Thermo-economic optimization of the impact of renewable generators on poly-generation smart-grids including hot thermal storage

Energy Conversion and Management 65 (2013) 75–83

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Energy Conversion and Management

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Thermo-economic optimization of the impact of renewable generatorson poly-generation smart-grids including hot thermal storage

M. Rivarolo ⇑, A. Greco, A.F. MassardoDIME – Thermo-chemical Power Group (TPG), University of Genoa, Italy

a r t i c l e i n f o

Article history:Received 18 July 2012Received in revised form 3 September 2012Accepted 3 September 2012Available online 11 October 2012

Keywords:Poly-generative smart gridRenewable energy sourcesThermo-economic time-dependentoptimization

0196-8904/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.enconman.2012.09.005

⇑ Corresponding author.E-mail address: [email protected] (M. Riv

a b s t r a c t

In this paper, the impact of not controllable renewable energy generators (wind turbines and solar pho-tovoltaic panels) on the thermo-economic optimum performance of poly-generation smart grids is inves-tigated using an original time dependent hierarchical approach.

The grid used for the analysis is the one installed at the University of Genoa for research activities. It isbased on different prime movers: (i) 100 kWe micro gas turbine, (ii) 20 kWe internal combustion enginepowered by gases to produce both electrical and thermal (hot water) energy and (iii) a 100 kWth adsorp-tion chiller to produce cooling (cold water) energy. The grid includes thermal storage tanks to manage thethermal demand load during the year. The plant under analysis is also equipped with two renewable non-controllable generators: a small size wind turbine and photovoltaic solar panels.

The size and the management of the system studied in this work have been optimized, in order to min-imize both capital and variable costs. A time-dependent thermo-economic hierarchical approach devel-oped by the authors has been used, considering the time-dependent electrical, thermal and cooling loaddemands during the year as problem constraints.

The results are presented and discussed in depth and show the strong interaction between fossil andrenewable resources, and the importance of an appropriate storage system to optimize the RES impacttaking into account the multiproduct character of the grid under investigation.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The development of poly-generation smart grids represents aninteresting solution to satisfy electricity and heat demand andemission reduction [1,2]: poly-generation smart grids generateelectricity and heating and cooling thermal power close to endusers, solving the main disadvantages of the centralized generationapproach, due to energy transmission [3]. In fact, the distributedgeneration approach has several benefits over the others, such as(i) reduction of transmission and distribution costs, which representabout the 30% of the costs related to electricity supply; local con-nections do not present high capital costs and energy losses of longdistances distribution lines; (ii) decrease of energy dissipation:piping and conversion devices dissipate almost 6% of producedenergy,[4] increasing costs and emissions; in a smart grid thesekinds of losses are avoided; (iii) increase of energy efficiency: thesimultaneous supply of electrical and thermal demand allows toreduce energy waste, improving system global efficiency; sincethermal energy transport is more difficult than electricity, distrib-uted generation approach (production close to users) is essential;

ll rights reserved.

arolo).

(iv) integration of renewable generators: traditional prime moverscould be easily integrated at local site with renewable generatorsdecreasing emissions [5].

The main goal of the present work is the optimization of apoly-generation smart grid, focusing on the effect of renewablegenerators and their correlation with the storage tank for hot ther-mal energy. To understand the influence of renewable generatorson the whole system, it is worth remembering that an optimalpoly-generation smart grid must assure the end users’ demands(multi product systems) simultaneously (heating, cooling and elec-trical demand).

