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A Comparative Study on Phasor and Frequency Measurement Techniques in Power Systems

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A Comparative Study on Phasor and Frequency Measurement Techniques in Power Systems A Comparative Study on Phasor and Frequency Measurement Techniques in Power Systems Aravinth Sridharan Vaskar Sarkar Department of Electrical Engineering Department of Electrical Engineering Indian Institute of Technology Hyderabad Indian Institute of Technology Hyderabad E-mail: [email protected] E-mail: [email protected] Abstract—The objective of this paper is to make a comparative to slow function like expansion planning. Hence, the real- study on different phasor and frequency measurement algorithms time measurement of power system quantities is helpful in available for power systems. The dynamic nature of the power improving the reliability of the power system network. With system signals has made the estimation of frequency and phasors difficult. Over the years, many digital algorithms have been an increase in the usage of power electronic devices and other developed to overcome these difficulties and to provide accurate nonlinear components, there is an increase in the harmonic real-time frequency and phasor measurements. In this paper, four contamination in power systems. It is, therefore, essential for different algorithms for frequency estimation and three different utilities to seek and depend on reliable models for accurate algorithms for phasor estimation are studied and compared. A estimation of phasor and frequency. Supervisory Control and case study is performed by considering a three-phase voltage signal with time-varying amplitude and frequency to verify the Data Acquisition (SCADA) is an existing real-time monitoring effectiveness of these estimation algorithms. and control system that is available for power systems. Due Index Terms—Amplitude, complex valued least squares, dis- to high latency in data flow and slower estimation techniques crete fourier transform, frequency, phase angle, phase locked used, the real-time dynamic variations in power system quan- loop, phasor, polynomial fitting, prony, smart discrete fourier tities are not observed by SCADA. transform. The synchronized phasor measurement over a wide re- NOMENCLATURE gion has led to the development synchrophasor measurement and Wide Area Measurement System (WAMS). The integral Actual signal frequency (rad/s). components of WAMS are the Phasor Measurement Unit Nominal signal frequency (rad/s). (PMU) and Phasor Data Concenterator (PDC). Synchronized ˆ Estimated signal frequency (rad/s). phasor measurement made with PMU provides high speed and Sampling frequency (samples/second). coherent real-time information of the power system that are Sampling window length (in terms of the number of not available in the traditional SCADA systems. The PDC is samples) for the least square estimation. generally used to collect data from several PMUs, rejects bad Number of samples per nominal frequency cycle of data and alignment of time stamped data obtained to create a the input signal. coherent record. Index representing the sampling instant. With the advent of digital processors, the computational Time variable. speed has increased significantly. Now, there is a need for Reference value of the time variable for the phase digital algorithms which can estimate the phasor and frequency angle calculation. accurately in real-time. Some of the available methods in Peak value of a sinusoidal signal. literature include zero crossing [1], wavelet transform [2], Actual phasor. modified zero crossing, and signal demodulation [3]. In pursuit ˆ Estimated phasor by ordinary DFT. of higher accuracy for frequency and phasor measurement, the Δ Signal frequency deviation from the nominal value optimization methods such as least mean square methods [4], (rad/s). Kalman filter [5], and Newton’s method [6] are being used. Δ Sampling time interval (s). These above optimization methods are not widely used in real Actual phasor angle. time application as convergence being the main problem. ˆ Estimated phasor angle by ordinary DFT. In this paper, a comparative study on different phasor and (.) (.) 