A New Approach for Assigning Costs and Fuels to Cogeneration Products

Transcription

1 Int.J. Appled Thermodynams, ISSN Vol.4, (No.3), pp.45-56, September200 A New Approah for Assgnng Costs and Fuels to Cogeneraton Produts Bert RLACH, George TSATSARONIS, Fran CZISLA Insttute for nergy ngneerng Tehnal Unversty of Berln Marhstr. 8, 0587 Berln - Germany Tel: , -228 Fax: mal: tsatsarons@et.tu-berln.de Abstrat Cogeneraton plants generate more than one produt (e.g., eletrty and steam) usng to some extent ommon fuel(s) and equpment tems. Several approahes have been suggested n the past for assgnng the osts assoated wth these ommon equpment tems and fuels to the produts of the plant. Some of these approahes use exergy-based or thermoeonom methods. The results, however, may vary wthn a wde range. Ths paper presents a new exergy-based approah for assgnng the fuel(s) used n a ogeneraton plant to the ndvdual produts of the plant. Combned wth a thermoeonom analyss, ths approah provdes the osts assoated wth the produt streams. The new approah s more flexble,.e. t allows engneers to atvely partpate n the fuel and ost assgnng proess. As expeted, the results obtaned wth ths approah dffer from the results obtaned from any of the prevous approahes, nludng the exerget ost theory and all prevous thermoeonom approahes. The applaton of the new approah s demonstrated usng a ombned heat and power plant.. Introduton Thermoeonom (exergoeonom) methods are powerful tools for the analyss, evaluaton and optmzaton of energy onverson systems, as they provde means to determne the nternal ost flows wthn a plant. The ost formaton proess throughout a plant from the fuel to the fnal produts s made transparent wth the ad of a thermoeonom analyss. The osts assoated wth the thermodynam neffenes ourrng n eah plant omponent are deteted. For every plant omponent, an exergy balane an be formulated. loss = + + () n, out, The exergy destruton L, D, D, L, and the exergy are a measure of the neffenes assoated wth the rreversble proesses tang plae n the th plant omponent. hen sngle omponents of a thermal system are onsdered, the exergy losses are usually zero: 0 (2) L, = Several thermoeonom approahes have been presented n the lterature (Frangopoulos, 983, Tsatsarons and nhold, 985, Valero et al., 986, von Spaovsy, 986, Tsatsarons and Ln, 990, Lazzaretto et al., 993, Penner and Tsatsarons, 994, Bean et al., 996, Valero et al., 999). They all have n ommon the use of ost balanes for the plant omponents: C = C + Z (3) out, n, and some auxlary equatons expressed expltly or mpltly. These auxlary equatons depend on the purpose of the omponent wthn the overall system, whh s expressed by the exerget effeny: Author to whom all orrespondene should be addressed. Int.J. Appled Thermodynams, Vol.4 (No.3) 45

