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Sustainability 2022, 14, 10125 12 of 39 The second part concerns the investments in the central unit (Equation (44)). As observed, this equation includes the variable and fixed costs related to the ICE, BOI, and DHN of the central unit, as well as the investment costs associated to STp and TStor. The third part is concerned with the investment costs of the DHCN pipeline network (Equation (45)). This equation comprises the fixed costs (related to the existence or absence of a given pipeline connection) and the variable costs (related to the actual size of each pipeline connection and whether it is for heating or cooling). cinv,u(u) = ∑j [fmgt Xmgt(j,u)·cmgt(j,u) + fice·Xice(j,u)·cice(j,u) + fhp·Xhp(j,u)·chp(j,u) + fabs·Xabs(j,u)·cabs(j,u)] + fboi·Sboi(u)·cboi+ fcc·Scc(u)·ccc + fpvp·Spvp(u)·cpvp + (43) fstp·Sstp(u)·cstp + fts·Sts(u)·cts + fts·Scs(u)·cts cinv,c = fice (Sice,c·cice,v + Xice,c·cice,f ) + fboi·(Sboi,c·cboi,v + Xboi,c·cboi,f ) + fstp·Sstp,c·cstp,c + fts Sts,c·cts,c + fnet·(cnet,f,c·Xnet,c + cnet,v,c·SH,net,c) cnet = fnet·∑u,v[cnet,f,c(1)·(Xtp(u,v) + Xcp(u,v)) + cnet,f,c(1)·Xnet(u,v) + cnet,v·(SH,net,c(u,v) + SC,net(u,v))] (44) (45) The total annual maintenance cost is obtained by the summation of Equations (46) and (47). Equation (46) represents the total annual maintenance cost related to a given user and comprises the maintenance cost associated to each considered component. This latter cost is considered proportional to the total amount of product from the component. Equation (47) contains the terms related to the maintenance costs of ICE and BOI, both from the central unit. These costs are also proportional to the total amount of product from each component. cman,u(u) = cman,mgt(u) + cman,ice(u) + cman,abs(u) + cman,hp(u) + cman,boi(u) + cman,cc(u) + cman,pvp(u) + cman,stp(u) (46) cman,c = cman,ice,c + cman,boi,c (47) Since the user’s electricity connection, in this case, has no direct link with the main electricity grid, all the operation costs/incomes related to buying/selling electricity to the grid is now concentrated exclusively in the DS (Equation (42)). With that in mind, the total annual operation cost is derived only from fuel-related costs and can also be split into the operation costs of the users (Equation (48)) and the operation costs of the central unit (Equation (49)). cope,u(u) = ∑m,d,h [cfue,chp(m)·(Fice(m,d,h,u) + Fmgt(m,d,h,u)) + cfue,boi(m)·Fboi(m,d,h,u)] (48) cope,c = ∑m,d,h [cfue,ice,c·Fice,c(m,d,h) + cfue,boi(m)·Fboi,c(m,d,h)] (49) The total annual CO2 emission due to electricity and fuel consumption is obtained through Equation (50). emtot = emel·∑m,d,h [Ebgt(m,d,h) − Esel(m,d,h)] + emf,chp ·∑m,d,h,u [Fice(m,d,h,u) + Fmgt(m,d,h,u)] + emf,boi ·∑m,d,h,u [(Fboi(m,d,h,u) + Fboi,c(m,d,h)] + (50) emf,cen ·∑m,d,h Fice,c(m,d,h) The CO2 emissions related to each type of fuel considered in this work (electricity and natural gas) are obtained in the specialized literature [47]. 3. Case Study Performing a MILP optimization through a mathematical model could be very time consuming, based on the detail level and the model complexity. One of the most influential characteristics is the time resolution (hours, weeks, months), which is strongly relatedPDF Image | Optimal Sharing Electricity and Thermal Energy
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