Wavelet, Kalman Filter and Fuzzy-Expert Combined System for Classifying Power System Disturbances

Transcription

1 Proceedings of the 4 th International Middle East Power Systems onference (MEPON ), airo University, Egypt, December 9-,, Paper ID 89. Wavelet, Kalman Filter and Fuzzy-Epert ombined System for lassifying Power System Disturbances.. bdelsalam,*,.. Eldesouy,.. Sallam, Member, IEEE eng.abdelazeem@gmail.com, azzaeldesouy@yahoo.com, aasallam@ucalgary.ca Dept of Electrical Engineering, Suez anal University, Ismailia, 45, Egypt Dept of Electrical Engineering, Port-Said University, Port-Said, 453, Egypt bstract: new algorithm for power system disturbance classification is proposed in this paper. It is a two-stage system that employs the great potentials of the discrete wavelet transform (DWT), Kalman filter and a fuzzy-epert system. For the first stage, the captured voltage waveform is passed through the DWT to determine the noise inside it. The covariance of this noise is then calculated and fed together with the captured voltage waveform to the Kalman filter to provide the amplitude and the slope of this waveform. These are considered as an input to the fuzzy-epert system in the second stage to determine the class to which the waveform belongs. Simulation and eperimental results confirm the aptness and the capability of the proposed system in power system disturbance detection and classification. eywords: Power quality, DWT, Kalman filter, Fuzzy epert system, Power System Disturbance. I. INTRODUTION ny variation in voltage, current or frequency which may lead to an equipment failure or malfunction is potentially a power quality problem. The widespread use of electronic equipment, such as information technology equipment, power electronics such as adjustable speed drives, programmable logic controllers, energy-efficient lighting, have led to a change in the nature of electric loads. These loads are simultaneously the major causes and the major victims of power quality problems. Due to their non-linearity, all these loads cause disturbances in the voltage waveform. One critical aspect of power quality (PQ) studies is the ability to perform automatic power quality data analysis and classification. n important step in understanding and hence improving the quality of electric power is to etract sufficient information about the events that cause the power quality issues. number of techniques have been investigated in literature for automatic classification of different types of power quality events. Such an automated PQ assessment requires a high level of engineering epertise and powerful tools. number of papers based on different techniques for * orresponding author detection and classification of power quality phenomena have been published over the past years. Theoretical foundations of voltage disturbances are for eample described in [-3]. Wavelet analysis has been used for identification of power system disturbances. The use of wavelets permits the study of a signal with different time-frequency resolution. Use of the coefficients of the high frequency decomposition of the discrete wavelet transform (DWT) has been proposed in the literature for identification and estimation of the related parameters of a voltage event [4-6]. In [7] an algorithm based on the energies of decomposed signals from wavelet multi resolution analysis (MR) was proposed to distinguish different classes of power quality events. This algorithm had drawbac that the phase shifts of the signals studied were not considered despite their impact on the results. Using the change in magnitude of the fundamental component of supply voltage, Kalman filter can be employed to detect and to analyse voltage event [8-9]. The results of Kalman filter depend on the model of the system used and the suitable selection of the filter parameters. If the selection of the Kalman filter parameters is not suitable, the rate of convergence of the results will be slow or the results will diverge. Epert systems have been proposed to identify, classify and diagnose power system events successfully for a limited number of events [9-]. Rules based epert systems are highly dependent on if..then clauses. If many event types or features are analyzed, the epert system would become more complicated and riss of losing selectivity would increase. nother drawbac is that these systems are not always portable due to the settings that depend mostly on the designer or operator of the systems for a particular set of events. two stage system for classifying the power system disturbances is proposed in this paper. In the first stage, the captured voltage waveform is passed through DWT to identify its noise. The covariance of this noise together with the captured voltage waveform is fed to the Kalman filter to enhance and speed up its rate of convergence. In the second stage, the outputs of the Kalman filter; the amplitude of the captured voltage waveform and its rate of change with time (slope), are passed through a fuzzy epert system that identifies the class to which the disturbance waveform 398

