Economic Evaluation of Transmission Expansion for Investment Incentives in a Competitive Electricity Market

Transcription

1 Iteratioal Ecoomic Joural Evaluatio of Cotrol, of Trasmissio Automatio, Expasio ad Systems, for Ivestmet vol. 6, o. 5, Icetives pp , i a Competitive October 2008 Electricity Market 627 Ecoomic Evaluatio of Trasmissio Expasio for Ivestmet Icetives i a Competitive Electricity Market Robert Fischer ad Sug-Kwa Joo* Abstract: With the shift of the electric power idustry from a regulated moopoly structure to a competitive market eviromet, the focus of the trasmissio expasio plaig has bee movig from reliability-drive trasmissio expasio to market-based trasmissio expasio. I market-based trasmissio expasio, however, a growig demad for electricity, a icreasig umber of trasmissio bottleecks, ad the fallig levels of trasmissio ivestmet have created the eed for a icetive to motivate ivestors. The expectatio of profit serves as a motivatioal factor for market participats to ivest i trasmissio expasio i a competitive market. To promote ivestmet i trasmissio expasio, there is a icreasig eed for a systematic method to examie trasmissio expasio for ivestmet icetives from multiple perspectives. I this paper, the trasmissio expasio problem i a competitive market eviromet is formulated from ISO ad ivestors perspectives. The proposed method uses parametric aalysis to aalyze beefits for ivestors to idetify the most profitable locatio ad amout for trasmissio additio. Numerical results are preseted to demostrate the effectiveess of the proposed method. Keywords: Electricity markets, parametric aalysis, trasmissio expasio.. INTRODUCTION Various optimizatio-based techiques [-6] have bee proposed for trasmissio expasio plaig i a vertically itegrated utility eviromet. With the shift of the electric power idustry from a regulated moopoly structure to a competitive market eviromet, the focus of the trasmissio expasio plaig has bee movig from reliability-drive trasmissio expasio [7,8] to market-based trasmissio expasio [9-2]. Referece [3] provides a i-depth discussio of the issues ad solutios methods i trasmissio expasio plaig. I [9], the formulatio of competitio i decetralized trasmissio expasio based o Lagragia Relaxatio (LR) techique is preseted to show trasmissio ivestmet ca be profitable i a competitive market. Mauscript received February 29, 2008; accepted May 28, Recommeded by Guest Editor Seug Ki Sul. This research was supported by the ND EPSCoR ad i part by the fosterig project of the Miistry of Kowledge Ecoomy (MKE). Robert Fischer was with the Departmet of Electrical ad Computer Egieerig, North Dakota State Uiversity, Fargo, USA. He is ow with Califoria ISO, CA, USA ( rfischer@caiso.com). Sug-Kwa Joo is with the School of Electrical Egieerig, Korea Uiversity, Seoul 36-70, Korea ( skjoo@korea.ac.kr). * Correspodig author. A procedure to idetify optimal trasmissio upgrades is proposed i [0] by computig cost of upgrades ad beefits. A techique of trasmissio plaig usig Beder s decompositio is preseted i [] to solve the complicated log-term etwork expasio problem by decomposig the ivestmet cost ad cogestio cost miimizatio problem ito etwork expasio problem (master problem) ad operatioal problem (slave problem). Market-drive power flow patters ad decisio aalysis scheme based o the regret of pla are icorporated i the trasmissio expasio method [2] to fid the best trasmissio expasio sceario. The ecoomic value of trasmissio expasio is highly depedet o the accuracy of load forecast, fuel costs, ad geeratio additios. Therefore, there is ucertaity i the ecoomic assessmet of trasmissio expasio associated with errors i load forecast fuel costs, ad geeratio additios. Referece [4] describes a probabilistic approach to evaluate the ecoomic value of trasmissio expasio cosiderig those ucertaities about future market coditios. I market-based trasmissio expasio, however, a growig demad for electricity, a icreasig umber of trasmissio bottleecks, ad the fallig levels of trasmissio ivestmet have created the eed for a icetive to motivate ivestors. I a competitive market eviromet, the expectatio of profit serves as a motivatioal factor for ivestors to ivest i trasmissio expasio. To promote ivest-

