Miodrag D. Kusljevic

Frequency Estimation of Three-Phase Power System Using Weighted-Least-Square Algorithm and Adaptive FIR Filtering

A new technique for estimation of the instantaneous frequency based on simultaneous sampling of three-phase voltage signals is presented. The structure consists of two decoupled modules: the first is for adaptive filtering of input signals, and the second is for frequency estimation. A suitable and robust algorithm for frequency estimation is obtained. This technique provides better performance, compared with the technique based on a single-phase signal in relation to waveforms with noise. The technique is particularly important when asymmetric sags generate zero voltage in one of the three phases. In addition, it allows the measurement of the instantaneous frequency value of real signals for single- or three-phase systems. To demonstrate the performance of the developed algorithm, computer-simulated data records and calibrator-generated signals are processed. The proposed algorithm has been put to test with distorted three-phase voltage signals.

A simple recursive algorithm for frequency estimation

A new approach to the design of a digital algorithm for local system frequency estimation is presented. The algorithm is derived using the maximum likelihood method. One sinusoidal voltage model was assumed. FIR digital filters used in papers, are used to minimize the noise effect and to eliminate the presence of the harmonics effect. The algorithm showed a very high level of robustness as well as high measurement accuracy over a wide range of frequency changes. The algorithm convergence provided fast response and adaptability. This technique provides accurate estimates with error in the range of 0.005 Hz in about 25 ms and requires modest computations. The theoretical basis and practical implementation of the technique are described. To demonstrate the performance of the developed algorithm, computer simulated data records are processed.

A New Power System Digital Harmonic Analyzer

In this paper, new digital instruments measuring power-quality indicators and harmonic analyzers are developed. A new technique for simultaneous local system frequency and amplitudes of the fundamental and higher harmonics estimation from either a voltage or current signal is presented. The structure consists of three decoupled modules: the first one for an adaptive filter of input signal, the second one for frequency estimation, and the third one for harmonic amplitude estimation. A very suitable algorithm for frequency and harmonic amplitude estimation is obtained. This technique provides accurate frequency estimates with error in the range of 0.002 Hz and amplitude estimates with error in the range of 0.03% for SNR = 60 dB in about 25 ms. The theoretical basis and practical implementation of the technique are described. To demonstrate the performance of the developed algorithm, computer simulated data records are processed. Data of the distribution power system voltage signals are also collected in the laboratory environment and are processed in a newly developed digital PC-based harmonic analyzer. It has been found that the proposed method really meets the need of offline applications. Even more, by using the parallel computation algorithms, this method should meet the need of online applications and should be more practical

A Simple Recursive Algorithm for Simultaneous Magnitude and Frequency Estimation

A new approach in the design of digital algorithms for simultaneous local system magnitude and frequency estimation of a signal with time-varying frequency is presented. The algorithm is derived using the maximum likelihood method. The pure sinusoidal voltage model was assumed. The investigation has been simplified because the total similarity to the state of the problem of dc offset and frequency estimation has been noticed. Finite impulse response (FIR) digital filters are used to minimize the noise effect and to eliminate the presence of harmonic effects. The algorithm showed a very high level of robustness, as well as high measurement accuracy over a wide range of frequency changes. The algorithm convergence provided fast response and adaptability. This technique provides accurate estimates in about 25 ms and requires modest computations. The theoretical bases of the technique are described. To demonstrate the performance of the developed algorithm, computer-simulated data records are processed. The proposed algorithm has been tested in a laboratory to establish its feasibility in a real-time environment.

Simultaneous Frequency and Harmonic Magnitude Estimation Using Decoupled Modules and Multirate Sampling

A number of measurement algorithms apply orthogonal signal components obtained by two orthogonal finite-impulse-response (FIR) filters. The most significant error in orthogonal FIR digital-filter-based measurement algorithms arises due to the FIR filters having different magnitude gains at frequencies other than the nominal power system frequency. In addition, although the FIR filters show complete rejection of harmonics when the power system frequency is equal to the nominal, this is not the case for other values of the power system frequency. To alleviate this drawback, the filter parameters have to be adapted during frequency estimation. Suitable implementations of adaptive filters that allow closed-form calculation of coefficients, such as cascade FIR comb filters and resonator-based filters, are present in the literature. In this paper, the advantages and pitfalls of these two techniques are addressed with regard to computational complexity, coefficient sensitivity problems, and convergence. As a result, an improved and very suitable combined algorithm based on parallel resonators with common feedback combined with an external FIR comb-filter-based module for frequency estimation that is applied on antialiasing-filtered and decimated input signal is proposed. The obtained simulation results allow us to establish the performance of the proposed algorithm by comparing its measurement precision with the results obtained using fast Fourier transform (FFT) implementations. It has been found that the proposed algorithm is suitable for real-time applications.

