Power Flow Tracing Based Congestion Management Using Firefly Algorithm In Deregulated Electricity Market

Transcription

1 Internatonal Journal of Engneerng Research and Development e-iss: X, p-iss: X, Volume 12, Issue 5 (May 2016), ower Flow Tracng Based Congeston Management Usng Frefly Algorthm In Deregulated Electrcty Market A. Ahamed Jeelan Basha 1, M. Antha 2 1 Assstant rofessor, Department of Electrcal Engneerng, Annamala Unversty, Annamala agar, Tamladu, Inda, pn Assocate rofessor, Department of Electrcal Engneerng, Annamala Unversty, Annamala agar, Tamladu, Inda, pn ,. Abstract:- Congeston Management (CM) s one of the crtcal and maor tasks performed by the system operator. It s consdered to be more mportant as t may ntate the cascadng outages whch forces the system to collapse. Snce few generators contrbute the lne overloadng n the CM problem, t s enough to reschedule ther outputs only. To dentfy the most contrbutng generator, power flow tracng approach s used n ths paper. FreFly (FF) algorthm s employed to reschedule the outputs of selected generators. The proposed method s tested on a standard IEEE 30 bus system and a practcal Indan utlty 62 bus system. Varous case studes are carred out on the test systems to demonstrate the effectveness of the FF algorthm and the obtaned results prove that FF algorthm s ndeed capable of gettng hgh qualty soluton for the CM problem. Keywords:- Deregulaton, congeston management, frefly algorthm, senstvty factor, generator contrbuton factor, power flow tracng. Lst of Symbols CC C g Total congeston cost to releve congeston Incremental and decremental prce bds submtted by generators at whch the generators are wllng to adust ther real power outputs to releve congeston. S MVA power flow n the lne - Maxmum MVA lmt of the lne - Actve power generated by the K th generator as determned by the system operator Actve power consumed by the m th load as determned by the system operator mn max Δ, Δ Mnmum and maxmum lmts of the change n real power adustment of the k th generator. g Total number of generators c Total number of partcpatng generators n the process of reschedulng k artcpatng generator. l on partcpatng generator. s umber of transmsson lne n the system. d Total number of loads n the system. m Indvdual load at each bus. L Total transmsson losses p Actve power generated by the k th generator after the process of reschedulng. f A u Mnmum and maxmum lmts of the k th generator. Voltage and angle at bus. Set of nodes supplyng the power drectly to the node. ower flowng from node to node, (nxn) upstream dstrbuton matrx. Vector of nodal through flows G Vector of nodal generatons. r Dstance between any two frefles Intal attractveness at r = 0 0 γ Lght absorpton coeffcent, whch controls the lght ntensty. 38

