Application of two-stage ADALINE for estimation of synchrophasor

Transcription

1 International Journal of Smart Grid and Clean Energy Application of two-stage ADALINE for estimation of syncropasor Ceng-I Cen a, Yeong-Cin Cen b, Cao-Nan Cen b, Cien-Kai Lan b a a National Central University, No. 300, Jongda Rd., Jongli City, Taoyuan County 32001, Taiwan b Asia University, No. 500, Lioufeng Rd., Wufeng, Taicung 41354, Taiwan Abstract Wit te development of smart grid, te accurate estimation of pasor measurement is increasingly significant to elp acieve te reliable transmission and distribution of power system. However, te power system frequency may deviate from its nominal value and lead to estimation errors for te most traditional approaces. To perform te accurate syncropasor measurement, a tecnique based on adaptive linear neural network (ADALINE) is applied. Wit te ig frequency resolution of autoregressive model, te variation of power system frequency can be effectively extracted. Troug te testing results corresponding to different power quality disturbances, te total vector errors of several uncertainty examinations for syncropasor measurement in IEEE Std. C can be maintained in te permissible range. Keywords: Adaptive linear neural network, syncropasor, autoregressive model, total vector error, power quality disturbance 1. Introduction Te application of syncropasors for te wide-area monitoring is one of important tecniques in te protection of power systems. In recent years, te estimation of syncropasors as suffered from interferences of power quality disturbances due to te widespread use of renewable generations and development of microgrids. Te power system frequency deviation, armonics/interarmonics, power quality events would lead to inaccuracy in te estimation of syncropasors wit te conventional fast Fourier transform (FFT) based metods [1]-[3]. In tis paper, a tecnique based on te adaptive linear neural network (ADALINE) is applied to deal wit tis problem. Te ADALINE is an adaptive filter, wic analyzes te power signals wit te Fourier series. Te advantages of ADALINE over te conventional FFT are te computational efficiency wit te recursive mecanism and te capability to track te dynamic trends of power parameters [4]-[6]. However, te estimation of conventional ADALINE would be deteriorated wen te power system frequency deviation and interarmonics are present [7]. Tis is because te decomposition model of ADALINE is still dependent on te Fourier analysis bases. From tis penomenon, it is revealed tat te estimation of frequency is te most important task to te accurate syncropasors. To improve suc problem, an autoregressive (AR) model is applied. Wit te ig resolution for te frequency estimation, te AR model can effectively detect te significant frequency components in a power signal. Since te AR model can be easily implemented wit te recursive mecanism, te analysis structure of ADALINE can be used. Wit te information of significant frequency components obtained in te first stage, te decomposition model of conventional ADALINE in te second stage can be remedied. In tis way, te estimation of syncropasors (including magnitudes and pase angles) would not be interfered wit te power quality disturbances. To verify te performance of developed two-stage ADALINE syncropasor Manuscript received May 14, 2013; revised July 28, Corresponding autor Tel.: ext ; address: q7296@yaoo.com.tw.

2 Ceng-I Cen et al.: Application of two-stage ADALINE for estimation of syncropasor 317 estimator, te evaluation index of total vector error (TVE) and related testing requirements in IEEE Std. C are applied [8]. In addition, several power system simulations and actual field measurements are performed to display te practicality and effectiveness of proposed syncropasor estimator. Wit te developed syncropasor estimator, te benefits can be obtained as follows. 1. Using te AR model to estimate te time-varying frequencies, te resampling process of syncronization is not necessary. 2. Te proposed two-stage ADALINE is not window-based tecnique, so no corrections or windowing issues would be encountered. 3. Te estimation results meet te compliance requirements in IEEE Std. C and te performance of proposed syncropasor estimator would not be interfered wit te power quality disturbances. 2. Solution Mecanism of Two-Stage ADALINE To perform te syncropasor estimation from te power signal contaminated wit power quality disturbances, te signal under analysis can be generally represented in te discrete-time form, y(n), of finite lengt N sampled at te time interval t by H sinusoidal components as H y( n) A ( n)cos( n ( n) t ( n)) (1) 1 were A ( n ) is te time-varying amplitude, ( n ) is te time-varying pase angle, ( n ) 2 f 1( n ) is te time-varying armonic radian frequency, and f 1 (n) is te time-varying power system frequency. After obtaining te amplitude and pase angles, te t armonic pasor Y (n) can be represented as j ( ) ( ( ) / 2) ( n Y n A n e ) (2) In order to evaluate te accuracy of pasor estimation, te TVE between te measured (MEAS) and expected (IDEAL) pasors at a given instant of time n is introduced in IEEE Std. C [8], as given in (3). Y _MEAS ( n) Y _IDEAL ( n) TVE ( n) 100% (3) Y ( n) _IDEAL In te traditional ADALINE metod, te signal model in (1) is furter decomposed as H y( n) A ( n)cos ( n)cos 2 f ( n) nt A ( n)sin ( n)sin 2 f ( n) nt 1 H w ( n)cos 2 f ( n) nt w ( n)sin 2 f ( n) nt (4) were w 2-1 (n) and w 2 (n) are te weigts of te ADALINE, wic can be obtained wit te gradient decent approac in (5), were W(n) = [w 11 (n), w 12 (n),, w 2H-1 (n), w 2H (n)] T, x(n) = [cos2πf 1 (n)nδt, sin2πf 1 (n)nδt,, cos2πhf 1 (n)nδt, sin2πhf 1 (n)nδt] T, α is te learning rate of ADALINE, and e(n) is te estimation error between te actual and measured signals at time instant n. e( n) x( n) W( n 1) W( n) W ( n) W( n) (5) T x ( n) x( n) Ten, te amplitude and pase angle of t armonic pasor can be obtained wit (6) and (7). A w w (6)

