Enhanced DFT Algorithm for Estimation of Phasor by PMU under Power Quality Events

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Volume 114 No. 12 2017, 515-523 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.

1 Volume 114 No , ISSN: (printed version); ISSN: (on-line version) url: ijpam.eu Enhanced DFT Algorithm for Estimation of Phasor by PMU under Power Quality Events Munukutla Naga Chaitanya 1 and M. B. Murali Krishna 2 Akula Durga 3 and Gajambekar Akshay Kumar 4 1 Assistant Professor, Department of EEE, K L University, Guntur, Andhra Pradesh, India. naga.6174@gmail.com 2,3,4 UG Student, Department of EEE, K L University, Guntur, Andhra Pradesh, India. Abstract Due to the increased penetration of distributed generators into the distribution system as well as due to various power electronic devices in the power network, there exists strong disturbances in electrical waveforms i.e., in amplitude,phase and frequency. These fluctuations need to be supervised and monitored for efficient energy management, safety and also protection purposes. Nowadays, this task is performed by Phasor Measurement Units (PMUs), which measure the phasor of voltage and current waveforms on a common timescale synchronized to the Coordinated Universal Time (UTC). Phasor Measurement Units (PMUs) are also expected to quickly measure fundamental frequencies and rate of change of such frequencies (ROCOF) by accurate parameter estimation algorithms. The commonly used algorithm for estimation of phasor is Discrete Fourier Transform (DFT). But it is observed that, its performance is effected by harmonic environments. In this paper, DFT algorithm was modified to improve its phasor estimation capability under such harmonic environments. Then, the performance of proposed algorithm is compared with the Least Square Error (LSQ), Recursive DFT algorithm. Simulation Results are also reported. Key Words and Phrases: Power quality disturbances, Phasor measurement unit (PMU), Recursive DFT algorithm, FIR filters

2 1 Introduction Phasor Measurement Units (PMUs), since their introduction in 1980s gave impetus to large-scale implementation of wide-area measurement systems (WAMS) using PMUs and phasor data concentrators (PDCs) in a hierarchical structure. Initially PMU technology applications are mostly concerned with the validation of system models, accurate postmortem analysis. With widespread application, they are able to perform linear state estimation and track dynamic phenomena in real time. Due to the utilization of time synchronized sampling for PMUs located over the entire power system, we are able to obtain simultaneously the individual phasor from individual PMUs located at remote areas also at same instants of time. This lead to the PMUs utility to improve protection and control functions [1]. In Power Systems, high voltage transmission and distribution lines are important links from the generating units to the end users. Protection of these lines using relays plays a vital role from the view point of security, economics and quality of power supplied. Hence correct action of relays is important in power systems. Due to DC offset present in fault current waveforms, the line relays tends to overreach. So, these DC offset components has to be removed from these waveforms [2]. As per [3] DFT based phasor estimation is the most commonly used technique in currently available PMUs. Two classifications of power system transients are electromagnetic transients and electromechanical transients. Electromechanical transients are characterized by magnitude and phase angle modulation of power system voltages and current with low frequency signals. They corresponding to the movement of rotors of large electric machines around the synchronous speed. Electromechanical transients are characterized by step changes in the magnitude and phase angles of the waveform. They contain sustained harmonics and non-harmonic content. Disturbances in phasor estimations due to harmonics can be eliminated by DFT based phasor estimators. With the advent of advanced microcontrollers and digital signal processors (DSPs) in relay implementation, DFT filter has gained importance for measuring fundamental and harmonic content of a waveform. DFT filter can be implemented in recursive and non-recursive forms. Recursive DFT is commonly used phasor estimation algorithm.errors are introduced during phase and magnitude estimation using DFT filter due to sampled signal dynamics and frequency deviations [4]. Different power quality events recorded at an industrial site consisted of interruption, sag, swell, harmonics, transients, system imbalance, frequency deviations and combinations of these disturbances [5].In [6] performance of recursive DFT when subjected to off-nominal frequency variations, decaying DC offsets, harmonics, inter-harmonics and noise was analyzed. Total Vector Error (TVE%) of recursive DFT under such scenarios is also observed. Based on the analysis, a frequency tracked phasor estimation algorithm-1 was developed in [7].This is done by estimating the fundamental frequency and then changing the nominal frequency of DFT, when there is a change in the system frequency. In this paper, Discrete Fourier algorithm is modified and novel algorithm is proposed. Basic recursive relations of Discrete Fourier algorithm are given in section II. Section III gives introduction to FIR filters and proposes the novel phasor estimation algorithm. Section IV includes the discussion on the results obtained from simulations. Finally Section V concludes up with the key points analyzed in this paper