2 628 Robert Fischer ad Sug-Kwa Joo met i trasmissio expasio, therefore, there is a icreasig eed for a systematic method to examie trasmissio expasio for ivestmet icetives. The ecoomics of trasmissio expasio eeds to be evaluated from multiple perspectives: Idepedet System Operator (ISO)/Regioal Trasmissio Orgaizatio (RTO) perspective or private ivestors perspectives. I this paper, the trasmissio expasio problem i a competitive market eviromet is formulated from ISO ad ivestors perspectives. With a varyig rage of lie capacities, the proposed method uses parametric aalysis to compute beefits for ivestors to idetify the most profitable locatio ad amout for trasmissio additio. The remaiig of this paper is orgaized as follows. I Sectio 2, the trasmissio expasio problem i a competitive market eviromet is formulated from ISO ad ivestors perspectives. Next, the parametric aalysis techique for trasmissio expasio is preseted to idetify the most profitable locatio ad amout for trasmissio additio i Sectio 3. Fially, umerical results are preseted to demostrate the effectiveess of the proposed method i Sectio TRANSMISSION EXPANSION FROM ISO AND INVESTORS PERSPECTIVES Trasmissio expasio ca sigificatly alter power flow patters i power systems, thereby ifluecig market prices ad welfare of market participats. To measure the overall beefits of trasmissio expasio, the beefits offered to differet market participats eed to be determied. The producer surplus (PS) of a geerator is the differece betwee price times the amout of power geerated ad the variable productio cost of geeratio for the amout of power produced. The total PS i a market is the summatio of all geerators PS. The cosumer surplus (CS) of a load is defied as the differece betwee the Value of Lost Load (VOLL) mius the price of the area times the demad of the area. Cogestio reveue (CR) is defied as differetial i source ad sik LMPs times the amout of power trasfer betwee source ad sik. Therefore, the total surplus (TS) of the system is the sum of the total CS, the total PS, ad the CR. The followig equatios describe these formulatios. PS = LMP P MC P, () i i i i CS = VOLL Di LMPi Di, (2) CR = ( LMP LMP ) F, (3) i j TS = PS + CS + CR, (4) where LMP i, j is the LMP price for the area i or j, P i is the amout of power produced at bus i, MC i is the margial cost of geeratio or producig the amout of power for bus i, D i is the power demad of the area at bus i, ad F is the power that flows through the trasmissio lie betwee buses i ad j. The ecoomic beefits of the trasmissio expasio ca be aalyzed from multiple perspectives: ISO perspective ad market players or private ivestors perspective. From the ISO perspective, the objective of the trasmissio expasio is to maximize the social welfare. The cost of the trasmissio lie is ot accouted for whe cosiderig the social beefit of the trasmissio expasio from the ISO perspective. Therefore, from the ISO perspective, the optimal locatio ad amout of trasmissio expasio ca be described as the oe that provides the largest social beefit to the etire market, as described i (5). { } Max SB( τ ), k (5) where SB( τ k ) is the social beefit for a varyig rage of lie capacity τ k for the cadidate site k. O the other had, from the market players or private ivestors perspective, the icreased reveue due to the trasmissio expasio must be greater tha the ivestmet cost of a trasmissio lie. For a curret trasmissio ower, there are two profitable trasmissio expasio scearios. The first sceario is for a trasmissio ower that does ot ow oe of the cadidate sites for expasio. Suppose that the trasmissio ower iteds to ivest i a cadidate site to gai icreases i the reveues from the preexistig lies that it does ow. Sice the ew trasmissio lie ca alter LMPs ad power flow patters i the systems, the trasmissio ower eeds to fid the optimal locatio ad amout of trasmissio additio to maximize the combied reveues from the ew lie ad its ow pre-existig lies. The followig equatio states that the optimal amout ad locatio of trasmissio additio is the cadidate sceario that maximizes the differeces betwee the combied reveues from both ew ad pre-existig lies ad the cost of the ew trasmissio lie: {( op τk hj τk T ( τk ))} Max Δ CR ( ) + CR ( ) C, (6) where Δ CRop ( τ k ) represets the chage i the reveue from the pre-existig trasmissio lie o to p due to the ew lie. CRhj ( τ k ) represets the reveue C τ is the from the ew trasmissio lie h to j. ( ) T k

