Optimization of a distributed trigeneration system with heating micro-grids for an industrial area

Transcription

1 2 nd Eropean Conference on Polygeneration 3 th March-1 st April, 211 Tarragona, Spain Maro Reini, Dario Boro, Cladio Covassin, Alberto De Nardi, Piero Pinamonti Optimization of a distribted trigeneration system with heating micro-grids for an indstrial area Optimization of a distribted trigeneration system with heating micro-grids for an indstrial area Maro Reini 1, Dario Boro 2, Cladio Covassin 1, Alberto De Nardi 1, Piero Pinamonti 2 1 Department of Mechanical and Naval Engineering, University of Trieste, via Valerio 8, Trieste, Italy 2 Energy and Trbomachinery Department, University of Udine, via delle Scienze 28, 331 Udine, Italy Abstract In the paper an optimization stdy of a distribted trigeneration system for an indstrial area is presented. The energy sers located in the area are connected by existent district heating (DH) micro-grids, than the reqired heat can be prodced by small scale CHP systems (e.g. micro gas trbines or internal combstion engine) or by a bigger and centralized CHP plant. Conventional integration boilers also can be installed inside the factories or in a centralized plant. The trigeneration system incldes a set of absorption chillers, powered by cogenerated heat, sed to prodce cooling energy in sbstittion of conventional vapor compression chillers. The optimisation has to determine the optimal strctre of the system, the size and the load of each component inside the optimal soltion, taking into accont also the thermal inertia of the DH network. The optimization is based on a Mixed Integer Linear Programming (MILP) model and it takes into accont as objective fnction the total annal cost for prchasing, maintaining and operating the whole trigeneration system. The model allows to generate different optimal soltions by varying the bondary economic conditions (amortization period of the eqipment, its capital cost, etc.), simlating different possible scenarios and estimating the possible energetic and economic savings. Keywords Optimization, Trigeneration system, District heating, Mixed Integer Linear Programming. 1 Introdction Distribted cogeneration (CHP) and trigeneration (CHCP) systems allow achieving economic and energetic savings, both in residential and indstrial sectors. Especially considering a set of indstrial sers, characterized by qite constant and high energy consmptions all year long, the adoption of sch a soltion can lead to increase the whole energy efficiency of the system (tilizing heat that otherwise wold be wasted) and ths to redce cost, primary energy tilization and pollting emissions. However, the expected performances cold not be obtained withot adopting the configration and the operation strategy reslting from an optimization procedre of the whole system [1-5]. The stdy presents the optimization of a distribted CHCP system, designed to spply thermal, cooling and electrical energy to six facilities located in an indstrial area in the north east of Italy. The layot and size of the network is predefined and the demands for electrical energy, cold water and steam are known in advance as well. All sers are connected each other throgh a district heating micro-grid, therefore the related prodction nits cold send heat to the DH (district heating) network, while only the prodction nits related to sers reqiring cooling power cold be eqipped with absorption chillers, driven by cogenerated heat. Heat and electric power cold be provided either by a big centralized CHP plant (internal combstion engine Corresponding athor: Maro Reini, reini@nits.it

