Research Article Active Power Oscillation Property Classification of Electric Power Systems Based on SVM

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1 Journa of Appied Mathematics, Artice ID , 9 pages Research Artice Active Power Osciation Property Cassification of Eectric Power Systems Based on SVM Ju Liu, 1 Wei Yao, 1 Jinyu Wen, 1 Haibo He, 2 and Xueyang Zheng 1 1 The State Key Laboratory of Advanced Eectromagnetic Engineering and Technoogy, Huazhong University of Science and Technoogy, Wuhan , China 2 Department of Eectrica, Computer, and Biomedica Engineering, University of Rhode Isand, Kingston, RI 02881, USA Correspondence shoud be addressed to Jinyu Wen; jinyu.wen@hust.edu.cn Received 24 January 2014; Revised 21 Apri 2014; Accepted 23 Apri 2014; Pubished 6 May 2014 Academic Editor: Hongjie Jia Copyright 2014 Ju Liu et a. This is an open access artice distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the origina work is propery cited. Nowadays, ow frequency osciation has become a major probem threatening the security of arge-scae interconnected power systems. According to generation mechanism, active power osciation of eectric power systems can be cassified into two categories: free osciation and forced osciation. The former resuts from poor or negative damping ratio of power system and externa periodic disturbance may ead to the atter. Thus contro strategies to suppress the osciations are totay different. Distinction from each other of those two different kinds of power osciations becomes a precondition for suppressing the osciations with proper measures. This paper proposes a practica approach for power osciation cassification by identifying rea-time power osciation curves. Hibert transform is empoyed to obtain enveope curves of the power osciation curves. Twenty samping points of the enveope curve are seected as the feature matrices to train and test the supporting vector machine (SVM). The tests on the 16- machine 68-bus benchmark power system and a rea power system in China indicate that the proposed osciation cassification method is of high precision. 1. Introduction Damping ratio is a key factor in eectric power osciations. With the interconnection of arge-scae power grids via high votage ong distance transmission ines, couping between synchronous generators becomes weaker which eads to poor or negative damping ratio of power systems [1, 2]. Power osciation has become a major probem threatening the security of arge-scae interconnected power systems [3, 4]. In order to safey operate the power system, monitoring cassification and suppression of the eectric power osciations in power grids has captured exponentiay increasing attention in power engineering community in the past decade. Thispaperfocusesontheactivepowerosciationproperty cassification probem. According to generation mechanism, active power osciations of eectric systems can be cassified into two categories [2]. One is free osciation resuted by negative damping ratio of power systems. It coud aso be caed negative damping osciation. Wordwide accepted expanation mechanism of this kind of power osciation is basedonthecompextorqueanaysismethodproposedby DeMeo and Concordia in 1969 [5]. When the reactance of transmission system is arge or power output of generators is high, the negative damping torque produced by agging phase of quick excitation circuit counteracts the origina positive damping of generators damping windings. This wi ead to negative damping ratio of power grids and cause a power osciation with increasing ampitude [6, 7]. Reducing transmission power of tie ines or instaing PSS equipment which enhances damping torque through phase compensation has been proved to be important measure for suppressing negative damping power osciation [8, 9]. Theotherkindofactivepowerosciationisforcedpower osciation, which is expained by the resonance mechanism [10, 11]. Power resonance of generators wi be provoked when the frequency of a sma periodic disturbance occurring at the power system is equa or cose to the system s natura frequency. This kind of power osciation is characterized by fast osciation start and rapid decay after osing osciation source. Some researchers have demonstrated that periodic