2 P, ε = (4) F, The auxlary equatons have been the subet of some researh amed at the development of generally applable rules for the formulaton of the auxlary equatons (Tsatsarons and Ln, 990, Torres et al. 996, Lazzaretto and Tsatsarons, 997 and 999). In ths paper, the rules suggested by Lazzaretto and Tsatsarons (999) are used. An mportant haraterst of exergoeonoms s the defnton of exergy related spef osts. C = (5) In terms of fuel and produt, the ost balane for the th omponent (q. 3) may be wrtten as follows: C = C + Z (6) P, F, The spef osts per unt of fuel and produt exergy are two mportant parameters for an exergoeonom evaluaton: F, C F, =, F, P, 2. Problem Defnton C P, = (7) Besdes provdng valuable nformaton for the evaluaton and optmzaton of energy onverson systems, an exergoeonom analyss alulates the osts of eah produt stream from the overall system. However, the osts obtaned for ogeneraton proesses of heat and power are not always satsfatory. In the followng, the ogeneraton system shown n Fgure s used as an example. The thermodynam data of the plant are gven n TABL I. The system onssts of fve omponents: ar ompressor (AC), ar preheater (APH), ombuston hamber (CC), gas turbne (GT) and heat reovery steam generator (HRSG). The ost data and exerget effenes of the plant omponents are gven n TABL II. A onventonal exergoeonom analyss (Bean et al., 996) leads to a ost per unt of exergy of $20.76/GJ for the thermal energy, whle the ost of the eletr power amounts to only $4.55/GJ (see TABL III). The fat that the ost of thermal exergy s muh hgher than the ost of eletr exergy ontradts our physal understandng, whh suggests that eletr power s more valuable than heat and should, therefore, be more expensve. An examnaton of the ost formaton proess wthn the plant demonstrates how the 46 P, Int.J. Appled Thermodynams, Vol.4 (No.3) relatvely hgh ost of thermal exergy and the low ost of eletr exergy are obtaned. The exergy of the ar flow s nreased by the ar ompressor, the ar preheater (old sde) and the ombuston hamber. As the produt exergy of the named plant omponents s added to the exergy of the ar/exhaust gas flow, the osts of the exerget produts of the three omponents are added to the ost of the flow: C = + (8) 4 C + CP,AC + C P,APH C P,CC th C = 0 (9) the ost per exergy unt at the nlet of the gas turbne results to + + P,AC P,AC P,APH P,APH P,CC P,CC 4 = (0) 4 In the gas turbne, the ar preheater (hot sde) and the heat reovery steam generator, exergy s removed from the exhaust gas flow. The exergy removal taes plae at the average spef ost at whh exergy unts were prevously suppled to the flow by upstream omponents,.e. 4. = = = () F,GT F,APH F,HRSG Ths model of the ost formaton proess mples that the exerget fuel of the gas turbne, ar preheater (old sde) and the heat reovery steam generator s omposed dentally from the exerget produts of the ar ompressor, ar preheater and ombuston hamber. The exerget produt of the ar ompressor, beng relatvely expensve due to the hgh nvestment osts of ths system omponent and the expensve mehanal power used to drve ths omponent, s partly onsumed n the heat reovery steam generator wth ts relatvely low exerget effeny. th the ost of exergy destruton defned as: C = (2) D,K F, D, ths results n a hgh ost of exergy destruton, and therefore, also n a hgh ost of the produt exergy, the thermal energy suppled by the HRSG. However, a areful observaton of the ogeneraton system reveals that the ompresson of the nlet ar stream s only requred for the subsequent expanson n the gas turbne. The steam generaton n the HRSG ould be realzed exlusvely wth the thermal exergy suppled by the ombuston hamber and ar preheater. As the ompressor serves only the gas turbne, and therefore the generaton of eletr power, all osts assoated wth t (.e., the ost of exergy destruton and the nvestment ost) should be harged exlusvely to the eletr power. 4

3 Fgure : Cogeneraton system Int.J. Appled Thermodynams, Vol.4 (No.3) 47

4 Fgure 2: Cogeneraton system wth splt exergy streams 48 Int.J. Appled Thermodynams, Vol.4 (No.3)

5 3. A New Approah to Cost Assessment In the followng, a new approah for assessng the osts of eah produt stream s presented. Ths approah allows the osts aused by sngle plant omponents ndvdually to be assgned to the varous fnal produts of the overall system. The new approah s based on a splttng of all exergy flows aordng to ther purpose wthn the overall produton proess. In order to eep tra of the exergy addtons to and removals from the flow streams servng the generaton of the ndvdual n fnal produts of the plant, eah exergy stream s dvded nto n omponents, where s the part of whh serves the generaton of the th fnal produt of the plant. n = (3) = The splttng of exergy streams an be expressed by the splttng fators y : n y = wth y (4) = = Fgure 2 shows the ogeneraton plant of Fgure wth splt exergy streams. The purpose of the exergy splttng s to assgn the exergy destruton of the sngle plant omponents, and the ost aused by t, to the ndvdual fnal produts of the overall system. Therefore, n addton to the splttng fators for exergy streams, a splttng fator x s defned for the th system omponent. The splttng fator determnes to what extent the x omponent serves the generaton of the fnal produt of the plant. For the exerget produt of the plant omponent, the followng equaton apples: P, = x wth x (5) P, n = = In the th system omponent, the fuel exergy s transformed nto produt exergy wth the exerget effeny. If a unt of produt ε exergy of a th omponent serves the generaton of the fnal produt of the overall system, the fuel exergy onsumed by the system omponent n order to generate ths unt of produt exergy must also be assgned to the generaton of the fnal produt. F, = P, (6) ε For a gven plant omponent the only reasonable assumpton s that eah exergy unt enterng the plant omponent s transformed nto produt exergy wth the same exerget effeny ε. ε = ε (7) Thus, the exerget fuel of the th omponent s apportoned among the fnal produts n the same way as the produt of the system omponent: F, = x (8) F, In the same way, for the exergy destruton: D, = (9) F, P, A part servng the generaton of the fnal produt, an be obtaned: to: D, = (20) F, P, Combnaton of equatons (5)- (20) leads D, D, = y wth x (2) D, n = = s the part of the exergy destruton of the plant omponent whh s assgned to the generaton of the fnal produt of the overall system. 4. Applaton to the Cogeneraton Plant In the followng, the new ost assessment approah wll be llustrated by applyng t to the ogeneraton system shown n Fgure. The ogeneraton plant has two fnal produts: eletr and thermal energy; therefore eah exergy flow has to be dvded nto two parts: = + (22) = x + x wth x + x (23) = Here y and y are the splttng fators for the th exergy stream. In the frst step, the splttng fators and x for the th system x omponent are defned aordng to the purpose of the omponent. The ar ompressor and gas turbne serve exlusvely the generaton of the eletr power. Therefore: x AC = x (24) AC = 0 x GT = x (25) GT = 0 The heat reovery steam generator serves the generaton of thermal energy only: x HRSG = 0 x (26) HRSG = Int.J. Appled Thermodynams, Vol.4 (No.3) 49