2 2 nd Eropean Conference on Polygeneration 3 th March - 1 st April 211 Tarragona, Spain ICE) or by small-scale CHP systems (ICE or micro gas trbines MTG), properly located close to, or inside, the factories. Conventional integration boilers and vapor compression chillers can also be installed inside the factories or in the centralized plant, and moreover each nit is connected to the electricity network. Ths, a centralization-decentralization problem arises: if the heat wold be prodce and exploit locally, investments may avoid in pipelines, bt, on the other hand, a single centralized energy conversion plant may entail (thank to scale economies) a smaller investment than many small decentralized conversion nits of comparable total capacity [6]. The optimal soltion is a compromise that depends on many variables; it is so very difficlt to find the best soltion withot solving an optimization problem. A problem nder similar conditions was handled by Sakawa et al. [7] and other literatre is available [8-11] dealing with the optimal design of district heating systems. However, these models generally consider residential sers, rather than indstrial ones. In [12] an example of optimisation models for indstrial district heating networks is developed. In previos works of the athors Mixed Integer Linear Program (MILP) models have been developed to optimize the design and operation of CHCP distribted generation systems in a tertiary sector scenario, considering different technologies and taking into accont the effects of varios economic spport policies [13-16]. In this stdy, the thermal inertia of the district heating network is also evalated now, applying the model to an indstrial scenario. The defined eqations are similar to those sed for describing the presence of a thermal storage [17-21], with the difference that thermal inertia can not be regarded as an option, in the optimal strategy definition, while the sage of the storage can be. The dynamic of the DH network cold affect the operation of the whole heating system. This is de to the time delays in the transportation of the heat from the prodction plant to the consmers, to the heat temporary stored in the pipes and to the heat losses. The transportation time varies for the individal ser according to the distance from the prodction plant and to the flow velocity in the pipes. To find the best operation of the system, it is therefore necessary to have an appropriate simlation model of the available district heating [22]. The model sed to solve the optimization problem is based on a Mixed Integer Linear Program (MILP) and its aim is to determine which is the best configration and operation in terms of both economical and environmental benefits. The objective fnction takes into accont the total annal cost for prchasing, maintaining and operating the whole trigeneration system. The optimization is sbjected to the constraints that express components operation, the energy balances of nodes, and to the economic bondary conditions (e.g. incomes from the sale of electricity, prices of fel and electricity, etc.). The optimization specifies the size, the kind and the location of cogeneration eqipments, absorption machines, integration boilers and compression chillers present in the sperstrctre, as well as the optimal operation of each component inside the optimal soltion. The conventional soltion can otherwise be adopted: all the electricity wold be boght from the grid, the thermal energy wold be prodced by boilers and the cooling energy by compression chillers, driven by electricity boght from the grid. 2 The case stdy The six sers considered in the stdy belong to different economic sectors, like food, frnitre, engineering and tertiary. Despite their prodction type is not homogeneos each of them is characterized by qite reglar energy demands along the year, that can be known in advance. As ser 1 reqires all the three kind of energy vectors (electrical, thermal and cooling power), its case is considered as a valid example to represent the energetic consmptions of a typical food company. It needs cooling energy at a very low temperatre in order to keep the food refrigerated (-25 C). figre 1, figre 2 and figre 3 represent its annal electrical, thermal and cooling consmption respectively, while the figre 4 shows the three cmlative energetic crves. 2

3 2 nd Eropean Conference on Polygeneration 3 th March - 1 st April 211 Tarragona, Spain User 1 electrical consmption kw hors Figre 1: User 1 electrical consmption User 1 thermal consmption kw hors Figre 2: User 1 thermal consmption 1 User 1 cooling consmption 1 User 1 energetic loads kw hors 8 6 kw hors Thermal load Cooling load Electricla load Figre 3: User 1 cooling consmption Figre 4: User 1 energetic loads It can be noted from figre 2 that the thermal load is higher dring coldest months, when heating is operating, while dring the remaining months only process heat is reqired. Figre 3 shows that cooling demand is higher than zero all year long (food mst always be kept cooled) and that the consmption is highest dring hottest months (smmer time). It is possible to see (figre 4) that electrical demand is constant for at least 4, hors a year. This is de to the constant load dring night. Taking into accont all the six sers aggregated demands, their electrical, thermal and cooling consmption profiles and the cmlative energetic crves are shown below (figre 5, figre 6, figre 7 and figre 8). Looking at the thermal trend of figre 6 it can be noted that process heat is needed dring central months too. Figre 7 represents the sm of the annal cooling consmptions of sers 1 and 2, as the other sers have not cooling demand. The electric load crve of figre 8 does not inclde the electricity needed to power the chillers. Total electrical consmption kw hors Total thermal consmption kw hors Figre 5: Total electrical consmption Figre 6: Total thermal consmption 3

4 2 nd Eropean Conference on Polygeneration 3 th March - 1 st April 211 Tarragona, Spain Total cooling consmption kw hors Figre 7: Total cooling consmption kw Total energetic loads Thermal load Cooling load Electrical load hors Figre 8: Total energetic loads Table 1: User energetic demands ELECTRIC HEATING COOLING Peak power [kw el ] Year dem. [MWh e ] Peak power [kw th ] Year dem. [MWh th ] Peak power [kw c ] Year dem. [MWh c ] User User User User User User Total Table 1 shows the pick power and the yearly energetic demand for each ser. Total pick power is the maximm horly energy demand of the all six sers, and it is lower than the sm of the single ser picks. In order to redce the variables nmber and the model complexity, it has been decided to represent the whole year by twelve typical weeks (1 week per month), each composed by seven days of 24 hors. This kind of discretisation allows keeping a realistic pictre of the actal annal behavior and also allows the thermal inertia of the network prodcing its effect on the optimal operation. Table 2: Component size and size limits COGENERATOR TYPES AND SIZES BOILER SIZES ABS./COMP. CHILLER SIZES Type Min kw Max kw Min kw Max kw kw Central Unit ICE Unit 1 TG Unit 2 ICE Unit 3 MTG Unit 4 MTG Unit 5 MTG Unit 6 MTG A preliminary analysis of the ser reqirements, shown in Table 1, have led to Table 2, that shows the minimm and maximm sizes considered in the optimization procedre for the machines that cold be installed. The table shows the same vale for minimm and maximm when the size is fixed in advance. The evalation of the system operative cost generally needs the horly costs of the energetic vectors to be defined (gas and electric energy) as both inpt and otpt. The model is applied to 4

