Congestion Management: Re-dispatch and Application of FACTS

Transcription

1 Congeston Management: Re-dspatch and Applcaton of FACTS Master of Scence Thess n the Internatonal Master Degree Programme, Electrc Power Engneerng KENNEDY MWANZA YOU SHI Department of Energy and Envronment Dvson of Electrc Power Engneerng CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden, 2006

2 Ttel Ttle n Englsh Congeston Management: Re-dspatch and Applcaton of FACTS Author Kennedy Mwanza You Sh Publsher Chalmers Unversty of Technology Göteborg, Sweden Subect Electrc Power Engneerng Examner Dr Tuan A. Le Date

3

4 Abstract Ths thess deals wth the transmsson congeston problem arsng from multple transactons n deregulated electrcty markets. Two congeston management approaches (re-dspatch and the applcaton of Flexble ac transmsson systems (FACTS)) have been studed n three market models (pool, blateral and the combned (hybrd)). An optmal power flow (OPF) framework has been used to smulate the consdered market models and the congeston problems. The IEEE 14-bus and the CIGRE 32-bus test systems have been used to demonstrate the robustness of the approaches. The obectves of congeston management are dfferent n dfferent market. In the pool market, the obectve functon s the mnmsaton of the amount of re-dspatched power. In the blateral market, mnmsng the transacton devatons s consdered as the obectve. In the hybrd model, the obectve functon s two pronged, mnmsng the pool re-dspatch and mnmsaton of devatons of the blateral contracts. Furthermore, the obectve of mnmsng the cost of congeston s appled n all the market models. The use of seres FACTS devces to allevate congeston s also demonstrated. In the pool market, congeston requres re-dspatch of generaton hence devatng from the market settlement. It has been shown that re-dspatch ncreases the system cost snce the out of mert generators are nvolved more than scheduled. The mnmsaton of redspatch n the pool therefore ensures that the devaton from the economcal settlement of the market s mnmsed. In the blateral market, the nterest s to mantan the desred transactons between contractng partes. To solve the arsng congeston n ths market model, the rescheduled transactons are forced to be as close to the scheduled transactons as possble. The changes to contracts are non-dscrmnatory, hence only contracts that affect the congeston are modfed. In order to meet the load requrements, power has to be suppled from the regulaton market. In the hybrd market model, a weghtng factor s used between the pool and blateral re-dspatch. The pool could be re-dspatched more than the transactons and vce versa, dependng on the weghtng factor. It has been found that when FACTS are ncluded n the network, the amount of redspatched power n the pool s greatly reduced resultng n an optmal operatng pont closer to that dctated by the market settlement. In the blateral market, the results show that the transactons may not need to be modfed when we have FACTS. The cost of congeston to the ISO also reduces when FACTS are employed. In order to ustfy the use of FACTS wth regards to congeston management, a smple cost beneft analyss has been proposed where the beneft from FACTS s consdered as avoded congeston costs that the system would have to bear otherwse. The resultng re-dspatched generaton schedules are only optmal as far as congeston s concerned under normal operatng condtons.e., N-0 contngency. The schedule s therefore tested for securty under the N-1 crteron. The contngency cases have been smulated and ranked usng an overload ndex and total power volatons arsng from the outages. A dc load flow and lne outage dstrbuton factors have been used for testng system behavours under varous contngency condtons. A comparson of the dc and ac load flow methods has been made and the results ndcate a small average absolute error. Keywords: congeston management, FACTS, TCPAR, TCSC, electrcty market v

5 Acknowledgements Ths work was carred out under the supervson of Dr. Tuan A. Le at the Dvson of Electrc Power Engneerng n the department of Energy and Envronment at Chalmers Unversty of Technology. Hs valuable gudance n performng ths work s gratefully apprecated. We would lke to acknowledge the followng students, wth whom we shared the offce, for ther cooperaton and useful dscussons we had: E. Banda, A. Ng un, R. Makalk, A. Helen, Johan and Danel. Kennedy dedcates ths work to hs wfe Audrey and hs chldren Wonan, Mtendere and Kondwan. He was sponsored by the Swedsh Insttute and greatly apprecates the opportunty granted hm to study n Sweden. He s also grateful to hs employers, ZESCO Lmted, for ther cooperaton and valuable assstance durng hs studes. Kennedy Mwanza You Sh v

6 Table of contents Abstract... v Acknowledgements... v 1 Introducton Present status of electrcty ndustry Market Structures Pool based market Blateral Market Hybrd Market Congeston Management n Deregulated Markets Nodal and Zonal prcng Re-dspatchng Counter tradng Market Splttng Auctonng Load curtalment FACTS Layout of the thess Re-dspatch and FACTS for Congeston Management: Theoretcal Background Optmal Power flow Modellng OPF DC Flow Modelng Comparson between DC and AC flow method An Overvew of FACTS Control of Power flow over a lne Thyrstor-Controlled Phase Angle Regulator (TCPAR) Thyrstor-Controlled Seres Capactor (TCSC) Concluson Optmal Redspatch And Congeston Management: Pool Market Perspectve Characterstcs of a Pool Market Prce determnaton Modellng of the pool market Congeston Management on IEEE 14 bus system Descrpton of the network Market settlement Results of Load flow Results of Re-dspatch Re-dspatch: Mnmsaton of cost Applcaton of FACTS for congeston management n the Pool Market TCPAR TCSC Economc consderaton for placement of FACTS Concluson v

7 4 Optmal Re-dspatch and FACTS Applcaton For Congeston Management: Blateral and Hybrd Market Perspectve Optmal Red-dspatch and FACTS Applcaton for Congeston Management n Blateral Market Characterstcs of a Blateral Market Congeston Management on IEEE 14-Bus System n Blateral Market Use of FACTS n Blateral Market Optmal Red-dspatch and FACTS Applcaton for CM n Blateral Market Characterstcs of a Hybrd Market Congeston Management on IEEE 14-Bus System n Hybrd Market Use of FACTS n Hybrd Market TCSC for mnmsaton of cost of congeston Concluson Results from the 32-Bus Test System Pool Market Market settlement Loadflow Mnmsaton of Re-dspatch Cost Mnmsaton Hybrd Market Transacton formulaton and Market settlement Loadflow Mnmsaton of re-dspatch Cost Mnmsaton Concluson Contngency Analyss Introducton Methodology Results for IEEE 14-bus system Results for CIGRE 32-bus system Concluson Concluson and Future Work Concluson Future Work Appendces v

