Optimal Production Planning for Small-Scale Hydropower

IN DEGREE PROJECT ELECTRICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2018

Optimal Production Planning for Small-Scale Hydropower

ANNA-LINNEA TOWLE

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

OPTIMAL PRODUCTION

PLANNING FOR SMALL-

SCALE HYDROPOWER Anna-Linnea Towle

Master’s Thesis

KTH

2018

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Abstract

As more and more renewable energy sources like wind and solar power are added to the electric

grid, reliable sources of power like hydropower become more important. Hydropower is

abundant in Scandinavia, and helps to maintain a stable and reliable grid with added irregularities

from wind and solar power, as well as more fluctuations in demand. Aside from the reliability

aspect of hydropower, power producers want to maximize their profit from sold electricity. In

Sweden, power is bid to the spot market at Nord Pool every day, and a final spot price is decided

within the electricity market. There is a different electricity price each hour of the day, so it is

more profitable to generate power during some hours than others.

There are many other factors that can change when it is most profitable for a hydropower plant to

operate, like how much local inflow of water there is. Hydropower production is an ideal case for

using optimisation models, and they are widely used throughout industry already. Though the

optimisation calculations are done by a computer, there is a lot of manual work from the spot

traders that goes into specifying the inputs to the model, such as local inflow, price forecasts, and

perhaps most importantly, market strategy. Due to the large amount of work that needs to be done

for each hydropower plant, many of the smaller power plants are not optimised at all, but are left

to run on an automatic control that typically tries to maintain a constant water level. In Fortum,

this is called, VNR, or vattennivåreglering (water level regulation).

The purpose of this thesis is to develop an optimisation algorithm for a small hydropower plant,

using Fortum owned and operated Båthusströmmen as a test case. An optimisation model is built

in Fortum’s current modelling system and is tested for 2016. In addition, a mathematical model is

also built and tested using GAMS. It is found that by optimising the plant instead of running it on

VNR, an increase of about 15-16% in profit could be seen for the year 2016. This is a significant

improvement, and is a strong motivator to being optimising the small hydropower plants.

Since the main reason many small hydropower plants are not optimised is because it takes too

much of employees time, a second phase of this thesis was conducted in conjunction with two

other students, Jenny Möller and Johan Wiklund. The focus of this portion was to develop a

centralized controller to automatically optimise the production schedule and communicate with

the central database. This would completely remove the workload from the spot traders, as well

as increase the overall profit of the plant. This thesis describes the results from both the Fortum

model and the GAMS model, as well as the mathematical formulation of the GAMS model. The

basic structure of the automatic controller is also presented, and more can be read in the thesis by

Möller and Wiklund (Möller & Wiklund, 2018).

Keywords: Optimisation, optimization, hydropower planning, self-adaptive, automatic control,

optimal planning

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Sammanfattning

Tillförlitliga energikällor som vattenkraft blir allt viktigare vart eftersom elkraftsystemet utökas

med fler förnybara energikällor som vindkraft och solenergi. I Norden finns det rikligt med

vattenkraft, vilket bidrar till att upprätthålla ett stabilt och pålitligt elnät även med ökade

oregelbundenheter från vindkraft och solkraft samt större variationer i efterfrågan. Bortsett från

vattenkraftens tillförlitlighetsaspekter vill kraftproducenter maximera sin vinst från såld el. I

Sverige läggs dagligen bud på effektvolym till spotmarknaden Nord Pool och ett slutgiltigt

marknadspris bestäms därefter av elmarknaden. Varje timme under dygnet motsvarar ett enskilt

elpris, därmed är det mer lönsamt att generera effekt under de timmar där priset är som högst.

Det finns många andra faktorer som påverkar när det är mest lönsamt för ett vattenkraftverk att

producera el, exempelvis hur stort det lokala inflödet av vatten är. Vattenkraftproduktion är idealt

för tillämpning av optimeringsmodeller, vilka är vanligt förekommande inom verksamhetsområdet.

Även om optimeringsberäkningarna utförs av en dator innebär optimeringen mycket manuellt

arbete för Fortums elhandlare som specificerar indata till modellen. Exempel på indata är lokalt

inflöde, prisprognoser och kanske viktigast av allt marknadsstrategi. På grund av den stora

mängden arbete som fordras för varje vattenkraftverk, optimeras inte produktionen för många av

de småskaliga kraftverken utan de regleras automatiskt med mål att upprätthålla en konstant

vattennivå. Denna typ av reglering kallas vattennivåreglering, VNR.

Syftet med examensarbetet var att utveckla en optimeringsalgoritm för ett småskaligt

vattenkraftverk, där Fortumägda vattenkraftverket Båthusströmmen används som testobjekt. En

optimeringsmodell utvecklades i Fortums befintliga system och testades för 2016. Dessutom har

en matematisk modell utvecklats och testades med GAMS. Det konstaterades att genom att

optimera produktionen från vattenkraftverket istället för att reglera den via VNR kan en

vinstökning med cirka 15-16 % för noteras år 2016. Detta är en väsentlig förbättring och är ett

starkt argument för att optimera produktionen från småskaliga vattenkraftverk.

Eftersom den främsta orsaken till att många småskaliga vattenkraftverk inte optimeras är den

utökade arbetsbelastningen det skulle innebära för de anställda, genomfördes en andra fas i

examensarbetet i samverkan med två andra studenter, Jenny Möller och Johan Wiklund. Fokus för

denna del var att utveckla en centraliserad styrenhet för att automatiskt optimera produktionsplaner

och kommunicera med det befintliga centrala systemet. Detta innebär att utökad arbetsbelastningen

från elhandlarna undviks, samt öka vattenkraftverkets totala vinst. Denna rapport beskriver

resultaten från både Fortum-modellen och GAMS-modellen, liksom den matematiska

formuleringen av GAMS-modellen. Även grundstrukturen för det självreglerande

optimeringsverktyget presenteras, mer kan läsas i rapporten av Möller och Wiklund (Möller &

Wiklund, 2018).

Nyckelord: Optimering, vattenkraftplanering, självreglerande, automatisk styrning, optimal

planering

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Acknowledgements

There are many people who I wish to thank for their help with this thesis.

I want to sincerely thank my suprvisors at Fortum, Zahra Faridoon and Hans Bjerhag, as well as

Erik Byström, for their continuous help and guidance throughout this project. Thank you also to

my intructor, Mikael Amelin, and supervisor, Meng Song, from KTH for their valuable support

and assistance. I am deeply grateful to the staff at Fortum for their help and advice from the very

beginning, and their willingness to teach me as much as I could learn.

Lastly, thank you to Jenny Möller and Johan Wiklund, with whom I worked on the second

portion of this thesis. It was a great collaboration, and one that I think improved the quality of

both of our works.

Anna-Linnea Towle

Stockholm

2018-06-08

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TABLE OF CONTENTS

Table of Contents .......................................................................................................................................... 4

List of Figures ............................................................................................................................................... 6

List of Tables ................................................................................................................................................. 6

1 Introduction ........................................................................................................................................... 7

1.1 Background ................................................................................................................................... 7

1.2 Focus and Assumptions ................................................................................................................. 7

1.3 Research Objectives ...................................................................................................................... 8

2 Electricity Markets ................................................................................................................................ 9

2.1 Nordic Electricity Market .............................................................................................................. 9

2.2 Supply and Demand .................................................................................................................... 11

2.3 Spot Market ................................................................................................................................. 13

2.4 System Spot Price ........................................................................................................................ 14

2.5 Area Spot Price ............................................................................................................................ 15

3 Hydropower System Characteristics ................................................................................................... 16

3.1 Hydropower Operation ................................................................................................................ 16

3.2 Reservoir Characteristics ............................................................................................................. 16

3.3 Structure of a Hydropower System ............................................................................................. 17

4 Hydropower Production planning ....................................................................................................... 19

4.1 Planning Concepts ....................................................................................................................... 19

4.2 Steering from Mid-term Planning ............................................................................................... 19

4.3 Volume Coupling ........................................................................................................................ 19

4.4 Resource Cost Coupling .............................................................................................................. 20

4.5 Short-term Planning .................................................................................................................... 21

4.5.1 Pre-Spot Planning ................................................................................................................ 22

4.5.2 Post-Spot Planning .............................................................................................................. 22

4.6 Hydropower Modelling Theory ................................................................................................... 22

4.6.1 Linear Programming ............................................................................................................ 22

4.6.2 Non-linear Programming ..................................................................................................... 23

4.6.3 Dynamic Programming ....................................................................................................... 23

4.6.4 Stochastic Programming ...................................................................................................... 23

5 Hydropower Planning Model: Fortum System .................................................................................... 25

5.1 Båthusströmmen .......................................................................................................................... 25

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5.2 Optimal Planning vs VNR Control Results ................................................................................. 26

6 Hydropower Planning Model: Theory ................................................................................................. 32

6.1 Nomenclature .............................................................................................................................. 33

6.2 Explanation of Flexibility of Model ............................................................................................ 34

6.3 Static Model ................................................................................................................................ 34

6.4 Iterative Updates Based on New Head ........................................................................................ 39

7 Optimal Planning Algorithm Results .................................................................................................. 40

8 Central Automatic Control .................................................................................................................. 45

8.1 Description .................................................................................................................................. 45

8.2 Communication Flow .................................................................................................................. 45

8.3 Final Program .............................................................................................................................. 46

9 Conclusion ........................................................................................................................................... 48

9.1 Thesis........................................................................................................................................... 48

9.2 Further Analysis .......................................................................................................................... 49

10 References ....................................................................................................................................... 50

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LIST OF FIGURES

Figure 1 Nordel electricity consumption by sector, 2008, source: (ENTSO-E, 2018) ................................ 11