3 Ecoomic Evaluatio of Trasmissio Expasio for Ivestmet Icetives i a Competitive Electricity Market 629 cost of a trasmissio lie that is depedet o lie capacity τ k i cadidate site k. The cost of a trasmissio lie ca be represeted as a aualized cost where the total cost of the trasmissio lie is allocated per year for a give time period [5]. If the reveues of trasmissio lies are greater tha the cost of the ew trasmissio lie, the the ew trasmissio lie will be a profitable ivestmet. The secod sceario for a trasmissio ower is similar to a private ivestor perspective. I this sceario, the ew lie will be added i a kow cogested lie. For a curret trasmissio ower of a cogested lie to add o to the pre-existig lie, the optimal amout ad locatio of trasmissio additio are described by the followig equatio: { hj τk T ( τk )} Max ΔCR ( ) C, (7) where Δ CRhj ( τ k ) represets the chage i the reveue from the ehaced trasmissio lie h to j due to chages i the lie capacity. For the private ivestor, the predicted trasmissio reveue for a give amout of lie additio has to be greater tha the cost of the trasmissio lie. However, due to the ivestors eed for profit, a profit margi, PM, must be iserted ito the locatio cosideratios as follows: { hj τk T ( τk ) hj} Max CR ( ) C PM. (8) Geerators also have the opportuity ad icetive to ivest i trasmissio lies due to the possibility that their market shares ad/or LMPs may icrease with the trasmissio additio. For geerators, the cost of buildig a trasmissio lie has to be justified by a icrease i PS. If the icreased PS from the lie additio is greater tha the cost of the trasmissio lie, the the ivestmet i the trasmissio lie is justified. The optimal locatio ad amout of trasmissio additio from a geerator s perspective are formulated as follows: { j τk T ( τk) } Max ΔPS ( ) C. (9) 3. PARAMETRIC ANALYSIS FOR TRANSMISSION EXPANSION LMP is becomig the stadard i may competitive electricity markets for eergy ad cogestio maagemet. I a LMP-based market, geerators are paid the LMP of the bus where they are located, while loads pay the LMP of the bus where they are located. LMP is defied as the cost of deliverig the ext MW of power without violatig ay system costraits [6]. The market optimizatio problem uder LMP ca be formulated as follows: Miimize Bi Pi (0) i A subject to: P D = 0 i i () i A i A Max F F (2) mi i i i max, P P P (3) where B i is the supply bid fuctio of geerator i i area A, P i is the supply quatity of geerator i, D i is Max the costat demad quatity at bus i, F is the maximum amout of power that ca be trasferred o the lie betwee buses i ad j, ad P i mi ad max Pi are the lower ad upper limits of geerator i, respectively. The above optimizatio problem is solved for the optimal amout of power produced by geerator i, i.e., the vector G x. I this study, all the costraits are represeted i terms of the vector G x. The power balace costrait ca be expressed i matrix form as follows: [ ] Gx = L D, (4) i A where the matrix of oes is a matrix where is the umber of geerators. Also, the iequality costrait ca be re-writte i terms of the vector G as follows: x max P T + A B Dx T A B x G, T x max A B P T A B Dx x 0 x 0. i (5) A G b (6) I (6), x represets the reactace of lie betwee buses i ad j. A 0 is a 2m matrix that represets the left-had side of the iequality matrix. The upper half ad lower half of A 0 represet the positive power flow ad the egative power flow i