3 2 Recursive DFT Algorithm The Discrete Fourier Transform (DFT) is widely used method for phasor estimation and is given by X (k) = 2 N N 1 x(k + n). e j(2πn/n) ( 2a) n=0 Here k is the sample number in the data window and N is the number of samples in a cycle of the fundamental frequency component. Power system frequency is time varying as the loads are not constant. Frequency estimator is used to track the changes in input signal frequency for accurate phasor measurement. As in real time, new samples keep on streaming into the digital device for phasor estimation; considerable amount of computational time can be saved by relating the DFT calculated in one data window to the new data window. A new data window is formed by considering the newest sample and removing the oldest sample from the old data window.hence after modifying the DFT for continuous fashion and also after phase adjustment the recursive phasor estimate is given by N 1 X N+r = {e jθ X N+r N (x N+r x r )e jrθ n=0 N 1 X N+r = {X N+r N (x N+r x r ) e jrθ } n=0 From [8],the way to measure the frequency and ROCOF for a sinusoidal signal given as x(t) = X m cos(θ(t)) (2b) (2c) The frequency is defined by f(t) = 1 2π (dθ(t) dt ) (2d) The rate of change of frequency (ROCOF) is given by ROCOF(t) = d ( 1 2π (dθ(t))) dt = df(t) dt dt We consider Total Vector Error (TVE) as the performance criteria for the proposed algorithm. It is an index which shows us the vector error between the theoretically computed phasor and the estimated one at a particular instant of time. It is defined as the square root of the squared sum of error between the real and imaginary parts of the estimated phasor to the actual phasor. It is given by the following equation: (2e) TVE = (X r(n) X r ) 2 + (X i (n) X i ) 2 X r 2 + X i 2 (2f) Here X r (n) is the real part of the estimated phasor, X r is the real part of the actual phasor, X i (n) is the imaginary part of the estimated phasor, X i is the imaginary part of the actual phasor at a particular instant n

4 3 Proposed Algorithm-2 It has been observed from the simulation studies in [6] that the factors affecting the phasor measurement process are observed to be: Off-nominal frequency variations due to power imbalance in the system. Decaying DC offsets which occur during switching actions or post fault conditions due to predominant inductiveness of power system. Inter-harmonic components and high frequency noise introduced due to sudden change in amplitude of the parameter under measurement. Here, the proposed algorithm targets the uncertainty in measurement due to interharmonic and decaying DC offsets. Errors due to decaying DC offsets can be reduced by passing the samples through DC rejection filters before computing the DFT. If the samples are passed through band pass digital filter which extract only fundamental components, the errors due to DC offsets, inter-harmonic components and high frequency noise may be reduced to greater extent. So, initially the sampled signal is passed through band pass finite impulse response (FIR) filter where unwanted components are filtered. Input Signal A/D Converter Digital Filter (Band Pass) Phasor Estimator (RDFT) f(tracked frequency) Phasor Components Fig.1: Block diagram of Proposed Algorithm-2 Then the filtered signal is sent for phasor estimation by RDFT algorithm. Here the pass band is adjusted around the system nominal frequency (i.e., 50 Hz) to obtain good results. Fig.1 shows the block diagram of proposed algorithm-2 The system function of FIR filter is H(z) = M 1 n=0 h[n]z n (3a) Where M is the length of the filter, and h[n] is the impulse response of the filter We have considered window method for the design of FIR filter. Although any of the Rectangular window, Hanning window, Hamming window, Blackman window, Kaiser window can be chosen as windowing function. But due to the flexibility to yield various transition widths and near optimum stop band attenuation Kaiser window is chosen. Kaiser window is defined by the formula [9]: 4 518

5 I 0 [β 1 (1 2n m 1 )2 W(n) = 0 n m 1 3(b) I 0 (β) I 0 [.]is the modified zero order Bessels function β is a parameter that depends on M M is the filter length. 4 Results and Discussions A. Parameter Selection In order to test the performance of the Proposed Algorithm-2 for phasor estimation, the technique is programmed using a digital computer in MATLAB programming environment. An Analysis was conducted using a disturbance waveform generated in simulation platform. The data samples are taken at 600 Hz, of the voltage waveform. In order to study the performance of the algorithm in section III, 34% third harmonic, % fifth harmonic, 0.23 % inter harmonic and 1 % random noise of fundamental was added. The fundamental frequency of the system is set to 50Hz. Following are the parameters selected for the design of band pass digital filter: A Sampling Frequency of 600 Hz. Pass band cut-off frequency is 0.132π to 0.202π Stop band cut-off frequency is 0.033π to 0.267π Stop band attenuation greater than or equal to 40dB Pass band ripple is 0.01 Stop band ripple is 0.01 Performance of the proposed algorithm-2 will be studied in preceding subsection. B. Performance Evaluation The synthetic voltage signal generated for testing the algorithm is given below: v(t) = 399.0e t/ sin(2πf 0 t + pi/6) sin(6πf 0 t + pi/3) sin(10πf 0 t + 5pi/6) + sin(2πf h t) + e(t) Where f h is Hz and e(t) is the random noise 5 519

