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1 URBAN ENERGY SUPPLY CHAIN A DISTRICT HEATING CASE Dias, Ana Carvalho Instituto Suerior Técnico, Lisoa, Portugal Astract Energy has ecome one of the most crucial rolems in the modern society which must e studied and solved. In this aer, we resent a model that otimizes an uran energy suly chain. This aer will not focus on a secific area of the suly chain such as roduction, distriution or storage ut aims to develo uantitative tools that can suort strategic decisions in heating suly chain design and oeration. The suggested mathematical model delineates the otimal configuration of a heating suly chain to fulfil the demand within one region (e. g. city). The decisions to e determined, y this model, were: the location, numer and caacity of the oilers to e installed; the reuired roduction of each oiler and the network configuration (location of ielines); flow rate of energy throughout the network and its direction as well as the total cost of the heating suly chain network. Moreover, the develoed model is mainly driven y heating demand, which is assumed to e reviously known. Illustrative examles were solved. Keywords: otimisation model, natural gas, uran energy suly chain, design, consumtion.. Introduction The energy suly chain otimisation rolem is aout determining the est solution for the design of this chain, trying to otain the most economical solution. Due to the threat of a disrutive climate change, the erosion of energy security and the growing energy needs of the develoing world, the energy suly chain rolem has ecome one of the most crucial rolems which must e studied and solved. It is imortant to adot new high efficient energy technologies and methods of sulying such energy. That otimisation will affect several asects like roduction and transort facilities. Heat sulies are related with the eriods of the day, tyes of consumers and also heat roduction and losses. On the tye of rolem in study several works have een ulished. Sugihara, Komoto and Tsuji roose a new model for determining uran energy systems in a secific area. It shows how imortant it is to adot new highly efficient energy technologies. This model considers 7 customers tyes searated in sectors: the residential sector is searated from the usiness and commercial sector, and different sets of energy system alternatives are designed for each sector. It takes into account District Heating and Cooling (DHC) system as a centralized-tye energy system. Three indices are evaluated, cost, CO emission and rimary energy consumtion and this model determines not only the caacity and oerational strategy of DHC, ut also the sharing of each energy as a system alternative. Soderman & Pettersson formulated a rolem with the aim of reducing the total cost of a distriuted energy system (DES), considering the roduction and consumtion of electrical ower and heat, ower transmissions, transort of fuel to the roduction lants, transort of water in the DH ielines and storage of heat. Çomaklı, Yüksel and Çomaklı study the energy and exergy losses occurring in the DH network system. It is a useful work due to the emhasis it gives to losses during heat distriution and the energy alance analysed on the ieline network. Some studies, like Dzenajavičienė, Kveselis, McNaught, and Tamonis remind the imortance of the economic situation on a articular area or city, existing heatgenerating sources, and the state of the heat suly and distriution ielines, fuel rices and many other factors. It is necessary to evaluate this item if some changes are eing lanned to occur. Related to economic asects is the total costs ortion that is the aim of several rojects. Morais & Marangon Lima is a good examle of it. This works gives imortance to transmission fare, lant Page

2 investment and fuel cost. The last one can e slit into two arts: the roduction and the transortation costs. Some methodologies for charging gas ieline and transmission network are roosed: MW-mile, gas-mile, invested related asset cost and the Aumman-Shaley (AS) Method. In Ajah, et al. the costs are analysed in a different way and divided into four categories. The urchase cost of the system comonents, the construction cost of the system, the installation cost and the oeration and maintenance cost. To conclude cost can e analysed in different ways, ut it should include as many comonents as ossile to make a realistic model. Any energy model is a simlified reresentation of the real system, so it is necessary to consider all the ossile arts to otain good results. In this aer a model is develoed to define the otimal configuration of a heating suly chain that fulfils the demand within a defined region (e.g. city). The heat demand is assumed to e reviously defined and reresentative of a real case. In this case the chosen fuel to roduce the reuired heat for the city is natural gas, ut it could e roduced from a variety of feedstock, like coil or oil at a wide range of sizes from country scale to household scale. For a etter aroximation of a real city different oulations distriution were used and analysed. The aim is to minimize the total cost of the network