Figure 2 Nordel electricity generation, 2008, source: (ENTSO-E, 2018) ................................................... 12

Figure 3 Production cost curve, source: (Nord Pool, 2017) ........................................................................ 13

Figure 4 Nordic power flow, source: (Statnett, 2018) ................................................................................. 14

Figure 5 Area price curves in a two area market, source: (Kerola, 2006) ................................................... 15

Figure 6 Hydropower plant operation, source: (Vattenfall, 2017) .............................................................. 16

Figure 7 Example hydropower system, source: (Hassis, 2011) .................................................................. 18

Figure 8 Water value function, source: (Hassis, 2011) ............................................................................... 21

Figure 9 Båthusströmmen Location (Google Maps, 2018) ......................................................................... 25

Figure 10 Marginal Water Value Curves for Båthusströmmen ................................................................... 27

Figure 11 2016 Week 1 Båthusströmmen Reservoir Level ......................................................................... 28

Figure 12 2016 Week 23 Båthusströmmen Reservoir Level ....................................................................... 29

Figure 13 2016 Week 40 Båthusströmmen Reservoir Level ....................................................................... 30

Figure 14 Optimal Planning Algorithm ....................................................................................................... 32

Figure 15 Piece-wise linear power curve .................................................................................................... 35

Figure 16 PWL example curve .................................................................................................................... 36

Figure 17 Week 1 Reservoir level and flow rate ......................................................................................... 40

Figure 18 Week 1 Reservoir level and electricity price .............................................................................. 41

Figure 19 Week 23 Reservoir level and flow rate ....................................................................................... 41

Figure 20 Week 23 Reservoir level and electricity price ............................................................................ 42

Figure 21 Week 40 Reservoir level and flow rate ....................................................................................... 42

Figure 22 Week 40 Reservoir level and electricity price ............................................................................ 43

Figure 23 Inflow and spillage for 2016 ....................................................................................................... 43

Figure 24 Optimised and VNR discharge comparison ................................................................................ 44

Figure 25 Information Flow of Central Control Unit .................................................................................. 46

Figure 26 Visual Basic Main Program (Möller & Wiklund, 2018) ................................................................ 47

LIST OF TABLES

Table 1 Båthusströmmen Simulation Comparison ...................................................................................... 30

Table 2 Algorithm Nomenclature ................................................................................................................ 33

Table 3 Test Case Parameters...................................................................................................................... 40

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1 INTRODUCTION

1.1 BACKGROUND Hydropower has been an important source of power in Sweden for centuries. Starting as early as

the 12th century, water power was used in sawmills, to mill grains, and to transport logs along

rivers. The industrial revolution (1871-1914) saw hydropower being used to supply electricity for

the numerous factories that had sprung up across Sweden, and the electrification of the railroads

motivated the building of the first large scale hydropower plants (Flood, 2015). Now hydropower

makes up about 41% of Sweden’s total generation capacity of almost 40000MW (ENTSO-E,

2018). Smaller hydropower plants, under 10MW, are often run-of-the-river plants, and aren’t

controlled as much as the larger plants. They are usually left to run on their own based on the

inflow of the river and the height of their own reservoirs. However, about 1GW of capacity in

Sweden comes from these small hydropower plants, and control and optimisation of them could

have a significant influence on the total productivity of the system (ENTSO-E, 2018). As more

and more variable renewable power sources like wind and solar are installed, the more need there

is for stable and predictable power to balance the electricity supply. Hydropower, a renewable,

fossil-fuel free power source with stable production, is the ideal solution to this growing problem.

1.2 FOCUS AND ASSUMPTIONS This thesis focuses on the optimisation and control of small hydropower plants, done in

cooperation with Fortum Sverige AB. The test case used is Båthusströmmen, a 3.3MW plant in

the river Dalälven, in Dalarna county, Sweden, owned and operated by Fortum. The plant

typically operates at water level regulation, meaning that it controls the discharge and spillage in

order to maintain a constant set water level in the reservoir. There are no hydropower plants

upstream of Båthusströmmen, and the closest hydropower plant and reservoir on the downstream

side is Trängslet, one of the largest reservoirs in Sweden. Since Båthusströmmen is so much

smaller than Trängslet, it has little to no effect on the downstream plant. For this thesis, it is

assumed that any changes to the operation of Båthusströmmen will not have any effect on the

operation downstream, so the entire river system need not be considered. For the operation

planning of Båthusströmmen, the main electricity market considered is the spot market, including

the predicted spot prices and actual spot bids.

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Optimisation for hydropower dispatch is quite common, and is used for the larger plants that

Fortum owns. Today, running an optimization algorithm for small plants takes too much time and

effort from the employees, who could instead focus on larger, more profitable plants. To get the

best of both worlds, an optimization algorithm is developed for Båthusströmmen, and a control

scheme to automatically run the optimization and send the chosen schedule to the central

database. The automatic control of Båthusströmmen is investigated and simulated using

Microsoft Visual Basic. Communication with the central database is established, and a control

scheme is developed to automatically run the optimisation algorithm and update the database

with new optimal schedules. This portion of the project is done in conjunction with two

undergraduate thesis students, Jenny Möller and Johan Wiklund (Möller & Wiklund, 2018).

1.3 RESEARCH OBJECTIVES There are two main objectives for this thesis. The first is to develop an optimal planning

algorithm that can be continuously run to plan the production at Båthusströmmen. This algorithm

will be based on similar algorithms used for general hydropower modelling, and will be able to

run at any time taking in updated inputs like spot price and local water inflow. Different methods

for optimisation are analysed, and a final method is chosen based on accuracy, flexibility, and run

time.

The second objective is to develop a control scheme to automatically control the hydropower

plant based on the optimal planning. The control scheme will then be implemented and tested.

This phase of the project is done in cooperation with two other thesis students.

Though Båthusströmmen is the focus of this work, both the optimal planning algorithm and the

control mechanism should be flexible enough to be applied to similar hydropower plants in the

future. This means that a response to all possible scenarios should be built into the control

system, and that the optimal planning algorithm should be able to run for similar plants in

different locations.

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2 ELECTRICITY MARKETS

2.1 NORDIC ELECTRICITY MARKET In 1991 Norway deregulated its electricity market, causing the power providers to act more

competitively and be more profit driven. A deregulated market ensures that the cheaper

generation options are used first, and the more expensive ones used only when necessary. It also

allows consumers to choose who they buy electricity from, promoting competition and

encouraging profitable investments (Rothwell & Gomez, 2003). In 1996, Sweden joined this

deregulated market and formed Nord Pool. Today, 380 customers from 20 different countries

trade in Nord Pool markets, generating around 420 TWh every year from the Nordic and Baltic

countries (Nord Pool, 2017). Within a power system, there are several key players: producers,

consumers, retailers, system operators, grid owners, and balance responsible players. These will

be explained briefly (Söder & Amelin, 2011).

Producers and Consumers

Producers are the owners and operators of power plants and consumers are the end users of

electricity. While the large economies of scale of electricity generation has resulted in very few,

but large, producers, consumers operate all throughout the power system, and are much more

numerous (Söder & Amelin, 2011). Consumers can be large industry or individual households,

with variable and sometimes difficult to predict consumption patterns.

Retailers

It would be very complicated for each individual consumer to purchase their electricity directly

from the producers, so retailers are available to act as middle men between the two. Retailers can

sell electricity to consumers in many ways, including offering a simple fixed price rather than a

price that varies throughout the day. This simplifies consumer sales, and places the risk of a

dramatic price change on retailers. Having many retailers also increases competition, both

between retailers and between producers (Söder & Amelin, 2011).

Grid Owners

An electric grid has very high investment costs, making it hard for different companies to enter

the market. This makes grid ownership a natural monopoly, and it is convenient to give some

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companies or municipal authorities control over an area of the same grid instead of having

several competing grids. Grid owners must operate and maintain the grid with an agreed upon

power quality, as well as measure the transfer of electricity from producers to consumers. Grid

owners may have to buy power to make up for electric losses in the grid. To cover this cost as

well as maintenance costs, they are allowed to charge grid tariffs to all users (Söder & Amelin,

2011).

System Operators

With so many players already in the market, it is best to have one player that oversees the total

day to day operation. System operators, ISOs1 or TSOs2, are administrators of the power system

and electricity trading. TSOs have the ultimate responsibility for maintaining the power balance

of the grid at all time. This involves maintaining a constant frequency of 50Hz and also voltage

and MVAr properties (Byström, 2018).

This means that system operators are usually responsible for post trading (see section Error!

Reference source not found.), and they are often also transmission grid owners (Söder &

Amelin, 2011). An electricity market, like Nord Pool, can have multiple system operators, each

of which controls a certain area. The system operator for Sweden is Svenska Kraftnät.

Balance Responsible Players

Every watt of produced power must be consumed immediately. Though companies promise to

produce a certain amount of power in advance (see section 2.3), there will always be small

deviations from the plan due to unpredictable things such as changes in consumption or loss of

production in a plant. When such deviations occur, producers have to be compensated for

generating more power or charged for not producing enough. Balance responsible players make

sure that this balance is maintained, and that all energy is correctly paid for. Likewise, there are

balance responsible players on the demand side accounting for any changes from planed

consumption. Electricity retailers are commonly balance responsible players acting on behalf of

their customers (Söder & Amelin, 2011).