3 International Journal of Smart Grid and Clean Energy, vol. 2, no. 3, October 2013 w 1 2 tan w2 1 However, te analysis in te above relationsip of ADALINE is based on te assumption tat te power system frequency is fixed to its nominal value. Once te power system frequency deviation and interarmonics are present, te estimation errors for te syncropasors would be increased. To deal wit tis problem, te two-stage ADALINE structure proposed by autors in [7] can be applied, as sown in Fig. 1. According to relationsip of autoregressive (AR) model, te sampled signal can be written wit linear prediction as [7] a y( n) a y( n m) a y( n m) 0 (8) 0 M M m m m1 m0 were coefficients a m s are real numbers and M is te estimation order of AR model. If it is possible to minimize te estimation error for eac n, te actual data sample and te estimated one will be identical. From [7], it is known tat te coefficients a m s are related to te transfer function of AR model, as expressed in (9). a z a z L a z a (9) were M M1 0 1 M1 M 0 j 2 f z t k e k 1,2,, M K, and f is te armonic frequency, wic is not necessary to be te integral multiple of power system frequency. Terefore, te AR model in (8) can be easily implemented wit ADALINE. Once te correct frequencies are obtained, te armonic pasors can be accurately calculated in te second stage of ADALINE. (7) y(n) (actual signal) first-stage ADALINE prefilter second-stage ADALINE y(n-1) y(n-2) y(n-m) a1 a2 am (measured signal in te first stage) yf - e1 updation algoritm analyze te frequencies for eac component f 1 f 2 f H sin cos sin cos f 1 f 1 f 2 f 2 sin f H w 1 w 2 w 3 w 4 w 2H 1 w 2H ys - e2 cosf H (measured signal in te second stage) updation algoritm Fig. 1. Solution structure of two-stage ADALINE. 3. Performance Evaluation for Proposed Measurement Mecanism To verify te performance of proposed two-stage ADALNE for te syncropasor measurement, several compliance tests listed in IEEE Std. C are performed [8], as sown in Table 1. Te test results wit conventional and proposed ADALINE metods are displayed in Fig. 2. From te comparisons, it is found tat te two-stage ADALINE metod meets te accuracy requirements of syncropasor measurement. Due to te assumption of fixed nominal power system frequency in te analysis model of conventional ADALINE, te estimation related to variations of frequencies in conditions C1, C4, and C5 would result in larger estimation errors.

4 Ceng-I Cen et al.: Application of two-stage ADALINE for estimation of syncropasor 319 Table 1. Compliance tests for syncropasor in IEEE Std. C [8] (a) Fig. 2. Maximum TVE of compliance tests for (a) P class and (b) M class in IEEE Std. C (b) Arbitrary Waveform Generator Examination Oscilloscope Data Acquisition CompactRIO Result Presentation Grapical User Interface Fig. 3. Experimental setup for armonic pasor estimation. Measurement System To realize te effectiveness of armonic pasor estimation, a measurement system based on LabVIEW and National Instruments (NI) CompactRIO is establised, as depicted in Fig. 3. A power signal in (10) is syntesized by te arbitrary waveform generator and extracted troug te analog-to-digital converter on CompactRIO wit sampling rate of 7680 Hz, wic is te integer multiple of nominal power system frequency. To examine te robustness of pasor estimation to te power quality disturbances, te power system frequency is set to be deviated from 60 Hz to 59.7 Hz, and 3rd and 5t armonics are included. vt ( ) sin( ) 0.3sin( ) 0.2sin( ) (10) From te amplitude measurement in Fig. 4, it is found tat tere are sligt influences on te estimated amplitudes wit te conventional ADALINE. Tis is because te power system frequency deviation only introduces very small disturbances for weigts in te calculation of amplitude in (6). In te proposed two-

5 320 International Journal of Smart Grid and Clean Energy, vol. 2, no. 3, October 2013 stage ADALINE, te effect of power system frequency deviation can be perfectly prevented. Due to te fixed nominal power system frequency used in te analysis model of conventional ADALINE, te estimated pase angles would rotate in te complex plane as illustrated in IEEE Std. C , as displayed in Fig. 5 (a), even toug te pase angles in (10) are fixed values. In tis way, te difficulty of pasor identification would lead to inconvenience in te related power system applications. On te contrary, te pase angles can be accurately detected and maintained in te fixed state by using te proposed solution mecanism, as represented in Fig. 5 (b). (a) Fig. 4. Te estimated amplitudes wit (a) conventional ADALINE and (b) proposed two-stage ADALINE. (b) (a) Fig. 5. Te estimated pase angles wit (a) conventional ADALINE and (b) proposed two-stage ADALINE. 4. Conclusions In tis paper, te two-stage ADALINE as been applied for te measurement of armonic syncropasors. Wit te ig frequency resolution of AR model, te accurate frequency information for eac armonic component can be obtained witout te traditional syncronization mecanism in IEC Std [9]. After feeding te extracted frequency information into te second stage of ADALINE, te original structure could perform te syncropasor measurement accurately. Different from te traditional metods illustrated in IEEE Std. C , te estimated armonic pasor wit proposed two-stage ADALINE would not rotate in te complex plane wen te power system frequency deviates from te nominal value. Tis is because variant pase angles would cause inconvenience for te identification of direction of power flow, operation of protective relays, and interconnection of power grids. Terefore, te proposed syncropasor measurement mecanism would provide accurate estimation results for te widearea monitoring. Acknowledgements Te autors would like to acknowledge te financial support by te National Science Council of Taiwan, Republic of Cina, under Grants NSC P for tis work. (b)

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