with the guarantee of satisfying all the customers heat demand. Costs associated with the heat roduction source and osition, and distriution network are the main asects that influence the final solution. The energy suly chain network configuration is reresented y a mathematical model which is formulated as a mixed-integer linear rogramming (MILP) model. The aer is organized as follows. Section resents a descrition of the roosed MILP model. Some single scale examles are exlained in Section. Section 4 includes an illustrative examle of a multiscale methodology. The influence of caital and oerational costs is descried in Section 5. Finally, conclusions and further research directions are resented in Section 6.. Concetual Model The network is descried as a static MILP model, which will e used to investigate a numer of strategic decisions. For the roduction facilities, the decisions are aout the numer of oilers to satisfy the total demand, the geograhic location, caacity and amount of heat to roduce in each oiler. The distriution system also involves decisions like the definition of the reuired ielines and the way they are distriuted in the system. Another imortant decision is to uantify the heat that is necessary to transort from one cell to another in order to satisfy the demand. The city will e divided into cells, which can e defined as internal or external cells. Each cell can exort or imort heat. It should e always resent that customers demand must e fulfilled in each cell of the city, even if it reresents an increase in costs. The roosed network consists of a set of roduction facilities and the distriution system associated. The construction of this network will e driven y heating demand. The mathematical formulation is comosed y the nomenclature, constraints and ojective function terms. Indices, arameters and decision variales are included in the nomenclature. The variales are further categorised into: continuous, integer and inary design variales.. Nomenclature Indices / grid osition/cell oiler tye d eriods of the day t tyes of consumers n average distance constraint index Sets = {, if is an internal cell} w = {, if is an external cell} internal osition outside osition Paramenters α -5 constant heat losses _ca oiler caacity in watt c_ce caital cost euiment cost c_etrans caital cost of ielines for external distriution c_itrans caital cost of ielines for internal distriution c_om oerational cost oeration & maintenance cost Page

3 d ε dist, hl in_t maxht maxn minhf min o_gas o_uming out_t π o,t r_rate size θ x y total demand of cell oiler efficiency distance of cell to midoint of cell heat losses W in er Km ieline inside temerature maximum heat transfer maximum numer of oilers er cell minimum distriuted heat flow minimum roduction oerational cost -natural gas oeration cost -uming ieline outside temerature i numer oulation in cell tye t roduction rate length of each cell ieline diameter m ascissa of cell ordinate of cell Continuous variales cc_rod caital cost: roduction cc_rod caital cost in cell : roduction (oilers) cc_trans caital cost: transort cc_trans caital cost: ielines used to transfer heat for cell cc_trans caital cost: ielines in cell davee average distance for external losses in davei average distance for internal losses in eloss external thermal losses ex total exorted heat in ht, imorted heat of cell distr. heat from to iloss internal thermal losses im total imorted heat in oc_om total oerational cost: oeration & maintenance oc_om oerational cost: oeration & maintenance cost in cell oc_rod total oerational cost: roduction oc_rod oerational cost: roduction in cell oc_trans total oerational cost: transort oc_trans oerational cost: transort within cell oc_trans oerational cost: transort in cell r, roduction of oiler in osition ref real roduction in z ojective function - total cost Binary Variales ie =, if the cell imorts heat; 0 otherwise yht, changing heat from to : = if heat is transferred from to ; 0 otherwise Integer Variales numer of oilers tye chosen in cell y,. Constrains Several constraints are defined: I. Heat alance includes all the heat transferred, individual heat demand and roduction and internal and external losses. im +ref =d+eloss +iloss + ex, II. () Boiler roduction, which is limited y its caacity through the euation: r, y, _ ca,, () In order to avoid unnecessary and inefficiency use of oilers, roduction must e higher than an estalish ercentage of oiler caacity: r, y. _ ca min,, () During oeration some losses occur during roduction, so efficiency of the oiler must e considered: ref = (r, ε), III. Heat transfer (4) Imortation to cell is defined as the sum of imortations from cells to : im = ht,, ex For exortation, the definition is similar. = ht,, (5) (6) Maximum heat transfer, reviously defined y the user. ht, yht, max ht d,, (7) Minimum heat transfer is shown in euation elow: Page