1 Independent system operator 2 Transmission system operator

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2.2 SUPPLY AND DEMAND The driving force behind electricity production and electricity cost is the balance between supply

and demand. The instant a light bulb is turned on, the total production throughout the system

must increase slightly to accommodate it. Electricity consumption, or demand, is usually quite

independent of the price. Demand fluctuation does, however, follow several patterns, including

daily and seasonal patterns. Households and industry both consume more electricity during the

morning than during the middle of the night. Industry especially has a larger consumption during

the week than on the weekends, as well as reduced consumption on holidays (Hassis, 2011). The

consumption also changes with temperature, usually increasing during colder temperatures to

supply electric heating. The breakdown of consumption in the Nord Pool area on 2008 is shown

in Figure 1 (ENTSO-E, 2018). Industry makes up about half of the consumption, influencing the

weekday pattern for overall consumption. Household consumption makes up over one quarter of

total consumption, contributing to the daily consumption pattern.

Figure 1 Nordel electricity consumption by sector, 2008, source: (ENTSO-E, 2018)

Hydropower is the largest source of electricity in Nord Pool, accounting for 58% of production in

2008 (ENTSO-E, 2018), as shown in Figure 2. It is also the most flexible, as there are few start-

up or ramping costs for the plants. In addition, it is one of few power sources that can store

28%

47%

22%

3%

Housing Industry (incl. energy sector)

Trade and Services (incl. transport) Other (incl. agriculture)

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energy, in the form of reservoir water, for the future. There are many factors that affect

hydropower supply, including inflow, profit maximisation plans, reservoir levels, etc. Since the

fuel for hydropower is water, it is essentially free. This means that hydropower can make a profit

even at low electricity prices, and has a large influence on the spot price of the electricity market.

This will be explained further in section 2.3.

Figure 2 Nordel electricity generation, 2008, source: (ENTSO-E, 2018)

Hydropower has high seasonal variations due to what is called the “spring flood”. This is when

all the snow melts and fills the rivers and reservoirs during the spring. This is an annual, large

event, and is prepared for by having low reservoir levels going into the spring. This means that

production increases during the winter and autumn as the reservoirs are emptied.

Nuclear power is the second largest resource, making up 20% of generation in 2008. Nuclear

power has high investment costs, but low variable costs, so producers want to always operate at

high levels (Hassis, 2011). Since nuclear and hydropower have such low operating costs and are

very predictable sources of power, they usually supply most of the load, together making up

around 80% of total generation.

The “other thermal” section is mainly coal and oil condensing, which have much higher variable

costs. Thermal plants have start-up and sometimes shut-down costs to operate, and the fuel itself

58%

20%

19%

3%

Hydro Nuclear Other thermal Wind

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is not free like with hydropower. In addition, there are costs based on CO2 emissions, driving the

variable costs higher. Therefore, production is highly dependent on the spot price, and the spot

price is also highly dependent on how much thermal power is needed to meet the demand.

The electricity price is calculated based on how supply meets demand. An example of supply and

demand curves is shown in Figure 3 (Nord Pool, 2017), where the demand is the dashed line and

the supply curve is made up of the available generation blocks. Here it is clear that hydro power

makes up a majority of the production, and keeps the price low. This price calculation will be

explained further in the following sections.

Figure 3 Production cost curve, source: (Nord Pool, 2017)

2.3 SPOT MARKET The electricity market is broken into two main times frames: the spot market (Elspot) for day

ahead sales, and the intra-day market for trading and balancing up to an hour in advance. The

spot market determines the spot price for the following day. Producers in each area submit bids

for how much power they want to sell for which price during each hour of the following day

(Faridoon, 2018) (Rasmussen, 2018). Bids consist of a piece-wise linear curve for how much they

want to buy or sell based on what the spot price is. These bids must be submitted to the electricity

market, Nord Pool, by 12:00 CET each day, and the market operator will release the realized spot

price at 12:42 CET. The realised spot price is calculated for each hour based on the supply and

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demand curve shown in Figure 3, using predicted consumptions and demand bids for the demand

and the production bids for the supply.

2.4 SYSTEM SPOT PRICE Within the Nord Pool market there are different bidding areas. In Sweden there are four areas,

SE1-4, each of which submits its own spot bid to the spot market.

Figure 4 Nordic power flow, source: (Statnett, 2018)

Generally, power flows from low to high price areas. The system price is the price that would

occur if there were no physical limitations on transmission between areas. The total consumption

from all areas should be met at the lowest cost. Theoretically, if one area could supply all of Nord

Pool at the absolute lowest price, only power plants in that area would generate power. There are,

however, practical limitations to this based on the transmission capacity between areas. When the

transmission limits are reached, areas are separated from each other and must have different area

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prices. Figure 4 shows the different areas in Nord Pool and an example of power flow between

areas.

2.5 AREA SPOT PRICE When transmission limits are reached, individual areas need to adjust their production to match

the area consumption, which results in an adjusted supply and demand curve. Figure 5 shows the

price curves for a two-area market where the transmission limits between the areas A and B have

been reached. Area A has much more demand than it can supply at the system price, so it must

import as much as possible from area B according to transmission capacity. The area price is set

to be where the difference between supply and demand is equal to the transmission capacity from

area B, resulting in an area price higher than the system price. Similarly, area B now has excess

power capacity. The area price is set to be where the difference between supply and demand is

equal to the export to area A, resulting in an area price lower than the system price. Note that

power always flows from lower price areas to higher price areas in order to generate as much

power as possible at lower prices (Kerola, 2006).

Figure 5 Area price curves in a two area market, source: (Kerola, 2006)

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3 HYDROPOWER SYSTEM CHARACTERISTICS

3.1 HYDROPOWER OPERATION Hydropower plants use running water to generate electricity. Figure 6 shows how a basic

hydropower plant is set up. A dam holds back water in a reservoir, making the upstream, or head

water level, higher than the downstream, or tail water level. This difference in height is called

head. The larger the head, the larger the potential energy in the water due to gravity, and the more

energy can be extracted by the turbine. The water flows through the intake rack and penstock and

turns the turbine, then flows out through the draft tube. The turbine is connected to the electrical

generator, which generates power and injects it into the local grid system. The amount of water

flowing through the turbine, and the rate of electric power (MW) production is controlled by

adjusting the guide vanes (Byström, 2018). The intake gate is fully open during operation , and

only closed during emergency-stop or for maintenance reason (Bjerhag, 2018).

Figure 6 Hydropower plant operation, source: (Vattenfall, 2017)

3.2 RESERVOIR CHARACTERISTICS There are several practical and environmental limitations on reservoirs. Environmental agencies

provide minimum and maximum water levels for each reservoir in order to not damage the

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surrounding ecosystems, and these limits must be obeyed. Other limits include practical limits on

how much the reservoir can physically handle, and also must be obeyed so as not to damage the

reservoir or plant. Since these rules must be followed, these are often called hard limits. There

are other tactical limits, often called soft limits or good will limits, that further constrain the water

levels in order to build in a margin of safety. If an environmental limit is exceeded, there is a

penalty, so producers don’t want to risk being too close to these limits in case something like a

large unexpected inflow occurs.

There can also be environmental or tactical limits on flow rate and ramping rate. For example, a

plant may be required to have a minimum flow rate in order for fish to continue moving

throughout the river. A producer may set their own flow rate limits to operate the generators most

efficiently, or they may set ramping limits (how fast the flow rate can change) to protect different

components. All of these limits can change throughout a year.

3.3 STRUCTURE OF A HYDROPOWER SYSTEM Hydropower plants are based on river systems and reservoirs. Unlike most electricity production

types, hydropower is able to store energy by keeping water in reservoirs just upstream of the

plants. This water is available, with certain limitations, to be used by the plant when it will be

most profitable.

Hydropower plants are located along a river, and a plant upstream has an effect on the plants

further downstream, creating a coupling effect between plants throughout an entire river system.

Hydropower plants have three main factors to consider when deciding how much power to

generate: reservoir levels, local inflow, and electricity price. The amount of power a plant

generates is based on how much water it discharges through its turbines. The amount of water

available to discharge is based on the reservoir level and the local inflow of water from the river

system. If there is too much local inflow, or if a large amount of inflow is expected in the future,

a plant may have to discharge water through spillways, or side exits, that do not run the water

through the turbines. The plant does not generate any power from spilled water, so it usually not

desirable, but the water is still available to be used by plants further downstream. When an entire

river system is considered, it may be worth it to spill water in an upstream plant in order to

provide water to a larger, more profitable plant downstream.

18 | P a g e

Figure 7 Example hydropower system, source: (Hassis, 2011)

Figure 7 shows an example river system with three reservoirs R1-3, plants P1-3, spillage s1-3, and

local inflow v1-3. The discharge is indicated by q1-3. The three plants are connected, and water

from plants and reservoirs 1 and 2 go to reservoir 3. The water level in R3 is increasing all the

time by v3, q1, s1, q2, and s2. It is decreasing by s3 and q3.

An important thing to consider is that water discharged from plant 1 does not immediately arrive

at reservoir 3, it takes some time to travel there through the river. This time delay is different

between each plant, and the time delays of spilled water and discharged water are often very

different. It is common for spilled water to take a much longer path, and thus take longer to reach

the next plant. Downstream plants will thus not be affected by changes in discharge or spillage

until sometime after the change occurs.

When planning hydropower production, local inflow is a very important parameter, but it can be

very difficult to predict. The inflow is affected by precipitation, melting snow, freezing ice, and

other weather related issues, meaning there are many sources of error. Throughout the river

system there are water flow measurement devices, or stream gauges, which report back the actual

inflow, but these devices can also report errors.

19 | P a g e

4 HYDROPOWER PRODUCTION PLANNING

4.1 PLANNING CONCEPTS As has been mentioned, hydropower has the ability to store energy in the form of reservoir

waters. This allows a plant to save water for hours when the electricity price is highest. This

planning is on the short-term horizon, from the day ahead to about 2-3 weeks ahead. Not only are

the hours of the day considered, but also the inflow and price forecasts for the coming weeks.

