Transfer Capability Computations in Deregulated Power Systems

Transcription

1 Proceedngs of the rd Hawa Internatonal Conference on System Scences ransfer Capablty Computatons n Deregulated Power Systems Mohamed Shaaban (St. M. IEEE Yxn N (S. M. IEEE Felx F. Wu ( Fellow, IEEE Center for Electrcal Energy Systems Department of Electrcal and Electroncs Engneerng he Unversty of Hong Kong Hong Kong ABSRAC Wth the recent trend towards deregulatng power systems around the world, transfer capablty computaton emerges as the ey ssue to a smoothly runnng power maret wth multple transactons. otal transfer Capablty (C s the basc measure for evaluatng Avalable transfer capablty (AC. hs paper presents the calculaton of C through an optmal power flow approach. he obectve functon s to mze the sum of the sendng end-end generaton and recevng-end load of specfed buses. he constrants are ac power flow equatons and system operaton lmts. Sequental Quadratc Programmng (SQP method s used for the optmzaton process. IEEE 0 bus system s used for testng the proposed algorthm and the results compared favorably wth that from the Contnuaton Power Flow (CPF method. Keywords: Electrc power deregulaton, total transfer capablty, optmal power flow.. INRODUCION he concept of compettve ndustres rather than regulated ones has become promnent n the past few years. Economsts and poltcal analysts have promoted the dea that free marets can drve down costs and prces thus reducng neffcences n power producton. hs change n the clmate of deas has fostered regulators to ntate reforms to restructure the electrcty ndustry to acheve better servce, relable operaton, and compettve rates. Deregulaton of the power ndustry was frst ntated n Unted Kngdom, followed sut n Norway and Australa. he U.S. electrcty ndustry has reportedly taen the plunge towards deregulaton. he Federal Energy Regulatory Commsson (FERC, recognzng the centralty of open transmsson to real competton, has mandated that transmsson must be open to all comers. FERC, n conuncton wth North Amercan Electrc Relablty Councl (NERC, endorsed the exchange of transmsson servce nformaton through Open Access Same-me Informaton Networ (OASIS. One of the man functons of the OASIS s to post Avalable ransfer Capablty (AC nformaton [] Avalable transfer capablty (AC s the measure of the ablty of nterconnected electrc systems to relably move or transfer power from one area to another over all transmsson lnes or paths between those areas under specfed system condtons. It s clear that AC nformaton s sgnfcant to the secure operaton of deregulated power systems as t reflects physcal realtes of the transmsson system such as customer demand level, networ paradgm, generaton dspatch and transfer between neghborng systems. In order to obtan AC, the total transfer capablty (C should be evaluated frst where C s the largest flow through selected nterfaces or corrdors of the transmsson networ whch causes no thermal overloads, voltage lmt volatons, voltage collapse or any other system problems such as transent stablty. Other parameters nvolved n AC calculatons are the ransmsson Relablty Margn (RM and Capacty Beneft Margn (CBM []. However, snce dedcated methodologes for determnng RM and CBM may vary among regons, sub-regons, and power pools, ths paper addresses the calculaton of C as the bass of AC evaluaton. One of the most common approaches for transfer capablty calculatons s the contnuaton power flow (CPF [, ]. CPF s a general method for fndng the mum value of a scalar parameter n a lnear functon of changes n nectons at a set of buses n a power flow problem. In prncple, CPF ncreases the loadng factor n dscrete steps and solves the resultng power flow problem at each step. CPF yelds solutons at voltage collapse ponts. However, snce CPF gnores the optmal dstrbuton of the generaton and the /00 $0 (c 000 IEEE