2 belongs. Several digital simulation results using MTL [] and practical test waveform are presented to satisfy and ensure the capability of the proposed system for classifying the disturbances successfully. II. THE PROPOSED SYSTEM The proposed system which consists of two stages as mentioned above is shown in Fig.. The two stages are performed with each new voltage sample; (i) evaluating a new value of the amplitude and slope using Kalman filter with the help of DWT, (ii) classifying the disturbance using fuzzyepert system according to the evaluated values. Fig. loc diagram for the proposed technique. Wavelet Transform Wavelet transform is a useful tool in signal analysis. The continuous Wavelet Transform (WT) of a signal (t) is defined as [3]. t b = ψ dt (), a X a b ( t) ( a ) t b ψ ( t) = ψ ( ) () a, b a a where ψ(τ) is the mother wavelet, and other wavelets are its dilated and translated versions, where a and b are the dilation parameter and translation parameter respectively, The discrete WT (DWT) alculations are made for chosen subset of scales and positions. This scheme is conducted by using filters and computing the so called approimations and details. The approimations () are the high-scale, low frequency components of the signal. The details (D) are the low-scale, high-frequency components. The DWT coefficients are computed using the equation: X = X = [ n] g [ n] (3) a, b j, j, n Z where a=j, b=j, j N, N. The wavelet filter g plays the role of ψ. The covariance of the details (D) is determined to be considered as an initial input to the Kalman filter.. Kalman Filter Kalman algorithm is applied in order to compute the amplitude of the waveform. The Kalman filtering performs the following operations [4].. First of all, it is necessary to have a mathematical description both of the system and of the measurement. The process will be estimated at time t + based on the nowledge of the a-priori process at time t. + = φk + w (4) Net, the state variables and the stochastic system model will be defined. It is assumed that the signal system under study (voltage signal) corresponds to a sinusoidal signal as is epressed in the following equation: s = sin( ω ΔT + θ ) (5) For the net time step +: s = sin( ω ( + ) Δ + ) (6) + T θ onsidering the state variables as the following: cos( θ ), = = sin( ) (7) θ, The following relationship can be obtained: = + = (8) + where ω is the angular frequency =π5 rad/s, and T is the sampling interval. onsequently, the measurement at time + may be related with the state variables at time +, as: T sin( ω( + ) ΔT ) z = + cos( ω( + ) ΔT ) = H + + (9) where H is the Matri giving the ideal connection between the measurement and the state vector at time t. The measurement of the process is assumed to occur at discrete points in time in accordance with the linear relationship: z = H + v () where v is the measurement error which is evaluated by DWT. The random process can be modeled by: ˆ ˆ = φ + () The estimation of the process covariance, P, in the net time step + can be obtained by the following equation: T P + = φ P φ + Q () Q is the covariance matri of w and is assumed to be equal to the identity matri in this model. The Kalman gain, K, can be computed as: T ( H P H + R ) K (3) T = P H R is the covariance matri of v. the value of R is not assumed but it is considered the covariance of the details coefficients of the first level of DWT of the measurement signal. With this information the state estimation can be updated nowing the measured ˆ ˆ + K z H ˆ (4) ( ) = 399

3 and the process covariance can be updated according to: P = ( I K H ) P (5) The waveform amplitude is directly computed at any time instant from the estimated state variables as follows: = ( + ) (6) and the slope is obtained from the following relationship: S = ( ) (7) ΔT where:, - are the waveform amplitudes at the time instants and - respectively..3 Fuzzy-Epert Systems It is usually appropriate to use fuzzy logic when a mathematical model of a process doesn't eist or does eist but is too difficult to encode and too comple to be evaluated fast enough for real time operation. The accuracy of the fuzzy logic systems is based on the nowledge of human eperts; hence, it is only as good as the validity of the rules. s the power system data is highly uncertain and the power disturbance monitoring is a pattern classification problem, the fuzzy epert system approach can be adopted for this problem. The outputs of the Kalman filter are considered as inputs to the fuzzy-epert system to classify the different waveform disturbances. The input variables membership functions of the fuzzy epert system are shown in Figs. & 3. For classifying the disturbance waveforms, five fuzzy sets are chosen for the amplitude (), the first input of fuzzy-epert, designated as VS (very small amplitude), S (small amplitude), N (normal amplitude), L (large amplitude), and VL (very large amplitude). The slope (S), the second input of fuzzy-epert, has three fuzzy sets that are designated as PS (positive slope), NS (negative slope) and ZS (zero slope). Degree of membership VS S N L VL amplitude (pu) Fig. Input amplitude membership function The output membership function is defined by five sets as shown in Fig. 4. These sets are designated as interruption, sag, normal, swell, and surge. ny output value which is not belonging to these sets represents the distortion. The crisp output of the fuzzy system can assume values between. and., where.5» Interruption.5» Sag.5» Normal.75» Swell.95» Surge. Degree of membership NS ZS Fig. 3 Input slope membership function Degree of membership Interruption Sag Normal Swell Surge Fig. 4 Output membership function The brief rule sets of fuzzy epert system are below:. If amplitude is VS and slope is PS) then output is INTERRUPTION.. If amplitude is VS and slope is ZS then output is INTERRUPTION. 3. If amplitude is VS and slope is NS then output is INTERRUPTION. 4. If amplitude is S and slope is NS then output is SG. 5. If amplitude is S and slope is ZS then output is SG. 6. If amplitude is S and slope is PS then output is SG. 7. If amplitude is N and slope is ZS then output is NORML. 8. If amplitude is N and slope is NS then output is NORML. 9. If amplitude is N and slope is PS then output is NORML.. If amplitude is L and slope is PS then output is SWELL.. If amplitude is L and slope is ZS then output is SWELL.. If amplitude is L and slope is NS then output is SWELL. 3. If amplitude is VL and slope is PS then output is SURGE. 4. If amplitude is VL and slope is ZS then output is SURGE. 5. If amplitude is VL and slope is NS then output is SURGE. III. SIMULTION RESULTS The eample taen for the study is a simple power system consisting of a generator supplying a power networ that comprises a short transmission line section and three loads (normal, heavy, and nonlinear loads) at the point of common coupling (P). The heavy and nonlinear loads are connected to the system through a circuit breaer as shown in Fig. 5. Different power quality events have been generated using the power system simulation tools, MTL - Simulin, Fig. 6. PS 4

