Elecric Power Sysems Research 58 (2001) 27 35 www.elsevier.com/locae/epsr A new mehod for classificaion and characerizaion of volage sags Mladen Kezunovic *, Yuan Liao Deparmen of Elecrical Engineering, Texas A&M Uni ersiy, College Saion, TX 77843-3128, USA Acceped 8 March 2001 Absrac This paper presens new sofware developmens relaed o sag classificaion and characerizaion. A new fuzzy rule based algorihm for classifying he ypes of volage sags is proposed. The volage sags are caegorized ino hree ypes, i.e. sags due o he fauls, large moor saring, or due o ineracion beween moor operaion and fauls. Three disincive feaures of sag waveforms are defined and exraced firs. Then a fuzzy logic based inference engine uilizing hese feaures as inpus is implemened for decision making. Also presened are he characerizaion mehods and suggesed monioring parameers for each of he hree ypes of sags. Finally he applicaion of he proposed characerizaion approaches for he equipmen sensiiviy sudy is illusraed. The resuls of case sudies are repored. The presened approach has been implemened in MATLAB. 2001 Elsevier Science B.V. All righs reserved. Keywords: Volage sag; Fuzzy logic; Paern classificaion; Parameer esimaion; Power qualiy 1. Inroducion Among various ypes of power qualiy disurbances in a power sysem, volage sags are paricularly roublesome since hey occur raher randomly and heir characerisics are difficul o predic. More imporanly, volage sags may cause rips or mis-operaions of indusrial equipmen. The increased use of sensiive elecronic conrol circuiry has made modern equipmen far more vulnerable o volage sag evens han ever [1,2]. As known, he rip or mis-operaion of modern equipmen can no jus be aribued o he sag magniude and duraion any more. Insead, oher facors like poin-on-wave, unbalance raio, and phase angle shif may also play an essenial role in he behavior of he modern loads during volage sag evens. In order o improve he immuniy or ride-hrough abiliy of he equipmen o he sag evens and hus enhance he coordinaion beween he sysem and he equipmen, a good appreciaion of how various sag parameers affec he equipmen operaing characerisics is very helpful [2 4]. * Corresponding auhor. E-mail address: kezunov@ee.amu.edu (M. Kezunovic). Serving such purposes, IEEE P1159.2 has iniiaed a projec on he sag characerizaion based on digially sampled daa. So far, his ask force has proposed a draf on he characerizaion of sags caused by he fauls. I is known ha he sags may be caused by large moor saring as well. In addiion, he ineracion beween he moor operaion and he fauls has also a significan effec on he volage sag characerisics [5,6]. Therefore, o accuraely characerize hese differen ypes of sags, perinen parameers need o be defined for each of hese hree ypes of sags. This paper conribues o his aspec. In order o selec appropriae algorihms for characerizaion, he volage sag waveforms need o be classified firs. Manual classificaion is edious, ime consuming and someimes even difficul. Therefore, his paper proposes a new fuzzy logic based sysem for auomaic sag classificaion. In he res of he paper, he fuzzy logic based sag classifier is described firs. Then he proposed characerizaion approaches for he hree ypes of sag evens are described. Nex, he equipmen sensiiviy sudy uilizing he characerizaion resuls is illusraed. Case sudies and resuls for he characerizaion and equipmen characerisic evaluaion sudies are repored. 0378-7796/01/$ - see fron maer 2001 Elsevier Science B.V. All righs reserved. PII: S0378-7796(01)00104-3