8 v

9 1 Introducton In ths chapter we ntroduce the dfferent electrcty market models and brefly dscuss the changes that have taken place n the electrcty market. We also look at what congeston s and the dfferent methods used for ts management. The optmal power flow as a tool for re-dspatch s also ntroduced. Lastly we gve an outlne and organsaton of the thess. 1.1 Present status of electrcty ndustry The tradtonal electrcty utlty can be descrbed as a vertcally ntegrated company (VIC) where generaton, transmsson and dstrbuton are under the umbrella of one management. The modern trend and practce s for open markets. Ths calls for separaton (unbundlng) of the generaton, transmsson and dstrbuton functons. The reasons for the reforms are many and vared both for the developng and developed countres [1]. The man motvaton for the unbundlng, n the developed countres, stems from the desre of governments and polcy makers to foster competton n power generaton thus drve the cost of electrcty down whle enhancng supply qualty and relablty [2]. In developng countres the man ssues have been hgh demand growth whch could not be matched wth nvestments n generaton and transmsson. The fnancers for the requred nvestments have forced the governments of these countres to under go restructurng wth the hope of achevng effcency n these companes [1]. The success of the reforms n the communcaton sector and arlnes also gave mpetus to the deregulaton process [3]. The underlyng argument has been that an open market system s more effcent than a monopoly. The market mechansms that have arsen out of deregulaton can be classfed nto Pool and Blateral. In most of the restructured electrc power systems both the pool and blateral market models coexst wth varaton from one system to another [4]. In ths thess we call ths combned market the hybrd market [5]. In the next secton, dfferent market structures wll be dscussed. At present the deregulated electrcty market comprses of generatng companes (Gencos), Transmsson companes (Trancos) and Dstrbuton Companes (Dscos) and these enttes are ndependent. Due to the economes of scale nherent n the transmsson system the Trancos are natural monopoles and operate under the authorty of a regulator. In the deregulated envronment, therefore plannng for generaton capacty nvestment and locaton of the same s therefore market drven. There may not be any coordnaton between transmsson and generaton nvestment. Ths has resulted n a marked ncrease n the level of rsk and uncertanty assocated wth transmsson operaton and nvestment [2]. 1

10 Introducton 1.2 Market Structures Pool based market A pool market s defned as a centralzed market place that clears the market for buyers and sellers of electrcty [5]. The market may be operated as a double aucton or sngle aucton. In a double aucton system the market operator or the ndependent system operator (ISO) receves both sell bds (from Gencos) and buy bds (from Dscos). The market prce s obtaned by stackng the supply bds n ncreasng order of prces and the demand bds n decreasng order of ther prces, the ntersecton pont determnes the market clearng prce [1]. In sngle aucton only the sell bds are receved and the prce s determned by the hghest accepted sell bd to ntersect wth the forecasted demand. The seller and buyer do not have any nteracton n the pool market mechansm. Prce determnaton s an optmsaton problem where the obectve functon s the maxmsaton of the socal welfare Blateral Market In the blateral market the buyers and sellers negotate the prce and amount of power traded between them. These contracts set the terms and condtons of agreements ndependent of the ISO. The ISO s responsble for ensurng that the blateral agreements are feasble.e. transmsson capacty s avalable Hybrd Market The hybrd model combnes the varous features of the prevous two market models. The partcpaton of a GENCO n the Pool s not oblgatory. Some GENCOs wll therefore have contracts and they can trade the excess capacty on the pool market. GENCOs wthout contracts submt ther sell bds to the pool market. The customers therefore have a choce to negotate a power supply agreement drectly wth supplers or may choose to accept the spot market prce [5]. Ths market model s the closest to the establshed markets for other goods and servces. In all the market mechansms the ISO has to execute the schedules and ensure the relablty and securty as well as handlng the emergences lke congeston n the system. 1.3 Congeston Management n Deregulated Markets The delvery of electrcal energy from pont to pont s partly governed by the capacty of the transmsson lnes and transformers. Congeston s sad to occur whenever the system state of the grd s charactersed by one or more volatons of the physcal operatonal or polcy constrants under whch the grd operates n the normal state or under any one of the contngency cases n a set of specfed contngences [6]. In other words congeston occurs when the transmtted power exceeds the capacty or transfer lmt of the 2

11 Introducton transmsson lne or transformer. The capacty of a transmsson lne or transformer may have dfferent values under dfferent condtons. Congeston, needless to say, s undesrable. A system wthout congeston wll have a unform prce (n nodal prcng). As soon as we have congeston, prces n some areas wll ncrease and n others decrease. Congeston therefore dstorts the market. Another dsadvantage of congeston s ncreased rsk of market manpulaton by some partcpants [7]. In the VIC the economc load dspatch was normally formulated as an optmal power flow (OPF) problem wth the obectve of mnmsng total generaton cost subect to, generaton lower and upper lmts, bus voltage lmts, power flow lmts of lnes and transformers and etc. Congeston was therefore ntrnscally managed at the dspatch stage. Ths would result n dfferent margnal costs at dfferent buses n the system n the case that congeston exsts otherwse the margnal cost wll be the same system wde. If we assume that the VIC charges a unform prce for power at all the buses, congeston would lead to hgher margnal costs and hence reduced revenues (f the unform prce s lower than the hghest margnal cost). Persstent congeston would therefore sgnal to the VIC to nvest n transmsson or generaton. In the deregulated market, congeston s lkely to occur more often snce the market for the sellng and buyng of energy may be settled wthout the constrants of the power system mposed. The ensung generaton schedules may result n some transmsson paths beng congested. Congeston management remans the central ssue n transmsson management n deregulated power systems [3]. Congeston management (CM) ncludes both the congeston relef actons and the assocated prcng mechansms [6]. In the past, cross border power tradng was carred out between utltes wth full knowledge of the constrants of the nter-connectors. In the deregulated market partcpants can make blateral contracts wth partes across borders and such transactons may not have any regard for the avalable capacty on the nter-connectors. Congeston across these nterconnectors may occur more n the deregulated than n the pre-deregulated era. The advent of the common carrer role for the transmsson brought about by open access has therefore resulted n very dfferent uses of the transmsson system than those for whch t was orgnally planned and desgned [6]. Snce nvestment n and locaton of generaton s market drven n a deregulated envronment and may not be coordnated wth transmsson plannng congeston s more lkely to occur. Wthout careful attenton to the nteracton of congeston management and the economcs of the energy market, market neffcences can take away the savngs deregulaton promses to socety [3]. Congeston may be allevated through varous ways. Among the techncal solutons we have outagng of congested lnes, operaton of FACTS devces and operaton of transformer tap changers. Among the non techncal solutons we have market based and non market based methods of CM [8]. Non market based methods are those where no form of market mechansm s used to allocate the scarce transmsson capacty but use other reasonable crtera. These nclude sharng of capacty on a pro rata bass where users share n proporton to ther 3

