Australan Journal of Basc and Appled Scences 5(: 854-85 0 ISSN -88 The Effect Of Phase-Shftng Transformer On Total Consumers Payments R. Jahan Mostafa Nck 3 H. Chahkand Nejad Islamc Azad Unversty Brjand Branch Brjand Iran. Department of Electrcal Engneerng Amrkabr Unversty of Technology (Tehran Polytechnc Tehran Iran. 3 Electrcal Engneerng Department Islamc Azad Unversty Brjand Branch Brjand Iran. Abstract: The electrcty supply ndustry s undergong a profound transformaton worldwde. After the deregulaton the transmsson networks are operated near ther operaton constrants and t causes some problems. The most mportant problem s the congestons n the transmsson network that would ncrease the LMPs. The ISO by managng transmsson flow can contrbute to socal welfare consderably. FACTS devces have the capablty to control power flow over the lnes. Therefore they can be used by ISO to manage congestons n the transmsson network. In ths paper a precse model of Phase shftng (PHS transformer s presented to nvestgate ts effects on the real tme LMPs. Ths model s a full AC that consders system securty constrants properly and can be used n real tme redspatchng of the power system. The proposed model s mplemented on the IEEE 4 bus test system and the results show the effectveness of PHS transformer n mprovng system securty and reducng LMP of load buses and therefore decreasng the total consumers' payment. Key words: Phase-Shftng Transformer ISO FACTS LMP. INTRODUCTION The power ndustry has been evolvng toward a market based approach n the Unted States and throughout the world for well over a decade (J. H.Chow et al. 005. By separaton n generaton transmsson and dstrbuton sectons n electrcty market transmsson network has an mportant role n the earned benefts of producers and consumers. After the deregulaton the transmsson networks are operated near ther operatons constrants. In real tme the congestons n the transmsson network have a consderable effect on LMPs (Bo Lu et al. 005. Under these condtons FACTS devces have an mportant role n socal welfare because they have the ablty to control the flow over the transmsson lnes. In addton to flexble transmsson operaton FACTS devces are able to mprove voltage stablty and damp power system oscllatons (Nadarajah Mthulananthan. & Naresh Acharya. 00. The market prces are the most mportant sgnals that partcpants of the market receve. In North Amercan electrcty markets the LMP prcng model s n use. LMP s the cost of provdng one MW more loads n a specfc area subject to ncremental cost of producers the cost of congeston and the cost of loss assocated wth t (Bo Lu et al. 005. In order to determne the LMPs an optmal power flow (OPF consderng securty constrants should be performed. The LMPs ncrease n buses that are domnated wth load consumpton and decrease n those wth extra producton when congeston occurs. By usng FACTS devces the flow over the transmsson network could be controlled and the congeston could be removed or at least be allevated. Therefore these devces have a consderable effect on the total socal welfare (Bo Lu et al. 005. FACTS devces have been effectvely used n several OPF problems wth dfferent objectve functons such as mprove voltage securty (LEHMKO STER C. 00 congeston management (SHAO W. & VITTAL V. 006 and generaton cost reducton (PALMA-BEHNKE R et al. 004. In (SCHAFFNER C. & ANDERSSON G. 003 the value of FACTS devces n the context of deregulated electrcty market s nvestgated. In ths paper we nvestgate the effect of phase-shftng transformer (PHS as one of the FACTS devces on the total consumers payment and generatons revenue. The proposed method s mplemented on the IEEE 4 test system and the results show the effectveness of usng PHS on the congeston management and consequently on the total socal welfare. The Models Of Transmsson Lne And Phase-Shftng Transformer: The PHS has the ablty to adjust the angle of the bus voltage. Therefore t can control the power flow on the lne. When a PHS s placed on a lne between buses and j ts actve and reactve power flow can be formulated as follows : Correspondng Author: R. Jahan Islamc Azad Unversty Brjand Branch Brjand Iran. 854