28 M. Kezuno ic, Y. Liao / Elecric Power Sysems Research 58 (2001) 27 35 2. The proposed sag classificaion algorihm This secion presens a fuzzy rule based classificaion sysem for idenifying he ypes of he sags. I is assumed ha he inpu waveforms have already been deeced as volage sag evens by anoher general classificaion sysem [2]. The mehod presened here furher classifies he sag evens ino faul relaed sags (FRS), large moor saring relaed sags (MSRS), or moor re-acceleraion relaed sags (MRRS). The MRRS are caused by he ineracion beween he faul and large moor operaion. The proposed classificaion sysem consiss of he feaure exracion phase and he decision making phase as illusraed in Secions 2.1 and 2.2, respecively. 2.1. Feaure exracion To demonsrae how disincive feaures for each ype of volage sags can be exraced, a number of sag waveforms of various ypes have been obained using Elecromagneic Transiens Program (EMTP). Figs. 1 3 show he ypical waveforms for each of he hree ypes of sags and he relaed rms plos obained by applying he Fourier ransform. The simulaion sensiiviy sudies have shown ha each ype of he sags has disinc characerisics. For he FRS, he iniial drop and he final recovery of he sag are very quick. For he MSRS, he recovery of he sag akes a long ime, normally ranging from several hundred milliseconds o several seconds. For he MRRS, a he beginning of he faul, he large moor acs as a volage source and hus reduces he volage drop. Afer he faul is cleared, he re-acceleraion of he moor deepens he sag and hus prolongs he recovery of he volage sag [6]. In addiion, he faul relaed sags normally resul in a relaively larger phase angle shif han he non-faul relaed sags. Fig. 2. A moor saring relaed volage sag signal and is rms plo. Based on he above analysis, he following hree feaures have been exraced and will be used as inpus o he decision-making sysem. 1. Iniial phase angle shif ( pasi ): This is defined as he difference beween he phase angle of he during-sag waveform and ha of he reference waveform. The reference waveform is defined as he pre-sag normal seady sae waveform. 2. Recovery period (RP): This is defined as he duraion enailed for he volage magniude o recover o is normal value. The recovery period is expressed in cycles of he fundamenal frequency. 3. Volage change (VC): This is defined as he difference beween he volage magniude a he iniial recovery ime and he volage magniude one cycle laer. Fig. 1. A faul relaed volage sag signal and is rms plo. Fig. 3. A volage sag signal caused by he faul and moor re-acceleraion and is rms plo.
M. Kezuno ic, Y. Liao / Elecric Power Sysems Research 58 (2001) 27 35 29 These parameers are obained using he following equaions. The nomenclaure is lised a he end of he paper. pasi =180[angle(V s [1]) angle(v 1 [1])]/ (1) where, V n [k] is he Discree Fourier Transform (DFT) for he samples conained in he nh daa window defined as N 1 V n [k]= [i+(n 1)N]e j 2 ki/n, i=0 n=1,2,...,round (L/N) (2) [i ]: he sampled signal, i=0,1,...,l 1, wih L he lengh of he signal. i s =index s{abs(wc 1 [k]) }/L wc 1 L (3) V s [k]= i s +N 1 i=i s [i ]e j(2 ki/n) (4) V rms [n]= 1 N 1 N 2 [i+(n 1)N] (5) i=0 V rms is defined as an array composed of V rms [n], n=1, 2,..., L rmswih L rms=round(l/n). V min =min(v rms) (6) i min =index min(v rms) (7) d V rms is defined as an array composed of V rms [n], n=i min,...,l rms d i re =index s(v rms 1.05V min ) (8) V fin =V rms [L rms] (9) d i ec =index s(v rms 0.96V fin ) (10) Then, we obain RP=i ec i re (11) d d VC= rms [i re +1] rms [i re ] (12) WC 1 [k] is he firs scale wavele deail coefficiens, k=1, 2,..., L WC 1, wihl WC 1 he lengh of he deail coefficiens. Daubechies-4 