12 Introducton requrements, frst come frst serve and preference for certan types of contracts [8]. The non market based methods for congeston management do not send any sgnals for nvestment and have no measure of the value of the congested lne. Market based methods are based on market mechansms and hence gve an ndcaton of the value of the scarce resource of transmsson capacty. These methods are brefly dscussed below Nodal and Zonal prcng In the nodal prcng scheme every bus n the grd s treated as a zone. The locatonal margnal prce (LMP) for each bus s determned by the ISO by carryng out an economc dspatch wth the flow lmts. The LMP becomes the prce and payment that buyers pay and the generators receve respectvely. The market s settled wth the network constrants hence congeston does not arse. Ths method of CM s practsed by the PJM n the USA [9]. In Zonal prcng system buses wth smlar LMPs are aggregated nto zones. The market s frst settled constrant free. Each zone wll have a prce for energy that buyers can pay and sellers receve. In the case that congeston occurs the ISO receves supplementary bds for ncrease and decrease of generaton. The most expensve supplemental bd for ncrease of generaton becomes the prce for that zone and the cheapest supplemental bd for decrease of generaton becomes the prce for that zone. In ths way the ISO earns congeston rent over the congested lnes. In case that there s no congeston the zonal prces wll be the same. The Calforna market mgrated from ths CM mechansm to the zonal prcng method [10] Re-dspatchng In ths method of CM the market s settled wthout the constrants of the transmsson system beng appled. If congeston occurs the ISO re-dspatches the generaton n such a way that congeston s gotten rd of. Ths wll ental the ISO purchasng power from hgh prce areas. The generators n the low prce areas wll be commanded to regulate downwards. Snce the ISO n essence s buyng power at a hgh prce and sellng t at a lower prce he ncurs a cost. The net cost ncurred by the ISO s an ndcaton of the congeston charge and s a sgnal for nvestment. The ISO drectly commands generators to up regulate or down regulate wthout the use of the market [11] Counter tradng Counter tradng s a modfed form of re-dspatchng the dfference beng that up and down regulaton power s obtaned from the market. The generators submt bds for up and down regulaton on the balancng market. Smlar to the re-dspatch the ISO wll ncur net cost n the purchase of regulaton power snce he has to use more expensve power for up regulaton. Sweden uses ths form of CM [12]. counter tradng may be vewed as a specal type of re-dspatchng. In ths thess we shall use these methods for clearng congeston. 4

13 Introducton Market Splttng In market splttng the market s frst settled wthout constrants appled. If the resultng schedules cause congeston on some lne(s) the market s then splt and settled separately wth the transfer lmt appled. The ISO purchases power from the low prce area and sells t n the hgh prce area. The ISO thus makes a proft. Norway uses ths CM method [11] Auctonng In auctonng the avalable capacty of a normally constraned path s auctoned by the ISO recevng bds from partes wllng to use the path. The lowest margnal bd accepted becomes the prce for transmsson on the path. Two forms of auctonng are n use.e. mplct and explct [11] Load curtalment By managng load, congeston can also be effectvely releved. The benefts result from reduced peak demand and reduced pressure on both electrcty generaton and dstrbuton systems. The amount of curtaled load should be as small as possble and the prce n the congested area should fall as much as possble. Whle there are many dfferent knds of curtalment algorthms, a parameter termed as wllngness-to-pay-to-avod-curtalment was ntroduced n [8] whch s regarded as a hghly effectve nstrument n settng the transacton curtalment FACTS Flexble AC transmsson systems (FACTS) s a new technology developed n recent two decades, and t has been wdely put n practce n the world. FACTS s defned by the IEEE as a power electronc-based system and other statc equpment that has the ablty to enhance controllablty, ncrease power transfer capablty. Nowadays, power producers and system operators all over the world are faced wth ncreasng demands for bulk power transmsson, low-cost power delvery and hgher relablty, to some extent; such ssues are beng allevated by the developng technology of FACTS. FACTS could be connected ether n seres or n shunt wth the power system or even n a combned pattern to provde compensaton for the power system. Varable seres capactors, phase shfters and unfed power flow controllers as the most used FACTS devces can be utlzed to change the power flow whch result n many benefts lke losses reduced, stablty margn ncreased etc. Due to such features of FACTS, ntegratng t nto the congeston management becomes more and more popular. Fgure 1-1 below has lsted most of the methods utlsed n CM. The lght-shaded methods are always consdered as remedal methods whch let the market functon as f 5