Increasing the size of renewable generators involves severaladvantages such as low environmental impact and fossil fuelconsumption reduction; on the other hand, renewable generatorspowered by solar and wind energy are intrinsically random overtime, thus their ‘‘unpredictable behaviour’’ could affect theoperating conditions of prime movers over time. Since primemovers are co-generative, modifying operating conditions affectsboth electrical and thermal production. Thus, by varying theoptimal size of renewable electrical generators, thermal storagesize and behaviour could be influenced too. Therefore, the mostimportant part of the analysis is represented by the integrationbetween prime movers constraints (continuous operation, high

Nomenclature

AbbreviationICE internal combustion engineLHV lower heating valuemGT micro gas turbinePV photo voltaicRES renewable energy sources

SymbolsC cost (€)c specific cost (€/kW h)cp specific heat (kJ/kg K)E electricity flow (kW h)F fuel consumption (kg)LS load storage factorM mass (kg)P power (k W)Q heat flow (kW h)Zvbcoge virtual variable cost (€)a res availability coefficient

DT temperature difference between storage inlet and outletg efficiency

Subscriptacq acquiredcap capitalcons consumedel electricalf fueli i-th stepin inputinst installednom nominalout outputprod producedreq requiredvar variablevirt virtual

76 M. Rivarolo et al. / Energy Conversion and Management 65 (2013) 75–83

performance, etc.) and the renewable production, which is randomaccording to wind and solar irradiation condition.

2. Prime movers and device test rig

The facilities installed are based on different kinds of technol-ogy with the aim to produce both electrical and thermal energy[6]: the poly-generation smart grid analyzed here is based on theone installed at the TPG laboratory of the University of Genoa[7–10].

Referring to Fig. 1 the poly-generative smart grid main compo-nents are [11]:

� 100 kWe Recuperated Micro Gas Turbine: It is the main primemover installed and produces the highest amount of both ther-mal and electrical energy; the machine is a Turbec T100 PHSSeries [12]. This commercial unit consists of a power generationmodule (100 kW of electrical power at nominal conditions), acogeneration heat exchanger located downstream of the recu-perator outlet (hot side).� 20 kWe Internal Combustion Engine: the internal combustion

engine installed is a FIAT TANDEM-T20-A, powered by naturalgas; this commercial unit generates 20 kW of electrical powerat nominal conditions; a co-generative heat exchanger (namedrecuperator) is placed downstream of the ICE outlet. It produces47.5 kW of thermal power at nominal conditions.� 100 kWc Adsorption Chiller: in order to generate cooling thermal

power, mGT T100 has been connected to an adsorption chillerLWM-W300 produced by LS. It is powered directly by themGT heat, assuring 100 kW cooling power generation.� Renewable generators: the grid also includes renewable genera-

tors, namely PV solar panels, model eco line 72/180–185 Wproduced by Luxor, and a wind turbine of MAGLEV series.� Storage tank: the grid analyzed is equipped with several storage

tanks (i.e., for hot and cold water of the whole grid, and for eachmain engines). However in this analysis only a global storagetank (Pufferspeicher series) [6] for hot thermal energy isconsidered.

The grid is also integrated with a 450 kW SOFC Hybrid SystemEmulator developed by the authors in collaboration with

Rolls-Royce FCS [13–16] for cogeneration applications, but it isnot considered in the analysis carried out in the present paper.

3. EPoMP multilevel thermo-economic optimization approach

To find out poly-generative smart grid optimal size and man-agement including RES, a time-dependent thermo-economic anal-ysis is mandatory. Thus, a model has been developed by theauthors and a modular program named EPoMP (Economic Poly-gen-eration Modular Program) has been created [17] starting from a pre-vious software for co-generative power plants only [18,19].

Fig. 2 shows the models flow-chart which is based on a hierar-chical optimization structure.

There are two different optimization levels: the low and thehigh level respectively. At the low level, lay-out and plant sizeare fixed (therefore capital costs are fixed) and the code finds thebest operational strategy, in order to minimize the function thatrepresents the hourly (or less time period) variable cost.

Cvar ¼ Fi �XN

i¼1

cfuel;i þ cel � Eacq þ cvirt � ðFv irt þ Evirt þ Q �virtÞ ð1Þ

Variable costs are made up of the following terms: (i) a term relatedto fuel consumption costs, (ii) a term related to electrical energycosts, and (iii) a term that represents ‘‘virtual costs’’.