wavele family is used in our work [2]. I is shown ha he ype of he wavele does no have a significan impac on he resuls because differen ype of waveles differs in he regulariy, symmery or compacness of suppor, ec. However, we mainly uilize he ime localizaion characerisics of he wavele for accuraely obaining he ime parameers of he evens. The wavele families of Daubechies wavele, Morle wavele, symles, coifles and biorhogonal spline waveles have been demonsraed o work similarly well for he applicaions presened here. is a pre-defined consan, seleced as 0.05 here. angle(.) gives he angle of he argumen in radians. index s(.) yields he index of he firs elemen ha is greaer han zero of he inpu array. index min(.) gives he index of he minimum value of he argumen. round(.) gives he ineger par of he argumen. min(.) gives he minimum value of he argumen. Eqs. (1), (11) and (12) give feaures for each single phase signal. If he inpu volages include hree-phase signals, hen he feaures for each phase are obained, and he larges value of he hree phases is seleced as he exraced feaure. 2.2. The proposed sag classificaion algorihm The rule ses of he fuzzy rule based sysem are presened as follows. 1. If RP is b 2 and pasi is a 1, hen MSRS=1; 2. If RP is b 2 and pasi is a 2 and VC is c 2 hen MRRS=1; 3. If RP is b 2 and pasi is a 2 and VC is c 1 hen MSRS=1; 4. If RP is b 1 hen FRS=1; In he above rules, a i, b i and c i are he membership funcions for he inpu feaures, and he following rapezoidal funcions are used o describe hem. Deailed descripion of his funcion is referred o [7]. (x)=rapmf(a, b, c, d) (x a)/(b a) a x b 1 b x c = (x d)/(c d) c x d 0 oherwise (13) The fuzzy pariions and he according membership funcions can be obained based on boh he saisical sudies and he exper s knowledge. Opinions from operaors can be convenienly incorporaed ino he sysem in pracical applicaions [7]. The membership funcions for he feaures are shown as follows. Iniial phase angle shif ( ): a 1 : rapmf( 0.18, 0.02, 4, 4.5) a 2 : rapmf(4, 4.5, 361, 362) Recovery period (cycles) b 1 : rapmf( 0.18, 0.02, 2, 4) b 2 : rapmf(1, 3, 1000, 1001) Volage change (p.u.) c 1 : rapmf( 0.18, 0.02, 0.04, 0.05) c 2 : rapmf(0.04, 0.05, 1.1, 1.2) The oupus of he classificaion sysem are he variables FRS, MSRS and MRRS whose values represen he degree o which he even belongs o each of hese caegories. The ype of he even will be seleced based on he larges membership value. In cases where wo or more ypes of sags have he same larges membership value, all of hem will be subjeced o furher analysis.
30 M. Kezuno ic, Y. Liao / Elecric Power Sysems Research 58 (2001) 27 35 2.3. E aluaion sudies A number of sag evens of he concerned ypes have been generaed by EMTP, and hen he proposed algorihm is applied for classificaion of hese evens. The correc idenificaion rae of he sysem is abou 99%. In mos of he mis-classified cases, he moor saring relaed sags are misakenly classified as faul relaed sags. This is because in hese cases he recovery ime of he moor saring may be oo shor for idenificaion. 3. The proposed approaches for characerizing sag evens Once he ype of he sag evens is idenified, hey can be furher characerized using he approaches described in his secion. In he following discussions, he volage is in p.u., ime in seconds, and angle in degrees unless specially specified. 