6 The ombuston hamber and ar preheater are nvolved n the produton proess of both heat and power. It s assumed that the ar preheater ontrbutes to the generaton of eah produt wth the same perentage as the ombuston hamber. x = x x = x (27) APH CC APH CC In the seond step, the splttng fators of the exergy flows leavng the overall system are defned. The exergy of the fnal produt of the system s, per defnton, exlusvely assgned to the fnal produt. e obtan for the eletr power: x 2 = x 2 = 0 (28) resultng n = 2 = 0 (29) 2 2 and for the thermal power: x 9 = 0 x (30) 9 = resultng n 9 = 0 = (3) 9 9 For eah stream that leaves the system and does not represent a fnal produt (e.g., exhaust gas or oolng water), the splttng fators must also be determned. In the ase of the ogeneraton plant, ths onerns the exhaust gas leavng the heat reovery steam generator. e assume that the exergy of streams s dvded between the fnal produts aordng to the power/heat rato of the overall system: are: x x 7 2 = (32) + ( ) = (33) + ( ) The exergy shares of the exhaust gas stream = (34) 7 x 7 7 = (35) 7 x 7 7 Ths s equvalent to the assumpton requred for the dstrbuton of the osts of the exhaust gas stream between the eletr and thermal power made n the exergoeonom analyss wthout dvson of the exergy flows. One the exergy splttng fators for all streams leavng the system have been defned, the parts of the exergy streams added to and removed from the materal streams by eah plant omponent have to be determned. th the ad of the splttng fators of the system omponents, 50 Int.J. Appled Thermodynams, Vol.4 (No.3) the fuel and produt of eah omponent s dvded nto two parts and, as well as P, and P, F, F,. Based on the splttng of the fuel and produt of the th system omponent, one equaton an be formulated for eah stream enterng the plant omponent, assumng that the extng streams are nown ether from downstream plant omponents or beause they are leavng the overall system. Ths way, all the exergy streams wthn the system an be determned. In the followng, the exergy streams and of the ogeneraton plant are alulated. At frst, the dea on whh the new approah s based wll be llustrated wth the help of the ar ompressor. From ts exerget effeny: P,AC 2 ε AC = = (36) F,AC and equatons (5)-(8), we obtan: = = x = (37) F,AC P, AC 2 AC AC = = x ( ) = (38) 2 = = x 0 (39) F,AC AC = = = x ( ) 0 (40) P,AC 2 AC 2 = The produt of the ar ompressor onssts n the nrease of the exergy of the ar stream passng through the ompressor. Thus: = + (4) 2 P,AC Ths equaton appled separately to the exergy parts and leads to: 2 2 = + = + x ( ) (42) 2 P, AC AC 2 = + = + x ( ) (43) 2 P,AC AC 2 Applyng quatons (42) and (43) n ombnaton wth quaton (24), the example of the ar ompressor llustrates an mportant aspet of the new approah: If a plant omponent serves exlusvely the produton of one fnal produt of the system (e.g., eletr wor), the exergy parts assoated wth the other fnal produts (e.g., heat) pass through the omponent unhanged. Thus, n the produton proess of the fnal produt, only those omponents partpate that ontrbute to the generaton of the fnal produt. ah system omponent that ontrbutes to more than one produt stream has the same thermodynam behavor (.e. the same exerget effeny) for eah ontrbuton. In Fgure 3 the flow sheets for generatng eletr and thermal energy are llustrated separately. 2

