Prime mover sizing for base-loaded combined heating and power systems

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1 17 Prime mover sizing for base-loaded combined eating and power systems P J Mago* and R Luck Department of Mecanical Engineering, Mississippi State University, Mississippi, USA Te manuscript was received on 27 December 2010 and was accepted after revision for publication on 15 Marc DOI: / Abstract: Tis article considers te problem of sizing prime movers for combined eating and power (CHP) systems operating at full load to satisfy a fraction of a facility s electric load, i.e. a base load. Prime mover sizing is examined using tree criteria: operational cost, carbon dioxide emissions (CDE), and primary energy consumption (PEC). Te sizing process leads to consider ratios of conversion factors applied to imported electricity to conversion factors applied to fuel consumed. Tese ratios are labelled, R CDE, R PEC depending on weter te conversion factors are associated wit operational cost, CDE, or PEC, respectively. Analytical results sow tat in order to acieve savings in operational cost, CDE, or PEC, te ratios must be larger tan a unique constant R Min tat only depends on te CHP components efficiencies. Savings in operational cost, CDE, or PEC due to CHP operation are explicitly formulated using simple equations. Tis facilitates te process of comparing te tradeoffs of optimizing te savings of one criterion over te oter two a task tat as traditionally been accomplised troug computer simulations. A ospital building, located in Atlanta, Georgia, was used as an example to apply te metodology presented in tis article. Keywords: CHP system, primary energy consumption, emission reduction, base-loaded, CHP system sizing 1 INTRODUCTION Advantages of combined eating and power (CHP) systems include power reliability during electric grid disruptions, and potential to reduce operational cost, carbon dioxide emissions (CDE), and primary energy consumption (PEC). CHP systems acieve ig efficiencies and operational cost savings by reclaiming some of te eat energy lost during te electric generation process and using tis recovered eat to elp offset te eating requirements of a facility. Power plants belonging to electric utilities deliver around 30 per cent of te primary energy consumed and te remaining energy is typically lost in te process *Corresponding autor: Department of Mecanical Engineering, Mississippi State University, 210 Carpenter Engineering Building, PO Box ME, Mississippi State, MS , USA. mago@me.msstate.edu of generating or transmitting te electricity [1]. In contrast, by reclaiming te oterwise wasted eat, CHP systems can potentially increase te overall efficiency above 80 per cent [2 4]. Over 3500 commercial, industrial, and institutional facilities troug te United States ave CHP systems installed [5]. In terms of emission reductions, several researcers ave evaluated and analysed te advantages of using CHP systems to reduce pollutants for different applications [6 10]. Sizing a CHP system sould be done by taking into consideration individual component efficiencies, system operating strategies, te electrical and termal demands to be met, and te main benefit to be obtained from te system operation [11 14]. Frequently, CHP systems are operated following te electric load (FEL) strategy or following te termal load (FTL) strategy. Wen operating under te FEL strategy, te power generation unit (PGU)

2 18 P J Mago and R Luck generates electricity to matc te electric demand of te building. However, wen operating under te FTL strategy, te PGU operates suc as to generate te eat necessary to matc te termal demand of te building. Te FEL and FTL operational strategies ave been investigated by several autors suc as: Cardona et al. [15], Mago et al. [16, 17], Hueffed and Mago [18], Fumo et al. [19], among oters. One of te major disadvantages of operating te CHP system using FEL or FTL strategies is tat te PGU does not always operate at full load, i.e. at te igest efficiency, because te electric and termal demands in buildings fluctuate wit te our of te day, level of activity, and weater conditions. Anoter CHP operation strategy consists in following te optimal operation as measured by a performance index based on operational cost, emissions, or PEC. Te use of linear programming to implement te following te optimal operation strategy as been investigated by several oter autors [20 26]. In general, one disadvantage of te FEL, FTL, and following te optimal operation strategies is te dynamic range of operation required from te PGU. Constantly varying te operation of a PGU results in increased maintenance costs, increased emissions, and diminised efficiency due to te resulting unsteadiness of te cyclical combustion process. Terefore, a strategy in wic te PGU is baseloaded, i.e. continuously operating at full load and optimal efficiency is wort investigating. Tis article examines a simple metodology to size base-loaded CHP systems wit respect to operational cost, CDE, PEC, and te overall CHP system efficiency. Several examples are used to illustrate te tradeoffs tat arise wen trying to balance operational cost, CDE, PEC, and te CHP system efficiency. 