The Research of Electric Energy Measurement Algorithm Based on S-Transform

Transcription

1 International Conerence on Energy, Power and Electrical Engineering (EPEE 16 The Research o Electric Energy Measurement Algorithm Based on S-Transorm Xiyang Ou1,*, Bei He, Xiang Du1, Jin Zhang1, Ling Feng1, Chang Ji1 and Wanjun Lei3 1 Sate Grid Chongqing Electric Power Research Institute, No. 8 Huangshan Road, Yubei, Chongqing, 4113, China Sate Grid Chongqing Electric Power Company, No. 1 Zhongshan Road, Yuzhong, Chongqing, 415, China 3 Xi An Jiaotong University, No. 8 The West Road o Xianning, Beilin, Xi'an, 7149, China packet transorm binary classiy the low-requency band and the high-requency band. The bandwidth o the requency band is smaller, the requency components is more single, but excessive allocation band will intensiy the complexity o the algorithmic and increase the algorithm error[1,]. Abstract Considering the present electric energy measurement algorithm with the deect o low accuracy o measurement and unable to separate the undamental wave and harmonic signal power when measurement the electric energy. This paper devises a ast and accurate electric energy measurement algorithm based on S-transorm. Theoretical analysis shows that the S-transorm can separate the signals into many components o dierent requency, without the need or dividing the requency band or many times to measure a harmonic component like wavelet packet algorithm, which greatly reduce the complexity o implementation and the subsequent error.in order to demonstrate the superiority o the method, this paper compares the results o the method based on S-transorm algorithm with the measuring results o using the method o wavelet packet transorm. Based on simulation analysis and experimental veriication shows that, whether it is stationary or non-stationary signals signal, the measurement result o the method based on Stransorm algorithm is greatly superior to the results which are obtained by wavelet packet transorm. Keywords-electric energy measurement S-transorm; harmonic decomposition; FFT I. S-transorm is a signal processing method came up with by R. G. Stockwell in 1996[3], equivalently the short-time Fourier transorm with the normalized gaussian window or the wavelet transorm with phase correction. S-transorm is very it or analyzing the singular signal and the unsteady state signal with its excellent time-requency resolution. Besides, compared with the continuous wavelet transorm, the S-transorm is more precise and has better resolution especially in high requency band. This paper puts orward a electric energy measurement algorithm based on S-transorm decomposition and reconstruction, simulation analysis shows that the algorithm perormance is excellent II. algorithm; S-transorm has the property o lossless inversion. the signal can be translated into a matrix with the inormation o requency and time by the theory o S-transorm algorithm. Then the matrixes containing the inormation o only one requency component can be gained by applying the linear separation on the matrix containing the inormation o the undamental component and the harmonic components change over time. Then the time-domain inormation o the undamental component and the harmonic components can be gained by applying inverse S-transorm on the matrix. The energy o undamental wave and harmonic wave can be gained INTRODUCTION As an important energy commodity, the accurate measurement o electrical energy related to the beneit o the generation side, supplier and the users. But with a large number o power electronic devices used in grid, resulting in a large number o grid harmonic signal, the electric energy metering device produce a great deal o measurement error, which will seriously aect the beneits o the generation side, supplier and the users in the grid and the rationality o the trade. At present, the common electric energy measurement method in the electric system is Fast Fourier Transormation (FFT. Because the FFT integrates the signal on the total timedomain, FFT is unable to analysis the signal locally, the requency spectrum o FFT has little time-domain inormation, only steady state signal can be analysis. So only the statistical property o the signal can be relected by the Fourier spectrum. But or the certain requency in the Fourier spectrum, the time o it begin and the time o it end can not be gained in the Fourier spectrum. So the FFT is not it or non-stationary signal. by the ormula u(k t i( t t. A. S-transorm Frequency Spectrum Decomposition and Time-domain Signal Reconstruction This paper draw out the S-transorm rom the short time Fourier transorm(stft. The deinition o STFT o Signal has been given as (1 : STFT (t, h( g(t e j d (1 In recent years, the method o wavelet packet transorm has been used in electric energy measurement. Compared with the FFT, the method o wavelet packet has the ability o localization analysis, it is very it or detecting the singular signal and the unsteady state signal. The method o wavelet 16. The authors - Published by Atlantis Press ELECTRIC ENERGY MEASUREMENT ALGORITHM BASED ON S-TRANSFORM The S-transorm deinition ormula can be gained by replacing the STFT rectangular unction window with Gaussion window. The Gaussion window is deined as ( : 39