2 Proceedngs of the rd Hawa Internatonal Conference on System Scences loadng together wth the system reactve power, t can gve conservatve transfer capablty results. hs paper features an OPF-based procedure for calculatng the total transfer capablty (C. he method s based on full AC power flow soluton whch accurately determnes reactve power flow, and voltage lmts as well as the lne flow effect. he obectve functon s to mze total generaton suppled and load demand at specfc buses. he mathematcal formulaton of the proposed method s presented and the algorthm s tested on the IEEE 0 bus system to show ts capablty.. PROBLEM FORMULAION he OPF-based C calculaton algorthm descrbed below enables transfers by ncreasng the load, wth unform power factor, at a specfc load bus or every load bus n the sn control area, and ncreasng the real power nected at a specfc generator bus or several generators n the source control area untl lmts are ncurred. he man assumptons for ths method are [5]: A current state estmaton of the power system s avalable and the operatng pont s secure and stable. he system s properly controlled and can provde enough dampng to eep steady-state stablty. he system has suffcently large stablty margn; hence t can survve dsturbances and shft to another stable operatng pont. System voltage lmt s reached before the system loses voltage stablty. Only thermal lmts and bus voltage lmts are consdered as well as generator actve and reactve power lmts. Mathematcally, C calculaton problem can be represented as: Maxmze J = f(x, u ( g( x, u = 0; mn h h( x, u h Where f(x, u s the obectve functon, x represents the system state varable vector and u the control parameter vector. g(x, u s the equalty constrant functon vector and h(x, u the nequalty constrant functon vector. he cost functon J s defned to be the sum of total generaton of a specfc generator or a group of generators (desgnated as S and total load of a specfc load bus or a cluster of load buses (desgnated as R,.e. S J = P + P ( d R Where P s the generaton at bus and the P s the load at bus d. he g(x, u = 0 s the power flow equalty constrant whch s descrbed [ 6]: φ = P V P Q = φ = Q V N = ref.bus, θ N V ( ref V ( = 0 cosθ + B snθ = 0 snθ B cosθ = 0 Where P, Q are the actve and reactve power necton at bus ; V θ s the voltage at bus and θ = θ θ ; + B s the correspondng element n system Y-matrx. he power necton at bus s defned as P = P L L ( P, Q = Q Q (4 Where P and Q are the real and reactve power generaton at bus, whle PL and QL the real and reactve load at bus. Wth bus voltages magntudes, ncludng the Ref. Bus, and bus voltage phase angles, except the Ref. Bus where θref.= 0, are taen as state varables x, It s evdent that f a set of u s gven x can be solved from Eq. (. he nequalty constrants are as follows, (a he generaton and load lmts: P mn Q P P ( S mn 0 P Q P Q ( d R (5.a Where P and mn P are the upper and lower lmts of the generator actve power at bus. Q and mn Q are reactve power lmts for generator. P s the upper lmt of the of the load actve power whch s constraned by dstrbuton faclty capacty. (b he bus voltage lmts appled to all buses n the networ: mn V V V (5.b (c he current lmts of transmsson lnes based on thermal consderatons: 0 I I (5.c Where I and I are the actual and mum current of lne - respectvely. I can be calculated from V, V and parameters of lne -. Equatons ( to (5 consttute the mathematcal model of the OPF-based C computaton. In ths study, the system state varables are: Voltage magntudes and phase angels of all buses except Ref. bus phase angle whch s set to be zero. he control varables are: /00 $0 (c 000 IEEE

3 Proceedngs of the rd Hawa Internatonal Conference on System Scences Real power output of generator (P, S. Real power of load d (P, d R. Reactve power of each generator (Q.. OPIMIZAION he advanced Sequental Quadratc Programmng (SQP method s selected to solve the C-OPF problem snce t was recently developed and proven to be an effectve method for constraned nonlnear programmng [7]. For the general purpose optmzaton problem n the form gven as (here both x and u n Eq. ( are consdered as x: Mn f ( x g( x = 0 ( =,,..., p h ( x 0 ( =,,..., m he correspondng Lagrangan functon L( x, λ s formed as p = = (6 L( x, λ = f ( x + λ g ( x + λ h ( x (7 m p+ Where λ (=,,,(p+m s the Lagrange multpler for the actve th equalty and nequalty constrant. We can defne a correspondng approxmate quadratc programmng subproblem. It can be proven that the QP sub-problem