Modeling and Optimization of a Hybrid System for the Energy Supply

8/11/2019 Modeling and Optimization of a Hybrid System for the Energy Supply

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Modeling and optimization of a hybrid system for the energy supply

of a Green building

Hanane Dagdougui a,b, Riccardo Minciardi a, Ahmed Ouammi c,, Michela Robba a, Roberto Sacile a

a Department of Communication, Computer and System Sciences (DIST), Faculty of Engineering, University of Genoa, Genoa, Italyb MINES ParisTech, Sophia Antipolis Cedex, Francec Unit des Technologies et Economie des Energies Renouvelables, CNRST BP 8027 NU Rabat, Morocco

a r t i c l e i n f o

Article history:

Received 28 July 2011

Received in revised form 23 May 2012

Accepted 27 May 2012

Available online 27 September 2012

Keywords:

Decision support systems

Optimization

Renewable energy systems

Green building

Smart grid

a b s t r a c t

Renewable energy sources (RES) are an indigenous environmental option, economically competitive

with conventional power generation where good wind and solar resources are available. Hybrid systems

can help in improving the economic and environmental sustainability of renewable energy systems to

fulfill the energy demand. The aim of this paper is to present a dynamic model able to integrate different

RES and one storage device to feed a Green building for its thermal andelectrical energy needs in a sus-

tainable way. The system model is embedded in a dynamic decision model and is used to optimize a quite

complex hybrid system connected to the grid which can exploit different renewable energy sources. A

Model Predictive Control (MPC) is adopted to find the optimal solution. The optimization model has been

applied to a case study whereelectric energy is also used to pump waterfor domestic use. Optimal results

are reported for two main cases: the presence/absence of the energy storage system.

2012 Elsevier Ltd. All rights reserved.

1. Introduction

The sustainable green building energy supply lead both devel-

oped and developing countries to make and implement new poli-

cies to improve efficiency in energy consumption, and to adopt

new alternatives like RES. Variable energy demands, intermittent

availability of renewable resources, different technological alterna-

tives to satisfy the different demands, and the possibility of inte-

grating storage and energy production systems give rise to the

exigency of defining criteria and strategies able to improve effi-

ciency and energy supply, and its environmental and economic

sustainability. Methods and models able to optimize such hybrid

systems for the specific case of a building are also welcomed be-

cause of the relevance that might have a Green building in terms

of environmental sustainability and energy efficiency.

In fact, in the EU and US, energy consumption in buildings has

even exceeded the energy consumption of the industrial and trans-

portation sectors [1]. Energy consumption of buildings accounts for

around 2040% of all energy consumed in advanced countries.

Over the last decade, more and more global organizations are

investing significant resources to create sustainable built environ-

ments, emphasizing sustainable building renovation processes to

reduce energy consumption and carbon dioxide emissions [1].

RES exploitation is one of the most important aspects of green

buildings. RES are defined as sources of energy that can be derived

from natural processes, and that can be replenished constantly, e.g.

energy generated from sun, wind, biomass, geothermal, hydro-

power [2]. The wind and solar energies are freely available and

environment friendly. The wind energy systems may not be tech-

nically viable at all sites because of low wind speeds and/or higher

unpredictability with respect to solar energy. Moreover, the avail-

ability of a specific resource depends on the specific season and

varies during the day. Integrating different RES in a hybrid system,

allowing their combined exploitation, is therefore becoming

increasingly attractive[3].

Hybrid renewable energy systems are becoming popular for re-

mote areapower generation applications dueto advances in renew-

able energy technologies and rise in prices of petroleum products.

Economic aspects of these technologies are sufficiently promising

to include them in developing power generation capacity [4]. Effec-

tive energy management of hybrid energy systems is necessary to

ensure optimal energy utilization and energy sustainability to the

maximum extent[5]. Hybrid systems can be considered as a rea-

sonable solution, capable to support systems that cover the energy

demands of both stand-alone and grid connected consumers that

can be integrated into residential, commercial, or institutional

buildings and/or industrial facilities. Furthermore, the hybrid

renewable energy systems are often the most cost-effective and

reliable way to produce power as well as to attenuate fluctuations

in power produced, thereby significantly reducing energy storage

0196-8904/$ - see front matter 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.enconman.2012.05.017

Corresponding author. Address: TEER, CNRST BP 8027 NU Rabat, Morocco.

Tel.: +212 666892377.

E-mail address: [email protected](A. Ouammi).