2 ower Flow Tracng Based Congeston Management Usng Frefly Algorthm In... I. ITRODUCTIO In a deregulated electrcty market, freedom s provded to partcpants to buy and sell electrcty. When the producers and consumers of electrc energy desre to transact power n bulk amount, unexpected congeston occurs due to volaton of physcal lmts n transmsson system. The undesrable effects of the congeston nclude preventon of new contracts, ncrease of the electrcty cost n some regons of the electrcty market whch endanger to the system securty and relablty. Congeston n a transmsson system cannot be allowed beyond a short duraton as t may ntate cascaded outages whch forces the system to collapse. Hence an effectve control acton strategy s necessary to reduce the lne overloads to the securty lmt n mnmum tme. A detaled survey report of several technques for congeston management has been reported n lterature [1]. Many Optmal ower Flow (OF) based congeston management schemes for pool and multple transacton systems are proposed n lterature [2-4]. In [5], an OF-based approach that mnmzes cost of congeston and servce cost s proposed. Ashwan kumar et al., solved the zonal CM problem usng AC Transmsson Congeston Dstrbuton Factors (TCDF) [6] and real reactve power reschedulng method [7]. However, t s necessary to compute the senstvty values for all the buses n the system whch n turn results n a large amount of computatonal effort. Many researchers have solved congeston management problem usng FACTS controllers n deregulated envronment [8-11]. In [12], Relatve Electrcal Dstance (RED) concept s employed to mtgate the transmsson overload by real power generaton reschedulng. Ths method mnmzes the system losses and mantans good voltage profle. However, the bds of ndvdual generatng unt and the reschedulng cost are not consdered n ths method. Many stochastc methods have also been used n the lterature to allevate transmsson lne congeston. Sudpta Dutta and Sngh [13] proposed a congeston management technque usng optmal reschedulng of generators based on generator senstvtes and artcle Swarm Optmzaton (SO) s used to mnmze the devatons of rescheduled generator power outputs. Balek [14] have proposed power flow tracng approach to determne the contrbuton of each generator and ths method s used for transmsson prcng n the deregulated market. Raathy and Harsh kumar employed power flow tracng approach to fnd the most contrbutng generators and used Dfferental Evoluton (DE) algorthm to reschedule ther outputs so that congeston may be allevated [15]. In ths paper, three methods are used to solve the congeston management problem usng frefly algorthm wth the obectve of mnmum reschedulng cost. The frst method (method - 1) consders all generators n the partcular area for reschedulng. In the second method (method - 2) generators are selected based on Generator Senstvty Factors (GSF) and ther outputs are rescheduled optmally usng FF algorthm to relve overload n transmsson lnes. The thrd method (method - 3) employs power flow tracng approach to dentfy the most contrbuted generators to the congested lne and only these generator outputs are rescheduled usng FF algorthm to allevate congeston. In ths paper, congeston due to dfferent lne outages, generator outages and wheelng transactons are consdered. The proposed method s tested on two test systems and the algorthm s valdated by comparng the results wth DE method. II. roblem formulaton The optmal congeston management of reschedulng based on mnmzng redspatch cost can be expressed as mnmze n c CC = C... (1) k Subect to, c g Gk g d O O O + Δ + = dm + L k c k 0 S, V δ mn mn f + g l,l k mn O l,l k = d m mn O dm k + L max max 0... (2)... (3) = Δ =... (4) max S, V δ V δ max max... (5)... (6)... (7) 39

3 ower Flow Tracng Based Congeston Management Usng Frefly Algorthm In... The power flow tracng algorthm for tracng the contrbuton of each generator n transmsson system and allocate a charges as usng the transmsson lne for each user. It s based on Krchhoff s current law and proportonal sharng prncple. There exst two methods for tracng the power flow namely upstream and downstream algorthms [14]. In ths work, the upstream tracng algorthm s proposed to fnd the contrbuton factors of each generator to the flow of power n the transmsson lne. The total nflow through node can be expressed as = + = C +, =1,2,3,.n... (8) C α u G α u G =... (9) Equaton (9) can be rewrtten as C = α u Or A u = G The (,) th element of A u s gven by G 1 for = [A u ] = u C = / for α 0 otherwse If A exsts then = G and ts th element s equal to 1 u = n A u k k= 1 1 Au... (10)... (11) 1 = 1,2,3,..n... (12) whch shows the contrbuton of the K th generator to th nodal power. A lne outflow n the lne from nodel can be calculated usng the proportonal sharng prncple, as n 1 = = Au... (13) k and n G D,k k= 1 k= 1 d α for all... (14) s the generaton contrbuton factor, whch s the flow n the lne - due to the K th d generaton and α s the set of nodes suppled drectly from node. Based on the generaton contrbuton factor, the generators are selected for the process of reschedulng. III. Frefly algorthm The frefly algorthm was developed by Xn-She Yang at Cambrdge Unversty n 2008 [16]. It s a meta-heurstc optmzaton algorthm, nspred by the flashng behavor of frefles. The prmary purpose for a frefly's flash s to act as a sgnal to attract other frefles. There exst three dealzed rules based on the maor flashng characterstcs of frefles [17]. These are the followng: (1) All frefles are unsex, and they wll move towards more attractve and brghter ones regardless of ther sex. (2) The degree of attractveness of a frefly s proportonal to ts brghtness whch decreases as the dstance from other frefly ncreases due to the fact that the ar absorbs lght. If there s no brghter or more attractve frefly than a partcular one, t wll then move randomly. (3) The brghtness or lght ntensty of a frefly s determned by the value of the obectve functon of a gven problem. A. Attractveness In the frefly algorthm, the attractveness functon β(r) of a frefly s descrbed as a monotoncally decreasng functon as gven by the followng functon: m β(r) β0exp( γr ),wth m 1... (15) By controllng ths parameter γ, FF algorthm has ablty to control ts modalty and adapt tself to the problem landscape [18]. 40

