Internatonal Conference on Advanced Electronc Scence and Technology (AEST 2016) Transformer wndng modal parameter dentfcaton based on poly-reference least-square complex frequency doman method Yanng L 1, a, Hong Yu2 and Xaoyan Zhu1 1 North Chna Electrc Power Unversty, Baodng, Chna Yunnan Power Grd Electrc Power Research Insttute Co., Ltd.,kunmng, Chna 2 Abstract. The modal parameter of transformer wndng, as drect reflectons of mechancal performance, s an mportant theoretcal foundaton n the feld of transformer manufacturng and detecton of wndng condton based on vbraton. To dentfy the modal parameters accurately, a modal experment on a 10 kv transformer wndng was conducted n ths paper. A PolyMAX method to dentfy wndng natural frequency and dampng rato was proposed usng the experment to dentfy transformer wndng modal parameters. And t uses modal confdence crteron to verfy. The frst four order modal parameters, ncludng natural frequency, dampng rato were extracted from the vbraton sgnal. The results demonstrate that all the natural frequences are far from two tmes of exctng frequency, whch ndcates that the desgn s approprate. The parameters verfes by MAC, whch verfes the effectveness of the proposed method n dentfyng modal parameters of transformer wndngs. Keywords: transformer; wndng; modal parameters; PolyMAX. 1 Introducton Transformer s one of the most mportant equpment n power system, and the stablty of power system s very mportant to the safety of power system. In normal operaton of the transformer, the wndngs are excted by the electrc power to generate vbraton. If the natural frequency of the transformer wndng s close to the exctaton frequency of the axal electrc power, the wndng wll produce a resonance phenomenon. Therefore, t s mportant to dentfy the natural frequency of the wndng, whch s of great sgnfcance to the desgn and manufacture of the transformer wth the natural frequency of the wndng. In addton, n the long run or short crcut mpact, the wndng may appear loose or deformaton, and the wndng mode parameters can be accurately dentfed and explored. At present, the analyss of the nherent characterstcs of the transformer wndngs s lmted to a smple model of the wndng. The model of sprng - pad s used to calculate the [1-2], but the model parameters are dffcult to be determned, and the smplfed model and the actual transformer wndng structure are qute dfferent. The fnte element modellng and smulaton analyss of the transformer wndng and the body mode of the transformer wndng and the body of L Yan, such as, has not been verfed. Wang Hongfang et al. Study the effect of [4] on the nonlnear vbraton characterstcs of a Correspondng author : hdlyanng@163.com 2016. The authors - Publshed by Atlants Press 796
wndngs, but the nherent characterstcs of the structure are dscussed. L Hongku et al. The exctaton vbraton of the transformer wndngs s carred out by [5]. But only the frst order natural frequency of the wndng s extracted, and the wndng dampng rato and vbraton mode are not gven. Because of the complex structure of transformer wndng, nonlnear strong, so the vbraton sgnal contans nose nterference. In the tme doman or frequency doman, the dentfcaton method of modal parameter dentfcaton method s lmted to the vbraton sgnal alone, and the dentfcaton accuracy s lmted, and s senstve to nose. In ths paper, the exctaton vbraton of a 10KV transformer wndng s excted, the PolyMAX method s used to dentfy the modal parameters of the transformer wndngs and the 4 order natural frequency and dampng rato are obtaned. Fnally, the MAC (modal confdence crteron) s used to verfy the dentfcaton results. 