Energy Conversion and Management 64 (2012) 351363

Contents lists available atSciVerse ScienceDirect

Energy Conversion and Management

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http://dx.doi.org/10.1016/j.enconman.2012.05.017mailto:[email protected]://dx.doi.org/10.1016/j.enconman.2012.05.017http://www.sciencedirect.com/science/journal/01968904http://www.elsevier.com/locate/enconmanhttp://www.elsevier.com/locate/enconmanhttp://www.sciencedirect.com/science/journal/01968904http://dx.doi.org/10.1016/j.enconman.2012.05.017mailto:[email protected]://dx.doi.org/10.1016/j.enconman.2012.05.017


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requirements [4]. In literature, the majority of papers have been fo-

cusedon the sizing of hybrid renewableenergy systems. Paskaet al.

[6]presented their experience of the design, build and exploitation

of many hybrid power systems. The results show that the proposed

hybrid plants are a good way to have available sources of electricity

which optimize utilization of primary energy sources. Ashok [7]

discussed different system components of hybrid energy system

and developed a general model to find an optimal combination of

energy components for a typical rural community minimizing the

life cycle cost while guaranteeing reliable system operation. Ekren

and Ekren [8] optimized an autonomous PV/wind integrated hybrid

energy system with battery storage. Bakos and Tsagas[9]reported

the technical feasibility and economic viability of a hybrid solar/

wind grid connected system for electrical and thermal energy pro-

duction, covering the energy demand of a typical residence in the

city of Xanthi (Greece). Reichling and Kulacki [10] modeled the per-

formance of a hybrid windsolarpower plant. They found that add-

ing solar thermal electric generating capacity to a wind farm rather

than expanding with additional wind capacity provides costbene-

fit. Dagdougui et al. [11] presented an overall optimization problem

in connection with a dynamic systemmodel, which is controlled in

real time to satisfy the hourly variable electric, hydrogen, and water

demands. Ouammi et al.[12]presented a practical methodology to

support decision makers in the evaluation of the wind exploitation

on a territory and the sustainability of the installation of a wind

power plant. Teleke et al. [13] developed a control strategy for opti-

mal useof thebatteryenergystorage. Papaefthymiou et al. [14] pre-

sented the wind-hydro-pumped storage hybrid power station of

Ikaria Island. Karki et al. [15]developed a methodology for an en-

ergy limitedhydro plant and wind farmcoordination using a Monte

Carlo simulation technique considering the chronological variation

in the wind, water and the energy demand. Zhang et al. [16]pre-

sented a multistage stochastic mixed integer programming model

for power generation in a day-ahead electricity market. Hyndman

and Fan[17]proposed a new methodology to forecast the density

of long-term peak electricity demand. Glanzmann and Andersson

[18] investigated a decentralized optimal power flow control foroverlapping areas in power systems. Abbey and Jos[19] studied

the problem of energy storage system sizing for isolated wind-die-

sel power systems. In[20], authors presented a building automa-

tion system, where the demand-side management is fully

integrated with the buildings energy production system, which

incorporates a complete set of renewable energy production and

storage systems. Ruther et al. [21] assessed the potential of grid

connected, building integrated photovoltaic generation in the state

capital, Florianopolis, in south Brazil. Al-Salaymeh et al. [22]stud-

ied the feasibility of utilizing photovoltaic systems in a standard

residential apartment in Amman city in Jordan. Hoes et al. [23] pro-

posed a concept that combines the benefits of buildings with low

and high thermal mass by applying hybrid adaptable thermal stor-

age systems and materials to a lightweight building. Braun andRther[24]showed the role of grid-connected building-integrated

photovoltaic in reducing the load demands of a large and urban

commercial building located in a warm climate in Brazil.

The aim of this paper is to define a dynamic optimization model

that is able to support decisions related to the operational manage-

ment of energy supply for a green building. Indeed, the model

could also be used for a more general grid-connected microgrid

characterized by different energy production plants and storage

systems, and, unlike the majority of works reported in the litera-

ture, is related to a system already sized and to the optimal control

of the overall system according to time-varying demands and re-

source availability.

Theinnovationcarried out by this study consistsin consideringa

mixed renewable energy sources and a storage system to feed aGreen building for its thermal and electrical energy needs in a

sustainable way. The systemmodel is embedded in a dynamic deci-

sion model and is used to optimize a quite complex hybrid system

connected to the grid. The optimization model has been solved for

twomain cases: thepresence/absence of theenergystoragesystem.

