Electricity transmission network optimization model of supply and demand the case in Taiwan electricity transmission system


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1 Electicity tansmission netwok optimization model of supply and demand the case in Taiwan electicity tansmission system MiaoSheng Chen a ChienLiang Wang b,c, ShengChuan Wang d,e a Taichung Banch Gaduate Institute of Management Sciences Nanhua Univesity Taiwan R.O.C. b Gaduate Institute of Management Sciences Tamkang Univesity Taiwan R.O.C. c Taichung Banch Powe Supply Depatment of Taiwan Powe Company Taiwan R.O.C. d Depatment of Finance Asia Univesity Wufong, Taichung Taiwan R.O.C. e Depatment of Industial Management National Yunlin Univesity of Science and Technology Touliu, Yunlin Taiwan R.O.C. heny Jounal of Infomation & Optimization Sciences Vol. 27 (2), No. 2, pp c Tau Publications /06 $
2 318 M. S. CHEN, C. L. WANG AND S. C. WANG Abstact The electicity system can be divided into powe geneation, tansmission and distibution subsystems fom the stuctue point of view. Electicity business is positioned as a public business and egulated by picing and quantities due to the high publicly utilization. The powe tansmission system is esponsible fo powe tansmission fom powe geneation plants to the aeas of powe utilization. Since thee is the chaacteistic that electicity needs to poduce and sell with immediate and instant balance, it is equied to constuct the complete powe tansmission netwok in chage of the powe dispatching in ode to povide stable electicity. The pice of puchases and sales is closely elated with the necessity of powe supply and demand. The pupose of this pape is to intoduce the optimization model of powe supply and demand in the independent powe tansmission netwok fo the maximization of consume and poduce s suplus in the libealization of electicity business. We apply this model to discussing the elationships of electicity quantity and pice of puchases and sales. In addition, the sensitive analysis is intoduced as well. We conclude that the maximal pofit of powe tansmission netwok will be deceased when quantity of powe utilization, cost of powe geneation and maintenance cost of tansmission netwok ae inceasing. Instead, the maximal pofit of powe tansmission netwok will be inceased when powe tansmission ate is inceasing. Keywods and phases : Electicity system, publicly utilization, powe tansmission netwok, consume and poduce s suplus, libealization of electicity business. 1. Intoduction Powe geneation and sales ae the enomous and complicated poductiondemand supply chain systems. As efeing to the electicity libealization counties in the wold, the electicity business is hoizontally divided into thee sectos, i.e. geneation, tansmission and distibution (including electicity sale). The geneation and distibution business ae open competition fo electicity multisupply. The tansmission netwok is defined as monopolistic public system and esticted by the effective egulation. It povides a fai electicity tansmission envionment with supply and demand in ode to eliminate the defect of inteacting subsidy and enhance efficiency maket opeation with classified into mandatoy and voluntay pool that combine with poduces and consumes contact. Each powe geneation secto can be poduced powes independently. Each distibution secto can be taken chage of powe maketing and distibution in its own aea. Both of them ae elatively
3 NETWORK OPTIMIZATION MODEL 319 independent and opeated businesses individually. The tansmission secto is esponsible fo the longdistance powe tansmission fom each powe plant to each distibution secto and kept electicity instantly balanced. It will cause powe shutdown when powe supply and demand ae not balanced (supply is lage than demand o demand exceeds to supply). The tansmission netwok is egaded as public fai institution to opeate the powe maket equitably since thee is economy of scale and monopoly in the whole wold. Howeve, most of the past eseaches focus on the picing of geneation and distibution system and less of tansmission system. The tansmission system is one of the key factos in the entie powe system that teats as the channel ole in the electicity supply chain system. This eseach is to popose the electicity supply and demand optimization model fo tansmission system and discuss its picing and quantity s elationship of powe acquisition and sales. Most of the past eseaches ae adopted unitay picing appoach except duing peak load. Howeve, it is uneasonable that consumes should not only pay unit vaiable cost but also shae poduces fixed cost in the industy with aveage cost deceasing. It will be the unfavoable influence fo element of poduction and allocation of eaning if the electicity picing is base on magin cost and fixed cost exclusively. Moeove, the demand cuve can t be estimated accuately so that it causes poduce s loss. Twopat taiffs efe to that poduce chages fixed utilization fee and vaiable poduct pice. It includes fixed cost and avoided