Short-term planning allows the river system to optimise production in its plants during the

coming weeks.

Yearly inflow and price changes are important as well. Every year there is a spring flood, and the

reservoirs must be relatively empty going into spring to accommodate this. Mid-term planning

takes place between the end of the short-term planning until about 1-2 years out. When the mid-

term plans are optimised, a start value for the reservoirs is found. This value is the end point for

the short-term planning, and provides steering for the short-term planning.

Similarly, long-term planning provides steering for where the mid-term planning should end up at

the end of its planning horizon. Long-term planning considers the time from the end of the mid-

term planning to about 3-5 years out. The coupling between these different planning periods

allows the models to be very specific in the short-term while still following an overall plan for the

coming years. This thesis focuses on the short-term planning. More about the actual models will

be discussed in the following sections.

4.2 STEERING FROM MID-TERM PLANNING As mentioned above, the mid-term planning period begins at the end of the short-term planning

period, and determines the end point for the short-term planning. There are two main ways to

provide this steering, or coupling, for the short-term optimisation: volume coupling and resource

cost coupling (Hassis, 2011).

4.3 VOLUME COUPLING With the volume coupling method, mid-term planning passes on the end reservoir volumes to the

short-term optimisation. This method provides more flexibility to choose which mathematical

models to use, but does not always take end prices into account well enough. Downstream

20 | P a g e

reservoirs depends highly on the flow of upstream reservoirs, not just their volume. This is

especially true because of the time delay between reservoirs. It is difficult to achieve consistent

coupling between models without taking this time delay into account in the final hours (Hassis,

2011). Volume coupling also does not consider the marginal value of water, which changes how

much the water is worth and may change the optimal plan.

4.4 RESOURCE COST COUPLING Water stored in a reservoir has the potential to create power in the future. When there is a lot of

water stored in a reservoir, adding a few more cubic meters does not increase the value of the

water significantly, so we say the marginal value of the water is low. When a reservoir is

approaching its lower limit, a few extra cubic meters of water makes much more of a difference,

so that water has a higher marginal value.

Resource cost coupling takes the marginal water value more into account. The mid-term planning

instead passes an end marginal cost value for each reservoir to the short-term planning. Figure 8

shows an example of a water value function. Each reservoir in a river system has its own water

value function. The future expected income increases with increased reservoir content, but the

slope decreases, meaning additional water is less valuable as the total reservoir content increases.

Note that the derivative of the water value function, or its slope, is the marginal water value

function. Points A, B, and C show the slope, or the marginal water value, at three different points.

At point A, the reservoir content is low, so adding more water increases the future income

significantly, shown here as a large slope. At point C, however, the reservoir content is high, so

the value of adding more water is not as significant, and the slope is lower. When the marginal

income in the short-term is larger than the future expected income, a marginal unit of water

should be used in the short-term.

21 | P a g e

Figure 8 Water value function, source: (Hassis, 2011)

By requiring the water value function to be at a certain point at the end of the short-term planning

period, the models can take price dependency better into account. Also, this improves the

flexibility of the model to adapt the resources to the inflow conditions and reduce the amount of

start/stop cycles (Hassis, 2011).

Since different reservoirs have different volumes and flow rates, it is beneficial to use reservoir-

specific water values (Hassis, 2011). This means assuming that marginal water values in a river

system are independent of each other for each reservoir. A major drawback of this is that short-

term optimisation is very sensitive to the relative difference between marginal water values and

short-term spot price.

4.5 SHORT-TERM PLANNING Short-term planning makes an optimal production plan starting from the day ahead to 3-4 weeks

out, and is used every day to plan the spot bids. Though the plan is for about 3-4 weeks, the next

day is the most important and is what is sent in as a bid to the spot market by 12:00 CET. All

plans consider when the plants are unavailable, for example for maintenance.

22 | P a g e

4.5.1 Pre-Spot Planning

Every morning the short-term model is used to plan the production for the next day. The inflow

and spot price forecasts, as well as the steering from the mid-term planning, are input into the

model, and the bid for the following day is formed. This optimisation considers several different

price scenarios and even different inflow scenarios, and the results are used to create a piece-wise

bid curve.

4.5.2 Post-Spot Planning

Once the actual spot prices have been determined and released at 12:42 CET, the short-term

model is run again. This time, the model has another constraint to generate exactly as much

power as was sold on the spot market per hour. It does not have to be generated by the same

plants as in the original optimisation in the pre-spot planning, so the plans can change in order to

be the most beneficial. The results of this optimisation are the production plans for the following

day, and are used by the dispatch center to actually run the plants and realize the production that

was promised. .

4.6 HYDROPOWER MODELLING THEORY There are many different methods for modelling hydropower systems, and the basic layouts have

been discussed thoroughly in literature, for example in (Söder & Amelin, 2011). The following

sections will introduce several mathematical methods for modelling.

4.6.1 Linear Programming

Linear programming is the simplest modelling method. The objective function and all constraints

are linear. It can efficiently solve large-scale problems, and will converge to global optimums

(Labadie, 2004). The most common linear programming method, simplex, is presented in (S.

Nash, 1996). When non-linear functions are required, separable programming is used to replace

them with piece-wise linear curves. Mixed Integer Linear Programming, MILP, allows the use of

both continuous and integer variables like binaries (Hassis, 2011). MILP is often used to

represent hydropower efficiency curves or unit commitment (deciding to have a unit, or a

generator and turbine pair, on). While linear programming is efficient, it often oversimplifies the

non-linearities of real life systems and is not the most accurate method.

23 | P a g e

4.6.2 Non-linear Programming

Non-linear programming is able to more accurately represent real-life systems like the efficiency

curves of hydropower plants. The most robust methods are successive linear programming (SLP),

successive quadratic programming (SQP), and the method of multipliers (MOM) (Labadie,

2004). All equations must be differentiable, which can sometimes be problematic and require

creative solutions. SLP is the most efficient non-linear programming method (Hiew, 1987), but it

does not always converge to a global optimum (Bazaraa, 1993). With SLP, the objective function

is often quite flat near the optimum, and this point can change very slightly each iteration,

preventing the model from converging. A penalty can be applied to prevent the optimal value

from changing too much between iterations, forcing it to converge (Belsnes, Wolfgang, Follestad,

& Aasgård, 2015).

4.6.3 Dynamic Programming

Discrete dynamic programming breaks large problems down into sub-problems that can be

solved sequentially each time period. It is often used when there are dynamic features like system

control variables (discharges and spillages) and state variables (reservoir levels) (Hassis, 2011),

and is often used when the state of the system depends on the previous system state and the time

of occurrence. Dynamic programming is a flexible method and works with both convex and non-

convex problems. However, as the number of state-variables increases, the calculation time

grows exponentially as every discrete dimension is tested. This is known as the “curse of

dimensionality” (Labadie, 2004). A different method, differential dynamic programming, was

developed by (Jacobson & Mayne, 1970) to solve the dimensionality problems using analytical

instead of discretized methods. Differential dynamic programming was applied to the Mad River

System in northern California, and it was determined that the same problem would have taken 16

times longer in an LP formulation (Jones, Willis, & Finney, 1986).

4.6.4 Stochastic Programming

Stochastic programming assumes all future decisions and consequences are random, not fixed.

This is as opposed to a deterministic problem where all values are treated as the truth (Labadie,

2004). The problem is broken into multiple stages where the objective function includes the

maximum benefit from the first-stage decisions and the total expected future benefit from the

later stages. If all different future scenarios have a known probability, the problem can be

reformulated with a deterministic formulation, but it is difficult to definitively calculate these

24 | P a g e

problems. Stochastic programming allows uncertainties to be accounted for and recommends the

best decisions to make based on these uncertainties. In hydropower planning, the main

uncertainties come from the inflow and price forecasts.

Stochastic successive linear programming, SSLP, adds the stochastic programming capability to

the SLP discussed in section 4.6.2 (Belsnes, Wolfgang, Follestad, & Aasgård, 2015). SHOP, a

modelling tool used throughout much of Scandinavia, already implements SLP. This may be a

good choice for hydropower modelling because in reality, the efficiency of a hydropower plant

changes based on the available head. More head means more energy stored in the water. This

relationship could be made non-linear, or it could be modelled using a first-order variable that

estimates how much higher the production would be with higher efficiencies due to a higher

head. In each iteration, the efficiencies are updated based on the reservoir level in the previous

round. (Belsnes, Wolfgang, Follestad, & Aasgård, 2015) found that this method performs very

similarly to the non-linear formulation, so a linear approximation accurately represents the

system while being simpler and more efficient.

25 | P a g e

5 HYDROPOWER PLANNING MODEL: FORTUM SYSTEM

5.1 BÅTHUSSTRÖMMEN Båthusströmmen is a small3 3.3 MW hydropower plant in Dalälven connected to the Hösthån

reservoir and is owned and operated by Fortum. It is the furthest upstream plant in its branch of

Dalälven, meaning there are no other plants upstream of Båthusströmmen. The next closest

downstream plant is Trängslet, one of the largest hydropower plants and reservoirs in Sweden.

Figure 9 Båthusströmmen Location (Google Maps, 2018)

Since Trängslet is so much larger than Båthusströmmen, 300 MW compared to 3.3 MW,

anything that Båthusströmmen does will not have any significant effect on Trängslet. This means

that Båthusströmmen can be modelled as an independent hydropower plant with no hydrological

coupling constraints (Bjerhag, 2018). This is an ideal case study since the impact of a single plant

can be analysed, and any results can be directly linked to changes in that specific plant instead of

some unknown factor throughout the river system.