0 Initial value of . frequency estimation algorithm that are available in power I. INTRODUCTION system is performed. The algorithms are tested with signals having time varying amplitude and frequency to verify their Real-time data of power system quantities has many appli- effectiveness. The algorithms that are employed in this paper cations ranging from rapid control action like relay functioning for frequency estimation include Prony method [7], Polyno- 978-1-4799-5141-3/14/$31.00 ⃝c 2016 IEEE mial Fitting (PF) [3], Complex Valued Least Square (CLS) [8], and Phase Locked Loop (PLL). For phasor estimation, the are considered are expressed with respect to the same time algorithms employed in this paper are Discrete Fourier Trans- variable. This in turn, indicates that the time reference should form (DFT) [9], PLL, and Smart Discrete Fourier Transform be considered to obtain all the voltage and current phasors. The (SDFT) [10]. relative phase angle between the voltage and current phasors The rest of the paper is organized as follows, Section II gives can be directly obtained as they are measured with respect a brief overview about the concept of phasor and time synchro- to the same time reference.Time synchronization in PMU is nization. In Section III, different phasor estimation algorithms provided by the GPS pulse signal. are explained. Section IV is focussed on explaining different The phasor concept was initially developed for pure sinu- frequency estimation algorithms. In Section V, a case study is soidal signal. However, the concept can be extended in the presented with the comparison details of the various estimation form of dynamic phasor for signals whose amplitudes and algorithms that are explained in the previous sections. Finally, phase angles are slowly varying with time. Since, the signal the paper is concluded in Section VI. parameters are varying with time, accurate time stamping of the estimated phasor quantities is required for reconstruction II. CONCEPT OF PHASOR AND TIME SYNCHRONIZATION of the signal. Time stamping is also helpful in comparing the A phasor can be defined as a complex equivalent of a measurements made by different PMUs located at different sinusoidal quantity whose amplitude, angular frequency and locations. The time stamping in PMU is provided by high phase angle are time invariant. The phasor mentioned above accuracy GPS clocks. The techniques that are available for can also be called as static phasor. Consider a sinusoidal input estimating static phasors may also be suitable for dynamic signal of frequency as follows, phasors. ()= cos(()) (1) III. PHASOR ESTIMATION TECHNIQUES ()= + . (2) A. Discrete Fourier Transform Its phasor representation is given by, DFT is a technique used in signal processing to calculate = √ ∕. (3) the amplitude and phase angle of individual signal frequency 2 components. The sinusoidal signal given in (1) is sampled = ( ) Phasor representation is possible only for single frequency times per cycle such that 2 . The discrete time component in a pure sinusoid. In real time systems, a sinusoid representation of the signal in (1) is given by, is often corrupted by harmonics and noise. So, it is necessary []= cos( Δ + ). to extract the single frequency component of the signal (usu- (7) ally the fundamental one) and then represent it by a phasor. The time reference can be set to be static or dynamic in The phasor representation of a signal is defined with respect the phasor calculation. The dynamic time reference is shifted to specific time variable. The time variable is specified with forward by one sampling time step with each new sample respect to a reference time instant. The time reference can be (i.e., = Δ ). On the other hand, in the static case, the defined as instant at which the specified time variable is set to time reference is always maintained at the time origin (i.e., zero. The phase angle given in (3) is measured with respect =0). The phasor representations of a signal with respect =0 to the time reference . Now, consider that the time to the dynamic and static time references are shown below. = reference is shifted to . When the time reference is 1) Dynamic time reference: The phasor representation of shifted, the time variable also changes. The time variable is the signal [] (7) with respect to the dynamic time reference now changed to . The relation between and is given by is obtained as follows. = + . Now, representing (1) with respect to the new time √ −1+ variable , we get, 2 ∑ ˆ []= [ + ]− ()= cos(( + )+) (4) = √ −1+ ()= cos( + + ). (5) 2 ∑ = ˜[ + ]−. (8) The phasor representation of (1) with respect to reference time = instant =0(or = ) is given by, 2 Here, = . Subscript “dr” stands for dynamic reference. = √ ∕{ + }. (6) Signal ˜[] contains [] as well as is polluted with super- 2 harmonics. The value of can be set to zero, if the phasors Time synchronization is required for providing a common are calculated based on the future samples. But, this introduces time reference for phasor measurement made at different a time delay of one cycle in phasor estimation. The value of locations. In power system, the active and reactive power is set to 1 − , when the phasors are calculated based on the flow in the grid are calculated using the power flow equations past signal samples. Equation (8) shows the non-recursive form based on the phasor values of the corresponding voltage and of phasor calculation. A recursive form of phasor calculation current quantities. The voltage
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