14 Introducton there are no constrants and leave t to the TSO to take measures to mantan system securty. By rasng the prce of the congested part of the network n order to reduce trade to releve the congeston, the heavy-shaded methods are so called prcng methods. Fgure 1-1 Summary of Congeston management methods Layout of the thess The report s dvded nto seven chapters. In the next three chapters, congeston management by re-dspatch s smulated usng three market models, pool, blateral and the hybrd. The results of the smulatons for the 14-bus test system are dscussed n these chapters and conclusons specfc to the chapters made. In chapter 5 we test the algorthms developed on the Cgre Nordc 32-bus test system for the pool and hybrd markets. Contngency analyss usng dc flow methods and lnear senstvty factors s carred out both on the IEEE 14-bus and the Cgre 32-bus test systems. The concluson and proposals for future work are presented n chapter 7. References [1] Bhattacharya, K., Bollen, M., H., J Daalder, J., E., Operaton of Restructured Power Systems Boston: Kluwer Academc Publshers, 2001 [2] Mutale, J., Strbac, G., Transmsson Network Renforcement Versus FACTS: An Economc Assessment IEEE Trans. On Power Systems vol.15 No.3, August

15 Introducton [3] Chrste, R., D., Wollenberg, B., F., Wangensteen, I., Transmsson Management n the Deregulated Envronment, Proc. IEEE, Vol.88, No.2, pp , Feb [4] Snha, A., K., Tulukdar, B., K., Mukhopadhyay, S., Bose, A., Pool Dspatch Strateges and Congeston Management n Deregulated Power Systems, IEEE, 2004 [5] Shahdepour, M., Yamn, H., L, Z., Market operatons n Electrc Power Systems Forecastng, Schedulng and Rsk Management 2002 [6] Bompard, E., Correa, P., Gross, G., Ameln, M., Congeston Management Schemes: A Comparatve Analyss Under a Unfed Framework IEEE, 2003 [7] Lommerdal, M., Soder, L., Smulaton of Congeston Management Methods, IEEE 2003 [8] Fang, R., S., Davd, A., K., Transmsson Congeston Management n an Electrcty Market, IEEE, 1999 [9] Rakar, S., Ilc, M., Assessment of Transmsson Congeston for Maor Electrcty Markets n the US, IEEE, 2001 [10] Alaywan, Z., Wu, T., Papalexopoulos, A., D., Transtonng the Calforna Market from a Zonal to a Nodal Framework: An Operatonal Perspectve IEEE, 2004 [11] Vres, L., J., Capacty Allocaton n a Restructured Electrcty Market: Techncal and Economc Evaluaton of Congeston Management Methods on Inter-connectors, IEEE 2001 [12] Svenska Kraftnät The Swedsh Electrcty Market and the Role of Svenska Kraftnäat,

16 2 Re-dspatch and FACTS for Congeston Management: Theoretcal Background In ths chapter we frst ntroduce the Optmal Power Flow as a tool for re-dspatch snce we are able to ncorporate dfferent obectve functons n t. The DC power flow method s also presented as an alternatve to the full ac flow method where speed of computaton may be of concern such as n contngency analyss. We ntroduce FACTS n general and descrbe the TCPAR and the TCSC. We also ntroduce the equatons for the modellng of these devces. 2.1 Optmal Power flow Optmal Power Flow (OPF) was defned n the early 1960s as an extenson of the conventonal economc load dspatch (ELD) problem to determne the optmal settngs for control varables whle satsfyng varous operatng constrants [1]. Based on the physcal laws of flow of electrcty, all knds of desred obectves, such as cost mnmzaton, power losses mnmzaton n the transmsson system etc, are acheved by ncorporatng correspondng control varables and system constrants. Commonly, OPF are also expressed as a mnmzaton of the shft of generaton and other controls from an optmum operatng pont when maxmzng system performance Modellng OPF In ths proect, re-dspatch s frstly consdered to allevate congeston problems. Market models nvolvng Pool, Blateral and Hybrd are establshed wth the common obectves beng mnmzaton of the absolute MW of re-dspatch. A constraned OPF model s utlzed to force the system to operate n a defensve manner by re-dspatchng the generaton of each unt n case of congeston. FACTS devces as another effectve way to manage congeston are ncorporated and examned n the OPF model. An OPF Model can nclude the followng [1]: 1) Obectve Functon: Due to the respectve features of dfferent market structures and dfferent ntentons, the obectve functons maybe dfferent. For nstance, the obectve functon n Pool market model s to mnmze the re-dspatched power whle n the Blateral market s to mnmze the transacton devaton. Further descrptons on the obectve functons n each Market model are gven chapters that follow. 2) Network equatons: Fgure 2-1 shows a smplfed transmsson lne usng a π equvalent crcut model. Let complex voltages at bus- and bus- are V δ and V δ respectvely. Two port equatons for the power flow computaton are derved as follows: 8

17 Re-dspatch and FACTS for Congeston Management: Theoretcal Background P, Q r X P, Q B sh B sh Fgure 2-1 Model of Transmsson lne The current flow from bus to bus can be expressed as: I e δ e δ ( G + B ) V V =. X Where 1 r and x form the seres mpedance of the G + B = r + x lne The apparent power flow from to can be expressed as: S * = V * I The astersk ndcates the conugate. From (2-1) and (2-2) t can be shown that the actve and reactve power flows P and Q respectvely can be expressed by: P = V 2 and Q G = V V V [ G Cos( δ δ ) + B Sn( δ δ )] ( B + B ) + VV [ B Cos( δ δ ) G Sn( δ δ )] sh (2-1) (2-2) (2-3) 2 (2-4) Smlarly P and Q are gven by P and Q [ G Cos( δ δ ) B Sn( δ δ )] = V 2 G V V (2-5) = V 2 ( B + B ) + V V [ B Cos( δ δ ) + G Sn( δ δ )] sh (2-6) 3) Power balance: In the economc load dspatch problem, we have a sngle constrant whch holds the total generaton to equal the total load plus losses. Snce the losses are ncorporated n the power flow equatons, the power balance equatons could be expressed as: 9