2 ANALYSIS 2.1 Operational cost analysis If a building wit a CHP system is to perform better tan a conventional reference building, te cost of operation of te reference building, Cost ref, sould be iger tan te cost of operation of te building wit a CHP system, Cost CHP Cost ref 4 Cost CHP Equation (1) can be expressed in terms of nominal or average building electrical and termal energy requirements, E b and F b, respectively; te PGU constant base-loaded electric generation ; te cost of electricity, Cost e ; te cost of fuel, Cost f ; te constant fuel energy consumption of te PGU, F pgu ; and te ð1þ nominal or average fuel energy consumption of te boiler, F boiler (Fig. 1) as follows E b Cost e þ F b Cost f 4 E grid Cost e þ F boiler þ F pgu Costf were E grid ¼ E b. Note tat E b and F b can be considered as known quantities obtained from te montly utility bills of te building. Also, equation (2) is very general in tat it applies to any averaging period, e.g. ourly, daily, montly, or yearly averages. Te ratio of electricity cost to fuel cost, is found by rearranging equation (2) as follows ¼ Cost e F 4 boiler þ F pgu! F b ð3þ Cost f Te fuel energy consumed by te PGU, te boiler, and te building eating system can be expressed as F pgu ¼ pgu F boiler ¼ Q boiler boiler Q F b ¼ ð6þ were pgu, boiler, and are te PGU efficiency, te boiler efficiency, and te eating system efficiency, respectively, Qboiler te eat supplied by te boiler, and Q te building eating load. Substituting equation (4) into equation (3) yields 4 R pgu þ F boiler F b were for notational convenience, R pgu is defined to be te reciprocal of te PGU efficiency, i.e. R pgu ¼ 1 ð8þ pgu Let be te efficiency of building eating system wen te CHP system and/or boiler are used to meet te building s eating load. Te eat required from te CHP system in order to meet te building s eating requirement is Q req ¼ Equation (7) can be expressed in two different forms depending on te magnitude of te eat recovered from te PGU, Q rec, and te magnitude of te eat required from te CHP system, Q req ð2þ ð4þ ð5þ ð7þ ð9þ

3 Prime mover sizing 19 If Q rec 5 Q req ten F boiler ¼ 0 and 4 R pgu F b If Q rec 5 Q req ten Q boiler ¼ Q req Q rec and 4 R pgu þ Q req Q rec boiler F b ð10þ ð11þ Te eat recovered from te PGU can be expressed as Q rec ¼ F pqu rs ð12þ were rs is te efficiency of te eat recovery system and a factor tat accounts for PGU energy losses before te eat recovery system. Using equation (4), equation (12) can be expressed as Q rec ¼ QCHP F pgu ð13þ were te fraction of eat recovered from te fuel energy consumed by te PGU, QCHP,is QCHP ¼ rs 1 pgu ð14þ Te two subsections to follow consider te cases described by equations (10) and (11). Before proceeding, it may prove useful to introduce te following notation. Define E 0 to be te CHP system electrical generation if te CHP system were to exactly meet te building eating requirement, i.e. if Q rec ¼ Q req An equation for E 0 is obtained by applying equations (4), (9), and (13) to Q rec ¼ Q req and solving for, i.e. E 0 Q ¼ pgu ¼ ð15þ QCHP QCHP R pgu Next, define E 00 to be te maximum electrical energy te CHP system is allowed to contribute. Te coice of E 00 depends on weter te CHP system is being sized to optimize operational cost, CDE, or PEC. Typical coices of E 00 include (a) te building electrical load E b, or (b) te CHP electrical generation associated wit a predetermined minimum system efficiency as will be sown later in tis article in te discussion leading to equation (51) If te CHP system produces more eat tan needed by te building (Q rec 4 Q req ) Since E 0 is te CHP system electrical generation if te CHP system were to exactly meet te average building eating requirement, ten te inequality Q rec 4 Q req implies tat 4 E 0 ð16þ Te above equation provides a lower bound on te PGU operation suc tat it will always meet te eating requirement of te building. Equation (10) is used below to determine te values of tat will provide savings over te reference case. First, rearrange equation (10) using equation (6) to obtain 4 R pgu ð17þ If te rigt-and side of equation (17) is positive (Case a), i.e. if < R pgu, ten 5 ð18þ R pgu However, if te rigt-and side of equation (17) is negative (Case b), i.e. if > R pgu ten 4 ð19þ R pgu Note tat equation (19) is obtained by dividing equation (17) by a negative number. Tis explains te reversal in te inequality symbol in equation (19). Case (a): If < R pgu, equation (18) provides and upper limit on wile equation (16) provides a lower limit. Te range of operation of te PGU is ten E E 000 were E 000 ¼ ðr pgu ð20þ Þ Ensuring tat te upper limit in equation (20) is indeed larger tan te lower limit by applying E 0 < E 000 along wit equations (15) and (20) results in 4 R pgu 1 QCHP ð21þ For notational convenience, te lower limit imposed by equation (21) is labelled as R Min ¼ R pgu 1 QCHP ð22þ Note tat all efficiencies are positive scalars and equation (22) implies tat R pgu > R Min. Combining equations (21) and (22) wit te assumption for Case (a), i.e. R pgu >, yields R pgu 4 4 R Min ð23þ Case (b):if > R pgu, ten equation (19) imposes a negative lower limit on wile equation (16) provides a positive lower limit. Since bot equations (16) and (19) must be satisfied, te more conservative positive lower limit imposed by equation (16) determines te range of operation of te PGU for tis case, i.e. > E 0.