3 Small hydropower plants here can be considered to be less than 10 MW

26 | P a g e

Båthusströmmen, as well as many other small hydropower plants, is run on VNR

(vattennivåreglering), or water level regulation (Faridoon, 2018). There is a simple controller

located in the plant that measures the water level of the reservoir and controls the amount of

discharge and spillage in order to maintain a constant water level. This type of control is used in

many small plants to simplify the operation. The central dispatch table is in charge of the

operation of every Fortum hydropower plant in Sweden, and there are many factors that have to

be monitored. Though an optimal schedule is created for each plant every day (see section 4.5),

the operators still must monitor the plants and adjust the schedule to account for any unexpected

changes, such as a larger inflow than expected. In order to be sure that the larger plants like

Trängslet are operating in the best way possible, the smaller, more “insignificant” plants are put

on automatic VNR control. This allows the operators to focus on the larger, more profitable

plants.

When on VNR control, plants like Båthusströmmen are not following an optimal dispatch

schedule and thus are not making as much profit as they could. The following sections show what

the operation of Båthusströmmen in 2016 would have looked like if an optimal dispatch schedule

were utilized instead of VNR control. The optimal schedule was made for January 1 to December

5 of 2016 using price forecasts made by Fortum and realized inflow values. The price forecasts

for the rest of December were not available. It is worth noting that 2016 was a leap year. The

optimisation was done as if a real spot trader were doing them, so a plan was created every day

for the following day, but considering up to 4 weeks ahead. The price forecasts are updated every

day, and the plans are assumed to have been followed exactly, with no unforeseen changes in, for

example, local inflow.

5.2 OPTIMAL PLANNING VS VNR CONTROL RESULTS A simple model was built in Fortum modelling system to model only Båthusströmmen and its

reservoir, Hösthån. The model uses the same constraints and efficiency curves as the current

model that Fortum uses for the other plants in Dalälven, but a marginal water value curve had to

be generated for Hösthån. Recall from section 4.4 that the water value curve can be used to give

the expected future value of the remaining water in a reservoir. The marginal water curve is

simply the derivative of a water value curve, and is used to estimate how much the water value

would increase by increasing the reservoir height. This curve is used in the model to create an

optimal schedule. The available curve was designed to simulate a VNR operation of

Båthusströmmen, and needed to be adapted to a more realistic curve. The new marginal water

value curve was created based on the existing curve as well as marginal water value curves of

similar plants. Two different curves were tested, and the difference in results was deemed to be

insignificant enough that a more accurate curve did not have to be generated, and the curves used

are just for calculation purposes.

In the original Fortum optimisation model, a model of Båthusströmmen is used more as a

placeholder for the rest of the model, and the reservoir level is only allowed to vary within a

20cm range. This means that the reservoir, Hösthån, had a capacity of 0.1Mm3. In the new model,

the reservoir is able to vary within a 2 meter range. This value was chosen based on the allowed

limits of similar sized plants. There are no known regulations for Båthusströmmen that would

27 | P a g e

limit the reservoir levels further (Faridoon, 2018). The original marginal water value curve and

two newly generated curves (V2 and V3) are shown below. The new curves represent the

reservoir having a 2 meter range, giving it a total usable capacity of 1Mm3. These curves were

generated based on the existing water value curves for similar sized Fortum plants, as well as

looking at water value curves for larger plants. The exact formulation of these curves is not the

focus of this thesis, and is a good candidate for further research.

Figure 10 Marginal Water Value Curves for Båthusströmmen

In total, 4 cases were simulated for Båthusströmmen:

1. VNR: Using the current model in the Fortum system with a 20cm range for reservoir

height and original marginal water value curve

2. V2: Using the model of Båthusströmmen with V2 of the marginal water value curve and a

2m range for the reservoir level

3. V3: Using the model of Båthusströmmen with V3 of the marginal water value curve and a

2m range for the reservoir level

4. Minimum Discharge (Min Q): Using the model of Båthusströmmen with V3 of the

marginal water value curve and 2m range for the reservoir level. There is also a lower

limit for the discharge to avoid many start/stops of the generator. Q here represents the

water discharged through the turbine.

Case 4 was added after the results from cases 2-3 showed that the generator should start more

than once a day. This adds a lot of wear and tear on the generator and turbine, and would require

a lot of extra maintenance. In addition, the maintenance cost is very high for Båthusströmmen

because it takes a worker about 2 hours to travel from Trängslet to perform the maintenance, plus

2 hours to return to Trängslet. Not only does the maintenance require a lot of time just in travel,

0

10000

20000

30000

40000

50000

60000

70000

0 0,2 0,4 0,6 0,8 1 1,2

Mar

gin

al W

ater

Val

ue

(EU

R/M

m3

)

Reservoir Filling (Mm3)

Marginal Water Value

Original

V2

V3

28 | P a g e

but it takes a worker away from Trängslet, a much more significant plant. Thus, case 4 was

simulated to prevent the generator from stopping unnecessarily.

Figure 11Figure 13 show the reservoir level for weeks 1, 20, and 40 respectively and for each of

the 4 cases. The realized reservoir level is also shown for comparison. The reservoir level is

measured in meters above sea level (masl). Case 1, the VNR case, forces the reservoir level to

vary only within a 20cm range. In reality, the VNR control kept the level nearly constant

throughout the year, only varying by a few centimeters. Case 2 and 3 utilize the full 2 meters of

reservoir level range, often causing the generator to turn off when the lower limit is reached. In

case 4, with a minimum discharge limit, the reservoir level does not dip as low because the

optimisation algorithm plans ahead to have enough water to satisfy the minimum discharge

constraint.

Figure 11 2016 Week 1 Båthusströmmen Reservoir Level

During June, the spring flood is still occurring, meaning that there is a lot of water running

through all of the rivers from ice and snow melt. This is why the reservoir level remains near the

upper limit during the spring and summertime.

493

493,5

494

494,5

495

495,5

496

16.1.4 0:00 16.1.5 0:00 16.1.6 0:00 16.1.7 0:00 16.1.8 0:00 16.1.9 0:00 16.1.10 0:00 16.1.11 0:00

Res

ervo

ir L

evel

(m

asl)

January 4-10, 2016

VNR V2 V3 MinQ Real

29 | P a g e


493

493,5

494

494,5

495

495,5

496

16.6.6 0:00 16.6.7 0:00 16.6.8 0:00 16.6.9 0:00 16.6.10 0:00 16.6.11 0:00 16.6.12 0:00 16.6.13 0:00

Res

ervo

ir L

evel

(m

asl)

June 6-12, 2016

VNR V2 V3 MinQ Real

30 | P a g e


Table 1 Båthusströmmen Simulation Comparison

% Increase

Profit

Total

Production

(MWh)

% Increase

Production

Total start-

ups

Realized

11192

40

Case 1: VNR -1.79 13215 18.08 615

Case 2: V2 2.89 11236 0.39 406

Case 3: V3 2.61 11224 0.29 421

Case 4: Min Q 15.05 9574 -14.46 0

Table 1 shows the increase in profit and production for the 4 cases as compared to the realized

operation. The profit here is calculated as the power sold at the predicted electricity price minus

the start-up cost of the generator. Every day there were new electricity predictions for the

493

493,5

494

494,5

495

495,5

496

16.10.3 0:00 16.10.4 0:00 16.10.5 0:00 16.10.6 0:00 16.10.7 0:00 16.10.8 0:00 16.10.9 0:00 16.10.10 0:00

Res

ervo

ir L

evel

(m

asl)

October 3-9, 2016

VNR V2 V3 MinQ Real

31 | P a g e

optimisation period, and the first day of predictions from each set was saved as the final predicted

price. The predicted electricity cost is used in the profit calculations, including the realized

version, to eliminate the influence of forecast error and focus solely on the optimisation. Cases 1-

3 have a lot of generator starts (and stops), at least one per day. This causes a high maintenance

cost, and thus not a very high increase in profit. The VNR case actually has a lower profit than

the realized operation. This discrepancy is most likely due to the fact that the optimised VNR

model was always considering the future value of water, not just the immediate spot sales. Case

4, however, has a 15.05% increase in profit as compared to the realized profit.

32 | P a g e

6 HYDROPOWER PLANNING MODEL: THEORY

When using the model at Fortum, the exact model formulation is not known. In addition, the

model cannot update the efficiency curve in between iterations, which would improve the

accuracy of the optimisation. The following chapter describes an optimisation model developed

to resemble, and improve, the Fortum model. First the theory is presented, then a case study is

presented in Chapter 7. This fictitious plant is comparable to Båthusströmmen and is also not

hydrologically coupled to other plants.

In addition to the reservoir upper level and minimum discharge constraints, a variable minimum

reservoir level constraint has been added. During the winter, the surface of the reservoirs freeze.

If the surface ice is cracked, which happens if the reservoir level varies too much, small cracks

can appear in the ice. These cracks allow cold air to flow through them into the running water

below, causing ice to form in the water and clog the intake grates of the power plant. This

phenomena is called frazil ice. To prevent this, the range for the reservoir level is restricted to just

20 centimeters during the winter time. This will limit the power production, but is a practical

limitation to prevent costly maintenance.

The second main difference between this model and the Fortum model is that the power-

discharge (PQ) curve is updated each iteration based on the reservoir level. When the reservoir is

completely full, there is more potential energy stored in the water because it has a larger head.

This means that the power that will result from the generator is greater than if the reservoir was at

its minimum level. In (Belsnes, Wolfgang, Follestad, & Aasgård, 2015), an iterative method for

updating the efficiency curve based on a new head is demonstrated. The following algorithm

implements this method on the PQ curve instead of the efficiency curve directly, since this is

what is practically available in many hydropower plants. A black box diagram of the described

algorithm is shown below.