2 t gt ( e ( So, the S-transorm [4] can be deined as (3 : (3 ( t j St (, h( e e d The result matrix gained by S-transorm: any row o the matrix shows the situation o amplitude and phase position change over time o a certain requency, the requency range rom direct current to Nyquist requency, any column o the matrix shows the amplitude and phase position o each requency component at a certain time. So separating each requency component can be realized by extracting the row element which represent each requency component and constituting a new matrix which is the same size o the matrix that aorementioned and applying S-transorm on it. Known rom the analysis above: S-transorm and the converse transorm is very important in metering the energy o each requency individually. Known as (4 : g( t dt e dt 1 ( t Time integration o the S-transorm as (5 : St (, dt ( t [ ( j ] h e e d dt h e e dt d ( t j [ ( ] h( e [ e dt] d j h( e d H( ( t j So, Time integration o the S-transorm is the Fourier spectrum o the signal [4] as (6 : (4 (5 In conclusion, S-transorm and inverse S-transorm can realize the separation o the matrixes representing each requency components and the reconstruction o the timedomain signal representing each requency components. B. Discrete S-transorm and Its Converse Transorm In order to apply the electric energy measurement algorithm in computer system, the S-transorm and its convers transorm need to be discretized as (7: j St (, x( mt ( e d j x( e m( t d j t (7 [ xte ( ] mt ( 1 F [ X( ] g( t I the sampling time is T, the sampling requency is s 1 T, the number o sampling points is N, the requency resolution is F s N. So t n T, m F, v p F. So the discrete S-transorm is (8 : Sn ( Tm, F N 1 p pn j m N X[ p me ] e, m p N 1 1 xk ( T, m N k the discrete converse S-transorm is (9 : m n (8 N1 N1 km 1 j N xk ( T { Sn ( Tm, F} e (9 N C. The Implement o Electric Energy Measurement Algorithm Based on S-transorm The time-domain signal o every requency components can be obtained by the S-transorm and the reverse transorm. I the harmonic voltage and harmonic current is and separately,the active energy o every harmonic in time quantum T is: j h( H( e d [ St (, dt] e j d (6 T n n n discret N 1 W u ( t i ( t dt u[ k][ i k] T (1 k 4

