Transient Stability Assessment of Power System Based on Support Vector Machine

Transcription

1 ransent Stablty Assessment of Power System Based on Support Vector Machne Shengyong Ye Yongkang Zheng Qngquan Qan School of Electrcal Engneerng, Southwest Jaotong Unversty, Chengdu , P. R. Chna Abstract Machne learnng methods are promsng tools for transent stablty assessment (SA) of power system. Support vector machne (SVM) s used to assess the transent stablty of power system after faults occur on transmsson lnes. Sngle machne attrbutes s studed as nputs of the SVM classfer. Expermental results n IEEE 50-generator test system shows that, attrbutes of sngle machne wth small nerta coeffcent are effectve n SA, and the SVM classfer wth RBF kernel usng these sngle machne attrbutes can acheve satsfyng classfcaton accuracy. Keywords: ransent stablty assessment, Support vector machnes, Sngle machne attrbutes 1. Introducton Electrc power systems are large-scale non-lnear systems where there are many knds of stablty problems. One of them s transent stablty, whch s defned as the ablty of a power system to mantan synchronsm after severe dsturbances. he purpose of transent stablty assessment (SA) s to determne f the contngency may cause power system nto angle nstablty, that s, to predct whether the power system could mantan synchronous operaton of generators when subjected to large dsturbances such as faults, load loss, capacty loss, etc. One of conventonal methods used for SA s the tme-doman numercal smulaton. hs method conssts of smulatng durng and post-fault behavors of the system for a gven dsturbance, observng ts electromechancal angular swngs durng a few seconds. It s usually used to estmate stablty status and to provde detaled operaton nformaton of the faulted systems as a benchmark. However, the smulaton method s nfeasble for on-lne SA manly due to ts tme-consumng computaton. Drect method s another conventonal approach used n SA, whch replaces the numercal ntegraton of the post-fault system equatons by a stablty crteron [1]. Although t s attractve for SA, t has always gven conservatve results snce ts defcency. Due to the lmtatons of tme-doman and drect methods, there have been great nterests n applyng machne learnng methods, whch are promsng for on-lne applcaton. [2] summarzed experences n applyng artfcal neural network (ANN) to SA. ANN requres long-tme tranng process and the selecton of the number of neurons n hdden layer s usually determned by a tral. Decson tree has been studed to be used n SA [3], [4]. hese methods provde mappng between the system varables and status wth the ad of tme-doman smulatons. Wth support vector machne (SVM) ntroduced by Vapnk and hs co-worker [5], many SA applcatons based on SVM have come forth [7], [8]. [7] dscussed the SVC wth polynomal kernel usng 224 nput varables. A ν -SVM wth thrteen features s appled n SA [8]. A SVM usng sngle machne attrbutes s proposed n ths paper. Case study usng IEEE 50- generator test system was presented to llustrate the proposed method. he paper s organzed as follows. Secton 2 provdes a smple revew of SA and a set of sngle machne attrbutes. We demonstrate the technques n Secton 3. In Secton 4 we present an expermental comparson among ANN, Decson tree and SVM, snce the frst two are always used n SA [9]. In Secton 5 we dscuss the results. Fnally, the concluson of our research s n Secton Sngle machne attrbutes As a benchmark of SA, tme-doman smulaton s gven as follows. For a gven dsturbance, the smulaton program alternately solves the nonlnear equatons representng the dynamcs of generators, and algebrac power-flow equatons representng the network. For llustraton, consder a mult-machne system. he moton of the th generator s descrbed as follows:

2 dδ = ω ωn, dt (1) dω M = Pm Pe, = 1,2,..., n. dt where δ = rotor angle of the th generator; ω = the speed of the th generator; ω n = the synchronous speed of the th generator; M = nerta coeffcent of the th generator; P m = mechancal power nput of the th generator P e = electrc power output of the th generator. For example, n IEEE 50-generator system, after a few seconds smulaton, power angles vs. tme are shown as Fg.1 (stable) and Fg.2 (unstable) for two dfferent dsturbances. Fg. 1: me-doman smulaton results for stable state. Fg. 2: me-doman smulaton results for unstable state. It s dffcult to decde attrbutes as nputs of the machne learnng. Generally, the post-fault varables of generator rotors are frst choces for SA. Inputs comprsng varables of all the generators make large nput dmenson because power systems are very large. Some researchers propose attrbutes ndependent of the sze of power system[10]. In ths paper, we try to use sngle machne attrbutes as nputs. Seven varables of a generator are chosen, such as machne angle, machne speed, machne termnal voltage, electrcal actve output power, electrcal reactve output power, the dervatves of machne angle and speed to tme. wenty-eght attrbutes, whch were the above varables n four dfferent moments, composed the nput space. One moment was durng the fault, others were after the fault. 3. Support vector machne classfer 3.1. Introducton to SVM SVM s based on theoretcal results from the statstcal learnng theory. It s a new and promsng technque for data classfcaton and regresson. In ths secton, we brefly ntroduce support vector machne classfer whch can be used for SA. Gven tranng data set ( x, y ), = 1,..., l where n x R and y { 1,1}, the am of SVM classfer s to separate two knds of data n hgh feature space by constructng an optmal hyperplane. SVM classfer solves followng prme problem: w, b, ξ mn l 1 w w + C ξ 2 = 1 (1) st.. y ( w φ( x ) + b) 1 ξ ξ 0, = 1,..., l. where w s weght vector of the hyperplane, C > 0 s penalty parameter proportonal to the amount of constrant volaton, ξ s slack varable, φ() s a mappng from nput space to feature space, and b s threshold. he dual of (2) s 1 mn α Q α e α α 2 st.. y α = 0 0 α C, = 1,..., l where α s a vector of l varables, e s the vector of all ones. he most frequently used kernel functons are as follows. Lnear kernel: K ( x, x ) = x x. j j Polynomal kernel: K( x, x ) = ( γ x x + r), γ > 0. j j

3 Radal bass functon kernel: 2 K( x, x ) = exp( γ x x ), γ > 0. j j Here, γ and r are kernel parameters Model selecton n SVM classfer Upon the data set prepared usng tme-doman smulaton, SVM classfer model was bult for SA. When tranng an SVM classfer model, there are some parameters to tune. hey would nfluence the performance of the SVM classfer model. kernel parameters and cost of error C should be decded before SVM classfer tranng. he process to search optmal values of these parameters s model selecton. In our experments, we consdered the radal bass functon (RBF) kernel. Note that γ s a tunable parameter assocated wth the RBF functon. hus, γ and C are two parameters needed searched n model selecton process[11]. o do ths, we dvded the tranng data nto two sets. One of them was used to tran a model whle the other, called the valdaton set, was used to evaluate the model. We used grd search technque to fnd the optmal values. he search result s shown n Fg.3. as 0.25, and the mnmum number of nstances per leaf was two. 4. Case study 4.1. est system IEEE 50-generator test system [13] was used to test the valdty of the proposed method, wth some generator was modfed. here are seven generators (Generator 1 to 6, 23) based on model ncludng subtransent effect and 43 generators based on classcal model. A large amount of transent stablty smulatons were carred out to obtan tranng and test sets. hree-phase short-crcut faults were created at nstance 0.1s and cleared at 0.2s and 0.25s. Under 90%, 100%, 110% and 120% of the basc load condtons, there were 1812 examples created for every generator. he attrbute vectors were acqured from those examples. hese vectors were characterzed as stable and unstable Result o every generator, 1196 examples were assgned as tranng set, and 616 ones comprsed test set. Usng grd search technque, the kernel parameter γ and the tradeoff parameter C of every classfers were optmzed by grd search. he correct classfcaton rate usng every generator attrbutes s shown n Fg.4, where H s nerta coeffcent of generator. he range of H s from to 2210 s. Fg. 3: Grd search for proper parameters. We bult the SVM classfer model usng the proper C and γ. SMO was used to tran the SVC model. When the tranng process fnshed, the SVM classfer s performance was assessed by test set. For comparson[12], two classfers based on ANN and Decson tree were traned usng the same tranng set. he ANN used n ths study s the MLP type. It conssted of three layers. he learnng rule was Momentum, whch provded the gradent wth some nerta, whle the amount of nerta was dctated by the momentum parameter. Decson tree was generated by C4.5. he confdence factor used for prunng was set Fg. 4: Correct classfcaton rates of classfers usng sngle generator attrbutes as nputs.