4 630 Robert Fischer ad Sug-Kwa Joo the trasmissio lie, respectively. b 0 represets the right-had side of the iequality matrix. I [6], the LMP at bus i is give by the followig equatio. dfl LMPi = λ μl, (7) dp j where LMP i is LMP at bus i, λ is the margial price at the referece bus, μ l is the shadow price of dfl lie l, ad is the shift factor for bus j o bidig dpj costrait l. The shift factors for the system correspod to the matrix A 0 due to the fact that A 0 is dfl the Jacobia matrix with respect to dp. i The dual variables represet the shadow prices of the primal problem. The shadow price represets the rate i chage of the objective fuctio with small chages i the right-had side (RHS) variables. There are two forms of duality: caoical ad stadard. I the dual simplex method, the primal must be represeted i caoical form. If the primal ad dual are represeted i stadard form, the primal dual method must be used. I this study, parametric aalysis is used to fid a directio for which the objective fuctio chages alog a certai directio based o perturbatios to the system. Parametric aalysis is performed o the RHS i the primal problem. The respose of the shadow price values with respose to chages i the lie capacities is of iterest. Therefore, parametric aalysis i the dual problem is coducted with respect to chages i the objective fuctio values. I order to coduct the parametric aalysis for the primal problem i equatio (0), cosider chages i the RHS variable i the followig geeric form of the optimizatio problem: Miimize c x (8) subject to: Ax b+δ b (9) x 0. (20) The chages i the RHS variable, i.e., Δ b, ca be solved for a give directio ad rage. I (9), Δ bi = αi τ is substituted for the chages i the RHS variable. α i is the pre-specified directio ad τ is the rage of chage for the chage i b i. The procedure for applicatio of the parametric aalysis for systematic chages i the b i parameters, described i [7], ca be summarized as follows: Step : Solve the iitial primal problem i equatio (0) usig dual simplex method with τ = 0. Step 2: Itroduce Δ bi = αi τ for chages i the RHS. Apply chages to the objective fuctio to fid how the objective fuctio value chages with variatios i τ. Step 3: Icrease τ as far as desired or util the right-side colum value of ay basic variable goes egative. Step 4: Coduct a iteratio usig the dual simplex method to fid the ew optimal solutio. Go back to step 3 ad repeat the iteratio process util oe of the basic variables becomes egative for chages to τ. Usig the above procedure, the LMP at bus i ca be represeted with respect to the chages i the trasmissio capacity as follows. base base base df l LMPi = λ μl, dp j (2) df l LMPi( τ) = λ( τ) μl ( τ), dp j (22) where λ( τ ) is the chage i the slack bus margial cost with respect to chage i the trasmissio capacity ad μl ( τ ) is the chage i the shadow price with respect to the chage i the trasmissio capacity. For simplicity, the load curves ca be represeted as a step fuctio where each step value is the average load for a give hour. The load curve ca also be represeted i peak load percetages. Usig this type of load data, aalysis ca be formulated for four days ad the exteded to a oe-year simulatio to represet the chagig loads for a year. The load chages ifluece prices ad the supply quatities of geerators. These chages ca be properly represeted by usig parametric aalysis for the RHS variables i the primal problem. The equality costrait is represeted i (23) ad (24), while the iequality costrait is represeted i (25). [ ] L Gx Di (23) [ ] i A L Gx Di (24) i A max P T + A B Dx T A B x G T x max A B P T A B Dx x (25) By combiig these equatios for use i the dual