4 20 P J Mago and R Luck Combining te results of Case (a) and Case (b), te following conclusions can be reaced. If te PGU was operated to meet te average eating demand for a facility, te PGU operation must at least satisfy te lower bound of > E 0. For favourable CHP operation, te smallest cost ratio allowable is given by te lower bound of > R Min. However, if in addition, it is known tat > R pgu ten te PGU operation sould not surpass te upper limit given by < E 000. On te oter and, if > R pgu, it would be advantageous to operate te PGU at > E 0.In eiter case, R pgu > R Min If a boiler supplements te CHP system ( Q req 4 Q rec ) Tis situation, leading to equation (11), is equivalent to under sizing te engine, i.e. < E 0. Using equations (4), (6), (9), and (13) in equation (11) and rearranging yields Q R lim ð24þ boiler were for notational convenience, R lim as been defined as R lim ¼ R pgu 1 QCHP ð25þ boiler Solving for, tere are two possibilities. If te left side of equation (24) is positive (Case a2), i.e. if > R lim, ten ð26þ ð R lim Þ boiler However, if te left side of equation (24) is negative (Case b2), i.e. if > R lim, ten ð27þ ðr lim Þ boiler Case (b2): R lim >. Te denominator of equation (27) is positive since R lim > but te numerator is negative for all practical applications. Since a negative upper bound on te engine operation is not feasible, it follows tat operational cost savings cannot be attained wen R lim >. Case (a2): > R lim, equation (26) provides a positive lower limit, E iv,on were Q E iv 1 ¼ 1 ð28þ ð R lim Þ boiler Combining te upper and lower limits for E iv 5 5 E 0 ð29þ Ensuring tat te upper limit in equation (29) is indeed larger tan te lower limit, i.e. E 0 > E iv, and using equations (15) and (28) results in 1 QCHP R pgu 1 QCHP boiler 5 ð R lim Þ R pgu ð30þ Using te definitions given by equations (22) and (25), equation (30) can be greatly simplified to yield 4 R Min ð31þ Neverteless, tis Case (a2) started wit te assumption tat > R lim, wic is anoter lower limit on * Bot constrains will be satisfied if te largest of te two lower limits is satisfied. 2.2 Savings analysis Te savings from te CHP system operation can be obtained as follows Savings ¼ Cost ref Cost CHP ð32þ Te above equation is basically te difference between left and rigt sides of equation (2). Using equation (2), cancelling terms, and simplifying, equation (32) can be expressed as Savings ¼ Cost e Cost f F pgu þ F boiler F b ð33þ If Q rec 4 Q req, ten F boiler ¼ 0. Using equations (3), (4), (6), and (8) in equation (33) and rearranging Savings Cost e ¼ 1 R pgu Q þ if 4 E 0 ð34þ Substituting ¼ E 0 þ E, and using equations (15) and (22), equation (34) can be expressed as follows Savings ¼ E 0 1 R Min Cost e þ E 1 R pgu ð35þ If < R pgu, te term in parenteses next to E is negative and te operational cost savings are reduced as E increases. Following equation (20), te bounds on E for tis case are given by 0 4 E 4 (E 000 E 0 ). If, on te oter and, < R pgu, ten operational cost savings improve by increasing E at te expense of rejecting some of te eat recovered by te CHP system. Following te previous discussion on Case (b), te bounds on E for tis case are given by 0 4 E 4 (E 00 E 0 ).