The electrical energy costs term represents the product of theelectrical energy purchased from external grid and the electricityspecific cost: when the electricity produced by the plant is not suf-ficient to satisfy the electrical load (which is one of the problemconstraints), electricity is purchased from the external grid. Aboutthe term ‘‘virtual flows’’, included in the cost function, it is impor-tant to underline that it is not a real cost, but rather represents en-ergy and mass exchanges between system and environment(electrical grid, fuel grid, storage system, etc.) necessary only tomeet the optimization procedure constraints during the calcula-tion. Since the costs implemented in EPoMP and associated to vir-tual flows are very high, to find the optimum conditions withoutany virtual energy or mass request (constraint violation such asthe gas flow rate or available electricity from the grid), the codeis forced to find a plant configuration which minimizes virtualflows [18] (i.e. zero virtual costs).

The main inputs of the model are: (i) electricity, heating, cool-ing, etc. load curves versus time; (ii) economic scenario where

Fig. 1. University of Genoa poly-generation grid laboratory.

Fig. 2. EPoMP code hierarchical structure.

M. Rivarolo et al. / Energy Conversion and Management 65 (2013) 75–83 77

the grid operates, including trade prices (fuel cost, energy cost,plant lifetime etc.); (iii) component capital costs vs. size; (iv) oper-ating and maintenance costs vs. time; (v) prime movers off designperformance curves; (vi) technology constraints for grid devices(i.e. starting time, flexibility, etc.).

Constraints of the problem are the balance equation betweensupply and demand of the components. For example, in the energybalance, the energy produced by the prime movers (ICE, gasturbines, etc.) in the system, the energy sold to the user and theenergy consumed by system components (i.e. electrolytic cells,etc.) are included:

Ereq ¼XN

i¼1

Ei;prod þ Eacq þ Evirt �XN

i¼1

Ei;cons ð2Þ

The same concept is the basis of the thermal energy balance:

Q req ¼XN

i¼1

Q prod þ Qvirt ð3Þ

At the high level, the plant component optimal size, minimizingtotal annual cost, is evaluated as the sum of variable costs Cvar cal-culated at low level analysis and capital plant costs Ccap.

Ctot ¼ Cvar þ Ccap ð4Þ

The plant total capital cost is the sum of the total capital cost ofany plant component.

Ccap ¼XN

i¼1

Ccap;i ð5Þ

Therefore, the approach optimizes simultaneously the plantcomponent sizes, together with plant operation management[18,19].

EPoMP, using two different optimization routines (one for eachlevel of the model at every iterative cycle), calculates the total an-nual cost changing the value of the component nominal size: inthis step virtual flows are very important to find the optimal com-ponent size, in order to determine the global minimum value of the

Table 1Capital costs for plant devices.

Device Capital cost (€)

PV panels 42,500Wind turbine 6000Adsorption chiller 40,000ICE 19,000mGT 130,000Thermal storage 34,700

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objective function. At low levels, only variable costs are optimized,reducing to zero the penalty costs associated with the virtual flowsthat would represent not satisfied constraints. At the high optimi-zation levels, the model also takes into account fixed costs, findingthe optimal size for plant components. At every optimization level,different constraints must be satisfied; if these conditions are notverified, strong penalties are applied and virtual costs associatedto virtual flows increase the objective function [17].

To build in a simple way complex plant configurations, a mod-ular visual approach has been developed by the authors (37 differ-ent modules are available at the moment), as already presented in[20]. For each component, four subroutines are developed to calcu-late (i) design and off design performance; (ii) capital costs; (iii)variable costs, and (iv) operating and maintenance costs. The cal-culation is then carried out by dividing the operational time (usu-ally a year) into a sufficient number of representative periods, onehour or less depending by the particular application.