Finally, unlike most contributions available in the literature, in this

paper, an overall optimization problem is defined in connection

witha dynamic system model, whichis to be controlled in real time,

on the basisof the (discrete time) observation of the systemstate.In

particular, specific state and control variables are defined to formal-

ize the dynamic hybrid system model, the objective function, and

the constraints of the optimization problem. The problem consid-

ered in this paper is quadratic with linear constraints. A Model

Predictive Control (MPC) approach is used in the problem formal-

ization and solutionin order to take into accountupdates in the sys-

tem state, forecasts of the energy flows from renewable sources,

and demand variations, which can be forecasted with some difficul-

ties. The approach followed in this paper is based on the repeated

formalization and solution of an optimization problem over a finite

horizon, on the basis of the current observed state and on the avail-

able forecasts of the quantities of interest.

2. The control architecture

Intelligent buildings have attracted lots of attention in recent

years. Recent papers [25,26]have focused on the inclusion in the

Building Automation System (BAS) of algorithms based on control

and optimization, with specific reference to a Model Predictive

Control (MPC) scheme. Specifically, in [25], attention is focused

on the heating system and state equations are formalized to de-

scribe the temperature behavior in the different buildings rooms

as a function of the external temperature and of the heat sources.

Instead, in[26], authors developed an operational control platform

for an intelligent building using a SCADA (Supervisory Control and

Data Acquisition) system to control temperature and luminosity in

huge-area rooms. Energy management systems require the inte-

gration and communication of different kinds of information. Thus,a specific communication network should be developed [27].

In this paper, a dynamic decision model for a green building is

described in detail. The developed model is thought as a part of a

general BAS based on a MPC controller that integrates plants, stor-

age systems, energy demands (for electricity, heat, and water

pumping), resource availability forecasts, through an appropriate

communication system.

Fig. 1reports the information flows necessary for the dynamic

decision model application. A general architecture that can host

such a dynamic decision model is reported in [26]. The optimiza-

tion package used in this paper can be integrated with a supervi-

sory system. Otherwise, the dynamic decision model can also be

implemented in the Matlab Software (like in [26]). The results of

the optimization algorithm can be sent to an actuator system thatgives commands to the thermal, electrical, and water systems (i.e.,

inputs to production plants, inverters, storage system, air condi-

tioning, water pumping, etc.).

The architecture is based on a centralized intelligence that re-

ceives forecasts for renewable resources availability, demands,

prices, and system state (i.e., level of charge of the storage system),

and, on the basis of an optimization model, gives commands to a

sub-set of the production plants, to the storage system, to the

pump, and to the connection between the building and the exter-

nal net. The commands are given to typical hardware (i.e., invert-

ers, switch with the external net, production plants, etc.) that can

be present in the building. Moreover, the central controller is sup-

posed to communicate with the local controllers present in the

production plants and in the storage system. The primary controlvariables are those entities over which the central controller may

352 H. Dagdougui et al. / Energy Conversion and Management 64 (2012) 351363


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physically decide. That is: the energy flows from/to the storage, the

production level of the plants that can be controlled, the energy

flows from/to the net, the status on/off of the pump. Other decision

variables are then used in this work for the electrical system (for

example, the splitting of the energy coming from the wind tur-

bine). These decision variables describe the theoretical behavior

of the energy flows, and, in fact, they are linked to the primary con-

trol variables through, for example, the energy balances present in

the overall system. For example, in the following, a variable is used

to define the energy from wind turbine/PV that is sent to the stor-

age system. In the case there is a very specific electrical network

(i.e., each plant is connected directly to the storage through specific

lines) this energy flow is the result of the energy balance among

production, loads, storage. Otherwise, this energy flow is sent to

the buildings grid and what the storage receives is undistinguish-

able, that is, one cannot know from which plant the flow comes.

However, also in the latter case, these variables can be defined as

secondary control variables that are linked through the primary

control variables through a set of constraints. Finally, it is impor-

tant to note that the aim of this paper is not the one of defining

a complete simulation model for the building subsystems (i.e.,

the electrical subsystem, the thermal subsystem, the water subsys-

tem). For this reason, simplified equations have been used to de-

scribe the electrical grid and the thermal subsystem, as well as

the plants and the storage.