2 2 Journa of Appied Mathematics disturbances of excitation circuit, turbine speed governor system, and active power oad coud stimuate forced power osciation [12 14]. Separating the periodic disturbance sources from the system is the most effective countermeasure to eiminate its infuence quicky [15]. Thus negative damping osciation and forced osciation have different generation mechanisms with different coping measures. It is extremey important and necessary to distinguish them from each other. However, both of them have simiar osciation forms with increasing ampitudes at initia stage and probaby deveop into a constant ampitude osciation in the end. Correct and rapid identification of the osciation property becomes a difficut probem to be soved. Nowadays, researches on power osciation cassification mosty concentrate on simuation after osciation accidents. System response curves of simuation under negative damping osciation condition and forced osciation condition are compared with the actua oscioscope records of power systems to judge the osciation property of power osciation accidents [16, 17]. An onine osciation property cassification method based on difference anaysis of the osciation curves is proposed in [18], but there is a certain error of the differentia cacuation. A fundamenta theory of forced power osciation in a power system has been recommended in [19], which has proved that the forced power osciation has different enveop curve from the negative damping osciation. Thus the active power osciation property coud be identified onine by distinguishing their enveop curves. Statistica earning theory and support vector machine (SVM) have given a systemic theoretica expanation about pattern recognition under circumstances of finite sampes. Many probems, ike mode-choosing, overfitting, noninear, disaster of dimensionaity, and oca minimum, which have ong hindered the deveopment of machine earning are now soved to a great extent [20, 21]. So far, SVM has successfuy been appied to many fieds ike faut diagnosis, speech recognition, image recognition and text cassification [22 24]. In [25], two types of SVM were impemented to effectivey cassify different kinds of power quaity disturbances. This paper proposes a practica approach for power osciation cassification by recognition of rea-time power osciation curves utiizing SVM. Hibert transform is empoyed to obtain enveope curves of the power osciation curves. Twenty samping points on the enveope curve of power osciation are seected for feature extraction. Then, forty power osciation curves are empoyed as sampes to train the supporting vector machine. At ast, three tests on the 16-machine 68-bus benchmark system and a rea power system in China indicate that the proposed osciation cassification method possesses good precision. The rest of this paper is organized as foows. In Section 2, a Hibert transform based osciation feature extraction scheme is proposed. Section 3 introduces a power osciation property cassification method utiizing SVM. Case study is undertaken on the 16-machine 68-bus benchmark system and a practica simpified power system of China to verify the effectiveness of the proposed osciation property cassification method in Section 4. Concusions are given in Section Feature Extraction of Power Osciations 2.1. Introduction of Power Osciations. When a free osciation happens in a power system, the rotor ange, rotation speed of synchronous generators, and reevant eectric variabes (such as the power fow of transmission ines and bus votages)wiosciateaccordingy,amongwhichthepower fow of transmission ine P ij canbeexpressedasfoows: P ij = n k i x i0 e λ it, (1) where k i denotes the participation factor of osciation pattern i; x i0 istheinitiavaueofstatevariabeaccordingtoosciation pattern i; λ i denotes the eigenvaue of the osciation pattern i. Generay λ i canbeexpressedas λ 1,2 = α ± jω. (2) In (2), α indicates the damping performance of the osciation; ω denotes the frequency characteristic of the osciation; the damping ratio of the osciation is defined as α ξ= α 2 +ω. (3) 2 The osciation curve of any free osciation mode can be expressed as P ij =B 1 e αt sin (ωt + φ 1 ). (4) Therefore, when any osciation mode with ξ < 0 (i.e., α > 0) exists in the power system, any sma disturbance woudstimuatethismodeandresutinapowerosciationof the tie ine with increasing ampitude as shown in Figure 1(a). That is the so-caed negative damping osciation. If a the damping ratios of osciation patterns are arger than zero, the sma disturbance occurring at the power system woud be restrained by the positive damping. For any forced osciation in the power system with an extreme disturbance ike h sin(ω d t), it can be expressed as a second-order system: x+2ξω x+ω 2 x=hsin (ω d t). (5) Soving (5), the osciation curve of forced osciation is P ij =B 1 e αt sin (ωt + φ 1 ) +B 2 sin (ω d t+φ 2 ). (6) Under the circumstance of ξ>0(i.e., α<0), the free osciation part B 1 e αt sin(ωt + φ 1 ) in (6)widecay.Butpower resonance woud be motivated and arge osciation woud foow as shown in Figure 1(b) if the osciation frequency ω d of the extreme disturbance is equa or cose to the system s natura frequency ω. From the anaysis above, it can be concuded that the enveope curve of negative damping osciation increases as B 1 e αt. The enveope curve of forced osciation wi increase at theinitiastage.thenittransitstoanosciationas(h/2(ω ω d )ω)e αt sin((ω ω d )t+φ 2 )+B 2 at the transitory stage. At ast it widiedowntoaconstantasb 2 at stabe stage [19]. Thus there is obvious distinction between the enveope curves of the two kinds of power osciations.