Due to their high importance in the poly-generative smart gridunder analysis in this paper, a short description of renewable gen-erators and thermal storage models is presented.

� Renewable generator module: the innovative aspect of this mod-ule is its ability to simulate the functional behaviour and theenergy production of any kind of renewable generator, includ-ing random aspects, such as wind turbines, hydraulic plants,solar panels, etc. Thanks to its generic nature, it is possible tosimulate several plant configurations. The module needs, asinputs: (i) solar radiation and wind curves [21] in order to takeproperly into account the random character of these energyresources; (ii) nominal size of the installed renewable genera-tor; (iii) number of the modules installed in the plant; (iv) kindof the installed renewable generators. Energy production iscomputed as the product of renewable generator installedpower and the availability energy curves, varying in each per-iod, as reported in Eq. (6):

Pprod;i ¼ Pinst � ai ð6Þ

ai is strictly related to renewable sources availability curves,thus it can assume all the values between 0 and 1. As far asthe economical analysis is concerned, for any kind of renewablegenerator, specific cost functions are implemented, in order tocalculate both fixed and variable costs.It is worth noting the innovative feature of this module; in astandard prime mover (ICE, mGT, etc.) powered by fuel,working conditions are optimized at hierarchical low leveltaking into account off-design curves, implemented in themodel, and satisfying load demands (constraints of the prob-lem) in each period; on the contrary, renewable generatorsbehaviour cannot be controlled by the users, since energyproduction amounts depend only on random renewablesources (water, solar, wind) availability curves.� Thermal storage module: the calculation is carried out over a

selected period of time, in order to predict the weighted averageperformance of the plants working under variable loads. Aninnovative method has been introduced to optimize storagemanagement, associating virtual costs with the filling and emp-tying operations [22] taking carefully into account that any kindof storage system moves the model toward a strong non linear-ity. These virtual terms are implemented in order to take intoaccount the management effect of the storage on the whole sys-tem. Virtual costs give priority to the nominal working condi-tions of prime movers in order to assure a high efficiency ofthe plant and they have been set in order to promote fillingoperation, in order to consistently guarantee a sufficient tanklevel [20,22]. According to these considerations, virtual specificinput and output costs have been defined as follows:

cin ¼ �cf

LHV � grealð7Þ

cout ¼cf

LHV � gnomð8Þ

The expression of virtual costs is strictly influenced from theload storage parameter LS, defined as follows:

LS ¼ Q prod � Q req ð9Þ

If LS assumes a positive value the storage is filling, therefore vir-tual costs Zvbcoge are calculated for each period as

Zvbcogei ¼ cin;i � LSi ð10Þ

If LS assumes a negative value the storage is emptying, thus vir-tual costs associated to emptying operation must beconsidered:

Zvbcogei ¼ cout;i � LSi ð11Þ

Storage level in the subsequent period Mi+1 strongly depends onthe LS parameter and on the mass in the storage at the presentmoment Mi:

Miþ1 ¼ Mi þ3600 � LSi

cp � DTnomð12Þ

In the filling case, the model also includes a control on the over-load condition to avoid the storage level to be higher to themaximum allowed by the volume of the tank: if this case is ver-ified, strong penalties costs are applied to avoid this condition.In the emptying case, the model includes a further control onthe total emptying condition: if the thermal energy containedin the storage tank is not sufficient to satisfy the load demand,strong penalties are applied.

3.1. Thermo-economic simulation

To achieve thermo-economic optimization, EPoMP needs a largenumber of input, most of them related to the economic scenariowhere the plant is installed. The main plant data considered hereare as follow:

Capital costs of each installed device have been chosen based onlaboratory plant data [6,12]. The assumed values are reported asfollow: See Table 1.

Energy cost: electricity cost has been assumed to be equal to0.20 €/kWh; for both hot and cold thermal energy a sale rate of0.10 €/kWh has been assumed [21].