poduce bankuptcy cisis whose picing adapts maginal cost picing. It is based on the cost and pofit picing in most of woldwide companies including Taiwan Powe Company. The electicity pice adjustment of Taiwan Powe Company concens about the factos of fuel cost and pice index. Some scholas, such as Chistodoulopoulos [1], Lindblom and Andesson [4], and Joskow and Kahn [3], have discussed the poduction and competitive picing stategy of each powe geneation plant and elative issues afte powe maket libealization. Thee is the chaacteistic of powe system that diffeent aw mateials can be poduced the same electicity. And the same electicity will ceate vaious utilizations by diffeent applications. Fo example, hydopowe, themal powe o nuclea powe plants can poduce the same electicity such as fequency and voltage with diffeent ow mateials. The same electicity can povide industial poduction mateials with diffeent
4 320 M. S. CHEN, C. L. WANG AND S. C. WANG utilization o enduses consumption. Fom the management point of view, thee is the chaacteistic of same supply function and vaious utilizations with diffeent usage fo powe supply and demand. In addition, electicity business is featued by high public utilization, consistency of poduction and maketing, economy of scale and technology. In the powe supply and demand system, geneation sectos poduce powe as much as possible in ode to opeate the invested equipments effectively and gain maximum pofits. And distibution sectos povide powe with high quality and low pice in ode to enhance uses will of usage and satisfy uses equiement of quality and pice. Tansmission netwok plays the ole to connect with geneation and distibution sectos. It is esponsible fo powe tansmission and egulation with powe geneation and distibution. It also undetakes the cost and powe loss duing tansmission pocess. Theefoe, the quality, eliability and picing decision of tansmission netwok affect whole electicity system, cost stuctue and electicity picing. The powe dispatching is esponsible fo Independent System Opeato (ISO) afte electicity maket deegulated in Califonia, U.S.A [6]. Powe geneating egulation has withdawn and pice is depended on maket competition. In England, the tansmission affai is esponsible fo National Gid Company (NGC). The powe geneation companies sign Pooling & Settlement Ageement (PSA) with NGC. PSA in England is tansmission system of cental enfocement combining tansmission netwok, electicity tade with dispatching. In the electicity tade system, consumes can choose powe povides when the quantity is highe than 100kw. It can be shown easonable powe pice though the competition of electicity etaile maket. In Austalia, electicity libealization affai ae esponsible fo National Gid Management Council (NGMC). It is divided into powe geneation, tansmission and distibution business into the competitive mechanism. Electicity tansmission netwok is opeated fo Victoia Powe Net (VPN). Powe dispatching and exchange ae esponsible fo Victoia Powe Exchange (VPE). The electicity pooling in Austalia is monopolistic and all powes fom geneation plants must be dispatched by VPE except small plants that electicity geneating is unde 30mw. The powe tansmission is in chage of Tans Gid (TG).
5 NETWORK OPTIMIZATION MODEL 321 The electicity evolution in New Zealand is to povide the best welfae via competition of powe geneation secto, uses option opening and contact exchange system with poduces and consumes. They egad the maket suveillance committee as an independent institute to supevise powe maket opeation, and implement elative egulation, and play the ole of coodination with agument fo all paticipants. New Zealand Tanspowe (NZT) of stateown entepise is in chage of tansmission netwok and powe dispatching. The powe tansmission pice is efeed to the conditions of tansmission netwok limitation and utilization by NZT. Electicity Copoation of New Zealand (ECNZ) announces powe tansmission pice and the condition of netwok utilization once pe two hous in ode to decide powe demand and pice that ae willing to pay accoding to given infomation. In Taiwan, the powe supply and demand changes fom egulatoy synthesis electicity business into open geneating business company. The pivate geneation plants sell electicity to synthesized electic business company with political contact, which doesn t calculate costs sepaately fo powe geneation, tansmission and distibution. Consideing the specialization and evolution in Taiwan powe maket and efeing to libealization model of electicity business in the whole wold [2], [5], [7], [8], [9], [10], [11], we assume that Taiwan powe business is divided into geneation, tansmission and distibution sectos. Powe tansmission secto is the monopolized public independent depatment. The pupose of this pape is focus on the Taiwan powe tansmission system. We conside Taiwan powe tansmission netwok independent and monopolistic. And we develop the optimization model of the electicity tansmission netwok that discusses supply and demand elationship of powe geneation, distibution and tansmission system with custome and poduce s suplus maximum point of view. And the sensitivity analysis is intoduced with decision vaiables and optimization solutions. 2. Constuct optimization model of electicity tansmission supply anddemand 2.1 The pespective of consume s suplus Accoding to supply and demand theoy of economics, demand cuve is declined fom uppe left to lowe ight in which means the vai