5 2 nd Eropean Conference on Polygeneration 3 th March - 1 st April 211 Tarragona, Spain sers located in the north-east of Italy and the price of boght and sold electric energy has been assmed constant (in previos works [13-16] the horly variation of price did not affect the optimal soltion, if a mean vale had been assmed). This choice is consistent with the real sitation where the energy market determines the energy prices, withot being affected by individal market operators. Moreover, according to Italian legislation, different vales of gas price have been assmed for spplying micro-gas trbines and boilers, becase of the different taxation level between cogeneration gas and gas for heating prpose, in the tertiary sector. Table 3 shows the energy prices sed in the application. Component prices have been considered constant, or linear vs. their size [6], in both cases cost coefficients are shown in Table 4. In the stdy, 2 years have been considered as life span for absorption machines, 15 years for cogenerators and boilers and 1 years for compression chillers. Table 3: Energy prices [ /kwh] Electricity prchased Electricity sold CHP gas Boiler gas,15,12,45,59 Table 4: Component cost Unit COGENERATOR BOILER ABS. CH. COMP. CH. Fix. cost [ ] Var. Cost [ /kw el ] Fix. cost [ ] Var. Cost [ /kw el ] Fix. cost [ ] Fix. cost [ ] Central , , , , , , , The sperstrctre As mentioned in the introdction, the six facilities involved in the stdy are spposed to be connected by an already existing heating network, and their energy demands are known in advance. They all can transfer heat to and from the network, if some constraints are respected, as well as exchange electricity with the electric grid. Figre 9 shows the sperstrctre, where all possible considered options are inclded. As it can be seen, in the centralized nit (nit ) a CHP system and a boiler can be adopted. Unit 1 can incorporate a CHP system directly connected with an absorption chiller, which cannot be driven by heat from the network de to the different temperatre levels, a boiler and a compression chiller. User 2 does not reqire heating energy, so that a boiler has not been inclded in the sperstrctre. In this nit a compression chiller and an absorption chiller, which can be powered either by cogenerated heat or by heat from the network, are enclosed. The remaining prodction nits have the same sperstrctre and they inclde only a CHP system and a boiler becase they do not reqire cooling energy. In those nits the sperstrctre is eqivalent, bt the components can have different sizes, as it can be seen in Table 2. 4 The MILP model Recently a lot of research works have been carried ot to optimize the design and operation of distribted cogeneration and trigeneration energy systems [23-25] integrated also with the district heating network [1, 5, 6, 21]. In a distribted generation context, the optimal soltion depends on the trade-off between the scale economies, which can play an important role in centralization option, and the additional costs of eqipment replication, connected to decentralized soltions. A MILP model has been sed for properly describing by means of binary variables the choice of centralized/decentralized components inside the sperstrctre, as well as the on/off operation of chosen components, in the optimal operation strategy. 5

6 2 nd Eropean Conference on Polygeneration 3 th March - 1 st April 211 Tarragona, Spain Figre 9: The sperstrctre The mathematical problem of optimizing the operation of a CHCP plant has to be generally regarded as a variational calcls problem, becase the optimization variables expressing partial load operation of each component are time dependent. However, a realistic description of the system may be represented by a MILP formlation by properly discretizing the load crves and approximating performance maps with a set of linear fnctions. In this work, the problem is regarded as a qasi-stationary one and a set of discrete time intervals of one hor describe the whole year. Previos works [13-16] have examined the optimization of both prodction nits and district heating networks, withot taking into accont their thermal inertia. In this paper, the network is assmed as already present, while the prodction nits are optimized considering also the thermal inertia of the pipes. This allows nderstanding if it plays an important role in the nit optimization or if it cold be neglected withot significantly affecting the optimal soltion. In the proposed model, different type of prodction nits have been introdced assming different kinds of internal sperstrctres (see Figre 9); it cold be easily generalized to varios indstrial areas, or to other kind of energy ser network. Model Constraints In the MILP optimization procedre, three main different types of constraints can be identified: Components constraints: relate otpt and inpt energy of each component; Energy balances: ensre that the amont of inpt energy is eqal to the otpt, for each time interval and for each node; Network constraints: relate thermal losses, thermal contribtions from the nits and thermal energy delivered to the sers, taking into accont also the thermal inertia. Component constraints In this paper the components (cogenerators, boilers, absorption machine and compression chillers) are of two kinds: components where the size is fixed and components where it is not. For the first set of components, a binary decision variable is introdced to express the existence, 6