Electrical and thermal load curves: The simulation has been car-ried out on an entire year time period, considering averagemonthly values for electrical, thermal and cooling demand values.Load curves versus time represent the problem constraints to avoidpenalties; they are shown in Fig. 3 and represent typical universitycampus energy demands, as reported in [21].

Fig. 4 shows the constraints of the problem, in particular: (i)cooling demand, satisfied by adsorption chiller, which is fueledby mGT heat; (ii) thermal demand, satisfied by a storage tank,

Fig. 3. Energy load demands.

Fig. 4. Scheme of the virtual and real energy flows of the polygenerative gridinstalled at University of Genoa laboratory.

M. Rivarolo et al. / Energy Conversion and Management 65 (2013) 75–83 79

whose level depends on operation of the prime movers (QmGT andQICE); (iii) electrical demand, satisfied by the prime movers (EmGT

and EICE) and renewable generators (ESP and EWT). As shown inFig. 4, electrical demand may also be satisfied by taking electricityfrom the external electrical network (i.e. when a peak demand ishigher than maximum installed plant production capacity). In thiscase, a limit to the electricity from the external grid is consideredfor contract cost reasons, and therefore a virtual cost may be ap-plied also for this connection.

The plant analysis has been performed on an entire year timeperiod (8760 hourly periods) considering the percentage load ofthe prime movers (mGT, ICE, adsorption chiller) as decision vari-ables at model low level; renewable generators (PV panels andwind turbine) installed power and thermal storage volume havebeen assumed as decision variables at high level optimization.Renewable generators have been considered in the range between1 and 25 kW for both PV panels and wind turbine; thermal storagevolume has been considered between 1 and 100 m3.

4. Results

Through the use of the EPoMP code, optimum values of 17 kWfor PV panels installed power, 3 kW for wind turbine size, and30 m3 for storage tank volume have been obtained.

To carry out a detailed analysis of the results for the differentaspects of the grid along the year, they have been properly orga-nized in ‘‘power or size vs. time plots’’ showing the entire yearbehaviour.

In Fig. 5, the mGT, the internal combustion engine, the renew-able generators productions and the electricity taken from the gridare shown; the electrical load demand is represented by a blackline.

Specifically, mGT production satisfies the base load, ICE supplieselectricity during peak periods and at night hours as well, when thedemand is lower and mGT would work at strong off design condi-tions, where efficiency is particularly low and emissions high. Insome periods, electrical demand could be higher than maximumprime movers production, thus the system has to buy electricityfrom the external network to satisfy the load demand, previouslyshown in Fig. 3. The electrical demand trend is nearly the samethroughout the entire year, no significant differences betweenthe seasons are evident. It is worth noting that the optimizationminimizes the number of mGT start-up and shut-down, which af-fects the operating life of the engine (similarly for ICE): the cost re-lated to these operations is considered in the fuel consumptionterm, included in Eq. (1).

As far as renewable generators are concerned, their behaviour isshown in Fig. 6.

It is worth remembering that their production follows not onlynight/day variation, but it also depends on the season of the yearand is substantially ‘‘random’’, therefore it is unpredictable andnot controllable. It is also necessary to highlight the great differ-ence between PV panels (17 kW) and wind turbine (3 kW) optimalsize.

Although both of them are uncontrollable generators, PV panelsfollow the night/day insulation (i.e. easily predictable) behaviour:this feature allows a less complex matching for PV panels withmGT and ICE, compared to wind turbine. In particular, since windturbine works even during night periods, a further size increasewould result in the shut-down of the ICE during night periods, athermal power reduction and greater difficulty in satisfying ther-mal load demand in classical morning peak periods. In this case,a larger storage would be necessary and plant capital costs wouldincrease. For this main reason, the optimal size of wind turbines islower than the size of photovoltaic panels.