3 The algorithm process o the electric energy measurement algorithm base on S-transorm is shown in Figure I. Voltage signal sampling Current signal sampling S-transor Active energy measurement Timerequency matrix decompositi on S- transorm converse reconstru cting timedomain signal FIGURE I. THE ALGORITHM PROCESS OF THE ELECTRIC ENERGY MEASUREMENT ALGORITHM BASE ON S-TRANSFORM III. SIMULATED ANALYSIS AND EXPERIMENTAL VERIFICATION A. Simulated Analysis The perormance o electric energy measurement based on S-transorm in the situation o steady state signal and unsteady state signal is simulated analyzed in MATLAB1a. The parameter is set as ollows: the requency o undamental wave 5Hz, the period o the undamental wave T.s, sample requency s 8Hz, simulation duration s 8Hz. In order to veriy that S-transorm is more accurate than the wavelet packet transorm, the simulate signal is constituted as in [5], the more accurate method can be ound out by comparing the theoretical value, the result o wavelet packet and the result o S-transorm. 1 Steady-state signal simulation I the input signal and contains 3rd, 5th and 7th harmonic, ut ( 1sin( t 14sin(6 t 1sin(1 t 3sin(14 t (11 t 4T it ( 1sin( t 4.5sin(6 t 4sin(1 t sin(14 t t 4T (1 The voltage waveorm and the current waveorm o every harmonic extracted rom Steady-state signal by S-transorm and its converse transorm is shown in Figure II and Figure III (in order to show the waveorm o the harmonic better, only 1T waveorm is shown in Figure II and Figure III, the result o the active energy measure is shown in Table I Hz voltage reconstruction signal Hz voltage reconstruction signal Hz voltage reconstruction signal Hz voltage reconstruction signal Time t/s FIGURE II. THE RECONSTRUCTION OF STEADY-STATE VOLTAGE SIGNAL FIGURE III. THE RECONSTRUCTION OF STEADY-STATE CURRENT SIGNAL TABLE I. THE SIMULATION DATA OF THE STEADY-STATE SIGNAL ACTIVE ENERGY reque ncy (Hz Hz current reconstruction signal Hz current reconstruction signal Hz current reconstruction signal Hz current reconstruction signal Times t/s Active energy/j o wavele t o S Truthvalue wavelet S (% (% Total Unsteady-state signal simulation The expression o the simulation signals are (13 and (14: 41

4 1sin( t t1t 1sin( t sin(6 t 1T tt 1sin( t sin(6 t ut ( 17 sin(1 t T t 5T 1sin( t sin(6 t 17 sin(1 t 15sin(14 t 5T t4t 1sin( t t1t 1sin( t sin(6 t 1T tt 1sin( t sin(6 t it ( 1.8sin(1 t T t5t 1sin( t sin(6 t 1.8sin(1 t 1.5sin(14 t 5T t4t FIGURE IV. THE RECONSTRUCTION OF UNSTEADY-STATE VOLTAGE SIGNAL (13 ( Hz voltage reconstruction signal Hz voltage reconstruction signal Hz voltage reconstruction signal Hz voltage reconstruction signal.7.8 Time t/s FIGURE V. THE RECONSTRUCTION OF UNSTEADY-STATE CURRENT SIGNAL The voltage waveorm and the current waveorm o every harmonic extracted rom unsteady-state signal by S-transorm and its converse transorm is shown in Figure IV and Figure V. The simulation result o S-transorm applying on unsteadystate signal comparing with the result o wavelet packet and the theoretical value is shown in Table II. TABLE II. THE SIMULATION DATA OF THE UNSTEADY STATE SIGNAL ACTIVE ENERGY Freq uenc y (Hz Hz current reconstruction signal Hz current reconstruction signal Hz current reconstruction signal Hz current reconstruction signal Time t/s Active energy/j o wavele t o S Truthvalue wavelet S (% (% Tota l As known in chart 1, when measuring the active energy o the steady state signal, the result o S-transorm is equal to the theoretical value i taking no account o the round-o error, the accuracy o S-transorm is ar above the wavelet packet transorm. As known in Table II, as or the unsteady state signal, the accuracy o S-transorm is above the wavelet packet transorm too. The result o the simulation shows that, S-transorm can extract each requency components eectively, it is very it or the active energy measurement o the steady state and the unsteady state signal. B. Experimental Veriication In order to veriy the eectiveness o the method mentioned above, a experimental platorm o electrical energy measurement is constructed. The experimental platorm is shown as Figure VI. 4