3. The system model

3.1. Notations

The following definitions will be used throughout this paper to

describe the system model:

EtX The output energy produced from the wind turbine

(wt), photovoltaic (pv), biomass (b) and flat plate

collector (fpc) [kWh], in time interval (t, t+ 1),

t= 0, . . ., T 1; indexXdesignates the renewable

energy system and belongs to the set [wt,pv, b,fpc]

EtY;h The energy provided from renewable energy systems

and electrical network (net) [kWh] for heating (the

building) in time interval (t,t+ 1); index Y belongs to

the set [wt,pv,b,fpc, net]

EtZ;e The energy provided from the renewable energy

system and the network [kWh] for electric supply

[kWh] in time interval (t,t+ 1); index Z belongs to the

set [wt,pv, net]

EtZ;p The energy from the renewable energy system and the

electrical network [kWh] used to supply electricity for

pumping water in time interval (t,t+ 1);

t= 0, . . ., T 1

EtW;net The surplus produced fromwt/pv [kWh] sent to the

electrical network in time interval (t, t+ 1);

t= 0, . . ., T 1; index W belongs to the set [wt,pv]~Etnet The overall energy that is sent to the network fromwt

andPVmodules [kWh] in time interval (t, t+ 1);

t= 0,. . .

, T

1Etnet The overall energy [kWh] that is taken from the

network in time interval (t, t+ 1)

EtZ;st The energy from wind turbine/PV that is sent to the

storage system [kWh] in time interval (t,t+1);

t= 0, . . ., T 1

Qtw The amount of potable water provided to the

household [m3/h] in time interval (t,t+ 1),

t= 0, . . ., T 1

CHte The energy provided from the storage system to the

electricity [kWh] in time interval (t, t+ 1),

t= 0, . . ., T 1

CHth The energy provided from the storage system to the

heating system [kWh] in time interval (t, t+ 1);

t= 0, . . ., T 1

CHtp The energy provided from the storage system to the

pumping [kWh] in time interval (t,t+ 1);

t= 0, . . ., T 1

CBt The level of storage system [kWh] at time instant

t, t= 0, . . ., T 1

3.2. Consumer profile

The hybrid energy generation system for a Green building

connected to the electrical network (that is considered in this

work) is reported inFig. 2. The proposed system is developed for

a household that has electrical, thermal and water pumping needs.

However, the systemis enough general to be exported to industrial

Fig. 1. The building MPC-based architecture.

H. Dagdougui et al. / Energy Conversion and Management 64 (2012) 351363 353


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and/or residential areas and/or microgrids with similar character-

istics. This hybrid system consists of photovoltaic modules (PV),

a wind turbine, a small biomass plant, a solar flat plate collector

(FPC), and a storage system, as well a connection with the electrical

network.

The optimization of such system aims to generate energy satis-

fying the dynamic demands (i.e., heating demand, electrical de-

mand, and domestic water demand), which correspond to real

data of a household (of six persons) in the Liguria region in winter

season. The FPC and biomass plant are exclusively used to ensure

heating demand. Either energy produced by the wind turbine or

the energy produced by the PV modules can be directly used to sat-

isfy a part of the electrical demand as well as the water demand

through pumping, and/or can contribute to supply the heating de-

mand. The energy surplus from wind turbine and the PV modules

can be sent to the storage system or/and to the network. The stor-

age system can receive electrical energy from PV modules and

wind turbine and can provide free energy for heating, electricity,

and pumping needs in cases of deficit in electricity. Furthermore,

the network connection offers the possibility to purchase electric-

ity in case of failure of the storage system. The overall interactions

between the components of the system are reported in Fig. 3.

In order to ensure the sustainability of the hybrid system, and

addressing the mismatch between the intermittencies of wind

and solar irradiation, the system presented in this paper integrates

both an internal storage system and a connection with the electri-

cal network.

The necessity of properly integrating the access to the storage

and the electrical network gives rise to an optimal control problem.

3.3. Energy from the wind turbine

The following model is used to simulate the electrical power

output of the wind turbine[28]:

Ptwt

0 vt

v

c

prvt2v2cv2rv

2c

vc6 vt 6 vr

pr vr6 vt 6 vf

0 vt vf

8>>>>>>>:

t 0; . . . ; T 1 1

where vt is the forecasted wind speed in time interval. It is worth to

mention that the wind speed is predicted by some meteorological

model and hence these predictions are retained as reliable ones.

Then, pr is the rated electrical power, vcis the cut in wind speed,

vr is the rated wind speed, and vfis the cut off wind speed.

In general, the wind speed measurements are given at a height

different than the hub height of the wind turbine. The following

equation is used to evaluate the wind speed at the desired height

[11,29]:

vt

v

t

data

lnHhub=z

lnHdata=z t0;. . .

; T1

2

where Hdatais the height of the measurement, Hhub is the hub height,

z is the surface roughness length, and vtdata is the forecasted wind

speed at the height of the measurements.