5 Prime mover sizing 21 Finally, if Q rec 5 Q req, using te same steps leading to equation (35) but tis time assuming tat F boiler 6¼ 0 yields Savings ¼ E 0 1 R Min Cost e þ E 1 R pgu F boiler ð36þ From Fig. 1, it is seen tat te fuel to te boiler can be expressed as F boiler ¼ Q req q rec ð37þ boiler Using equations (9) and (13) followed by equations (4) and (8), and substituting ¼ E 0 þ E yields F F boiler ¼ b E 0 QCHP ð þ EÞR pgu ð38þ boiler boiler Combining equations (38) and (36) wit te definitions given in equations (15) and (25) and rearranging Savings ¼ E 0 1 R Min þ E 1 R lim ð39þ Cost e As discussed previously, wen Q rec 5 Q only Case (a2) yields operational cost savings and only wen > R Min > R lim. It follows tat all te terms in parentesis in equation (39) are positive and E sould be selected as large as possible. Following equation (29), te bounds on E for Case (a2) are (E iv E 0 ) 4 E 4 0. It follows tat te most savings are obtained by selecting E ¼ 0. In summary, in order to acieve any savings, te cost ratio must be larger tan R Min defined in equation (22). If in addition, > R pgu, ten te largest savings are acieved by meeting te average termal load of te building resulting in R pgu & E 0. If, on te oter and, > R pgu, ten operational cost savings occur wen E 00 > > E 0 wit te largest savings at ¼ E 00, albeit, potentially at a significant loss of CHP efficiency depending on ow muc recovered eat is rejected. After determining te operational cost savings from te CHP system, te capital cost tat can be invested on te CHP system to acieve a desired payback period (PBP) can be expressed as CapitalCost ¼ PBP CostSavings 2.3 Primary energy, carbon emissions, and CHP system efficiency ð40þ For te CHP system to be able to reduce te PEC compared wit te reference case te following inequality must old PEC ref 4 PEC CHP Tis equation can be furter expanded as ð41þ E b CF PEC,e þ F b CF PEC,f 4 E grid CF PEC,e þ F ð42þ boiler þ F pgu CFPEC,f were CF PEC,e and CF PEC,f are te site-to-primary energy conversion factor for electricity and natural gas, respectively. Similarly, considering reduction in CDE, favourable CHP operation requires CDE ref 4 CDE CHP and tis equation can be expressed as ð43þ Fig. 1 Scematic used to develop te model

6 22 P J Mago and R Luck E b CF CDE,e þ F b CF CDE,f 4 E grid CF CDE,e þ F ð44þ boiler þ F pgu CFCDE,f were CF CDE,e and CF CDE,f are CDE conversion factors for electricity and natural gas, respectively. Since equations (42) and (44) ave te same form as equation (2), all te results from subsections 2.1 and 2.2 wit te exception of te capital cost, i.e. equation (40), can be modified to apply to PEC and CDE, respectively, by substituting te cost ratio,, by te following PEC and CDE ratios R PEC ¼ CF PEC,e CF PEC,f ð45þ R CDE ¼ CF CDE,e ð46þ CF CDE,f Anoter important parameter tat can be used to size te PGU is te CHP system efficiency, wic is defined as CHP ¼ þ Q useful ð47þ F pgu were Q useful ¼ Q req if Q rec 4 Q req or Q useful ¼ Q rec if Q rec 5 Q req. Furtermore, define 8 >< Q req Q rec if Q rec 5Q req ¼ ð48þ >: 1 if Q rec 5 Q req Ten equation (47) can be expressed as CHP ¼ F pgu þ Q rec F pgu or CHP ¼ pgu þ QCHP ð49þ Using equations (4), (13), and (15), g can be expressed in terms of as follows 8 < E 0 if 5E 0 ¼ ð50þ : 1 if 5 E 0 Equations (49) and (50) sow tat te igest CHP efficiency is obtained wen 4 E 0. As is increased by an amount E above E 0, te CHP efficiency diminises. 2.4 Simplifications for te bounds (E 00 E 0 ), (E 000 E 0 ), and (E iv E 0 ) Next it is sown tat equations for te bounds on E can be elegantly formulated in terms of te minimum CHP efficiency (for te case of E 00 ) or in terms of te cost ratios. Tis will allow te decision process for sizing te PGU to be succinctly described using simple equations. For te case wen Q rec 5 (Case (b)), te value of te upper limit E 00 may be based on te smallest CHP efficiency allowable. Using equations (48), (49), and (15), te value of corresponding to a prescribed CHP is E 00 ¼ ð þ 1ÞE 0 ð51þ were ¼ QCHP CHP pgu 1 It follows tat ðe 00 E 0 Þ ¼ E 0 ð52þ Using equations (8), (15), (20), and (22), te bound (E 000 E 0 ) and E 000 can be expressed as ðe 000 E 0 Þ ¼ E 0 R Min E 000 ¼ E 0 R pgu and R pgu R Min R pgu ð53þ Finally, using