Figure 14 Optimal Planning Algorithm

In reality, this model should also consider whether or not the plant or generator is available or if, for

example, it is down for maintenance.

33 | P a g e

6.1 NOMENCLATURE The sets, indices, parameters, and variables are described below. Here, a unit is a generator-turbine pair.

PWL stands for piece-wise linear, used to represent nonlinear curves.

Table 2 Algorithm Nomenclature

Sets and Indices

Set T, index t Time

Set I, index i Unit, including generator and turbine

Set J, index j Spillage gates

Set A, index a Linear segments for PWL PQ curve

Set N, index n Indices for binary values in PQ PWL curve

Set W, index w Linear segment for PWL water value curve

Set H, index h Indices for binary values in water value PWL curve

Variables

pi,t Power produced by unit i at time t (MW)

Qi,t Discharge through unit i at time t (m3/s)

Sj,t Spillage through gate j at time t (m3/s)

Mt Reservoir level at time t (masl, meters above sea level)

qi,a,t Amount of discharge for segment a of power curve (m3/s)

yi,n,t Binary variables for PQ PWL curve

dt Binary variable for discharge lower limit

zj,t Binary variable for spillage lower limit

WVt Water value of the reservoir (€)

mw,t Width of segment, reservoir level (meters)

kh,t Binary variable for water value PWL curve

ui,t Unit commitment binary for generator i

𝑠𝑖,𝑡+ Start-up binary for generator i

𝑠𝑖,𝑡− Stop binary for generator i

Parameters

Pt Spot price (predicted or real) at time t (€/MW)

Vt Inflow to reservoir at time t (m3/s)

Δxi,a Initial power per segment for unit at defined head (MW)

Δqi,a Width of segment, discharge (m3/s)

M0 Initial reservoir height (masl)

𝑄 Minimum discharge (m3/s)

�̅� Maximum discharge (m3/s)

𝑆 Minimum spillage (m3/s)

𝑆̅ Maximum spillage (m3/s)

𝑀𝑡 Minimum reservoir level (masl)

�̅� Maximum reservoir level (masl)

𝑝 Minimum power (MW)

�̅� Maximum power (MW)

TE Time equivalent, converts water flow to reservoir height, unit is hour equivalents/m

𝑊𝑉𝑤𝑠𝑙𝑜𝑝𝑒

Slope of segment w of water value curve

Δmw Width of reservoir level segments (meters)

34 | P a g e

Ci Start-up cost for generator I (€)

ui,0 Initial state of generator, on or off

6.2 EXPLANATION OF FLEXIBILITY OF MODEL For this simple test case, only one plant with one generator (i=1) and one spillway (j=1) is used.

However, the algorithm is written in such a way that a more complex system could be used as

well. If more plants are added to the model, the hydrological coupling between them must be

added as well. This is highly dependent on the river system, especially the connection and travel

time between plants. Only one plant was used for this thesis both as a proof of concept and also

to be able to clearly see the benefit of using optimal planning. By using just one plant, any

changes in production are trackable, and are not dependent on many factors caused by the

coupling with other plants.

The model is implemented in GAMS, a commercial optimisation program.

6.3 STATIC MODEL A basic hydropower model is presented below where all parameters remain the same between

time steps except the electricity price and local inflow.

Objective Function

The goal of the model is to maximise the profit from the sales to the spot market. Often in

hydropower optimisation the future value of water is also included in the objective function, as it

is here. The water value curve is found by integrating the marginal water value curve in Figure

10. Version 3 of the curve is used in this simulation. Mid-term steering, as described in section

4.2, is not utilized here. That function will be explored later on in this thesis. Thus, the objective

function is

𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒 ∑ (𝑃𝑡𝑡∈𝑇,𝑖∈𝐼 𝑝𝑖,𝑡 − 𝐶𝑖𝑠𝑖,𝑡+ ) + 𝑊𝑉𝑒𝑛𝑑 ( 1 )

Hydrological Constraint

There are no plants connected up- or downstream, so there are no hydrological couplings to

consider. The plant is therefore only affected by the local inflow, discharge, and spillage, as well

as the local hour equivalent of the reservoir. This hour equivalent, TE, is based on the size and

shape of the reservoir, and converts m3/s to reservoir height in meters.

𝑀𝑡 = 𝑀𝑡−1 +𝑉𝑡 − ∑ 𝑄𝑖,𝑡 − ∑ 𝑆𝑗,𝑡𝑗∈𝐽𝑖∈𝐼

𝑇𝐸

∀𝑡 ∈ 𝑇 ( 2 )

Piece-wise Linear Power-Discharge Curve

The power generated by the plant is based on the discharge and is represented by a piece-wise

linear curve. Figure 15 shows an example of such a curve for a single unit during time-step t.

35 | P a g e

Figure 15 Piece-wise linear power curve

The above graph shows variables for one unit (i), which is omitted from the subscripts. The

following constraints describe the piece-wise linear curve (Almassalkhi & Towle, 2016).

𝑄𝑖,𝑡 = ∑ 𝑞𝑖,𝑎,𝑡

𝑎∈𝐴

∀𝑡 ∈ 𝑇 ( 3 )

𝑝𝑖,𝑡 = ∑ 𝑞𝑖,𝑎,𝑡

∆𝑥𝑖,𝑎

∆𝑞𝑖,𝑎𝑎∈𝐴

∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 4 )

𝑦𝑖,1,𝑡∆𝑞𝑖,1 ≤ 𝑞𝑖,1,𝑡 ≤ ∆𝑞𝑖,1 ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 5 )

𝑦𝑖,2𝑎−2,𝑡∆𝑞𝑖,𝑎 ≤ 𝑞𝑖,𝑎,𝑡 ≤ 𝑦𝑖,2𝑎−1,𝑡∆𝑞𝑖,𝑎 𝑓𝑜𝑟 𝑎 ∈ 𝐴 − {1, 𝑒𝑛𝑑}, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 6 )

0 ≤ 𝑞𝑖,𝑎,𝑡 ≤ 𝑦𝑖,2𝑎−2,𝑡∆𝑞𝑖,𝑎 𝑓𝑜𝑟 𝑎 ∈ 𝐴{𝑒𝑛𝑑}, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 7 )

𝑦𝑖,2,𝑡 ≤ 𝑦𝑖,1,𝑡 ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 8 )

𝑦𝑖,𝑛+2,𝑡 ≤ 𝑦𝑖,𝑛,𝑡 𝑓𝑜𝑟 𝑛 ∈ 1,2,4,6 … 𝑒𝑛𝑑 − 2, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 9 )

𝑦𝑖,𝑛+3,𝑡 ≤ 𝑦𝑖,𝑛,𝑡 𝑓𝑜𝑟 𝑛 ∈ 2,4,6 … 𝑒𝑛𝑑 − 4, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 10 )

Let’s break this down. Equations ( 3 )-( 4 ) show how the total power and discharge are

calculated as the sum of the segments that make up the curve. Equations ( 5 )-( 7 ) limit the size

36 | P a g e

of qi,a,t to the size of each segment ∆𝑞𝑖,𝑡. The use of the binary variable yi,n,t in equations ( 5 )-( 10

) makes sure that the curve is utilized in order, meaning that qi,3,t can only be non-zero if qi,1,t and

qi,2,t are at their maximum values. For example, Figure 16 shows the same curve as above but

with values filled in for ∆𝑞𝑖,𝑎 and ∆𝑥𝑖,𝑎 .

Figure 16 PWL example curve

Suppose we want to calculate the shown point, where the discharge is 7.5 m3/s and the power is

15MW. This means that qi,1,t=3, qi,2,t=3, and qi,3,t=1.5. Equations ( 5 ) and ( 6 ) become:

𝑦𝑖,1,𝑡 ∗ 3 ≤ 𝑞𝑖,1,𝑡 ≤ 3

𝑦𝑖,2,𝑡 ∗ 3 ≤ 𝑞𝑖,2,𝑡 ≤ 𝑦𝑖,3,𝑡 ∗ 3

𝑦𝑖,4,𝑡 ∗ 3 ≤ 𝑞𝑖,3,𝑡 ≤ 𝑦𝑖,5,𝑡 ∗ 3

And equation ( 7 ) becomes

0 ≤ 𝑞𝑖,4,𝑡 ≤ 𝑦𝑖,6,𝑡 ∗ 3

In order for qi,1,t=3 and qi,2,t=3, 𝑦𝑖,1,𝑡 , 𝑦𝑖,2,𝑡 , and 𝑦𝑖,3,𝑡 must be set to 1, making

37 | P a g e

3 ≤ 𝑞𝑖,1,𝑡 ≤ 3

3 ≤ 𝑞𝑖,2,𝑡 ≤ 3

The next segment variable, qi,3,t can be any value in its allowed range, so 𝑦𝑖,4,𝑡 must be 0, and

𝑦𝑖,5,𝑡 must be 1, resulting in

0 ≤ 𝑞𝑖,3,𝑡 ≤ 3

The last segment must be empty, since the desired point is to the left of the entire segment. To set

𝑞𝑖,4,𝑡 to 0, 𝑦𝑖,6,𝑡 must also be 0, making

0 ≤ 𝑞𝑖,4,𝑡 ≤ 0

These binary choices force a segment q to either be full, partially full, or empty. To ensure that

the segments are “filled up” in order from left to right, equations ( 8 )-( 10 ) are used. From this

example, equation ( 8 ) becomes

𝑦𝑖,2,𝑡(1) ≤ 𝑦𝑖,1,𝑡(1)

The values are shown in parenthesis, and the equation holds true. Equation ( 9 ) becomes

𝑦𝑖,3,𝑡(1) ≤ 𝑦𝑖,1,𝑡(1)

𝑦𝑖,4,𝑡(0) ≤ 𝑦𝑖,2,𝑡(1)

𝑦𝑖,6,𝑡(0) ≤ 𝑦𝑖,4,𝑡(0)

The above equations are all true. Lastly, equation ( 10 ) becomes

𝑦𝑖,5,𝑡(1) ≤ 𝑦𝑖,2,𝑡(1)

Once again, this constraint holds true. That the segments must fill up in order is called an

adjacency constraint in (Almassalkhi & Towle, 2016). Since the power in each linear segment,

xi,a,t is based on the discharge from each linear segment, qi,a,t, those too will fill up in order and

the total power will be the correct value, 15, from this example.

