Predicting Power Grid Component Outage In Response to Extreme Events. S. BAHRAMIRAD ComEd USA

Transcription

1 1, rue d Artos, F PARIS CIGRE US Natonal Cottee http : // 016 Grd of the Future Syposu Predctng Power Grd Coponent Outage In Response to Extree Events R. ESKANDARPOUR, A. KHODAEI Unversty of Denver USA S. BAHRAMIRAD CoEd USA M. BOLLEN Luleå Unv of Technology Sweden SUMMARY An accurate forecast of the power syste coponent outages durng extree events s an essental task to prove pre-event syste preparedness and post-event syste recovery and accordngly nze the undesred afterath of these events. A achne learnng ethod, based on Support Vector Machnes (SVM), s proposed n ths paper as a vable approach to forecast the coponents whch can potentally fal durng an antcpated extree event. In partcular, a cubc kernel SVM s proposed to classfy between operatonal and daaged coponents after the extree event based on the event characterstcs. The extree event can be of the nature of a weather event or a natural dsaster, where n ether case the proposed approach s capable of developng sutable predcton odels. The proposed ethod can be traned on hstorcal data of the past extree events. The perforance of the proposed ethod n effectvely predctng potental coponent outages s valdated usng two defned etrcs, naely precson and recall. Nuercal studes ndcate that the proposed ethod can be used to effectvely predct the outages. KEYWORDS Power syste reslence, extree event, achne learnng. Rozhn.Eskandarpour@du.edu

2 1. INTRODUCTION Extree events, such as hurrcanes, snowstors, floods, earthquakes, etc., cause outages n crtcal lfelne systes and result n nconvenence for resdents lvng n dsaster areas [1]. The electrcty nfrastructure, as a crtcal lfelne syste, whch s spread over wde geographcal areas to transfer bulk power fro centralzed power plants to dstrbuted load centres, s not an excepton to ths pact. Consderng the large pacts of extree events on electrc power systes, ncludng local and natonal losses n range of bllons of dollars every year [], a vable predcton, response, and recovery s of sgnfcant portance. In other words, the power syste needs to becoe ore reslent n response to these events. The concept of reslence n power systes, ntally ntroduced n [3], deternes the resstance of the power grd and ts ablty to wthstand extree changes. Power syste reslence has turned nto a progressvely essental affar as the frequency and the ntensty of extree whether events have sgnfcantly grown n recent years. The consderable consequences of extree events on the electrcty nfrastructure, whch s spread over a broad geographcal area and hence vulnerable to be largely pacted, shows the value and portance of an effcent forecastng of the potental daages to power syste coponents whch would accordngly enable effcent response and recovery schees. Tradtonally, the power syste coponent outages were predcted holstcally (.e. at the syste level but not at the coponent level) or were estated usng probablstc approaches followng a predefned probablty dstrbuton functon [4, 5]. These ethods suffer fro several drawbacks, n whch the holstc ethods are not useful n anagng the grd coponents and the probablstc ethods ay not be accurate and could further vary for dfferent regons and events. Machne learnng approaches, on the other hand, have shown a great perforance on learnng fro and akng predctons on exstng data. These approaches buld a odel fro an exaple tranng set of observatons wthout explctly defnng the probablstc odel, and predct data-drven decsons as outputs. One of the challenges n achne learnng approaches s to have adequate nuber of saples for tranng to extract necessary features to tran the odel. As for extree events, these data can be easly derved fro past events. In ths paper, a achne learnng ethod s proposed to deterne the power syste coponent outages n response to an antcpated extree event. The rest of the paper s organzed as follows: Secton presents the proble stateent and proposes the achne learnng ethod for outage predcton; Secton 3 presents sulaton results on a test syste; and Secton 4 concludes the paper.. MACHINE LEARNING METHOD FOR OUTAGE PREDICTION The state of each coponent n the power syste n the path of an upcong hurrcane can be consdered as (a) daaged, whch eans the coponent s on outage, or (b) operatonal, whch eans the coponent s n servce. The path and the ntensty of the hurrcane can be antcpated fro weather agences. In order to classfy the daage state of the power syste coponents, dfferent features can be extracted fro hstorcal data. In ths paper, we explore two an features of the wnd speed and the dstance of the each coponent fro the center of the hurrcane. A Support Vector Machne (SVM) [6] s used for ths purpose and to further deterne the decson boundary between the daaged and operatonal data ponts. 1

3 Gven a set of tranng exaples, an SVM classfes the nto two classes by fndng the best hyperplane that separates tranng exaples of one class fro the other class. The best hyperplane s defned as the hyperplane wth a clear gap that s as wde as possble. Fgure 1 shows the support vectors and optal hyperplane n a separable two class classfcaton of SVM. γ Margn Support Vectors Support Vectors Fgure 1. Support vectors and optal argn n SVM The data for tranng s a set of ponts x (x ϵ R D) along wth ther categores y (y = ±1), the classfcaton task can be wrtten as: h T ( x) = sgn( w x ). w, b + b (1) where w s the noral vector to the hyperplane separatng tranng exaples, b / w s the perpendcular dstance fro the hyperplane to the orgn, and sgn s the sgn functon,.e., sgn(z) = 1 f z 0, and sgn(z) = 1 otherwse. h(x) s the output of the classfer wth the a of h(x )=1 f y =+1 and h(x )= 1 otherwse. We can then defne a large functonal argn that representng a confdent predcton as: T ( w x b) γˆ = y + () We can defne geoetrc argn (shown n Fgure 1) as: ˆ γ γ = (3) w Gven a tranng set S = {(x, y); =1,,}, the geoetry argn of the decson hyperplane (w,b) wth respect to S s defned to be the sallest functonal argns of ndvdual tranng exaples, as: γ γ = n (4) = 1,...,

