∆$ (3-14)

In this equation -0T corresponds to the electric power demand and /-)<) the price to buy electricity from the grid.

Equation(3-15) limits the amount of electricity that can be consumed locally:- NIJN ≤ -0T (3-15)

Additional constraints are included to prevent exceeding the operational limits of the prime mover. This is summarized in Equations (3-16) to (3-19):

0 ≤ !- ≤ !O<P (3-16) 0 ≤ !- ≤ !O<P (3-17) !O(F ∙ - ≤ !- ≤ !O<P ∙ - (3-18) O(F ∙ - ≤ - ≤ O<P ∙ - (3-19)

3.4 Application to a Case Study

The previously described control strategies are applied to a cogeneration device installed in a multi-family house. The objective is to compare the performance of the


control strategies in energetic and economic terms. The studied building has a yearly heat and electricity demand of 120 MWhth and 11 MWhel, respectively. The analyzed electric and thermal loads come from measured data provided by the LINEAR project14.

The CHP system is illustrated in Figure 8. It consist of an internal combustion gas engine as prime mover, an auxiliary gas boiler to cover the peak demand and a perfectly stratified thermal-storage tank. The heat demand of the house should be always met either by the CHP, the auxiliary boiler or the heat discharged from the thermal-storage tank. The electricity generated by the CHP can be used to meet the electricity demand of the house or it can be fed into the grid. Additional electricity demand can always be balanced by the grid.

Figure 8: Schematic representation of the analyzed CHP system. It consists of a prime mover, an auxiliary boiler and a thermal buffer. The electricity generated by the CHP can be used either to meet the internal demand or fed into the grid.

3.4.1 CHP Sizing

The ‘maximum rectangle’ technique described in [81] was used to determine the installed capacity of the CHP. In order to apply this methodology, the heat demand has to be sorted in a descending order to obtain the so called ‘load duration diagram’ (see Figure 9). Afterwards, the biggest rectangle that can be inscribed under the load-duration curve (also known as monotonic curve) is obtained. The intersection between the rectangle and the vertical axes corresponds to the optimal thermal capacity for the

14 http://www.linear-smartgrid.be/


micro-CHP device (point A in Figure 9). The remaining heat demand should be covered by an auxiliary boiler.

Figure 9: Maximum rectangle method: the largest rectangle (dashed lines) that can be inscribed under the monotonic curve (black) determines the thermal capacity of the CHP (point A).

The results of the maximum rectangle method indicate that for the studied dwelling the CHP should have a thermal capacity of approximately 13kWth. Consequently, the micro-CHP Ecopower plus was selected as model for the simulations.

It must be noted that the largest rectangle method is only “correct” in the absence of thermal-storage. If thermal-storage is present, the largest rectangle does not indicate the “optimal” installed thermal capacity. However, for practical purposes, the largest rectangle method is still assumed to be appropriate.

The Ecopower micro-CHP is a gas driven engine that enables full modulation between 1.2 and 4.5 kWe (3.8 to 12.5 kWth). The steady state characteristics were measured and provided by [76]. They are shown in Figure 10.

0

20

40

60

80

0 2000 4000 6000 8000 10000

Ther

mal

load

[kW

]

Duration [h]

A


Figure 10: Technical characteristics of the micro-CHP Ecopower plus. The figure shows the linear relationship between generated electric energy and primary fuel energy (dashed line); and between generated electric energy and thermal energy.

Clearly, there is a linear relationship between the electric and thermal output, as well as between the electric output and the primary fuel use (see Figure 10). Thus the value of the parameters ath, ap, bth and bp is obtained using a linear regression as reported in Table 7.

Table 7: Steady state characteristics of the commercial CHP device Ecopower that was used as prime mover in the case study of this chapter.

O<P [kWe] O(F [kWe] αth bth αp bp

Ecopower 4.7 1.2 3.88 0.80 2.54 0.69

3.4.2 Gas and Electricity Prices

For this work the gas price is assumed to be constant and equal to 0.04 €/kWhp. Afterwards, the influence of this parameter will be assessed by performing a sensitivity analysis (see Subsection 3.5.4.2).

The price to buy electricity from the grid is taken to be equal to 0.15 €/kWhe at night and 0.22 €/kWhe during the day. This price is indicative of the tariff applied to residential users in Belgium. The NREL [82], suggests that the remuneration that renewable and distributed energy generators receive for the electric energy fed into the grid should reflect the status of the electric system. For this reason, the present

0

36

912

15

1821

0 1 2 3 4 5

Prim

ary/

The

rmal

pow

er [

kW]

Electric power [kW]

Electric vs primary Electric vs Thermal


work uses day-ahead market prices as a proxy to remunerate the excess of electricity fed into the grid [28].

It is important to highlight that there is no clear agreement regarding the market structure for participants of a VPP. Thus this model employs both retail and wholesale market prices. In the future, the electric system regulator should establish the market rules.

3.4.3 Sizing of the Thermal-Storage Tank

The capacity of the thermal-storage tank is expressed in relation to the thermal energy generated by the CHP during one hour. The term relative storage capacity (RSC), defined in [83], will be used to denote the ratio between the storage capacity of the thermal-storage tank and the thermal output of the CHP during one hour time step, as shown in Equation (3-20):

"e = !O<P !O<P ∙ ∆$ (3-20)

To recall, in this equation, !O<P is the maximum storage capacity, !O<P is the maximum thermal output of the CHP and ∆$ is the time step. In this particular case one hour. The RSC is taken to be 2. The influence of this parameter is assessed later (see Section 3.5.3).

This thesis uses a model of a perfect stratified storage tank. The capacity of the storage tank is estimated using Equation (3-21):

!O<P = U ∙ 94 ∙ ∆% (3-21)

where U is the mass of water in the storage tank in kg, 94 is the specific heat capacity

of water, which is equal to 4.18 J/(kg K) and ∆% is the temperature difference. In this particular case, it is assumed that cold temperature in the tank is 40°C and the hot temperature 70°C. The size of the storage tank is 690 liters.

Additionally, in the following chapters it is assumed that the temperature of the hot water supplied by the CHP unit is always greater than the hot temperature of the storage tank.


3.4.4 Reference Case

The studied control strategies are compared against a reference scenario in which it is assumed that the heat demand is met making use of a boiler with an efficiency of 90 % and the electricity is bought from the grid at residential price.

3.5 Results and Discussion

This section presents a discussion about the obtained results for the case study defined in Section 3.4. First, in Section 3.5.1 several parameters are analyzed such as the electricity and heat generation for each strategy. Afterwards, in Section 3.5.2 the cost reduction with respect to the reference case is calculated. Finally, the net present value is calculated in Section 3.5.3 and the influence of the investment cost and the gas price are assessed in Subsection 3.5.4.1 and 3.5.4.2, respectively.

3.5.1 Electricity and Heat Generation

Table 8 gives the total thermal and electric energy generated by the CHP during one year. The results are shown for each of the studied strategies. Table 8 shows that with the electricity-driven strategy, more than half of the heat demand is met using the auxiliary boiler. The CHP generates less electrical and thermal energy than when the other strategies are applied.

On the other hand, the heat-driven and economic optimization give similar results. The amount of thermal energy generated by the CHP in the heat-driven strategy equals to 82 MWth, whereas, in the optimization case the CHP generates 78 MWth. (The CHP generates 5 % less thermal energy when controlled with an optimization algorithm).

Table 8: Amount of electrical / thermal energy generated by the CHP system over a year.

Heat-Driven Electricity-Driven Economic

Optimization

CHP Electricity [MWh/year] 27.4 18.5 26.1

CHP Heat [MWh/year] 81.9 56.6 77.6

Boiler [MWh/year] 39.6 64.0 43.5

Figure 11 compares the share of the different ways of heat production for the different cases. As the system is not allowed to dump heat, the total amount of thermal energy

Results and Discussion 41

produced by the CHP should be used inside the house to meet the heat demand. Additional heat demand should be met using the auxiliary boiler.

In the figure, the black area represents the amount of heat generated by the auxiliary boiler, whereas the blue section corresponds to the thermal energy delivered by the CHP (directly, or with a time delay via the thermal-storage buffer). Around 65 % of the heat demand can be met by the CHP when the heat-driven and economic-optimization controls are used. Using the electricity-driven algorithm, 47 % of the heat demand is met by the CHP.

Figure 12, shows the electricity use. The yellow area represents the amount of electricity imported from the grid. The black part corresponds to the self-consumption of electricity. Finally, the blue area equals to the amount of electricity that is fed into the grid.

Using the electricity-driven strategy, almost the total internal electrical demand can be met by using the CHP. The remaining 3 % is bought from the grid. Additionally, 7 MWh are fed into the grid. By comparison, the heat-driven and optimization strategies buy only 5 and 10 % of electrical energy respectively and feed in around 15 MWh per year (being approximately 55 % of the total electricity generated).

As mentioned before, it is important to remark the resemblance between the heat-driven and the economic-optimization algorithms. Both control strategies produce very similar results with respect to heat and electricity generation and use. This is due to the fact that the economic-optimization finds it profitable to use the micro-CHP mainly when the heat demand is high and this is the main idea behind the heat-driven control.

This observation is explained in Figure 13. This figure compares the heat-driven (left panels) and the economic-optimization (right panels) strategies. The figure shows the heat demand and generation for three days, characteristic for the three different seasons (i.e., winter, intermediate and summer time). The solid areas illustrate the heat demand. The dashed lines correspond to the thermal energy production of the CHP, while the solid lines represent the thermal energy charged to or discharged from the storage tank.


Figure 11: Thermal energy production for the different strategies. The black area represents the heat produced by the auxiliary boiler. The blue section corresponds to the heat generated by the CHP denoted as ‘CHP T’.

Figure 12: Electricity imports, exports and on-site use for the different scenarios. The yellow share corresponds to the amount of electricity that is bought from the grid. The black portion represents the on-site use of the electricity generated by the CHP, while the blue area shows the part of the electricity that is fed into the grid.

-20

0

20

40

60

80

100

120

140

REF ELECT DRIVEN HEAT DRIVEN OPTIM

Hea

t pr

oduc

tion

[MW

h/ye

ar]

Aux. Boiler Tank losses CHP T

0

5

10

15

20

25

30

REF ELECT DRIVEN HEAT DRIVEN OPTIM

Elec

tric

ity g

ener

atio

n [M

Wh/

year

]

in-house From grid To grid


During the winter day, the operation of both strategies is very similar. The CHP is operated most of the time serving as base load for the heat demand15. The same situation arises during the intermediate season. In this case, however the difference between the studied strategies is more notorious. The heat-driven operation tends to follow the heat demand operating at part load when the heat demand is lower than the maximal possible thermal output of the CHP.

Finally, during summer, the difference between both strategies is clear. The heat-driven strategy operates the CHP mostly at part load. Whereas, the economic-optimization control activates the cogeneration device less. However, when it is activated it operates at maximum capacity when possible.

This fact indicates that the economic-optimization algorithm makes better use of the thermal-storage buffer, this can also be observed in Figure 13. The efficiency of the CHP at full load is larger than during modulation. Thus, even when the heat demand is lower than the maximum thermal output of the CHP, the optimization delivers the full capacity and the remaining thermal energy is stored in the thermal buffer. This way, a larger amount of fuel can be saved.

It is expected that these results are valid for Stirling engine micro-CHPs as well. These kinds of engines can achieve higher electrical efficiencies at full load [76]. Fuel cells reach a high efficiency both at full and part-load operation [74]. However, experimental evidence shows that part load operation accelerates the wearout of the device [84]. For this reason, the full-load operation is also recommended like it is scheduled in the economic-optimization.

15 Recall that the auxiliary boiler meets the remaining heat demand however for illustration purposes it was not shown in Figure 13.


Figure 13: Comparison between the heat-driven (left panels) and economic-optimization (right panels) strategies for the different seasons. The gray area corresponds to the heat demand. The dashed line represents the thermal power generated by the CHP and the solid line corresponds to the thermal power charged to (negative values) or discharged from (positive values) the storage tank.


3.5.2 Cost Savings

This section estimates the actual cost reduction obtained by installing a CHP system and controlling it applying the studied algorithms. Towards this aim first the operational cost is calculated for all control strategies as explained in Equation (3-5).

Table 9 summarizes the results. First, the yearly cost is given followed by the percentage savings with respect to the reference scenario. The table shows that the largest savings are achieved using the optimization strategy followed by the heat-driven control. Using the electricity-driven strategy, the cost decreases 17 % with respect to the reference case.

Table 9: Estimation of the operational cost for the different control strategies and cost savings with respect to the reference scenario.

Reference Heat-Driven Electricity-Driven Economic-Optimization

Cost Cost Savings Cost Savings Cost Savings

Total [€/year] 7782 6265 19 % 6436 17 % 6090 22 %

The variation of the cost reduction throughout the year is analyzed in Figure 14. Comparing the heat-driven and economic-optimization strategy, it can be deduced that, as expected, the behavior during the heating season (i.e., winter time) is very similar.

Nevertheless, during the intermediate and summer seasons the optimization performs better, saving a larger amount of cost. This result can be explained by recalling Figure 13. That figure shows that the optimization algorithm tends to operate the CHP at full load. This measure reduces fuel cost (at full load, the CHP has larger efficiency).

Additionally, it is remarkable that the electricity-driven strategy performs slightly better than the heat-driven strategy during summer. During the latter season, the electric demand becomes more prominent compared with the heat demand. Consequently, as explained by Hawkes [85], it is more profitable to follow the electric demand than the heat demand.

Looking further at Figure 14, it is important to mention that the larger savings are obtained in the intermediate season. During winter, the large heat demand results in large fuel cost to cover this demand. On the contrary, in summer the low heat demand limits the savings opportunities. This is especially noticeable in July. This month has


the lowest heat demand and electricity demand compared to the rest of the year. As a result, there is a visible reduction of savings in all strategies during this month.

Figure 14: Operational cost reductions during the year for the different control strategies (monthly savings). The largest difference between the economic-optimization and heat-driven strategy appears in summer.

3.5.3 Influence of the Storage Capacity

In order to study the impact of the thermal-storage capacity, on the overall system performance, the RSC was varied continuously from 0 (i.e., no thermal-storage tank installed) to 4. Figure 15 illustrates the cost savings with respect to the reference scenario depending on the relative storage capacity.

It is clear and according to the expectations, that by installing a thermal-storage device of 1 RSC significant cost savings can be achieved (e.g., the cost reduction increases from 18 % without thermal-storage tank to almost 22 % in the optimization case).

It is also noteworthy that the effects of a further increase in the storage tank capacity are almost negligible. In fact, a larger capacity of the thermal-storage tank leads to a slight cost increase in the heat-driven operation.

These results are corroborated by other authors; Haeseldonckx, et al., [81] report that the optimal thermal buffer should be able to store between two to three times the

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thermal outputs generated during one hour by the CHP. For this reason, further in this work, an RSC of 2 will be assumed unless a different value is specified.

Figure 15: Cost reduction of the different control strategies using different relative thermal-storage capacities (RSC). The graph shows how introducing a heat buffer leads to larger cost reduction, but without substantial further effect beyond RSC > 1.

3.5.4 Net Present Value

To finalize this chapter, the economic profitability of the studied cogeneration system is assessed. Towards this aim, the net present value (NPV) is estimated for each of the studied control strategies. The NPV is obtained using Equation (3-22):

Vo = −8 + V^1 + W3$C_--k R-k8

(3-22)

In the equation, V equals to the sum of all the revenues and expenses during the economic lifetime (LT) of the project. According to [86], the life time of a micro-cogeneration project is about 15 years. The discount rate (W3$C) is fixed first to 6 % [87]. Afterwards, this parameter is varied to analyze its influence in the decision process. Finally (8) is the initial investment cost, in this case 3500 € per kWe installed capacity. The effect of this parameter is also analyzed in Section 3.5.4.1.

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The results are summarized in Table 10. It is obvious that the largest NPV is attained when the cogeneration device uses economic-optimization control. In contrast, a negative NPV is obtained when the electric driven strategy is applied. Furthermore, the discounted cash flow is depicted in Figure 16.

Table 10: Net present value for the different control strategies.

Heat-driven Electricity-driven Economic-Optimization

NPV [€] 29.21 -1628 1735

The figure shows that using the economic-optimization strategy a positive cash flow can be obtained after 13 years of operation. The heat-driven strategy, on the other hand, starts to receive positive income after the year 15. Whereas, the electricity-driven obtains positive cash flow after 19 years.

Figure 16: Discounted cash flow with the different control strategies. It can be seen that with the electricity-driven strategy, the resulting cash flow is always negative during the project life time (15 years). On the other hand, the heat-driven control obtains positive cash flow after 15 years, whereas in the economic-optimization case, it becomes positive after 13 years.

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The following Sections 3.5.4.1 and 3.5.4.2 analyze the influence of several parameters such as the rate of discount, the investment cost and the gas price.

3.5.4.1 Sensitivity on the Investment Cost

In the previous section, it was found that with the actual investment cost a very low or even negative NPV results in the heat-driven and electricity-driven strategies. Assuming that, in the coming years, the investment cost for the micro-CHP prime movers will decrease due to economies of scale, the NPV can be recalculated considering two different values for the investment cost 2500 and 3000 €/kWe installed capacity instead of the reference value of 3500 €/kWe.

Additionally, when using the NPV in a decision process, it is important to select the appropriated discount rate. The discount rate is usually associated with the opportunity cost of capital for this project when compared to other potential investments. If the project, for example, is compared to investing in bonds, the resulting rate of return is low. Nevertheless, a private investor can reach larger internal rates of return and would prefer to use them as reference for his chosen discount rate. For this reason, the NPV was evaluated for three different discount rates (3 %, 6 % and 10 %).

Figure 17 depicts the results. The figure shows that, with the actual investment cost of 3500 €/kWe and a high discount rate (10 %), the CHP project turns to be non-profitable in all cases. If the discount rate is 10 %, the investment cost must decrease at least by 15 %, for the resulting NPV to become positive. This might be a barrier for the penetration of micro-CHPs in the residential sector.

Additionally, it is important to consider how the investment cost can substantially affect the payback time. With a discount rate of 6% and a low investment cost (2500 €/kWe) the payback time ranges from 8 years for the economic-optimization to 11 years for the electricity-driven control. These values are lower than those reported in the reference case (see Section 3.5.4). The lowest payback time is achieved with the economic-optimization strategy when a discount rate of 3% and an investment cost of 2500 €/kWe are assumed. In this case, the payback time is only 7 years.


Figure 17: NPV for the three studied control strategies using different discount rates and varying investment cost. If the considered discount rate is 10 % the CHP project is non profitable with the actual investment cost of 3500 €/kWe installed capacity.

3.5.4.2 Sensitivity on the Gas Prices

Finally, the influence of the gas price is analyzed and the results are presented in Figure 18. Three different prices are considered (0.02, 0.04 and 0.06 €/kWh), recall that the chosen “reference” price is 0.04 €/kWh. As in the previous section different discount rates are evaluated. It is clear that the gas price has a large influence on the profitability of the project. If the gas price increases to 0.06 €/kWh, the NPV turns negative for all cases independent of the discount rate considered. In a similar way, if the gas price is as low as 0.02 €/kWh the project is always profitable independent of the discount rate.

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Figure 18: NPV for the three studied control strategies using different discount rates and changing the gas price.

Furthermore, the gas price also influences the payback time considerably. Considering a discount rate of 6% and a low gas price (0.02 €/kWh), the payback time ranges from 8 and 10 years for the economic and electricity-driven control, respectively. On the other hand, the payback time increases to 28 years in the best case (economic-optimization) when the gas price is as large as 0.06 €/kWh.

In the following chapter, it is assumed that a VPP pays the same gas price as the small and medium sized enterprises (i.e., 0.04 €/kWh). However, currently there is no agreement regarding the gas price that will be paid by residential micro-CHPs aggregated in VPP. Clearly this can affect the results substantially and increases the uncertainty regarding the profitability of micro-CHPs.