Thus,

Etwt PtwtDt t 0; . . . ; T 1 3

3.4. Energy from the PV modules

The power generated from PV modules can be calculated using

the following formula[30]:

P

t

pv SpvgpvpfgpcG

t

t0;. . .

; T1

4

where Spv is the solar cell array area, gpv is the module referenceefficiency, pfis the packing factor, gpcis the power conditioning effi-ciency andGt is the forecasted hourly irradiance, that is predicted

by some meteorological model and hence these predictions are re-

tained as a reliable ones.

Thus,

Etpv Ptpv:Dt t 0; . . . ; T 1 5

3.5. Energy from the biomass heating plant

Energy provided by the biomass heating plant depends on the

used biomass quantity ut

[m

3

] in time interval (t, t+ 1), the bio-mass volumetric mass (VM) [kg m3] (i.e., the ratio between the

dry mass [kg] and the volume [m3]), the lower heating value

(LHV) [MJ kg1]. The LHV assumes that the latent heat of vaporiza-

tion of water in the fuel and the reaction products is not recovered.

Then, it can be calculated once higher heating value (HHV) and

moisture content (MC) are known. The HHV is the total energy re-

lease in the combustion with all of the products at 273 K in their

natural state when water has released its latent heat of condensa-

PV modules

Wind turbine

Biomass unit

Flat plate

collector (FPC)

Electrical Network

Heating/cooling

Electricity

Water

Energy storage

system

Hybrid system

Green building

Fig. 2. Energy flows between the hybrid system and the green household.



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tion. In the considered work, the HHV is evaluated from the

basic data analysis of biomass. The biomass MC represents the

water amount present in the biomass and it can be expressed as

a percentage of the dry weight. As regards production plant, the

plant is supposed to operate at the maximum productivity level.

The following equation provides the plant developed energy Etb

[kWh]:

Etb fgbhLHVutVM t 0; . . . ; T 1 6

wheregbh is the plant efficiency and fis a conversion factor [kWh/MJ].

3.6. Energy from the flat plate collector

The useful thermal energy extracted from the water collector

depends on the instantaneous incident solar irradiation, the plate

area, and its efficiency. That is[31],

Etfpc gfpcAfpcGtDt t 0; . . . ; T 1 7

where gfpcis the efficiency of the solar flat plate collector,Afpc[m2] is

the area andGt is the forecasted hourly irradiance, that is predictedby some meteorological model and hence these predictions are re-

tained as reliable ones.

3.7. Thermal, electrical and water needs

The hourly energy that can be used in time interval ( t,t+ 1) for

heating,Eth, is expressed by:

Eth Etwt;h E

tpv;h E

tfpc;h E

tb;h E

tnet;h CH

th t 0; . . . ; T 1

8

The hourly electrical energy, Ete, that can be used in timeinterval

is expressed by:

Ete Etwt;e E

tpv;e E

tnet;e CH

te t 0; . . . ; T 1 9

The hourly energy Etp that can be used in time interval for

pumping water is given by:

Etp Etwt;p E

tpv;p E

tnet;p CH

tp t 0; . . . ; T 1 10

The amount of pumped water is proportional to the energy used

for this purpose, that is:

Qtw

Etpqgh

gps t 0; . . . ; T 1 11

The energy that is sent to the electrical network is composed by

the surplus produced by the wind turbine and the surplus pro-

duced by the PV modules, i.e.,

~Etnet Etwt;net E

tpv;net t 0; . . . ; T 1 12

The energy that is taken from the network is given by:

Etnet Etnet;h E

tnet;e E

tnet;p t 0; . . . ; T 1 13

The energy productions by the wind turbine and the PV mod-ules in each time interval can be used for different purposes: to

supply electrical demand, heating demand, water demand, sent

to the storage system or sold to the network. Thus, the following

equations hold:

Etwt Etwt;h E

twt;e E

twt;p E

twt;net E

twt;st t 0; . . . ; T 1 14

Etpv Etpv;h E

tpv;e E

tpv;p E

tpv;net E

tpv;st t 0; . . . ; T 1 15

3.8. The storage system state equation

The storage system works as an inventory for the electrical en-

ergy that can, in this way, be stored. Specifically, a state equationfor the storage system can be written. That is,

Flat platecollector (FPC)

Wind turbine

Biomass unit

PV modules

Heating

Pumping water

Electricity

Electrical

Network

tewtE ,

thwtE ,

thpvE ,

thfpcE ,

thBE , t

hnetE ,

tepvE ,

tpwtE ,

tppvE ,

tpnetE ,

tenetE ,

tnetpvE ,

tnetpvE ,

Storage

systemt

stwtE ,

t stpvE ,

thCH

tpCH t

eCH

Fig. 3. Architectural system interactions.