In Fig. 7 the mGT and the ICE thermal productions are shown;storage tank supply is also shown; thermal demand is repre-sented by black line. During the winter season thermal power

Fig. 5. Electrical power vs. time plots.

Fig. 6. Renewable generators behaviour vs. time (note: since wind energy is fully random, electricity generated by wind turbine is not repetitive for different days or monthsof the year, while PV generation is mainly related to day and night solar insulation with possible cloud effects considered in the model).

80 M. Rivarolo et al. / Energy Conversion and Management 65 (2013) 75–83

production (cogeneration effect) exceeds the demand at midday,when a peak of electrical demand is present, and in the late after-noon. Since the prime movers are co-generative, surplus heat pro-duced is used to fill the storage tank. Likewise, during nighthours, since ICE works to cover electrical demand, its thermalpower production, which exceeds the demand, is sent to the stor-age. As Fig. 7 shows, the storage tank operates to cover thermalload in the early morning, when thermal demand presents a peakand the prime movers are not sufficient to satisfy the thermal de-mand, and in the afternoon, when electrical demand gets lowerand co-generative prime movers are off (in the case of MCI) orwork at strong part load (mGT). In the other seasons, in particularin summer, thermal demand gets low: as consequence, a highersurplus thermal power amount is present, a fact that could bringstrong economical penalties due to storage tank overfilling. Sincehot and cooling thermal demands are complementary (see Fig. 3),a significant part of the thermal power surplus generated by mGTis used by adsorption chiller (see Fig. 4) in the summer, supplyingthe cooling demand and avoiding thermal storage overfilling.Thermal power used by chiller is represented in dashed lined yel-low columns in Fig. 7.

Cooling thermal demand is supplied by the adsorption chillerwhich is powered directly by mGT. In the case under investigation,cooling power demand is zero and the adsorption chiller does notwork during the winter. It is worth noting (see Fig. 3) that coolingpower load demand is practically complementary to thermal loaddemand; it is the highest in summer (when thermal load demandis the lowest) and zeros out in winter (when thermal load is thehighest). Thus, the surplus thermal power produced by mGT insummer time, that would not be necessary in the storage tank,finds an application in the adsorption chiller, allowing coolingpower production without any additional fuel cost.

Storage tank behaviour during the year is shown in Fig. 8 wherestorage tank level vs. time for each season is reported. The poly-generation plant with renewable generators (continuous line) re-sults are compared to the only fossil configuration (dashed line),investigated in a previous work [21], considering the same loadcurves shown in Fig. 3.

Without renewable generators, electrical energy is produced bytraditional prime movers only (mGT and MCI). Due to their co-gen-erative nature, all the heat produced is sent to storage tank, with-out any dissipation. Thus, as Fig. 8 shows, tank level gets higher

Fig. 7. Thermal power vs. time plots.

Fig. 8. Storage tank level vs. time plots.

M. Rivarolo et al. / Energy Conversion and Management 65 (2013) 75–83 81

and the minimum volume to avoid overfilling penalties is 45 m3.Since renewable generators produce only electrical energy, theirintegration in the poly-generation system implies lower co-gener-ative device utilization, therefore a lower thermal storage maxi-mum filling of 30,000 kg, as Fig. 8 shows: storage tank optimaldimension is reduced, allowing a significant decrease in terms ofvolume and capital costs.

Analyzing the whole grid operating period, it is worth notingthat starting level and final level are the same. This result proveshow prime movers operation, renewable generators size and en-ergy load demands are perfectly balanced. Storage tank levels gethigher in summer, when the demand for heat is low, while it getsempty in winter, when the demand for heat is higher.

Fig. 9 compares economic results for the poly-generative sys-tem plant lay-out, considering two different cases: (a) withoutany renewable production (configuration A); (b) including 17 kWphotovoltaic panels and 3 kW wind turbine installation (configura-tion B). For both cases, annual cash flows are reported, including

revenues and costs: revenues (on the left) are represented by elec-trical, hot and cooling thermal energy selling, costs are composedof the depreciation rate, gas consumption and electricity purchasedfrom external network.