2 Basc prncple 2.1 PolyMAX modal dentfcaton method The PolyMax modal dentfcaton method s used n ths paper, also known as mult reference least square complex frequency doman method (Polyreference for complex frequency doman method), proposed by the Belgan B. Peeters and H. van der Auweraer professor n 2004, and s based on the least square estmaton theory and the mpulse response functon and the poles and resdues between the complex exponental relatonshp, and use the matrx of frequency response functon as a fttng functon n the frequency doman analyss method. The method s frst by sngle pont exctaton mult-pont vbraton pckup system response measurement ponts and between the exctatons s obtaned the frequency response functon, by the frequency response functon and through the standard algorthm. Fnally, we get requred for the model parameters. At the same tme, the method s not lmted by the sze of the dampng, the ntensty of the mode and the nterference of the nose. Because the pulse functon contans all the nformaton of the mode, t can be used to dentfy all the modal parameters of the structure system. Basc calculaton procedures are as follows: H ( ω) computng test system transfer functon H ( ω) obtaned based on the measured nput sgnals xt () and yt (),as follows: [ H ( ω)] l m [ B( ω)] = [ A( ω)] l m m m (1) Wheren, B( ω) s a frequency doman representaton of the output sgnal yt (); A( ω) to form a frequency doman output sgnal xt (); m s the number of the reference channel nput stmulus; l s the total number of channels n response to an output. If B( ω) and A( ω) can be expressed as follows: r [ B( ω)] = Z [ β ] p r= 0 p r= 0 r l m r [ A( ω)] = Z [ α r] m m (2) (3) For any frequency ω, lsts of equatons as represented by (1) can be measured accordng k. If we take a dfferent frequency, a suffcent number of lsts (over determned) equaton, t to [ H ( ω )] 797
can polynomal coeffcents [ β ] and[ α ]( r = 0,1,, p) obtaned by the least squares estmaton of r r the numerator and denomnator of the matrx to be determned. [ β ], [ α ] are real-valued coeffcents of each element, they are set to the complex s possble. r r [ α ] appears on the denomnator of the equaton s the nonlnear parameter dentfcaton problem. r However, a certan degree of lnearzaton, the varable of the lnear least-squares estmaton problem. α ( r = 0,1,, N 1) n the denomnator polynomal coeffcents based on known and gven the r α = I, and construct ts adjont matrx for egenvalue decomposton, we can get the system poles N and modal partcpaton factors, as follows: 0 I 0 0 0 0 0 0 V = VΛ 0 0 0 I T T T T α0 α1 αn 2 αn 1 (4) Λ characterstc value for the matrx (dagonal matrx), dagonal elements λ ( = 1, 2,, pn) as follow: λ = e p t or * p t e (5) * p, p = σ ± jω d (6) Modal dampng rato as follows: ξ σ σ = = ω 2 2 σ + ωd (7) In all matrces obtaned polynomal coeffcents A and B, the frequency doman usng the least squares method the modal shape, the fttng functon as follows: ψ l ψ l L H( ω) = ( + ) + U N T * H r r r r * 2 r= 1 jω pr jω pr ω (8) 2.2 Verfcaton based on MAC After the test analyss s completed n order to prevent the ntroducton of false mode or the loss of real mode, t s necessary to verfy the modal parameters n order to use MAC to verfy the applcaton. MAC s the correlaton coeffcent of two modal vectors ψ1 and ψ 2, as follows: ψψ 1 2 = 1 MAC = L L ( ψψ )( ψψ ) L 1 1 2 2 = 1 = 1 (9) The modal vector s ndependent of each other, and the MAC value between the two real modes should be close to 0. 798
3 Experment and smulaton 3.1 Expermental descrpton In ths paper, the hgh voltage wndng of a power transformer wth S9-630/10, the rated voltage of 10kV, and the connectng group are Y0. In order to be able to smulate the mechancal characterstcs of hgh voltage power transformer wndng, the wndng s the same as that of the power transformer. The transformer s carred out wth a KISTLER8763 acceleraton sensor, and the senstvty s 2mV/g, whch s arranged on the wndng surface by the metal clamp. At the top of the wndng, the B&K4808 electromagnetc excter s used to stmulate the wndng. The exctaton sgnal s whte nose sgnal, and the bandwdth s 20 khz, whch s provded by the dgtal sgnal generator and connected to the electromagnetc excter by the power amplfer. The electromagnetc excter s used to measure the exctaton sgnal and the expermental scene s shown n Fg. 1. Fgure 1. Overall vew of transformer wndng modal experment The expermental apparatus ncludes sgnal acquston and analyss system, charge amplfer, vbraton acceleraton sensor, vbraton