Comparison of High Frequency Detailed Generator Models for Partial Discharge Localization

Transcription

1 J Electr Eg Techol.25; (?): ISSN(Prit) ISSN(Olie) Compariso of High Frequecy Detailed Geerator Models for Partial Discharge Localizatio S. M. Hassa Hosseii ad S. M. Hosseii Bafghi * Abstract This paper presets partial discharge localizatio i stator widig of geerators usig multi-coductor trasmissio lie (MTL) ad RLC ladder etwork models. The high-voltage (HV) widig of a 6kV/25kW geerator has bee modeled by MATLAB software. The simulatio results of the MTL ad the RLC ladder etwork models have bee evaluated with the measuremets results i the frequecy domai by applyig of the Pearso s correlatio coefficiets. Two PD geerated calibrator sigals i khz ad MHz frequecy rage were ijected ito differet poits of geerator widig ad the sigals simulated/measured at the both eds of the widig. For partial discharge localizatio i stator widig of geerators is ecessary to calculate the frequecy spectrum of the PD curret sigals ad the estimate the poles of the system from the calculated frequecy spectrum. Fially, the locatio of PD ca be estimated. This theory applied for the above geerator ad the simulatio/measured results show the good correlatio for PD Locatio for RLC ladder etwork ad MTL models i the frequecy rage of khz (khz<f<mhz) ad MHz (MHz<f<5MHz) respectively. Keywords: Geerators, Partial discharge, Pearso s correlatio coefficiets, Multi-coductor trasmissio lie model, RLC ladder etwork model.. Itroductio Geerators are cosidered to be oe of the essetial ad costly equipmet's of power system. Idetifyig isulatio faults i the best possible time prevets the appearace of irreparable damages. Partial discharge (PD) is oe of the most importat isulatio faults. The first step i the study of partial discharge is precise modelig of trasformer widig i high frequecies. I this paper two detailed RLC ladder etwork ad MTL Models have bee applied for partial discharge studies. The validity of frequecy rag of this two models are differet. The fudametal elemets of the ladder etwork model are the lumped R, L ad C elemets ad the frequecy limitatio for the validity of this model is i the rage of a few hudred khz. The fudametal elemets of MTL model are distributed parameters. The model accuracy will be expaded over MHz frequecy rage. The published works o the machies is more focused o the RLC ladder etwork model i past [-6]. While the published works o MTL modelig is mostly cocetrated o modelig of electrical rotatig machies ad also o oly the homogeous trasformer widigs igorig the frequecy depedecy of the widig isulatio parameters [7-2]. This paper Correspodig Author: Dept. of Electrical Egieerig, South Tehra Brach, Islamic Azad Uiversity, Tehra, Ira. (Smhh@azad.ac.ir) * Dept. of Electrical Egieerig, South Tehra Brach, Islamic Azad Uiversity, Tehra, Ira. (mojtaba.hoosiy@gmail.com) Received: April 4, 24; Accepted: February 3, 25 compares the two well-kow MTL ad RLC ladder etwork models ad used these models for PD studies i high frequecy rage khz<f<5mhz. 2. MTL Model MTL theory deals with a etwork of N coductors coupled all together, characterized by its iductace matrix [L], ad capacitace matrix [C]. I the MTL model, widigs parameters are cosidered as distributed parameter ad widig behavior is described by trasmissio lie equatios. MTL model for turs of oe coil is depicted i the Fig. [3]. For developig the model a sigle tur is cosidered as the basic elemet of aalysis. Fig. shows a electrical machie widig with three turs i series coectio. I this figure, Z r is the impedace for represetig the Fig.. Widig model with three turs i series coectio Copyright c The Korea Istitute of Electrical Egieers This is a Ope-Access article distributed uder the terms of the Creative Commos Attributio No-Commercial Licese ( liceses/by-c/3./) which permits urestricted o-commercial use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. 79