18 Re-dspatch and FACTS for Congeston Management: Theoretcal Background = PG PD P (2-7) QG QD + V 2 B sh = Q Where, PG and QG are the generated actve and reactve powers whlst PD and QD are the correspondng actve and reactve power demand at each bus respectvely. B sh s any shunt devce connected at bus. 4) General constrants: A set of power system lmts, such as lmts on generator actve and reactve power, lmts on the voltage magntude at each bus, and power flow lmts on transmsson lnes are ncluded n the OPF model. These operatng constrants guarantee that the dspatch of generaton does not force the transmsson system nto volatng any lmts, whch may lead to a danger to the system. (2-8) Voltage lmts mn max V V V, NB NB s the set of all generaton and load buses. Generaton lmts mn max P P P, NG Q mn max Q Q, NG Transmsson lmts 2 2 max ( P + Q ) S, Regulaton angle of TCPAR mn max σ σ σ (2-9) (2-10) (2-11) (2-12) (2-13) Adustable reactance of TCSC mn max x x x TCSC (2-14) TCSC TCSC 5) Contngency constrants: Constrants that represent operaton of the system after contngency outage could also be ncluded n the OPF model. By ncorporatng contngency constrants, f contngency happened, the resultng voltages and power flows would stll be wthn lmts. The contngency constrants are based on general constrants such as followngs: V mn V (wth some lne out) S, (wth some lne out), NB V max (2-15) max S (2-16), When these post-contngency constrants are contaned n an OPF model, ths specal type s called a preventve-dspatch OPF. 10

19 Re-dspatch and FACTS for Congeston Management: Theoretcal Background For dfferent applcatons, OPF model has a flexble manner to acheve dfferent obectves. When we use OPF model to solve some specfc problems n whch the fast computaton s hghly apprecated, a dc power flow method nstead of full ac power flow method s used DC Flow Modelng A full ac flow s the most accurate method of calculaton, but ts complexty can obscure relatonshps and prolong the computaton tme. Owng to the foregong, the dc model becomes useful n specfc cases. The dc model greatly smplfes the power flow by makng a number of approxmatons ncludng: 1) completely gnorng the reactve power balance equatons 2) assumng all voltages magntudes are dentcally one per unt and 3) gnorng lne losses by settng lne resstance to zero and assumng that the transmsson angles are small. Hence the dc model reduces the power flow problem to a set of lnear equatons[2] the power flow over a transmsson lne then becomes: 1 (2-17) max P = ( δ δ ) P x where x lne reactance n per unt δ phase angle at bus δ phase angle at bus The total power flowng nto bus, P s the sum of generaton and load at bus whch equals the sum of the power flowng away from the bus on transmsson lne 1 (2-18) P = P = ( θ θ ) x When a TCPAR s nserted n a lne the dc power flow equaton (2-17) becomes: 1 max P = ( δ δ + σ ) P x (2-19) Comparson between DC and AC flow method The accuracy of DC power flow soluton depends upon the power system. It s easy to fnd cases n whch the results are dentcal, such as a two bus system wth generators at each bus, regulatng ther termnal to 1.0 per unt, connected by a lossless transmsson lne. Alternatvely, t s also easy to conceve cases n whch the DC power flow results are totally wrong. For nstance, n a two bus system wth a generator at one end and a 11

20 Re-dspatch and FACTS for Congeston Management: Theoretcal Background constant power load at the other end whch s greater than the total generaton of ths system, the soluton for AC power flow s nfeasble whle the DC power flow wll ndcate a normal soluton. For a large system, such errors ntroduced wth DC power flow are hard to be detected. Power losses, as one of the most obvous dfference between DC and AC power flow algorthm, can be reasonably compensated by ncreasng the total dc load by the amount of the ac losses. Hence when the transmsson losses are allocated to the bus loads, n other words, the accuracy of DC powder flow s hghly ncreased. Computatonally the dc power flow has at least three advantages over the standard full ac power flow. Frst, by ust solvng the real power balance equaton, the amount of equatons s about half the sze of full ac problem. Second, the dc power flow s nonteratve and saves much more tme than full ac power flow. Thrd, because the B matrx depends on the confguraton of system and t only need to be calculated once. Therefore, gettng ntal soluton wth the dc power flow s about ten tmes faster [3] than the regular ac power flow ntalzaton. For subsequent solutons, the dc flow s even faster snce solvng for θ wth a modfed P would only requre a forward or backward substtuton. For contngency analyss, these speedup advantages of dc load flow are serously taken nto account. 2.2 An Overvew of FACTS The transmsson system of an electrc power network forms the delvery system of electrc power from the generaton centres to the load centres. The transmsson network s also needed to pool power plants and load centres n order to mnmze the total power generaton capacty and fuel cost [4]. The transmsson nterconnectons make t possble to make avalable generaton resources n one part of the network to other parts of the network. Ths may translate to economc advantage through the lowerng of electrcty prce because of the use of low cost generaton whch would otherwse not be accessble. The buldng of transmsson network can at tmes be a substtute to buldng new generaton capacty. Ths s true where generaton n other parts of the network may be n excess but transmsson of the power s lmted by the capacty of the transmsson network. Buldng or ncreasng the transmsson capacty n ths scenaro may be more cost effectve than the buldng of a new generaton staton [4]. The nterconnectons of the transmsson networks, called the grd, may result n overloads of certan transmsson paths whle others are relatvely lght loaded. The flow of power n a crcut s nversely proportonal to the mpedance of the crcut. The low mpedance paths therefore may get overloaded before the hgher mpedance paths reach ther capacty loadng. Ths results n a lmtaton of the amount of power that can be transmtted through a network though enough capacty may be avalable! Furthermore due to ths physcal law of the flow of electrc current, power does not flow n accordance to predetermned contract paths! Inadvertent lne flows, called loop flows, are nevtable. 12