at the -th teraton s equvalent to another QP sub-problem defned as: Mn f ( x s + 0.5s [ H ] s g ( x + g ( x h ( x + h ( x s = 0 ( =,,..., p s 0 ( =,,..., m Where [H] s a postve defnte matrx that s taen ntally as an dentty matrx and updated n subsequent teratons so as to converge to the real Hessan matrx of the Lagrangan functon of Eq. (7 whch wll be explaned below. he vector s to be optmzed s served as the search drecton,. e. x + = x + α s (9 Where α s the optmal step length along the search drecton s found by mnmzng the mert functon [7]: Mn. f ( x + + (8 p m + + λ g ( x + λ p+ [0, h ( x (0 = = he update of the Hessan matrx H after the -th teraton to mprove the quadratc approxmaton s gven as [7] H + = H H d d H /( d H d + γγ /( d d where + d = x x γ = θ Q + ( θ H d Q = + + xl( x, λ xl( x, λ.0 ( f d Q 0. d Hd θ = 0. 8d Hd (otherwse d Hd d Q ( Where L s gven by Eq. (7 and the constants 0. and 0.8 can be changed based on numercal experence. Usng the above mentoned equatons, C calculaton procedure can be summarzed as follows: Step : Calculate base load flow to get x (0 and assume ntally the Hessan matrx s unty Step : Evaluate the gradents of the obectve functon and constrant functons Step : Solve QP sub-problem n Eq. (8 to get optmal search drecton s Step 4: Fnd optmal step length α and update x by Eq. (9 Step 5: Update the Hessan matrx [H] by Eq. ( Step 6: Chec convergence. If t s converged, then output results and stop; otherwse go to step to next teraton. 4. IEEE 0 BUS ES RESULS he IEEE 0-bus system, shown n Fgure, s adopted as the test system. he system has areas wth generators n each area. enerators n each area are assumed to belong to the same owner and the loads belong to the same load servng entty. ransactons between dfferent control areas are nvestgated,.e., C wll be evaluated between areas. he base load flow s gven n the Appendx. Some buses retan low voltage profle le buses 7, 8, and 9, whle lne 6-8 s more than 90% loaded. Several cases are studed wth three case results presented below. Case : the transfer capablty from area to area Usng the proposed OPF-based C method, the generaton of area ncreases from 56. MW to 7 MW and the load at area from 84.5 MW to 99 MW. he loads are modeled as a constant power factor load. he actve loadng vector of area, excludng ntermedate or zero loadng buses, after and before ths transacton s shown n table. C s 99 MW and the lmt was the overloadng of lne -. Snce the obectve functon mzes the total generaton n area and the total load n area, both the generaton and load ncrements are not unformly dstrbuted n each area. Hence, usng a common loadng factor, typcally of CPF method, mght lead to n a conservatve C results due to the mproper allocaton of generatons and loads. EPRI Voltage SABlty (VSAB [8] /00 $0 (c 000 IEEE

4 Proceedngs of the rd Hawa Internatonal Conference on System Scences was utlzed for calculatng the transfer between area and by CPF. C calculated wth CPF s 88.5 MW whch s more conservatve than the one obtaned by the proposed method. he overload of lne 6-8 was the lmtng condton usng CPF. Clearly CPF ncremented the load wth only 5 MW that was enough to trgger the overload n lne 6-8 whch was almost fully loaded before ths transacton occurs. Case : the transfer capablty from area to area he loads n area ncrease gradually wth the generaton of area ncreased accordngly. he proxmty of lnes -, 5-, and 6-8 to be overloaded were the lmtng condton n ths case. Usng the suggested method, the generaton at area s ncreased from 48.5 MW to 94.9 MW whle the load at area s ncreased from 84.5 MW to 9.5 MW. C s found to be 9.5 MW. Contnuaton power flow results was 89.5 MW when lne 6-8 s % overloaded. he dscrepancy between C results of both methods s sgnfcant partcularly for ths case. VSAB scales up the generaton n the same loadng drecton regardless of lmts mposed on lne 6-8 but the proposed OPF method dentfes that nstantly and redspatches power generaton and load dstrbuton of specfed sources and sns as well as reactve power generaton to avod any overloadng or other volatons. from further ncrease n the specfed transfer. he load actve power vector of area n bus number sequence