4 ht, yht, d min hf,, (8) Exort to one cell and imort from that cell is not allowed in this model. yht, + yht,,, (9) Heat transfer from any cell to external cells is also not authorized. yht,w = 0,,w (0) I. Facility caital cost cc _ rod = II. cc _ trans= ( (y, c _ ce )) Transort caital cost c _itrans+ c _ etrans III. ( davei size ( davee ) t (o Production oerational cost,t )) () (4) IV. Heat losses External and internal losses will occur during heat transfer. External losses in cell are exlained aove. eloss = ( dist, yht, hl), () Where dist, reresents the distance etween cell and cell. Internal losses refer to losses which occur within the cell. Can e defined as: iloss = davei hl size o, t, t. Ojective function () The ojective of the roosed model is to minimise the overall cost of a ossile natural gas network chain. To find the otimal solution, costs will e analysed and divided in two sectors: caital and oerational costs. Figure shows the oeration and caital costs and its sudivisions. It is also in evidence what can influence the values of each cost. oc_rod= ( (r IV., r_rate o_gas)) Transort oerational cost Transort to midoint cell: oc _ trans P = (htpp,p dist, ) o _ uming, PP Transort within the cell: oc _ trans (5) (6) (7) The sum of these two caital costs gives the total transort cost in cell, which is calculated y the following exression: oc _ trans = (oc _ trans + oc _ trans ) (8) V. Oeration and Maintenance oerational cost oc _ om = = davei P d o_uming, (y, c _ om ) (9) VI. General Ojective Function Comining the cost terms derived in section aove, the total heat suly chain cost can e reresented as follow: z = oc _ rod + oc _ trans + oc _ om + + cc _ trans + cc _ rod (0) Minimizing z corresonds to the aim of this work, which can e easily and shortly defined as the minimisation of the suly chain total cost. Figure : Oerational and Caital Costs Page 4

5 . Single Scale Results The model descried efore will e alied to a virtual city with distinct oulation distriutions for a etter aroximation of a real case study. Uniform, normal and random distriutions will e analysed and differences etween inut data are exlained. In a single scale alication a city defined y a regular 4 y 4 grid is studied and all results will e resented and comared. In this study case, the outside area of the city is also taken into account. The single scale alication looks to the city and outside area as a whole and shows one ossile network design. Figure shows the structure in study. Tale : Poulation and Heat Demand uniform distriution Cell Poulation Demand index Commercial Residential (MW) 50 50, , , , , , , , , , , , , , , ,5 Figure : Proosed Model Structure Uniform oulation distriution is the first case study that is analysed. A city is divided in sixteen cells, all with the same size. Each grid cell has km length and is identified with an index. The area surrounding the city is also divided into suare cells of eual size. Reducing the total costs while satisfying the demand is the aim of this case study. Some decisions will e made, on whether oilers should e located or how should e the distriution network. Boiler caacity and uantity of heat roduced are also art of the decisions. In a uniform distriution, oulation is the same within every cell and is euality distriuted according to the tyes of consumers, as shown in Tale. Demand (exressed in megawatts, MW) deends only on the oulation and tye of consumers in each cell, and the otimisation will assume these values as constant. Production can e different from one grid to another; oilers can e located either inside or outside the city, although the same demand must e satisfied in every cell. It is exected, as a result, that oilers will e also uniformly distriuted in this network. Normal oulation distriution must e studied since it is known that oulation will grow in uran areas, ut not uniformly in all arts of the city. Uranization is exlained y several gloal and local factors. As gloal factors we have the national and international market growth and economic gloalization. Local factors include the oulations socioeconomic situation, housing availale and land-use olicies. According to a normal distriution, there will e a high oulation concentration and density in the middle of the city while in neighouring areas the tendency is to have low oulation concentration. Conseuently energy demand will e higher in cells located at the mid-oint of the city and it is exected that oilers will e installed in a igger uantity in central cells and will not e uniformly distriuted all over the city. In real cases, sometimes there are some areas with non-uniform oulation distriution due to some hysical and human factors that can affect oulation density. Physical factors include resources, climate and relief (shae and height of land); while human factors are of olitical, social and economic reasons. Due to what is mentioned aove, it is imortant to analyse a random oulation distriution. According to a random distriution, some unoulated areas will exist in the city or sarsely oulated areas, which means areas with few eole and where normally it is difficult to live. However, there Page 5