21 Re-dspatch and FACTS for Congeston Management: Theoretcal Background In order to ncrease the amount of power to be transmtted one s faced wth the opton of ether upgradng the exstng transmsson lnes or buldng new ones. The upgrade of transmsson lnes by upgradng the conductor may not be effectve f loop flows already exst. Ths acton may be self defeatng [4]. The buldng of new transmsson lnes, apart from beng expensve s beng met by obectons from envronmental actvsts. The tme taken to acqure servtudes from land owners and consents from the dfferent publcs can be very long. Ths has made constructon of new transmsson lnes an almost mpossble task. The power system comprses of control devces that are largely mechancal n operaton. In dynamc events the power system s therefore uncontrollable to a large extent due to the slow response of mechancal devces. Furthermore the mechancal devces cannot be operated as often as desred owng to the mechancal wear resultng from such duty. The foregong dffcultes of upgradng exstng lnes and constructon of new transmsson lnes and control of the power system can be partly overcome by the use of power electronc devces collectvely referred to as Flexble AC Transmsson System controllers (FACTS). FACTS help to ncrease the use of avalable capacty of the exstng lnes (e.g. elmnaton of loop flows, control of power flow etc). These devces are not an alternatve to constructng new transmsson networks or upgradng transmsson lnks but make t possble to use exstng transmsson network up to or close to ther thermal lmts. The IEEE defne FACTS as alternatng current transmsson systems ncorporatng power electronc-based and other statc controllers to enhance controllablty and ncrease power transfer capablty. A FACTS controller s defned as a power electronc-based system and other statc equpment that provde control of one or more AC transmsson parameters. FACTS devces can broadly be categorzed as shunt, seres, combned seresseres and combned seres-shunt [4]. In ths thess, we shall demonstrate the use of FACTS devces, specfcally the thyrstor controlled seres capactor (TCSC) and the thyrstor controlled phase angle regulator (TCPAR) n managng congeston n the varous electrcty market models. Some benefts of FACTS nclude [4]: Control of power flow as ordered Increase the loadng of lnes to ther thermal capabltes. Increase system securty through the rasng the transent stablty lmt, lmtng short crcut currents and overloads. Provde greater flexblty n locatng new generaton snce lne flows can be controlled Reduce reactve power flows allowng the lnes to carry more actve power Reduce loop flows Increase utlzaton of lowest cost generaton as shall be demonstrated n ths thess 13

22 Re-dspatch and FACTS for Congeston Management: Theoretcal Background 2.3 Control of Power flow over a lne In order to understand the prncples of operaton of the FACTS we need to understand the parameters that flow of power depends on. Consder a two bus system n Fgure 2-1. For a lossless lne (2-3) can be expressed as: P or P = V V VV = [ B Sn( δ δ )] Sn ( δ δ ) X (2-20) Snce the transmsson lne consdered s lossless P and P wll have the same absolute value. If we make the magntudes of the voltages at both buses equal V = V V = Then (2-20) becomes 2 V Snδ P = X (2-21) Where δ = δ δ Actve power flow can be regulated by varyng one of the parameters n (2-21). Increased flow can be acheved by reducng X, hence makng the lne electrcally shorter. Ths prncple s utlzed n the thyrstor controlled seres capactor. Power flow can also be regulated by varyng the transmsson angle. The thyrstor controlled phase angle regulator uses ths prncple. The varaton of the actve power P aganst varaton of the transmsson angle for varous values of the seres reactance of the lne s shown n Fgure

23 Re-dspatch and FACTS for Congeston Management: Theoretcal Background Fgure 2-2 Power angle curves for dfferent values of seres reactance The seres mpedance of a transmsson lne s domnated by the reactance from the nductance. It s generally acceptable to assume that the seres mpedance of a transmsson lne s nductve. Control of mpedance can therefore be acheved by nsertng a varable seres capactor, referred to as a thyrstor controlled seres capactor (TCSC). The angle dfference between the sendng end and recevng end of a transmsson lne can be controlled by nsertng a thyrstor controlled phase angle regulator (TCPAR). Other FACTS devces nclude STATCOM, SSG, SVC, TSC, TSR SVG, SSSC, IPFC, TSSC, TCSR, TSSR, UPFC, IPC [4]. In ths thess we look at the TCSC and the TCPAR to allevate congeston n a power market Thyrstor-Controlled Phase Angle Regulator (TCPAR) The TCPAR s also called a thyrstor controlled phase shftng transformer (TCPST) and s defned by IEEE as a phase-shftng transformer adusted by thyrstor swtches to provde a rapdly varable phase angle. The TCPAR controls power flow through a transmsson lne by regulatng the effectve phase angle between the two buses of the lne. TCPARS can help elmnate loop flows. The TCPAR apart from the steady state voltage and power flow control can also be used to handle dynamc events on the power system. Ths functon s however beyond the scope of ths thess and shall not be dscussed any further. The phase angle of the system voltage s controlled by necton of a quadrature component to one of the termnal bus voltage [4]. Fgure 2-3 shows the concept and basc mplementaton of a phase angle regulator, only a sngle phase s shown. The wndngs of the three phase transformer are connected n delta on the prmary sde. A proporton of ths voltage (whch s lne to lne) s nected n the approprate phase through a seres nserton transformer as shown n the fgure below. For small angular adustments between the termnal bus voltage and the regulated voltage (.e. V a and V a + V bc ), the resultant angular change wll be proportonal to the nected voltage and the voltage magntude wll reman the same. When the angle s apprecably large the magntude of 15

24 Re-dspatch and FACTS for Congeston Management: Theoretcal Background the system voltage wll ncrease (V a + V bc wll be apprecably larger than V a ) and, for ths reason the TCPAR s often referred to as a quadrature booster transformer (QBT). Fgure 2-3 TCPAR usng thyrstor tap changer and ternary proportoned wndngs for dscrete voltage control For power flow control the TCPAR can be consdered as a voltage source wth a controllable ampltude and phase angle. Fgure 2-4 shows a two machne system wth a phase angle regulator nserted at the sendng end bus. 16

25 Re-dspatch and FACTS for Congeston Management: Theoretcal Background Fgure 2-4 Two machne model wth a TCPAR and the correspondng phasor dagram for a quadrature booster From Fgure 2-4 the mathematcal relatonshps of the voltages are: V = V + V seff V σ 2 2 ( V ) seff = + V σ Cos σ = Snσ = V V V seff σ V seff (2-22) (2-23) (2-24) (2-25) In the above equatons the symbols n bold denote vectors or complex quanttes whle the ones not n bold are scalars and therefore denote magntude only. If a lossless lne has a TCPAR nstalled the power transfer s then governed by: V. Vseff P = Sn( δ σ ) X (2-26) In (2-26) we want to decrease the effectve angle between Vs and Vr. From (2-24) and (2-25) t can easly be shown that (2-26) can be smplfed to: 17