3 Journa of Appied Mathematics 3 Active power (MW) 800 Enveope curve Time (s) (a) Negative damping osciation Active power (MW) Time (s) (b) Forced osciation Enveope curve Figure 1: Power osciation curve of tie ine Hibert Transform. Hibert transform (HT) [26] offers an effective approach to extract enveope curves as osciation features for different kinds of power osciations. For the foowing power osciation signa in a power grid: u (t) =A(t) cos φ (t). (7) HT coud be appied to acquire its compex conjugate signa V (t) =H[u (t)] = 1 + π u (τ) dτ. (8) t τ V(t) is a sinusoida signa simiar to u(t). Itcoudbe expressed as V(t) = A(t) sin φ(t). u(t) and V(t) constitute a HT pair which makes up the foowing HT anaytic signa: Namey, w (t) =A(t) cos φ (t) +ja(t) sin φ (t). (9) w (t) =A(t) e jφ(t), A (t) = u 2 (t) + V 2 (t). (10) Therefore, the ampitude A(t) of HT anaytic signa refects goba change trend of the signa. A(t) represents the enveope of the osciation signa and coud be cacuated by using (8) when the anaytic signa is a signa with intrinsic osciation mode Feature Extraction. The enveope curve of power osciation wi be obtained by HT after the power osciation in power grid is detected by the wide area measurement system (WAMS). Then the enveope curve is normaized according to the steady vaue before osciation happens. Finay, twenty eveny spaced points on the enveope curve are seected in every 2T interva (T is osciation period of the power osciation) to constitute a group of feature matrices as shown in Figure 2. It is we known that the power osciation in a power system generay combines various swing modes. If there is ony one dominant osciation mode, the osciation ampitude of other osciation modes is sma compared with the dominant osciation mode. The infuence of other osciation modes on dominant osciation mode can be negected. If there are two or more than two dominant osciation modes, the dominant Active power (pu) Time (s) Figure 2: Extraction of the eements in the feature matrices. osciationmodewithpositivedampingratiowidecayafter seconds or minutes. Then ony the osciation mode with negative damping ratio retains. Meanwhie, the data used for power osciation feature extraction contains 40 cyces of the osciation curve. After severa cyces, ony the osciation mode with negative damping ratio wi retain and be used for the osciation property cassification. However, the power osciation with two negative damping osciation modes has simiar expression with forced power osciation. The beat-frequency osciation wi aso be perceivedinthepowerosciationwithtwonegativedamping osciationmodes.itishardtodistinguishtheforcedpower osciation and the power osciation with two negative damping osciation modes. However, the power osciation with two negative damping osciation modes is very unusua in power system; thus the negative damping power osciation in this paper is the power osciation with ony one negative damping osciation mode. Under this premise, the feature matrices can represent the power osciation property of the system. Difference of adjacent points of the feature matrices denotesthechangedirectionoftheenveopecurveandthe second-order difference denotes its change tendency. As for negative damping osciation, the variation rate of the enveope curves is generay positive with osciation ampitude growing more and more rapidy. This means that the firstorder and second-order difference of adjacent points from the feature matrices shoud aso be positive. However, for forced osciations, the enveope curve has minimum and maximum points. This indicates that the first-order or second-order difference of adjacent points coud be zero or negative.