6 will e also some areas with high concentration of oulation, laces that are densely oulated. In all cases, the consumtion er erson according to the eriod of the day and tyes of consumers is the same and is shown in Tale. Some arameters are defined reviously to resolve the rolem, like values to calculate heat losses and oiler characteristics. Tale : Consumtion in W er erson Periods of the day Tye of consumers Commercial Residential Morning Afternoon Evening some cells satisfy their local heating demand with heat transfer from neighouring cells. Heat exortation from one cell to another is a more economical alternative than estalishing a new roduction facility in those areas where there is just a small ortion of demand to fulfil. It should also e mentioned that heat imortations minimize the total cost and avoid heat losses within the cell. Pielines are used to deliver hot water from the oint of roduction to consumers, and short distances are referale as visile in the Figure.. Results In Figure the cell index is enclosed within a circle in the middle of each cell. Boiler symols mean that there exists, at least, one oiler according to the size of the symol. The total numer of oilers is indicated near each symol. Heat transfers are reresented y an arrow, which indicates the heat transfer direction. The numer in the middle of each transortation link, i.e. arrow, denotes the corresonding transfer heat from one cell to another one. Figure : Network Structure for Otimal Solution - Case (uniform distriution) Figure shows that, for the uniform oulation distriution, oilers aear also uniform distriuted. Outside ositions are not occuied and the most common situation is one medium and one small oiler installed in internal ositions. It is also used just one or two medium oilers in internal ositions and there is a roduction facility in every cell, which means that every cell will roduce its own heat. However, Figure 4: Network Structure for Otimal Solution - Case (normal distriution) Figure 4 shows the otimal network solution for normal oulation distriution, where most of the oulation is situated in the middle of the city. In Figure 4 it is visile the contrast of colours etween internal cells. Internal cells with a dark colour reresent laces with higher energy demand, while cells with right colours are used for regions with lower demand, and normally with a small numer of inhaitants. Boilers are uniformly distriuted ut a larger numer in the middle of the city is installed, where there is more energy demand to satisfy. The tye oilers are not necessary to ensure all the heat transfer to customers, so there will not e any oiler in ositions outside the city. In some cases, like cells located in the corner, it is cheaer to transfer the heat from neighouring cells instead of setting u a new roduction facility. Page 6

7 of distriution is different. Case reresents the most exensive otion due to the higher numer of installed oilers. Although, this otion imlies a small uming cost, it has exensive costs with euiment and maintenance. 4. Multiscale network design Figure 5: Network Structure for Otimal Solution - Case (random distriution) In Figure 5 the results for a random distriution are resented. Although it is a random oulation distriution, it was ossile to redict areas with higher roaility of having installed oilers. These areas are essentially to right and ottom left corners. The model confirms this idea (see Figure 5). Areas with two tyes of oilers and areas with no roduction facility are visile, due to the random energy demand. However, the heat transfer configuration seems a little confusing; this energy network reresents the most economical otion for this oulation distriution. The random distriution used does not need any oiler of tye installed in outside cells of the city. In order to satisfy all the city demand oilers tye and are reuired (higher numer when comared to case ). Tale : Cost for Possile Network Configuration Costs for Possile Network Configuration Case Caital Cost Oerational Cost Total Costs In section, the virtual city is reresented y a grid structure ut it is treated as a whole lock, using a single scale method. However, this otimization can e used in another ersective where the solution from single scale is catured and again overall costs is minimized ut this time in an individual cell. The aim is to rovide an otimal or near-otimal solution that the single scale methodology was unale to otain in an efficient way. Figure 6 shows this multiscale concet CASE Cell 0 Cell 9 Cell CASE 4 Cell Cell 4 9 It can e seen from Tale that euiment costs in all cases are the most exensive section in this network. All the roduction facilities used in this network reresent around 60% of total costs. And the total caital costs reresent 75% against 5% of oerational costs. Curiously the total cost of the network in case is , which is the cheaest otion when comared with the other cases. All otions have the same numers of inhaitants and energy demand within the city, only the tye Figure 6: Multiscale concet The first ste is to solve the single network energy rolem. The identification of the macroscale variales and the macroscale structure of the rolem, such as heat alance and losses, heat transfer constrains, oerational and caital costs is done. Then the micro scale model is solved where each cell is divided into several arts as reviously done for the gloal region. This is found on the model descried in section 4 with some changes. Some Page 7