equations (8), (15), (22), (25), and (28), te bound (E iv E 0 ) and E iv can be expressed as E iv E 0 ¼ E 0 R Min E iv ¼ E 0 R lim and R MinR lim R lim ð54þ Te equations presented in tis section are summarized in a flow cart presented in Fig. 2. It can be observed tat wit te average ourly electric and termal energy needed by te building in a year, te optimum PGU size of te CHP system could be obtained. It is important to note tat te same flow cart can be used to optimize te system based on operational cost, PEC, or CDE by canging R by, R PEC or R CDE, respectively, and canging CF by Cost e, CF PEC,e,orCF CDE,e, respectively. In addition, it can be seen tat tree pats could be follow using te flow cart Pat O-A if Q rec 5 Q req and R < R pgu Pat O-B if Q rec 5 Q req and R > R pgu Pat O-C if Q rec 4 Q req Te evaluation of te system will follow any of te above-mentioned pats depending on te parameter being optimized. As mentioned before, one application of te results of tis article is a metodology to size te PGU for a base-loaded CHP system operation from montly utility bills, i.e. retrofit or existing buildings. However, te proposed metodology can also be applied if ourly wole-building simulation data is available, i.e. new construction or existing buildings. 3 RESULTS To apply te metodology described in section 2, te building montly electric and termal loads need to be known. Tese can be obtained from te utility bills of te building. However, in tis article, te montly electric and termal loads are obtained from a simulation using EnergyPlus [27] and te results are used

7 Prime mover sizing 23 Fig. 2 Flow cart to summarize te equations presented in section 2 as te reference case. A ospital building, wit five floors, wit a total floor area of m 2 was selected to apply te metodology. Te building was evaluated in Atlanta, Georgia. Te reference building used in tis investigation is part of te U.S. Department of Energy s bencmark building models [28]. Table 1 presents te total electricity and natural gas consumption per year as well as te yearly ourly average electric and termal loads for te building. Table 2 sows te CHP system parameters, wile Table 3 presents te site-to-primary energy conversion factors, te cost, and te CDEs conversion factors for electricity and natural gas. Te natural gas CDEs factor includes te precombustion CDEs for fuel delivery to te building as well as te on-site CDEs resulting from fuel combustion. Te implementation of te flow cart presented in Fig. 2 is illustrated using te example presented below. 3.1 Example: Hospital located in Atlanta, Georgia 1. Compare, R PEC, and R CDE wit R pgu ¼ 3.33 ¼ 2:31! 5 R pgu R PEC ¼ 3:25! R PEC 5 R pgu

8 24 P J Mago and R Luck Table 1 Electricity and natural gas consumption for te evaluated building (Reference) in Atlanta, Georgia E b (kw/year) Eb (kw) F b (kw/year) Fb (kw) Values presented in tis table are obtained from Energy Plus. Parameter Table 2 R CDE ¼ 3:38! R CDE 4 R pgu CHP system parameters Value PGU efficiency, pgu 0.3 Factor tat accounts for energy losses, 0.9 Boiler efficiency, b 0.8 Heat recovery system efficiency, rec 0.8 Heating coil efficiency, 0.8 Table 3 Site-to-primary energy conversion factors, CDEs conversion factors, and cost for electricity and natural gas Value CF y PEC,e (kw/kw) 3.4 CF y PEC,f (kw/kw) R PEC 3.25 CF CDE,e * (ton/kw) CF CDE,f * (ton/kw) R CDE 3.38 Cost e * ($/kw) Cost f * ($/MBtu) ($/kw) 11.2 (0.0382) 2.31 * Values obtained in August 2010 [29]. y Values obtained from reference [30]. Since R CDE > R pgu any PGU size will provide operational emission savings. On te oter and, since < R pgu and R PEC < R pgu it is desirable to find a PGU size tat result in an improvement of te PEC and cost wit respect to te reference case. 2. Case a (Pat 0-A): Selecting te PGU size suc as Q rec 5Q req by using te values presented in Table 1 ( E b ¼ 1139:5 kw and F b ¼ 446:6 kw) and Table 2, and optimizing te system based on cost ( < R pgu ), te range of operation of te PGU can be found using equation (20) as 266 kw kw It is important to mention ere tat a 266- or 437- kw PGU will produce 266 or 437 kw in a time step of 1. (a) Te savings of CDE emissions can ten be calculated for eac PGU size as follows: PGU ¼ 266 kw! Savings Cost ¼ $6.739 per