6 322 M. S. CHEN, C. L. WANG AND S. C. WANG ation of pice is opposite diection with puchase quantity. And supply cuve is extended fom lowe left to uppe ight in which means the supply quantity will incease when the pice is ising. The elationship of demand and supply is shown in Figue 1. Figue 1 Supply (S) and demand cuve (D) Consume s Suplus (CS) efes to the diffeence between the maximum pice a buye is willing and able to pay fo a good o sevice and the pice actually paid. When P 0 is a maket pice that is in the demand cuve D, demand volume is esponse to Q. The aea of P 0 OQ 0 E is the pice that consumes actually pay. The aea of AOQ 0 E is the pice that consumes ae willing and able to pay. The diffeence between both is aea AP 0 E that means custome s suplus. The elationship of demand cuve and CS is shown as following. Figue 2 Relationship of demand cuve and consume s suplus
7 NETWORK OPTIMIZATION MODEL 323 In economic theoy, the final poduct and sevice s pice is decided by supply and demand of maket in the completely competition envionment. The final pupose of all economic activities is to consume. So consumes ae the main decision make in the whole activities. The diection of economic activities is decided by consumes will and poduces play the ole offeing a good sevice. Thee ae featues that electicity can t be stoed and equies fo immediate sales afte geneation in the electicity maket. The successful opeation of electicity maket should be poceed and coodinated with powe geneation, tansmission and enduse consistently. The enduse is willing to consume electicity that is detemined by the needs of timing and the timing pice. The powe geneation plant is willing to poduce electicity that is detemined how many pofits it can get in the timing pice. The powe tansmission netwok concens about the balance of all necessay expenses and evenues. Theefoe, timing picing of powe tansmission netwok has an impact on the pice of demand (P d ) and pice of supply (P s ) fo powe geneation plants, and egulated diffeence between the volume of powe geneation and consumption. The powe supply and demand s balance is that the volume of electicity supply (including all kinds of powe supply) should satisfy the use s demand (including all kinds of demand) adequately. Othewise, the powe shotage o oveloading will be happened. Howeve, thee will be powe loss duing the tansmitting in the tansmission netwok. We define means the effective powe tansmission ate in tansmitting, then we can get: 0 < < 1, The powe demand of use s maket (q d ) = The powe supply of geneation maket (q s ) effective powe tansmission ate (). The use s pice in time t fo uses is q d (P d (t)). The sale s pice in time t fo geneation plants is q s (P s (t)). It means the powe egulation oganization should adjust volume of powe supply and demand accoding to the pice of supply P s (t), pice of demand P d (t) and unit pice of powe tansmission y in diffeent time t. The pupose of the pape is to analyze the elationship of supply and demand of powe geneation, tansmission and distibution maket.
8 324 M. S. CHEN, C. L. WANG AND S. C. WANG 2.2 Model assumption and notation This pape is to discuss the elationship of electicity supply and demand fo powe geneation, tansmission and distibution in peiod of time. The assumption and notation is as following: P = f (Q) : Demand function of powe distibution maket, whee f is the continuously stict deceasing concave function of Q, i.e., f (Q) so and f (Q) < 0 Q, f (0) C (0) > 0. : Powe effective tansmission ate, whee 0 < < 1. i.e., the effective unit powe volume that is tansmitted fom geneation to distibution maket. Q : Powe consumption volume of distibution maket. Q : Powe geneating volume of geneation maket. y : Powe tansmission cost paid to powe tansmission netwok that the unit powe volume of geneation maket (which is equal to unit powe volume of distibution maket) tansmits to distibution maket. y ) ( Q p 1 = C ( ) Q p 2 = C + y : Powe tansmission cost paid by the unit powe volume of distibution maket. : Supply function of powe geneation maket (excluding tansmission cost). : Supply function of powe distibution maket (including tansmission cost). Whee, C is the continuous stict inceasing convex function and satisfies the following conditions: ( ) ( ) ( ) C Q > 0, C Q > 0, C Q > 0, Q, f (0) > C (0), o C (Q) > 0, C (Q) > 0, C (Q) > 0 Q. A : Powe tansmission cost of tansmission netwok, including the appotion cost of facilities assets evaluation in existing tansmission netwok, cost of equipments eplacement, inteest and maintenance cost.