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CBt1 CBt Etwt;st Etpv;st CH

tp CH

th CH

te t

0; . . . ; T 1 16

4. The optimization problem

The decision variables of the optimization problem are Etwt;h,

Etpv;h, Etfpc;h, Etb;h, Etnet;h, Etwt;e, Etpv;e, Etnet;e, Etwt;st, Etpv;st, CHte, CH

th, CH

tp, while

CBt are state variables.

The objective function (to be minimized) is characterized by the

sum of different terms that are properly weighted: the deviation

from the various demands (electrical, thermal, domestic water),

the energy that is taken from the net (i.e., the system has the objec-

tive not to depend from the net but only from the produced energy,

when possible) and the energy in the storage system (that should

be maximized during the optimization horizon and at the end of

the optimization horizon). That is,

ZXT1t1

Etwt;h Etpv;h E

tfpc;h E

tB;h E

tnet;h CH

th E

tDh

2

aXT1t1

Et

wt;e Et

pv;e Et

net;e CHt

e Et

De2

bXT1t1

Etwt;p Etpv;p E

tnet;p CH

tp

qgh gps Q

tDw

!2

uXT1t0

Etnet cXT1t0

CBt qCBT t 0; . . . ; T 1 17

wherea, b,u,c andq are weighting factors.The constraints of the optimization problem are represented by

equations reported in Section 3. Moreover, there is a constraint re-

lated to the storage system. That is,

CBt 6 Cmax t 0; . . . ; T 1 18

whereCmax is the size of the storage system.However, obviously, the energy sent to the network must be

less than the sum of the energy produced by the wind turbine

and photovoltaic module.

~Etnet Etwt E

tpv t 0; . . . ; T 1 19

Instead, as regards biomass and flat collector plant, the pro-

duced energy can be less or equal to the available potential. In fact,

biomass may not be used (also because if it is summer, heating

does not work and heating cannot be sent to the network), and

water for heating passing through the plate collector may be

stopped. This implies the following relations

Etb;h Etb t 0; . . . ; T 1 20

Etfpc;h E

tfpc t 0; . . . ; T 1 21

The problem is here solved using mathematical programming

techniques through a commercial optimization package [32]. In

particular, the optimization problem is solved for two specific case

studies: presence/absence of the storage system. In the latter case,

thus, the variables related to the storage system are known and set

equal to zero.

5. Application to case study

The proposed dynamic decision model has been tested for the

Capo Vado site, which is the windiest one of Liguria region, in Italy

[33]. It is assumed that the forecasted data from which the optimi-

zation problem must be solved are exactly equal to the historicaldata recorded in the site, and which consist of the hourly wind

speed, recorded at the height of 10 m, and the hourly solar irradi-

ance (seeFig. 4).

The wind model described by Eqs. (1)(3)has been applied to

the specific case study, using the wind turbine G-3120 35 kW.

The parameters assume the following values: vc= 3.5 [m/s],

vr= 11 [m/s], vf= 25 [m/s], Pr= 35 [kW], Hhub= 30.5 [m],

Hdata= 10[m], z0= 0.03 [m]. For the PV modules, it is assumed

Spv

= 100 [m2],gpv

= 0.11,gpc

= 0.86, andPf

= 0.9.

Fig. 5 shows the hourly energy that is produced by the wind tur-

bine, and the PV modules. In fact, the figure demonstrates that the

wind energy is ranged between 0.35 kWh at 1:00 and 17 kWh at

19:00. However, for the solar modules, the energy output reaches

its maximum, 4.85 kWh, at 12:00. It is evident that the energy pro-

duction coming from the wind turbine is higher than the energy

produced from the PV modules. This fact is mainly due to the high

wind speed and the low solar radiation in the winter season.

5.1. Optimal results: absence of the storage system

In this case, additional constraints are introduced: all state and

control variables related to the storage system are set equal to

zero. Moreover, the related state equation has been eliminated.Figs. 6 and 7 show the obtained optimal results. Specifically,

Fig. 6shows how electrical energy is produced, whileFig. 7is re-

lated to the energy that is necessary for the pump (to satisfy the

domestic water demand).

According toFig. 6, the mainly part of the energy dedicated to

satisfy the electrical energy demand, approximately 66% comes

from the wind turbine, 18% comes from the PV modules, whereas

16% is taken from the electrical network (grid) between 1:00 and

7:00, this behaviour is mainly attributed to either the low wind

speed, absence of solar radiation and non-existence of storage

system.