2 Compariso of High Frequecy Detailed Geerator Models for Partial Discharge Localizatio termial coditios, short ad ope circuit. The voltage V s is the surge at the begiig of the widig. Surge impedaces ad coefficiet of propagatio ca be estimated of the followig Eqs. [7-]. Z i = i i ωa v s c + c + 2k cos( ) v s () ω ωtaδ jω γ = + + vd 2σμ 2v v (2) s s s where k: iter-tur capacitace, a: turs average legth d: disks gap, v s : velocity The first ad secod terms i the (2) are represetig the ski effect ad the dielectric losses respectively. σ, μ ad d are the coductivity, permeability ad the widig coils gap respectively. The details of modelig ad the parameters estimatio for a ihomogeeous widig (realizig frequecy depedet parameters) are discussed i []. 2. PD Aalyses for MTL model Accordig to the Fig. we have these telegraphs equatios: Vt It = L( ) x t It Vt E = C( ) + C t x t i Eqs. (3) ad (4), V t ad I t are the voltage ad curret vectors. The order is equal to the umber of turs i a coil. L ad C are square matrices of the iductaces ad capacitaces i the coil while E o ad C o deotes the excitatio fuctio ad capacitace from oe tur to the static plate. To study the PD pheomea the excitatio fuctio do t exist so i the (4): E = t By solve the Eqs. (3) ad (4) ad by isertio of (5), oe ca obtai followig equatios: (3) (4) (5) Vi( x) = Ai exp( Γ ( ω) x) + Bi exp( Γ ( ω) x) (6) Ii( x) = [ Ai exp( Γ( ω) x) Bi exp( Γ ( ω) x)] z (7) i Eqs. (6) ad (7) are 2 equatio ad cotai 2 udefied parameters (A i ad B i ). By usig the termial coditios we have: Ir = Is2 Ir2 = Is3 Vr =Vs 2 Vr2=Vs 3 ad Ir / 3 Vr3 Zr (8) 2-2 equatios are available. For two other equatio ca be simulated by a capacitace C B coected at the lie-ed. The, I = jωc v (9) ( s) B ( s) if the eutral ed is at earth potetial, V r( N ) = () If a PD curret pulse I PD is ijected ito the k th tur of the widig, (8) is modified whe i=k-: I ( k) = I ( k ) + I () s r PD With applyig Eqs. (8) to () i Eqs. (6) ad (7), the coefficiets A i ad B i have bee calculated ad the the curret due to PD pulse ca be calculated i the geerator termials. Is() Vs() V s (2) I PD = [ Y ] V s ( k ) V s( ) I R( ) V R( ) I V s() s() V s (2) V s (3) V s( k ) = [ T ] I PD V s( ) V R( ) I R( ) (2) (3) where: [Y ] is a ( + ) ( + ) matrix. If matrix [Y ] is iverted ad re-arraged, it is possible to get Eq. (3). Hece, if the lie-ed voltage, the eutral-ed curret ad the PD curret are kow all other voltages ad currets ca be calculated. 7 J Electr Eg Techol.25; (3): 79-78

3 S. M. Hassa Hosseii ad S. M. Hosseii Bafghi 3. RLC Ladder Network A PD geerated withi a geerator widig ca have a associated frequecy rage betwee a few khz to hudreds MHz Fig. 2 shows a RLC ladder etwork model [3]. Fig. 2. RLC ladder etwork model for geerator widig (PD occurs i ode 2) The PD occurrece ca be simulated as a curret pulse ijected ito the etwork. To obtai the output curret through the eutral poit i such a circuit, it is very coveiet to use state-space equatios as follows: with x = Ax + Bu y = Cx + C2x (4) x A B = [ i( t ), i 2( t ),..., i N ( t ), v ( t ), v 2( t ),..., v N L R L N = Θ M Θ G = K Θ ( t )] C = [,,...,, G S,,..., ]; C 2 = [,,...,, G S,,...,]; K,...,,,...,,..., ; = ( r ) Note that the positio of i vector K is decided by the iput positio. L, Θ ad G are the iductace, capacitace ad admittace matrices of this system. The frequecy respose ca be calculated by takig the Laplace trasform of Eq. (4). Y ( s) = ( C+ C2S)( SI A) B (5) U( s) with regard to the uit distributio for the PD curret source, the frequecy spectrum of the system ca be evaluated accordig the bellow equatio: T I Eq. (6) oly the matrix B is related to the positio of the PD curret source locatio. The matrix A is ot affected by the positio of the PD curret source, also, the system structure does ot affect by this discharge. Therefore, the poles of the system, which are the eigevalues of the matrix A, are completely determied oly by the system (matrix A). O the other had the poles of frequecy spectrum of the sigal cotai the iformatio of the PD source locatio. Based o the above theory, for the PD curret detectio ad PD locatio, the three bellow steps will be dow:. The frequecy spectrum of Y (s) has bee calculated from PD curret sigal. 