9 NETWORK OPTIMIZATION MODEL 325 As the elationship of consume s suplus, poduce s suplus and unit tansmission cost is shown as Figue 3. Figue 3 Relationship of consume s suplus, poduce s suplus and decision vaiable y of tansmission netwok In Figue 3: Value of aea ABD is the consume s suplus coesponded to y. Value of aea BCD is the poduce s suplus coesponded to y. Value of aea CEGD is powe tansmission eaning fo Powe Regulation Oganization of tansmission netwok. Value of aea ACD is the value of social welfae coesponded to y (i.e., sum of consume s suplus and poduce s suplus). As we know: the geate of y, the less of Q y. Theefoe, aea ACD is the inceasing function of Q y (i.e., aea ACD is the deceasing function of y ). Moeove, the close Q y appoached to Q 0, the geate aea ACD coesponded to Q y. It means the powe tansmission eaning may not incease since the will of poduction and consumption is deceases when y inceases.
10 326 M. S. CHEN, C. L. WANG AND S. C. WANG 2.3 The optimization model of consume s suplus and poduce s suplus maximum when the eaning of powe tansmission netwok is achieving to A The pupose of libealization is to deegulate the stateowned entepise that is esticted by govenment egulation and poo pefomance in ode to enhance coopeation competitiveness. Take Taiwan powe maket fo example. Taiwan Powe Company (TPC, the stateowned company which monopolizes the Taiwan powe maket) needs to evaluate assets, and calculates appotion cost of facilities, inteest, maintenance cost and equipment eplacement cost fo the base of powe tansmission cost A. In addition, powe tansmission netwok is established by govenment what is independent and fai institution. It should be supevised by Congess (Legislative Yuan) and equied to pay in suplus to the state teasuy. Theefoe, the suplus should be consideed when A is calculated. As above assumption, we constuct the tansmission model that is maximized the weighted aveage of consume and poduce s suplus as following: The Objective function Max π(q y) = Max π(q) 0 y y 0 Q Q 0 Q = w 1 [ f (Q) C (Q)]dx 0 ( ) Q ( ) + w 2 f (Q) C Q f (Q) Q C dx (1) 0 [ ( )] Subject to π(q) = Q f (Q) C Q A. Whee Q y is the stict deceasing function of y (as shown in Figue 3). Weight w 1 and w 2 ae nonnegative constant. The optimal solution of this model shall be: Assume y and Q ae the optimal solution of Fomula (1). And let Q = Q y. Fom Fomula (1), we have: π(q) = g(q) w 1 ( 1 1 ) π(q). (2) Q Q Whee, g(q) = w 1 [ f (x) f (Q)]dx + w [ ( ) C Q ( C x ) ] dx.
11 NETWORK OPTIMIZATION MODEL 327 Q Since g (Q) = w 1 f 1 Q ( ) Q (Q)dx + w 2 dx > 0. 0 So g(q) is the stict inceasing function of Q. (3) Fom Fomula (1) and (2), we have the elationship π(q) and Q shown in following: 0 Figue 4 Relationship of objective function π(q) and volume Q [ Fom Figue ( )] 4, Q is satisfied the constaint of this model: π(q) = Q Q f (Q) C A, the necessay and sufficient condition of Q is: Q [Q (1) A, Q(2) A ]. Any Q in [Q(1) A, Q ] is witten as Q 1. One of Q in [Q, Q (2) A ] is witten as Q 2 and let π(q 1 ) = π(q 2 ). Fom Fomula (2) and (3), we have: π(q 2 ) = g(q 2 ) w 2 ( 1 1 ) π(q 2 ) > g(q 1 ) w 2 ( 1 1 ) π(q 1 ) = π(q 1 ). It means the optimal solution Q 2 of this model should be satisfied Q 2 [Q, Q (2) A )]. In addition, fom the Fomula (2), (3) and Figue 4, we have: π (Q) = g (Q) w 2 ( 1 1 ) π (Q) > 0 Q [Q, Q (2) A ] (4)
12 328 M. S. CHEN, C. L. WANG AND S. C. WANG i.e., π(q) is the stict deceasing function of [Q, Q (2) A ]. Theefoe, the optimal solution Q 2 of this model is satisfied the following: [ ( Q π(q 2 ) = Q 2 f (Q ) C )] 2 = A. It means Q 2 = Q(2) A. (5) If π(q 2 ) > A, then δ > 0 is existed, we can get π(q 2 + δ) > A. Q 2 + δ is the feasible solution of this model and we can get the in equation π(q 2 + δ) > π(q 2 ) fom Fomula (4). Since it is contadicted with assumption that Q 2 is the optimal solution of this model, so we have Fomula (5) poved. 3. Sensitivity analysis 3.1 Influence of demand function f changes The electicity tansmission netwok should egulate the supply and demand of electicity and set easonable time s pices (P(t)) fo efeence of geneation plant and enduse in ode to balance supply and demand in the whole system. Time s pice affects the investment and opeation of geneation plants and will of enduses. It is necessay to conside powe geneation cost (k), maintenance cost of tansmission netwok (A), tansmission expense of unit quantity fo distibution maket (y), powe loss (1 ) and the ight of consumes in ode to each the maximal welfae when tansmission netwok detemines the time s pice. The maintenance cost of powe tansmission netwok (A) includes appotion of tansmission facilities depeciation and egulaly maintenance expense. In the electicity system, geneation plants ae supplies when tansmission netwok is demande. Tansmission netwok is supplie when all kinds of enduses (including diffeent powe utilization) ae demandes. Fom figue 3 we have: p = f (Q) = f 1 (Q) + f 2 (Q) + f 3 (Q). Whee, f 1, f 2, and f 3 ae demand functions of powe utilization fo industy, commecial and household.