8 variales are added to maintain the same model ideology. One random cell will e studied, ut the surrounding cells will e also used to reresent the heat exortations and imortations. Both models are connected and the results are analysed simultaneously. This methodology will e alied to case of chater where the chosen cell is numer 0. The revious otimisation solution (section.) will e comared with the results of the multiscale techniue and discussed accordingly. It is exected that the total costs will e minimized and it is ossile to see the energy network configuration within one cell. 4. Results The final results alied to cell 0 of case (see section.) are shown in Figure 7. Tale 4: Costs for ossile network configuration case 4 Costs for Possile Network Configuration - Case and 4 in Case (cell 0) Case 4 Total Caital Cost Total Oerational Cost Extra Cost (imorted heat) 77 Total Costs The cost comarison shown in Tale 4 illustrates the decrease of the total costs when alying the multiscale method. In cell 0 the total costs is now , while it was in case study. Rememering that the energy demand and all the conditions are the same, this ossile network configuration reresents an excellent imrovement, with a costs reduction y almost 0%. It is also shown that alying this multiscale method it is ossile to satisfy all the energy demand of this art of the city in an efficient way, reducing the total roduction (real roduction decreases from 9.9 to 7.9 MW) and decreasing the total costs of the network. Figure 7: Network structure for otimal solution case 4 The first ig difference in this network is the reduced numer of roduction facilities. In case, cell numer 0 has oilers, while in this case it reuires only medium oilers installed in internal cells. In this case, oulation is random distriuted and, as occur in case, oilers are set u in cells with higher energy demand. This is only ossile due to a etter location of each roduction facility when the multiscale concet is alied. Boilers are located in cells that have more heat demand, instead of eing in the middle. It is also visile that every suare of cell 0 will imort heat from the external osition instead of only one heat transfer to the middle of the analysed cell; however this is the most economical otion for this network. In this case, there is another imortant oint which should e mentioned: the heat losses within the cell are reduced in almost 50%, from case study to case study 4. Decrease of heat losses during transfers contriutes to a etter solution of the otimization model. It ermits to satisfy the heat demand of the cell with a low roduction uantity, which has a ositive effect in ojective function. 5. Influence of costs These examles will e the last ones and the aim of it is to analyse and understand the influence of costs in the network configuration. Two otions are studied: in otion caital costs are douled and oerational costs remain its initial values is the. In otion caital costs reserve its value while oerational costs douled. 5. Results In otion (see Figure 8) the result showed a tendency to imlement oilers of tye in outside ositions, to satisfy all the heat demand. It is visile that the majority Page 8

9 of the oilers are not set u inside the city and reresent 77% of real roduction. Heat transfers are mainly from outside installed oilers to internal arts of the city. According to this inut data, the ossile network structure contains oilers in the model to ensure the heat demand. Tale 5 illustrates the costs difference etween these two otions. It should e rememer that the total costs of case one (that have the same oulation distriution and heat demand) is 055. Tale 5: Costs for Possile Network Configuration - Case 5 Costs for Possile Network Configuration Case 5 in Otion Otion Total Caital Cost Total Oerational Cost Total Costs Conclusions Figure 8: Network Structure for Otimal Solution Case 5 otion, increase caital costs Figure 9 defines the otimal energy network configuration that reresents the most economical alternative that guarantee the roduction of all the heat demand and its transfer to consumers, using the inut data of otion. This case certifies the heat demand with oilers, almost three times the numer of oilers in otion. Every cell has it own oiler and, in this case, the total heat travelled distance is short that in the first otion. In otion two the heat ass through 6 km of underground ielines while in otion one this distance increase to almost 60 km. Only oilers of tye one and two are chosen to roduce all the necessary heat and, in contrast with case one, it does not occur any heat transfer from outside to internal cells. Boilers located in internal cells reresent 00% of total heat roduction. Figure 9: Network Structure for Otimal Solution - Case 5 otion, increase oerational costs This aer roosed a model for uran energy systems in a secific area. It was extended to three different cases: single scale, multi scale methodology and influence of costs. The versatility of the model was examined using different oulation distriutions within