5 5Hz 15Hz 5Hz FIGURE VIII. THE RECONSTRUCTION OF STEADY STATE CURRENT SIGNAL FIGURE VI. EXPERIMENTAL PLATFORM The experimental platorm is made up o, data processing circuit(using DSP chip TMS3F8335 o TI company, and D/A conversion circuit. The analog signal conditioning and sampling circuit turn the high voltage and large current into low voltage and small current, than a signal satisying the A/D sampling chip s inputting requirement can be obtained ater high requency iltering, A/V transormation and scaling transormation. This is the sampling work o the voltage and current, apply S-transorm algorithm to realize electric energy measurement and is the core cell o the electric energy measurement system, it can output the value o the electric energy; D/A transorm circuit turn the output o the data processing circuit into analog signal, and then show the result on the oscilloscope. 1 Steady state signal I the steady state signals are (15 and (16: ut t t ( 8sin( 4sin(6 3 sin(1 t6 t T it ( 6sin( t 3sin(6 t 1.5sin(1 t t T (15 (16 The waveorm o the signal ater decomposition and reconstruction is shown as Figure VII and Figure VIII, the measure result is shown in Table Ⅲ. TABLE III. THE EXPERIMENTAL DATA OF THE STEADY-STATE SIGNAL ACTIVE ENERGY requen Active energy/j o S cy (Hz Truth-value S (% Total The experimental result shows that, S-transorm can realize the decomposition and reconstruction o the steadystate signal, and it s high measuring accuracy can satisy the requirement o practical application. Unsteady-state signal I the unsteady-state signals are (17 and (18: 8sin( t tt ut ( (17 8sin( t 6sin(6 t 3 T t4t 6sin( t tt it ( (18 6sin( t sin(6 t Tt4T The waveorm o the signal ater decomposition and reconstruction is shown as Figure IX and Figure X, the measure result is shown in Table IV. 5Hz 15Hz 5Hz 15Hz 5Hz FIGURE IX. THE RECONSTRUCTION OF UNSTEADY STATE VOLTAGE SIGNAL FIGURE VII. THE RECONSTRUCTION OF THE STEADY STATE VOLTAGE SIGNAL 43

6 5Hz 15Hz [5] Teng Zhaosheng, Luo Zhikun, Sun Chuanqi,Gao Yunpeng, Tang Qiu. Harmonic Energy Measurement Based on Wavelet Packet Decomposition and Reconstruction Algorithm [J]. Transactions o China Electrotechnical Society, 1, 5(8:-6 FIGURE X. THE RECONSTRUCTION OF UNSTEADY STATE CURRENT SIGNAL TABLE IV. THE EXPERIMENTAL DATA OF THE UNSTEADY-STATE SIGNAL ACTIVE ENERGY requen Active energy/j o S cy (Hz Truth-value S (% Total The experimental result shows that, S-transorm can realize the decomposition and reconstruction o the steadystate signal, and it s high measuring accuracy can satisy the requirement o practical application. IV. CONCLUSION The electric energy measurement algorithm based on S- transorm can extract the harmonic signal o dierent requency accurately and reconstruct the time-domain signal. Then the energy o each harmonic component can be obtained. When measuring the electric energy, the method based on S- transorm compared to wavelet packet can avoid a lot o problems, these problems such as very complex operating to obtain each harmonic component by applying binary average division to requency band many times, or the closer requency can not be separated thoroughly or interere each other, but the S-transorm can well deal it. The simulated analysis and the experimental veriication show that the accuracy o the method based on S-transorm is higher than the method based on wavelet packet transorm both o steadystate signal and unsteady-state signal. So S-transorm can satisy the requirement o present electric energy measurement. REFERENCES [1] Mallat S. A wavelet tour o signal processing[m]. second edition (wavelet analysis & its applications. San Diego: Academ ic Press, [] Julio Ban, Diego R I. A new method or measuremento harmonic groups in power systems using wavelet analysis in the IEC standard ramework[j]. Electric Power Systems Research, 6, 76(4: -8. [3] Hongchun Shu. Application o signal processing in Power Engineering [M].Beijin: China Science Publishing, 9, [4] R. G. Stockwell, L Mansinha and R P Lowe, Localization o the complex spectrum: The S-transorm, IEEETrans. Signal Processing, vol. 44, no. 4, pp , April