4 ower Flow Tracng Based Congeston Management Usng Frefly Algorthm In... B. Dstance The dstance between any two frefles and at x and x, respectvely, s the Cartesan dstance d x x (x,k x,k ) k1 r 2... (16) where x,k s the k th component of the spatal coordnate x of the th frefly. 2 2 In 2-D case, we have r x x ) ( y y )... (17) ( C. Movement The movement of a frefly s attracted to another more attractve (brghter) frefly s determned by the followng equaton: 2 x x β exp ( γr )(x x ) α(rand 0. )... (18) Where the frst term s the current poston of a frefly, the second term s used for consderng a frefly s attractveness to lght ntensty seen by adacent frefles and the thrd term s the random movement of a frefly n case there s no other brghter ones. FF algorthm subdvdes the populaton nto subgroups due to the fact that local attracton s stronger than long dstance attracton. As a result, FF algorthm can deal wth hghly non lnear, mult-model optmzaton problem effcently. In the lterature, FF algorthm s consdered as generalzaton to DE algorthm [18]. From equaton (18), t s seen that when γ s zero and β s set to 1, then FF algorthm becomes a smplfed verson of DE 0 wthout mutaton and crossover rate s controlled by β 0. Hence standard FF algorthm ncludes DE as ts specal case. As a result, FF algorthm has all the advantages of DE algorthm and hence ts performance s very effcent than DE algorthm. The mplementaton of FF algorthm for congeston management problem s depcted n the flowchart shown n Fg

5 ower Flow Tracng Based Congeston Management Usng Frefly Algorthm In... Start Input system data to obtan power flow analyss soluton o Is any lne congested? Yes Calculate GSF and GCF to congested lne Select the generators for reschedulng based on GSF and GCF Specfy frefly parameters and maxmum number of teratons (K max ) Intalze frefles wth poston Set teraton count K=1 Evaluate frefles ftness Update frefles poston as per equaton 18 K = K+1 o K = K max? Yes Optmal soluton s obtaned. rnt congeston cost Stop Fg. 1: Flow chart for FF algorthm based congeston management problem IV. Results and Dscusson The proposed FF algorthm s employed to solve congeston management problem usng power flow tracng approach. Standard IEEE 30-bus and a practcal 62 bus Indan utlty systems are used to llustrate the effectveness of proposed algorthm. Optmal reschedulng of (method-1, method-2 and method-3) actve power of generators to releve congeston n the overloaded lnes s done by FF algorthm. 42