3.1. Characerizaion of FRS The parameers for characerizing FRS include he minimum rms value V min, maximum rms value V max, average rms value V ave, final rms value V fin, peak value V p, sag saring ime s, sag end ime e, sag duraion sd, iniializaion angle ini, iniial phase angle shif pasi, iniial phase angle shif rae r pasi, end angle end, end phase angle shif pase, end phase angle shif rae r pase, oal harmonic disorion THD, rms magniude unbalance raio r ub, and hree-phase phase angle difference deviaion PADD [2,3]. pasi, V min and V fin are given by Eqs. (1), (6) and (9), respecively. The oher parameers are obained as follows. V max =max(v rms) (14) V ave =ave(v rms) (15) i p =index max{abs( [i ])} (16) V p = [i p ] (17) s =i s /f s (18) i e =index e{abs(wc 1 [k]) }/L wc 1 L (19) e =i e /f s (20) sd = e s (21) i zi =index z( [i ], i s ) (22) ini =360(i s i zi )f 0 /f s (23) r pasi = pasi f 0 (24) i ze =index z( [i ], i e ) (25) end =360(i e i ze )f 0 /f s (26) pase =180[angle(V e [1]) angle(v s [1])]/ (27) r pase = pase f 0 (28) round(n/2) THD= abs(v s [k]) 2 (29) k=2 r ub =[max(v rmssabc ) min(v rmssabc )]/ave(v rmssabc ) (30) PADD=180max{abs(P pad )}/ (31) In he above equaions, we have defined V rmss = 1 N 1 N 2 [i+i s ] (32) i=0 V rmssabc is defined as he array composed of V rmssa, V rmssb, and V rmssc ha are obained by applying Eq. (32) o phase a, b and c volage signal, respecively. i e +N 1 V e [k]= [i ]e j(2 ki/n) (33) i=i e P ab =angle(v sa [1]) angle(v sb [1]) (34) P bc =angle(v sb [1]) angle(v sc [1]) (35) P ca =angle(v sc [1]) angle(v sa [1]) (36) V sa, V sb and V sc are obained by applying Eq. (4) o phase a, b and c signal respecively. P pad =[P ab 2 /3, P bc 2 /3, P ca 2 /3] (37) abs(.) gives he absolue value of he argumen index e(.) yields he index of he las elemen ha is greaer han zero of he inpu array index max(.) gives he index of he maximum value of he argumen index z(.,.) gives he index of he posiive zero crossing poin of he firs array argumen ha is closes o and prior o he second scalar argumen max(.) gives he maximum value of he argumen ave(.) gives he mean of he argumen 3.2. Characerizaion of MSRS Compared o he characerizaion of FRS, characerizaion of MSRS enails wo new parameers, i.e. sag recovery ime re and recovery duraion rd. On he oher hand, he end angle, end angle shif and end angle shif rae are eliminaed because he MSRS volage recovers very slowly and i is hard o accuraely define and compue hese hree parameers. I is also found ha wavele ransform can accuraely locae he saring and end ime of FRS, bu usually fails o do so for MSRS. Hence, he following differen approaches for characerizing MSRS are described. Fig. 4 depics he rms plo of a ypical MSRS signal for illusraing he definiions of some parameers. In he figure, re is he sag recovery ime and e is he end ime of he sag. re and e can be compued as follows.
M. Kezuno ic, Y. Liao / Elecric Power Sysems Research 58 (2001) 27 35 31 Table 1 Parameers for he sag shown in Fig. 1 Sag parameers Values Fig. 4. Illusraion of MSRS parameers. re =(i re +i min 1)/f 0 (38) e =(i ec +i min 1)/f 0 (39) rd = re s (40) sd = e s (41) i min, i re and i ec are referred o Eqs. (7), (8) and (10), respecively. Parameers V min, V max, V ave, V fin, V p, s, ini, pasi, r pasi, THD, r ub and PADD are calculaed in he same way as FRS. 3.3. Characerizaion of MRRS Compared o MSRS, one new parameer, he iniial rms value V ini is added. This reflecs he fac ha he moor in MRRS acs as a volage source a he beginning of he faul, and hus he volage gradually reduces o he lowes magniude raher han suddenly reducing o he lowes value as in FRS or MSRS. All he oher parameers are he same as hose for MSRS excep ha he recovery ime re is calculaed in a differen way. Fig. 5 shows he rms plo of a ypical MRRS volage signal. V ini and re are obained as follows. V