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Measurement of power quality indices using advanced spectrum estimation methods

Introduction The quality of voltage waveforms is nowadays an issue of the utmost importance for power utilities, electric energy consumers and also for the manufactures of electric and electronic equipment. The proliferation of nonlinear loads connected to contemporary power systems has triggered a growing concern with power quality issues. The inherent operation characteristics of these loads leads to deterioration in supply quality as discontinuities and nonstationarities are introduced to the system. On one hand, these loads may be highly sensitive to the quality of its power source [2] . The voltage waveform is expected to be a pure sinusoidal with a given frequency and amplitude. Spectrum analysis of power-line frequency-distorted sinusoids is an up-to-date problem, closely connected to the power quality measurement. The estimation of the interharmonics is very important for control and protection tasks. To control power quality problems, standards have been established worldwide identifying the various aspects of the problem and defining the acceptable limits of many of its known measures [3] [2] [4] . However, they generally refer to periodic signals which allow an “exact” definition of harmonic components and require only a numerical value to characterize them. When the spectral components are time-varying in amplitude and/or in frequency (as in case of non-stationary signals), a misleading use of the term harmonic can arise and several numerical values are needed to characterize the time-varying nature of each spectral component of the signal. The IEC Standard drafts 61000-4-7 and 61000-4-30 deal with signals which are timevarying. They, for practical purpose, define the harmonic (interharmonic) frequency as an integer (not integer) multiple of the fundamental frequency. There are many different approaches for measuring harmonics, like FFT, application of adaptive filters, artificial neural networks, SVD, higher-order spectra, etc [7] [4] [5] . In this paper the characteristics of power system signal components are estimated using Short-Time Fourier Transform (STFT for comparison with more advanced methods), the Prony model, ESPRIT and root-Music methods. Prony method is a technique for modeling sampled data as a linear combination of exponentials and has a close relationship to the least squares linear prediction algorithms used for AR and ARMA parameter estimation. Recent methods of spectrum estimation are based on the linear algebraic concepts of subspaces and so have been called “subspace methods” [7] The model of the signal in this case is a sum of sinusoids in the background of noise of a known covariance function. Most of the power quality indices used are based on the individual harmonic components of current and voltage waveforms. Conventionality, the Fourier transform