4 Sne we are axzng the functonal argn of the decson hyperplane (w,b), we can axze the geoetry argn (as t s scale nvarant), whle nzng w. Then, the optal hyperplane paraeters (w,b) can be found by optzaton proble: n s.t. γ, ω, b y 1 w ( ) t ( ) ( w x + b) 1, = 1,..., (5) Ths s a quadratc prograng proble, whch can be solved by a Lagrange dualty. Solvng the dualty, the fnal hyperplane only depends on the support vectors (.e., saples ponts that are n the argn) and SVM needs to fnd only the nner products between the test saples and the support vectors (of whch there s often only a sall nuber). In case that the tranng data cannot be separated by a hyperplane (whch coonly happen, especally n case of the hurrcane data), SVM can use a soft argn. Ths can be solved by a penalty paraeter c and a regularzaton (often L1 or L) as follows: n s.t. γ, ω, b 1 w + c = 1 ε ( ), ( ) t ( y w x ) + b, ε = 1,..., 1 ε 0, = 1,..., (6) In other words, tranng exaples can have a argn less than one, and f an exaple has functonal argn 1-ε (wth ε >0), the objectve functon s ncreased by cε. Fndng a proper value of c depends on the shape of classes, whch are often unknown. Therefore, c s often found by testng the perforance of the classfer on a valdaton set. The dea of axu-argn hyperplane, whch s dscussed above, s based on the assupton that tranng data are lnearly separable, whch s not the case n any practcal applcatons. In order to apply SVM to nonlnear data, kernel ethods [6] can be used. The dea of kernel ethod (kernel trck) s to ap nput features to hgher deotons that can be lnearly separable and ft the axu-argn hyperplane n the transfored feature space. Kernel trck sply states that for all x1 and x n the nput space X, a certan functon k(x1,x) can be replaced as nner product of x1 and x n another space. For exaple a polynoal kernel can be defned as: ( x x ) ( x x ) d k, =. (7) j j Tranng saples ay stll be non-lnearly separable n the transfored feature space. Therefore, ultple SVM are traned wth varous knds of kernels (e.g. polynoal wth dfferent degrees, Gaussan, etc.) and the best kernel s found perally fro the result on a valdaton set. The role of the penalty paraeter can be also portant n fndng the best settng for the proble. To evaluate the perforance of the classfer, usually a subset of hstorcal data s reserved as the valdaton/test set. Reportng the general accuracy of predcton cannot be suffcent as 3

5 nuber of saples ay not balance n the test set. The F 1-Score s a coon and relable easure of classfcaton perforance [7] whch wll be tested on the test hstorcal data: PR F = 1 (8) ( P + R) where P and R represent precson and recall etrcs, respectvely. Precson s defned as the nuber of correctly predcted outages dvded by the total nuber of predcted outages, and the recall s defned as the nuber of correctly predcted outages dvded by the total nuber of actual outages. Precson can be seen as a easure of a classfer exactness and recall can be thought of as a classfers copleteness. A hgher value of the F 1-Score, whch s a nuber between 0 and 1, ndcates a better forecastng and justfes the vable perforance of the exstng decson boundary. 3. CASE STUDY As hstorcal data for the past extree events at coponent level are lted, we have generated 300 saples of each coponent state followng a noral dstrbuton functon wth a sall Gaussan nose so that the data can be dstngushable. The saples belong to two classes of coponents wth hgh probablty of falure and coponents that can survve the extree event. The features are noralzed to [0, 1] based on the axu consdered values of wnd speed and dstance. These saples are shown n Fgure. Fgure. Generated saples for two dfferent classes A k-fold cross valdaton (k=5) s perfored to easure the perforance of the proposed ethod, where the generated data s splt nto tranng and valdaton subsets. Durng the tranng of the syste, the SVM odel s only traned on the tranng subset and valdated on the subset that s not traned on. Dfferent kernels (lnear, polynoal Quadratc and Cubc) wth dfferent range of penalty paraeter (c=0.01, 0.1, 1, 10, 100) are traned. Aong the traned SVM, polynoal Cubc kernel wth c=1 had the best overall classfcaton accuracy on the 5 fold of valdaton set. The fnal result s the average accuracy over all k folds. The average overall classfcaton accuracy of the proposed classfcaton odel s 96.0% wth the average F 1-Score of 95.97% for predctng outage. Table 1 shows the confuson atrx of 4

6 classfyng coponents nto two classes of outage (havng hgh probablty of falure) and noral condton based on the dstance to the center of extree event and the wnd speed that they can wthstand. As observed, the proposed ethod can classfy the outage coponents fro noral condton wth hgh accuracy. The proposed odel s a general fraework that can be proved by extractng ore features (.e. dfferent types of coponents, etc.) and can be easly adopted to hstorcal data f the coponent-level outage data are avalable. Table 1. Confuson Matrx of classfyng syste coponent durng extree event Actual Predcted Noral Outage Noral 96.7% 3.3% Outage 4.7 % 95.3% 4. CONCLUSION Predctng power syste outages at the coponent level s an portant factor n schedulng power syste response and recovery aganst extree events. In ths paper, a achne learnng based outage predcton odel was proposed to deterne the probable outage of power syste coponents based on hstorcal event data and specfc event characterstcs. A case study on synthetcally generated data showed that the proposed odel can effectvely predct outages whle offerng a great generalzaton capacty for new saples n the test subset. The generated data was aed to study the effect of hurrcanes on the syste, but the proposed odel s applcable to a varety of extree events, and also able to consder a wde range of other features n addton to hurrcane speed and coponent dstance. 5

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