sensor, power amplfer and sgnal generator. Fgure 2. Sgnal generator, power amplfer and sgnal acquston system 3.2 Modal test of transformer wndng In the nteracton of the leakage magnetc feld and current of the transformer wndngs, the electrc power wll be changed wth the pulse of current and the magnetc feld strength, whch causes the wndng vbraton. When the sudden short crcut, the transformer wndng s easy to produce the loose and the deformaton under the huge short-crcut current. After the wndng loose and the deformaton wll cause a greater mbalance electrc exctaton force, and form a vcous crcle, the wndng s damaged, even lead to serous accdent of the transformer. Therefore, the capacty of the transformer s the key to the desgn of large capacty transformer. Short crcut force can be classfed as the axal force, radal to force and crcumferntal force (of spral wndng), the role of axal force makes the wndng n the axal drecton s compressed, resultng n axal dsplacement and axal mechancal vbraton; radal force makes the wndng s compressed, wndng stretch; crcumferntal force the wndng generates torson effect. In the course 799
of the short crcut, the transformer wndngs are generated under the acton of short crcut force. The dynamc force n the wndng s not only short of short crcut electromagnetc force, but also the frcton force of nerta force, elastc force and dsplacement of the wndng. The dynamc process s very complcated, whch s nfluenced by the electromagnetc, mechancal, materals and other factors. In general, the calculaton of the dynamc process of the transformer wndng, the axal movement of the transformer wndng under the axal force and the radal movement of the transformer under the acton of the radal drecton. Therefore, ths study tests the axal mode and the radal drecton of the transformer wndng. 3.2.1 Transformer wndng axal modal test The purpose of the test s to measure the axal vbraton of the wndng, and the natural frequency and the correspondng vbraton mode of the wndng of the transformer are obtaned. In the experment, the whte nose s used to motvate, and there are 20 vbraton acceleraton sensor measurng ponts. Fg. 3 s the locaton of the vbraton sensor. Fgure 3. Vbraton sensor locaton dagram The exctng pont s located n the promnent part of the concave steel. The excter adopts elastc suspenson, vertcal exctaton, exctaton rod ends a force sensor. Fg. 4 for the excter placed n knd. Fgure 4. The vbrator s placed n the physcal dagram Fgure 5. The A phase wndng frequency response functon 800
Fg. 5 s a phase wndng axal expermental modal testng the vbraton sgnal frequency response functon s the result of the superposton, usng a sem logarthmc coordnate representaton. You can see from the fgure, the frequency response functon have obvous peak superposton results n 229Hz, 322Hz, 501Hz. Usng the PolyMAX method to dentfy the natural frequency of the A phase wndng, the frst 4 order natural frequency of the wndng s obtaned as shown n Table 1. Tab. 2 and Fg. 6 gves the MAC values of the natural frequences of the dfferent frequences and the MAC dagrams. By chart shows, the A phase wndng under normal operatng condtons, the frst 4 order of the axal vbraton natural frequency dfference s larger, and are far away from the exctaton frequency of the wndng s 2 tmes that of 100Hz, the structure s more reasonable. At the same tme, the MAC value of the 2 order modes can be consdered to be effectve n extractng the natural frequency of the 4 order vbraton. Table 1. Four order natural frequency of wndng Order 1 2 3 4 Frequency(Hz) 230 322 510 724 Dampng rato(%) 1.71 0.62 1.70 1.54 Table 2. MAC values of the frst four order modes of the A phase wndng Order 1 2 3 4 1 1 0.06 0.04 0.06 2 0.06 1 0.02 0.02 3 0.04 0.02 1 0.01 4 0.06 0.02 0.01 1 Fgure 6. MAC dagram of the frst four order modes of A phase wndng 3.2.2 Transformer wndng ampltude mode test The purpose of the test s to measure the frequency and vbraton of the transformer wndngs and the natural frequency and the correspondng vbraton mode of the transformer wndng. In the experment, the sne sweep exctaton s used to measure the 20 vbraton acceleraton sensor. 801