6 ower Flow Tracng Based Congeston Management Usng Frefly Algorthm In... FF algorthm parameters are as follows: γ = 1.0, =0.5, 0 = 0.2, number of frefles are taken as 6 and 100 total generatons are consdered. Smulaton studes are carred out on Intel core 2 Duo (1.8 GHz) processor n MATLAB envronment. 4.1 IEEE 30 bus system The standard IEEE 30 bus test system conssts of 6 generator buses, 24 load buses and 41 transmsson lnes wth a base load demand of MW. The system s dvded nto 3 areas wth two generators n each area. Incremental and decremental costs submtted by Generaton Companes (GECOs) are assumed to be same and t s taken slghtly more than the margnal cost [19]. rce bds submtted by GECOs for congeston management are gven n Table-1. Table 1: Generator prce bds Incremental / Generator decremental number rce bds ($/MWh) G 1 35 G 2 40 G 3 42 G 4 44 G 5 48 G 6 36 A. Lne outage In ths case, the outage of transmsson lne connected between buses 14 and 15 n area 2 (lne no. 24) s consdered. Due to ths, the transmsson lne connected between buses 1 and 2 n area 1 gets congested. FF algorthm s used to releve congeston by reschedulng n all the three methods. In method 1, all the generators (G 1, G 2, G 3, G 4, G 5, G 6 ) are rescheduled. In method 2, senstve generators are dentfed usng GSF and only most senstve generators are rescheduled to releve congeston. In method 3, Generator Contrbuton Factors (GCF) are calculated usng power flow tracng method and only the generators whch contrbute more to the congeston are rescheduled. Table-2 shows the GSF and GCF for all the generators correspondng to the outaged lne. Table 2: GSF, GCF for outage of lne no. 24. Congested Lne 1-2 G 1 G 2 G 3 G 4 G 5 G 6 GSF GCF From the table, t s noted that n method 2, most senstve generators (G 1, G 5 & G 6 ) need to be rescheduled to allevate congeston. In method 3, most contrbutng generators (G 1 and G 6 ) are requred to be rescheduled. The congeston cost s calculated usng the prce bds submtted by the generators and are gven n Table-3. To valdate the proposed method, the obtaned results are compared wth that of DE method. It s evdent from the comparson that the FF algorthm gves mnmum congeston cost n all the methods than DE method. The change n real power output of the generators n all the three methods s shown n Fg. 2. Table 3: Comparson of congeston cost Methods Congeston Cost( $/hr) DE [15] FF algorthm Method-1 (All) Method-2 (GSF) Method-3 (GCF)

7 ower Flow Tracng Based Congeston Management Usng Frefly Algorthm In... Fg. 2: Rescheduled power of partcpatng generators. The obtaned results clearly depct the superorty of the FF algorthm over DE as the proposed algorthm has all the advantages of DE algorthm whch s already mentoned n secton-iii. The obtaned results also ustfy that the FF algorthm performs well than DE algorthm Bus Indan utlty system The test system conssts of 19 generator buses, 89 transmsson lnes and 11 tap changng transformers wth load demand of 2908 MW. The system s separated nto three areas wth sx generators n area 1 and area 3 respectvely, whereas area 2 has seven generators. The network topology and the data for the Indan utlty 62 bus system are found n [20]. rce bds submtted by GECOs for congeston management are gven n Table- 4. Table 4: Generator prce bds Gen o. G 1 G 2 G 3 G 4 G 5 G 6 G 7 G 8 G 9 Inc/ dec rce bds (Rs/MWh) A. case 1: Lne outage In ths case, the lne connected between the buses 61 and 62 (lne no. 88) s consdered to be outaged. Because of ths outage, lne connected between the buses 55 and 58 gets congested. In method 1, all generators n that area 1 (G 1, G 12, G 13, G 14, G 15, G 16, G 17 ) are rescheduled to releve congeston. Table-5 shows the GSF and GCF of all generators correspondng to ths outaged lne. Based on ths, the generators (G 1,G 13, G 14, G 15, G 17 ) need to be rescheduled n method 2. In method 3, the generators G 1, G 15, G 17 are to be rescheduled to releve congeston. The congeston costs obtaned n three methods are gven n Table-6 and t s nferred that method-3 gves a mnmum congeston cost as compared to DE method. Fg 3 shows the change n real power output of the generators n all three methods. Table 5: GSF, GCF for the outage of lne no. 88 Congested Lne G 1 G 2 G 3 G 4 G 5 G 6 G 7 G 8 G 9 GSF GCF