Fig. 7 shows the hourly energy consumed by the pump, the

mainly part of this energy which is equal to 54% comes from the

wind turbine, and 30% of energy needs are supported by the elec-trical grid, while small part, less than 16% comes from the PV

modules.

The total energy surplus sold to the electrical network is re-

ported in Fig. 8. One can note that the contribution of the wind tur-

bine is dominated during all the day with a percentage of 94%,

while, a small part is sold from the PV modules between 9 h and

15 h which constitutes only 6% of the energy sold, this fact is due

to the low irradiance on winter season.

5.2. Optimal results: presence of the storage system

The optimal results to satisfy electrical energy needs of the

household are shown inFig. 9.

Approximately 55% results from wind turbine, 18% derives fromPV modules, 15% from the storage system and 12% from the grid.

The electrical energy demand reaches its higher hourly peak value

of 2.4 kWh at 18:00 and a minimum of 1.3 kWh at 04:00. The

hourly periods have been defined throughout the day: period A

(16 t< 7), period B (76 t< 15) and period C (156 t6 24). During

period A, the electrical energy needs were totally provided by the

wind turbine and the electrical grid, this combined contribution

is owing to both, low wind speed and absence of the solar radia-

tion, in addition, within this paper, it is assumed that initially the

storage system is empty. During the period B, and apart from time

7:00, the demand has been satisfied by various energy flows com-

ing from PV, wind turbine and storage system.

Finally, in the time period C, the electrical energy demand is en-

sured by both the wind turbine and storage system with dominantcontribution from wind energy.



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0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h)

Windspeed(m/s)

0

100

200

300

400

500

600

Solarirradiance(W/m)

Wind-10 m

Wind-hub heightsolar

Fig. 4. Hourly wind speed and solar irradiance of the considered representative day at Capo Vado site.

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h)

Energyproduced(kWh)

Wind

Solar

Fig. 5. Hourly energy produced.

No storage system

0

0,5

1

1,5

2

2,5

3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h)

Electricalenergyflow(kW

h)

Grid

Solar

Wind

Fig. 6. Electrical energy management (absence of storage system).



8/13

No storage system

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h)

Energysenttothepump(kWh)

Grid

Solar

Wind

Fig. 7. Energy demand of pump (absence of storage system).

No storage system

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h)

Energysoldtothenetwork(kWh)

Solar

Wind

Fig. 8. Energy sold to the electrical network (absence of storage system).

With storage system

0

0,5

1

1,5

2

2,5

3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h)

Electricalenergyflow

(kWh)

Storage system

Grid

Solar

Wind

Fig. 9. Optimal electrical energy control (presence of storage system).



9/13

With storage sysytem

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h)

Energysenttoth

epump(kWh)

Storage system

Grid

Solar

Wind

Fig. 10. Energy demand of pump (presence of storage system).

With storage system

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Time (h)

Energysenttothestoragesystem(kWh) Solar

Wind

Fig. 11. Energy sent to the storage system (presence of storage system).

With storage system

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h)

Storagesystemlevel(kWh)

Fig. 12. Storage system level.



10/13


11/13

5.3. Environmental impacts & benefits

One interesting issue is here related in understanding how

many greenhouse gas (GHG) emissions are avoided through the

use of a green building.

To this end, it is necessary to compare the emissions produced

by the green building and the emissions that would have been pro-

duced using conventional combustibles.

As regards CO2, the emissions produced by the green building

are zero, except when electrical energy from the main grid is used.

To calculate this quantity, the emission factor of the Italian electri-cal mix (0.465 kg CO2/kWhel) reported in[34]has been used.

Emissions generated by fossil fuel combustibles have been

calculated for two combustibles: coal and natural gas. For CO2,

the following equation is adopted:

COt2c fe;cfo;cQ

tD;c c 1;2 t 0; . . . ; T 1 22

where fe;c;fo;c are respectively the emission and oxidation factors,

that can be used when combustible c,c= 1,2, is used (and reportedin[34]), andQtD;cis the combustible flow of kind c, that needs to be

0

0,5

1

1,5

2

2,5

3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h)

Electricalenerg

y(kWh)

Provided

Demand

Fig. 15. Electrical energy satisfaction.

0

2

4

6

8

10

12

14

16

18

20

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h)

CO

2reduction(kg)

Coal (best practice)

Natural gas (CCGT)

Fig. 16. Hourly CO2 gas reduction.