2. The poles of the system have bee estimated from the frequecy spectrum. 3. The locatio of PD source has bee estimated from poles of the system. Step ca be calculated easily through the use of a fast Fourier trasform (FFT). The secod step ca be estimated from the trasfer fuctio of the widig model as followig: [4-6] β ( S ) Y ( S) = (7) α( S ) where α ( S ) ad β ( S ) are polyomials ad defied by bellow: α( S) = αs + α S α S + α (8) m β ( S) = b S + b S bs + b (9) m m m applyig Eqs. (8) ad (9) i Eq. (7), the followig equatio is obtaied: where ad Y ( S) = X ( S) θ (2) m X( S) = S Y( S)... SY( S) S... S (2) [... b... b b ] θ = α α (22) m After obtaiig the coefficiets, the poles of the system ca be estimated from the roots of polyomial α ( S ). The third Step is a oliear optimizatio problem. The objective fuctio is to miimize the differece betwee the eigevalues of matrix A ad the calculated pole. The eigevalues ad pole frequecies to be arraged i descedig ascedig Y ( s) = ( C+ C2S)( SI A) B U ( s) (6) L R L N eig ( A ) = eig ( ) poles roots ( α( S )) = = (23) Θ M Θ G 7

4 Compariso of High Frequecy Detailed Geerator Models for Partial Discharge Localizatio Fially, with the poles of the system, the locatio of the PD ca be estimated 4. Fast Trasiet Over-voltage s I this sectio the widig of geerator has bee modeled oce usig MTL ad ext with RLC ladder etworks. The the fast trasiet over-voltages have bee computed betwee turs. The aalysis was carried out for a 6 kv/25 kw test geerator. Table ad 2 show the geerator specificatio ad coil parameters. At this paper the coil parameters have bee evaluated from two methods, the first by usig the COMSOL software ad the geometry ad custom shape of coils with FEM methodology ad the secod by measurig the parameters usig covetioal methods i the laboratory. The results of the fast trasiet over-voltage betwee coils have bee show i the Figs. 3, 4 ad 5 for measured MTL ad RLC models respectively. This figures show the absolute value of voltage betwee coils with respect to applied iput voltage. Fig. 4. Ratio of MTL model computed voltages to the applied iput voltage ( khz<f<5mhz) 4. Pearso s correlatio coefficiet Correlatio is a useful techique to ivestigate the Table. Specificatio of the uder the test geerator Rated voltage 6 V Rated power 25 kw Rated speed 5 r.p.m Rated frequecy 5 Hz Widig Coectio star --- Number of turs per phase Number of coils per phase Number of turs i a coil --- Coductor dimesios.5*236 mm Table 2. Parameters of the geerator coils Real Estimated Li(mH) R(Ω).35.4 Ki (PF) Ci (PF) Fig. 3. Ratio of measured voltage to the applied iput voltage ( khz < f < 5MHz) Fig. 5. Ratio of RLC ladder etwork model computed voltages to the applied iput voltage ( khz < f <5MHz) relatioship betwee two quatitative, cotiuous variables. It measures the stregth ad directio of a liear relatioship betwee two variables. This correlatio coefficiet is preseted by the followig equatio: r = ( U mi U m )( Usi Us ) i = 2 2 ( U mi U m ) ( Usi Us ) i = i= (24) where U m is the measured value of variable ad U s is its simulated value. r could be a umber betwee ad -. A positive value of r meas a positive liear relatioship; a egative value of r meas a egative liear relatioship. The correlatio is ideal as approaches ad it is ot desirable to approach -[7]. Cosiderig the measuremet results show i Fig. 4 ad usig SAS software to compute the correlatio coefficiet, the accuracy of the MTL ad RLC ladder etwork model ca be studied. Tables 3 ad 4 show these coefficiets for the RLC ladder etwork model ad the MTL model simulatios for respectively. These coefficiets are the best meas for evaluatio of the models. Cosiderig the last row of Table 3 it is obvious that the RLC ladder etwork model ca preset the best results for the frequecy rage of khz < f < MHz. The last row of Table 4 idicates that the MTL model ca represet the 72 J Electr Eg Techol.25; (3): 79-78