A Simple Method for Design of Adaptive Filters for Sinusoidal Signals

Filtering of input signals in algorithms for measurement of power system electrical parameters is very important. Filters are used to minimize the noise effect and eliminate the presence of higher order harmonics. In addition to that, a number of measurement algorithms apply orthogonal signal components obtained by two orthogonal finite-impulse response filters. The frequency response of the filters must have nulls at the higher order harmonic frequencies that are expected to be present in the signal and must have a unity gain at the main harmonic frequency. In the case of a time-varying frequency, the filter parameters have to be adapted during frequency estimation. In this paper, a simple method for online design of digital filters for sinusoidal signals is proposed. It is based on closed-form solutions for calculating filter coefficients. A simple linear algorithm for frequency estimation was used, and a derived algorithm for online adaptation of the filter coefficients is computationally very efficient. The number of subsections in the cascade and data window lengths can also be changed, depending on the frequency variations during measurement.

An Adaptive Resonator-Based Method for Power Measurements According to the IEEE Trial-Use Standard 1459–2000

This paper proposes an accurate and computationally efficient implementation of the IEEE Standard 1459-2000 for power measurements. The algorithm has two stages. In the first algorithm stage, the voltage and current signals are processed in parallel, and their spectrums are estimated independently of each other. Signal harmonics are estimated in a wide range of frequency using an efficient algorithm with reduced complexity. The algorithm is based on a recently introduced common structure for recursive discrete transforms and consists of digital resonators embedded in a common negative feedback loop. In the second algorithm stage, the unknown power components and other power quality indices are calculated according to definitions in the IEEE Standard 1459-2000. To demonstrate the efficiency of the proposed algorithm, the results of computer simulations and laboratory testing are presented. The laboratory results show accurate input power component estimates for a nonlinear load with rapid input current amplitude changes. In addition, a simple LabView implementation, based on the point-by-point processing feature, demonstrates the techniques modest computation requirements and confirms that the proposed algorithm is suitable for real-time applications.

A Simultaneous Estimation of Frequency, Magnitude, and Active and Reactive Power by Using Decoupled Modules

A new practical technique for simultaneous local system frequency, magnitude, and active and reactive power estimation from voltage and current signals is presented. The technique consists of two phases using decoupled modules: the first phase estimates the frequency, and the second one estimates the magnitudes and the active and reactive power. The third important part is the adaptive bandpass and low-pass finite-impulse-response (FIR) filters that extract the fundamental and dc components, respectively. The most important point of this paper is the mathematical model that transforms the problem of estimation into an overdetermined set of linear equations. A very suitable algorithm for the aforementioned parameter estimation has been obtained. The algorithm showed a very high level of robustness and high measurement accuracy over a wide range of frequency changes. The algorithm convergence provided a fast response and adaptability. This technique provides accurate frequency estimates with errors in the range of 0.002 Hz and magnitude and power estimates with errors in the range of 0.03% for SNR = 60 dB in about 25 ms and requires reduced computations.

Simultaneous Reactive-Power and Frequency Estimations Using Simple Recursive WLS Algorithm and Adaptive Filtering

A new simple approach to the design of digital algorithm for simultaneous reactive-power and frequency estimations of local system is presented. The algorithm is derived using the weighted-least-square method. During the algorithm derivation, a pure sinusoidal voltage model was assumed. Cascade finite-impulse-response (FIR) comb digital filters are used to minimize the noise effect and to eliminate the presence of harmonics effect. The most important point of this paper is the mathematical model that transforms the problem of estimation into an overdetermined set of linear equations. The investigation was simplified because the total similarity to the state of the problem of the active-power and frequency estimations was noticed. The only difference is the adaptive phase shifter applied to the voltage signal. In addition, coefficient-sensitivity problems of the large-order FIR comb cascade structure are overridden by using a multirate (decimation) digital signal processing technique. Even more, by using antialiasing filters, the parameter estimation accuracy is improved. The effectiveness of the proposed techniques is demonstrated by both simulation and experimental results. The algorithm shows a very high level of robustness, as well as high measurement accuracy over a wide range of frequency changes.

Multiple-Resonator-Based Power System Taylor-Fourier Harmonic Analysis

In this paper, a new approach to the harmonic estimation based on the linear transformation named Taylor-Fourier transform has been proposed. A multiple-resonator-based observer structure has been used. The output taps of the multiple resonators may fix not only the complex harmonic values but also, according to the actual resonator multiplicity, their first, second, third, fourth, and so on, derivatives at the corresponding frequency. The algorithm is recursive, which allows its implementation in embedded environment with limited memory. The estimation technique is suitable for application in a wide range of frequency changes, transient conditions, and interharmonics presence, with benefits in a reduced complexity and computational effort. To demonstrate the performance of the developed algorithm, computer simulated data records are processed.