7 2 nd Eropean Conference on Polygeneration 3 th March - 1 st April 211 Tarragona, Spain a binary and a continos variable, for each time interval, are introdced to express respectively the on/off stats of the component and the load level. In the following eqations, the decision variables are typed in bold, index h represent time interval, and index the energy nit associated to a ser, inside the sperstrctre. The other coefficient typed in italic, derived from a linear regression of the machine performance crves. The cogenerators with fixed size can be modelled as: Hcog = p Ecog + q opcog (1) Fcog = r Ecog + s opcog (2) Ecog opcog Ecog Ecog opcog (3) opcog h, excog (4) The absorption machines can be modelled as: Habs = a Cabs + b opabs (5) Cabs op_abs Cabs Cabs opabs (6) opabs h, exabs (7) The compression chillers can be modelled as: Ech = c Cch + d opch (8) Cch opch Cch Cch opch (9) opch h, exch (1) Eqations 1, 2, 5 and 8 relate the main energy prodct of the component with its inpt consmption and sbprodct, eqations 3, 6 and 9 determine the lower and pper load limits while the eqations 4, 7 and 1 state that the relate component can be trned on only if it is present in the sperstrctre. If the size is not known in advance, a binary variable represents the existence of the component; a continos variable represents the size, whereas a binary and a continos variable, for each time interval, represent the on/off stats and the load level respectively. Another axiliary continos variable has to be introdced to make the model linear, for each time interval. The cogenerators can be modelled as: Hcog = e Ecog + f o pcog + g δ (11) Fcog Ecog I = l Ecog + m opcog + n δ (12) II I opcog + Ecog δ Ecog Ecog opcog + Ecog δ (13) ( opcog ) δh scog scog +, (14) scog 1 scog opcog δ scog opcog (15) scog excog scog scog excog (16) opcog h, excog (17) The boiler can be modelled as: Fboi = j Hboi + k opboi + w γ (18) Hboi I II I opboi + Hboi γ Hboi Hboi opboi + Hboi γ (19) ( opboi ) γ h sboi sboi +, (2) sboi 1 sboi opboi γ sboi opboi (21) sboi exboi sboi sboi exboi (22) opboi, exboi (23) h II II 7

8 2 nd Eropean Conference on Polygeneration 3 th March - 1 st April 211 Tarragona, Spain Taking into accont that the size is a decision variable, some more constraints have to be introdced with respect to the modelisation presented before. Eqations 15, 16, 21 and 22 are needed to express the size variation options, keeping the model linear; they also express the lower and pper limits for the size of each component. Energy balance constraints Ecog + Eby Edem Ech Esel (24) Hcog h, = h, + + Hin Habs Hwas Hdem = h, + Cch Cdem Cwas = Hboi (25) Cabs (26) In eqation 25 Hin expresses heat sent to other sers throgh the network. It is negative when the ser receives energy from the heating network. Network constraints Following constrains represents the network behavior, taking into accont the energy stored (eq. 27), the energy losses throgh pipelines (eq. 28), the energy balance (eq. 29) and other constraints (eq. 3, 31) assring that heat can be sent to the ser only if the temperatre of the water inside the network is greater than a minimm level depending on the ser type. 2 π d Qgridh = l ρ cp ( t h t h 1 ) (27) 4 Qwash = k ( t t tgrond) (28) Hin Qgrid h Qwash = (29) Hin H max λ (3) t h t min λ (31) Objective Fnction The Objective Fnction represents the total annal cost (eq.35) and incldes investment costs of components (eq.32), prchasing electricity cost, income from the sale of electricity, cost of fel sed in cogenerators and boilers (eq. 33), and machine maintenance costs (eq. 34). invcost + Coabs = Ccog exabs I excog + Coch + Ccog exch II scog + Cboi 8 I exboi + Cboi II sboi ( Cby + Cgcog Fcog + Cgboi Fboi Csel Esel ) ( Mcog + Mboi Hboi + Mabs Cabs + Mch Cch ) opcos t = Eby (33) mcos t = + (32) Ecog (34) Fobj = opcos t + mcos t + invcos t (35) This objective fnction is linear with respect to independent variables described before and it has to be optimized sbjected to constraints expressed in eqations The existence and the on/off stats of each component have been described in the model by means of binary variables. The existence variables are generally decision variables dring the optimization process, bt can also be set by the analyst to enable or to force the choice of some components. For example, when determining the optimal soltion of conventional energy spply system, consisting of boilers and refrigerators, the integer variables corresponding to cogenerators and absorption machines are set to zero. 5 Reslts The optimization problem has been solved in five different scenarios; the reslts, presented in table 5, are compared with the case of conventional energy spply. The six sitations are: Case, conventional energy spply;