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3.6 Conclusions

Traditionally, a CHP device was operated to follow the heat demand known as heat-driven strategy. This operation was motivated by the fact that most prime movers (except for fuel cells) have low electric efficiency. As a consequence, using the CHP to generate electricity at moments when the heat cannot be used results in a non efficient use of primary energy.

Nevertheless, the use of thermal-storage tanks opens the possibility to use other strategies such as: electricity-driven and economic optimization. When comparing the three strategies, the results indicate that for the studied CHP system the economic-optimization control performs better than the heat-driven and the electricity driven control.

Assessing the heat-driven and economic-optimization algorithms, it is observed that, during the winter, the behavior of these strategies is very similar. However, in the intermediate season and summer, when the heat demand is low, the optimization algorithm obtains an economic advantage. This is because during these seasons, instead of using the CHP in part load to follow the heat demand closely (as the heat-driven strategy does), the economic-optimization strategy operates the CHP at maximum capacity whenever possible, filling the thermal buffer to meet later the heat demand.

Furthermore, the results indicate that during summer, when the electric demand becomes more important than the heat demand, it is more profitable to use an electricity-driven control.

The results of this chapter motivate the use of economic optimization. It was shown that with this operation strategy a larger NPV can be obtained. The following chapters use the explained optimization algorithm of this Chapter 3 as basis for building up their respective models.

53

4. Self-Balancing Using Virtual Power

Plants

The content of this chapter is adapted from: J. Zapata, J. Vandewalle, and W. D’haeseleer, “A comparative study of imbalance reduction strategies for virtual power plant operation,” In: Applied Thermal Engineering (2014), pp. 847-857.

4.1 Introduction

The large penetration of distributed generation (DG) in the electric grid yields an important challenge to the operation of the energy system. Several DG technologies have an intermittent output that is very difficult to forecast (i.e., wind and solar). This increases the imbalance error of the system. To balance the total generation and consumption of power in real time reserve, power is used. Nevertheless, increasing the use of reserve power adds a significant cost factor for operating the grid. In order to counterbalance this problem, it is proposed to group different distributed generation technologies into a virtual power plant.

This chapter aims to answer the first research question of this thesis, namely: “What is the potential to use a VPP comprising micro-CHP technologies to help reducing the imbalance error due to the imperfect forecast?”

The most important contributions of this chapter can be summarized as:

1. The ability of residential micro-CHP devices to reduce imbalances due to forecast errors of RES is assessed by applying a rolling horizon optimization to a VPP.

2. A comparison between different imbalance reduction strategies is performed in terms of reducing imbalance-error and the achieved economic benefits.

The remaining of this chapter is organized as follows: Section 4.2 provides a general description of the studied case. Section 4.3 outlines the optimization algorithm; this algorithm is divided in two main parts, the day-ahead optimization explained in 4.3.1 and the actual day optimization. Two strategies were used for the actual day

54 Self-Balancing Using Virtual Power Plants

optimization, a ‘forced self-balance’ strategy described in 4.3.2 and an ‘economic self-balance’ strategy illustrated in 4.3.3. The most important assumptions regarding the CHP system and the prices are given in Section 4.4. Section 4.5 briefly describes the forecasting techniques used. The results are presented in Section 4.6. Finally, Section 4.7 summarizes the work and states the conclusions.

4.2 Problem Description

The present study evaluates the ability of residential micro-CHPs to reduce the imbalance of small decentralized PV installations. Real residential gas and electric demand profiles have been made available by the LINEAR project16 . These data have been collected during measurements performed on 57 houses and it represents a characteristic sample of the Flanders region with respect to annual electric and thermal consumption, dwelling type and number of inhabitants.

In order to obtain a realistic heat demand profile based on the gas-demand profile, it is assumed that both variables are proportional. This assumption is justified by the fact that 83 % of the residential gas demand in Flanders is used for space heating. Hence, the conversion factor is equivalent to the boiler efficiency [88].

In this case study, only the houses where annual heat demand is larger than 20,000 kWh are taken into account. According to [89], considerable benefits when using micro-CHP instead of traditional heating systems (i.e., condensing boilers) can only be obtained in households with large heat demand. Only three of the available profiles fulfill this condition.

Therefore, the considered VPP consists of three detached dwellings and a PV facility. Each dwelling has a micro-CHP system (CHP prime mover, boiler and thermal-storage tank) installed. The CHP system is similar to the one illustrated in the previous chapter (see Figure 8). The prime mover is an internal combustion engine. This kind of technology was selected since it represents the largest number of CHPs that are installed in Belgium at the moment [90]. The small solar power station has a maximum output of up to 32 kW.

16 http://www.linear-smartgrid.be/

Problem Description 55

There is no heat-grid connection between the houses. In contrast, the electricity generated by micro-CHP can be used either to meet the common electric demand or can be sold in the exchange market. As the main goal of this study is to evaluate the ability of residential micro-CHPs to compensate the forecast error of a PV installation, all other influences are neglected. For that reason, it is assumed that the solar power station is not connected to the houses and the PV output will always be sold into the DA market.

Figure 19 illustrates the case study. It is assumed that the VPP operator will bid a certain amount of electricity into the DA market. The day-ahead bid, consists of the expected PV generation plus the electric energy generated by the CHP that was not used for internal consumption. During the actual day, if the VPP fails to deliver the contracted electric energy due to forecast errors, the difference is settled in the balancing market. For this reason, during every time step, the CHP generation is rescheduled in order to reduce the imbalance.

Figure 19: The studied case consists of a VPP that aggregates a group of residential micro-CHPs with a photovoltaic installation. The micro-CHPs output are rescheduled every time step in order to reduce the imbalance due to forecast errors of PV generation.

The analysis is performed for three representative weeks for three different seasons (summer, intermediate and winter). The imbalance reduction and the economic advantages are compared among the different seasons and scenarios.


Since the study evaluates the reduction of imbalance errors caused by the forecast deviation of PV output, other error sources such as deviations of heat demand and electricity price forecast are not considered.

4.3 Optimization Algorithm

The optimization uses a MILP model that is solved by the optimization software CPLEX. It is performed at two different points in time: the day previous to the delivery and in the actual day. The first optimization (DA optimization), has the objective to find an operational schedule for the CHP and boiler that minimizes the energy cost of the households. The results of this optimization are the base for the self-balance strategies as shown in Figure 20.

Figure 20: Two step optimization. On the Day-ahead (D-1), the optimization decides the optimal schedule of the CHPs. During the actual day (D), a self-balance routine is performed to re-schedule the CHPs aiming to reduce the imbalance error.

In the DA optimization, a large part of the electricity generated by the CHP is used to meet the local demand; this is due to the fact that the day-ahead prices are most of the time not high enough to motivate the use of the CHP for selling electricity to the grid. Nevertheless, the system allows to feed excess electricity into the grid and thus this part of the optimization also estimates the amount of electricity generated by the CHP that is going to be sold in the DA-market.

Optimization Algorithm 57

Near real time balancing optimization is performed during the actual day using a rolling-horizon approach as illustrated in Figure 21. This technique is also known as Model Predictive Control (MPC). At each time step, the actual PV output is obtained and the imbalance errors estimated. The optimization is performed for the entire time horizon, in the actual case for 24 hours which are split in 15 minutes time steps, using a forecast of the future PV generation; yet only the first time slot is implemented. The procedure is repeated during the next periods.

Figure 21: Rolling-horizon optimization: Every time step the optimization is performed for the whole time horizon; however, only the first time step is implemented.

Two different approaches are evaluated for the self-balancing strategy. First, a ‘forced strategy’ reduces the imbalance error regardless of the price. This strategy gives the maximum theoretical possible imbalance reduction under the optimization conditions. A second approach or ‘economic strategy’ intends to minimize the total operational cost including the imbalance cost. These strategies are compared against a ‘reference scenario’ in which no self-balancing is performed; thus the forecast deviations are settled in the imbalance market.

Furthermore, the ‘economic strategy’ is evaluated considering both perfect prediction of the imbalance prices and a forecast that is performed using autoregressive models (ARIMA) as explained in Section 4.5.2. In summary, four scenarios are studied, namely a ‘reference scenario’ (REF), a ‘forced self-balancing’ (FS) and an ‘economic self-balancing’ with perfect prediction (ES-P) and with forecast (ES-F). The characteristics of these scenarios are summarized in Table 11.


Table 11: Summary of the four studied scenarios.

Scenario Reference Forced Self-Balance

Economic Self-Balance

Perfect Forecast

Reschedule objective

No reschedule Minimize imbalance volume

Minimize cost including imbalance penalty

Minimize cost including imbalance penalty

Imbalance price information

No information No information Actual imbalance price

Forecasted imbalance price

4.3.1 Day-Ahead Optimization Algorithm

The objective of the day-ahead optimization algorithm to minimize the operational cost of the system is expressed in Equation (4-1):

UZ[ = ^- + - − -# − "-#_R-k

(4-1)

The operational cost is equal to the sum of the fuel cost of the CHPs and the boilers- , - plus the cost of the electricity that has to be bought from the grid to meet the remaining electricity demand -# minus the revenues due to the

electricity that is sold to the grid "-+(.

The constraints that limit the operation of the CHP units and boilers are explained in Section 3.3 (see Equations (3-6) to (3-19)), they apply to each individual CHP unit. The electricity generated by the VPP, - , is equal to the sum of the individual electricity generated by each CHP device:

- = F,- F (4-2)

In addition, the minimal up and down times of the CHPs are taken into account. For each individual CHP unit, new sets and z are created: = [1,2, … , X%F] (4-3)

z = [1,2,… , E%F] (4-4)


In these equations, X%F and E%F represent, respectively, the minimal up-time and minimal down-time of each CHP unit, being one hour in this particular case. The constraints on the minimal up and down time become: F,- − F,- − F,- ≤ 0 (4-5)

F,- − F,- − F,-) ≤ 1 (4-6)

4.3.2 Actual Day Optimization - ‘Forced Self-Balancing’

The objective function of the second optimization problem is to minimize the imbalance volume. As stated in Equation (4-7):

UZ[ = -0 R20 − -1 0RR-k

(4-7)

where -0 R20 is the actual electric output of the PV and CHP installation and -1 0R is the forecasted output of these variables. This optimization is performed every time step once the real PV output is obtained. Although the objective function is different, the optimization has the same constraints previously explained and described in Equations (3-6) to (3-19).

An additional equation is included to estimate the imbalance error:

∆- = -;GHIJK + - GHIJK − d-;JIKQJN + - JIKQJNh (4-8)

In this equation, ∆- is the imbalance error, which is estimated by subtracting from

the scheduled PV, -;GHIJK , and CHP electric power generation,- GHIJK, the

actual output of these variables -;JIKQJN and - JIKQJN. 4.3.3 Actual Day Optimization - ‘Economic Self-Balancing’

The objective function is expressed in Equation (4-9):

UZ[ = ^- + -_R-k

(4-9)

The aim is to reduce the total operational cost - , including the imbalance cost -. Thus, the VPP can decide every time step whether it is profitable to reduce its imbalance internally or whether it is better to settle the difference in the imbalance market.


The fee that the VPP has to pay for the imbalance depends on its own positions (i.e., if it is generating more or less than the forecasted output) and on the imbalance prices as shown in Equation (4-10):

- = ∆- ∙ /- − ∆- ∙ /- ∙ ∆$ (4-10)

Where ∆- and ∆ - are, respectively, positive and negative imbalances of

the VPP and the corresponding positive and negative imbalance tariffs are /- and /-. It is important to remind that if the VPP has a positive imbalance, the

additional energy generated is sold to the TSO (Transmission System Operator) - see Section 2.2.2 - and the VPP receives compensation (except in case of negative prices). Therefore, the positive imbalance cost has a negative sign in Equation (4-10).

An additional constraint has been added to avoid that the VPP takes advantageous positions in the market that could be penalized by the TSO (see Equation (4-11)):

∆- ≤ ∆- (4-11)

This equation requires the total imbalance of the VPP to be lower or equal than the

imbalance caused by the PV installation, ∆ -, due to prediction errors.

4.4 Assumptions

4.4.1 Cogeneration System

The cogeneration system consists of a prime mover, a thermal buffer and an auxiliary boiler similar to the ones used in Section 3.4 and illustrated in Figure 8. The prime mover was sized for each house using the ‘maximum-rectangle’ method as explained in Section 3.4.1.

The capacity of the thermal-storage tank is calculated in such a way that the thermal buffer is able to store two hours of the maximum thermal output generated by the CHP (see Section 3.4.3). It is assumed that the thermal-storage tank starts and ends empty. The optimization does not allow dumping heat in the environment.

Finally, the auxiliary boiler covers the remaining heat demand. The boiler efficiency is assumed to be constant and equal to 90 %.

Forecasting 61

4.4.2 Electricity and Gas Prices

For the present work it is assumed that the price for the local electric energy corresponds to a typical residential tariff which amounts to 0.15 €/kWh at night and 0.22 €/kWh during the day. With regard to the DA price, the values are obtained from the BELPEX17 internet platform and correspond to the year 2012. It is also assumed that the VPP will pay a gas price equal to the price that is paid by small and medium sized enterprises which in the case of Belgium is equivalent to 0.04 €/kWh18.

The imbalance prices are publicly available at the internet page of ELIA19. The working mechanisms of the Belgian balancing market have been explained in Section 2.2.2.

4.5 Forecasting

4.5.1 Forecasted and Measured Photovoltaic Data

The PV profile used was measured at a fixed rooftop PV installation at the KU Leuven Campus in Belgium. The data is available in fifteen minutes time steps [91]. The historical power generation of the modules was used to obtain a simulated forecast. This was done making use of autoregressive models as explained by Bacher, et al., [92] and Pedro and Coimbra [93].

First, the PV data was normalized using the methodology described by Bacher, et al., [92]. This kind of model assumes that the PV output can be explained by a combination of deterministic and stochastic factors. The method employs measurement from previous years to determine the base output of the PV.

The methodology is further illustrated in Figure 22. First the PV output of the previous year is arranged as a function of the time of the day (i.e., as a fraction of the day

being 1 the end and 0 the beginning) and day of the year (see panel a). Afterwards,

using quantile regression, a smooth surface that covers the measured PV output closely is found. This is shown in the right panel. As in [93], no mathematical expression is derived from the surface, only interpolation is employed in order to find the base model.

17 BELPEX is the Belgian Power Exchange for anonymous, cleared trading in day-ahead electricity. 18 Since the structure of the market for a VPP is not yet clearly established the model employs both retail and wholesale market prices. In the future, the regulator should clarify the rules for the market. 19 ELIA is the Belgian transmission system operator (TSO) for electricity.


a) b)

Figure 22: PV base model. The left panel shows the PV output as a function of the time of the day and the day of the year. The right panel presents a model of the PV output under base conditions.

Once the PV output is normalized, the deviation from the base model is estimated making use of an autoregressive moving average technique (ARIMA). Details on how to fit an ARIMA model can be found in Appendix A. The resulting model that best fits to the normalized PV output is a seasonal ARIMA (0,1,2) (0,1,0)96. The seasonality corresponds to a daily correlation. Recall that the data is in 15 minute time steps and thus the total number of time steps per day is 96.

4.5.2 Imbalance Price Forecast

In the ‘economic self-balancing’ with forecast20, the objective is to minimize the total cost. For this reason, a prognosis of the imbalance prices should be incorporated in

20 The ‘economic self-balancing’ with perfect prediction makes use of the actual imbalance prices serving as best case scenario.

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the optimization. In [94], it is suggested that there is a linear relationship between the day-ahead market price, the imbalance price and the net regulating volume (NRV)21.

The imbalance price is formulated as a linear combination of the NRV and the day-ahead market price. A linear fit is expressed in Equations (4-12) and (4-13) for the values of the year 2012. Note that both equations are very similar. This is due to the fact that, as mentioned before, in Belgium there is a single imbalance price for positive and negative regulation that only differs by α and β in case of large imbalance (see Section 2.2.2).

/- = /-0 + 0.19 ∗ V" + 13.7[c€/kWh] (4-12)

/- = /-0 + 0.18 ∗ V" + 15.5[c€/kWh]

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Using a linear fit proves to be a sufficiently accurate measure for the purpose of this research since the aim of the study is to establish the methodological and conceptual principles. Nevertheless, as explained before, the algorithm was performed with and without perfect forecast in order to have an idea of the value of a perfect prediction.

It is assumed that the day-ahead market prices are known in advance. Thus, only a forecast of the NRV is needed in order to predict the positive and negative regulating prices.

Forecasting the NRV is a challenging task due to its unpredictable nature. Nevertheless, a good approximation can be found using autoregressive models as explained in [90]. Once the NRV forecast is obtained, the values are fitted to Equations (4-12) and (4-13) and the positive and negative imbalance prices are estimated.


The results of the three different implemented strategies are compared. The first criterion to be evaluated is the ability to decrease the imbalance error, or in other words, the capacity to comply with the original day-ahead schedule. The second criterion is the total operational cost including the fuel cost and the imbalance cost. Since the DA revenues are the same for all scenarios (only differing between seasons) they are not included in the comparison.

21This is the reserve power that Elia had to activate in the specified 15 minutes to preserve the balance in the system.


4.6.1 Day-Ahead Schedule Compliance

Figure 23 illustrates the results of the DA schedule compliance on a typical winter day22.The left side of the figure depicts the ‘reference scenario’, whereas the plot in

the middle corresponds to the ‘forced self-balance’ strategy and the right figure represents the ‘economic self-balance’ approach using perfect prediction.23

In the figures, the black line indicates the amount of electric power that was bid into the DA market while the shaded area represents the actual electricity that was delivered. Looking at the figures, it is clear that using rescheduling to self-balance, either by aiming to reduce the imbalance error or the total cost, the difference between the electricity bid DA and the actual dispatch can be largely reduced.

Figure 23: Reference and self-balancing scenarios on a winter day. In the self-balancing scenarios the actual delivered electricity (shaded areas) follows closely the DA bid (black line)24.

22 The calculations were performed for a week, the figures show only one day to facilitate the visualization. 23 The results of the economic rescheduling with forecasted prices look very similar to those with perfect prediction and therefore are not shown. 24 In the figures RT DISP stands for real time dispatch.

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Similarly, Figure 24 illustrates the studied scenarios on a summer day. In this case, only the ‘forced self-balance’ approach decreases the difference between the actual output and the DA bid. On the other hand, the ‘economic self-balance’ strategy performs poorly in reducing the DA schedule deviations, suggesting that it is not profitable to do so during this day. This observation is elaborated further in the Section 4.6.2.

Figure 24: Reference and self-balancing scenarios on a summer day. Same convention as in Figure 23.

In a further step, the compliance with the DA schedule (i.e., imbalance error reduction) is calculated with respect to the ‘reference scenario’. Table 12 summarizes the results. The first column shows the remaining imbalance in the reference case. Afterwards, the corresponding positive and negative imbalance errors resulting from the self-balancing strategies are presented.

It can be observed that the remaining imbalance error (particularly the positive imbalance) in spring and summer is larger than in winter. The results of the ‘forced self-balance’ strategy indicate that it is theoretically possible to achieve a large compliance with the DA schedule using micro-CHP (up to 95 % in winter).

0

4

8

12

16

20

0:00

10:3

0

21:0

0

Elec

tric

ity [

kWh/

h]

Reference

0:00

10:3

0

21:0

0

Forced Self-Balance

0:00

10:3

0

21:0

0

Economic Self-Balance 'Perfect Prediction'

RT DISP

DA BID


Regarding the ‘economic self-balancing’ strategies, both with and without perfect price forecast, the results show that the amount of imbalance error reduction is lower in comparison with the ‘forced self-balance’ strategy. For instance, during winter, the ‘forced self-balance’ strategy was able to decrease the negative imbalance volume by 95 %. However, the ‘economic self-balancing’ only reduces 22 % of this imbalance volume. These numbers suggest that in some cases instead of using the CHP to reduce the imbalance, it is better to settle the difference in the market. Particularly in summer, for example, there is a minor effort to reduce negative imbalance (only 2.7 % lower than the reference case). This is due to the fact that the low heat demand lowers the motivation to turn on the CHP in order to compensate for insufficient electricity generation.