4 4 Journa of Appied Mathematics Optima hyperpane Positive Negative Optima margin Figure 3: A cassification exampe in a two-dimensiona space based on SVM [27, 28]. Therefore, the feature matrices obtained in this paper at east contain the osciation characteristic of the power osciation which coud be utiized for power osciation property cassification. Besides, the feature matrices extraction of power osciation curves wi be the foundation of the foowing work. 3. Osciation Property Cassification Based on SVM 3.1. Basic Theory of SVM. SVM-based cassification method is estabished on the basis of structura risk minimization principe and VC theory (Vapnik and Chervonenkis theory) [27]. In order to obtain exceent capabiity of generaization according to a certain amount of sampes, the SVM-based cassification method seeks the best compromise between the compicationofthemodeanditsearningcapacity.theprincipe idea of SVM is as foows: it firsty maps the input vectors in sampe space into some high or even infinite dimensiona feature space through some noninear mapping function φ(x). And then the noninear and noncassifiabe probem in the origina sampe space is transformed into a inear and cassifiabe probem in the high dimensiona feature space. At ast, in this feature space, a inear decision surface is constructed with specia properties that possess the argest separation margin between the two casses just as shown in Figure 3. For the given inear and separabe training patterns {(x i,d i )}, x i R n, d i {1, 1}, x i denotes the ndimensiona input vector and d i denotes the cass of the sampe. For further expanation, 1 denotes the positive cass and 1 denotes the negative cass. These two sets are ineary separabe on the condition that there are a vector ω and scaar b which satisfy ω x i +b 1, if x i positive sampe set, namey y i =1, ω x i +b 1, if x i negative sampe set, namey y i = 1. (11) If the vector ω has the minimum norm, then the hyperpane y=ω x+bseparates the training data with a maxima margin. It is the unique and optima hyper pane for cassification of the train data. If the training data in the input space is noninear, in order to construct a hyper pane to cassify the noninear sampes, one first has to map the input vector x into a higher dimension feature space by function φ(x) andthentakesthesignofthe function y=ω φ(x) +b. (12) Considerthecasewhenthetrainingdatacannotbecassified without error. Penaty constant C and some nonnegative variabes ξ i are introduced to punish the incorrect cassification. Then this idea can be expressed formay as an optimization probem as foows: min s.t. ξ i 1 2 ω 2 +C d i [ω φ (x i )+b]+ξ i 1 ξ i 0. The Lagrange function for this probem is L (ω, b, ξ, Λ, R) = 1 2 ω 2 +C ξ i r i ξ i, α i (d i [ω φ (x i )+b]+ξ i 1) (13) (14) where the nonnegative mutipiers Λ T =(α 1,α 2,...,α ) and R T =(r 1,r 2,...,r ) arise from the constraint in (13). Using the conditions for the minimum of this function at the extreme point L =ω 0 α i d i φ(x i )=0, (15) ω ω=ω 0 L = b b=b 0 α i d i =0, L ξ i ξi =ξ i0 =C α i r i =0. From (15), ω 0 canbeobtainedas ω 0 = (16) α i d i φ(x i ). (17) Thus the decision function in (12) is transformed into the foowing form: y= d i α i K(x,x i )+b. (18)

5 Journa of Appied Mathematics 5 Substituting the expressions for ω 0, b 0,andξ i0 to the Lagrange function (13), F (Λ) = i α 1 α 2 i α j d i d j K(x i,x j ). (19) j=1 The origina convex optimization probem is aso transformed into a quadratic optimization probem: min Λ F (Λ) = s.t. α i d i =0, 0 α i C. i α 1 α 2 i α j d i d j K(x i,x j ) j=1 (20) Under this circumstance, the optima Lagrange s mutipicator α 0 i can be obtained by using the Kuhn-Tucker condition in quadratic programming probem. As for the optima hyperpane agorithm, the vector ω can be written as a combination of the training data ω 0 = d i α 0 i φt (x i ). (21) According to (21) and(18), the cassification function of the training data can be obtained as y=sgn [ d i α 0 i φt (x i )φ(x) +b]. (22) From (12) (22), ξ i denotes the sack variabe and K(x i,x j ) is the kerne function. K(x i,x j ) is the convoution of dot product by φ(x i ) and φ(x j ) in the feature space: K(x i,x j )=φ T (x i )φ(x j ). (23) The input parameters of the kerne function are the training data x i of power system, and the kerne function for the SVM is independent of the power system. Any function that satisfies Mercer s condition can be used as kerne function [27]. By empoying different kinds of kerne functions, different earning machines with arbitrary types of decision surface can be constructed. The most commony used three kerne function wi be empoyed in this paper [28]: inear function: sigmoid function: K(x i,x j )=(x i x j +1) d, (24) K(x i,x j )=tanh (x i x j θ), (25) radia basis function: K(x i,x j )=exp ( x 2 i x j 2σ 2 ). (26) Start Input historica data and osciation future extraction Parameter initiaization for the SVM mode Obtain the optima parameter of the SVM mode Osciation incidence detection Cassify the osciation properties of the power osciation curves Property cassification of the osciation incident End Yes Figure 4: Fow chart of the osciation property cassification Procedures of the Osciation Property