7 Fgure 3: Flow sheets showng the separate generaton of eletr and thermal energy Int.J. Appled Thermodynams, Vol.4 (No.3) 5

8 The ar ompressor has four enterng flows (exergy parts and of the nlet ar and the mehanal wor), therefore four equatons are needed. The exergy part of the nlet ar flow s alulated wth quaton (42). For the exergy part power, we obtan from quaton (37) x AC of the mehanal = (44) The exergy part an be determned wth quaton (22). In the followng, only the equatons for the exergy part servng the generaton of the eletr energy are gven. The next plant omponent to be onsdered s the ar preheater wth the exerget effeny: 3 2 ε APH = (45) 5 6 Its produt s added to the ar flow. = (46) x APH P,APH The fuel of the ar preheater s subtrated from the hot gas stream. = (47) 6 5 xaph F,APH quatons (46) and (47) provde the means for alulatng the exergy parts for the two streams enterng the ar preheater: = + x ( ) (48) 2 3 APH 2 3 = + x ( ) (49) 5 6 APH 5 6 For the ombuston hamber wth the exerget effeny: 4 3 ε CC = (50) 0 e obtan the followng equaton related to the nlet ar stream: get: = + x ( ) (5) 3 4 CC 3 4 For the fuel,.e. the natural gas flow we = (52) 0 xcc 0 The exerget effeny of the gas turbne: + 2 ε GT = (53) 4 5 leads to the equaton: = + x ( ) (54) 4 5 GT 4 5 The last plant omponent s the heat reovery steam generator wth the exerget effeny: 9 8 ε HRSG = (55) 6 7 and the followng relatons for the exergy parts servng the generaton of the eletr energy: = + x ( ) (56) 8 9 HRSG 8 9 = + x ( ) (57) 6 7 HRSG 6 7 wth quaton (26) we obtan: = (58) 8 9 = (59) 6 7 The system of equatons to be solved onssts of (a) the defntons of the splttng fators of the plant omponents (quatons (24) to (27)), (b) the splttng fators of the streams leavng the overall plant (quatons (28), (30), (32)), () the equatons for the alulaton of the exergy parts assoated wth the produton of the eletr energy (quatons (29), (3), (34), (42), (44), (48), (49), (5), (52), (54), (56), (57)), and (d) quaton (22) appled to eah stream. Note that only four equatons are formulated for the splttng fators of the fve omponents. One degree of freedom s needed to ensure that the overall exergy balane of the plant s fulflled. The exergy streams enterng the overall system are alulated based on the splttng fators of the omponents and the streams leavng the plant. As the exergy of the ar stream enterng the ompressor s zero, the exergy parts and of ths stream are also zero: = 0 (60) = 0 (6) hen quaton (60) s also onsdered n the equaton system, the exergy parts servng the generaton of the eletr and thermal energy an be alulated. The exergy parts of the flow streams of the ogeneraton plant are gven n TABL I. The equatons formulated for the nlet streams of a omponent an be generalzed as follows: If the exergy stream beng onsdered s "ontnuous",.e. t appears n the defnton of the exerget effeny as an exergy dfferene (Lazzaretto and Tsatsarons, 999), n out we obtan: n = + x ( ) (62) out n out 52 Int.J. Appled Thermodynams, Vol.4 (No.3)

