Low Sampling Rate Technology for UHF Partial Discharge Signals Based on Sparse Vector Recovery

Transcription

1 017 nd Internatonal Semnar on Appled Physcs, Optoelectroncs and Photoncs (APOP 017) ISBN: Low Samplng Rate Technology for UHF Partal Dscharge Sgnals Based on Sparse Vector Recovery Qang GAO, Q LIU, Zhannan GUO, Yuhao GAO, Zhen LI ABSTRACT *The detecton of the partal dscharge (PD) s one of the mportant way to montorng the state of the power equpment n substaton. The detecton and localzaton of PD sgnal especally for ar-nsulated power equpment based on ultra-hgh frequency (UHF) method need a hgh samplng rate sgnal acquston system whch can lead to hgh hardware cost. Therefore, n ths paper we propose a low samplng rate algorthm based on sparse vector recovery. The experment n laboratory ndcates that by our proposed algorthm the PD sgnal can be well recovered wth the use of only 10% of the orgnal sgnal data, whch can sgnfcantly reduce the samplng rate for the PD detecton and localzaton. INTRODUCTION Safety and stablty are essental requrements for power system operaton. Therefore, t s necessary to montor the state of the power equpment n substaton. Deteroraton of nsulaton s one of the major reason for equpment falure, whch wll produce partal dscharge (PD) [1,]. Therefore, the detecton of PD sgnal s an effectve way for Condton Montorng and Dagnostcs (CMD) n substaton. Among the PD detecton methods, ultra-hgh frequency (UHF) electromagnetc waves s the most effectve method due to ts excellent senstvty and propagaton speed [3]. For the exstng UHF PD measurement technques, due to lmted hardware condtons such as analog to dgtal converson, t s often dffcult to meet the requrement of hgh samplng rate. Acquston of hgh-qualty UHF PD sgnal data wll lead to hgh hardware cost. Compressed sensng (CS) algorthm ndcates that f a sgnal has sparsty n a space, t can be well recovered by from a part of ts data [4,5]. Therefore, n ths paper, we propose a low samplng rate measurement algorthm based on sparse Qang Gao 1,*, Q Lu 1, Zhannan Guo, Yuhao Gao 3, Zhen L 4 1 Electrc Power Research Insttute of State Grd Laonng Power Supply Co. Ltd., Shenyang, Chna Shenyang Keka Electrc Power Technology Co. Ltd., Shenyang, Chna 3 Hube Unversty of Technology, Wuhan, Chna 4 State Energy Smart Grd R&D Center (Shangha), Shangha, Chna Correspondng author: @qq.com 444

2 vector recovery. Frstly, acqurng a part of the UHF PD sgnal data, whch can sgnfcantly reduce the samplng rate. Then by sensng matrx the sparse vector recovery model s constructed. Fnally, the whole PD sgnal can be recovered by reconstructon algorthm. An experment s performed n hgh-voltage laboratory to verfy the effectveness of our proposed algorthm. The results ndcate that wth the use of only 10% of the sgnal data the PD sgnal can be well recovered and the error rate of the recovery s about 10.8%. SPARSE VECTOR RECOVERY The sparsty of the orgnal sgnal n a space s the bass of the sgnal recovery. Let X denotes an orgnal sgnal n R N, then usng a N N matrx Ψ -1 to acqure S, whch s the sparse form of X. -1 S = Ψ X (1) Sparse vector S should be a N 1 vector and only has k nonzero elements (k <<N). Ψ -1 can be FFT transform matrx, DCT transform matrx or others transform matrx. Our goal s measurng only m data (m<n) and usng these m data to recover the orgnal N data, whch can reduce the samplng rate. Therefore, a m N measurng matrx Φ s used: Y = ΦX () where Y s a m 1 vector, whch s also the data that we actually measured. The constructon of Φ s presented n secton Ⅲ. Combnng wth (1) we have: Y = ΦΨ S = ΘS (3) Where Θ s a m N sensng matrx, Θ=ΦΨ. Equaton (3) s the sparse vector recovery model. Accordng to the CS theory, by ths model we can use the reconstructon algorthm to get the recovered sparse vector S and then usng the nverse transformaton to get the recovered orgnal sgnal X (presented n secton Ⅳ). The flow chart of proposed low samplng rate measurement algorthm based on sparse vector recovery s shown n Fg. 1. Fgure 1. The flow chart of proposed low samplng rate measurement algorthm based on sparse vector recovery. 445

3 MESUREING MATRIX In addton to the sparsty of S, the approprate measurng matrx Φ s also mportant to the sparse vector recovery. Accordng to the theory of CS, Θ should satsfes the Restrcted Isometry Property (RIP) condton [6,7], as shown n (4): ΘS 1 ε 1+ ε (4) S where ε (0,1). Drectly usng (4) to judge whether the RIP condton s dffcult. Lterature [8,9] verfed that f the correlaton between Φ and Ψ s weak, then Θ can satsfy RIP condton at a hgh probablty. The correlaton µ between can be denoted as: µ ( Φ, Ψ ) = N max ϕ, ψ (5) 1, j N where φ and ψ s the element n Φ and Ψ respectvely. Lterature [10] ndcate that the correlaton between the Gaussan random matrx and other matrx s weak, therefore the measurng matrx Φ s set as a m N Gaussan random matrx n ths paper. RECONSTRUCTION ALGORITHM Snce m<n, (3) s an underdetermned equaton that cannot be solved drectly. Accordng to the CS theory, S can be well recovered from the measurement Y by solvng l 1 -mnmzaton model [11]. As shown n (6): S = arg mn S s. t. Y = Φ X = ΦΨS (6) The algorthm for solvng ths model manly ncludng convex optmzaton algorthm and greedy algorthm. The accuracy of the convex optmzaton algorthm s hgh, but the operaton s more complcated and the operaton speed s slow. The accuracy of the greedy algorthm s slghtly lower than that of the convex optmzaton algorthm, but the complexty of the algorthm s small and the operaton speed s faster. For the PD measurement, the fast measurement speed s needed. Therefore, n ths paper, orthogonal matchng pursut (OMP) algorthm [1] s used to solve l 1 -mnmzaton model, whch s a greedy algorthm wth fast computaton speed and small algorthm complexty [13]. Fnally, by nverse transformaton the recovered orgnal sgnal X can be acqured, as shown n (7): 0 X = ΨS (7) j 446