our ¼ $ per year PGU ¼ 437 kw! Savings Cost ¼ $0 per year Terefore, te optimum PGU size based on cost is 266 kw wic yields 5.68 per cent reduction wit respect to te reference case. (b) Te total PEC and CDE for tis case are PGU ¼ 266 kw! PEC ¼ kw/year Savings PEC ¼ kw (10.22 per cent reduction) CDE ¼ 6715 ton/year Savings CDE ¼ 802 ton/year (10.67 per cent reduction) PGU ¼ 437 kw! PEC ¼ kw/year Savings PEC ¼ kw (9.86 per cent reduction) CDE ¼ 6703 ton/year Savings CDE ¼ ton/year (10.84 per cent) (c) Te capital cost tat can be invested for a PBP of 2 years is given by PGU ¼ 266 kw! Capital Cost ¼ $ PGU ¼ 437 kw! Capital Cost ¼ $0 (d) Te CHP efficiency can be determined as PGU ¼ 266 kw! g ¼ 1! CHP ¼ PGU ¼ 437 kw! g ¼ 0.608! CHP ¼ Case b (Pat 0-A): Selecting te PGU size suc as Q rec 5Q req and optimizing te system based on PEC (R PEC < R pgu ), te range of operation of te PGU can be found using equation (20) as 266 kw kw Terefore, 266 kw would also give te optimum value based on PEC. Te upper limit can be neglected since it is iger tan te upper limit obtained for cost savings (437 kw). 4. Case c (Pat 0-B): Selecting te PGU size suc as Q rec 5Q req and optimizing te system based on CDE (R CDE > R pgu ). Te equations indicate tat bigger engines would result in result in larger emission reductions. For tis case, two bounds could be imposed to determine te maximum PGU size based on CDE. Te first bound is te upper limit obtained for CDE tat would produce te same cost as te reference case (437 kw). Te oter bound can be te efficiency of te CHP system. Tis parameter can be a fixed value depending on te incentives and requirements of tat specific application. A CHP efficiency of at least 60 per cent is required most of te time to qualify for government incentives. Terefore, using an efficiency of 60 per cent te oter bound for te PGU size based on operational cost (E 00 )is E 00 ¼ 447 kw Tis engine size would provide te iger emission savings (11 per cent) wile increasing te cost above te reference case by approximately 1 per cent. 5. Case d (Pat 0-C): Selecting te PGU size suc as Q rec 5 Q req, and optimizing te system based on

9 Prime mover sizing 25 cost ( > R lim, te range of operation of te PGU can be found as 104 kw kw An engine size of 104 kw would ave te same operational cost as te reference case. However, te CDE and PEC would only be sligtly better tan te reference case and muc iger tan te one obtained for Case a, b, or c. 6. Discussion: For te case presented in te example, te optimum PGU size based on cost and PEC was determined to be 266 kw wile te optimum based on te CDE tat would produce te same cost as te reference case was determined to be 437 kw (Pat 0-A optimized based on cost). Terefore, te new range of operation, based on typical PGU sizes, was selected as 280 and 420 kw. Following te flow cart wit te new PGU sizes, te adjusted results for tese two options are presented in Table 4 and Fig. 3. In general, te results presented in Table 4 illustrate tat te optimum PGU size varies wit te Table 4 Results obtained for te optimization of te ospital in Atlanta, Georgia PGU ¼ 280 kw PGU ¼ 420 kw Operational cost savings ($/year) PEC savings (kw/year) CDE savings (ton/year) CHP efficiency (%) Capital cost ($) (2 years PBP) ratios, R CDE, and R PEC. Also, it is important to igligt tat for some locations; cost may be te most convenient parameter use for selecting te PGU size wile for oter locations CDE may be used as te deciding factor to size te PGU. Wen applying te metodology presented in tis article using montly electric and termal loads average, it is important to consider tat if te termal load cange significantly from mont to mont te metodology may not give te best PGU size for te evaluated application. For tese cases, it is recommended to apply te proposed base loading metodology using weekly or ourly averages for te electric and termal load. In te latter case, prime mover sizing can be accomplised by considering te array of results for every our of PGU operation during a typical year. 4 CONCLUSIONS Te problem of sizing base-loaded prime movers for CHP systems was considered. PGU sizing was examined from te perspective of reductions in operational cost, CDE, and PEC. Explicit equations for savings were obtained in terms of te conversion factor ratios, R CDE, and R PEC. Regardless of weter savings in cost, CDE, or PEC were examined, it was found tat, for favourable savings, te same minimum bound, R Min, applied to eac of te conversion factor ratios. R Min was sown to be an intrinsic % Reduction wit respect to te reference case and CHP system efficiency PGU = 280 kw PGU = 420 kw 0 Cost PEC CDE CHP Efficiency Fig. 3 Reduction of te operational cost, PEC, and CDE wit respect to te reference case and te CHP efficiency for two different PGU sizes for te ospital