Table 1

Daily GHG reductions.

Energy sources CO2(kg) SO2(kg) NOx (kg)

Coal (BP) 180 2.2 0.8

Natural gas (CCGT) 81 0.09

BP: Best Practice.CCGT: Combined Cycle Gas Turbine.

Table 2

GHG emissions (absence/presence of storage system).

Energy sources Green-house gases emission (no storage system)

CO2 (kg) SO2 (kg) NOx (kg)

Panel A

Coal (BP) 39 0.48 0.18Natural gas (CCGT) 17 0.02

Green-house gases emission (with storage system)

Panel B

Coal (BP) 20 0.25 0.09

Natural gas (CCGT) 9.3 0.01



12/13

used to satisfy the household energy demand in time interval

(t, t+ 1). This flow has been calculated using average data relevant

to the average characteristics of plants present in Italy [34].

The avoided emissions are finally calculated subtracting this

quantity to the emissions that could be generated by fossil fuels.

Fig. 16shows the CO2 reduction by using the proposed hybrid

energy system for a household instead of producing the house-

holds needs by the conventional fossil fuel (coal and natural gas).

Similar considerations can be derived for other GHG gas emis-

sions (i.e., SO2 and NOx, in this work). The only difference is that

there is not an emission factor of the Italian electrical mix. In this

case, data related to the typical plants present in Italy have been

used.

In Table 1, the GHG reductions are shown during the considered

day. As notated in the previous sections, the hybrid system is con-

nected to the electrical network, so part of energy demand is satis-

fied by the grid which is supposed to be a non-renewable energy

system. Thus, an assessment of the GHG emissions should be done.

Table 2reports the evaluation of the GHG emitted for both system

configurations (presence/absence of the storage system). It can be

summarized that large amount of GHG can be avoided by coupling

the storage system to the hybrid energy system. Specifically,

approximately 50% of the GHG emissions are reduced. The environ-

mental impacts have been reduced significantly by implementing

the storage system, which, in fact, enhance the reliability of the

proposed green hybrid energy system.

Other impacts related to the different management options and

in particular related to the costs of the purchased electrical energy

can be calculated. It is important to note that, in this paper, a spe-

cific objective related in the problem formalization to costs has not

been included. This means that the optimal solution does not find

the minimum costs related to policies of purchasing/sales of the

electrical energy. However, an interesting analysis is related to

the daily cost of the electrical energy taken from the net in case

where the storage is present or not. Specifically, considering the

optimal results reported inFigs. 5, 6, 8, and 9, and taking the elec-

trical energy prices from data available during the day for the Ital-ian electrical market, the following conclusions can be drawn for

one day:

If the storage is not present, the overall daily cost is equal to

6.5.

If the storage is present, the overall daily cost is equal to 3 .

6. Conclusion

A dynamic decision model for the energy management of a

household has been proposed. The model is able to define the opti-

mal energy flows management in a building characterized by a mix

of renewable energy resources (solar, biomass, wind) to satisfy dif-

ferent demands (electric, heating and water). A dynamic decisionmodel has been developed and applied to a household located at

Capo Vado (Liguria Region). Optimal results to satisfy all the energy

demands are found for a testing day with presence/absence of the

storage system. Moreover, an analysis about the avoided emissions

is reported and the importance of having a storage system is dem-

onstrated also under this point of view. The developed decision

model can also be used for real time management, through a

MPC approach that is adopted for the dynamic decision model

solution.

It should be noted that, in the case of absence of the energystor-

age system, since there are no state equations and available energy

varies in each time interval, the optimization problem can be run

at each time interval in a separated way, and is in fact static.

Future developments of the present work regard the possibilityof introducing stochastic issues both in demand and resource pre-

dictions. In this case, in order to reduce the overall complexity of

the problem, dynamic programming could be used. Then, the mod-

el could be detailed from the electrical, thermal and technological

point of view. Moreover, an objective function based on energy

prices could also be adopted in order to consider the green-build-

ing as an energy producer.

Moreover, a multi-objective approach could be formalized to

take into account economic and environmental issues, as well as

the objectives weighted in the current version of the objective

function.

Finally, the inclusion of the developed dynamic decision model

in a decision support system that can allow the user to interact

with the mathematical models could be helpful for the energy

management of the household.

Acknowledgments

Authors wish to thank ARPAL (Agenzia Regionale per la Protezi-

one dellAmbiente Ligure), that has kindly collected and made

available the important historical data set at the basis of this work.

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Documents

Modeling and Optimization of a Hybrid System for the Energy Supply