Fgure 7. Overall frequency response dagram of wndng The superposton of Fg. 7 for the A phase wndng radal modal experment test the vbraton sgnal obtaned by frequency response functon. You can see from the fgure, the frequency response functon have obvous peak superposton results n 6.75Hz and 20Hz. Usng the PolyMAX method to dentfy the natural frequency of the A phase wndng, the frst 3 order natural frequency of the wndng s obtaned as shown n Table 3. Table 4 and fgure 8 gves the MAC values of the natural frequences of the dfferent frequences and the MAC dagrams. By chart shows, A phase wndng under normal operatng condtons, the frst 2 order of the natural frequency of the frequency dfference s larger, and are far away from the exctaton frequency of the wndng s 2 tmes that of 100Hz, the structure s more reasonable. At the same tme, the MAC value of the 2 order modes can be consdered to be effectve n extractng the natural frequency of the frst 2 order vbraton. Table 3. Two order natural frequency of wndng Order 1 2 Natural frequency(hz) 6.75 20 Dampng rato(%) 5.22 4.79 Table 4. MAC values of the two order mode of the wndng Order 1 2 1 1 0.32 2 0.32 1 Fgure 8. MAC dagram of the frst two order mode of wndng 4 Concluson In ths paper, the vbraton test of the transformer wndngs s carred out. The PolyMAX method s used to dentfy the modal parameters of the transformer wndngs. The 4 order natural frequency and 802
dampng rato of the transformer wndngs are extracted. The MAC value and the MAC chart are ntroduced. Expermental results show that the modal parameter dentfcaton based on PolyMAX method has good nose resstance, and ts accuracy s hgher than that of the tradtonal frequency doman dentfcaton method. At the same tme, because of the expermental transformer wndng s a pe col structure, and large power transformer wndng structure s same, so ths paper s also used n 220kV and 110kV and other hgh voltage grade power transformer wndng modal parameters dentfcaton, dentfcaton results can provde bass for transformer desgn, manufacture and vbraton based wndng state detecton. References 1. SHAO Yuyng, XU jan, RAO Zhush, et al. Applcaton reseach of detecton transformer wndngs deformaton based on vbraton frequency response analyss[j]. Journal of Shang ha Jaotong Unversty, 44 (9):1223-1228, (2010). 2. GUO jan, LIN Heyun, XU Zhong, et al. Analyss of axal stablty of power transformaton wndngs usng fnte element [J]. Hgh Voltage Engneerng, 33 (11):209-212, (2007). 3. LI Yan, ZHOU We, JING Yongteng, et al. Axal vbraton analyss of transformer actve part under short crcuts [J]. Advanced technology of Electrcal Engneerng and Energy, 31(3):49-53, (2012). 4. WANG Hongfang, WANG Naqng, LI Tongsheng. Axal vbraton equvalent one degree analyss of power transformer wndng under short crcut [J]. Transformer of Chna Electrotechncal Socety, 15 (5):39-41, (2000). 5. LI Hongku, LI Yan. Axal vbraton modal analyss of transformer wndngs under dfferent level of precompresson[j] Electrc Machnes And Control, 14(8): 98-101,(2010). 6. Brat Peeters, Heram Van der Auweraer, Patrck Gullaume, et al. The PolyMAX frequency doman method: A new standard for modal parameter estmaton [J]. Shock and Vbraton, 11:95-409, (2004). 7. Carmona R, Hwang W L, Torresan B. Mult-rdge detecton and tme frequency reconstructon[j]. IEEE Transacton on Sgnal Processng, 1999(47):480-492. 8. Peeters B, Gullaume P. Automotve and aerospace applcatons of the LMS PolyMAX modal parameter estmaton method[c]//proceedngs of the 22th Internatonal Modal Analyss Conference,Dearborn,USA,January,(2004). 9. Gullaume P, Verboven P, Vanlandut S, et al. A poly-reference mplementaton of the leastsquares complex frequency doman estmator[c]//proceedngs of the 21th Internatonal Modal Analyss Conference. Kssmmee, USA, February, (2003). 10. [10] GENG Chao, WANG Fenghua, HUANG Hua, et al. Transformer Wndng Modal Parameter Identfcaton Based on Complex Morlet Wavelet Transform [J]. Journal of Shangha Jaotong Unversty, 47 (12):1981-1986, (2013). 803