Table 12: Remaining imbalance for the different scenarios [kWh].

Season Reference Forced Self-Balance

Economic Self-Balance

Perfect Forecast

POS NEG POS NEG POS NEG POS NEG

Winter 69.3 105.4 15.6 5.0 32.2 73.7 19.2 81.0

Spring 267.8 206.5 139.7 100.2 205.0 144.4 206.5 150.9

Summer 300.1 137.4 163.4 56.8 190.0 133.7 180.6 133.6

POS =Positive imbalance; NEG=Negative imbalance

4.6.2 Total Operational Cost

Next, the total operational cost is subject to evaluation. This cost includes the fuel cost of the CHP, the auxiliary boiler and the imbalance cost. The results are illustrated in Figure 24, Figure 25 and summarized in Table 13.

In Figure 24 the cost difference between the reference and the ‘forced self-balancing’ scenario is illustrated. The three cost components are included (fuel cost for the boiler and CHP and the imbalance cost). In the graph, a positive amount indicates an increase of the cost and a negative amount a decrease.

During winter, the CHP is forced to generate more electric energy in order to compensate the forecast error of the PV installation. As a consequence, the cost of the CHP increases. This leads to a decrease in the cost of the boiler since the CHP is simultaneously generating more heat. This is possible and still profitable in this season due to the large heat demand.


Figure 24: Cost change for the ‘forced self-balance’ strategy with respect to the ‘reference scenario’. A positive change denotes a cost increase while a negative change is a decrease.

Figure 25: Cost change for the ‘economic self-balance’ strategy with respect to the ‘reference scenario.’ A positive change denotes a cost increase while a negative change is a decrease.

-20 -15 -10 -5 0 5 10 15 20

Winter

Spring

Summer

Cost reduction/increase with respect to reference [€/week]

Total

Imbalance

CHP

Boiler

-20 -15 -10 -5 0 5 10 15

Winter

Spring

Summer

Cost reduction/increase with respect to rererence [€/week]

Total

Imbalance

CHP

Boiler


On the other hand, during summer and spring, there is a large positive imbalance (see Table 12). Thus, the CHP is forced to reduce the electric output in order to compensate for the excess of PV energy. Opposite to what was expected, this leads to an increase in the imbalance cost during both seasons. This is because as explained in Section 2.2.2, the TSO pays to the BRP for positive imbalance errors (i.e., generation surplus). If the price paid by the TSO is large, reducing the positive imbalance error will decrease profits (see Figure 26 for an insight into this case). According to Figure 24, the ‘forced self-balancing’ strategy is only profitable during winter (see also Table 13).

Similarly, Figure 25 illustrates the cost difference between the ‘economic self-balancing’ strategy with perfect prediction of the prices and the ‘reference scenario’. In this case there is a total cost reduction in all seasons (see also Table 13). Particularly, it can be observed that the CHP is used less to compensate negative imbalance during winter, leading to a larger cost reduction than the observed with the ’forced strategy’. On the other hand, during summer CHP generation decreases considerably due to two reasons: first the lack of PV generation is mostly settled in the imbalance market and consequently increasing the imbalance cost, which is more convenient than using the CHP in this season due to the extra fuel cost. Second, the CHP is turned off at some times to compensate the extra PV generation, leading to savings in the primary energy cost. These results are also supported by the findings of the previous section (see Table 12).

Table 13: Difference in the operational cost with respect to the ‘reference scenario’.

Difference [€/week]

Winter Summer Spring

FS ES-P ES-F FS ES-P ES-F FS ES-P ES-F

Boiler -9.27 -2.28 0.29 6.75 9.52 10.42 2.35 -1.25 -0.77

CHP 9.50 -1.42 -3.94 -5.74 -16.46 -17.00 -0.45 0.90 0.01

Imbalance -1.42 -0.44 0.07 2.18 3.02 3.58 1.12 -2.34 -1.12

Total -1.18 -4.15 -3.57 3.20 -3.92 -3.01 3.02 -2.69 -1.87

FS= Forced strategy; ES-P=Economic strategy perfect prognoses; ES-F =Economic strategy with forecast

Table 14 summarizes the total cost per week for the three studied strategies (and the cases with and without perfect prediction) and the percentage change of the cost with respect to the ‘reference scenario’. The first column corresponds to the ‘reference scenario’ where the imbalance error is settled in the market. Afterwards, the results of


the ‘forced self-balancing strategy’ and the ‘economic self-balancing’ are shown. A negative percentage value indicates a cost decrease.

The main findings of Table 14 are summarized as follows:

• The cost increase that occurs in summer and spring with the forced schedule reflects that, even though it is theoretically possible to use micro-CHP devices to reduce imbalance, it is not always profitable to do so.

• The perfect prediction gives always the maximum theoretical cost savings that can be achieved by implementing the ‘economic self-balancing’ methodology. Nevertheless, the difference between the forecasted and the perfect prediction is not large. In summer, for example, the cost of the ‘economic strategy’ using perfect prediction is only 1.5 % lower than the cost when using a forecast (the difference in other seasons is of the same magnitude). This indicates that in this case improving the quality of the forecast does not lead to a significant increase of the profits.

Table 14: Cost of the different strategies and change with respect to the ‘reference scenario’ (A negative change indicates a cost decrease).

Reference Forced Self-Balancing

Economic Self-Balancing

Perfect Forecast

Cost

(€/week)

Cost

(€/week)

Change (%)

Cost

(€/week)

Change (%)

Cost

(€/week)

Change

(%)

Winter 406.7 405.5 -0.3 402.5 -1.0 403.1 -0.9

Summer 93.2 96.4 +3.4 89.3 -4.2 90.2 -3.2

Spring 136.6 139.6 +2.2 133.9 -1.2 134.7 -1.4

Total 636.5 641.5 +0.8 625.7 -1.7 628.1 -1.3


Furthermore, observing the results of Table 13 and Table 14 it is important to highlight that the actual cost difference between the reference case and the studied strategies is very small. This can result from the fact that the VPP aggregator consists of CHPS with an ICE. This kind of technology has a low electric efficiency and a large heat to power ratio. For that reason, the imbalance cost reduction does not compensate the increase of fuel cost of the CHP. Similar results are found in [59] and [95]. In [95] it is stated that the benefits provided by micro-CHP technologies largely depend on the heat-to-power ratio and the load patterns. Thus the self-balancing strategies might be evaluated in other kinds of buildings (e.g., service buildings) and with other kinds of CHP technologies (e.g., fuel cells). Nonetheless, this is out of the scope of this work.

Finally, Figure 26 explains one of the reasons of the poor economic performance of the ‘forced self-balancing’ technique. Figure 26 shows the remaining positive imbalance for the different strategies on a spring day. The upper panel illustrates also the actual imbalance price (black) and the imbalance price forecast (gray). The second and third panel corresponds to the ‘economic strategy’ with and without perfect prediction respectively (black and dotted lines) and the panel at the bottom illustrates the ‘forced strategy’ (dashed line). The shaded gray area in all plots correspond to the reference scenario where no self-balancing is applied.

Looking at the ‘forced self-balance’ strategy (dashed line) the remaining imbalance is much lower than in the ‘reference case’ (gray area), whereas in the other cases there is almost no change of the imbalance error. This is due to the fact that, as shown in the upper panel, the positive imbalance prices during this period are large (up to 27c€/kWh). The large prices reflect the need of the TSO for up regulation, thus the TSO will pay to the VPP for its extra energy. As the ‘forced self-balance’ strategy does not take the prices into account, it reduces the imbalance by decreasing the CHP operation, but therefore it loses the opportunity to make profit.

On the other hand, though the forecast is not able to follow the peaks of the imbalance prices, the behavior of the ‘economic self-balance’ strategy with and without perfect prediction is nearly the same. This can be explained using the concept of the profitable price that is elaborated in [96]. According to this concept in an economic optimization the CHP operates only if the price paid for the electricity is larger than the cost of producing electricity with the CHP this cost is defined in Equation (4-14):

= ¤ ∝ ∙ /12 − ! &'()*+ . /12 ¦ ∙ Δ$ (4-14)

In this equation corresponds to the cost of producing electricity with the CHP, assuming that the heat produced has equal cost as the heat produced in a boiler.


Figure 26: Remaining imbalance for the different scenarios: ‘forced self-balance’ (FS) and ‘economic self-balance’ with perfect prediction and with forecast (ES-P and ES-F). The first panel shows the actual imbalance price and forecast. The shaded areas in the three lower panels correspond to the remaining imbalance of the reference case. The FS strategy (dashed line) reduces the positive imbalance even when the imbalance tariffs are large. ¨o stands

for the cost for producing the electricity with the CHP.


This cost represents a threshold: once the electricity price is larger than this threshold (no matter how large) the CHP operation is considered profitable. Consequently, the forecast does not have to predict the actual values but should be good enough to predict whether the imbalance prices are larger than the profitable cost to operate the CHP.

An example is shown in Figure 26 around the hour 16:00. The forecast fails to predict that the imbalance price will be larger than the profitable cost (dashed line first panel)25 and thus the ‘economic self-balance’ strategy with forecast decides to decrease the CHP operation and meet the heat demand with the help of the boiler. During the rest of the time the forecast is good enough and the operation with and without forecast is the same.


In this chapter, an optimization algorithm was designed to operate a virtual power plant that consists of several micro-CHP systems and a PV installation. The optimization algorithm uses a mixed integer linear programming model that fixes the amount of electricity that is going to be produced by the CHP the day before. During the actual day, a rolling horizon approach reschedules the operation of the CHP in order to compensate the imbalance error.

Three different strategies are compared: The first or ‘reference scenario’, does not make use of any rescheduling strategy but settles the imbalance error in the market. The second one, or ‘forced self-balancing’ strategy, forces to reduce the imbalance error without taking into account the imbalance tariffs. The ‘forced self-balancing’ strategy gives an idea of the maximum reduction that is theoretically possible. The last approach, ‘economic strategy’, aims to decrease the total cost (including the imbalance cost). This last strategy was implemented with and without perfect prognosis.

The results show that using the rescheduling strategy (either to reduce imbalance or cost), the deviation between the scheduled electricity and the actual delivery can be substantially reduced (up to 95 % in winter with the ‘forced strategy’ approach).

25 The operational cost changes with the electrical efficiency the one estimated for the example was calculated assuming the maximum electrical efficiency.


However, this imbalance error reduction comes at a cost. This cost increase has to be weighed against the cost of settling the deviations in the balancing market. If the balancing tariffs are not taken into account, there is a risk of facing profit losses.

The results of this chapter show that the economic advantages of using micro-CHP to balance a PV installation are limited. In the best case, assuming perfect forecast of prices and generation, the savings are lower than 2 %. These low numbers seem not to be enough to motivate a VPP operator to implement a self-balance technique. The reasons behind these numbers are the low electric efficiency (24.8 %) of the studied CHP technology. As a consequence, imbalance cost reduction does not compensate the extra primary energy cost.

Similar conclusions are reported by other authors in the literature. Zdrilic, et al., [97] have studied a VPP that consists of a wind farm, a solar installation and a conventional gas turbine. It was found that it is better to cover the forecast deviations buying the electricity from the day-ahead market than using the gas turbine. D’hulst, et al., [98] have assessed the possibility to balance a large-scale PV installation making use of an industrial CHP unit; the results predict a possible imbalance volume reduction of more than 80%. Houwing, et al., [58] have demonstrated that micro-CHPs can help to reduce the imbalance error of wind generators by 73%. The simulations of Houwing, et al., [58] are limited to one month in winter. As a consequence, the seasonal effects are not evaluated.

In this chapter, the remaining imbalance error is not allowed to be larger than the PV forecast error (see Equation (4-11)). This constraint implies that the CHPs can deviate from their planned schedule only to compensate for the PV forecast errors. This assumption limits the opportunities to provide passive balancing using the micro-CHPs. The potential of providing passive balancing is extensively analyzed in the next chapter.

75

5. Passive Balancing Using Micro-CHPs

The content of this chapter is adapted from: Zapata Riveros, J., Donceel, R., Van Engeland, J. & D’haeseleer, W. “A new approach for near real-time micro-CHP management in the context of power system imbalances – A case study”. In: Energy Conversion and Management 89, (2015), pp. 270–280

5.1 Introduction

The present study aims to develop a methodology to assess the feasibility of providing balancing services making use of an aggregation of 13 micro-CHP devices. The day before, the aggregator nominates his energy in the day-ahead market, during the actual day the pool offers balancing services by exploiting his flexibility.

The first approach for offering flexibility on near real time is the ‘self-balancing’ studied in the previous chapter. This chapter does not aim to reduce the local imbalance due to forecast errors or to actively participate in the reserve power market. The studied portfolio consists exclusively of micro-CHP devices. The objective is to offer near real time passive balancing services to the system operator using the flexibility of the aggregator.

Passive balancing occurs when a BRP participates in the balance of the electric power system even when it is not actively selected in the merit-order mechanism. In other words, when the internal imbalance of the BRP has the opposite direction of the total system imbalance. The Belgian market design, not only allows but also incentivizes this mechanism as a key point to minimize residual imbalance [25].

The major contribution of this chapter is to develop a near real time balance optimization that enables a CHP aggregator to find the optimal operation strategy that at the same time maximizes his revenues and contributes to resolve the system imbalance using the ability of the aggregator to change the scheduled electric output of the CHPs at the time of delivery.

Additionally, the effectiveness of the methodology is tested in a hypothetical case study that resembles the actual situation of the Belgian energy markets and CHP installations. This includes an assessment of the influences of several parameters on

76 Passive Balancing Using Micro-CHPs

the optimization such as the gas price, the boiler efficiency and governmental support of CHP given by the Flemish government by means of CHP certificates.

The remainder of this chapter is organized as follows: Section 5.2 explains in detail the methodology developed. The optimization algorithm is presented in Section 5.3. The assumptions related to the case study are described in Section 5.4. The most important results are discussed in Section 5.5. Section 0 presents a sensitivity assessment. Finally, Section 5.7 summarizes the conclusions and gives suggestions for future work.

5.2 Methodology

The strategy developed in this work enables an aggregator to find the optimal nomination and dispatch of the devices in order to participate in the wholesale energy market. The aggregator is composed of a group of micro-CHPs that are equipped with auxiliary back-up boilers and thermal-storage tanks. The configuration for each member of the aggregator is shown in Figure 27. The heat demand of the building is met using either the CHP, the back-up boiler or the heat stored in the thermal-storage buffer. On the other hand, the electricity generated by the CHP is aggregated and sold in the electricity market. Self-consumption of electricity is not considered in this chapter.

Figure 27: Configuration of the cogeneration system for each member of the aggregator. The thermal load is always met using either the CHP or the back-up boiler. The electricity generated is aggregated and sold in the exchange power market.

The objective of the optimization is not only to maximize the revenues from selling the electrical energy in the day-ahead market, but also to increase the profits by using the

Methodology 77

flexibility of the aggregator during the actual day of delivery. In other words, the goal is to find the optimal dispatch of the CHP devices that at the same time reduces the imbalance of the system and gives economic benefits to the aggregator. To reach this aim, two optimizations are performed at different time periods. Figure 28 illustrates the optimization process.

Figure 28: Two step optimization: In the previous day, the day-ahead optimization decides the optimal schedule of the CHPs. In the actual day, once the actual NRV is obtained, the real time optimization reschedules the CHPs in order to reduce the system imbalance.

The first optimization is performed the day before the actual delivery (day-ahead (DA) optimization). This optimization uses information regarding day-ahead prices and heat demand in order to find the optimal volume that should be bid in the day-ahead market. Both the thermal demand and day-ahead prices are assumed to be perfectly predictable as the focus of this work is on the real time optimization.

The day-ahead bids serve as inputs for the near real time balancing optimization. This optimization aims to reschedule the operation of the aggregator in order to reduce the system imbalance. Every time step, the aggregator evaluates the system demand for up/down regulation by checking the actual NRV (see Section 2.2.2. for further insight into the Belgian electricity market). Afterwards, he decides if it is profitable to adjust his position to provide balancing services to the system.

Near real time balancing optimization is performed during the actual day using a rolling-horizon approach as explained in the previous chapter (see Figure 21). At each time step the actual value of the imbalance prices and system imbalance is obtained. The optimization is performed for the entire time horizon, in the actual case for 24 hours that are split in 15 minutes time steps, using a forecast of the future imbalance


tariff and the NRV, yet only the first time slot is implemented. The procedure is repeated during the next periods.

The forecast of the NRV was estimated using ARIMA see Appendix A for details about ARIMA models). The resulting model that best fits the NRV of the system is a seasonal ARIMA (3,1,4) (0,1,0)96. The seasonality corresponds to a daily trend.

On the other hand, due to its variable nature, forecasting the positive and negative imbalance tariffs is more challenging. For this reason more stable parameters are defined as short term premiums (STP); these variables contain useful information about the relationship between the MDP/MIP and the day-ahead-price πtDA and are illustrated in Equations (5-1) and (5-2):

e%o1- = ¬Eo- − /-0

(5-1)

e%o2- = ¬fo- − /-0 (5-2)

Subsequently, these new variables are fitted with an ARIMA (3,1,3) with no seasonal lags. Once the prognoses of the STPs are obtained, the imbalance tariff forecast can be estimated using Equations (5-1) and (5-2). It is assumed that the current values for MDP, MIP and /-0 are perfectly known. In reality the prices are only available after the 15 minute window expired. A detailed description of the forecasting process can be found in [90].

Both the day-ahead and near real time balancing optimizations are performed using mixed integer linear programming. They are implemented in GAMS (using the Matlab/GAMS link) and solved using the CPLEX 12.0 solver.

5.3 Optimization Algorithm

As described before the optimization is divided in two different linear programming algorithms: a day-ahead optimization explained in 5.3.1 and a near real time optimization described in 5.3.2.

5.3.1 Day-Ahead Optimal Nomination

The objective of the day-ahead optimization is to find the optimal schedule for the CHP aggregator that maximizes the total revenues of the system as expressed in Equation (5-3):


max 6 = d"-,F0 − -,F h-F

(5-3)

In this equation, the sets ‘n’ and ‘t’ correspond to the number of CHPs that belong to

the aggregator and the time, respectively. Similarly, "-,F0 represents the profits

obtained from selling the electricity in the day-ahead market, and -,F is the

corresponding total operational cost.

In order to estimate the day-ahead revenues, the electric power scheduled -,F is

multiplied by the day-ahead market prices /-0, which are assumed to be known. The considered time step (∆$) is 15 minutes:

"-,F0 = d-,F ∙ /-0h ∙ ∆$

(5-4)

Next, the operational cost is estimated using Equation (5-5):

-,F = /12 ∙ d-,F + -,F h ∙ Δ$

(5-5)

In this equation /12 is the fuel cost and -,F , -,F are respectively, the primary

fuel consumption of the CHP and boiler.

Equations (3-6) and (3-7) describe the relationship between electric and the thermal output of each CHP and the electric output and the primary energy, the heat demand constraint is described in Equation (3-8), the state of charge of the thermal-storage buffer is estimated in Equation (3-9), the primary fuel consumption of the boiler is calculated using Equation (3-10), Equations (3-16)-(3-19) ensure that the micro-CHPs operate within the technical limits.

Additionally, the minimum start up and down time are modeled using equations (4-3)-(4-6).

Recall that contrary to the previous cases, in this chapter all the electricity generated by the micro-CHPs is sold in the electricity market; thus self-consumption is not considered.

5.3.2 Near Real Time Balancing Optimization

The near real time balancing optimization enables to adjust the schedule of the aggregator in order to reduce the system imbalance and at the same time obtain extra


revenues. This occurs because, as explained in Section 2.2.2, if the position of the aggregator helps to reduce the system imbalance, he will obtain economic benefits.