s [9.7,, 6., 8.,.5, 9.0,., 9.5,., 5.48] MW. he loads on bus and bus are the only ones to experence an ncrease durng the optmzaton process. he ncrease of loads s extremely non-unform. C calculated usng CPF s much less than ts counterpart usng the proposed OPF method. C equals to 6 MW by CPF because of the overload of lne -. he crtcal load of area of the nose pont for that case s 57 MW wth voltage volatons and 5 lne overloads. hs confrms agan that the system usually hts the operaton lmts at a much lower loadng condton than t hts the nose pont. hs result ustfes the assumpton made n earler secton. In these tests, the developed program converges very well n OPF calculaton snce t uses Newton s method n solvng nonlnear equatons and starts from a steady state operatng pont. However t should be ponted out that SQP method has the possblty of convergng to a local mnmum/mum especally n a hghly nonlnear system. herefore further tests on stressed and ll-condtoned systems are requred CONCLUSION A new formulaton for OPF to calculate the otal ransfer Capablty C s reported n ths paper. he obectve functon s the total generaton and load ncrease on specfc source and sn nodes. he thermal lmts of transmsson lnes, voltage bounds of buses, and upper and lower lmts of generator power are consdered as well as load flow equatons. he advanced sequental quadratc programmng method s extended for C calculaton. An algorthm has been developed and tested on the IEEE 0-bus system. Computer results show that the proposed method s very effectve, and wth good convergence characterstcs as well, n determnng C. he man conclusons of the paper are: Area Area Area Fgure. IEEE 0-bus system 6 he proposed OPF-based C algorthm wors well n determnng C between dfferent areas subect to system operaton lmts. able. Actve loadng of area n MW for a transacton between area and area Bus # Before After OPF-based C approach can re-dspatch generator reactve power outputs and optmally dstrbute the ncrement of loads and generatons on the specfc buses, therefore t can reach the mum C, whle he CPF technque usually gves a conservatve estmaton of C for the lac of the optmzaton functon. ACKNOWLEDEMEN Case : the transfer capablty from area to area he transfer capablty between area and area s 07 MW usng the proposed technque. he overload that too place n lne 5-7 hndered the algorthm he authors would le to than EPRI, USA for ther nd donaton of VSAB software for our academc research /00 $0 (c 000 IEEE 4

5 Proceedngs of the rd Hawa Internatonal Conference on System Scences REFRENCES [] ransmsson ransfer Capablty as Force, Avalable ransfer Capablty Defntons and Determnaton, North Amercan Electrc Relablty Councl, Prnceton, NJ, June 996. [] V. Aarapu and C. Chrty, he Contnuaton Power Flow: A ool for Steady State Voltage Stablty Analyss, IEEE ransactons on Power Systems, Vol. 7, No., pp. 46-4, February 99. [] H. D. Chnag, A. J. Fluec, K. S. Shah and N. Balu, CPFLOW: A practcal ool for racng Power System Steady-State Statonary Behavor Due to the Load and eneraton Varatons, IEEE ransactons on Power Systems, Vol. 0, No., pp. 6-64, May 995. [4]. C. Eebe, J. ong, J.. Waght, J.. Frame, X. Wang and W. F. nney, Avalable ransfer Capablty Calculatons, PE-- PWRS [5 ] M. Shaaban, Y. N, H. Da and F. Wu, Consderatons n Calculatng otal ransfer Capablty, Proc. Of the Internatonal Conference on Power System echnology, Beng, Vol., pp , August 998. [6] A. J. Wood and B. F. Wollenberg, Power eneraton, Operaton, and Control, John Wley & Sons, nd edton, 996. [7] S. S. Rao, Engneerng Optmzaton: heory and Practce, John Wley & Sons, rd edton, 996. [8] Powertch Labs Inc., Voltage Stablty Analyss Program (VSAB User s Manual, Prepared for EPRI, USA, 997. APPENDIX IEEE 0 bus system data otal load of area = 84.5 MW otal load of area = 56. MW otal load of area = 48.5 MW Current generaton of area = 87 MW Current generaton of area = 56. MW Current generaton of area = 48.5 MW Avalable generaton of area = 60 MW Avalable generaton of area = 70 MW Avalable generaton of area = 05 MW he operatng pont of the 0-bus system (P/Q: MVA Bus Area V Angle eneraton Load No. No. (p.u. (deg. P Q P Q /00 $0 (c 000 IEEE 5