ini =V rmss (42) re =i min /f 0 (43) Fig. 5. Illusraion of MRRS parameers. Minimum rms value (p.u.) 0.56 Maximum rms value (p.u.) 1.0 Average rms value (p.u.) 0.89 Final rms value (p.u.) 1.0 Peak value (p.u.) 1.45 Sag saring ime (ms) 199.83 Sag end ime (ms) 300.61 Sag duraion (ms) 100.78 Sag iniial angle ( ) 354.48 Sag iniial phase angle shif ( ) 12.57 Sag iniial phase angle shif rae ( /s) 752.44 Sag end angle ( ) 22.50 Sag end phase angle shif ( ) 12.63 Sag end phase angle shif rae ( /s) 740.58 Toal harmonic disorion 0.018 rms magniude unbalance raio PADD ( ) 0.415 19.62 3.4. Characerizaion examples This secion presens he characerizaion resuls for several ypical sag evens. Parameers for characerizing he sag evens shown in Figs. 1 3 are shown in Tables 1 3, respecively. 4. Sudy of equipmen sensiiviy during sag evens One imporan purpose of sag characerizaion is for equipmen sensiiviy sudy, i.e., how various sag parameers affec he equipmen operaing characerisics. Through equipmen sensiiviy sudy, one can explain why a specific load failed during a sag even, or predic how well a load will perform during a paricular Table 2 Parameers for he sag signal shown in Fig. 2 Sag parameers Values Minimum rms value (p.u.) 0.881 Maximum rms value (p.u.) 1.0 Average rms value (p.u.) 0.936 Final rms value (p.u.) 0.977 Peak value (p.u.) 1.415 Sag saring ime (ms) 50.2 Sag recovery ime (ms) 909.1 Sag end ime (ms) 924.8 Sag duraion (ms) 874.6 Recovery duraion (ms) 15.7 Iniializaion angle ( ) 33.43 Iniial phase angle shif ( ) 1.25 Iniial phase angle shif rae ( /s) 58.20 Toal harmonic disorion 0.034 rms magniude unbalance raio 0.0064 PADD ( ) 0.16
32 M. Kezuno ic, Y. Liao / Elecric Power Sysems Research 58 (2001) 27 35 Table 3 Parameers for he sag signal shown in Fig. 3 Sag parameers Values Minimum rms value (p.u.) 0.0061 Maximum rms value (p.u.) 1.0 Iniial sag rms value (p.u.) 0.1231 Final rms value (p.u.) 1.0 Average rms value (p.u.) 0.882 Peak value (p.u.) 1.423 Sag saring ime (ms) 50.2 Sag recovery ime (ms) 200.0 Sag end ime (ms) 455.8 Sag duraion (ms) 405.7 Recovery duraion (ms) 255.8 Iniializaion angle ( ) 332.10 Iniial phase angle shif ( ) 144.22 Iniial phase angle shif rae ( /s) 1.72 10 4 Toal harmonic disorion 0.018 Rms magniude unbalance raio 0.217 PADD ( ) 4.38 sag even. In he following secion, he overall approach for he equipmen sensiiviy sudy is described firs, and hen case sudies for illusraing he proposed mehods are presened. 4.1. O erall approach The overall srucure for evaluaing he equipmen behavior under volage sag evens is depiced in Fig. 6. The inpus are he volage sag waveforms ha can eiher be recorded in he field or be generaed by specific simulaion packages. The oupus are he operaing characerisics of he equipmen during he specified sag evens. The block volage sag characerizaion compues he various sag parameers. The block sag parameer uning allows he user o une or edi he sag parameers, obained from he block volage sag characerizaion, o cerain values. The recorded volage sag waveforms provide us wih a se of iniial sag parameers based on which furher uning can be made. However, he recorded waveforms are opional and if hey are unavailable, he user can inpu any desired iniial sag parameers and hen une hem for esing. In eiher case, by uning he sag parameers such as he sag magniude, sag duraion, Fig. 6. The overall srucure for equipmen behavior evaluaion. Fig. 7. The esing sysem diagram. phase angle shif, ec. he sofware allows he user o observe and sudy how specific sag parameers affec he operaing characerisics of he equipmen under es. This is wha we call