5 Ecoomic Evaluatio of Trasmissio Expasio for Ivestmet Icetives i a Competitive Electricity Market 63 simplex method, every RHS variable is depedet o a value of the load, as show i (26). Di i A D + i [ L ] i A max [ ] P L T A B D x T Gx A B x T A B max P T A B D x x (26) I order to use parametric aalysis, the loads are represeted as peak load percetages. The percetages have to be represeted with respect to the smallest percetage due to positive chages i the RHS. The startig poit is at the smallest percetage or ad each poit from the startig poit is a percetage added o to this poit. The load value is represeted with respect to τ i terms of a teth of a percet or ay give percetage as follows: D+ D α ( L% ) α D 2 + D2 α ( L% ) α D L% = D, 3 D3 α ( L% ) + α M D m + Dm α ( L% ) α (27) where is the size of the percetage to be α examied. For a variety of percetages larger tha oe, the equatio τ = α ( L% ) ca be substituted i the RHS of (27). Now parametric aalysis ca be applied for the τ values to determie the rages ad how the additioal trasmissio capacity affects the system by usig the procedure for parametric aalysis. Usig the formulatios preseted i Sectio 2 ad the parametric aalysis, the followig procedure is used for idetifyig the profitable locatio ad amout of trasmissio additio: Step : Solve both the primal optimizatio problem i (0) ad its dual problem with τ equal to zero. Step 2: Apply parametric aalysis to the results of the optimizatio problem for icreased load perturbatios. Table. Ivestmet criteria usig parametric aalysis with varyig rage variable. Market Players ISO Ivestmet Criteria m ( ( τ ) ( τ ) ) ( ( τ )) ( τ ) ( ) LMP P LMP P MC P P P i= m base + ( LMPi( τ k) LMPi ) Di Max i= L t + (( LMPi( τk) LMPj( τk) ) H x A B * P( τk) s ) i, j A base base t base ( ( LMPi LMPj ) H x A B * P s ) base base base i k i k i i i i k i k i l Geerator Max λτ ( k) μl ( τk) Pi( τk) MCi( Pi( τk) ) Pi( τk) CT ( τk) m L i= l= df dp i Trasmissio Ower { Δ hj ( τk ) T ( τk )} Max CR C {( Δ op ( τk ) + hj ( τk ) T ( τk ))} Max CR CR C { hj k T k hj} Private Ivestor ( τ ) ( τ ) Max CR C PM

6 632 Robert Fischer ad Sug-Kwa Joo Step 3: Apply parametric aalysis for each cadidate locatio. Step 4: The cadidate locatio ad amout of τ that fulfills the equatios listed i Table describe the profitable locatio ad amout of trasmissio expasio based o the ivestor s perspective. Table describes the optimal locatios ad amout of lie additio. From a ivestor s poit of view, these are the best locatios for trasmissio expasio. However, there may be other locatios that provide icreased surpluses ad reveues but ot at the level described by the equatios i Table. Nevertheless, these other locatios ad amouts ca still be cosidered good locatios to ivest i as log as values i the equatios remai positive. 4. NUMERICAL RESULTS I this sectio, a 0-bus umerical example is preseted to demostrate the effectiveess of the proposed method. The test system is show i Fig. ad the data values for the test system are listed i Tables A-A4 i Appedix A. I order to aalyze each Fig.. 0-bus test system. time period for a te-year duratio, the percetages from the IEEE test system [8] were iserted ito the load duratio curve. With the load duratio percetages ad the times that that load percetage occurs i a year, geeratio levels, LMP, PS, SB, CR, ad CS are computed to fid the amout i questio for a give year. Usig the predicted loads for from the Califoria Eergy Commissio [9], the load icreases for a te-year period ca be simulated. 4.. Best locatio ad amout from ISO perspective The 0-bus umerical example was aalyzed for a te-year time period startig i Oce parametric aalysis was performed for the load icreases, lies, 4, 6, 7, 8, ad were idetified as cogested lies i the system for varyig loads over a te-year period. This system also displays iterestig LMP characteristics. The majority of the LMP prices for the base case are below the margial cost at the slack bus. Therefore, if the price of cogestio decreases, the the LMP prices will icrease. If the shadow prices decrease (or icrease), the the LMP prices will icrease (or decrease). This aalogy is used i order to uderstad the chages to the system. Parametric aalysis was applied to the six cadidate locatios for the icreasig loads for a te-year period. The geeratio levels, PS, SB, CR, CS, ad LMP were recorded with respect to chages to the cadidate locatios. Table 2 idetifies the amout of trasmissio additio where the cadidate locatios have their highest social beefit. These values are listed i Table (Mill $) Lie at 49 MW Table 2. Social beefits for cadidate lies. Lie 4 at 96 MW Lie 6 at 5 MW Lie 7 at 68 MW Lie 8 at 24 MW Lie at 4 MW Year Year Year Year Year Year Year Year Year Year Year Total