Figure 29 illustrates the global idea behind the balancing optimization; at each time step, the actual NRV and imbalance prices are obtained. The sign of the NRV determines the kind of regulation needed by the system. If the NRV is positive, there is need for up regulation. On the contrary, if the NRV is negative, the system will call for down regulation. The aggregator will provide up/down regulation only if it is profitable; otherwise, it will keep the scheduled output (null regulation).

Figure 29: Near real time balancing optimization. The nature of the regulation depends on the sign of the NRV. When NRV is positive, up regulation is needed. Otherwise, there is a need for down regulation. The aggregator only performs up or down regulation if it is profitable.

As explained before, the optimization is performed in a rolling-horizon approach. This implies that the decision of whether or not a regulation action is profitable depends not only on the actual time step, but also on the expected values for the entire optimization period.

The objective of the optimization is to maximize the actual day revenues; see Equation (5-6):

max 6 `d∆"-,F g ∆-,F h-

F

(5-6)

The variable ∆-,F corresponds to the cost difference between the actual electric

energy delivered and the scheduled electricity.

The value of ∆"-,F represents the revenue obtained from using the flexibility in the

balancing market and is estimated as shown in Equation (5-7):

Application to a Belgian case study 81

∆"-,F ` ∆-,F ∙ /- ∙ ∆$

(5-7)

In the equation /- correspond to the imbalance tariff and ∆-,F is the difference

between the electric power generated and planned.

The flexibility of the aggregator depends on his ability to change his output during the actual day, still complying with the heat demand constraints and the technical constraints explained in Section 3.3. At each time step, the aggregator reschedules his dispatch in order to help the TSO resolve his imbalance. Naturally, this operation is performed only when the aggregator can obtain economic benefits; otherwise the aggregator prefers to keep his scheduled output (∆-,F ` 0). Finally, Equation (5-8) controls the direction of the electric-output change. In order to steer balancing into the correct direction that helps to correct the system imbalance, the electric-output change has to have the same nature as the NRV (i.e., positive or negative). In this way, when the TSO has a deficit (NRV>0), the aggregator tends to generate more electricity (i.e., up regulation) than planned the day before. In the contrary case, when the TSO has a surplus (NRV<0), the aggregator tries to reduce his output (i.e., down regulate) with respect to his nomination.

d∆-,F ∙ V"-h- ≥ 0

F (5-8)

5.4 Application to a Belgian case study

The following sections explain in detail the case study. A global description including the types of CHPs and dwellings involved in the model is given in Section 5.4.1. Afterwards, the general assumptions regarding the boiler, thermal-storage tank (Section 5.4.2), the electricity and gas prices (Section 5.4.3) are stated.

5.4.1 Description of the Case Study

The explained methodology has been applied to a hypothetical Belgian case study. Data regarding the installed capacity of micro-CHP in Belgium was collected from three representative institutions of the different Belgian regions [99]–[101]. According to this information, the total micro-CHP installed power is 1.4 MWe, the larger part of the installed capacity (more than 98 %) corresponds to Internal Combustion Engines (ICE) with nominal power larger than 6 kWe. Additionally, there is a large number (approximately 108 units) of small Stirling engines (1kWe) that are only used for


residential dwellings. However, Stirling engines represent only 6 % of the total installed capacity.

In order to reduce the computational burdens, a small aggregator who holds the characteristics of the Belgian situation is studied. The analyzed aggregator has a total installed capacity of 114 kWe of which 6 % are Stirling engines, corresponding to a total of 6 units with capacity of 1 kWe each. The remaining micro-CHPs (7 units) are ICEs. The characteristics of the CHPs that integrate the aggregator are displayed in Table 15.

Table 15 shows also the type of dwelling in which each micro-CHP is installed. The heat demand of these buildings results from actual measurement provided by the IEA annex 54 [102]. The optimization was performed for three weeks that are representative for each season in 2012 (one winter, one summer and one intermediate week). Other assumptions for the base case scenario are explained in the following sections (see Section 5.4.2 and Section 5.4.3).

Table 15: Characteristics of the CHPs that belong to the aggregator and type of dwelling in which they are installed.

No Of CHPs

CHP Type Minimum +<-* [kWe]

Maximum +<-* [kWe]

Minimum !+<-* [kWth] Maximum !+<-*

[kWth] Heat Demand

6 Stirling engine

1.0 1.0 5.7 5.7 Household

2 ICE 5.5 5.5 12.5 12.5 Small hotel

1 ICE 5.5 5.5 12.5 12.5 Small office

1 ICE 5.5 5.5 12.5 12.5 Small greenhouse

1 ICE 9.0 18.0 26.0 36.0 Medium office

1 ICE 9.0 18.0 26.0 36.0 Medium greenhouse

1 ICE 25.0 50.0 46.0 81.0 Large office

5.4.2 Auxiliary Boiler and Thermal-Storage Tank

All members of the aggregator are assumed to have the same type of boiler with a constant efficiency of 90 %. Afterwards, a sensitivity analysis is conducted to assess the influence of this value; see Section 5.6.1.

As explained in Section 3.4.3, the capacity of the thermal-storage tank is calculated in such a way that the thermal buffer is able to store two hours of the maximum thermal output generated by the CHP.

Results from the Case Study 83

If the amount of energy in the storage tank at the end of the week is larger than at the beginning, extra money is accounted for to compensate this energy (or subtracted in the case that less energy is found at the end of the period); this is called the storage settlement.

Additionally, dumping heat from the storage is allowed in certain extreme cases26 but if this occurs the aggregator has to pay an extra fine (to avoid intentionally dumping for economic reasons).

5.4.3 Gas and Electricity Prices

All boilers and CHPs belonging to the aggregator use natural gas; the price of the gas is assumed to be constant and equal to 0.04 €/kWh [103]. The imbalance prices are available on the Elia website [33]. Prices from 2012 have been used for this assessment. Day-ahead prices of 2012 are taken from the Belpex website [28].

The characteristics of the market prices are summarized in Table 16. This table also reports the total amount of up and down regulation required by the TSO during each week.

Table 16: Average day-ahead and imbalance prices of the studied weeks and total demand for up and down regulation.

Summer Autumn Winter

Average day-ahead price [€/MWh] 42 50 58

Average positive imbalance price [€/MWh] 35 63 87

Average negative imbalance price [€/MWh] 37 65 89

Total up regulation [GWh] 2.2 8.2 14.5

Total down regulation [GWh] 17.3 15.1 5.9

5.5 Results from the Case Study

This section gives a detailed description of the results of both the day-ahead optimization (Section 5.5.1) and the near real time optimization (Section 5.5.2).

26 When forecasts are not accurate, dumping can be inevitable because the storage tank would otherwise be overheated.


5.5.1 Results from the Day-Ahead Optimization

The day-ahead optimization aims to find an optimal schedule for the aggregator which maximizes the profits of selling the electricity in the day-ahead market. Table 17 shows the amount of electric power scheduled the day-ahead per dwelling and season.

It is remarkable that during the three seasons none of the CHP installed in households was scheduled and the boiler was used to meet the heat demand, indicating that for these dwellings selling the electricity generated by CHP at day-ahead prices is not profitable due to the low electrical efficiency of the installed CHP.

It is also noteworthy that during summer only the CHP in the hotels are scheduled to sell electricity to the day-ahead market; this result from the fact that hotels are the only buildings with significant heat demand during summer.

Table 17: Scheduled day-ahead electric output per dwelling and season [kWe/week].

CHP Type Dwelling Summer Autumn Winter

Stirling engine 1 kWe

Household 1 0 0 0 Household 2 0 0 0 Household 3 0 0 0 Household 4 0 0 0 Household 5 0 0 0 Household 6 0 0 0

ICE 5.5 kWe

Small hotel 1 528 2310 2156 Small hotel 2 374 1953 2112

Small office 0 132 1820 Small

greenhouse 0 154 1991

ICE 18 kWe Medium office 0 3418 7154 Greenhouse 0 0 5346

ICE 50 kWe Large office 0 4149 21084

An example of the results of the day-ahead optimization is given in Figure 30. This figure shows the resulting day-ahead schedule for the winter week of the ICE (50 kWe) installed in a large office.

The first and second panels of Figure 30 illustrate the day-ahead prices and the heat demand, respectively. The third and fourth panels correspond to the day-ahead schedule of the CHP and the state of charge (SOC) of the storage tank as a percentage of the maximum storage capacity.


From the figure it is clear that the economic-optimization forces the CHP to operate during day-hours when the day-ahead price and heat demand are large. On the other hand, the storage tank is effective at detaching the heat delivery from the electricity generation. In most of the cases, the storage-tank is charged in the evening when the day-ahead prices are still considerably large and it is discharged at night when the DA prices and heat demand drop.

Figure 30: Day-ahead schedule ICE (50 kWel) installed in the large office during the winter week. The figure displays: the day-ahead price (first panel), thermal load [kW] (second panel), scheduled electrical output [kW] (third) and storage state of charge [%] (last panel) of the office. The CHP is used when day-ahead prices and heat demand are large.


Finally, the monetary results of the day-ahead schedule are summarized in Table 18. Even though the optimization aims to maximize the profits, see Equation (5-3), the operational cost is most of the time larger than the day-ahead revenues. For this reason Table 18 reports the ‘day-ahead cost’. This corresponds to the operational cost minus the day-ahead revenues. As expected, the highest costs appear in winter when the heat demand is larger.

If the aggregator does not perform balancing, the overall cost would be equal to the ‘day-ahead cost’. Thus this ‘day-ahead cost’ is used as a base for comparison in the following sections.

Regarding Table 18, it is interesting to remark that even though the micro-CHPs installed in households were not scheduled, a day-ahead cost appears. This is the cost of the primary energy needed by the boiler to meet the heat demand of these dwellings. Other buildings such as the offices and greenhouses do not present a cost during summer. This implies that there is no heat demand during this season.

Table 18: Day-ahead cost per week (operational cost minus day-ahead revenue) [€/week].

CHP Type Dwelling Summer Autumn Winter

Stirling engine 1 kWe

Household 1 1.5 18.2 35.6 Household 2 22.6 38.5 69.9 Household 3 0.3 8.9 35.3 Household 4 48.5 34.2 58.7 Household 5 5.7 25.4 58.2 Household 6 1.7 12.1 38.9

ICE 5.5 kWe

Small hotel 1 93.3 144.7 159.2 Small hotel 2 64.9.0 85.0 100.0

Small office 0.0 7.4 97.4 Small greenhouse 0.0 4.6 91.6

ICE 18 kWe Medium office 0.0 111.1 187.1 Greenhouse 0.0 0.0 155.0

ICE 50 kWe Large office 0.0 71.7 571.8

Total day-ahead cost 238 562 1659

5.5.2 Results from the Near Real Time Balancing Optimization

The balancing optimization has the objective to maximize the revenues obtained by changing the physical position of the aggregator during the actual day in order to help resolve the system imbalance. The results are listed in Table 19 as ’real-time profit’. This figure includes the extra profits made from selling the deviations in the balancing market, and the difference in fuel cost as expressed in Equation (5-6). It is notable


that during all the three weeks (one in winter, one in summer and one in autumn) some significant real-time profits are achieved.

Table 19: Day-ahead cost, real-time profit, settlement and total cost using a rolling-horizon optimization.


Day-ahead cost [€/week] 238 562 1659

Real-time profit [€/week] 8 33 83

Settlement [€/week] 2 11 0

Total cost [€/week] 228 518 1576

The table also reports the day-ahead cost obtained from the previous optimization (see Section 5.5.1) and the storage settlement that (as mentioned in Section 5.4.2) is the money received depending on the amount of energy that remains in the storage tank at the end of the period.

The total cost is calculated as the difference between the day-ahead cost and the real-time profits (including the storage settlement). The table shows clearly that due to the extra real-time profit the total cost decreases in all cases compared to the case when only day-ahead optimization is performed. The relative decrease is larger in summer (5 %) and more moderate in winter (2.5 %).

Figure 31 illustrates the real-time profits per type of building and per installed capacity. During summer, the only buildings that obtain extra profit are the hotels. This is because during this season there is a large demand for down regulation (see Table 16) and the only buildings scheduled to sell electricity to the day-ahead market are the hotels.

On the other hand, during winter the houses receive the largest amount of real-time revenues per installed capacity. The CHPs installed in this kind of building are never scheduled day-ahead. This increases the opportunities of providing up regulation, which is largely needed during this week.


Figure 31: Real-time profit per type of building per installed electrical capacity [e/kW] for all simulated weeks.

The amount of energy that was up/down regulated is reported in Table 20. The table also reports the real-time profits obtained while performing these operations. During the studied winter week there was large demand for up regulation. In contrast, during the other seasons more down regulation was required.

Table 20: Results of the near real time optimization in terms of amount of energy and total profit.


Regulation type UP

DO

WN

NU

LL

UP

DO

WN

NU

LL

UP

DO

WN

NU

LL

Energy change [kWh/week] 389 210 0 1007 1042 0 2124 595 0

Real time Profit [€/week] -7 11 4 -34 67 0 20 27 36

The real-time profit reported corresponds to the extra profit obtained depending on the actions performed (i.e., up/down/null regulation) at the actual time slot. Nevertheless, it is important to recall that the rolling-horizon optimization might sacrifice profits in the actual time slot foreseeing larger incomes in the future. For this reason, there is some extra profit even when no regulation is performed (null regulation).

The same reasoning explains why the real-time profit in the case of up regulation during summer and autumn is negative. Performing up regulation in the actual time slot, even when the prices are not favorable, gives the opportunity to turn off the boiler or perform down regulation in a later time slot.


Figure 32 explains this in detail. The first panel, illustrates the real-time profits (gray area) obtained by one of the studied houses during one winter day. These profits, result from the difference between the extra balancing profits (dashed line) minus the change in the fuel cost (black solid line). The second panel, shows the scheduled and real-time electric power generated by the CHP in the same house. The third panel, depicts the scheduled and real-time use of the auxiliary boiler. Finally, the last panel corresponds to the state of charge of the storage tank (SOC) as a percentage of the maximum storage capacity. In the day-ahead schedule the storage was not used.

It can be observed that the CHP was not scheduled on the day-ahead. However, in real time between 10:00 and 19:00 the CHP operates providing up regulation and charging the storage tank. At some points during this period, the imbalance revenues are lower than the extra fuel cost, resulting in negative real-time profits (e.g., between 12:30 and 14:00).

These losses can be partially compensated after 18:00, when the CHP is turned off following the expected schedule (null regulation). The heat stored in the tank can be used to meet the heat demand. As a consequence, the fuel cost decreases and thus the real time profits increases.


Figure 32: Scheduled and real-time operation of a micro-CHP system installed in a residential building during winter. The first panel corresponds to the balance revenues, The second and third panel represent the day-ahead schedule and real-time operation of the CHP and boiler respectively. The bottom panel shows the state of charge of the storage tank as a function of the total storage capacity.

Sensitivity Assessment 91

5.6 Sensitivity Assessment

The influence of some of the most important parameters such as the boiler efficiency, the gas price and the use of CHP certificates is evaluated in the following sections.

5.6.1 Boiler Efficiency

In Section 5.4.2, it was stated that for the base case the efficiency of the boiler was assumed to be 90 % (LHV). However, there exist some commercial devices (such as condensing boilers) with higher efficiency. For this reason the optimizations were performed assuming an efficiency of 97 % and the outcomes are compared to the base case in Table 21.

Table 21: Day-ahead cost, real-time profit, settlement and total cost assuming a boiler efficiency of ηb=97 %. This is to be compared with Table 19 where ηb=90 %; the difference is expressed in percentage between parentheses.


Day-ahead cost [€/week] 221 (-7.1%) 543 (-3.38%) 1578 (-4.3%)

Real-time profit [€/week] 1 (-87.5%) 40 (+21.2%) 110 (+32.5%)

Settlement [€/week] 2 (0%) 16 (45.4%) -3 (-%)

Total cost [€/week] 219 (-3.9%) 486 (-6.2%) 1480 (-6.9%)

The table shows the results obtained when the boiler efficiency is 97 %. Next to it the percentual change with respect to the base scenario (ηb=90 %) is given. It is clear that in all the cases the total day-ahead cost decreases as a result a reduction of the fuel cost.

The real-time profits are also affected. For instance, during summer the low heat demand and the larger boiler efficiency discourage the use of the CHP for balancing. This result in a reduction of the real-time profits.

Contrarily, in the winter week, the real-time profits increase. This can be explained as follows due to the larger boiler efficiency, the CHPs are scheduled less in day-ahead than in the base case (ηb=90 %); consequently, the chances to provide up regulation increase, which was largely required during this week (see Table 16).

5.6.2 Sensitivity on the Gas Price

The influence of the gas price on the results was evaluated by performing the optimization for three different prices (0.03, 0.04 and 0.06 €/kWh). This is reported in Table 22. Recall that the gas prices for the base case is 0.04 €/kWh.


As expected, increasing the gas price leads to an increase in the day-ahead cost (i.e., the operational cost is larger). Consequently, the micro-CHPs are scheduled less in all the seasons. This effect impacts the real-time profit in different ways depending on the season. During summer for example, less day-ahead scheduling results in a large decrease of the real-time profit since, there is a large need for down regulation in this week (see Table 16).

In contrast, during winter, the opportunities for up regulation are larger than in the summer week. This implies that if the CHPs are scheduled less frequently in the day-ahead market, the opportunities to provide up regulation are larger and thus the profits increase.

On the other hand, the effects of decreasing the price are less visible but still remarkable; in general, the day-ahead cost is lower and the CHPs are scheduled more often than in the base case. During winter, due to the large up regulation need, increasing the day-ahead schedule decreases the real-time profits.

During summer and autumn the real-time profits increase. The CHPs are scheduled more often with the low gas prices. This implies more opportunities to regulate down and leads to an increase of real-time profits. Additionally, during the studied autumn week, negative values for the positive imbalance prices appear. Thus, if due to the low gas prices the CHPs are scheduled in the moments of low positive imbalance prices, a small growth of the real-time profits can be obtained, as the TSO will pay the aggregator for reducing his output.

Table 22: Day-ahead cost, real-time profit, settlement and total cost with different gas prices.


Gas price [€/kWh] 0.03 0.04 0.06 0.03 0.04 0.06 0.03 0.04 0.06

Day-ahead cost

[€/week] 168 238 358 371 562 895 1072 1659 2686

Real-time profit

[€/week] 16 8 0 39 33 84 52 83 424

Settlement [€/week] 1 2 0 7 11 12 3 0 5

Total cost [€/week] 149 228 358 432 518 799 1017 1576 2258

Sensitivity Assessment 93

5.6.3 CHP Certificates

The ‘CHP certificate system’27 are incentives given by the Belgian government, more specifically the Flemish region of Belgium, to promote the use of CHP. This section studies the influence of the CHP certificates on the provision of passive balancing.

CHP certificates are granted as one certificate per MWh absolute primary energy saved compared to separate generation of electrical and thermal energy [100]. Only CHPs with a relative primary energy saving larger than 0% are qualified to obtain certificates. The number of certificates a CHP installation receives is based on the absolute Primary Energy Saving (PES) and a banding factor (bf) as stated in Equation (5-9):

¨o = 67 ∗ oe (5-9)

CHPC is the number of CHP certificates. For the case of the micro-CHPs considered in this work the bf is one. The PES [MWh] is determined as shown in Equation (5-10):

oe = ∙ ° ±² + ³´³²±´ − ³²µ,

(5-10)

where E is the electrical energy generated in MWh, αQ and αE are, respectively, the thermal and electrical efficiency of the CHP plant, and ηQ and ηE are the thermal and electrical efficiency of the reference system, respectively, and specified by law as ηQ=0.9 and ηE=0.5 for the studied case. According to [100], the minimum price for the CHP certificates is 31 €/certificate. This price is taken as constant for the optimization.