Cassification. When power osciation happens, active power osciations at substation, tie ine, and generator termina wi be detected by WAMS. The osciation property can be we cassified by training historica data with SVM agorithm. Figure 4 gives the fow chart of the osciation property cassification. The foowing procedures wi be empoyed. (1) Input historica data and osciation future extraction. Coect the power osciation data of the power osciation incidence that has happened. And then extract the osciation feature of the power osciation data by the proposed method in Section 2 as the training data for the SVM. (2) Parameter initiaization for the SVM mode: Lagrange mutipier α and threshod b are assigned with random number. (3) Obtain the optima parameter of the SVM mode. Based on training sampes, the objective function of (20) is estabished and the optima probem is soved using Kuhn-Tucker condition to obtain the optima α and b. (4) Power osciation incidence detection: judge whether the power osciation ampitude of the fifth cyce is arger than 50 MW or not for any 500 kv tie ine and recordtheosciationcurvefortheosciationproperty cassification. (5) Cassify the osciation properties of the power osciation curves. Cassify the property of the power osciation curves recorded by the WAMS from different No

6 6 Journa of Appied Mathematics G 15 G 14 G G 8 G G G G G G G G 3 G G 7 12 G 2 G Figure 5: Simuation exampe of IEEE16-machine 68-bus benchmark system buses at the power grid using the trained SVM mode in procedure (3). As for the recognized resut of the osciation curves, 1 represents the negative damping osciationand 1 represents the forced osciation. (6) Property cassification of the osciation incident: if the quantity of 1 is much more than 1, the osciation incident is negative damping osciation. Ese if the quantity of 1 is much more than 1,the osciation incident is forced osciation. 4. Simuation Verification 4.1. Tests on 16-Machine 68-Bus System. The circuit diagram of IEEE16-machine 68-bus benchmark system is shown in Figure 5. Some forced osciating sources with osciation frequency cose to the natura osciation frequency of the generators are appied at different nodes in the power grid and ninety-six sampes of power osciation curves are obtained. Then sixty-four power osciation curves under the negativedampingconditionareobtainedbyoweringthegain of power system stabiizer (PSS). Twenty forced power osciation curves (represented by C1) and negative damping power osciation curves (represented by C2), respectivey, are seected for training and the remaining 120 osciation curves areusedfortesting.tabe 1 gives the simuation resut for the osciation property cassification based on the proposed method. A 2 2confusion matrix is constructed to show the cassification performance for each case. The diagona eements represent the correcty cassified power osciation types. The off-diagona eements represent the miscassifications. As we can see from Tabe 1, different kerne function for SVM mode wi bring different cassification precision for power osciation curves. When sigmoid function is seected as kerne function, the mode has highest accuracy. Therefore, thispaperadoptsthisfunctionaskernefunctionforsvm mode. Since noise is omnipresent in eectrica power system, Gaussian white noise is considered in the cassification of power osciations. Different eves of noises with the noise to signa ratio vaues ranging from 5% to 10% were considered. As the noise to signa ratio increases, the adaptabiity of SVM mode decreases and the precision of the power osciation property cassification degrades. Tabe 1 shows that the precision of the power osciation property cassifycation is sti above 88% even with the noise to signa ratio rising up to 10%. Thus the SVM-based proposed method can effectivey cassify different kinds of the power osciation. 4.2.AnaysisofForcedPowerOsciationinaReaIncident. In 2008, a therma power pant was asynchronousy connected to the Centra China Power Grid through 110 kv transmission ines.powerosciationswereobservedinhenan,hunan,and Jiangxi power grids. The whoe osciation duration was about two minutes with 0.7 Hz osciation frequency at initia stage andthentheosciatorypowerofthetieineincreased graduay. When the osciation stabiized, the osciatory frequency of the power grid was 0.62 Hz and the osciatory ampitude of the active power of tie ine between Henan and Hubei was about 250 MW. Subsequenty, the 110 kv transmission ine in the faut region was cut off and the osciation died down quicky. This power osciation incident was cassified as a typica forced power osciation incident and the therma power pant was the osciation source [29]. The active power oscioscope record of Yao-Shao tie ine is given in Figure 6. Eeven additiona active power oscioscope records of different tie ines are seected for the osciation property cassification. The support vector machine trained at Section 4.1 is empoyed to identify the osciation property of the eeven active power oscioscope records and the resut is shown in Tabe 2. It can be seen that ony one power osciation curve is misidentified as negative damping osciation and the other ten osciation curves are a identified as forced osciation.