8 ower Flow Tracng Based Congeston Management Usng Frefly Algorthm In... Table 6: Comparson of congeston cost Methods Congeston cost (Rs/hr) DE [15] FF algorthm Method-1 (All) Method-2 (GSF) Method-3 (GCF) Fg. 3: Rescheduled power of partcpatng generators B. case 2: Wheelng transactons In ths case, multlateral transacton s carred out n the test system and ther detals are lsted n Table- 7. After carryng out these wheelng transactons, t s found that the transmsson lnes connected between buses and get congested. Tables 8 and 9 show the GSF and GCF correspondng to these congested lnes. In method 1, all generators n the area 1 (G 1, G 12, G 13, G 14, G 15, G 16, G 17 ) are rescheduled to releve the congeston. Based on GSF n method -2, sx most senstve generators (G 1, G 5, G 6, G 15, G 16, G 17 ) and n method-3 most contrbuted generators (G 1, G 6, G 15, G 17 ) need to be rescheduled. The rescheduled power of dfferent generators by all the three methods are shown n Fg. 4. The congeston cost obtaned n these methods are gven n Table-10 and mnmum congeston cost s found to be Rs/hr n method-3 when compared to other methods (All & GSF). Table 7: Detals of multlateral wheelng transactons ower nected Load Bus o. Amount (MW) Bus o. Amount (MW) Total 149 Total 149 Table 8: GSF for the multlateral wheelng transactons. Congested Lne G 1 G 2 G 3 G 4 G 5 G 6 G 7 G 8 G

9 ower Flow Tracng Based Congeston Management Usng Frefly Algorthm In... Table 9: GCF for the multlateral wheelng transactons. Congested Lne G 1 G 2 G 3 G 4 G 5 G 6 G 7 G 8 G Table 10: Comparson of congeston cost obtaned from FFA. Congeston Cost Methods (Rs /hr) FF algorthm Method-1 (All) Method-2 (GSF) Method-3 (GCF) Fg.4: Rescheduled power of partcpatng generators C. case 3: Generator outage In ths case, outage of generator 12 at bus 37 causes congeston of lnes connected between buses and In method 1, all generators n that area 1 (G 1, G 13, G 14, G 15, G 16, G 17 ) are rescheduled to releve congeston. GSF and GCF correspondng to these congested lnes are gven n Tables 11 and 12 respectvely. Based on GSF, generators G 1, G 6, G 15, G 16 and G 17 need to be rescheduled. In method-3, most contrbutng generators (G 1, G 15, G 17 ) are rescheduled. Fg. 5 shows the change n real power output of the generators n all the three methods. The congeston cost obtaned n all the three methods are gven n Table 13. From ths table, t s nferred that method-3 gves least congeston cost ( Rs/hr) than other two methods. The convergence characterstcs of frefly algorthm s shown n Fg. 6. From ths fgure, t s revealed that GCF based FF algorthm reaches the optmal soluton n early teraton. Table 11: GSF for the outage of generator 12. Congested Lne G 1 G 2 G 3 G 4 G 5 G 6 G 7 G 8 G

10 ower Flow Tracng Based Congeston Management Usng Frefly Algorthm In... Table 12: GCF for the outage of generator 12. Congested Lne G 1 G 2 G 3 G 4 G 5 G 6 G 7 G 8 G Table 13: Comparson of congeston cost obtaned from FFA Congeston Cost Methods (Rs /hr) FF algorthm Method-1 (All) Method-2 (GSF) Method-3 (GCF) Fg. 5: Rescheduled power of partcpatng generators. Fg. 6 Convergence characterstcs of frefly algorthm 47