Limit Constraints

𝑄 ≤ 𝑄𝑖,𝑡 ≤ �̅� ∀t ∈ T, i ∈ I ( 11 )

𝑆 ≤ 𝑆𝑗,𝑡 ≤ 𝑆̅ ∀t ∈ T, j ∈ J ( 12 )

𝑝𝑖 ≤ 𝑝𝑖,𝑡 ≤ 𝑝�̅� ∀t ∈ T, i ∈ I ( 13 )

𝑀𝑡 ≤ 𝑀𝑡 ≤ �̅� ∀t ∈ T ( 14 )

38 | P a g e

Note that the discharge has a minimum level, as was determined to be best from the simulation in

Chapter 5. The reservoir lower limit can also be different for different time steps. This is to

prevent frazil ice from forming, as explained previously.

Piece-wise Linear Water Value Curve

Similarly, the water value curve must also be represented as piece-wise linear. The marginal

water value curve in Figure 10 has reservoir filling volume on the x-axis, and so will the water

value curve that is derived from it. To more easily implement the water value curve, the x-axis is

converted from volume(Mm3) to reservoir height (masl). The reservoir, within the available

reservoir levels, is assumed to be rectangular, so the height increases linearly with the volume.

WVt = ∑ mw,tWVwslope

w∈W

∀𝑡 ∈ 𝑇 ( 15 )

Mt = ∑ mw,tw∈W

∀𝑡 ∈ 𝑇 ( 16 )

𝑘𝑖,1,𝑡∆𝑚1 ≤ 𝑚1,𝑡 ≤ ∆𝑚1 ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 17 )

𝑘𝑖,2𝑤−2,𝑡∆𝑚𝑤 ≤ 𝑚𝑤,𝑡 ≤ 𝑘𝑖,2𝑤−1,𝑡∆𝑚𝑤 𝑓𝑜𝑟 𝑤 ∈ 𝑊 − {1, 𝑒𝑛𝑑}, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 18 )

0 ≤ 𝑚𝑤,𝑡 ≤ 𝑘𝑖,2𝑤−2,𝑡∆𝑚𝑤 𝑓𝑜𝑟 𝑤 ∈ 𝑊{𝑒𝑛𝑑}, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 19 )

𝑘𝑖,2,𝑡 ≤ 𝑘𝑖,1,𝑡 ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 20 )

𝑘𝑖,ℎ+2,𝑡 ≤ 𝑘𝑖,ℎ,𝑡 𝑓𝑜𝑟 ℎ ∈ 1,2,4,6 … 𝑒𝑛𝑑 − 2, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 21 )

𝑘𝑖,ℎ+3,𝑡 ≤ 𝑘𝑖,ℎ,𝑡 𝑓𝑜𝑟 ℎ ∈ 2,4,6 … 𝑒𝑛𝑑 − 4, ∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 22 )

Start-up Costs

Lastly, the generator starts need to be kept track of and the start cost subtracted from the profit.

With a minimum discharge constraint the generator should not have to turn off, but the start cost

should be included just in case a constraint must be violated in order to reach a solution. For this,

the time when the generator is on (unit commitment) must be kept track of. If a minimum

discharge constraint larger than zero is set, the unit will never turn off, so these equations can be

omitted.

𝑢𝑖,𝑡 − 𝑢𝑖,𝑡−1 = 𝑠𝑖,𝑡+ − 𝑠𝑖,𝑡

− 𝑓𝑜𝑟 𝑡 = 2 … 𝑒𝑛𝑑, ∀𝑖 ∈ 𝐼 ( 23 )

𝑢𝑖,𝑡 − 𝑢𝑖,0 = 𝑠𝑖,𝑡+ − 𝑠𝑖,𝑡

− 𝑓𝑜𝑟 𝑡 = 1, ∀𝑖 ∈ 𝐼 ( 24 )

39 | P a g e

6.4 ITERATIVE UPDATES BASED ON NEW HEAD The above static model does not change between iterations. In reality, the efficiency of the

turbine/generator is greater when there is greater head since there is more potential energy stored

in the water. This change in efficiency can be represented by updating the power curve each time

step (Belsnes, Wolfgang, Follestad, & Aasgård, 2015). The entire power curve is scaled based on

the most efficient point. This update is shown below. Note that the index a=best refers to the

point on the curve with the best efficiency, and a=rest refers to the remaining points. Note also

that instead of using the segment variables, 𝑥𝑖,𝑎,𝑡, the points on the graph, or the y-coordinates,

are updated. The segments are then reformed from the new points. The points here are

represented as 𝑥𝑖,𝑎,𝑡𝑝

.

𝑥𝑖,best,𝑡𝑝 = 𝑥𝑖,min 𝑒𝑓𝑓,𝑡−1

𝑝 + (𝑥𝑖,best,𝑡−1𝑝 − 𝑥𝑖,min 𝑒𝑓𝑓,𝑡−1

𝑝 )𝑀𝑡−1

�̅�

∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 25 )

𝑥𝑖,𝑟𝑒𝑠𝑡,𝑡𝑝

= 𝑥𝑖,𝑟𝑒𝑠𝑡,𝑡−1𝑝 𝑥𝑖,𝑏𝑒𝑠𝑡,𝑡

𝑝

𝑥𝑖,𝑏𝑒𝑠𝑡,𝑡−1𝑝

∀𝑡 ∈ 𝑇, 𝑖 ∈ 𝐼 ( 26 )

This update is done outside of the above model. For example, the optimisation is done every day

for the following day and considering the next several weeks. The optimisation will be done

using the original PQ curve, then the optimal schedule for the first hour is kept. The PQ curve is

updated as shown above, and the program iterates and runs the optimisation again starting from

the second hour. This continues until the full 24 hours are planned. It was decided that iterating

through each hour of the planning period (up to 4 weeks) was not necessary, and that just

iterating through the desired day was sufficient. This was decided because adding more iterations

greatly increased the calculation time, and the changes in the curve were very small between

hours. Since only the first 24 hours are kept, they are the only ones where the PQ curve is

updated. This could be a subject for further research.

40 | P a g e

7 OPTIMAL PLANNING ALGORITHM RESULTS

Once again, 2016 was chosen as the simulation year. For the electricity price predictions, the

realized spot price was used with an introduced random error of up to 4%. The inflow was

generated based on real measurements and with a random error of up to 6%. The results for the

optimal planning algorithm are shown below. The parameters used are shown below.

Table 3 Test Case Parameters

M0 495.4 masl

𝑄 3 m3/s

�̅� 24 m3/s

𝑆 0 m3/s

𝑆̅ 252 m3/s

𝑀𝑡 495.0 masl (December 1-February 29) , 493.5 masl (March 1-November 30)

�̅� 495.5 masl

𝑝 0 MW

�̅� 3.3 MW

TE 350 hour equivalents/m

C 151 €

u0 1, on

The following graphs show the reservoir level, discharge, spillage, and electricity price for week

1, 23, and 40 of 2016.

Figure 17 Week 1 Reservoir level and flow rate

0

5

10

15

20

25

30

495,44

495,45

495,46

495,47

495,48

495,49

495,5

495,51

01-04 01-05 01-06 01-07 01-08 01-09 01-10 01-11

Flo

w R

ate

(m^3

/s)

Res

ervo

ir L

evel

(m

asl)

January 4-10, 2016

M (masl) Discharge (m3/s) Spillage (m3/s)

41 | P a g e

Figure 18 Week 1 Reservoir level and electricity price

During the winter, the reservoir level is more tightly restricted to stay above 495.0 masl. There is

no spillage needed during week 1. There is a clear correlation between the electricity price and

the reservoir level in Figure 18 where the drops in reservoir level occur when there are spikes in

electricity price.


0

20

40

60

80

100

120

495,44

495,45

495,46

495,47

495,48

495,49

495,5

495,51

01-04 01-05 01-06 01-07 01-08 01-09 01-10 01-11

Elec

tric

ity

Pri

ce (€

/MW

)

Res

ervo

ir L

evel

(m

asl)

January 4-10, 2016

M (masl) Price (Eur/MW)

0

5

10

15

20

25

30

495,48

495,485

495,49

495,495

495,5

495,505

06-06 06-07 06-08 06-09 06-10 06-11 06-12 06-13

Flo

w R

ate

(m^3

/s)

Res

ervo

ir L

evel

(m

asl)

June 6-12, 2016


42 | P a g e


During the summer the reservoir level is allowed to decrease until 493.5 masl, but the spring

flood is in full effect. At this time there is a large amount of inflow, so the reservoir level does

not get too low. During the fall, shown in Figure 21 and Figure 22, the reservoir level changes

daily based on the price, but still does not go below approximately 495.47 masl, refilling during

the night when the electricity price is low.