7 Ecoomic Evaluatio of Trasmissio Expasio for Ivestmet Icetives i a Competitive Electricity Market 633 2, alog with the correspodig social beefit for each year. As ca be see i Table 2, the optimal locatio ad amout of trasmissio additio from a social perspective is lie 6 at 5 MW of additioal trasmissio capacity Profitable locatio ad amout for trasmissio ower For the cost formulatio of the trasmissio lie, the aualized cost ad legths of the trasmissio lies are arbitrarily chose umbers i order to demostrate the formulatios. The aualized cost of the trasmissio lie k is the chose as 250 $/ (MW km year) ad the lie legths are give i Table A-2 of Appedix A. The amout of power that the lie carries per MW built is take from the total amout of hours that the lie is cogested i the oe-year simulatio. Table A-4 i Appedix A shows these amouts for each year. For lies, 4, 6, 7, 8, ad the lie legths are 325, 500, 75, 8, 25 ad 40 miles, respectively. The average lie cost is calculated as show i Table A-7 i Appedix A. The locatios to cosider for profitable locatio from the ivestors perspectives are the same as from the ISOs. However, the capacity value is differet due to the loss of reveue from the trasmissio lie cost. From the trasmissio ower s perspective, it is assumed that each lie is owed by a differet trasmissio ower ad that it takes five years for each lie to be built ad put ito service, i.e., 200. For case oe, where the ivestor ows a separate locatio withi the system, the ew ower makes the cogestio reveue from the ew lie ad the icreased trasmissio reveue, due to expasio, from the pre-existig lie. Hece, the ew reveue must be greater tha the aual costs of the ew lie. Table 3 shows the trasmissio owers that will receive icreased reveue alog with the amouts of capacity additio required for each cadidate. It ca be observed from Table 3 that the most profitable locatio ad amout of trasmissio expasio for case is lie 4 with 0 MW of trasmissio additio. These results cofirm lie 4 as beig the most profitable locatio for the ivestmet of the trasmissio additio for lie 6 because lie 4 has the highest LMP prices o its borderig bus. The high trasmissio reveue from lie 4, alog with lie 6 beig the oly lie with icreased productio reveue, elevated the trasmissio ower o lie 6 to the best ivestmet locatio. Lie 4 is the locatio where the LMPs were most dramatically chaged due to large chages i the shadow prices. For the secod case, the ivestor i the trasmissio lie is the ower of the cadidate lie, idicatig that the lie additio is profitable whe the additio icreases the trasmissio reveue to more tha the curret value. For this umerical example, the oly cadidate locatio that had icreased reveue was lie 7. Table 4 shows the icreased reveue ad capacity amout. The cadidate locatio o lie 7 was the oly locatio with a positive icrease i trasmissio Cadidate Lie Table 3. Trasmissio reveues for cadidate locatios ad lies that have icetive to ivest. Icetive Lie Cost of Cadidate ($) Max Reveue ($) Capacity Additio (MW) Profit Margi /MW /Year ($) Profit over 6 years ($) 2 8,250 83, ,200 62,883, ,000 22, ,90 5,079,62, ,750 22, No profit No profit 8 43,750 68, , ,467, ,750 93, ,395,733,25,779 43,750 3, No profit No profit ,750 29,279 5 No profit No profit 2,020 23, ,28 257,900,83 2 2,020 23, ,573 26,438, ,020 24, ,70 268,673, ,020 22, , ,058, ,250 38, ,843 9,645, ,250 38, ,843 9,645, ,000 2, ,200 25,027, ,000 2, ,200 25,027,995