11 ower Flow Tracng Based Congeston Management Usng Frefly Algorthm In... V. Concluson Ths paper presents the formulaton of congeston management problem to mnmze congeston cost and s solved usng FF algorthm. The generators responsble for congeston are dentfed usng power flow tracng algorthm. artcpatng generators are found usng generator shft factor also. IEEE 30 bus and 62 bus Indan utlty systems are consdered for the purpose of llustraton. In ths paper congeston s smulated by consderng crtcal lne outage, generator outage and performng wheelng transactons. In all the cases, frefly algorthm s capable of gvng optmal soluton wth least congeston cost. To valdate the result, t s compared wth that of DE method. Comparson ensures that the proposed method s effectve for CM problem wth good convergence characterstcs. Reference [1] Ashwan kumar.; Srvastava, S.C.; Sngh, S..: Congeston management n compettve power market: A bblographcal survey. Electrc ower Syst. Res. 76(1-3), (2005) [2] Fang, R.S.; Davd, A.K.: Optmal dspatch under transmsson contracts. IEEE Trans. ower Syst. 14(2), (1999) [3] Fang, R.S.; Davd, A.K.: Transmsson congeston management n an electrcty market. IEEE Trans. ower Syst. 14(2), (1999) [4] Glatvtsch, H.; Alvarado, F.: Management of multple congested condton n unbundle operaton of power system. IEEE Trans. ower Syst. 13(3), (1998) [5] Jan, F.; Lamont, J.W.: A combned framework for servce dentfcaton and congeston management. IEEE Trans. ower Syst. 16(1), (2001) [6] Ashwan Kumar.; Srvastava, S.C.; Sngh, S..: A zonal congeston management usng ac transmsson congeston dstrbuton factors. Electrc ower Syst. Res. 72(1), (2004) [7] Ashwan Kumar.; Srvastava, S.C.; Sngh, S..: A zonal congeston management approach usng real and reactve power reschedulng. IEEE Trans. ower Syst. 19(1), (2004) [8] aresh Acharya.; Mtulananthan,.: Locatng seres FACTS devces for congeston management n deregulated electrcty markets. Electrc ower Syst. Res. 77(3-4), (2007) [9] Kumar, A.; Mttapall, R.K.: Congeston management wth generc load model n hybrd electrcty markets wth FACTS devces. Int. J. Electrcal ower Energy Syst. 57, (2014) [10] Esmal, M.; Shayanfar, H.A.; Moslem, R.: Locatng seres FACTS devces for mult-obectve congeston management mprovng voltage and transent stablty. Eur. J. Oper. Res. 236(2), (2014) [11] Kumar, A.; Sekhar, C.: Comparson of Sen Transformer and UFC for congeston management n hybrd electrcty markets. Int. J. Electrcal ower Energy Syst. 47, (2013) [12] Yesuratnam, G.; Thukaram, D.: Congeston management n open access based on relatve electrcal dstances usng voltage stablty crtera. Electrc ower Syst. Res. 77(12), (2007) [13] Sudpta Dutta.; Sngh, S..: Optmal reschedulng of generators for congeston management based on partcle swarm optmzaton. IEEE Trans. ower Syst. 23(4), (2008) [14] Balek, J.: Tracng the flow of electrcty. IEE roc-gener. Transm. Dstrb. 143(4), (1996) [15] Raathy, R.; Harsh kumar.: ower flow tracng based congeston management usng dfferental evoluton n deregulated electrcty market. Int. J. Electrcal Eng. Informatcs. 4(2), (2012) [16] Yang, X.S.; He, X.: Frefly algorthm: recent advances and applcatons. Internatonal Journal of Swarm Intellgence. 1(1), (2013) [17] Yang, X.S.: Frefly algorthm, stochastc test functons and desgn optmzaton. Int. J. of Bo-Inspred Comput. 2(2), (2010) [18] Fster, I.; Yang, X.S.; Brest, V.: A comprehensve revew of frefly algorthms, Swarm Evol. Comput. 13, (2013) [19] Coneo, J.; Mlano, A.; Bertrand, R.G.: Congeston management ensurng voltage stablty. IEEE Trans. ower Syst. 21(1), (2006) [20] Gnanadass, R.; arayana rasad adhy.; Manvannan, K.: Assessment of avalable transfer capablty for practcal power systems wth combned economc emsson dspatch. Electrc ower Syst. Res. 69(2), (2004) 48