10 26 P J Mago and R Luck CHP system parameter in te sense tat it depends solely on te efficiencies of te CHP equipment. Anoter important CHP system parameter is te reciprocal of te PGU efficiency, i.e. R pgu ¼ 1 pgu. It was found tat if te CHP system recovered more eat tan required by te building and te cost ratio is larger tan tis parameter, ten savings will be proportional to te size of te PGU up to an upper limit, E 00, usually determined by te electric demand of te building or te minimum CHP efficiency allowable. On te oter and, if te cost ratio is smaller tan R pgu, te savings will occur only if te CHP electric generation is below a value of E 000 wic is, in turn, depends on te eat demand of te building and on te ratio of conversion factors under consideration. If te CHP system is undersized in te sense tat it recovers less eat tan required by te building, ten favourable savings require tat te CHP electric generation be larger tan a limit E iv tat depends on te eat demand of te building and te conversion factor under consideration. A flowcart was developed to summarize te process, equations, and bounds required to assess te savings. In order to illustrate te process of sizing te prime mover, a ospital located in Atlanta, Georgia, was used as an example. A PGU size of 266 kw provides te maximum reductions on cost and PEC. However, from te emissions point of view, a bigger engine would result in additional emission savings at te expense of a reduced overall CHP efficiency. FUNDING Tis work was supported by te MSU Micro-CHP and Bio-Fuel Center. ß Autors 2011 REFERENCES 1 Te U.S. Department of Energy. Combined eat and power basics, available from ttp://www1.eere. energy.gov/industry/distributedenergy/cp_basics. tml (accessed September 2010). 2 Jalalzade-Azar, A. A comparison of electrical- and termal-load following CHP systems. ASHRAE Trans.110, Moran, A., Mago, P. J., and Camra, L. M. Termoeconomic modeling of micro-chp (microcooling, eating, and power) for small commercial applications. Int. J. Energy Res., 2008, 32(9), Hueffed, A. and Mago, P. J. Influence of prime mover size and operational strategy on te performance of CCHP systems under different cost structures. Proc. IMecE Part A: J. Power and Energy, 2010, 224(5), Te U.S. Department of Energy, Combined eat and power: a decade of progress, a vision for te future, available from: ttp://www1. eere. energy.gov/industry/distributedenergy/ (accessed September 2010) 6 Mago, P. J., Fumo, N., and Camra, L. M. Metodology to perform a non-conventional evaluation of cooling, eating, and power systems. J. Power Energy, 2007, 222, Pierluigi, M. and Cicco, G. Assessment of te greenouse gas emissions from cogeneration and trigeneration systems. Part II: analysis tecniques and application cases. Energy, 2008, 33(3), Möllersten, K., Yan, J., and Moreira, J. R. Potential market nices for biomass energy wit CO 2 capture and storage - opportunities for energy supply wit negative CO 2 emissions. Biomass Bioenergy, 2003, 25(3), Walund, B., Yan, J., and Westermark, M. Increasing biomass utilisation in energy systems: a comparative study of CO 2 reduction and cost for different bioenergy processing options. Biomass Bioenergy, 2004, 26(6), Mollersten, K., Yan, J., and Westermark, M. Potential and cost-effectiveness of CO 2 reductions troug energy measures in Swedis pulp and paper mills. Energy, 2003, 28(7), Sayane, S. and Sokrollai, S. Selection and sizing of prime movers in combined eat and power systems. Proceedings of ASME Turbo Expo, 2004, pp (Vienna, Austria)14 17 June Actionenergy. Combined eat and power for buildings. Good practice guide (GPG388), April Zogg, R., Rot, K., and Brodrick, J. Using CHP systems in commercial buildings. ASHRAE