4 Fig.5 System configuration of the model used for testing. The generated signals are mied with random white noise of zero mean and the signal to noise ratio (SNR) is 3 db. Each generated waveform consists of 5 cycles of a voltage waveform sampled at a rate of 6.4 Hz, which is equal to 8 samples per cycle. The following case studies are presented to illustrate the aptness of the proposed system: Fig. 7 Voltage interruption: waveform, slope and classification system output voltage source Resistive load To File voltage.mat Z_source Universal ridge + - P Vabc Demu a b c. a b c Scope Load a b c. Z_feeder three phase short circuit fault Heavy load single line to ground fault Fig. 6 MTL simulation bloc diagram of the simulated system Voltage Interruption: an interruption may be seen as a loss of voltage on a power system. Such disturbance describes a drop of 9-% of the rated system voltage for duration of.5 cycles to min. waveform of the voltage interruption generated by a 5 cycle three phase short circuit fault at P is shown in Fig. 7. Output of the Kalman filter, slope, is shown in Fig. 7. The output of the fuzzy epert system is shown in Fig. 7. It is observed that the proposed system can accurately detect the interruption in the distorted waveform. The tracing error, which is defined as the difference between the actual and the estimated values of the amplitude voltage, is found to be less than.8%. Voltage Sag: voltage sage is a decrease of -9% of the rated system voltage for duration of.5 cycles to min. The sag disturbance is generated by the occurrence of a single line to ground fault for 5 cycles at the end of the short transmission line. The results are shown in Fig. 8. The tracing error of results is less than.%. Voltage Swell: in the case of voltage swell, there is a rise of to 9% in the voltage magnitude for.5 cycles to min. The swell is generated by disconnecting the heavy load for 5 cycles. From the results depicted in Fig. 9, the proposed system clearly detects and classifies the swell disturbance. The tracing error is less than.4% Fig. 8 Voltage sag: waveform, slope and classification system output Fig.9 Voltage swell: waveform, slope and classification system output. Voltage surge: the surge occurs on disconnecting the heavy load for one-quarter cycle as shown in Fig., where the amplitude is suddenly increased from to 3 p.u. Such a distorted waveform is tested by the proposed system and the 4

5 results are shown in Fig., and (d). The tracing error of the magnitude is less than.5% Fig. Voltage surge: waveform, slope and classification system output Voltage distortion: distortion of the voltage waveform is generated by connecting the nonlinear load for 5 cycles where the harmonic is generated. The original distorted waveform and the corresponding Kalman filter and fuzzy epert system outputs are shown in Fig.. Signal Fig. of the captured voltage. The voltage sag occurs at t=.s for 5 cycles while the outage is started at t=.3 s and ends at t=.4 s. The swell is initiated at t=.6 s and persists for 5 cycles while the harmonic distortion is generated at t=.8 s for 5 cycles. The output slope of the Kalman filter is shown in Fig. 3, while the output of the fuzzy epert system is shown in Fig. 4. omparing the output waveform of Fig. 4 with the output membership function, Fig. 4, it is observed that the proposed system has successfully detected each disturbance included in the captured voltage waveform with an average tracing error of less than.5% Fig. 3 of the captured voltage.75 Fig. Voltage distortion: waveform, amplitude, slope and (d) classification system output..5 omparing the results of the proposed system shown fin Figs. 7 through with the output membership function, Fig. 4, it is observed that each category of the simulated waveforms is successfully detected and classified. nother case study is reported to test the overall performance of the proposed system. In this case, the voltage waveform at P which is captured for fifty cycles and consists of sag, interruption, swell, and harmonic distortion as shown in Fig. is applied to the proposed system Fig. 4 Output of fuzzy-epert system In addition, the proposed system is computationally simple in comparison to Fourier linear combiner based approach [9] and yields classification in short time as it needs two samples to evaluate the amplitude and slope of the captured voltage waveform instead of the whole cycle as in [9]. The Kalman filter, on the other hand, yields more accurate results as the initial value of the measurement error covariance is not assumed and instead it is accurately etracted with the help of DWT. 4