9 2 nd Eropean Conference on Polygeneration 3 th March - 1 st April 211 Tarragona, Spain Case 1, global optimal soltion; Case 2, optimal soltion forcing the existence of the cogenerator in the central nit; Case 3, optimal soltion with a redced life span for all components (15 years for absorption machines, 1 for cogenerators and boilers and 7 for compression chillers); in this case the relative weight of capital cost increases in the Objective Fnction; Case 4, optimal soltion if the costs of gas and electricity were higher of 25%, decreasing the relative weight of capital cost in the Objective Fnction; Case 5, optimal soltion if absorption chillers can not be installed. Table 5: Optimization reslts Case Case 1 Case 2 Case 3 Case 4 Case 5 Cogenerators [kw] Central Unit Unit Unit Unit Unit Unit Unit Boilers [kw] Central Unit Unit Unit Unit Unit Unit Unit Absorption chillers [kw] - Unit Unit Compression Chillers [kw] Unit Unit Total cogenerated electricity [MWh] Total cogenerated heating [MWh] Total dissipated heating [MWh] ~ ~ Total investment cost [k ] Annal investment cost [k /y] Prchased electricity cost [k /y] Sold electricity income [k /y] Cost of natral gas [k /y] Maintenance cost [k /y] Operating cost [k /y] Objective fnction [k /y] % with respect to traditional case - -13,65% -12,77% -11,19% -17,58% -6,55% PBP [years] - 5,38 6,34 6,89 3,49 1,36 TEP CO2 Emission PES - -41,21% -52,32% -4,89% -41,27% 12,57% The optimal soltions obtained in cases 1 to 4 allow the achievement of economical savings, while the CO 2 emissions increase by abot 4-5%. This is de to the low EERs of the absorption chillers, especially when low temperatre cooling vector is reqired. The PES for a 9

10 2 nd Eropean Conference on Polygeneration 3 th March - 1 st April 211 Tarragona, Spain simple trigeneration system obtained varying the ratio α r (between the heat directly tilised by the sers and the total cogenerated heat) can be lower than zero, if the greatest part of the cogenerated heat is sent to the absorption machines (figre 1). Fcog Hcog Habs PES = 1 (36) ; α r = (37) 1 Cabs Hcog Habs Hcog Ecog + η COP η el t 6 Conclsions Figre 1: Primary Energy Savings vs. α r The model sed to optimise the problem dealing with an indstrial distribted trigeneration system is based on a Mixed Integer Linear Program and it helps to determine the best system configration and operation in economical terms. Environmental benefits can also be evalated after having determined the optimal soltion. Looking at the reslts presented in table 5, it can be noted that optimal soltions generally inclde both distribted cogenerators and absorption machines, as they allow redcing the total annal cost. Case 1: comparing it with traditional case, for CHP machines and an absorption chiller are installed, while only two boilers are inclded in the optimal soltion. This global optimal soltion does not inclde the central CHP nit, ths it reveals that in the specific application the decentralised soltion is economically more convenient than the centralised one. Case 2: forcing the existence of the central CHP nit, the objective fnction does not change significantly, bt the pay back period increases. Case 3: diminishing machines life span, the optimal strctre does not change compared to case 1, except for the addition of some boilers. As the relative weight of investment costs increases in the optimal soltion and the operation costs are almost the same, economic saving is lower. Case 4: in a ftre scenario the primary energy costs are expected to increase; the optimal strctre does not change with respect to the one obtained in case 1, bt the reslts show that the economical savings are even higher compared to the conventional energy spply. Therefore the pay back period of the total investment is shorter. Case 5: disabling the installation of absorption machines the optimal soltion brings to lower economical savings with respect to the previos cases, bt CO 2 emissions are redced compared to the conventional energy spply, de to the low EERs of the absorption chillers, especially when low temperatre cooling vector is reqired. Moreover the pay back period is lower than 2 years. Integration throgh district heating micro-grids of varios indstrial factories, located in the same area, allows a rational tilization of available heat, so that some sers can be satisfied only by the recovered heat from other prodction nits. The effect of the thermal inertia of the grid has shown a negligible effect on the optimal strctre, bt has modified the optimal operation, therefore the objective fnction reslt worse by abot 2%. 1