26 Re-dspatch and FACTS for Congeston Management: Theoretcal Background P 12 2 V V = Snδ + σ Cosδ X V (2-27) AssumngV = V V. = When we nsert a TCPAR n a lne wth losses (2-3) s modfed thus: s 2 V G V V G Cos( δ + σ ) + B Sn( δ + σ ) [ ] P (2-28) = seff seff s Where P denotes actve power flow wth a TCPAR nserted and V seff s the effectve sendng end voltage (refer to Fgure 2-4). Usng the relatonshps n (2-24), (2-25) and other well known trgonometry denttes, (2-28) can be reduced to: [ G Cos( δ + σ ) + B Sn( δ + σ )] s 2 2 = V T G VV T P (2-29) Usng the same arguments as above (2-4), (2-5) and (2-6) for P, Q,Q can be modfed to ncorporate a TCPAR and the resultng expressons are: s 2 2 P V T G V V T G Cos δ + σ B Sn δ + σ (2-30) Q Q [ ( ) ( )] 2( B + Bsh ) + VV T[ BCos( δ + σ ) GSn( δ + σ )] ( B + B ) + V V T[ B Cos( δ + σ ) + G Sn( δ + σ )] = s s 2 = V T 2 = V sh (2-31) (2-32) Where 1 T = Cos( σ ) The dfference between P s (2-29) and P (2-3) gves the addtonal power flow over the lne and ths can be consdered as an necton of addtonal power at bus. s P = P P The bus necton at bus s then gven by: s P = P P s = V 2 K 2 G V V [ Snδ B Cosδ ] K G Smlarly actve power necton at bus s gven by: P s [ Snδ + B Cosδ ] (2-33) = V V K G (2-34) Followng the same reasonng as above the bus nectons for reactve power at bus and are gven by: 2 2 Q = V K B + B + VV K G Cosδ + B Snδ (2-35) ( sh ) [ ] K[ G Cosδ B Snδ ] Q = V V (2-36) 18

27 Re-dspatch and FACTS for Congeston Management: Theoretcal Background Where K = tanσ The admttance matrx of the system need not be modfed when usng the necton model above. The two port equatons can then be wrtten generally as: s P = P P P (2-37) And smlarly s Q Q Q Q = (2-38) The equatons are no longer symmetrc. When consderng P, P s zero and for P, P s zero. The necton model for the TCPAR can now be represented as shown n Fgure 2-5. r X S B sh B sh S Fgure 2-5 Inecton model for TCPAR As earler dscussed the loadng of a transmsson lne may be restrcted by the transmsson angle. In such cases a TCPAR can be employed. Wth a QBT the transmtted real power s plotted aganst the phase angle dfference of the bus voltages of the transmsson lne for varous values of the regulaton angle n Fgure

28 Re-dspatch and FACTS for Congeston Management: Theoretcal Background Fgure 2-6 Varaton of transmtted actve power wth transmsson angle for varous values of TCPAR regulaton angle We observe that the transmtted power ncreases wth ncrease regulaton angle snce the effectve sendng voltage has ncreased. The maxmum power transmtted on an uncompensated lne occurs at a transmsson angle of 90 degrees. From Fgure 2-6 we observe that wth a regulaton angle of 10 degrees the maxmum power transfer s acheved at 80 degrees. It s mportant to note from Fgure 2-6 that the amount of power transmtted over a lne wth a natural phase angle dfference of say 20 degrees can be ncreased by ncreasng the regulaton angle and at the same tme the power can be reduced by decreasng the regulaton angle. Overall the QBT does not ncrease the maxmum transmttable power for the lne sgnfcantly but makes t possble to ncrease the power flow at a gven prevalng phase angle dfference. Transmsson lnes are normally operated n a defensve manner meanng that the system needs to be stable even after a contngency. Transmsson angles of less than 45 degrees are typcal for stablty reasons. The ratng of the TCPAR s gven by: VA= Vσ * I max (2-39) Where I max s the maxmum contnuous lne current. It should be noted that the ratng of the TCPAR s much less than the ratng of the crcut snce the nected voltage s small compared to the crcut voltage. 20

29 Re-dspatch and FACTS for Congeston Management: Theoretcal Background The result of the use of the TCPAR s that the transmtted power can be ncreased or decreased for a gven transmsson angle. The flow of power s therefore not totally restrcted to the prevalng transmsson angle as s the case n an uncompensated lne Thyrstor-Controlled Seres Capactor (TCSC) The IEEE defnes the TCSC as a capactve reactance compensator whch conssts of a seres capactor bank shunted by a thyrstor-controlled reactor n order to provde a smooth varable seres capactve reactance. Seres capactve compensaton works by reducng the effectve seres mpedance of the transmsson lne by cancellng part of the nductve reactance. Hence the power transferred s ncreased as earler demonstrated n Fgure 2-2. A basc set up of a TCSC s shown n Fgure 2-7. Fgure 2-7 Set up of TCSC The mpedance of ths crcut s that for a parallel LC crcut and s gven by: X c X l ( α) X TCSC ( α ) = Xl( α) Xc (2-40) Where π (2-41) X l ( α) = X L π 2α Snα α s the frng angle, X L s the reactance of the nductor and X l s the effectve reactance of the nductor at frng angle α and s lmted thus: X (α ) L X l Care s taken for the crcut n Fgure 2-7 not to resonate otherwse the transmsson lne would be an open crcut! In our smulatons the TCSC s taken as contnuous varyng capactor. The effectve seres transmsson mpedance s gven by: X eff = ( 1 k) * X where k s the degree of seres compensaton k X TCSC = 0 k 1 X 21