13 NETWORK OPTIMIZATION MODEL 329 Diffeent timing and time s pices can geneate diffeent quantity of powe demand fo diffeent kinds of utilization. Fo example, the powe utilization fo industy is consumed diffeent quantities of powe in diffeent seasons and timing fo diffeent industies. The demand fo commecial utilization is also vaious with diffeent commecial activities and diffeent time. So does the quantity demand fo the household utilization quantities. Geneally, the powe utilization of household is less fom midnight to ealy moning. This is the diffeence of peak and offpeak time fo powe supply and demand. Theefoe, the time s pices ae necessay to be consideed in powe picing. The discussion and analysis of Figue 3 is based on the time inteval, that is, the cuve f is diffeent caused by diffeent time. When f is inceasing to f 1, that is f 1 > f, the optimal powe quantity is inceasing fom Q f to Q f 1 in Fomula (5). Figue 5 illustates the elationship as following: C ( Q f Figue 5 The optimal solution Q moves fom Q f to Q f 1 when f is inceasing to f 1 In ) addition, the ) magin cost powe geneation is inceasing fom to C ( Q f1 fom Figue 5. Figue 6 illustates the elationship of powe utilization quantity and powe tansmission cost as following. When the quantity of powe
14 330 M. S. CHEN, C. L. WANG AND S. C. WANG utilization is fom Q f to Q f 1 the cost of powe tansmission will be changed fom y f to y f 1. Figue 6 Influence when both demand function f and maginal demand function f 1 incease The value of optimal tansmission unit cost y and electicity pice p fo distibution maket depend on f, C and. 3.2 Influence of optimal solution fo powe tansmission efficiency changes The powe tansmission efficiency is highe when tansmission efficiency is less that is geate. Geneally speaking, tansmission efficiency is elated with the tansmission distance, esistance of tansmission wie and netwok stuctue. When powe tansmission efficiency is inceasing to 1, that is 0 < 1 < 1, we have Q < Q 1 fom Figue 5 and P > Q 1 shown in Figue Influence of optimal solution when lowe limit of tansmission cost A is inceasing to A 1 We have Q A 1 < Q A fom Fomula (5) and Figue 6. Then we can get P A > P A 1 and y A > y A 1, that is y A > y A 1, fom Figue 8.
15 NETWORK OPTIMIZATION MODEL 331 Figue 7 Influence of optimal solution when is inceasing to Figue 8 Influence of Q and y when the lowe limit of tansmission cost A is inceasing to Q 3.4 Influence of powe geneation magin cost when C is inceasing to C 1 If the elationship of powe geneation magin cost is as following: C < C 1, C < C 1.