11 2 nd Eropean Conference on Polygeneration 3 th March - 1 st April 211 Tarragona, Spain Nomenclatre ABS Absorption machine Habs Heat reqired by ABS [kwh] BOI Boiler Hboi Heat prodced by BOI [kwh] Cabs Cooling prodced by ABS [kwh] Hboi, Hboi BOI load limits [kwh] Cabs, Cabs ABS load limits [kwh] Hcog Cogenerated heat [kwh] Cboi', Cboi'' BOI cost [, /kwh] Hdem Heat demand [kwh] Cby Cost of prchased electricity [ /kwh] Hin Cch Cooling prodced by CH [kwh] Hmax Heat from DH network to the ser [kwh] Maximm heat transferred from the DH to the ser [kwh] Cc Cch CH load limits [kwh] Hwas Heat wasted[kwh] Ccog', Ccog'' CHO cost [, /kwh] invcost Investment cost [ /year] Cdem Cooling energy demand [kwh] l Length of the DH [m] Cgboi Cost of fel sed in BOI [ /kwh] Mabs ABS maintenance cost [ /kwh] Cgcog Cost of fel sed in CHP [ /kwh] Mboi BOI maintenance cost [ /kwh] CH Compression chiller Mch CH maintenance cost [ /kwh] CHCP Cogenerated heat, cooling and power Mcog CHP maintenance cost [ /kwh] CHP Cogenerated heat and power mcost Maintenance cost [ /year] Coabs ABS cost [ ] opabs ABS stats Coch CH cost [ ] opch COMP stats cp Water specific heat [kj/kg] opcog Cogenerator stats Csel Price of sold electricity [ /kwh] opcost Operation cost [ /year] Cwas Cooling energy wasted [kwh] PES Primary energy saving d Diameter of the DH [m] Qgrid Heat stored in the DH [kwh] DH District heating network Qwas Heat wasted [kwh] Eby Prchased electricity [kwh] sboi BOI size [kw] Ech Electricity reqired by CH [kwh] sboi, sboi BOI size limits [kw] Ecog Electricity prodced by CHP [kwh] scog CHP size [kw] Ecog, Ecog CHP load limits [kwh] scog, scog CHP size limits [kw] Edem Electricity demand [kwh] t Temperatre [ C] Esel Sold electricity [kwh] tgrond Grond temperatre [ C] exabs ABS existence tmin Min. temperatre for receiving heat from the DH [ C] exboi BOI existence γ Additional decision variable exch CH existence δ Additional decision variable excog CHP existence ηel Power generation mean electric efficiency Fboi Fel reqired by BOI [kwh] ηt Thermal plants mean efficiency Fcog Fel reqired by CHP [kwh] λ Additional decision variable Fobj Objective fnction (annal cost) [ ] ρ Water density [kg/m 3 ] All other symbols not reported here are linearization coefficients coming from linear regressions of the eqations. References [1] Crti V., von Spakovsky M. R., Favrat D., 2, An environomic approach for the modeling and optimization of a district heating network based on centralized and decentralized heat pmps, cogeneration and/or gas frnace. Part II: Application, International Jornal of Thermal Sciences, Vol 39, No 7, pp [2] Aringhieri R., Malcelli F., 23, Optimal operation management and network planning of a district heating system with a combined heat and power plant, Annals operation researc Vol 12, pp [3] Lazzarin R., Noro M., 26, Local or district heating by natral gas: Which is better from energetic, environmental and economic point of views?, Applied Thermal Engineering, Vol 26, No 2-3, pp [4] Heffed A. K., Mago P. J., Chamra L. M., 29, Effect of the power generation nit operation on the energy, economical, and environmental performance of CCHP systems for a small commercial bilding, Proceedings of AMSE/IMECE 29, November 13-19, 29, Lake Bena Vista, Florida, USA. 11

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