Aust. J. Basc & Appl. Sc. 5(: 854-85 0 Pj V Y cos( VV jyj cos( j j j Qj V Y sn( VV jyj sn( j j j ( ( Where and j are ndces of buses P j and Q j are actve and reactve power flow j and Y j are angle and magntude of network admttance matrces and V are angle and magntude of bus voltage and j s the phase of PHS transformer. If the PHS transformer s placed between buses and j and regulates the angle of the bus a negatve sgn must be used before j n ( and (. If the PHS transformer regulates the angle of bus j the postve sgn must be used n ( and (. The actve and reactve power flow on the transmsson lnes can be formulated as follows: Pj V Y cos( VV jyj cos( j j Qj V Y sn( VV jyj sn( j j Problem Formulaton: Optmal power flow s a non-lnear optmzaton problem wth equalty and non-equalty constrants. The objectve of the model s to mnmze the cost of supplyng demand subject to constrants. In ths paper the consumers are assumed to be flexble namely; they can reduce ther consumpton when the prces ncrease. Consumers are allowed to bd for 5% of ther total consumpton. The objectve functon can be formulated as the followng (T. Zheng. & E. Ltvnov. 006: Mnmze bu Pu bl Where b u s the bd of producer u at bus for ncreasng output power P u s the amount of power that producer u at bus ncreases. b s the consumers bd and L s the amount of load reducton at bus. The constrants of the problem are as follows: Load Balance: Pu ( KG PD( Pj : U J Qu QD( Qj U J Where P D and Q D are loadng parameter actve power consumpton and reactve power consumpton at bus respectvely. KG s the loss dstrbuton factor. Pj and Qj are actve and reactve power flow over the lne between and j respectvely. Capacty Constrants For Onlne Unts: mn Pu Pu Pu Pu mn and P u are upper and lower bonds of onlne unts. Ramp rate constrants: SE Pu Pu RUu SE Pu Pu RDu ȘE RD u and RU u are ramp up and ramp down capablty of unt u at bus respectvely. Pu s the power producton of unt u at bus before contngency. 855
Aust. J. Basc & Appl. Sc. 5(: 854-85 0 Load reducton constrants: L 0.5L T T Where L s the total demand at bus. Voltage lmts: mn V V V Transmsson lnes transfer capablty constrants: Mnmze bu Pu bl Physcal constrants of PHS transformer: mn j j j mn Where j and j are the mum and mnmum phase regulaton of the PHS transformer. The LMPs are calculated based on the dual of the load balance equaton as follows: LMP These prces nclude the ncremental generaton cost of unts congestons cost and losses cost. Smulaton And Results: The IEEE 4 bus test system s used to mplement the method. The sngle lne dagram of ths system s showed n the fgure. Ths system has 6 plants wth 305 MW total generaton capacty and total 850 MW demand n peak hour. Fg. IEEE 4 bus test system Table : Producers bd for ncreasng output Unt No. Bus No. Upward generaton Prce Unt No. Bus No. Upward generaton Prce 3 4 5 6 8 4 4 0 0 4 4 0 0 8 0 3 4 5 5 5 5 5 6 8 856
Aust. J. Basc & Appl. Sc. 5(: 854-85 0 0 3 4 5 6 3 3 3 5 8 8 8 6 8 30 3 3 3 3 3 5 5 Table : Loads bd for decreasng consumpton Load no. Bus no. Prce for decreasng demand Load no. Bus no. Prce for decreasng demand 0 0 0 30 0 3 0 3 3 0 4 0 4 4 30 3 5 0 5 5 30 4 6 0 6 6 30 5 8 0 40 6 0 8 8 40 0 0 30 Fg. : LMP of all buses The model has been mplemented usng GAMS. The CONOPT solver whch s good for solvng non-lnear problems s used here. The PHS transformer s assumed to be between buses and 3 and ts phase regulaton range s between -30 to 30 degrees. Snce the most crtcal contngency s the outage of lne between bus 0 and 3 we only solve the problem for ths contngency. Producers and consumers bd prces are shown n tables and. In real tme the LMPs after contngency are calculated for dfferent loadng condtons. The problem s solved n base case (wthout PHS and n the presence of PHS. The prces for both cases are shown n fgure. In the presence of the PHS transformer the problem s feasble up to loadng factor of 4 percent whle wthout t the problem can be feasble only to percent. In the lght loadng condtons snce there s no congeston over the transmsson network the LMP of all buses are equal n two cases (wth and wthout PHS transformer. The congeston occurs when the loadng of the system s greater than 5 percent n base case. For ths case when congestons occur the LMP of buses fall down n whch generaton s trapped. In contrast LMP of busses whch are domnated by the loads ncrease. Therefore the total consumers' payment ncreases sgnfcantly. The PHS transformer s able to remove the congestons by controllng the flow over the lne. Thus the system can be operated up to percent loadng wthout any congeston. In ths way the consumers payment wll decrease consderably. The load reducton for base case occurs at loadng factor greater than percents whch results n ncrease of the LMPs sharply. The PHS transformer prevents the load reducton up to percent loadng factor. The LMPs of four buses are shown n fgure 3. It can be seen that for buses 3 and 3 n the presence of PHS transformer LMPs are hgher than the base case. Because when congeston occurs the generaton wll be trapped n these buses. In contrast the buses 3 and have hgher LMPs n the base case. Because they are domnated by the consumpton so that congeston n the transmsson network wll ncrease ther LMPs. The PHS transformer s able to remove or allevate the congeston and as a result the LMPs wll decrease. 85