he equipmen sensiiviy sudy. The block volage sag generaor [8] reconsrucs he volage sag waveforms based on he uned sag parameers. The consruced volage waveforms serve as he volage source for esing he equipmen. The volage sources can eiher be one phase or hree phase depending on he equipmen being evaluaed. The equipmen model allows developmen of mahemaical models for he equipmen. Through he sensiiviy sudies, he operaing characerisics of he equipmen during various sag evens can be evaluaed and responses abulaed. For example, by changing only he phase angle shif while fixing all he oher sag parameers a specified values, we can obain one able describing he equipmen operaing characerisics versus he phase angle shif. In he same way, he operaing characerisics of he equipmen versus oher parameers can be obained and archived. By comparing he parameers of a specific sag even wih he saved equipmen operaing characerisics, auomaic equipmen behavior diagnosis can be realized. 4.2. Case sudies This secion presens he case sudies for equipmen sensiiviy sudy. The firs equipmen under evaluaion is an inducion moor fed by a curren-conrolled PWM (pulse widh modulaion) inverer. The moor is raed as 3 HP, 220 V and 60 Hz. The DC volage is obained by a 6-pulse diode bride. The capacior size a he DC side is 4.4 10 3 F. The inverer is buil using six MOSFET blocks [9]. The speed conrol loop uses a proporional-inegral conroller o obain he slip frequency reference ha is used o conrol he ampliude and frequency of he hree-phase conrolled oscillaor ha produces he curren references for he curren
M. Kezuno ic, Y. Liao / Elecric Power Sysems Research 58 (2001) 27 35 33 Fig. 8. The DC link volage during a FRS even. conroller. Fig. 7 shows he esing sysem diagram. In he figure, he sag generaor generaes he sag waveforms wih specified parameers. The recifier provides he DC volage for he variable speed drive (VSD). Fig. 8 plos he DC link volage during a FRS even. The roor speed variaion is drawn in Fig. 9. The volage sag has a magniude of 88% of he pre-sag volage and lass abou 750 ms. I can be seen ha he moor speed has a 3% drop. In conras, Fig. 10 depics he DC link volage during a MSRS even ha has he same magniude as he FRS excep ha he MSRS has an addiional recovery ime of abou 200 ms. The moor speed is ploed in Fig. 11. I is noed ha he recovery ime of he MSRS even has caused a 100 ms delay for he recovery of he moor speed compared wih FRS. Anoher equipmen under evaluaion is an asynchronous machine (ASM) direcly conneced o he AC bus. The ASM implemens a hree-phase inducion machine (wound roor or squirrel cage) modeled in he Fig. 10. The DC link volage during a MSRS even. dq roor reference frame. I has raed values of 3 HP, 220 V, 60 Hz and 11.87 NM. Figs. 12 and 13 show he drasic variaions of he elecromagneic orque and he moor speed during a FRS wih a 40 of phase angle shif and no magniude reducion. The speed of he moor has a maximum drop of 15%. This illusraes he imporance of including he phase angle shif for he equipmen performance evaluaion. The effecs of oher sag parameers on he equipmen operaing characerisics can be evaluaed similarly. In pracice, variable speed drives or ASM direcly conneced o he AC bus are usually proeced by he relaying sysem ha rips he AC supply when he AC volage or DC link volage drops below a pre-specified level. Through he equipmen sensiiviy sudy, criical values for he even parameers can be found ha may be useful for he coordinaion beween he proecion sysem and he equipmen. Fig. 9. The roor speed during he FRS even. Fig. 11. The roor speed during he MSRS even.