The objective function of the day-ahead optimization is modified in order to include the certificate revenues:

max 6 =d"-,F0 + "-,F# − -,F h-F

(5-11)

In this equation, "-,F# are the CHP certificate revenues. These revenues are subject to

the characteristics of each CHP device, expressed as ac and bc in the linearized Equation (5-12):

"-,F# = d3 ∙ -,F + 6 ∙ -,Fh ∙ ∆$ (5-12)

27 In the Walloon region of Belgium, a different support scheme exists; this work only considers the Flemish system.


In this equation, -,F is a binary variable that indicates the on/off status of each CHP

unit at a given time. The objective function of the near-real-time optimization is also adapted to take the certificate revenues into account:

max 6 =d∆"-,F + ∆"-,F# − ∆-,F h-

F

(5-13)

The variable ∆"-,F# is the extra gain or loss (in case of down regulation) of

CHP-certificate revenues.

The results of the performed optimizations with the CHP certificates taken into account, are visualized in Table 23. As expected, with the CHP-certificate revenues, the day-ahead cost decreases; see Equation (5-11). However, only during summer the real-time profit increases. Similar to the case in which low gas prices are evaluated (see Section 5.6.2), the CHP certificates incentivize the day-ahead schedule of the CHP providing more opportunities to down regulate during summer.

Table 23: Day-ahead cost, real time profit, settlement and total cost assuming the abolishment of CHP certificates. The percentage in parentheses refers to a comparison to the case with certificates.


Day-ahead cost [€/week] 213 (-10% 465 (-17%) 1313 (-20%)

Real time profit [€/week] 14 (75%) 22 (-30%) 26 (-67%)

Settlement [€/week] 1 (0%) 11 (19%) 3 (-)

Total cost [€/week] 198 (-13%) 432 (-16%) 1284 (-18%)

Finally, Figure 33 compares the cases with and without certificates by summing up the cost and revenues of the three weeks. This gives a rough estimate of the yearly behavior. As mentioned before, without certificates the day-ahead cost increases, but at the same time the real-time profit increases as well. Nevertheless, the real-time-profit increase is not large enough to compensate the loss of certificate revenues.

Consequently, if the Flemish government removes the CHP-certificates mechanism, passive balancing might mitigate but not compensate for the absence of certificates. Nevertheless, this statement should be further assessed by applying the developed methodology to a larger case study that takes into account the whole year.


Figure 33: Comparison of the total cost and profits for the cases with and without CHP certificates.


This chapter assesses the possibility of providing ‘passive balancing’ making use of an aggregation of micro-CHPs. The aggregator bids his electricity in the day-ahead market. During the actual day, the aggregator is allowed to deviate from its day-ahead schedule only when this deviation contributes to alleviate the total system imbalance.

The methodology is based on two mixed integer linear programming optimizations. The first optimization is performed the day before the actual energy delivery and the second one runs continuously using a rolling-horizon approach. Three weeks are simulated, a summer, a winter and an autumn week.

The results indicate that providing passive balancing can lead to a total cost decrease of about of 2.5 % in winter and around 5 % in summer and autumn. These results are valid even if an increase on the gas price is considered or in case that CHP certificates are removed.


In the reviewed literature, only two studies, Abdisalaam, et al., [70] and Lampropoulos [71], explicitly consider passive balancing with distributed units. Abdisalaam, et al., [70] have studied the possibility of providing real-time balancing services with an aggregation of flexible residential loads. Lampropoulos [71] have assessed the economic benefits of a battery energy-storage system that provides passive balancing. Though these studies do not consider micro-CHPs, they also conclude that passive balancing can lead to a slight increase in the profits.

These extra profits nevertheless are highly dependent on the day-ahead prices, the imbalance prices and the position of the TSO. These variables fluctuate largely and are uncertain at the moment of making the nomination for the day-market. In the next chapter uncertainties are explicitly modeled using stochastic optimization.

97

6. Bidding of a VPP in the Day-Ahead

Market under Uncertainty

The content of this chapter is adapted from: Zapata Riveros, J., Bruninx, K., Poncelet, K., and D’haeseleer. “Stochastic bidding strategies for VPPs considering CHPs and intermittent renewables”. Submitted to: Energy Conversion and Management. (2015)

6.1 Introduction

Energy efficiency and renewable-energy sources are fundamental parts of the European energy policy. For this reason, efficient distributed generation technologies such as combined heat and power coupled to district heating (CHP-DH) and renewables (RES) technologies are promoted. Additionally, the flexibility that CHP-DH offers to the system is seen as an option to integrate intermittent RES. From a market perspective, this could be done by aggregating RES and CHP in a virtual power plant (VPP).

This chapter describes a methodology developed to assess the optimal bidding strategy of a VPP composed of a CHP-DH and RES generators. The VPP operator nominates its energy to the day-ahead market the day before the actual delivery (D-1). In real time, any deviation from the day-ahead schedule is settled in the imbalance market.

Trading in the electrical power market brings along several uncertainties such as the evolution of the prices, the actual generation and load, among others. The objective of this chapter is to develop a methodology to coordinate the participation of CHP-DH and RES in the day-ahead market (D-1) and estimate the economic benefits of using the CHP-DH to compensate for the uncertainty on day-ahead prices, RES forecasts and imbalance tariffs making use of different strategies. The uncertainties are explicitly modeled using a two-stage stochastic program.

This chapter starts by defining the concept of stochastic programming and by providing an illustrative example that helps to understand the need for stochastic optimization when dealing with uncertainties (Section 6.2). After the general introduction, Section

98 Bidding of a VPP in the Day-Ahead Market under Uncertainty

6.3 describes the case study in detail and outlines the optimization problem. The results are presented in Section 6.4. Summary and conclusions are given in Section 6.5.

6.2 Introduction to Stochastic Optimization

In the liberalized energy market, players are often required to make decisions under a level of uncertainty. This uncertainty stems from several sources such as: the unpredictability of demand, the development of the energy prices or the availability of resources [104].

In the previous chapters, the optimization problems were modeled using a deterministic approach. The unknown data were approximated by forecasts. To deal with the effects of uncertainty, a rolling-horizon optimization was performed.

However, stochastic programming offers a possibility to explicitly include this uncertainty in the optimization process. The uncertainty is specified by scenarios which are possible realizations of the stochastic process. A scenario is associated with a probability of occurrence.

The objective of a stochastic optimization is to find a single solution for a certain first-stage variable that is feasible for all possible scenarios and at the same time maximizes or minimizes the desired objective function [105]. In other words, the solution of a stochastic programming is optimal with respect to all scenarios, but not for a particular one [106]. In this thesis a ‘two stage stochastic programming with recourse model’ is used and the rest of the discussion will focus on this type of model.

Two stage stochastic programming requires that some of the decisions should be taken under uncertainty (‘first-stage decisions’). Once each of the considered scenarios is known, a new set of decisions is taken to respond to the observed outcome (‘second-stage decisions’) [106].

Next, an illustrative example will be given to clearly illustrate the advantages of using stochastic optimization. This example makes use of the same stochastic variables that are used to describe the optimal bidding strategy of a CHP-DH and RES generators in Section 6.3.1.

This simple case deals with a wind-farm operator who has to decide about the amount of energy to be nominated in the day-ahead market. The decision should be taken the day before under uncertainty regarding the actual generation and the price

Introduction to Stochastic Optimization 99

development. The producer faces three different scenarios that are described in Table 24.

On the day of delivery, if the expected energy does not match the actual generation, the generator is penalized28. Thus once the uncertainties are revealed, the generator should decide on the actual generation in order to minimize the imbalance penalties.

Table 24: Illustrative example: characteristics of each scenario and expected values.

Scenario Probability Wind generation

[MWh]

Day-ahead Price

[€/MWh]

Imbalance Penalty

[€/MWh]

1 1/3 19 25 10

2 1/3 17 45 70

3 1/3 6 80 110

Expected value 14 50 63

The problem aims to maximize the expected profits among all scenarios Y. This is expressed in Equation (6-1):

∀ω:max6 = .¹Sºk

∗ ^0 ∙ /¹0 − ∆¹ ∙ /¹_

(6-1)

In this equation, 0 is the day-ahead bid or the first-stage decision. The day-ahead price and imbalance penalties scenarios are represented by /¹0 and /¹ , respectively. The probability of occurrence of each scenario is equal to.¹ and ∆¹ corresponds to the imbalance volume, which is estimated using Equation (6-2):

∀ω:∆¹ = ¹R − 0

(6-2)

The total imbalance is equal to the day-ahead bid minus the actual energy generation ¹R(second-stage decision). Finally, Equations (6-3) and (6-4) limit, respectively, the day-ahead bid and the actual generation. The wind energy scenarios are represented

by E¹ST:

28 For the sake of simplicity this example assumes that the generator is always penalized regardless of his position and the position of the SI. This does not correspond to the real market behavior as explained in Section 2.2 , but it serves well for the illustrative purpose of this example.


0 ≤ 0 ≤ SO<P d¹STh

(6-3)

0 ≤ ¹R ≤ ¹ST

(6-4)

A common approach to formulate the wind generator’s problem is to replace the uncertainties with their expected values (see Table 24), thinking of them as a sort of forecast. Results are in this case obtained via deterministic models. In the studied example, the deterministic model assumes that the actual wind output is known and it is equal to the expected value. Thus if the output is known, there is no reason to deviate from it and pay an imbalance tariff. As a consequence, the day-ahead bid equals the expected wind generation, 14 MWh in this case.

Following, the deterministic solution is evaluated for the considered scenarios, the results are summarized in Table 25.

Table 25: Illustrative example: results obtained by replacing the scenarios by the expected value in a deterministic optimization.

Scenario DA Bid

[MWh]

Actual Dispatch

[MWh]

Imbalance

Volume

[MWh]

DA Profit

[€]

Imbalance Cost

[€]

Total Profit

[€]

1 14 14 0 350 0 350

2 14 14 0 630 0 630

3 14 6 8 1120 880 240

Expected profit [€] 407

Afterwards, the stochastic problem is solved. It results in a DA bid equal to 17 MWh, which is larger than the deterministic one (see Table 26 and compare with Table 25). This solution is evaluated for all scenarios, the results of the stochastic optimization are reported in Table 26. In this case, the stochastic optimization accepts a larger imbalance cost in order to obtain larger benefits in the day-ahead market.

Consequently, using stochastic optimization leads to larger profits than when the deterministic solution is applied. The difference between the expected profits of the stochastic program (446 €) and the expected profits obtained when fixing the uncertain parameters to their expected value (407 €) is called the value of the stochastic solution (VSS). In this particular case the VSS equals 39 €.

Introduction to Stochastic Optimization 101

Table 26: Illustrative example: results of the stochastic programming. In comparison with the deterministic solution (see Table 25), the stochastic DA bid is larger, leading to larger profits.

Scenario DA Bid

[MWh]

Actual

Dispatch

[MWh]

Imbalance

Volume

[MWh]

DA Profit

[€]

Imbalance cost

[€]

Total Profit

[€]

1 17 17 0 425 0 425

2 17 17 0 765 0 765

3 17 7 10 1360 1210 150

Expected Profit [€] 446

Nevertheless, the advantages of using stochastic optimization are not limited to an increase in profit. Assume that the wind producer is facing imbalance penalties that are largely spread. In other words, the possible imbalance penalties are either very large or very small as illustrated in Table 27. However, the expected value remains the same as in the previous case.

Table 27: Illustrative example: characteristics of each scenario and expected values with spread imbalance penalties.

Scenario Probability Wind generation

[MWh]

Day-ahead Price

[€/MWh]

Imbalance Penalty

[€/MWh]

1 1/3 19 25 5

2 1/3 17 45 10

3 1/3 6 80 175

Expected Value 14 50 63

In this case, the solution of the deterministic equivalent does not change, the day-ahead bid equals the expected value of 14 MWh. Table 28 shows the results of applying the deterministic solution to the new set of scenarios described in Table 27.


Table 28: Illustrative example: results of the deterministic equivalent with spread imbalance penalties. Note the wind producer faces large cost in scenario 3.

Scenario DA Bid

[MWh]

Actual Dispatch

[MWh]

Imbalance

Volume

[MWh]

DA Profit

[€]

Imbalance cost

[€]

Total Profit

[€]

1 14 14 0 350 0 350

2 14 14 0 630 0 630

3 14 6 8 1120 1400 -280

Expected Profit [€] 233

It is important to remark that using the deterministic solution, in this case if scenario 3 occurs, instead of obtaining some profit, the producer will face larger cost. This is because the deterministic optimization does not account for the possibility of obtaining different wind outputs that could deviate from the day-ahead bid neither about the possible realizations of the imbalance penalties.

On the other hand the stochastic optimization takes the uncertainty into account during the decision process. Thus it can offset potential losses. Table 29 presents the results of the stochastic optimization using the scenario set defined in Table 27. In this case the DA bid is equal to 6 MWh. This optimization reacts to the large imbalance penalty by sacrificing some day-ahead profit in order to reduce the risk of obtaining large imbalance cost. Note that in this case the large cost of scenario 3 is avoided and the VSS is even larger than in the original problem (67 €).

Table 29: Illustrative example: results of the stochastic programming with spread imbalance penalties.

Scenario DA Bid

[MWh]

Actual Dispatch

[MWh]

Imbalance

Volume

[MWh]

DA Profit

[€]

Imbalance Cost

[€]

Total Profit

[€]

1 6 6 0 150 0 150

2 6 6 0 270 0 270

3 6 6 0 480 0 480

Expected profit [€] 300

Methodology 103

In summary, stochastic programming allows to explicitly account for the uncertainty of the system. This enables not only to optimize for forecast conditions, but also for less likely but still possible scenarios that might lead to large profits losses. For instance in the given example, in the deterministic equivalent approach it was not possible to model the possible deviations from the expected output, this lead to lower profits.

Additionally, if the model is limited to use the expected value as forecast, the deterministic solution is optimal for that specific case. Nevertheless, if the actual observation differs from the forecast, the deterministic solution is no longer optimal and can actually lead to large profit losses. Stochastic programming is able to hedge this risk by finding the optimal solution considering all possible outcomes of the considered scenarios. This is especially important when the uncertain variable is largely spread and thus the risk of losses is high. After this introduction on stochastic programming, the next section describes the case study.

6.3 Methodology

The present study assesses the optimal dispatch of a hypothetical virtual power plant in Belgium. The VPP system consists of a CHP–DH together with uncontrollable RES generators (i.e., photovoltaic and wind energy). Figure 34 gives a detailed description of the studied system; the DH plant or CHP system consists of a prime mover, an auxiliary boiler and a thermal-storage unit that meet the heat demand of the community. On the other hand, the electricity generated by the VPP is traded in the electric power market. In other words, the DH plant is not responsible for meeting the electrical demand of the community.


Figure 34: Distribution of the electricity and heat connections for the studied case. The CHP system is composed of a prime mover, an auxiliary boiler and a thermal buffer. The electricity generated is traded in the electricity market.

The VPP controller makes a nomination on the day-ahead market considering the expectations for renewable energy generation in its portfolio, DA and imbalance prices, while the heat demand is assumed to be known. During real time, the deviations between the day-ahead nomination and the actual dispatch have to be settled in the balancing market via the imbalance mechanisms.

In order to account for the uncertainties that the VPP faces, a stochastic program is developed. As explained before, in a stochastic program the uncertainty is represented using a set of scenarios.

The stochastic program studied in this work is illustrated in Figure 35. When bidding electricity in the day-ahead and imbalance market the decision process can be split into two different stages. In the first-stage, the decisions have to be taken under uncertainty regarding the future RES generation and prices. In this study, the first-stage decisions correspond to the day-ahead bidding.

During the second-stage, the day-ahead prices are known, it is also assumed that at this point the VPP operator has a more accurate forecast regarding the realization of the RES and thus decisions regarding the dispatched volume are taken.

Methodology 105

Figure 35: Two-stage stochastic programming for the VPP. The first-stage decisions correspond to the day-ahead bids, whereas the second-stage decisions are related to the actual dispatch.

The day-ahead bid (i.e., first-stage decision) is obtained using 10 day-ahead, 10 imbalance and 10 renewables scenarios that were combined in order to obtain a total of 1000 scenarios.

The day-ahead bid is fixed and its quality is evaluated by repeating the optimization with a larger number of scenarios, in this case a combination of 10 day-ahead, 50 imbalance and 50 renewables scenarios. In this way the results are validated in a larger set of scenarios. This process is called ‘re-evaluation’. From the re-evaluation process the second-stage decisions are obtained or in other words the actual dispatch per scenario. Figure 36 visualizes the entire optimization process.


Figure 36: The results of the stochastic optimization are evaluated using a larger set of scenarios. During the re-evaluation process, the DA bid (first-stage decisions) are fixed and the second-stage decisions (or the actual dispatch) are obtained.

Three different bidding strategies are studied: ‘static’, ‘flexible DA’ and ‘flexible RT’ as stated in Table 30. The major difference between the studied strategies relies on the actual dispatch. The ’static’ case does not adjust the scheduled output of the CHP.

On the other hand, the ‘flexible DA’ and ‘flexible RT’ strategies differ from each other in the information available at the moment of performing the reschedule (second-stage decision). In other words, the ‘flexible DA’ reschedules the CHP output for the whole day depending on the RES scenario, but under uncertainty regarding the imbalance price. In contrast, the ‘flexible RT’, allows the VPP to adjust its position at each time step depending on the RES generation and imbalance price scenarios.

The ‘flexible RT’ case is performed using a rolling-horizon approach; at each time step the observed imbalance prices of each scenario are obtained. The optimization is performed for the entire time horizon; for each imbalance price scenario, the expected value estimated as the weighted average among all imbalance prices scenarios was used as forecast. The procedure is repeated for each period.

Methodology 107

Table 30: Summary of the different bidding strategies: ‘static’, ‘flexible DA’ and ‘flexible RT’

Case Dispatch Re-Evaluation Known Variables

Static Dispatch equals to DA schedule

No re-evaluation

Flexible DA One dispatch per RES scenario

• Day-ahead price • RES generation

Flexible RT One dispatch per RES and Imbalance prices scenarios

• Day-ahead price • RES generation • Actual imbalance price

It is important to remark that both the ‘flexible DA’ and ‘flexible RT’ correspond to two extreme cases. When deciding on the actual dispatch, the ‘flexible DA’ assumes that the VPP operator has no knowledge regarding the imbalance prices. In contrast, the ‘flexible RT’ assumes complete knowledge of the imbalance prices for the current time step.

In reality, every 3 minutes the TSO provides actualized information on the current imbalance volume. From this information the VPP can obtain a very accurate forecast of the imbalance price in order to perform ‘passive balancing’29. However, the forecast can still deviate from the actual imbalance price and thus the real benefits lie between the economic savings of these two cases ‘flexible DA’ and ‘flexible RT’ operation.

The stochastic optimization was formulated as a mixed integer linear program (MILP). The model has been developed in GAMS, and is solved using the commercial solver CPLEX.

6.3.1 Stochastic Optimization Model

The objective is to maximize the revenues obtained by the VPP as stated in Equation (6-5):

∀$, ∀\, ∀W, ∀Z:max 6 =».,».+».(d"-,,0 + "-,¼,½,¾ − -,¼,½ h¿-k ÀÁ

¾k À½k À

¼k (6-5)

In this equation, % is the time horizon, in this particular case, two days from which only the first one is implemented (the second day is considered to enforce an optimal behavior in the storage tank). The studied day is divided in 15 minutes time steps.

29 As explained in Chapter 5, passive balancing is a measure implemented by the Belgian TSO to allow the market participants helping to reduce the total system imbalance at real time.


Furthermore in Equation (6-5), S, R and I represent the sets of scenarios of day-ahead prices, RES generation and imbalance prices, respectively.