Aust. J. Basc & Appl. Sc. 5(: 854-85 0 Fg. 3: LMPs of 4 buses at dfferent loadng condtons The total consumers' payment s shown n the fgure 4. It s lower n the presence of the PHS transformer because n ths case LMPs are lower than the base case. In loadng factor of 8 and percent the total consumers payment dfference between two cases s notceable. In these two loadng condtons the PHS transformer prevents load curtalment by managng congeston n the transmsson network whch results n ncrease of the LMPs sharply. The congeston and load curtalment occur n both cases for loadng condtons hgher than percent. Therefore ther dfference s not as much as 8 and percent loadng condtons. Fg. 4: Total consumers payment at dfferent loadng condtons The total producers' revenue and consumers' payments are shown n fgure 5. When the loadng of the system ncreases due to congestons that happen n the transmsson network the dfference between the consumers payment and producers revenue ncreases The PHS transformer s able to manage the congeston and consequently decreases the congeston cost and consumers' payment. Concluson: In ths paper the effect of PHS transformer on the LMPs n real tme market s nvestgated. A full AC model s used and securty constrants are consdered. The IEEE 4 bus test system s used to mplement the model under worst contngency and dfferent loadng condtons. In the low loadng condtons the LMPs are same for the base case n whch there s no PHS transformer n the network and the case that a PHS transformer s added to the system. When the loadng of the system ncreases some lnes of the system wll be congested and consequently busses wll have dfferent LMPs. The LMPs would ncrease n load buses and decrease n the buses that generaton s trapped. Therefore total consumers payment would ncreases and total generaton revenue wll decrease. The PHS transformer s able to control the flow over the lnes and consequently releves the transmsson network congestons. Therefore an ndependent system operator can use PHS transformer for 858
Aust. J. Basc & Appl. Sc. 5(: 854-85 0 managng the transmsson network n order to decrease congeston cost and consequently total consumers payments. Furthermore the results show that the power system s able to operate at hgher loadng condtons n the presence of PHS transformer. Ths means that nvestment n the transmsson network can be postponed by usng a PHS transformer. 8 x 0 6 4 $ Wthout FACTS 0 3 4 5 6 8 0 Loadng Factor (% Wth FACTS 6 4 $ 8 x 0 Total GenCo Revenue Total Demand Payment Total GenCo Revenue Total Demand Payment 0 3 4 5 6 8 0 Loadng Factor (% Fg. 5: Total Generatons revenue and Consumers payment REFERENCES Bo Lu Zuy L and Mohammad Shahdehpour Impact of Phase Shfters on Locatonal Prces J. ENERGY ASCE / APRIL 005. IEEE Task Force IEEE relablty test system IEEE Trans. Power App. Syst. (8: 04 054. Nov. /Dec.. J.H. Chow R.W. DE Mello and K. W.Cheung "Electrcty Market Desgn: an ntegrated approach to relablty assurance" Proceedng of the IEEE 3( Nov. 005 LEHMKO STER C. Securty Constraned optmal power flow for an economcal operaton of FACTSdevces n lberalzed energy markets IEEE Trans. Power Delv (: 603 608. Apr. 00. Nadarajah Mthulananthan Naresh Acharya A proposal for nvestment recovery of FACTS devces n deregulated electrcty markets Electrc Power Systems Research (00: 65 03. PALMA-BEHNKE R. VARGAS L.S. PE REZ J.R. NU N EZ J.D. TORRES R.A: OPF wth SVC and UPFC modelng for longtudnal systems IEEE Trans. Power Syst. 004 (4: 4 53. R. Za rate-m~nano A.J. Conejo F. Mlano OPF-based securty redspatchng ncludng FACTS devces IET Gener. Transm. Dstrb. 008. (6: 8 833 SCHAFFNER C. ANDERSSON G. Determnng the value of controllable devces n a lberalzed electrcty market. IEEE Power Tech Bologna Italy 003. SHAO W. VITTAL V. LP-based OPF for correctve FACTS control to releve overloads and voltage volatons IEEE Trans. Power Syst. 006 (4: 83 83. T. Zheng E. Ltvnov "Ex Post prcng n Co-Optmzed Energy and Reserve market" IEEE Trans. Power Syst. (4: NOV 006. 85