J., 2005, 47(9), Al-Sulaiman, F. A., Hamdullapur, F., and Dincer, I. Trigeneration: a compreensive review based on prime movers. Int. J. Energy Res., 2010, 35(3), Cardona, E., Piacentino, A., and Cardona, F. Matcing economical, energetic and environmental benefits: an analysis for ybrid CHCP-eat pump systems. Energ. Convers. Manage., 2006, 47, Mago, P. J., Fumo, N., and Camra, L. M. Performance analysis of CCHP and CHP systems operating following te termal and electric load. Int. J. Energy Res., 2009, 33, Mago, P. J., Hueffed, A., and Camra, L. M. A review on energy, economical, and environmental benefits of te use of CHP systems for small commercial buildings for te Nort American climate. Int. J. Energy Res., 2009, 33(14), Hueffed, A. K. and Mago, P. J. Influence of prime mover size and operational strategy on te performance of combined cooling, eating, and power systems under different cost structures. J. Power Energy, 2010, 224, Fumo, N., Mago, P. J., and Camra, L. M. Cooling, eating, and power energy performance for system feasibility. Proc. IMecE Part A: J. Power and Energy, 2008, 222(5),

11 Prime mover sizing Co, H., Luck, R., Eksiouglu, S. D., and Camra, L. M. Cost-optimized real -time operation of CHP systems. Energy Build., 2009, 41(4), Kong, X. Q., Wang, R. Z., and Huang, X. H. Energy optimization model for a CCHP system wit available gas turbines. Appl. Term. Eng., 2005, 25(2 3), Rong, A. and Ladelma, R. An efficient linear programming model and optimization algoritm for trigeneration. Appl. Energy, 2005, 82, Henning, D. Cost minimization for a local utility troug CHP, eat storage and load management. Int. J. Energy Res., 1998, 22(8), Ladelma, R. and Hakonen, H. An efficient linear programming algoritm for combined eat and power production. Eur. J. Oper. Res., 2003, 148, Torin, E., Brand, H., and Weber, C. Long-term optimization of cogeneration systems in a competitive market environment. Appl Energy, 2005, 81, Co, H., Luck, R., and Camra, L. M. Supervisory feed-forward control for real-time topping cycle CHP operation. ASME J. Energy Resour. Tecnol., 2010, 132(1), U.S. Department of Energy. EnergyPlus Version 5.0., Torcellini, P., Deru, M., Griffit, B., Benne, K., Halverson, M., Winiarski, D., and Crawley, D. In Proceedings of te DOE Commercial Building Bencmark Models in ACEEE Summer Study on Energy Efficiency in Buildings, Pacific Grove, California, August U.S. Department of Energy. Environmental Protection Agency, Energy Star Program, Target Finder, available from ttp://energystar.gov/ (accessed August 2010) 30 Fumo, N. and Camra, L. Analysis of combined cooling, eating, and power systems based on source primary energy consumption. Appl. Energy, 2010, 87, APPENDIX Notation CF CDE CF PEC Cost CHP Cost e Cost f emission conversion factor (ton/kw) primary energy conversion factor cost of operation of te building using CHP ($) cost of electricity ($/kw) cost of fuel ($/kw) Cost ref E 0 E 00 E 000 E iv E b E grid F b F boiler F pgu Q boiler Q pgu Q rec Q req R CDE R PEC R pgu R Min boiler rs pgu QCHP Subscripts e f pgu cost of operation of te reference building ($) CHP electricity wen Q rec ¼ Q req (kw) maximum electricity allowed from te CHP system (kw) upper limit on CHP electricity if < 1/ pgu (kw) lower limit (kw) electric energy consumption of te building (kw) electricity imported from te grid (kw) electricity generated by te PGU (kw) fuel energy consumption of te reference building (kw) boiler fuel energy (kw) PGU fuel energy (kw) eat supplied by te boiler (kw) eating load (kw) eat rejected from te PGU (kw) net useful eat recovered from te PGU (kw) eat required from te CHP system (kw) conversion factor ratio due to CDE conversion factor ratio of electricity cost to fuel cost conversion factor ratio due to PEC 1 pgu lower bound for te conversion factor ratios boiler efficiency eating system efficiency for te reference system eating system efficiency wen using a CHP system efficiency of PGU eat recovering system PGU fuel to electricity conversion efficiency fraction of eat recovered from te fuel energy consumed by te PGU factor tat accounts for PGU energy losses before te eat recovery system electricity fuel eating coil power generation unit

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