7 Journa of Appied Mathematics 7 Tabe 1: Testing resut of 16-machine 68-bus benchmark system. Kerne function Poynomia kerne function RBF kerne function Sigmoid kerne function Signa type No noise 5% noise 10% noise C1 C2 C1 C2 C1 C2 C C C C C C Precision 95.80% Precision 92.50% Precision 88.30% C1 C2 C1 C2 C1 C2 C C C C C C Precision 96.70% Precision 94.20% Precision 88.30% C1 C2 C1 C2 C1 C2 C C C C C C Precision 98.30% Precision 95.80% Precision 90.80% Osciation type Tabe 2: Identification resut of oscioscope records of forced osciation incidence. C1 (forced osciation) C2 (negative damping osciation) Identification resut Number 10 1 C1 Considering identification error, forced osciation is chosen as the fina identification resut, which is consistent with the anaytica resut of the incident [29] Anaysis of Negative Damping Osciation in a Rea Incident. In 2005, a wide area power osciation took pace in CentraChinaPowerGridandthewhoeosciationastedfor about five minutes. The power osciation frequency was about 0.77 Hz. Large power fuctuations were detected at the Three Gorges Hydroeectric Power Pant and its nearby power pants in Doui, Jiangin, Longquan, and Wanxian. Then theoperatorofthepowergridincreasedtheoutputreactive power of the Three Gorges Hydroeectric Power Pant and decreased the active power output of Huangongtan Power Pant in northwest Hubei. Subsequenty, the osciation decayed graduay unti it died out. The incident was a typica negative damping power osciation [18]. Figure 7 shows the active power oscioscope record of the second Long-Dou tie ine during the power osciation. Twenty active power oscioscope records of different tie ines at the power grid areseectedtoidentifytheosciationpropertybythesvm trained in Section 4.1. The identification resut is shown in Tabe 3. Taking identification error into consideration, the resut in Tabe 3 indicates that the osciation incident beongs to negative damping osciation, which is aso consistent with the anaysis resut [18]. 5. Concusions Active power osciation in power systems can be cassified into two types: negative damping osciation and forced osciation. Athough their osciation curves are simiar, the adopted suppressing contro strategies are totay different. Active power (MW) :55:20 17:55:40 17:56:00 17:56:20 17:56:40 17:57:00 Time (hh:mm:ss) Figure 6: The active power oscioscope record of Yao-Shao tie ine. Active power (MW) :10 21:20 23:00 23:50 24:40 25:30 26:20 Time (mm:ss) Figure 7: The active power oscioscope record of the second Long- Dou tie ine. Thus the osciation property cassification is the premise for suppressing the power osciation. To propery identify the osciation property, the paper proposed an osciation property cassification method utiizing the SVM. Through the simuation anaysis, it can be concuded that the enveope curves of the negative damping osciation and forced osciation are different and can be used as the feature for cassification. As noise is omnipresent in eectrica power system,

8 8 Journa of Appied Mathematics Osciation type Tabe 3: Identification resut of oscioscope records of negative damping osciation incidence. C1 (forced osciation) C2 (negative damping osciation) Identification resut Number 2 18 C2 Gaussian white noise is considered in the research of power osciation cassification. With the increase of the noise to signa ratio, the adaptabiity of SVM mode decreases and the precision of the power osciation property cassification degrades. However, even with the noise to signa ratio reaching up 10%, the precision of the power osciation property cassification is sti above 88%. Moreover, two rea incidents in the rea power systems are used to verify the proposed cassification method. Resuts show that the identified resuts from the proposed method is the same with the postincident anaytica identification resut, whie the postanaytica identification is an offine time consuming method ony appied after the osciation happens. The proposed method can be appied onine and provides guidance for the dispatcher to seect the correct suppressing contro (the negative damping one or the forced osciating one) during the osciation period to stop the propagation of osciations. Confict of Interests The authors decare that there is no confict of interests regarding the pubication of this paper. Acknowedgment This work was supported by the Nationa Natura Science Foundation of China (nos and ). References [1] R. Thirumaaivasan, M. Janaki, and N. Prabhu, Investigation of SSR characteristics of hybrid series compensated power system with SSSC, Advances in Power Eectronics, vo. 2011, Artice ID , 8 pages, [2] L. Chen, Y. Min, and W. Hu, An energy-based method for ocation of power system osciation source, IEEE Transactions on Power Systems,vo.28,no.2,pp ,2013. [3] A. N. Hussain, F. Maek, M. A. Rashid, L. Mohamed, and N. A. M. 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