The revenues result from the difference between the profits obtained in the DA and imbalance (IMB) market "-,,0 and "-,,,+,( respectively and the operational cost of the

CHP-DH -,,,+ . Recall that "-,,,+ is the result from settling the deviations between the

planned and delivered electricity in the imbalance market; for this reason, this variable can take positive or negative values.

The revenues are weighted over all scenarios. The probability of occurrence of each scenario is equal to., for the day-ahead prices scenarios, .+ for the RES generations scenarios and .( for the imbalance price scenarios.

The electric power scheduled to be traded on the day-ahead market -0 is calculated in Equation (6-6):

∀$:-0 = d- + -h (6-6)

In this equation, - corresponds to the scheduled electric power of the CHP and - to the traded RES generation.

The day-ahead bid is calculated as Equation (6-7):

∀$:-0 = d-0h ∙ ∆$ (6-7)

It is important to remark that the day-ahead bid -0 does not depend on the scenarios.

On the other hand, the DA RES nomination - is limited to the maximum and minimum possible values achieved by the RES scenarios at each time step:

∀$: O(F d-,+h ≤ - ≤ O<P d-,+h (6-8)

The actual electricity dispatched -,,,+R depends on the realization of the scenarios as stated in Equation (6-9):

∀$, ∀\, ∀W ∶ -,,,+R = d-,,,+ + -,+h (6-9)

where -,,,+ is the actual electricity dispatched by the CHP. The imbalance error ∆-,,,+

represents the difference between the actual electric power delivered/consumed and the day-ahead schedule. This is expressed in Equation (6-10):

∀$, ∀\, ∀W:∆-,,,+ = -,,,+R − -0 (6-10)

Methodology 109

The profits are calculated as the sum of the revenues obtained from trading electricity in the day-ahead market and the imbalance market as stated in Equations (6-11) and (6-12):

∀$:"-,,0 = -0 ∙ /-,,0 ∙ ∆$ (6-11)

∀$, ∀\, ∀W, ∀Z:"-,,,+,( = ∆-,,,+ ∙ /-,( ∙ ∆$ (6-12)

In Equations (6-11) and (6-12), /-,,0 corresponds to the day-ahead price and /-,( to

the imbalance price [€/MWh]. The imbalance revenues can be either negative or positive depending on the nature of the system imbalance (SI) and the imbalance tariff.

The heat balance is described in Equation (6-13):

∀$, ∀\, ∀W:d!- + !- h + ∆!-,,,+ + ∆!-,,,+ = !-*O<F + !-,,,+ (6-13)

According to this equation the optimization must ensure that the heat demand is met during every time step for all scenarios, using the CHP !- , the boiler !- or the heat that is charged to or discharged from the thermal-storage buffer !-,,,+ .

Additionally, the variables ∆!-,,,+ and ∆!-,,,+ represent the difference between the

actual thermal power delivered by the CHP and backup boiler and their planned thermal power output, respectively.

The CHP plant is constituted by three internal combustion gas engines. Equation (6-14) states the relationship between the electrical and thermal power output of each unit. Similarly, Equation (6-15) links the primary energy use to the thermal and electrical power production. Looking at this equation, it is clear that once the optimal electrical output is selected, the thermal output is settled simultaneously and vice versa.

∀$, ∀[: -,F = !-,F ¤¦-,F (6-14)

∀$, ∀[: -,F = K,ÃÄ³² -,F = K,ÃÄ

³´ -,F

(6-15)

In these equations,-,F is the primary fuel consumption of each individual CHP unit [, and are, respectively, the thermal and electrical efficiency of the CHP plant.


-,F is a binary variable that indicates the on/off status of each CHP unit. This variable

is independent of the scenarios and cannot change during real time generation.

The total electricity generation - and primary energy - use of the CHP plant are estimated as the sum of the total electricity generation and fuel consumption among the individual units, as stated in Equations (6-16) and (6-17):

∀$:- = -,F TIÅ

Fk (6-16)

∀$: - = -,F TIÅ

Fk (6-17)

The start-up cost is calculated using Equation (6-18):

∀$, ∀[:-,F,-<+-_>4 ≥ /-,F,-<+-_>4d-,F − -,Fh (6-18)

In this Equation /-,F,-<+-_>4 is a positive parameter that represents a fixed cost for

starting up the machines. The fuel consumption of the boiler - is calculated as shown in Equation (6-19):

∀$:- = !- &'()*+ , (6-19)

It is assumed that the boiler has constant efficiency &'()*+. The total operational cost of the system is estimated as the sum of the primary energy cost of the CHP system and the start-up cost: see Equation (6-20):

∀$:-,,,+ = /-12 ∙ ∆$ ∙ d- + - + ∆-,,,+ + ∆-,,,+ h + -,-<+-_>4 (6-20)

In Equation (6-20) ∆-,,,+ and ∆-,,,+ correspond to the fuel use difference that

appears when the CHP system is rescheduled and /-12 is the fuel price.

The state of charge (SOC) of the storage tank !-,,,+ is calculated using Equation (6-21). The efficiency of the storage tank30 &,- is assumed to be constant. Recall that !-,,+ is

30 The efficiency of the storage tank represents the percentage of thermal energy that is preserved by the storage after it has been stored during one time step of 15 minutes. For example, a storage tank with an efficiency of 90 % is charged with 1kWh_thermal after 15 minutes, only 0.9 kWh_thermal remains.

Methodology 111

the average thermal power (kWthermal) that is charged to/discharged from the storage tank every time step; consequently, it can take both positive and negative values:

∀$, ∀\, ∀W:!-,,,+ = &,- ∙ !-,,,+ +!-,,,+ ∙ ∆$ (6-21)

Equations (6-22) - (6-23) ensure that the optimization does not exceed the operational limits of the CHP.

∀$, ∀[, ∀\, ∀W: -,F ∙ !O(F ≤ !-,F + ∆!-,F,,,+ ≤ !O<P ∙ -,F (6-22)

∀$, ∀[, ∀\, ∀W:-,F ∙ O(F ≤ -,F + ∆-,F,,,+ ≤ O<P ∙ -,F (6-23)

Equations (6-24) and (6-25) prevent exceeding the operational limits of the storage tank and boiler

∀$, ∀\, ∀W: 0 ≤ !-,,,+ ≤ !O<P (6-24)

∀$, ∀[, ∀\, ∀W:0 ≤ !-,F + ∆!-,F,,,+ ≤ !O<P (6-25)

6.3.1.1 Case Specific Constraints

The previously explained equations apply to the ‘flexible DA’ case; in this subsection, the necessary modifications to these equations for the other cases are described.

First, the ‘static’ case is modeled by setting the variables ∆-,,,+ , ∆!-,,,+ , ∆!-,,,+ , ∆-,,,+ , ∆-,,,+ to zero. In other words, the CHP is not

allowed to deviate from its scheduled output.

On the other hand, the ‘flexible DA’ and ‘flexible RT’ have the same day-ahead schedule; thus, it is only necessary to modify the equations that involve RT decisions. This is because in ‘flexible DA’ the imbalance volume decision ∆-,,,+ is considered

independent of the imbalance price /-,( scenarios. In other words, the imbalance

volume is settled before knowing the imbalance prices but with knowledge of the RES generation and day-ahead prices.

In contrast, in the ‘flexible RT’ case the imbalance volume is estimated depending on the imbalance price scenarios and thus several variables become dependent of these scenarios such as:-,,,+,( , -,,,+,( , !-,,,+,( , -,,,+,(R , !-,,,+,( , ∆-,,,+,( , ∆!-,,,+,( , ∆!-,,,+,( , ∆-,,,+,( , ∆-,,,+,( , ∆-,,,+,( and consequently the equations where these variables appear

are also dependent on the imbalance tariffs.


6.3.2 Application to a Case Study

The developed methodology is applied to a hypothetical case study that assumes a large penetration of renewable energy and the installation of a district heating facility in the city of Leuven (Belgium) which resembles a typical small European city. The heat demand profile is approximated through a bottom-up approach. Data concerning the building stock of Leuven, provided by the municipality [107], is combined with heat demand benchmarks [108] and synthetic load profiles [109] to create the heat demand profile.

It is assumed that the thermal energy is sold to the community at a constant retail price. As a consequence, they do not influence the optimization results. For this reason these revenues are not included in the optimization.

The size of the CHP is estimated using the maximum rectangle method; see Section 3.4.1. It is assumed that the DH system is operated by three parallel internal combustion gas engines (ICGE). Each ICGE has a maximum electrical output equal to

18 MWe. The electrical and thermal efficiency are = 44 % and = 48 %,

respectively.

Regarding the renewable generation it is assumed that the total installed capacity amounts to 20 MWe, of which 14 MWe corresponds to solar panels and 6 MWe to wind turbines. These numbers reflect the current (2014) proportion of photovoltaic and wind installation in Belgium. The renewable energy scenarios are based on data provided by the Belgian TSO [33].

The optimization will be performed for three different weeks, each representing the behavior of a season (summer, intermediate and winter). The total heat demand and the RES generation of each of the studied weeks are summarized in Table 31.

Table 31: Heat demand and RES generation of the studied weeks.

Summer Intermediate Winter

Heat demand [MWh/week] 1199 2598 6169

RES generation [MWh/week] 1201 1011 879

Finally, the day-ahead and imbalance price scenarios are also based on historic data of the Belgian electricity market [28], [33]; the gas price is assumed to be constant and equal to 39 €/MWh. The gas price corresponds to the average price that was paid by small and medium sized enterprises in 2014 [103].

Methodology 113

6.3.3 Scenario Generation and Reduction

As mentioned before, to represent the uncertainty that stems from the renewable energy forecast errors, the day-ahead and imbalance prices, the underlying stochastic processes are approximated using a group of scenarios. A scenario corresponds to a possible realization of the stochastic process, thus a large enough scenario representation should capture the variability and uncertainty of the random variables.

The statistical scenario generation technique developed in [110], [111] and described in detail in [112], is used in this thesis to generate a large set of scenarios. This technique makes use of historical forecast errors (e.g., difference between the forecasted variable and the measured output of this variable during the previous years) to create different scenarios. Once the ‘error scenarios’ are obtained, they are added to the actual forecasted variable (e.g., wind power forecast of the next day) to obtain the different scenarios for each variable (e.g., wind scenarios).

Yet, using a large number of scenarios is computationally expensive. Therefore, a reduction technique is necessary to trim the number of scenarios. Towards this aim, a modified version of the fast-forward scenario reduction algorithm that includes the inherent characteristics of the optimization problem is implemented, as described in [112], [106]. The scenario generation and reduction technique is explained in detail in Appendix B.

For the purpose of this work, a total of 200 day-ahead, 200 imbalance and 200 renewables scenarios were generated independently. Nonetheless, for computational efficiency, required because of the extensive scope of the problem, the orginal set was reduced to 10 scenarios for each parameter in the first optimization, resulting in a total number of 1000 combinations of scenarios. Afterwards, as explained before, the reevaluation process has used a larger number of scenarios leading to a total of 25000 combinations of scenarios31.

6.3.4 Limiting the Imbalance Volume

The results obtained when applying the optimization described in 6.3.1 during the intermediate season for the ‘flexible DA’ case are illustrated in Figure 37. In this figure, the black line represents the scheduled CHP electrical power, the shaded area

31 For the re-evaluation process the combination of 10 day-ahead, 50 imbalance and 50 renewables scenarios was used. Leading to a total of 2500 scenarios.


corresponds to the actual electrical power delivered by the CHP32. It can be observed that at several moments the CHP was scheduled to operate at maximal output, whilst, it only delivers the minimum capacity (e.g., see Figure 37 between 14:00 and 16:00). In contrast, when the CHP was scheduled to provide the minimum electrical power, it delivered the maximum power.

Figure 37: Resulting original DA bid (solid line) and actual dispatch of the CHP (gray area). The difference between day-ahead schedule and real-time dispatch creates a large imbalance of the order of 40 MW.

This behavior creates a very large imbalance volume, of the order of 40 MW. The aim of this large imbalance volume is to profit from the price difference between the day-ahead and balancing markets.

This occurs because the VPP operator does not have enough information regarding the market reactions. The imbalance prices are calculated ex-post once the total system imbalance is known. If, for example, the VPP operator expects large imbalance prices at a certain hour (meaning that the system is short) he, as well as other market participants, might decide to create large positive deviations. This might result in an overcompensation of the system leading to surplus of energy which is generally characterized by very low imbalance prices. As a consequence, the VPP will not only lose profits due to the low imbalance prices, but also lose the opportunity to trade large amounts of energy in the day-ahead market.

Similar results are reported by Fleten, et al., [113] and Vardanyan, et al., [114]. These authors agree that, though the results are ‘optimal’ from a modeling perspective, a

32Keep in mind that the electric energy traded in the day-ahead market is composed of the electricity generated by the CHP and the RES generation. Nevertheless, for illustration purposes only the electricity bided by the CHP appears in Figure 37.

Methodology 115

real player will have several reasons to avoid this behavior. One of these reasons, apart from the profit loss, is that, as mentioned before, the TSO expects unbiased bids from the market player. If the TSO realizes that a player is performing arbitrage, he can be penalized. The reason for this is that the imbalance market will be affected if several players behave this way.

For these reasons, a penalty function is implemented to limit the imbalance volume caused by the VPP. In the present work a piecewise linear function is used to limit the imbalance volume [113]. This function emulates the expected behavior of the market by penalizing large deviations from the DA schedule.

The penalty function is illustrated in Figure 38. This function is regarded in [113] as a type of risk model named ‘shortfall cost’. Thus the definition of the parameters?1-,,,+ ,?2-,,,+ ,?3-,,,+ ,?CD, ?CDiand ?CDÈ, shown in Figure 38, depends

completely on the preferences of the user, in this case, on how much the VPP operator is willing to trade in the imbalance market.

In this particular case, if the total imbalance is between 0 and 20 % of the total installed capacity, the resulting penalization is equal to 3 % of the day-ahead price. For deviations between 20 % and 30 % the penalty is equal to the day-ahead price realization. From 30 % and above, the marginal penalty is 10 times the value of the day-ahead price. As such, a player will only deviate from his DA schedule if large profits are to be expected.


Figure 38: Volume penalty function. This piecewise linear function was used to penalize imbalance volumes [113]. Large deviations from the DA schedule are strongly penalized.

The following constraints are added to the model in order to include the penalty function. First, the absolute value of the total imbalance is split in the three pieces that comprise the penalty function ?1-,,,+ ,?2-,,,+ ,?3-,,,+ as shown in Equation (6-26):

∀$, ∀\, ∀W: ∆-,,,+ = ?1-,,,+ + ?2-,,,+ + ?3-,,,+ (6-26)

Splitting the imbalance volume makes it possible to penalize large imbalance more than the small deviations as shown in Equation (6-27):

∀$, ∀\, ∀W: -,¼,½; = d0.3 ∙ ?1-,,,+ p ?2-,,,+ p 10 ∙ ?3-,,,+ h ∙ /-,(0 ∙ ∆$ (6-27)

In this equation -,¼,½; corresponds to the total imbalance penalty. The

variables?1-,,,+ ,?2-,,,+ and?3-,,+ are constrained using Equations (6-28) - (6-31):

∀$, ∀\, ∀W: ?1-,,,+ x ?CD ∗ O<P; (6-28)

∀$, ∀\, ∀W: ?2-,,,+ x ^?CDi g ?CD_ ∗ O<P; (6-29)


∀$, ∀\, ∀W: ?3-,,,+ x ^?CDÈ g ?CDi_ ∗ O<P; (6-30)

where ?CD, ?CDiand ?CDÈ represent the percentage deviation of the schedule with respect to the total installed capacity of the VPP O<P; ; in this case, 20 %, 30 % and 100 %, respectively.

Finally, the deviation penalty is included in the objective function as follows:

∀$, ∀\, ∀W, ∀Z:max6 `».,».+».(d"-0 p "-,¼,½,¾ g -,¼,½ g -,¼,½;h¿-k

ÀÁ¾k

À½k

À¼k

(6-31)

Recall that, when applied to the ‘flexible RT’ case, the previously stated Equations (6-26) to (6-31) are dependent also on the imbalance-price scenarios.

The resulting DA schedule and actual dispatch using the designed penalty function are depicted in Figure 39. The results correspond to the same analyzed scenario shown in Figure 37. It can be concluded that using a volume penalty function decreases the deviation between the day-ahead schedule and actual dispatch; thus, more realistic day-ahead market bids are obtained. In Section 6.4, further results using this model are reported.

Figure 39: Resulting DA bid (solid line) and actual dispatch of the CHP (gray area) when using an imbalance volume penalty. This methodology is effective in limiting the schedule deviations.


As stated in Equation (6-5), the total profits of the studied VPP can be estimated as the profits for trading the electricity in the day-ahead and imbalance market minus the operational cost. These figures are broken down in Table 32 for each of the studied strategies.


Table 32: Day-ahead profit, fuel cost and imbalance profit for the different bidding cases and studied seasons. [k€/week].

Summer Intermediate Winter

St

atic

Flex

ible

DA

Flex

ible

RT

Stat

ic

Flex

ible

DA

Flex

ible

RT

Stat

ic

Flex

ible

DA

Flex

ible

RT

DA revenues 145.1 150.0 150.0 208.6 208.4 208.4 340.0 338.6 338.6

Fuel cost 96.3 95.5 91.7 193.9 191.6 180.8 416.8 415.8 398.9

Imbalance revenues

-1.3 -1.1 1.3 -5.6 -4.9 -4.3 -4.7 -1.57 1.3

Total profits 47.5 53.4 59.6 9.1 11.9 23.3 -81.5 -78.8 -58.9

Table 32 shows that the operation of the VPP leads to economic profits during all seasons except for winter. During winter due to the large heat demand, the total revenues are not enough to offset the fuel cost. Nevertheless, it is important to recall that this cost should be reimbursed through sales of heat. Thus, the minimum heat unit cost that should be charged to the consumer, to cover at least the operational cost of the district heating during winter, lies between 9.5 €/MWh and 13.6 €/MWh33. During the other seasons this heat unit cost is negative. However, it is important to remember that in this work the investment and maintenance costs are not taken into account.

In addition, from Table 32 it can be deduced that in comparison with the ‘static’ operation, the ‘flexible DA’ operation results in larger relative increase of the profits during summer and the intermediate season than during winter. The largest profits are achieved when the ‘flexible RT’ operation is applied. During winter the difference between the ‘flexible RT’ operation and the ‘static’ case amounts to approximately 5 % of the fuel cost.

As explained before, the main difference between ‘flexible DA’ and ‘flexible RT’ relies on the information available at the moment of taking the dispatch decisions. Figure 40 illustrates this further.

33 The heat unit cost was estimated dividing the total operational cost by the heat demand of the season.


Figure 40: Comparison between ‘static’, ‘flexible DA’ and ‘flexible RT’ cases. The upper panel shows both the CHP electrical power scheduled DA (solid line) and the actual electrical dispatch (gray area). The second panel depicts the expected RES generation (solid line) and the actual RES output (gray area). The third panel shows the total remaining imbalance of the VPP and finally, the last panel illustrates the day-ahead (black line) and imbalance prices (gray line).

The first column corresponds, to the ‘static’ case, the second column to the ‘flexible DA’ case and the third column to the ‘flexible RT’ strategy for a specific imbalance price scenario, between 8:00 and 14:00. The upper panels illustrate both the day-ahead and


real-time electrical power generation of the CHP34. The same parameters are depicted in the second panel for the RES. The total remaining imbalance (RES error plus CHP deviation) is shown in the third panel. Finally, in the bottom panel the DA and imbalance prices are shown.

Looking at the figures it can be observed that the ‘flexible DA’ strategy uses the cogeneration unit to compensate the lack of generation of the RES. This is done by increasing the output of the CHP on real time. The remaining imbalance is zero. This is done because during the dispatch optimization (re-evaluation) the ‘flexible DA’ strategy does not have information on a specific imbalance price scenario, but on a large set of scenarios that can take positive or negative values and thus, it decides to minimize the total imbalance volume.