34 M. Kezuno ic, Y. Liao / Elecric Power Sysems Research 58 (2001) 27 35 Fig. 12. The elecromagneic orque during a FRS even. 5. Conclusions A novel fuzzy logic based sag classifier for disinguishing beween he sags relaed o he fauls, large moor saring, or o he moor re-acceleraion is described in his paper. Also presened are he suggesed characerizaion mehods and parameers for he hree ypes of sag evens. The applicaion of he characerizaion resuls for he equipmen sensiiviy sudy is illusraed. Our implemenaion of he algorihm in MATLAB shows ha he conribuions presened in he paper have promise for pracical applicaions. 6. Nomenclaure V min V max minimum rms value maximum rms value Fig. 13. The roor speed during he FRS even. V ave V fin V ini V p s e sd rd ini pasi r pasi end pase r pase THD r ub PADD V n [k] V s [k] V sa [k], V sb [k] and V sc [k] V e [k] i s i e i p i min i zi i ze f 0 f s [i] L N j WC 1 [k] L WC 1 P ab P bc average rms value final rms value sag iniial rms value peak value sag saring ime sag end ime sag duraion sag recovery duraion iniializaion angle iniial phase angle shif iniial phase angle shif rae end angle end phase angle shif end phase angle shif rae oal harmonic disorion hree phase rms magniude unbalance raio hree-phase phase angle difference deviaion he Discree Fourier Transform (DFT) of he signal in he nh daa window he Discree Fourier Transform (DFT) of he signal in he firs window afer he sag even V s [k] applied o phase a, b and c signals respecively he Discree Fourier Transform (DFT) of he signal in he firs window afer he sag recovery sag saring poin sag end poin insananeous volage peak poin minimum rms volage cycle index he las posiive zero crossing poin of he pre-sag waveform he las posiive zero crossing poin of he during-sag waveform he fundamenal frequency of he sysem he sampling frequency of he signal he sampled signal of phase A, B, or C, i=0, 1,..., L 1 he lengh of he signal he number of samples in one daa window (one cycle) he imaginary uni he firs scale wavele deail coefficiens, k=1,2,...,l WC 1 he lengh of WC 1 [k] a pre-defined consan, seleced as 0.05 here he angle difference beween phase A and phase B volages he angle difference beween phase B and phase C volages
M. Kezuno ic, Y. Liao / Elecric Power Sysems Research 58 (2001) 27 35 35 P ca P pad he angle difference beween phase C and phase A volages he array composed of P ab, P bc, and The developmens repored in his paper are funded by he Texas Higher Educaion Coordinaing Board Advanced Technology Program. The co-funding is provided by TXU Elecric and Gas and Relian Energy HL&P. P ca V rms an array composed of V rms [n], n= 1,2,...,L rms L rms lengh of V rms defined as round (L/ N) V rms [n] rms value of he signal in he nh daa window (cycle) V rmss rms value of he signal in he daa window immediaely afer he sag occurrence V rmssabc an array composed of V rmssa, V rmssb, and V rmssc V rmssa, V rmssb, V rmss applied o phase a, b and c V rmssc signals respecively d V rms an array composed of V rms [n], n= i min,...,l rms i re sag recovery index in cycle sag end index in cycle i ec Acknowledgemens References [1] IEEE Projec 1346 Working Group, Elecric Power Sysem Compaibiliy wih Indusrial Process Equipmen, par 1: Volage Sags, IEEE Indusrial and Commercial Power Sysems Technical Conference, Irvine, CA, USA, May 1 5, 1994, pp. 261 266. [2] Mladen Kezunovic and Yuan Liao, Auomaed volage sag characerizaion and equipmen behavior analysis, Inernaional Conference on Power Qualiy, Elecrical Power Sysems World 99, Chicago, November 1999. [3] IEEE P1159.2, Task Force on Characerizaion of a Power Qualiy Even Given an Adequaely Sampled Se of Digial Daa Poins, web sie: hp://grouper.ieee.org/groups/1159/2/ keyps.hml. [4] E.R. Collins and A. Mansoor, Effecs of volage sags on AC moor drives, Proceedings of he 1997 Texile, Fiber, and Film Indusry Technical Conference, 97CH36100, May 6 8, 1997, pp. 1 7. [5] J.C. Das, Effecs of momenary volage dips on he operaion of inducion and synchronous moors, IEEE Trans. Ind. Appl. 26 (4) (1990) 711 718. [6] Mah H.J. Bollen, The influence of moor re-acceleraion on volage sags, IEEE Trans. Ind. Appl. 31(4) (1995) 667 674. [7] John Yen, Reza Langari, Fuzzy Logic: Inelligence, Conrol, and Informaion, Prenice Hall, Englewood Cliffs, NJ, 1999, pp. 3 18, 63 68. [8] Mladen Kezunovic, Yuan Liao, A novel mehod for equipmen sensiiviy sudy during power qualiy evens, IEEE PES Winer Meeing, 2000, Singapore. [9] MahWorks, Inc., MATLAB Manuals, May 1997..