6 Fig 2a Fig 2b Fig 2c Figure.2a,2b,2c: Plot of Gain-Response of band pass filter and frequency spectrum before and after filtering Fig.2 shows the gain-frequency response of the multi pass band filter and frequency spectrum before and after filtering. It is observed from the frequency spectrum, the designed band pass filter effectively filtered inter-harmonic components, decayind DC offsets and high frequency noise in the contaminated signal. Estimated Phasor magnitude, angle and TVE obtained with LSQ, RDFT and Proposed Algorithm-2 as phasor estimator Fig 3a 6 520

7 Fig 3b Fig 3c Figure.3a,3b,3c: TVE for LSQ, RDFT, Proposed Algorithm-2 during decaying DC offset and harmonic distortions. Plot of Phase angle, Magnitude shown in Fig.3.The maximum TVE(%) for LSQ, RDFT, Proposed Algorithm-2 are 0.71%, 3.75%, 1%.From this, it can be inferred that the Proposed Algorithm-2 gives a better phasor estimate when compared to RDFT algorithm but LSQ algorithm shows better performance over the described algorithms. But the transient oscillations in proposed algorithm-2 are less when compared to other algorithms. From the analysis of above results, Max.TVE (%) of LSQ or Proposed algorithm-2 is 1% which is in compliance with IEEE C standard [10] for phasor estimation 5 Conclusion In this paper, recursive DFT algorithm has been modified by providing a band pass digital filter at its input. Then, the performance of the proposed algorithm is evaluated by a synthetic voltage signal generated. Although the proposed algorithm shows a better performance in estimating the phasor, there is an inherent difficulty of properly tuning the parameters of the digital filter

8 6 References WaldemarRebizant,JanuszSzafran,AndrzejWiszniewski, Digital Signal Processing in Power System Protection and Control, Springer Publication. Jaime De La Ree,Virgilio Centeno,James S. Thorp, A. G. Phadke, Synchronized Phasor Measurement Applications in Power Systems, IEEE Trans. On Smart Grid,Vol.1,No.1,pp.20-27,June A.G. Phadke and B. Kasztenny, Synchronized phasor andfrequency measurement under transient conditions, IEEETrans. Power Del., vol.24, pp , Jan Hatem A.Darwish and MagdyFikri, Practical Considerations for Recursive DFT Implementation in Numerical Relays,IEEE Trans.PowerDel.,Vol.22,Jan/07. T. Lin and A. Domijan, Recursive algorithm for real-time Measurement of electrical variables in power systems, IEEE Tran. Power Del., vol. 21,pp.15-22, Munukutla Naga Chaitanya, Dr. G.V. Siva Krishna Rao Performance Evaluation of Recursive DFT as Phasor estimator in PMUs under Power Quality Disturbances, IJERT, Volume 4, Issue 9, Sep Munukutla Naga Chaitanya, Dr. G.V. Siva Krishna Rao Frequency Tracked Phasor Estimation Algorithm for PMU during Off-nominal frequency Variations, IJPSM, Issue 1, Jun A.G.Phadike, J.S. Thorp, and M. G. Adamiak, A new measurement technique for tracking voltage phasors, local system frequency, and rate of change of frequency, IEEE Trans. On Power Systems and App., Vol. PAS-102, pp, , Vinay K.Ingle, Jhon G.Proakis, Digital Signal Processing Using MATLAB V.4, Book Ware Companion Series. IEEE Standard for synchrophasor measurements for power systems, IEEE Standard C ,Dec

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FREQUENCY TRACKED PHASOR ESTIMATION ALGORITHM FOR PMU DURING OFF-NOMINAL FREQUENCY VARIATIONS

TJPRC: International Journal of Power Systems & Microelectronics (TJPRC: IJPSM) Vol. 1, Issue 1, Dec 2016, 51-58 TJPRC Pvt. Ltd. FREQUENCY TRACKED PHASOR ESTIMATION ALGORITHM FOR PMU DURING OFF-NOMINAL