the city, changing the oerational and caital costs and alying the multiscale concet. The model was firstly exlored using a single scale techniue was alied to three situations. Different oulation distriutions were alied to a virtual city, although all the situations have the same numer of inhaitants. The inut data was alike in terms of the characteristics of oilers, heat transfers and losses and costs definition. They also utilised the same transortation modes. Uniform, normal and random distriutions were defined and analysed. The key difference etween these three configurations lied in the heat demand in each cell due to different oulation density. The reason ehind this variation was to study the effect of ossile oulation distriution in the design of a heating network structure as well as to comare the differences in costs. The second art considered a multiscale concet that alied to the results from case study. One cell was chosen and the aim was to otimize and understands the difference etween the results. The network configuration within the cell was defined and the total cost decrease when realied the otimization model. It means that it is ossile to otimize the final solution using the multiscale techniue, due to aroriate oilers ositions according to oulation distriution and decrease of heat losses. Page 9

10 The third art studies the influence of caital and oerational costs. This model was alied in a city with the same oulation distriution that case one: uniform distriution. The results were ovious and conclusive. When caital costs are exensive the tendency is to invest in oilers with maximum caacity to avoid high fixed costs with euiment. Heat transfers tend to increase from external cells to internal ositions. In contrast with this examle, when oerational costs are exensive the otimal configuration resents a large numer of roduction facilities installed within the city. The aim in this case is to avoid costs etween the heat transfer and distriution to customers, so heat travel distance tends to e minimized and numer of oilers within the city tends to increase. As a gloal conclusion it can e said that the greatest imortance of this roject lies in a model that is ale to ma some of the future energy suly chain configurations. References Ajah, Augustine N.; Patil, Anish C.; Herder, Paulien M. and Grievink, Johan (006) Integrated concetual design of a roust and reliale waste-heat district heating system, Issue 7 (7), Pages Aselund, Audun and Jordal, Kristin (007) Gas conditioning - the interface etween CO cature and transort, Issue (), Pages Bejan A. (995) Theory of heat transferirreversile ower lants--ii. The otimal allocation of heat exchange euiment, Issue (8), Pages Benonysson, Atli; Bøhm, Benny and Ravn, Hans F. (995) Oerational otimization in a district heating system, Issue 5 (6), Pages BP Imerial College Uran Energy System Project, First Annual Reort, Decemer 006. Chang, Yoon-Suk; Jung, Sung-Wook; Lee, Sang-Min; Choi, Jae-Boong and Kim, Young-Jin (007) Fatigue data acuisition, evaluation and otimization of district heating ies, Issues 4-5 (7), Pages Çomaklı, Kemal; Yüksel, Bedri and Çomaklı, Ömer (004) Evaluation of energy and exergy losses in district heating network, Issue 7 (4), Pages network ased on centralized and decentralized heat ums, cogeneration and/or gas furnace. Part II: Alication, Issue 7 (9), Pages Dahm, J. (00) District Heating Pielines in the Ground - Simulation Model, Version. Davis, P.; Burn, S.; Moglia, M. and Gould, S. (007) A hysical roailistic model to redict failure rates in uried PVC ielines, Issue 9 (9), Pages Dzenajavičienė, E.F.; Kveselis, V.; McNaught, C. and Tamonis, M. (007) Economic analysis of the renovation of small-scale district heating systems - 4 Lithuanian case studies, Issue 4 (5), Pages Garrard A.; Fraga E.S. (998) Mass exchange network synthesis using genetic algorithms, Issue (), Pages Larsen, Helge V.; Bøhm, Benny; Wigels, Michael (004) A comarison of aggregated models for simulation and oerational otimisation of district heating networks, Issues 7-8 (45), Pages 9-9. Lazzarin, R.; Noro, M. (006) District heating and gas engine heat um: Economic analysis ased on a case study, Issues - (46), Pages Li, Lianzhong and Zaheeruddin, M. (004) A control strategy for energy otimal oeration of a direct district heating system, Issue 7 (8), Pages Luo, Lingai; Fan, Yilin; Toundeur, Daniel (006) Heat exchanger: From micro- to multi-scale design otimization, Issue (), Pages Morais M. S. and Marangon Lima J.W. (007) Comined natural gas and electricity network ricing, Issues 5-6 (77), Pages Nystedt, A.; Shemeikka, J.; Klout, K. (006) Case analyses of heat trading etween uildings connected y a district heating network, Issue 0 (47), Pages Soderman, J. and Pettersson, F. (006) Structural and oerational otimisation of distriuted energy systems, Issue (6), Pages Sugihara, H.; Komoto, J. and Tsuji, K. (00) A Multi-Ojective Otimization Model for Uran Energy Systems in a Secific Area, Issues 6-9 (5), Pages 7-4. Curti, V.; Favrat, Daniel and von Sakovsky, M.R. (000) An environomic aroach for the modeling and otimization of a district heating Page 0