5 S. M. Hassa Hosseii ad S. M. Hosseii Bafghi Table 3. Pearso correlatio coefficiet for RLC ladder etwork ad MTL model for khz < f < MHz Coil No AVR. RLC MTL Fig. 6. PD pulse measured i circuit i a laboratory Table 4. Pearso correlatio coefficiet for RLC ladder etwork ad MTL model for MHz < f < 5MHz Coil No AVR. RLC MTL Fig. 7. The PD pulses measured i the khz rage (the PD has bee ijected i ode 6) respose of geerator better tha ext model for the frequecy rage of MHz<f<5MHz. The above-metioed coclusios ca be draw from Figs. 3, 4 ad 5 as well. 5. Result of PD Localizatio I order to estimate the locatio of PD i geerators with more reliability, it is better to verify the accuracy of the models that will be used i PD localizatio first. So it is recommeded to measure ad record the frequecy spectrum of the geerator i the first step. The the simulatio results must be compared with the measuremets. If simulatio results were satisfactory, the models ca be used for PD localizatio. Otherwise the models must be modified or the parameters of the model must be optimized before PD localizatio. At the first, PD pulses have bee ijected by the PD calibrator i the differet part of the widig. The the curret sigals measured/simulate i the ed of the widig. These PD sigals have bee geerated i khz ad MHz frequecy rage that used for RLC ladder etwork ad MTL models respectively. Fig. 6 shows the PD pulse studies circuit i a laboratory. The PD pulse to be geerated i the khz rage has bee show i Fig. 7. Figs. 8, 9 show the compariso betwee the curret Fig. 8. The compariso of curret ad the spectrum (PD has bee ijected i ode for RLC ladder etwork model) Fig. 9. The compariso of curret ad the spectrum (PD has bee ijected i ode 6 for RLC ladder etwork model) 73

6 Compariso of High Frequecy Detailed Geerator Models for Partial Discharge Localizatio spectrum for RLC model ad measuremets results. The PD pulse to be geerated i the MHz rage has bee show i Fig.. The Figs., 2 show the compariso betwee the curret spectrum for MTL simulated model ad measuremets results. I this sectio from the frequecy spectrum of the curret sigals, ad poles estimate of the system, the locatio of PD ca be estimated alog the widig. The these results compared with real positio. Table 5 shows the compariso betwee the real positio ad the simulated estimated positio of PD (Depedig to the ode). 6. Coclusio Fig.. The PD pulses measured i the MHz rage (the PD has bee ijected i ode 6) Fig.. The compariso of curret ad the spectrum (PD has bee ijected i ode for MTL model) This paper compared the measuremet ad simulatio results of trasiet over voltages ad the partial discharge localizatio i the widigs of a 6kV/25kW geerator. Voltages alog the geerator widigs were simulated by applyig MTL ad RLC ladder etwork theory. The results of the trasiets voltage calculated i the coils of the widig were compared with laboratory measuremet. A relatively good correlatio observed betwee measuremet ad RLC Ladder Network model simulatio results for the frequecy rage of khz < f < MHz. However i the rage of the frequecy MHz < f < 5MHz, the MTL model, provides a better agreemet betwee the simulated ad the measured voltages. A algorithm for partial discharge localizatio has bee developed i this paper. The approach is based upo frequecy spectrum aalysis of PD curret sigals. PD pulses have bee ijected by the PD calibrator i the differet part of the widig. The the PD sigals measured or simulate i the ed of the widig. These PD sigals have bee geerated i khz ad MHz frequecy rage that used for RLC ladder etwork ad MTL models respectively. A relatively good correlatio have bee observed betwee measuremet ad RLC ladder etwork model simulatio