Abstract
Many models of phasor measurement units (PMU) have been implemented; however, few dynamic models have been developed when the power system parameters change. It is necessary to use a method that can somehow estimate the frequency and correct the phasors. The conventional way to determine frequency is to detect zero crossings per unit time. However, this method has many drawbacks such as high cost and low accuracy. Also, after the frequency determination, the phasor should be corrected by suitably modifying the algorithm without omitting any data. This chapter presents different estimation techniques such as discrete Fourier transform (DFT), smart discrete Fourier transform (SDFT) that may be used to estimate the phasors. These estimated values would be incorrect if the input signals are at an off-nominal frequency and the phase angles would drift away from the true values. To correct this issue, first of all, the off-nominal frequency has been estimated using different techniques such as least error squares and phasor measurement angle changing, and then it is used to correct the phasors.
TopLiterature Review
In the power system phasor, amplitude, phase angle and frequency are variables which may be critical and used by many power system control and protection applications. The fast and accurate measurements of these variables are still considered in a contemporary topic of research interest. Many phasor estimation algorithms as the Newton method, Kalman filtering and level tracking, least square algorithm (Giray, M.M., & Sachdev, M.S.,1989; Girgis, A.A., & Brown, R.G., 1981) techniques have also been proposed for synchrophasor computations in (Phadke, A. G., & Thorp, J. S., 1988), a raised cosine filter (RCF) is used to compute phasors during power oscillations and dynamics. The RCF filter needs a comparatively large (4cycles) computational time windows. This algorithm has a very slow time response.
Discrete Fourier Transform (DFT) is widely used as phasor estimation algorithm of fundamental frequency (Nguyen, C.T., & Srinivasan, K., 1984; Sachdev, M.S., & Giray, M.M., 1985; Ouadi, A., Bentarzi H., 2009). Due to their good harmonic rejection property conventional DFT algorithm achieve excellent performance when the signal contains only fundamental frequency and integer harmonic frequency components.
Performance of the DFT algorithms deteriorates at off nominal frequencies and in the presence of DC decaying components as will be exposed in chapter 3. The smart DFT algorithm (Gurusinghe, D.R., Rajapakse, A. D., & Narendra, K., 2012, Ouadi, A. et al., 2010), where the sampling approach is maintained at fixed frequency and fixed window length. The power system frequency is estimated then the estimated phasors are compensated as a function of the estimated frequency. The used technique can be extended for accurate phasor of any harmonic (Girgis, A.A., & Brown, R.G., 1981). The lower frequency components, as the DC decaying which may introduce fairly large error in the phasor estimation (Johns, A.T., & Salman S.K., 1995; Phadke, A. G., & Thorp, J. S., 1988). For improving the DFT phasor accuracy, these unwanted components must be filtered using digital band pass filter and then conventional DFT is performed. This will be the issue of chapter 5 for designing the digital band pass filters algorithms able to remove unwanted components.
Key Terms in this Chapter
Phasor Measurement Unit (PMU): Has been defined by the IEEE as “a device that produces Synchronized Phasor, Frequency, and Rate of Change of Frequency (ROCOF) estimates from voltage and/or current signals and a time synchronizing signal”. A common time source (GPS) may be used for synchronization. The resulting measurement is known as a synchrophasor.
Phasors Estimation: Phasors that consists of the magnitude and phase angle of an electrical phasor quantities such as voltage or current of the power grid can be estimated using a different techniques such as the Newton method, Kalman filtering and level tracking, least square Discrete Fourier Transform, Smart Discrete Fourier Transform. PMU can capture samples from a signal waveform in quick succession and reconstructing the phasor quantity in the form of an angle and a magnitude measurement.
Smart Discrete Fourier Transform (SDFT): The Smart DFT algorithm developed by (Phadke, A. G., et al., 1977) is used to estimate correctly the instantaneous frequency and then the phasor amplitude and phase angle.
Discrete Fourier Transform (DFT): Is the algorithm that transforms the time domain signals to the frequency domain components. The DFT phasor calculation has an error when the power system operates at off-nominal frequencies.