In contrast, in the ‘flexible RT’, the CHP does not compensate for the lack of electric power generation of the RES but decreases its generation to create a larger negative imbalance. The reason for creating this negative deviation is the negative imbalance tariff that appears in this scenario. A low imbalance penalty is an indication that the system is long. Thus when the CHP generates a negative imbalance, it not only increases the profits of the VPP operator by saving fuel cost, as shown in Table 32, but it also helps the grid to alleviate the total system imbalance.

The behavior of the different operating strategies among the three studied seasons is illustrated in Figure 41. The first figure shows the heat demand (gray area) and thermal power generated by the CHP (blue line) and boiler (red area) of a characteristic day of each week. The illustrated parameters correspond to the dispatched amounts for a specific scenario combination.

When analyzing Table 32, it was stated that during winter the ‘flexible DA’ operation and the ‘static’ case result in a large cost and the difference between these two cases was almost negligible when compared against the fuel cost.

A first reason for this is clear when looking at Figure 41. During the winter, due to the large heat demand, the CHP is running almost continuously, leaving less flexibility available. In addition, Table 31 shows that during this season the RES generation is low. As a consequence, lower imbalance volumes due to renewables appear.

34 Recall that the total bid is the combination of the CHP and RES expectation and the heat demand. Nevertheless, for illustration purposes, Figure 40 shows the CHP and RES generation separately.


On the other hand, Table 32 also shows that the cost reduction achieved using the ‘flexible RT’ operation is related to a decrease in the fuel cost. This is also visible in Figure 42 during the intermediate and winter seasons. In comparison with the other strategies, in real time, the ‘flexible RT’ operation uses the CHP less, activating the boiler more often. As the day-ahead schedule of both the ‘flexible DA’ and ‘flexible RT’ is the same, it can be deduced that the ‘flexible RT’ operation decreases its output, generating negative imbalance in order to obtain benefits from the imbalance prices.

As explained before, creating an additional imbalance does not necessary aggravate the situation of the electric grid (‘passive balancing’). In fact, in Belgium the imbalance prices are an indication of the status of the system. Thus a low imbalance price suggests that there is excess of generation in the grid. As a result, by slightly decreasing the output of the CHP, the VPP owner is not only saving fuel but also helping the grid and will be remunerated for this via the imbalance mechanism.


Figure 41: Comparison of the heat flow for the different strategies. The gray area corresponds to the thermal demand. The blue line represents the thermal power output of the CHP. The black line shows the average power charge to (negative values) or discharged from (positive values) the storage tank. Finally, the red area corresponds to the thermal power provided by the auxiliary boiler.

6.5 Conclusions and Further Work

This work was focused on developing a bidding strategy for a VPP composed by a CHP-DH and RES generation. The bidding strategy was estimated using stochastic optimization. This optimization takes into account uncertainty regarding RES electric

Conclusions and Further Work 123

power generation, day-ahead and imbalance prices. As a consequence, the CHP operation was scheduled not only to cover the heat demand but also to compensate for the possible forecast errors of the RES.

In the literature, several studies use stochastic programming to account for uncertainties. The case of optimal wind-power integration in the electric-power system has been extensively studied ([72], [115]–[117]). Similar to the work developed in this chapter, other studies assess the coordination of dispatchable and RES generators. Garcia-Gonzalez, et al., [118] evaluate the coordination of a wind farm and a pumped hydro-storage plant (PHS). Pandžić, et al., [67] analyze a VPP that aggregates a wind power plant with a PHS and a conventional electric-power plant using stochastic optimization. These studies do not assess the specific interaction with heat demand (CHP unit), neither the benefits that a VPP can obtain from using its flexibility in real time to react to the imbalance prices.

In this PhD thesis, three different strategies were assessed: ‘static’, ‘flexible DA’ and ‘flexible RT’ operation. In the first strategy the RES forecast errors are settled in the imbalance market and the CHP flexibility provided by its thermal-storage tank is not used. The other strategies use this flexibility to accommodate the forecast errors. In the ‘flexible DA’ case the CHP is rescheduled only once when accurate information regarding the RES generation is obtained. On the other hand, the ‘flexible RT’ adjusts the CHP output every time step depending on the actual imbalance price. These strategies were applied to a hypothetical case study that uses the Belgian city of Leuven as an example.

Furthermore in order to obtain realistic DA bids, a volume penalty was implemented to penalize large deviations from the original schedule.

The results of the ‘flexible DA’ case show a significant profit increase during summer and the intermediate season. In contrast, during winter, the difference between the ‘static’ and the ‘flexible DA’ case is negligible compared with this fuel cost. Better results are obtained when the ‘flexible RT’ strategy is applied. In this case when the VPP is allowed to react to the imbalance prices, thereby changing its position close to real time, the profits increase in all seasons.

This indicates that CHP-DH could help not only to reduce the cost due to the forecast errors but may also help the grid to reduce the system imbalance. However, this economic advantage should be valued against the additional investment needed to perform the accurate control on a real time basis. Further work should assess the investment, maintenance and operational costs needed to perform real time control and the effects of considering other technologies such as heat pumps in the VPP.


Additionally, estimating the impact of passive balancing on the grid was out of the scope of this work; further research should be done in this area to confirm the assumption that using passive balancing can help to reduce the system imbalance.

125

7. Summary and Conclusions

This work has explored different control strategies for the optimal techno-economic operation of a group of distributed electricity generation devices fully incorporating thermal demand aspects. Special focus has been given to what was called CHP systems, consisting of a CHP device, a back-up boiler and a thermal-storage tank, to examine its ability to provide flexibility to support the grid and to integrate renewable generation. The following sections (7.1, 7.2 and 7.3) answer the three research questions, that have been addressed in this research and that are stated in the introduction of the thesis. Section 7.4 summarizes the general findings of this PhD thesis. To finalize, Section 7.5 gives recommendations for further work.

7.1 Self-Balancing Using Residential micro-CHPs

The first question assessed in this work is the evaluation of the potential to use micro-CHP to balance especially meteorological forecast errors, to reduce the local imbalance volume and the associated imbalance penalties.

Self-balancing is the process of rescheduling electric power generators in order to balance their portfolio ex-ante (i.e., before the hour of delivery) aiming to accommodate forecast deviations. In the case considered in this thesis, self-balancing was assessed in a VPP that consisted of a group of residential dwellings, equipped with micro-CHPs and photovoltaic installations.

The developed methodology is based on two linear optimization programs. The first one ‘day-ahead optimization’, aims to find the optimal schedule of the micro-CHPs. The second one, ‘self-balancing’, was implemented in a rolling-horizon approach. Each time step, once the actual output of the PV has been obtained, the optimization decides on the optimal dispatch of the micro-CHPs.

If the imbalance prices are appropriately designed, a VPP operator should have sufficient incentives to always reduce his imbalance ex-ante. Nevertheless, reducing this imbalance comes at a cost. In this thesis, two different cases were analyzed, a ‘forced self-balancing’ and an ‘economic self-balancing’ strategy. In the former one, the VPP is forced to minimize the deviations whilst disregarding the imbalance prices. In contrast, the economic self-balancing strategy takes the imbalance tariffs into account and performs self-balancing only if it is profitable to do so.

126 Summary and Conclusions

The results show that, due to its flexibility, micro-CHPs are able to effectively reduce the imbalance volume. The largest imbalance volume reduction is achieved in winter when around 95 % of the forecast errors can be compensated by the micro-CHPs using the ‘forced self-balancing’ strategy. On the other hand, the imbalance volume reduction in summer and spring is moderate (50 % in spring and 60 % in summer).

However, this imbalance volume reduction is not always in line with the reduction of the imbalance cost. The reason for this is twofold. First, forcing the CHP to operate in order to compensate for the lack of generation of renewables implies an increase of the operational cost that has to be weighed against the cost paid to settle the imbalance in the market. Second, in case of surplus generation by renewables compared to the original forecast, the VPP is rewarded if the imbalance of the VPP helps to reduce the total system imbalance.

It was found that during spring and summer, forcing an imbalance reduction using micro-CHPs can lead to an increase in the total operational cost. In addition, using the ‘economic self-balancing’ during summer results in an imbalance volume reduction of only 2 %.

This is especially critical since the largest generation of PV is expected during the summer season, whilst that season is usually also characterized by the largest forecast deviations. However, at the same time, during summer the heat demand is the lowest and consequently the motivation for using CHPs is low.

Additionally, the results show that with the best case scenario namely ‘economic self-balancing’ with the perfect price forecast, a total cost saving of 4 % in summer and 1 % in winter can be achieved. This level of savings does not seem to be enough to motivate CHP owners to join a VPP to provide self-balancing services. In addition, the implementation of this kind of strategy requires extra investment in ICT that should be offset by the additional profits.

In conclusion, the ‘self-balancing’ strategy in the analyzed case study is not yet considered as economically profitable. Nevertheless, this technique should be studied for other dwellings with a larger and more constant heat demand and with other CHP devices that have better electrical efficiencies.

Passive Balancing with an Aggregation of micro-CHPs 127

7.2 Passive Balancing with an Aggregation of

micro-CHPs

The second question addressed in this thesis is the possibility to provide passive balancing making use of micro-CHPs. Passive balancing occurs when a BRP contributes to restore the balancing of the system without being actively selected by the TSO via the merit-order mechanism. In other words, passive balancing is when the internal imbalance of the BRP has the opposite direction of the total system imbalance.

The potential of passive balancing was assessed for an aggregation of micro-CHP devices installed in different dwellings, including households and service buildings such as hotels, greenhouse facilities and offices. All electricity generated is traded in the electric power market (i.e., self-consumption is not considered).

The methodology is based on two different optimizations: a ‘day-ahead optimization’ that aims to find the optimal nomination for the day-ahead market and a ‘near real time optimization’. The latter has been implemented in a rolling-horizon approach that decides on the actual dispatch of the CHP, taking into account the actual values of the imbalance prices, the net regulation volume (NRV) and the forecast of these variables.

According to the day-ahead optimization, the micro-CHPs are scheduled to operate when the heat demand and the prices are large. However, it was observed that the domestic micro-CHPs were not scheduled at any time. This is because residential micro-CHPs have lower electrical efficiencies and higher heat to power ratios than the larger counterparts. Thus, as the electricity of the aggregator is sold at day-ahead price, the domestic micro-CHPs cannot generate electricity at competitive prices and have no motivation to operate. Instead, the households make use of the boiler to meet the heat demand. This indicates that domestic micro CHPs are more appropriate for covering the electric self-consumption of the household.

The results from the day-ahead optimization are used as input for the near real time optimization. In the actual day the VPP is allowed to deviate from its schedule and to create a deviation in the opposite direction of the system imbalance. This is performed only when it is profitable to do so. This operation leads to an extra ‘real time profit’.

In conclusion, passive balancing leads to a total cost decrease in all the seasons compared to the case when only day-ahead optimization is performed. The cost decrease is larger in summer (around 5 %) and moderate in winter (about 2.5 %).

In addition, the influence of several parameters such as the gas price, the boiler efficiency and the governmental support (or CHP certificates) was investigated. These


parameters were varied in a sensitivity assessment. The results indicate that even when the analyzed parameters change, there is always an opportunity to obtain extra economic benefits providing passive balancing.

Nevertheless, it was also demonstrated that the opportunities to provide passive balancing depend largely on the day-ahead schedule. For instance, if the CHPs were scheduled to operate at maximum load, it is not possible to provide up regulation; vice versa, if the CHPs are at minimum load or not operating, down regulation is impossible.

For this reason, it is expected that large profits could be achieved if the expectations of imbalance prices are taken into account already in the day-ahead optimization. This was investigated by developing and applying the stochastic program (see Chapter 6). By using stochastic optimization, it is possible to make decisions before observing the actual stochastic parameter, in this case the imbalance prices. The uncertainty is characterized by a probability distribution of the parameter.

Finally, it is important to remark that, during this work, it was assumed that the aggregator can react to the actual imbalance prices and net regulation volume. However, this information is known only ex-post. This fact can decrease the estimated benefits and increase the risk that the VPP has to take when providing passive balancing.

7.3 Bidding of a VPP under Uncertainty

The final research question that was investigated in this thesis is the added value of using CHP combined with district heating networks (DH) to compensate for the uncertainties regarding electricity generation and market-price development.

The analyzed VPP consists of a CHP system linked to a district heating network and to a large installation of PV and wind energy generators. The VPP nominates its electricity in the day-ahead market and settles the difference between the planned electricity generation and actual electric power generation in the imbalance market

Stochastic programming was used to explicitly model the uncertainties of the system. Using a small example, it was demonstrated that stochastic programming should be preferred over a deterministic model when uncertainty is present. This is because stochastic programming leads not only to larger profit but also helps to hedge against very large losses.

In this work, a two stage stochastic programming approach is used. The first-stage decisions (i.e., the decisions that are taken under uncertainty) are the optimal day-

Bidding of a VPP under Uncertainty 129

ahead bids. The second-stage decisions (i.e., the decisions that are taken once the uncertainty is resolved) are the actual dispatch of the CHP-DH and RES generation.

The study considers three different strategies: ‘static’, ‘flexible DA’ and ‘flexible RT’ operation (recall, DA stands for day-ahead; RT stands for real time). In the static case, the forecast deviations are always settled in the imbalance market. In contrast, the ‘flexible DA’ and ‘flexible RT’ approaches use the CHP to accommodate the forecast errors of the RES generation. The difference between these two cases is that in the ‘flexible DA’ philosophy the reschedule is performed once a day when more accurate information on the RES generation is obtained, whereas in the ‘Flexible RT’ case, the reschedule is performed every time step once the actual imbalance prices are known.

The results of the ‘flexible DA’ case show a moderate profit increase during the summer and the intermediate season. In contrast, during winter, the difference between the ‘static’ and the ‘flexible DA’ case is negligible compared with this fuel cost. Better results are obtained when the ‘flexible RT’ strategy is applied. In that case, i.e., if the VPP is allowed to react to the imbalance prices changing its position close to real time, the profits increase in all seasons.

This price difference stems from the fact that the ‘flexible RT’ strategy has complete knowledge of the actual day-ahead prices and thus can profit from this information by generating small deviations to provide passive balancing. Nevertheless, the actual system status is known only ex-post and thus the real savings lie in between the ‘flexible DA’ and ‘flexible RT’ cases.

It was also observed that the heat demand substantially influences the possibility of operating a CHP using a ‘smart strategy’. It is clear that during winter the large heat demand motivates the CHP device to operate in a more continuous way leaving less space for flexibility. An additional fact in winter is that the amount of RES generation (considered in this study-mainly PV) is moderate in comparison with other seasons. As a consequence, the forecast deviation is also lower and thus compensating for these errors is less attractive for the VPP operator.

During summer, some savings can be achieved by down regulating. However, the motivation to operate the CHP are low during this season due to the low heat demand. Consequently also the opportunities to provide flexibility are small.


7.4 General conclusions

The work done during this PhD research demonstrates that cogeneration units can play an important role for increasing the flexibility of the electric-power system. This flexibility stems from the thermal-storage tank that decouples the thermal demand from the electric-power generation. This way, cogeneration systems can help to compensate forecast errors of RES-E, increase the VPP profits by providing passive balancing and mitigate the effects of system uncertainties.

From the results of the self-balancing strategy, it is clear that it is not always profitable to use a strategy that aims to reduce the own imbalance of the VPP. However, providing real-time balancing services or passive balancing can be a profitable option. This is because this strategy takes into account the information provided by the Belgian balancing market in order to steer the own position in the opposite direction of the expected system imbalance. Nevertheless, this expected imbalance is still subject to uncertainties. The last part of this work demonstrates that the system uncertainties can be accounted for using stochastic programming and that cogeneration coupled with a district-heating network can help to cope with this uncertainty.

Furthermore, it is shown in all the evaluated cases that the economic benefits of exploiting the flexibility of cogeneration units largely depend on the type of CHP, the kind of building, the information available and the seasonal variation.

Finally, it was demonstrated that cogeneration systems can provide real-time services to the electricity grid and that in the investigated case studies these new market opportunities result in moderate economic benefits.

7.5 Recommendation for Further Work

A first recommendation for further work is to apply the developed algorithms to other CHP technologies (e.g., fuel cells) and to other distributed devices such as heat pumps. With regard to fuel cells, this kind of technology promises large electric yields and excellent performance at part load. Heat pumps differ from CHP in that they are suitable for well-insulated dwellings with lower heat demand. The HPs are largely promoted due to their proven efficiency and in the following years, it is expected that an increasing number of heat pumps in households and service buildings will be installed.

Future work on the electricity market and the electric power system modeling should consider the impact of the intraday market. During the development of this work, it

Recommendation for Further Work 131

was assumed that the VPP operator could bid the electricity in the day-ahead market and settle the imbalance errors in the balancing markets, thus neglecting the importance of the intraday market. Nowadays, this assumption is valid since the liquidity of the intraday market is low. Nevertheless, during the last years an increasing interest in the intraday market has appeared. Several countries across Europe are cooperating to improve the liquidity of this market. It is believed that a correctly functioning intraday market could help to adjust the forecast errors ex-post without making use of the reserves.

During most of the development of this thesis the investment cost has been ignored, not only the cost related to the CHP system itself but also the upfront cost related to the ICT necessary to implement the smart strategies and control a wide range of distributed generation devices. Taking these costs into account deserves to be looked at in future work.

Another recommended line of research is to analyze the impact of passive balancing in the electrical system. This work assumes that providing passive balancing helps the grid operator by reducing the total system imbalance. Nevertheless, this statement was not examined in all consequences and the implementation of passive balancing could lead to several situations that might jeopardize the stability of the grid. For example, if several market players simultaneously decide to deviate in the opposite direction of the system imbalance, they might overcompensate the system and thus create a new imbalance. Another potential hazard appears if the signal given is incorrect and there is room for the market players to not comply with their balancing obligations.

133

Appendix A. Forecasting Using ARIMA

Models

ARIMA is a forecasting methodology based in time series models. A time series is a set of values observed sequentially through time. ARIMA models consist of three different parts: Autoregressive (AR), integration (I), and moving average part (MA)35.

The autoregressive part assumes that a time series can be described as a combination of some previous observed values, plus a random error term [119] as shown in Equation (A-1):

É- = ÊÉ- + ÊiÉ-i+…+Ê4É-4 + Ë- + 9 (A-1)

Where the parameters Ê- are the coefficients of the autoregressive polynomial, Ë- is the error term and Ì is the maximum lagged value or the order of the polynomial. On the other hand, the moving average part assumes that the time series can be expressed as being dependent on the previous estimation error terms plus white noise error [119] this is expressed in Equation (A-2):

É- = Ë- + ÍË-+ÍiË-i +…+ÍyË-y + 9 (A-2)

In this equation Í- are the coefficients of the moving average polynomial and Î is the order of this polynomial. Combining the AR and MA models the basic ARMA model is obtained as shown in Equation (A-3):

É- = ÊÉ-+…+Ê4É-4 + Ë- + ÍË- +…+ÍyË-y (A-3)

This expression is generalized in Equation (A-4):

Ï1 − Ê(Ð(4(k Ñ É- = 9 + Ï1 − ÍÒÐÒy

Òk Ñ Ë- (A-4)

35 Not all the ARIMA parts are necessary to represent a specific time series.

134 Beknopte samenvatting

The operator B is called Backshift operator. It expresses the length of previous data needed by the model to provide forecast (e.g., B1yt=yt-1, B2yt=yt-2 and so on). The integrative part of the ARIMA implies taking the differences between successive observations (see Section A.1.1.1 for further explanation). It can be mathematically expressed as (A-5):

Δ- = ^1 − Ð_É- (A-5)

In this equation ? indicates the amount of times the time series has to be differentiated. The complete ARIMA Expression is given in Equation (A-6):

Ï1 − Ê(Ð(4(k Ñ ^1 − Ð_É- = 9 + Ï1 − ÍÒÐÒy

Òk Ñ 3- (A-6)

A.1 Box Jenkins Procedure

The procedure for forecasting a time series using an ARIMA model or Box Jenkins procedure is depicted in Figure 42. It consists of four different steps [120]:

Step 1 Model identification

Step 2 Estimation of the parameters of the model

Step 3 Model validation

Step 4 Forecasting/scenario generation

The following sections give a description of each of the Box Jenkins procedure steps.