0

5

10

15

20

25

30

35

40

45

50

495,48

495,485

495,49

495,495

495,5

495,505

06-06 06-07 06-08 06-09 06-10 06-11 06-12 06-13

Elec

tric

ity

Pri

ce (€

/MW

)

Res

ervo

ir L

evel

(m

asl)

June 6-12, 2016


0

2

4

6

8

10

12

14

16

18

20

495,465

495,47

495,475

495,48

495,485

495,49

495,495

495,5

10-03 10-04 10-05 10-06 10-07 10-08 10-09 10-10

Flo

w R

ate

(m^3

/s)

Res

ervo

ir L

evel

(m

asl)

October 3-9, 2016


43 | P a g e


During most of the year there is no need to spill any water. However, during the spring flood the

inflow is well over the upper discharge limit, so some water must be spilled.

Figure 23 Inflow and spillage for 2016

0

5

10

15

20

25

30

35

40

45

495,465

495,47

495,475

495,48

495,485

495,49

495,495

495,5

10-03 10-04 10-05 10-06 10-07 10-08 10-09 10-10

Elec

tric

ity

Pri

ce (€

/MW

)

Res

ervo

ir L

evel

(m

asl)

October 3-9, 2016


0

50

100

150

200

250

300

01-01 02-20 04-10 05-30 07-19 09-07 10-27 12-16

Flo

w r

ate

(m3

/s)

Inflow and Spillage

Spillage Inflow

44 | P a g e

Even when the reservoir level is allowed to go to the lower limit of 495.0 masl, it remains

relatively high. This is most likely due to the fact that mid-term steering was not used in this

model, so the end water value was always a part of the objective function. This causes the model

to want to maintain a high reservoir level at the end of the planning period (short term) to have a

high end water value, and high objective function. To see the effect of the optimised planning, a

simple VNR simulation was done where the discharge exactly equalled the inflow. When the

inflow was larger than the allowed discharged, the remaining inflow was spilled. Using this

‘VNR’ discharge schedule, the benefit of using an optimising algorithm can be seen. For

example, week 1 discharge from the VNR and optimised versions are shown below. While the

VNR discharge remains quite constant, the optimised discharge varies throughout each day,

following the price.

Figure 24 Optimised and VNR discharge comparison

The optimal discharge plan varies much more on an hourly basis than the VNR discharge in order

to optimise the profit. There is a 16% increase in profit during 2016 by using the optimisation

algorithm. This is comparable to the 15% increase from case 4 in section 5.2, so the discussed

algorithm is similar to that implemented in the Fortum model.

0

5

10

15

20

25

30

04-jan 05-jan 06-jan 07-jan 08-jan 09-jan 10-jan 11-jan

Dis

char

ge (

m3

/s)

VNR vs Optimised Discharge January 4-10, 2016

VNR Optimised

45 | P a g e

8 CENTRAL AUTOMATIC CONTROL

8.1 DESCRIPTION The algorithm described above is capable of planning the operation of a hydropower plant for

varying lengths of time. With this in mind, it can be used for the mid-term planning as well as

short-term planning. As described in section 4.2, steering from mid-term planning can ensure that

future factors are considered. The above algorithm can be used for mid-term planning, which

then passes the steering, in the form of a reservoir water value, to a short-term planning model.

This short-term planning model will have two main differences: the objective function will no

longer consider future value of stored water, and there will be an additional steering constraint.

Equation ( 1 ) becomes

𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒 ∑ (𝑃𝑡𝑡∈𝑇,𝑖∈𝐼 𝑝𝑖,𝑡 − 𝐶𝑖𝑠𝑖,𝑡+ ) ( 27 )

The steering constraint will simply be

𝑊𝑉𝑒𝑛𝑑 = 𝑊𝑉𝑠𝑡𝑒𝑒𝑟𝑖𝑛𝑔 ( 28 )

where WVsteering is the water value at the end of the short-term optimisation as determined in the

mid-term optimisation. With the mid-term and short-term planning algorithms, a hydropower

plant can be optimised in real time.

The following section describes the implementation of the planning algorithms with Fortum’s

central control. This work was done in collaboration with Jenny Möller and Johan Wiklund for

their Undergraduate thesis, titled “Optimisation tool for automated planning and control of

production in small-scale hydropower plants ” (Möller & Wiklund, 2018). For more details on

the results of the implementation, please refer to their thesis. Note that this work is written in

Swedish.

8.2 COMMUNICATION FLOW There exists already a controller in Båthusströmmen that controls the turbine to maintain a set

value. Right now this set value is the reservoir level, since it is running on VNR. This controller

can also receive other set values, such as the optimal schedules from the algorithm, and can send

different measurements back to the central database. The controller and the central database are

connected via a SCADA system, which ensures the proper communication flow and sets

standards for communication within the network (A. Daneels, 1999). Figure 25 shows how

information flows through the system, including the central database (Time-series), the central

controller where the algorithm is executed, and the local controller at the plant.

46 | P a g e

Figure 25 Information Flow of Central Control Unit

At Fortum there are already tools built in Excel to communicate with the central database, so the

central controller was written in Microsoft Visual Basic to take advantage of these tools. The

central controller reads the input values it needs, executes the algorithm, then writes the optimal

schedules back to the database, which are then automatically sent to the local controller at the

plant. In practice, the central controller will be a program located on a central server.

8.3 FINAL PROGRAM Initially the algorithm was rewritten to run in Visual Basic using the Microsoft Solver

Foundation, but the model was too large to be solved. Finally, communication was set up

between the Visual Basic project and a model built in GAMS. Since the algorithm was already

tested in Chapter 6, the main focus here was establishing communication between the database,

the Visual Basic project, and the GAMS code, as well as utilizing both the mid-term and short-

term algorithms. The Visual Basic project acts as the central controller, so it is capable of running

the algorithms and communicating with the database in real time. The basic structure of the code

is shown in Figure 26. For a detailed axplanation, refer to (Möller & Wiklund, 2018).

Due to security and licensing reasons, the full GAMS code was not able to be implemented on

the Fortum system, so the optimisation could not be tested at the same time as the communication

with the database. Both parts have been proven and tested separately, but have yet to be fully

implemented in the system. There are also several functions that should be added as options in a

real system, such as considering the availability of the plants, allowing the operators to override

the optimisation schedule and even disable the automatic optimisation, and of course adding

more plants to the program. With more plants comes a more complicated algorithm, but the

principles behind it are the same.

47 | P a g e

Figure 26 Visual Basic Main Program (Möller & Wiklund, 2018)

48 | P a g e

9 CONCLUSION

9.1 THESIS Hydropower has been a staple in the Nordic power system since its creation, and has been an

important source of power for centuries. The fact that hydropower is so consistent and reliable

means that it’s role only gets more and more important as more variable power sources, like wind

and solar, are added to the grid. Hydropower is used to balance out the irregularities of wind and

solar power production, as well as total demand in the system. Today, spot and intraday traders at

Fortum work with hydropower dispatch and the system operator, Svenska Kraftnät, to optimally

run their hydropower plants every day. This requires complex optimisation models to be run and

checked every day, and a lot of manual work for the traders. Besides running the optimisation,

they must check important inputs like price and inflow forecasts, maintenance, desired power,

etc. Fortum owns many large hydropower plants throughout the Nordic system, and it is crucial

that these important plants are run efficiently and optimally. In order to allow the traders to focus

on these important plants, many smaller plants are left to run on their own, often just maintaining

a constant reservoir level (VNR). Though they are still producing power and contributing to the

total profit, they are not being optimally run based on the electricity price. The purpose of this

thesis has been to investigate the added benefit of optimising small hydropower plants, using

Båthusströmmen as a test case.

This thesis was broken into two parts: developing an optimisation algorithm and simulating

Båthusströmmen for a years’ time, and working with two other thesis student on implementing a

real time program to automatically optimise and plan the schedule for Båthusströmmen. The

development of the algorithm is the main focus of this thesis, and included two separate

simulations in itself. First, a simulation of 2016 was done using Fortum’s existing optimisation

program. A model was made both to run on VNR and to optimise with more flexible reservoir

level limits. The results showed that by optimising the schedule for Båthusströmmen for 2016,

approximately a 15% profit could be seen.

Next, a new model was developed in GAMS to optimally plan the operation of Båthusströmmen,

including an additional function to update the power-discharge (PQ) curve based on the changing

reservoir level. This model was also simulated for 2016, both as VNR and with more flexible

limits. It was found that by optimising the plant with flexible reservoir limits, an increase in profit

49 | P a g e

by 16% could be realized. These results are similar to the results from the existing Fortum model,

verifying its validity.

The next phase, implementation, was done using Microsoft Visual Basic as a centrally located

program to automatically run the optimisation throughout the day, taking the load off of the

traders and allowing smaller plants like Båthusströmmen to be operated optimally. The

communication with the database was successfully done, and a full program to automatically run

both a mid-term and short-term optimisation in real time was made. More on this phase can be

read in (Möller & Wiklund, 2018).

9.2 FURTHER ANALYSIS Båthusströmmen is a single small hydropower plant in Sweden, chosen as a test case because it is

not hydrologically coupled to other plants (see section 5.1). There are, however, dozens of other

small hydropower plants that are currently on VNR which could be made to run based on an

optimal planning algorithm, generating more profit for Fortum. It is difficult to estimate the

increase in profit for most plants since there are many hydrological couplings in a river system. A

change in production at one plant can affect several others, and the entire river system needs to be

modelled at once. However, it can safely be said that by implementing an optimisation algorithm

for these plants, more profit stands to be made.

Furthermore, more research could be done on the water value and marginal water value curves,

both for Båthusströmmen and other plants. The cost of starting a generator is also up for debate,

since there are many factors that affect it, and much more research can be done in this area.

Another potential source of error is from the original PQ curve. Input-output curves like this are

generally measured at installation, and can change over time. Without accurate measurements,

the generators may not perform as expected.

50 | P a g e

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Optimal Production Planning for Small-Scale Hydropower