A novel instantaneous power factor measurement method based on wavelet transform

Abstract: Power components definitions contained in the IEEE Standard 1459-2000 for unbalanced three-phase systems with nonsinusoidal situations are represented in the frequency domain based on Fourier transform (FT). However, FT suffers from the high computational effort especially when the number of phases increases and it is unable to provide information concerning time content because it provides only an amplitude-frequency spectrum. On the other hand, the discrete wavelet transform (DWT) preserves both time and frequency information while reducing the computational effort through dividing the frequency spectrum into bands and thus overcomes the limitations of FT. In this paper the three-phase power components definitions contained in the IEEE Standard 1459-2000 are reformulated using the DWT and thus redefined in the time-frequency domain. Also in order to study system unbalance, the concept of symmetrical components is defined in the wavelet domain. The results obtained from applying the IEEE Standard definitions and the DWT-based definitions to balanced and unbalanced three-phase systems under nonsinusoidal operating conditions, indicate that the DWT-based definitions are very accurate and the problem of spectral leakages can be reduced by suitable choice of the mother wavelet and the wavelet family. The DWT-based definitions are useful in studying nonstationary waveforms.

Abstract: The proliferation of nonlinear load in the electric power system leads to steady-state waveform harmonic distortion. Since harmonic distortion has harmful effects on the electric power system, there is a need to analyze and hence accurately measure their values which is an issue of great concern especially in a deregulated environment. Conventional Fourier based analyzing tools have some limitations concerning frequency and time resolutions. Although wavelet transform overcomes these limitations, it suffers from the problem of spectral leakage which is related to the choice of the wavelet family and the mother wavelet used in the analysis. In order to minimize these errors, this paper presents an approach to select the most suitable wavelet family and the most suitable mother wavelet to achieve accurate measurement of steady-state harmonic distortion using the discrete wavelet transform (DWT). The proposed algorithm is simple and proves to be accurate when applied to two cases of different distortion level.

Abstract: The definitions of power components that are contained in the IEEE Standard 1459-2000 [IEEE Std. 1459-2000, Definitions for the measurement of electric quantities under sinusoidal, non-sinusoidal, balanced or unbalanced conditions, 2000] are based on the Fourier transform (FT) which is suitable only for the case of stationary waveforms. However, for nonstationary waveforms, the FT produces large errors. Therefore, the power components based on this transform become inaccurate. A new approach based on the wavelet packet transform (WPT) for defining these power components is developed in this paper. The advantages of using the wavelet transform are that it can accurately represent and measure nonstationary waveforms, providing uniform frequency bands while preserving both time and frequency information. In addition, this paper addresses the problem of choosing the most appropriate mother wavelet for power components measurements. The results of applying both approaches to stationary and nonstationary waveforms show that the currently used definitions according to the IEEE Standard 1459-2000 result in large errors for the case of nonstationary waveforms while the proposed approach (WPT based) gives more accurate results in this situation.

Abstract: Three-phase rectifiers with low harmonics and power factor correction have been receiving wide interest in the last years. The proposed method is based on the rectifier with near sinusoidal currents which is called RNSIC and which functions as power factor compensation in a wide range of load currents. The decrease of input current harmonics, below the limits imposed by IEEE 519/1992 and IEC 61000-3-4 international standards, allows the decrease of THD, reduces the reactive power, hence the increase in real power factor. The performance of the proposed RNSIC in power factor correction (PFC) regime is verified by simulation, as well as by experimentation, under different loads.

Abstract: Power quality indices play an important role in decision making in deregulated competitive environments. Useful power quality indices require clear and accepted definitions of power components as well as the RMS values of voltage and current. This is especially true in case of non-stationary distorted waveforms, where neither a frequency-domain–based approach using fast Fourier transform tools nor a time-domain–based approach using real-time data give satisfactory results. Wavelet transform is able to represent any distorted waveform in a time-frequency spectrum while preserving relevant information in both time and frequency domains. Different methods have been proposed in an attempt to define power components in the wavelet domain. This article offers a critical evaluation of the current state-of-the-art concerning this topic. The article also offers conclusions and suggested future work.

Abstract: Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions. In L/sup 2/(R), a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi (x). This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters. Wavelet representation lies between the spatial and Fourier domains. For images, the wavelet representation differentiates several spatial orientations. The application of this representation to data compression in image coding, texture discrimination and fractal analysis is discussed. >

Abstract: Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

Abstract: Existing definitions for power terms in alternating current systems work well for single-phase and three-phase systems where both voltages and currents are sinusoidal with respect to time. This paper clarifies and proposes definitions for power terms that are practical and effective when voltage and/or currents are distorted and/or unbalanced. It also suggests definitions for measurable values that may be used to indicate the level of distortion and unbalance.

Abstract: The recursive pyramid algorithm (RPA) is a reformulation of the classical pyramid algorithm (PA) for computing the discrete wavelet transform (DWT). The RPA computes the N-point DWT in real time (running DWT) using just L(log N/spl minus/1) words of storage, as compared with O(N) words required by the PA. L is the length of the wavelet filter. The RPA is combined with the short-length FIR filter algorithms to reduce the number of multiplications and additions. >

Abstract: This paper provides the theoretical basis for and demonstrates the practical application of power and rms measurements directly from the wavelet transform data associated with each voltage current element pair. The voltage and current wavelet transforms are derived from concurrent measurements using a common orthonormal wavelet basis. The advantage of using the wavelet transform data directly is that it provides the distribution of the power and energy with respect to the individual frequency bands associated with each level of the wavelet analysis. Frequency separation into the various wavelet levels is achieved using IIR filters because their magnitude characteristics are much better than typical FIR filters of equivalent complexity. The IIR polyphase network strategy yields a simpler wavelet filter bank design.