Beknopte samenvatting 135

Figure 42: Box Jenkins procedure to build an ARIMA model. It consists of four different steps identification, estimation, validation and forecast.

A.1.1 Model Identification

The objective of the model identification is to find the order of the autoregressive and moving average polynomials as well as, the order of the differentiating term. In other words, to define the values of ′Ì′, ′Î′ and ‘?′in Equation (A-6).

The model identification technique used in this PhD thesis is based on a graphical evaluation of the autocorrelation and partial autocorrelation functions. This step aims at identifying three main characteristics of the time series: stationarity, seasonality and the order of the AR and MA polynomial.

A.1.1.1 Stationarity

In order to apply ARIMA models it is required that the described series is stationary. Stationarity condition implies that both the mean and the variance are constant over the time. The Box-Cox transformations recommend two methods to make a series stationary [120]:

The variance can be make stationary by applying logarithms. Differencing a time series can make the mean stationary.

The amount of differentiation needed to stationarize a time series determines the value of ‘?′(see Equation (A-6)). This value is obtained by iterative differentiating the time


series until stationary behavior is observed (In general no more than two differentiations are necessary).

Figure 43 a) shows an example of the autocorrelation of a non-stationary series. A non-stationary series is characterized by an autocorrelation plot with very slow decay. Figure 43 b) shows the same time series after a first differentiation is applied, the ACF looks more stable i.e. the lags decrease faster. In conclusion, in this case the stationarity is obtained after a first differentiation consequently, the order of ‘?′ is 1.

a) b)

Figure 43: non-stationary time series with slow decay (a) and same series after first differentiation (b) stationary is achieved after applying a first differentiation.

A.1.1.2 Seasonality

The next step in the identification process is to check for seasonality. Seasonal variation is defined as the predictable movement of a time series around the trend line that occurs at regular seasonal intervals. Typical examples of series that exhibit seasonal behavior are the electricity prices, the heat demand among others.

Seasonal ARIMA (SARIMA) models are an extension of ARIMA models that are able to handle with seasonal time series. The general expression of a SARIMA model is described in Equation (A-7):

Ï1 − Ê(Ð(4(k Ñ »1 − Φ(Ð(

(k À ^1 − Ð_^1 − Ð_É- = 9 + Ï1 − ÍÒÐÒyÒk Ñ Ï1 − ΘÒÐÒ

Òk Ñ 3- (A-7)

Where P is the order of the seasonal AR component and Φj the coefficients of the seasonal AR polynomial. Q gives the order of the seasonal MA polynomial which coefficients are denoted by Θj. Finally the seasonal differentiation order is D. In the case of SARIMA the difference operator is modified to include the seasonal components

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of period S, by introducing the lag-s difference operator [121]. This is shown in Equation (A-8):

Ö\É- = É- − É-, = ^1 − Ð,_É- (A-8)

Autocorrelation plots are used to determine if a time series presents seasonal patterns. The ACF of a time series with cyclical behavior presents significant autocorrelation at lags that are multiples of the period. An example of this is shown in Figure 44. This time series displays significant lags with a periodicity of 24.

Figure 44: ACF of a time series that exhibits seasonal behavior. In this case significant lags appear with a period of 24.

A.1.1.3 Order Identification

After identifying stationarity and seasonality the next step is to find the appropriated order for the AR and MA polynomials. This task is performed inspecting the ACF and PACF graphs. In general identifying the adequate ARMA model is a trial and error procedure. Nevertheless a group of five common patterns can be used as indication to approximate several time series [122]:

ARIMA (1,0,0) also known as the “AR signature” in this pattern the ACF decays exponentially and the PACF displays a spike at lag one and no significant correlation for the other lags.

ARIMA (2,0,0) in this case the ACF of the differenced series present a sine wave shape pattern or a set of exponential decays. The PACF present a sharp cutoff after the second lag.


ARIMA (0,0,1) this pattern is also known as the “MA signature” The characteristics of this pattern is an ACF that cuts off sharply at lag 1 and a slow decay in the PACF.

ARIMA (0,0,2) in this pattern the ACF shows spikes at lags 1 and 2. The PACF exhibits a sine-wave shape.

ARIMA (1,0,1) this pattern exhibits exponential decays in both the ACF and PACF.

These rules are summarized in Table 33:


Table 33: Typical ACF and PACF of the most common ARIMA models once the series is stationary.

ACF PACF

ARIMA (1,0,0) Exponential decay

Single significant peak at lag 1

ARIMA (2,0,0) Sinosoidal decline

Significant peak at lags 1 and 2

ARIMA (0,0,1) Significant negative peak at lag 1

Negative exponential decay

ARIMA (0,0,2) Single significant negative peaks at lags 1 and 2

Sinosoidal decline

ARIMA (1,0,1) Exponential decay

Negative exponential decay


A.1.2 Estimation

After identifying the order of the polynomial (i.e., the values of p, d, q) it is necessary to calculate the parametersÊ,…,Ê4,Í,…,Íy (See Equation (A-6)). There are several

methods for estimating these parameters. The general procedure uses an optimization function that maximizes the probability of obtaining the observed data [122]. In practice, several computer programs can be used to estimate this parameters. In the case of this PhD thesis, the Matlab function “arima” was used to obtain the parameters of the forecasted variables.

A.1.3 Model Verification

The verification process tests if the selected ARIMA is appropriated to represent the studied time series. A common way to check the model is to evaluate the residuals (i.e., the difference between the original time series and the estimated model). A good model should produce statistically independent residuals or white noise. This can be evaluated looking at the ACF of the residuals [120]. The typical ACF of white noise do not present significant values. Figure 46 illustrates the ACF of white noise.

Figure 45: Typical ACF of white noise, in this kind of series no significant lag is present

If the selected ARIMA model is adequate, it can be used for forecasting. Otherwise if the ACF of the residuals has significant lags a new model should be selected. This process is repeated until the resulting residuals correspond to white noise. If two models give the same results it is advisable to choose the one that has less AR and MA terms.

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141

Appendix B. Scenario Generation and

Reduction Techniques

B.1 Scenario Generation

The scenario generation technique used in this work is described in detail in [111], [123] and [112]. It is based in the inverse transform sampling method. This method is extensively used in statistics to generate random numbers from a particular continuous or discrete probability distribution function.

Before starting with the generation technique, it is necessary to gather historical data of previous forecast and measurements of the studied variable, as well as the prognoses for the studied time horizon (e.g., next day).

The first step consists in dividing the historical forecast data in equidistant power levels as shown in Figure 46. Afterwards, the corresponding historical measurements are allocated to the same bin as the forecast. For example in the figure the first couple of points (measurement and forecast) belongs to the second power level.

Figure 46: the first step in the scenario generation technique requires to divide the forecast in power levels and associate the actual measurement to the corresponding power level.


The next step is to estimate the empirical cumulative distribution function (ECDF) of the measured data within each power level. The ECDF approximates the distribution of the error for each power interval.

To further clarify, in this work the procedure to obtain the renewables scenarios started by gathering the data of the expected RES generation for the next day and historical forecasts and measurements.

In this example the forecast is split into 18 power levels, the corresponding measurements are assigned to each level. Within each power level the ECDF is estimated. To estimate the ECDF, a histogram is generated; in this specific case the histogram has 45 bins. The ECDF is calculated as the cumulative sum of the histogram bins. This procedure is illustrated for the 7 power levels in Figure 47.

a) b)

Figure 47: Histogram of the measured data in power level 7 and corresponding empirical cumulative distribution function.

The idea behind the inverse transform method is to generate random numbers that follow a particular distribution, starting from a normal uniformly distributed random sample. For instance in this particular case the aim is to generate random numbers that follow the distribution of the RES forecast error on each power level.

The method starts by generating normal uniformly distributed random variables. A total of ‘d’ realizations of normal vectors ′×′ are generated, where ‘d’ is the desired number of scenarios to be generated and ′×′ is defined in Equation (B-1):

× = ^Ø, Ø, … , ØÙ)R (B-1)


In this equation Ú corresponds to the time horizon. The vector× follows a multivariate normal distribution as expressed in Equation (B-2):

×~V(Ü8, Σ) (B-2)

Where Ü8 is a vector of zeros and Σ is a covariance matrix as shown in Equation (B-3):

Σ ` Þß, ß,i . . ß,Ùßi, ßi,i . . ßi,Ù: : ⋱ :ßÙ, ßÙ,i . . ßÙ,Ùá (B-3)

With

ßF,O ` 9D(×F, ×O, ), [,U ` 1,2,… , Ú (B-4)

The covariance (Equation (B-4)) represents the interdependence structure of the forecast errors over the lead time. It is estimated using the exponential function shown in Equation (B-5):

ßF,O ` 9D(×F , ×O) ` CtÌ ¤g |[ g U|Ë ¦ , 0 ≤ [, U ≤ Ú (B-5)

In this equation Ë controls the strength of correlation. Figure 48 illustrates the covariance matrix Σ used in this work; the time horizon is one day with 15 minutes time step. The selected Ë for this case is equal to 50.


Figure 48: Visualization of the covariance matrix. The diagonal elements are equal to zero.

Once the normal random numbers are generated it is possible to transform them to follow the desired distribution. The inverse transform method is mathematically defined in Equations (B-6) and (B-7):

Φ(×-) ` ã 1√2/ CPå iæ ?tçKè

(B-6)

o- ` -dΦ(×-)h

(B-7)

Where - stands for the inverse of the cumulative distribution function (CDF) at time step t and Φ(×-) is the CDF of the random variable×-. An example of the application of the inverse transform method is shown in Figure 49. At certain hour the given forecast is equal to 0.3622 [p.u.]. This corresponds to the 7th power level. The distribution of the error for this level interval is shown in the left part of Figure 49. The right panel corresponds the CDF of the normal random variable. For the analyzed hour and scenario, the random variable equals to 1.8, the resulting probability for this value is Φ(×-) ` 0.964. According to the inverse transform method:

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o- ` -(0.964) (B-8) o- ` 0.12Ì. (B-9)

The resulting error of this scenario is 0.12 [p.u.]. This procedure is repeated until the desired number of scenarios is obtained. Note that though the examples in this annex focus on the generation of wind forecast errors scenarios. The same methodology is applied to generate the scenario for the day-ahead and imbalance prices.

Figure 49: Inverse transform method. Starting from a standard normal random value of 1.8, the resulting error is 0.12 in the power level 7th.

B.2 Scenario Reduction Technique

In order to explicitly represent uncertainty in a decision process, large number of scenarios are usually required. Nevertheless, due to computational burdens large numbers of scenarios can make the problem intractable (i.e., no solution can be found). For this reason a scenario reduction technique is needed to trim the number of scenarios. A good scenario reduction technique retains the most important information that characterizes the stochastic process.

The scenario reduction technique applied in this work is described in [106]. It is based on the ‘probability distance’ concept. The probability distance helps to quantify the closeness between two different scenarios that represent the same stochastic process.

In the present work the ‘Kantorovich distance’ is used to choose a set of reduced scenarios that is close enough to the original set. This problem is known as the Monge-Kantorovich mass transportation problem and is defined in Equations (B-10) and (B-11):


EÚ^!, !′_ ` UZ[&êëìëí î^Y,Yï_¹∈ñ¹ò∈ñ

&^Y, Yï_óëôëõ

(B-10)

Subjectto

&^Y,Yï_ ≥ 0,∀Y ∈ Ω, ∀Y′ ∈ Ω,, &^Y,Yï_¹ò∈Ω

`.¹,∀Y ∈ Ω, &^Y,Yï_¹∈Ω =¹ï, ∀Y′ ∈ Ω,

(B-11)

In Equation (B-11) λ and correspond to the probabilities of scenarios Y and Yï in the original scenario set Ω and in the selected set of scenarios Ω\, respectively. For a two stage stochastic programming, the Kantorovich distance can be expressed as given in Equation (B-12):

EÚ^!,!′_ ` /¹ min¹ò∈ñ^‖É^Y_ − É^Yï_‖_¹∈ñ/ñ (B-12)

The scenario reduction algorithm is an iterative method. The following section gives an example of the scenario reduction technique.

B.2.1 Example of the Scenario Reduction technique

Suppose that the imbalance price for certain day can be represented by a set of 4 scenarios depicted in Table 34:

Table 34: Imbalance price scenarios and corresponding probability of occurrence.

1 2 3 4

É^Y_[€/¬þℎ] 50 45 85 100 .¹ 0.25 0.20 0.40 0.15

The kantorovich distance is used to reduce the total number of scenarios to two. The procedure to obtain the reduced set of scenarios is described as follows:

Step 0: The process initializes estimating the cost function î^Y, Yï_ = ‖É^Y_ − É^Yï_‖,∀Y,Yï ∈ Ω, where Ω = u1,2,3,4v. The resulting values of î are shown in Equation (B-13):


î = 0 5 35 505 0 40 5535 40 0 1550 55 15 0 €/¬þℎ

(B-13)

Step 1: In this step the iterative process starts. The aim is to select the first scenario. This scenario can be interpreted as the most equidistant from all scenarios. Thus, the chosen scenario is the one that minimizes the resulting Kantorovich distance:

? = .iD^1,2_ + .ÈD^1,3_ + .D^1,4_ = 22.5 ?i = .D^2,1_ +.ÈD^2,3_ + .D^2,4_ = 25.0 ?È = .D^3,1_ +.iD^3,2_ + .D^3,4_ = 19.0 ? = .D^4,1_ +.iD^4,2_ + .ÈD^4,3_ = 29.5

(B-14)

In this case the minimum distance is obtained in scenario number 3. Thus this is the first selected scenario:

Ω,[] = u3v, Ω[] = u1,2,4v

(B-15)

In this equation Ω represents the set of scenarios that has not been selected and Ω, correspond to the set of selected scenarios.

Step i: Once the first scenario is selected the cost matrix can be updated by using the formula shown in (B-16).

î|(|^Y, Yï_ = minî(^Y, Yï_, î(^Y, Yï(_∀ω,ω′ ∈ Ω( (B-16)

The updated matrix keeps the original columns and rows of the selected scenario. The remaining elements are replaced by the minimum between the original value and the value of the selected scenario in the same row.

Applying Equation (B-16) to the given example:

î|i|^1,2_ = minuD^1,2_, D^1,3_v = 5

î|i|^1,4_ = minuD^1,4_, D^1,3_v = 35

(B-17)

148 Beknopte samenvatting î|i|^2,1_ = minuD^2,1_, D^2,3_v = 5

î|i|^2,4_ = minuD^2,4_, D^2,3_v = 40

î|i|^4,1_ = minuD^4,1_, D^4,3_v = 15

î|i|^4,2_ = minuD^4,2_, D^4,3_v = 15

Hence, the resulting cost matrix is:

î|i| = 0 5 35 355 0 40 4035 40 0 1515 15 15 0 €/¬þℎ

(B-18)

Once again the Kantorovich distance is calculated using the updated cost matrix î|i| ?|i| = /iî|i|^2,1_ + /î|i|^4,1_ = 3.25 ?i|i| = /î|i|^1,2_ + /î|i|^4,2_ = 3.5 ?|i| = /î|i|^1,4_ + /iî|i|^2,4_ = 16.75

(B-19)

It can be seen that scenario 2 has the lowest Kantorovich distance Therefore:

Ω,i = Ω,∗ = u3,1v, Ω = Ω∗ = u2,4v,

(B-20)

Step Ω, + : Once the desired amount of scenarios is reached, the probabilities should be distributed among the selected scenarios. This is done by adding the probability of the scenarios that has not been selected to that of the closest selected ones. This process is mathematically described in Equation (B-21):

/¹∗ k/¹ + /¹ï¹ò^¹_ (B-21)


Applying this to the illustrative example: Scenario 1 is closer to scenario 2 since in the original matrix Ω∗D^2,1_ = 5 whereas D^2,3_ = 40. On the other hand, scenario 3 is

closer to scenario 4 since in Ω∗^D^4,1_ = 50whereas D^4,3_ = 15_, consequently:

/∗ = / + /i = 0.45 /È∗ = /È + / = 0.55 (B-22)

As a result, the required number of scenarios with their corresponding probabilities are obtained.

151

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163

List of Publications

Articles International Journals with Review

a. Accepted

• Zapata Riveros, J., Donceel, R., Van Engeland, J. and D’haeseleer, W. (2015). A new approach for near real-time micro-CHP management in the context of power system imbalances – A case study. Energy Conversion and Management 89, 270–280.

• Zapata Riveros, J., Vandewalle, J., and D’haeseleer, W. (2013). “A comparative study of imbalance reduction strategies for virtual power plant operation,” Applied Thermal Engineering vol. 71 (2) p. 847-857.

b. Submitted and under review

• Zapata Riveros, J., Bruninx,K., Poncelet, K., and D’haeseleer (2015).

“Stochastic bidding strategies for VPPs considering CHPs and intermittent renewables” submitted to Energy Conversion and Management.

International Conferences

• Poncelet, K., Zapata Riveros. J., D’haeseleer, W. The potential of district heating networks in Belgium – barriers and opportunities. International Gas Union Research Conference. Copenhaguen, Denmarkt, 17-19 September 2014.

• Zapata Riveros, J., D’haeseleer, W., Vandewalle, J. (2013). Reducing

imbalances with virtual power plant operation. International Conference on Microgeneration and Related Technologies. Naples, Italy, 15 − 17 April 2013.

• Vandewalle, J., Zapata Riveros, J., Keyaerts, N., D’haeseleer, W. (2012). The

impact of a dynamical gas-pricing mechanism on the gas demand at distribution level. 12th IAEE European Energy Conference. Venice, Italy, 9 − 12 September 2012.

164 List of Publications

• Zapata Riveros, J., Vandewalle, J., D’haeseleer, W. (2012). Assessment of

different distributed generation technologies for a virtual power plant. IAEE European Energy Conference. Venice, Italy 9 − 12 September 2012.

Other Symposia

• Zapata Riveros, J., (2014), Bidding of a VPP in the day-ahead market under uncertainty: profit optimization & risk aversion. Young Energy Engineers and Economists Seminar. Dresden, Germany, April 2014.

• Zapata Riveros, J., (2012), Reducing imbalances with virtual power plant

operation. Young Energy Engineers and Economists Seminar. Florence, Italy December 2012.

International Reports

• Entchev, E., et al., Integration of Micro-Generation and Related Energy Technologies in Buildings, IEA ECBCS annex 54 (to be published in 2015).

National Reports

• Zapata Riveros, J., (2012), Work Package 4, Deliverable 4.3.1. Natural gas and distributed generation Concept: Micro CHP –Individual storage. LINEAR project.

• Six, D., et.al., (2012) Work Package 3, Deliverable 3.6. Final report storage

concepts and optimal combination with production technologies in the smart grid. LINEAR Project.

165

Short Curriculum

Juliana Victoria Zapata Riveros

Born: April 24, 1985 Medellín (Colombia) Secondary School: 1997-2002 Colegio La Presentación Ibagué (Colombia) University: 2009-2010 Master in Energy Science and Technology Swiss Federal Institute of Technology in Zurich, ETHZ, (Switzerland) Faculty of Information Technology and Electrical Engineering, Faculty of Mechanical and Process Engineering 2003-2007 Electronic Engineer University of Ibagué (Colombia), Faculty of Engineering Work: 2011-2015 PhD Researcher University of Leuven, Faculty of Mechanical Engineering (TME) Research group Energy & Environment/ Energy Institute April- September 2008 IAESTE Internship Swiss Federal Laboratories for Material Science and Technology, EMPA, (Switzerland)