8 634 Robert Fischer ad Sug-Kwa Joo reveue, because the decrease i shadow prices icreased the odal price at bus 5, a borderig bus of lie 7, while the LMP at bus 4 stayed costat Profitable locatio ad amout for geerators. I order for a geerator to have a icetive to ivest i a trasmissio lie, PS for the geerator has to icrease to a amout greater tha or equal to the cost of the trasmissio lie. Usig the same techique used for fidig the most profitable locatio ad amout for trasmissio owers, oe ca idetify the locatios that icrease PS. The cadidate locatios ad each icetive geerator with a positive icrease i PS are described i Table 5. It ca be observed Table 4. Trasmissio reveues for cadidate locatios ad lies that have icetive. Profit over Cadidate Cost of Max Capacity Profit Margi 6 years Lie Cadidate ($) reveue ($) Additio /MW/Year ($) ($) 7 2,020 2,8 68 MW 6,95,26 Cadidate Lie Table 5. Producer surpluses of geerators due to trasmissio lie additios. Icetive Geerator Cost of Cadidate ($) Max reveue ($) Capacity Additio Profit Margi /MW /Year ($) Profit over 6 years ($) 2 8, , ,324 2,935, , , ,607 3,273, ,250,059, ,32 5,869, ,250 57,43 05 No Profit No Profit 25,000 4,392, ,267,686 25,606,6 2 25,000 29,82, ,057,290 74,343, , , ,535,85, ,750 2,836, ,792,964 6,757, , , ,964 5,045, ,750 3,002, ,958,47 7,750,502 2, , ,957,66, ,020 37, ,409 22, , , ,956,33, ,250 79, ,32 889, ,250 4, ,2 498, , , ,79,339, ,250 43,542, ,5,60 26,069, ,000 7,097, ,087,57 42,525, ,000 7,594, ,584,743 45,508, ,000 4,395, ,385,229 26,3,374 Cadidate Lie Icetive Lie Cost of Cadidate ($) Table 6. Private ivestor s profit. Max reveue ($) Capacity Additio (MW) Profit Margi /Year ($) Profit over 6 years ($) 2 8,250 3,377, ,296,88 9,777, ,000 24,744, ,69,720 47,78, ,750 5,980, ,936,64 35,69, ,020 08,082, ,080,80 648,48, ,250 3,756, ,725,236 22,35,46 0, , ,943,739,658

9 Ecoomic Evaluatio of Trasmissio Expasio for Ivestmet Icetives i a Competitive Electricity Market 635 from Table 5 that geerator 6 will gai the largest PS icrease for a icrease i lie capacity o lie Profitable locatio ad amout for private ivestors From the private ivestor perspective, the ew trasmissio reveue gaied by the icreased lie capacity must be greater tha the cost of the trasmissio additio, i additio to a profit margi. Usig parametric aalysis, each of the cadidate s trasmissio reveue ca be examied. This aalysis also icludes the predicted amout of lie flow o the lie. For this umerical example, there must be a additio of at least 0 MW. There are two possibilities for the trasmissio reveue o a cadidate locatio: the reveue is elimiated due to the LMPs risig to the same amout, ad the reveue is reduced due to shadow prices i other parts of the system. The first case is examied for a poit beyod the relief of cogestio, while the umerical example of the secod case oly examies the additio through the relief of the cogestio o the lie. The cadidate locatios ad each lie for private ivestor reveue are described i Table 6. Table 6 shows that the locatio for a private ivestor to make the greatest profit is lie 7 with a additio of 68 MW. Lie 7 results i the oly positive icrease i trasmissio reveue for a icrease i lie capacity. The positive icrease, alog with the additio of 68 MW, made lie 7 the most profitable locatio for a private ivestor to make the most profit. 5. CONCLUSIONS I this paper, the trasmissio expasio problem i a competitive market eviromet is formulated from ISO ad ivestors perspectives. The approach based o parametric aalysis is proposed to compute beefits for ivestors to idetify the profitable locatio ad amout for trasmissio additio. The parametric aalysis results could be exteded to iclude the chages to the margial cost fuctios based o fluctuatios i fuel costs, bilateral cotracts, ad gamig. Oce the methodology for parametric aalysis is cofigured for the chages i the system, the aalysis ca determie the chages to the shadow prices for rages of the ew values. With these rages, both the extreme ad the average case scearios ca easily be represeted. REFERENCES [] L. L. Garver, Trasmissio etwork estimatio usig liear programmig, IEEE Tras. o Power Apparatus ad Systems, vol. PAS-89, o. 7, pp , September 970. APPENDIX A Table A-. Load data for 0-bus test system. Bus Load (MW) Table A-2. Lie data for 0-bus test system. From Bus To Bus Impedace (P.U.) Capacity (MW) Legth (Miles) Lie Lie Lie Lie Lie Lie Lie Lie Lie Lie Lie Lie Lie