4 As to the seven generators, the performances of ther attrbutes as SVM classfer nputs are shown n able 1. Generator number Inerta coeffcent (s) (C, γ ) Correct rate (%) (131072, 8) (256, 16) (131072, 1) (512, 2) (32768, 2) (256, 16) (8192, 32) able 1: Performances of seven generators attrbutes as SVM classfer nputs. For comparson wth tradtonal classfers, we chose Generator 1 s attrbutes as nputs. After tranng, models of three classfcatons were checked n test set. he performances are shown n able 2. All the computatons presented n ths paper were performed on Intel Celeron, 1.50 GHz, PC. Machne learnng classfers ranng tme (s) Correct rate (%) Kappa statstc MLP ree RBF-SVM able 2: Performances of three classfers on test set. 5. Dscusson In the transent stablty assessment usng machne learnng method, the key step s the selecton of system varables. In power system smulaton, generators wth detaled model provde suffcent nformaton n power system stablty and control. We chose sngle machne varables as nputs rather than all machnes or abstract attrbutes. he sngle machne attrbutes we proposed can effectvely predct the system state n transent stablty assessment. he attrbutes of generators wth smaller nerta coeffcent can gve satsfyng results. As shown n Fg.4, correct classfcaton rates decrease wth nerta coeffcent ncreasng. Model selecton s another key problem n SVM. Kernel parameters and C should be proper. Otherwse, the classfer showed poor performance. We used smple grd search to fnd optmal parameters. he reason s that exhaustve parameter search could fnd optmal values. In our experment, we used other search technques, but the result was unsatsfyng. here are some suggestons for mprovement n our study. he frst s usng proper feature selecton to ncrease the correct classfcaton rate and computng speed. Another s usng other kernel functon to mprove the performance of SVM classfer. 6. Conclusons We have presented sngle machne attrbutes as nputs of SVM classfer n assessng transent stablty of power system. Extensve testng was performed on the IEEE 50-generator test system under varous loadng condtons. he attrbutes of machnes wth smaller nerta coeffcents showed better performance. Based on the theory of statstcal learnng, SVM classfer shows better performance than tradtonal methods n SA. References [1] M. Pavella, D. Ernst, D. Ruz-Vega, ransent stablty of power systems: a unfed approach to assessment and control. Boston: Kluwer cademc Publshers, [2] Y. Mansour, E. Vaahed, M. A. El-Sharkaw, Dynamc securty contngency screenng and rankng usng neural networks. Neural Networks, IEEE ransactons on, 8: , [3] S. Rovnyak, S. Kretsnger, J. horp, D. Brown, Decson trees for real-tme transent stablty predcton. Power Systems, IEEE ransactons on, 9: , [4] L. Wehenkel, M. Pavella, E. Euxbe and B. Helbronn, Decson tree based transent stablty method a case study. Power Systems, IEEE ransactons on, 9: , [5] C. Cortes, V. Vapnk, Support-vector networks. Machne Learnng, 20: , [6] C. Bo-Juen, C. Mng-We, J. Chh, Load forecastng usng support vector Machnes: a study on EUNIE competton Power Systems, IEEE ransactons on, 19: , [7] L. S. Mouln, S. A. da, M. A. El-Sharkaw and R. J. Marks, Support vector machnes for transent stablty analyss of large-scale power systems. Power Systems, IEEE ransactons on, 19: , [8] X. Wang, S. Wu, Q. L and X. Wang, v-svm for transent stablty assessment n power systems. ISADS Proceedngs, pp , 2005.

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