30 Re-dspatch and FACTS for Congeston Management: Theoretcal Background As the delay angle s vared X l vares as gven by (2-41) and also X TCSC vares as n (2-40). The TCSC has two modes of operaton around the crcut resonance dependng on the value of the frng angle. The TCSC can operate n the nductve mode,.e. for frng angles greater than zero but less than the upper lmt, dctated by the resonance band but less than 90 degrees. In the capactve mode, the frng angle s greater than a lower lmt, dctated by the resonance band and less than 90 degrees. In our smulatons, we use only the capactve regon hence the compensaton level vares from zero to the maxmum level of 0.7. Fgure 2-8 shows a transmsson lne wth a TCSC. Fgure 2-8 Transmsson lne wth TCSC The necton model for the TCSC s derved n a smlar way as for the TCPAR. The modfed 2 port equatons and the power nectons are gven n the followng equatons: P C = V G V V ( G cosδ + B snδ ) (2-42) 2 ' ' ' Q P Q C C C = V ( B + B ) V V ( G snδ B cosδ ) (2-43) 2 2 ' ' sh ' ' ' ' = V G VV ( G cosδ B snδ ) (2-44) = V ( B + B ) + V V ( G snδ + B cosδ ) (2-45) 2 ' sh Power nectons can therefore be expressed as: c 2 P V G V V ( G cosδ + B snδ ) P Q Q c c c Where G B ' ' = (2-46) 2 = V G V V ( G cosδ B snδ ) (2-47) 2 = V B V V ( G cosδ B snδ ) (2-48) 2 = V B + V V ( G snδ + B cosδ ) (2-49) = ( r 2 x + x C 2 r ( x )( r 2 C 2x + ( x 2 2 xc ( r x + xcr ) = ( r + x )( r + ( x x ) 2 ' r G = and 2 r + ( x xc) ' B = r 2 ( x + ( x x c ) x ) c 2 C ) x 2 ) C ) 2 ) 22

31 Re-dspatch and FACTS for Congeston Management: Theoretcal Background From the expressons for the nectons.e. (2-46) through (2-49) we observe that the TCSC results n symmetrc expressons for the nectons. The fnal power flow on a lne can therefore be wrtten as: c c P = P + P c Q = Q + Q c Fgure 2-5 can also be used to represent the necton model of the TCSC. 2.4 Concluson Ths chapter has gven an ntroducton on OPF modellng as well as DC flow method. In ths proect, a constraned OPF ncorporated wth full ac flow s used for smulatng and analyzng congeston management n IEEE 14-bus system, whle a securty-constraned OPF ncorporated wth dc flow s used when analyzng the contngency problems and smplfyng ntrcate multple bus systems lke CIGRE 32-bus system. We have also ntroduced FACTS devces such as TCPAR and TCSC whch can be used n power systems to control power flow over lnes. Wthout FACTS nstalled the power flows are governed solely by Krchoff s Laws. Ths may result n undesrable loadng levels.e. congeston of some corrdors whlst other lnes are lghtly loaded. Congeston n a counter trade or re-dspatch envronment s solved by down regulatng the cheaper generators and up regulatng the more expensve ones untl the congeston s cleared. By drectng power flow congeston can be allevated by mnmal use of out of mert generators. FACTS devces can be ncorporated n power flow algorthms usng the necton models. The necton models do not requre the modfcaton of the system admttance matrx. Usng the TCPAR we have demonstrated that power flow n a congested lne can be reduced. It has also been shown that nstallaton of a TCSC n a transmsson lne can ncrease the power flow on that lne. Installaton of FACTS devces may ncrease the losses on the lne n whch they are nstalled f the resultng power s more than n the case wthout FACTS. References [1] Bhattacharya K., Bollen M., H., J., Daalder J., E., Operaton of Restructured Power Systems 2001 [2] Wood AJ, Wollenberg BF, Power Generaton Operaton and Control, second edton 1996 [3] Thomas J.Overbye, Xu Cheng, A Comparson of the AC and DC Power Flow Models for LMP Calculatons Proc. 37 th Hawa Internatonal Conference on System Scences-2004 [4] Hngoran, N. G., Gyugy L., Understandng FACTS: concepts and technology of flexble transmsson systems, IEEE Press,

32 3 Optmal Redspatch And Congeston Management: Pool Market Perspectve In ths chapter the pool market s descrbed n detal and the equatons descrbng the market are developed. We formulate the obectve of the market settlement. It s also explaned why the market settlement generaton schedule may not be the preferred generaton schedule for the network when we take techncal constrants n consderaton. Re-dspatch s descrbed n the presence of congeston on transmsson lnes. Two obectve functons for re-dspatch are formulated: mnmsaton of absolute generaton re-dspatch and mnmsaton of net payment by ISO. The results for the smulaton of the 14bus IEEE test case are presented. The use of FACTS devces for congeston management s also nvestgated. The use of the TCPAR and TCSC to manage congeston s nvestgated. An economc assessment for the optmal locaton of the FACT devce s proposed. 3.1 Characterstcs of a Pool Market A pool market s characterzed by many producers and accompaned by many consumers. Of all the electrcty markets the pool market tres to emulate a true compettve market. The producers of the tradable commodty are the generatng companes (GENCOs). They compete for the rght to supply energy to the grd, and not to specfc customers [1]. The competton s by way of sell bds comprsng of the amount of energy and ts prce. The buyers also compete for buyng power and bd as hgh as possble to ensure partcpaton n the trades. If a GENCO s sell offer s too hgh t may be reected. In the same way f a customer s buy bd s tool low t may be reected n the market. [1]. Ths market type s complex snce t requres an organsed market structure. The players n ths market are: market operator (as the market admnstrator), GENCOs, marketers, aggregators, traders, DISCOs, consumers and others. In ths market all dealngs.e. buyng and sellng of electrcty s transparent and s managed by the market operator or the ISO whatever the case may be. The market operator wll receve sell offers from GENCOs detalng the amount of energy blocks and the respectve unt prces. The offers from the generator, n the lght of competton, wll be reflectve of the margnal cost of the GENCO. If we assume that the cost functon of the GENCO s quadratc as n (3-1), then the prce of the bd wll be based on a margnal cost functon of the form gven n equaton (3-2). 2 C( ) ap + bp c (3-1) ρ ( ) = g ( ) g ( ) + = 2aΡ g ( ) + b Where a, b and c are cost coeffcents for the generator. In a double aucton market, the market operator wll also receve buy bds from the consumers. The buyng prce by the consumer s equal to the margnal beneft derved from usng electrcty. In a sngle aucton market no demand bds are receved and the (3-2) 24