9 Ths equaton an be appled regardless of whether the exergy stream n onsderaton belongs to the fuel or produt of the omponent. If the enterng exergy stream s an "nterrupted" one, we obtan: n = x (63) n One the exergy parts are determned, the exergoeonom ost balanes and auxlary equatons presented n prevous exergoeonom approahes (e.g. Bean et al. 996, Lazzaretto and Tsatsarons 999) an be appled separately for eah fnal produt of the system. For ths purpose, the non-exergy related osts (.e. nvestment, operaton and mantenane osts) of the th system omponent are apportoned among the fnal produts of the system usng the applable splttng fators for ths omponent: Z n = = x Z or, formulated for the ogeneraton plant: Z and: Z (64) = x Z (65) = x Z (66) The ost balane of the th omponent related to the generaton of the fnal produt reads: C = C + Z (67),out,n The requred auxlary equatons are formulated aordng to the f-rule and p-rule (Lazzaretto and Tsatsarons 999), based on spef osts per unt of exergy related to the ndvdual fnal produts of the plant: C = (68) As an example, the ostng equatons obtaned for the ar preheater are gven. For the produton of eletr energy, the followng equatons are obtaned: C + + (69) 3 C 6 = C 2 + C 5 Z APH 6 5 = (70) The ostng equatons related to the produton of thermal energy are dental, wth the supersrpt beng replaed by. The osts of the exergy flows obtaned wth the new approah are gven n TABL I, the nvestment osts and osts of exergy destruton of the omponents related to the generaton of thermal and eletr energy are lsted n TABL II. The osts of the fnal produts of the system are shown n TABL III. The spef osts per unt of exergy alulated wth the new approah amount to $7.05/GJ for the eletr energy and $4.89/GJ for the thermal energy. These results obtaned wth the new approah agree wth the expeted produton osts. If we set the non-exergy-related osts of all system omponents to zero: Z = 0 (7) and dvde all ost values by the ost per exergy unt for the fuel of the overall system: = (72) F,tot 0 e alulate the exerget osts (Lozano and Valero, 993),.e. the exergy unts of fuel requred to generate a unt of exergy n the system. The exerget osts of the flow streams and the exerget osts per unt of fuel and produt exergy for the omponents of the ogeneraton plant obtaned wth the new approah and wthout splttng of the exergy flows are shown n TABLS I and IV. The exerget osts are denoted wth the supersrpt 0. The exerget osts of the fnal produts are gven n TABL III TABL III. COSTS OF TH FINAL PRODUCTS ITHOUT XRGY SPLITTING AND ITH TH N APPROACH thout exergy splttng New Approah el $4.55 /GJ $7.05 /GJ th $20.76/GJ $4.89 /GJ C el $572 /h $84 /h C th $950 /h $683 /h 0 el.780 GJ/GJ.847 GJ/GJ 0 th GJ/GJ 2.32 GJ/GJ 5. Conlusons The systemat applaton of the new approah may be summarzed as follows: ) The fnal produts of the plant are dentfed. 2) The splttng fators of the system omponents are defned dependng on the purpose of eah omponent. 3) The splttng fators for the exergy streams leavng the overall system are determned. 4) For eah omponent wth m enterng exergy streams, m equatons of the form of quaton (62) or quaton (63) are formulated Int.J. Appled Thermodynams, Vol.4 (No.3) 53

10 TABL I. THRMODYNAMIC AND COST DATA OF TH FLO STRAMS ITHIN TH COGNRATION PLANT flow Thermodynam data Costs wthout exergy splttng New approah: exergy shares and osts m T p C 0 C C 0, 0, No. [g/s] [ C] [bar] [M] [$/h] [$/GJ] [GJ/GJ] [M] [M] [$/h] [$/h] [$/GJ] [$/GJ] [GJ/GJ][GJ/GJ] TABL II. XRGTIC FFICINCY AND COST DATA FOR TH COMPONNTS OF TH COGNRATION PLANT Comp. Costs wthout exergy splttng New approah: splttng fators and osts є Z C D f p x Z Z C D C D f f p p % [$/GJ] [$/GJ] [$/GJ] [$/GJ] [-] [$/h] [$/h] [$/h] [$/h] [$/GJ] [$/GJ] [$/GJ] [$/GJ] AC CC APH GT HRSG TABL IV. XRGTIC COSTS OF FULS AND PRODUCTS OF TH COMPONNTS OF TH COGNRATION PLANT wthout e. splttng New approah Comp. 0 F 0 P 0, F 0, F 0, P 0, P [GJ/GJ] [GJ/GJ] [GJ/GJ] [GJ/GJ] [GJ/GJ] [GJ/GJ] AC CC APH GT HRSG Int.J. Appled Thermodynams, Vol.4 (No.3)