4 EXPERIMENTAL VERIFICATION Expermental Scheme An experment s performed n hgh-voltage laboratory. as shown n Fg.. A standard PD emtter s used to produce PD, then a UHF sensor s used to receve the UHF PD sgnal. The dstance between the PD emtter and the UHF sensor s eght meters. Fgure. The pcture of expermental ste. The waveform of the orgnal UHF PD sgnal s shown n Fg. 3. The number of data ponts N s Then a part of the orgnal UHF PD sgnal data s chosen and used to recover the whole orgnal UHF PD sgnal. To evaluate the performance of the recovery, we calculated the error rate σ under dfferent the number of the samplng ponts m. The defnton of σ s shown n (8), where x and x are the element of X and X respectvely. Fgure 3. Orgnal PD sgnal. Fg. 4 shows the performance of the sgnal recovery under dfferent m. From Fg. 4 we can see that, when the number of samplng ponts s 00, whch means, wth only 0% of the UHF PD sgnal data, the recovered PD sgnal has almost no dfference wth the orgnal PD sgnal. When the number of samplng ponts s reduced to 100, the nose of the recovered PD sgnal ncrease, but the recovered sgnal stll contans the man nformaton of the orgnal PD sgnal data. When the number of samplng ponts down to 50, the nose of the recovered PD sgnal s large, but the contour of the orgnal PD sgnal can stll be seen. When the number 447

5 of samplng ponts s reduced to 0, the nose of the recovered PD sgnal s very large. N 1 = = N x x = 1 x σ (8) (a) m=00 (b) m=100 (c) m=50 (d) m=0 Fgure 4. The recovered PD sgnal at dfferent samplng rate. Fg. 5 shows the trend of the error rate as the number of samplng ponts changes. It can be seen from Fg. 5 that when the number of samplng ponts s lower than 50, the error rate s very hgh and the recovered PD sgnal s serously dstorted. As the number of samplng ponts ncreases, the error rate decreases rapdly. When the number of samplng ponts s 100, the error rate drops to 10.8%. Wth ths error rate, the most of the nformaton of PD sgnals can be recovered. When the number of samplng ponts s greater than 300, the error rate s close to zero and the PD sgnal can be accurately recovered. Therefore, wth the use of 10% of the PD sgnal data can realze a satsfactory recovery performance. Ths recovered PD sgnal s acceptable for PD detecton whle the samplng rate s sgnfcantly reduced. 448

6 Fgure 5. The relatonshp between error rate and the samplng rate. CONCLUSIONS Ths paper proposes a low samplng rate algorthm based on sparse vector recovery and get some conclusons: (1) From the effect of the PD sgnal recovery we can see that the recovery accuracy s lower than the theoretcal accuracy of CS algorthm. The man reason for ths result s that there s a lot of nose ncluded n PD sgnal and there are also some errors n the measurement process. In the sgnal recovery process, these noses and errors are further amplfed. () The effect of the recovery s related to the sparse degree of the orgnal PD sgnal n a space. More sparsty wll brng better performance. (3) From the expermental results, only 10% of the PD sgnal data can be used to recover nearly 90% of the orgnal PD sgnal, whch can greatly reduce the samplng rate of PD measurement and therefore reduce the correspondng hardware cost. Therefore, the measurement technology n ths paper s worthy to be used n practcal applcaton. ACKNOWLEDGEMENT Ths work was supported by the State Grd scence and technology project. REFERENCES 1. M. S. Abd Rahman, P. L. Lewn, and P. Rapsarda, Autonomous localzaton of partal dscharge sources wthn large transformer wndngs, IEEE Transactons on Delectrcs and Electrcal Insulaton, vol. 3, no., pp , Hujuan Hou, Gehao Sheng, and Xuchen Jang, Robust Tme Delay Estmaton Method for Locatng UHF Sgnals of Partal Dscharge n Substaton, IEEE Transactons on Power Delvery, vol. 8, no. 3, pp , H. R. Mrzae, A. Akbar, E. Gockenbach, and K. Mralkhan, Advancng new technques for UHF PD detecton and localzaton n the power transformers n the factory tests, IEEE Transactons on Delectrcs and Electrcal Insulaton, vol., no. 1, pp , E. J. Candes, and M. B. Wakn, An Introducton to Compressve Samplng, IEEE Sgnal Processng Magazne, vol. 5, no., pp. 1-30, J. Romberg, Imagng va Compressve Samplng, IEEE Sgnal Processng Magazne, vol. 5, no., pp. 14-0,

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