6 IV. EXPERIMENTL RESULTS Fig. 5 shows a test waveform that is obtained from the IEEE Project Group 59. [5]. The sample frequency used is fs=/5 36 Hz, or 56 samples per 6 Hz cycle. The proposed technique is applied on this test waveform. Kalman filter is used to etract the fundamental frequency amplitude and its slope as shown in Figs. 6 & 7 from the practical waveform. The fuzzy epert system output shows that the test waveform contains a voltage sag disturbance, Fig. 8, and there are not harmonic contents in it Fig. 5 The practical captured waveform. amplitude (pu) Fig. 6 The amplitude of the practical waveform Fig. 7 The amplitude slope of the practical waveform V. ONLUSIONS system based on the DWT, Kalman filter and fuzzyepert system is proposed in this paper for classifying power system disturbances. The DWT is used to etract the noise of the captured waveform. The covariance of this noise is calculated and applied to the Kalman filter with the captured voltage waveform to improve its performance. The Kalman filter is then used to estimate the amplitude and the slope of the waveform which become the inputs to the fuzzy epert system for classification of the waveforms. Several simulation and eperimental tests have been conducted to validate the performance of the proposed system. The results show that the proposed system performs very well in the detection and classification of various power system disturbances. REFERENES [] M. H. J. ollen, "Understanding Power Quality Problems, Voltage Sags and Interruptions". Piscataway, NJ: IEEE Press,. [] M. H. J. ollen and I. Y. H. Gu, "Signal Processing of Power Quality Disturbances", Wiley_IEEE, 6 [3] ngelo aggini, "Handboo of Power Quality" John Wiley & Sons, 8 [4]. Elmitwally, S. Farghal, M. Kandil, S. bdelader, and M.Elateb, Proposed wavelet-neurofuzzy combined system for power quality violations detection and diagnosis, Proc. IEE, Gen. Transm. Distrib., vol. 48, no., pp. 5, Jan.. [5] S. Santoso, J. P. Edward, W. M. Grady, and.. Parsons, Power Quality Disturbance Recognition Using Wavelet-ased Neural lassifier Part : Theoretical Foundation, IEEE Trans. Power Del., vol. 5, no., pp. 8, Feb.. [6] S. Santoso, J. P. Edward, W. M. Grady, and.. Parsons, Power Quality Disturbance Recognition Using Wavelet-ased Neural lassifiers-part : pplication, IEEE Trans. Power Del., vol. 5, no., pp. 9 35, Feb.. [7] Z. L. Gaing, "Wavelet-based neural networ for power disturbance recognition and classification" IEEE Trans. Power Del, Vol. 9, No. 4, pp , October 4. [8] E. Perez and J. arros, " Proposal for On-Line Detection and lassification of Voltage Events in Power Systems", IEEE Trans Power Del, vol 3, no. 4, pp. 3-38, October 8. [9] P.K. Dash, S. Mishra, M.M.. Salama,.. Liew, lassification of Power System Disturbances Using Fuzzy Epert System and Fourier Linear ombiner, IEEE Trans. Power Del, Vol. 5, No., pp , pril. [] M. Reaz, F. hoong, M. Sulaiman, F. Yasin and M. Kamada, " Epert System for Power Quality Disturbanc lassifier", IEEE Trans Power Del, vol, no. 3, pp , July 7. [] E. Styvatatis, M. H. J. ollen and I. Y. H. Gu, "Epert System for lassification and nalysis of Power System Events", IEEE Trans Power Del, vol 7, no., pp , pril. [] Power System locset. User`s Guide, The Math Wors, Inc., Natic, M,. [3] Stephane Mallat, ' Wavelet Tour of Signal Processing' cademic press, US, 999. [4]. Girgis, W. hang, E. Maram, " Digital Recursive Measurement Scheme for on-line Tracing of Power System Harmonics", IEEE Transactions on Power Delivery, Vol. 6, No. 3, pp. 53-6, July 99. [5] Fig. 8 Fuzzy-epert system output 43