16 332 M. S. CHEN, C. L. WANG AND S. C. WANG Since dπ(q) is the stict deceasing function of Q and C is the total dq cost of powe tansmission system, π(q) must decease when the powe tansmission cost inceases. 3.5 Relationship of the decisive vaiable and optimal solution What the quantity Q changes affects the volume P fom Fomula (5). The demand cuve P = f (Q) = f 1 (Q) + f 2 (Q) + f 3 (Q) is the stict deceasing function and f < 0. Theefoe, f (Q) is deceasing when Q is inceasing. π(q) is inceasing when inceases, that is effective powe tansmission ate. π(q) is deceasing when powe geneation quantity C inceases. The total welfae is deceasing when powe tansmission netwok evenue A Inceases. As the discussion mentioned, we have the conclusion what π (Q) and y change shown as following table when f is inceasing to f 1, is inceasing to 1, C is inceasing to C, and A is inceasing to A 1. Table 1 The vaiation of optimal solution when vaiables change Vaiable f f 1 1 C C 1 A A 1 π (Q) + y + + NOTE: + means inceasing, means deceasing 4. Conclusion The industial libealization is a tend and electicity libealization is unavoidable in electicity maket. The electicity business opeated by each division is the efficient appoach to achieve libealization. As we eview the efeences in the whole wold and ou discussion in this pape, the business of powe geneation and distibution ae suitable to be libealized and opeated independently. Howeve, libealization of powe tansmission business, which is special of stuctue, can t pomise stable of powe tansmission and achieve the maximum goal of society welfae. As the discussion mentioned in this pape, thee ae some conclusions and ecommendations as below:
17 NETWORK OPTIMIZATION MODEL 333 (1) We intoduce the supply and demand optimization model of powe tansmission netwok and analyze the elationship of decisive vaiables. (2) In the model we constuct, we fix powe geneation cost C and analyze powe demand f 1, f 2 and f 3 in diffeent time peiods. We can apply this model to peak and offpeak time peiods of powe utilization. (3) The contibution of this pape focuses on the supply and demand of powe tansmission system which is not familia with scholas. We think thee ae the chaacteistics of monopolization and uniqueness fo powe tansmission system. It is not suitable fo libealization and equies a fai oganization esponsible fo egulation. Nevetheless, the libealization can be pomoted both fo supply pice in the geneation maket and demand pice in the utilization maket. Howeve, the supply pice in powe geneation maket and demand pice in powe utilization maket can be libealized. (4) The tansmission secto should be an independent institute to adjust electicity while the geneation and distibution sectos should be libealized. Howeve, the synthesized electic business includes the thee sectos. Theefoe, synthesized electic business doesn t each the utmost efficiency. So synthesized electicity business is not suitable fo libealization. (5) Taiwan powe tansmission business isn t suitable fo libealization unde consideation of the existent envionment and tansmission netwok stuctue. (6) We suggest setting up the Powe Regulation Oganization (PRO) in chage of the powe dispatching and to define the electicity pice of puchases and sales fo powe tansmission netwok in ode to egulate the balance and stability of powe supply and demand. Refeences [1] Th. Chistodoulopoulos (1995), Telecommunications in Geece: a study of poduction stuctue and natual monopoly issue, Intenational Jounal of Poduction Economics, Vol. 38 (2/3), pp [2] Z. Geoganta (1997), The effect of a libealized maket pice mechanism on total facto poductivity: the case of the agicultual cop industy in Geece, Intenational Jounal of Poduction Economics, Vol. 52 (1/2), pp
18 334 M. S. CHEN, C. L. WANG AND S. C. WANG [3] P. L. Joskow and K. Edwad (2002), A quantitative analysis of picing behavio in Califonia s wholesale electicity maket duing summe 2000, The Enegy Jounal, Vol. 23 (4), pp [4] T. Lindblom and B. Andesson (1998), Stategic moves at the pospect of a deegulated electicity maket, Intenational Jounal of Poduction Economics, Vol , pp [5] D. S. Paticio (2002), Responses to electicity libealization: the egional stategy of a Chilean geneato, Enegy Policy, Vol. 301 (5), pp [6] C. R. Roach (2002), Measuing maket powe in the U.S. electicity business, Enegy Law Jounal, Vol. 23 (1), pp [7] A. Saua (1995), Economic valuation of geneation system eliability using custome outage costs in India, The Indian Economic Jounal, Vol. 44 (2), pp [8] F. M. Tiago (2002), The Potuguese enewable enegy maket, Enegy Law Jounal, Vol. 23(2), pp [9] C. K. Woo and N. Toyama (1986), Sevice eliability and the optimal inteuptible ate option in esidential electicity picing, Enegy Jounal, Vol. 7 (3), pp [10] C. K. Woo and U. Tain (1988), The cost of electic powe inteuptions to commecial customes, in Special Issue on Electicity Reliability, Enegy Jounal, Vol. 9, pp [11] W. Xing and E. E. Wu (2003), Economic evaluation of pivate powe poduction unde uncetainties, Electical Powe and Enegy Systems, Vol. 25, pp Received August, 2005
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