It is worth noting that installation of renewable generators(configuration B) implies increasing revenues; moreover, it has pri-mary effects on the whole thermo-economic annual results:

(a) Electrical energy increase, since new configuration includes17 kWe solar panels and 3 kWe, installed power increasesfrom 120 kW to 140 kW, thus during peak hours electricitypurchased from the external grid is reduced. Since renew-able generators are non controllable, higher values for theirsizes (i.e. 20 kW solar panels, 5 kW wind turbine) would notallow the problems constraints and the capital and variablecosts increase largely;

(b) Fuel consumption decrease, since prime movers average utili-zation is reduced;

Fig. 9. Poly-generation grid annual cash flows (revenues and costs): configuration A includes only fossil systems; configuration B also includes RES.

82 M. Rivarolo et al. / Energy Conversion and Management 65 (2013) 75–83

(c) Depreciation rate increase, since capital costs are higher. Tosum up, total annual costs are nearly constant, since effects(b) and (c) balance each other; on the other hand, revenuesget higher since electrical energy increases, thus introducingthe renewable generators is significant from a thermo-eco-nomic point of view. Moreover, annual fuel consumption isreduced by 13.5 tons: since specific methane emissions are2.75 kg CO2/kg CH4, about 37 tons/year of CO2 can beavoided thanks to renewable generators production.

5. Conclusions

In this paper, the influence of renewable non-controllablesources on thermo-economic performance of a poly-generationsmart grid, similar to the one installed in the laboratory of the Uni-versity of Genoa [6], has been investigated.

The analysis has been carried out using a software for poly-gen-erative system optimization, named EPoMP, developed by theauthors [17,20], to find out the optimal management and size forboth renewable generators and hot storage system.

The results allow the following main conclusions to be carriedout:

� Two different renewable non-controllable generators have beenconsidered, namely photovoltaic panels and wind turbines.Although both of them are random generators, PV panels followat least the alternation night/day, a feature which allows a bet-ter matching with prime movers compared to wind turbine (forwind energy the random grade is higher). For this reason, theoptimum result is higher for PV panels (17 kW) than for windturbine (3 kW).� Since renewable generators considered here produce only elec-

trical energy, optimal size has been optimized by also takinginto account that the poly-generative system must satisfythermal and cooling demands throughout the year too. Sincethey are non controllable, higher renewable sizes (i.e. 20 kWsolar panels, 5 kW wind turbine) would not allow the prob-lems constraints and the capital and variable costs increaselargely.� Renewable generator utilization influences the storage system

optimal size too; since co-generative prime movers workingtime and load (they operate largely at part load) is reduceddue to RES generators, thermal energy production is lowerand storage optimal volume decreases (in this case from 45 to30 m3) allowing a reduction in storage tank capital costs too.� The optimized system integrated with non-controllable renew-

able generators has been compared with the same poly-gener-

ative plant without RES installed; the main result is thatoptimizing solar panels, wind turbine sizes and system manage-ment allows an increasing of annual revenues, while annualcosts are nearly constant since capital costs increase, but vari-able costs reduce.

It is worth noting that the model developed here can be appliedto any poly-generative plant including any kind of renewable gen-erator. Moreover, the presented results have a generalized value,since the method takes into account the type and size of the primemovers, the energy load profiles, the plant location, and the eco-nomic scenario.

Acknowledgments

This work has been partially supported through the EU-FP7European Project E-HUB, Grant Agreement No. 260165.

The authors wish to thank the colleagues at TPG working on thegrid design and installation Mario Ferrari, Matteo Pascenti, AlbertoNicola Traverso, Loredana Magistri, Alberto Traverso and FrancescoCaratozzolo for their help in the design and modelling of the differ-ent parts of the grid including the hybrid System Emulator.

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