11 dependng on whether the exergy stream beng onsdered s a ontnuous or an nterrupted one. 5) The exergy parts servng the generaton of eah fnal produt are alulated. 6) The nvestment osts of the plant omponents are apportoned among the fnal produts of the system wth the ad of the splttng fators of the plant omponents. 7) The ost balanes and auxlary equatons of the omponents are formulated separately for eah exergy form and the osts of the exergy flows and the fnal produts of the plant are alulated. The new exergoeonom approah leads to results that dffer sgnfantly from the results obtaned wth onventonal thermoeonom or other approahes. Appled to a ogeneraton plant, the new approah provdes among these approahes the best ost estmates for the osts of the fnal produts generated n the same system. One spef haraterst of the new approah les n the freedom left to the engneer to defne the purpose of eah system omponent through the splttng fators to be used for ths omponent. As the equatons for the alulaton of the exergy streams follow a fxed sheme and the same ost balanes and auxlary equatons are appled as n prevous exergoeonom approahes, the man addtonal tas s the defnton of the splttng fators of the plant omponents. These splttng fators depend on the udgment of the engneer, and are therefore to some extent arbtrary. The nfluene of the assumed splttng fators on the osts of the fnal produts of the ogeneraton plant used as an example was nvestgated by rlah (2000). hle n a smple energy onverson system le the ogeneraton plant onsdered n ths artle a physally reasonable and well thought-out defnton of the splttng fators s feasble, t mght get very omplated n a more omplex plant. The pratablty of the method, therefore, depends on the omplexty of the analyzed system. Further researh and applatons of the presented approah, partularly applatons to more omplex systems, are requred. Nomenlature Symbols ost per unt of exergy [$/GJ] C ost rate [$/h] exergy rate [M] m mass flow rate [g/s] n number of produt streams for the overall system[-] p pressure [bar] T temperature [ C] x splttng fator for equpment[-] y splttng fator for exergy streams [-] Z non-exergy-related ost rate [$/h] Gree Symbols ε exerg effeny [-] Subsrpts D exergy destruton F exergy of fuel stream plant omponent L exergy loss P exergy of produt Supersrpts servng the generaton of the th produt stream of the plant servng the generaton of eletr energy servng the generaton of thermal energy 0 only fuel osts are onsdered Referenes Bean, A., Tsatsarons, G., Moran, M. 996, Thermal Desgn and Optmzaton, J. ley, New Yor. rlah, B., 2000, Zuwesung zu den Kosten energentensver Prozesse, Dploma Thess, Tehnal Unversty of Berln, Insttute for nergy ngneerng. Frangopoulos, C., 983, Thermoeonom Funtonal Analyss: A Method for the Optmal Desgn or Improvement of Complex Thermal Systems, PhD Thess, Georga Insttute of Tehnology. Lazzaretto, A., Maor, A., Ren, M., 993, XSO: xergoeonom Symbol Optmzaton for nergy Systems, Part I and II, Proeedngs of nergy Systems and ology, pp , Kraow. Lazzaretto, A., Tsatsarons, G., 997, On the uest for Obetve quatons n xergy Costng, Proeedngs of the ASM Advaned nergy Systems Dvson, AS-Vol. 37, pp Lazzaretto, A., Tsatsarons, G., 999, On the Calulaton of ffenes and Costs n Thermal Systems, Proeedngs of the ASM Advaned nergy Systems Dvson, AS-Vol. 39, S , (ed.: Aeves, S. M., Garmella, S., Peterson, R.). Lozano, M. A., Valero, A., 993, Theory of the xerget Cost, nergy The Internatonal Journal, Vol. 8, No. 3, pp Penner, S. S., Tsatsarons, G. (eds.), 994, Invted Papers on xergoeonoms, nergy Int.J. Appled Thermodynams, Vol.4 (No.3) 55

12 The Internatonal Journal, Vol. 9, No. 3, pp Torres, C., Valero, A., Serra, L., Lozano, M. A., 996, The Produtve Struture and Thermoeonom Theores of System Optmzaton, AS-Vol. 36, Proeedngs of the ASM Advaned nergy Systems Dvson. Tsatsarons, G., Ln, L., 990, On xergy Costng n xergoeonoms, Computer-Aded nergy Systems Analyss, Ameran Soety of Mehanal ngneers, AS-Vol. 2, pp. -, (ed.: Tsatsarons, G., Baura, R.A., Kenney,.F., Restad, G.M.), New Yor. Tsatsarons, G., nhold, M., 985, xergoeonom Analyss and valuaton of nergy-converson Plants Part I and II, nergy The Internatonal Journal, Vol. 0, No., pp Valero, A., Lozano, M. A., Munoz, M., 986, A General Theory of xergy Savng Part I and II, Computer-Aded ngneerng of nergy Systems, AS-Vol. 2-3, pp. -2. Valero, A., Correas, L., Serra, L., 999, On-lne Thermoeonom Dagnoss of Thermal Power Plants, Thermodynam Optmzaton of Complex nergy Systems, (ed.: Mamut,., Bean, A.), NATO Sene Seres 3, Hgh Tehnology, Vol. 69, Kluwer Aadem Publshers, Dordreht, Netherlands. Von Spaovsy, M. R., 986, A Pratal Generalzed Analyss Approah to the Optmal Thermoeonom Desgn and Improvement of Real-orld Thermal Systems, PhD Thess, Georga Insttute of Tehnology 56 Int.J. Appled Thermodynams, Vol.4 (No.3)