results for the frequecy rage of khz (khz < f < MHz), however i the frequecy rage of MHz (MHz < f < 5MHz), the MTL model have bee provided the better agreemet betwee the simulated ad the measured for PD Locatio. Refereces Fig. 2. The compariso of curret ad the spectrum (PD has bee ijected i ode 6 for MTL model) Table 5. Compariso betwee real positio ad the simulatio estimated positio of PD Real positio PD() PD(6) PD() Estimated (RLC) 6 2 Estimated (MTL) 6 2 [] R. Rudederg, Performace of travellig waves i coils ad widigs, AIEE Tras., pp. 3-45, 94. [2] P. I. Fergastad ad T. Herikse, A calculatio method for impulse voltage distributio ad trasferred voltage i trasformer widigs, IEEE Tras. Power APP. & SYS., vol. 97, o. 3, pp , May [3] T. J. Lewis, 'The trasiet behavior of ladder etworks of the type represetig machie ad trasformer widigs', i Proceedigs of IEEE PES,, Pt.2, pp , 954. [4] K. Coric, B. Filliat, C. Kiey, ad W. Muller, Distributio of very fast trasiet overvoltages i trasformer, i Proceedigs of CIGRE, pp , 74 J Electr Eg Techol.25; (3): 79-78

7 S. M. Hassa Hosseii ad S. M. Hosseii Bafghi 992. [5] K. L. Christiase, ad A. Pederse, 'Trasiet surges ad motor protectio', i Proceedigs of IEEE PES Proceedigs of the electrical isulatio coferece, 68C6-EI-87, pp. 48-5, 968. [6] R. L. Naile, 'Trasiet surges ad motor protectio', i Proceedigs of IEEE PES Idustrial ad commercial power system techical coferece, Seatel, USA, May 979. [7] W. T. Weeks, 'Multicoductor trasmissio-lie theory i the TEM approximatio: IBM J. Res. & Dev, 972. [8] M. Popov, v. sluis, R.P.P.smeets, complete aalysis of very fast trasiets i layer-type trasformer widigs, Iteratioal Coferece o Power Systems Trasiets, Lyo, Frace, Jue 27. [9] K. J. Koric ad T. R. Thompso, 'Steep-froted switchig voltage trasiets ad their distributio i motor widigs, Part 2. i Proceedigs of IEE Proc Electro. Power Applicatio, pp , 982. [] M. Popov, L. V. Sluis, ad G. C. Paap, Computatio of very fast trasiet over voltages i trasformer widigs, IEEE Tras. Power Delivery, vol.8, o.4, pp , Oct. 23. [] A. K Agrawal ad H. M. Fowles, Applicatio of modal aalysis to the trasiet respose of multicoductor trasmissio lies with braches, IEEE Tras. EMC, pp , 979. [2] G. N. Petrove., ad A. I. Abromov, 'Overvoltage stresses i the tur isulatio of electrical machiery widigs durig electromagetic trasiets: Electrichestov, 954, p [3] P. J. Mclare ad H. Oraee, Multi-coductor trasmissio lie model for the lie ed coil of large AC machies, i Proceedigs of IEEE Coferece, pp , 985. [4] H. G. Seddig, The partial discharge calibratio problem i rotatig machies, i Proceedigs of IEEE Witer power meetig Pael sessio 92TH425 9PWR, pp , 992. [5] P. G. Mclare ad M. AbdelRahma, Modelig of large AC motor disk for steep-froted surge studies, IEEE Tras. Id. Appl., vol. 24, o. 3, pp , 988. [6] I. J. Kemp ad G. C. Stoe, Calibratio difficulties associated with partial discharge detectors i rotatig machie applicatios, Proceedigs of 8th coferece o Electrical ad electroic isulatio, Chicago, USA, pp , 978. [7] SAS/STAT Users Guide ver. 6: 4th ed., vol. 2. Cary, CA, SAS Istitute, Ic., 99d. S. M. Hassa Hosseii was bor i Tehra, i 969. He received the B.Sc degree i electrical power egieerig from Mashhad Ferdowsi Uiversity, Mashhad, Ira i 993. He received the M.Sc ad Ph.D degrees i electrical power egieerig i 2 ad 25 from Islamic Azad Uiversity South- Tehra Brach ad Sciece & Research Brach, Tehra, Ira, respectively. His research iterest is trasiet modelig of trasformers ad geerators, Partial Discharge, High Voltage Egieerig. S. M. Hosseii Bafghi was bor i Bafgh, Ira, i 986. He received the B.Sc. ad M.SC degrees i electrical power egieerig from Islamic Azad Uiversity of Mehriz ad South Tehra Brach i 29 ad 23 respectively. Sice 2, He joied as a lecturer of Electrical Egieerig Departmet, Faculty of Egieerig Islamic Azad Uiversity Bafgh Brach. His research iterest is trasiet ad PD modelig of Geerators. 75