10 636 Robert Fischer ad Sug-Kwa Joo Geerator Geerator 2 Geerator 3 Geerator 4 Geerator 5 Table A-3. Geerator bid data for 0-bus test system. Steps(MW) Price($/MWh) Steps(MW) Price($/MWh) Geerator Geerator Geerator Geerator Geerator

11 Ecoomic Evaluatio of Trasmissio Expasio for Ivestmet Icetives i a Competitive Electricity Market 637 Table A-4. Hours per year that additio lies will carry power. Year (H) lie lie 4 lie 6 lie 7 lie 8 lie Average Table A-5. Aualized cost of cogested lies for 0-bus test system. Lie Lie 4 Lie 6 Lie 7 Lie 8 Lie COST($/MWh) COST($/year) 8,250 25,000 43,750 2,000 3,250 0,000 [2] S. T. Y. Lee, K. L. Hocks, ad E. Hyilicza, Trasmissio expasio of brach-ad-boud iteger programmig with optimal cost-capacity curves, IEEE Tras. o Power Apparatus ad Systems, vol. PAS-93, pp , August 974. [3] C. Dechamps ad E. Jamoulle, Iteractive computer program for plaig the expasio of meshed trasmissio etworks, Elect. Power & Eergy System, vol. 2, o. 2, pp , April 980. [4] A. Moticelli, A. Satos, Jr, M. V. F. Pereira, S. H. Cuha, B. J. Parker, ad J. C. G. Praca, Iteractive trasmissio etwork plaig usig a least-effort criterio, IEEE Tras. o Power Apparatus ad Systems, vol. PAS-0, pp , October 982. [5] M. V. F. Pereira ad L. M. V. G. Pito, Applicatio of sesitivity aalysis of load supplyig capacity to iteractive trasmissio expasio plaig, IEEE Tras. o Power Apparatus ad Systems, vol. PAS-04, pp , February 985. [6] R. Romero ad A. Moticelli, A hierarchical decompositio approach for trasmissio etwork expasio plaig, IEEE Tras. o Power Systems, vol. 9, o., pp , February 994. [7] S. Kag, T. Tra, J. Choi, J. Cha, D. Rho, ad R. Billito The best lie choice for trasmissio system expasio plaig o the side of the highest reliability level, KIEE J. Electr. Eg. Techol., vol. 4-A, o. 2, pp , [8] T. Tra, J. Choi, D. Jeo, J. Chu, R. Thomas, ad R. Billito A study o optimal reliability criterio determiatio for trasmissio system expasio plaig, KIEE J. Electr. Eg. Techol., vol. 5-A, o., pp , [9] H. A. Gil, E. L. da Silva, ad F. D. Galiaa, Modelig competitio i trasmissio expasio, IEEE Tras. o Power Systems, vol. 7, o. 4, November [0] N. S. Rau, Trasmissio cogestio ad expasio uder regioal trasmissio orgaizatios, IEEE Power Egieerig Review, vol. 22, o. 9, pp , September [] G. B. Shrestha ad P. A. J. Foseka, Cogestio-drive trasmissio expasio i competitive power markets, IEEE Tras. o Power Systems, vol. 9, o. 3, pp , August [2] R. Fag ad D. J. Hill, A ew strategy for trasmissio expasio i competitive electricity markets, IEEE Tras. o Power Systems, vol. 8, o., pp , February [3] G. Latorre, R. D. Cruz, J. M. Areiza, ad A. Villegas, Classificatio of publicatios ad models o trasmissio expasio plaig, IEEE Tras. o Power Systems, vol. 8, o. 2, pp , May [4] Trasmissio Ecoomic Assessmet Methodology (TEAM), [5] D. Kirsche ad G. Strbac, Fudametals of Power System Ecoomics, Joh Wiley & Sos,

12 638 Robert Fischer ad Sug-Kwa Joo New York, [6] A. L. Ott, Experiece with PJM market operatio, system desig, ad implemetatio, IEEE Tras. o Power Systems, vol. 8, pp , May [7] F. S. Hillier ad G. J. Lieberma, Itroductio to Operatios Research, McGraw-Hill, 200. [8] Reliability Test System Task Force of the Applicatio of Probability Methods Subcommittee, IEEE reliability test system, IEEE Tras. o Power Apparatus ad Systems, vol. PAS-98, o. 3, pp , November/ December 979. [9] Califoria Eergy Commissio Homepage, Robert Fischer received the M.S.E.E. degree from the North Dakota State Uiversity i Curretly, he is a Market Ivestigatio Egieer at the CAISO. His research iterests power systems, ivolvig ecoomics, ad market optimizatio. Sug-Kwa Joo received his M.S.E.E. ad Ph.D. degrees from the Uiversity of Washigto, Seattle, i 997 ad 2004, respectively. Curretly, he is a Assistat Professor i the School of Electrical Egieerig at Korea Uiversity. From 2004 to 2006, he was a Assistat Professor i the Departmet of Electrical ad Computer Egieerig at North Dakota State Uiversity. His research iterests iclude multi-discipliary research related to power systems, ivolvig ecoomics, iformatio techologies, optimizatio, ad itelliget systems.