Harmonics and Phasor Estimation for a Distorted Power System Signal

The controlling, operating and monitoring of electric devices has been possible because of the knowledge of power system parameters. The relay functionality in power systems is influenced by the two vital power system parameters which are frequency and harmonics. Hence in power systems, phasor estimation is of utmost importance. These computations not only facilitate realtime state estimation, but also improve protection schemes. However, in the presence of power frequency deviation, the phasor undergoes rotation in the complex plane. Interconnection of power grids and distributed generation systems becomes difficult because of this phenomenon. Hence, in this report different algorithms are studied and implemented for the estimation of phasor. The parameters estimated are limited to voltage amplitude and phase, change of frequency and rate of change of frequency. In this thesis, Singular Value Decomposition (SVD) technique and Recursive Least Square (RLS) algorithms are used to estimate the amplitude and phase for different harmonics present in a distorted power system signal. Simple DFT algorithm is used to estimate the phasor variation, change of frequency and rate of change of frequency when deviated from the nominal frequency

Modified fast frequency acquisition via adaptive least squares algorithm

A method and the associated apparatus for estimating the amplitude, frequency, and phase of a signal of interest are presented. The method comprises the following steps: (1) inputting the signal of interest; (2) generating a reference signal with adjustable amplitude, frequency and phase at an output thereof; (3) mixing the signal of interest with the reference signal and a signal 90 deg out of phase with the reference signal to provide a pair of quadrature sample signals comprising respectively a difference between the signal of interest and the reference signal and a difference between the signal of interest and the signal 90 deg out of phase with the reference signal; (4) using the pair of quadrature sample signals to compute estimates of the amplitude, frequency, and phase of an error signal comprising the difference between the signal of interest and the reference signal employing a least squares estimation; (5) adjusting the amplitude, frequency, and phase of the reference signal from the numerically controlled oscillator in a manner which drives the error signal towards zero; and (6) outputting the estimates of the amplitude, frequency, and phase of the error signal in combination with the reference signal to produce a best estimate of the amplitude, frequency, and phase of the signal of interest. The preferred method includes the step of providing the error signal as a real time confidence measure as to the accuracy of the estimates wherein the closer the error signal is to zero, the higher the probability that the estimates are accurate. A matrix in the estimation algorithm provides an estimate of the variance of the estimation error

Efficient Spectral Power Estimation on an Arbitrary Frequency Scale

The Fast Fourier Transform is a very efficient algorithm for the Fourier spectrum estimation, but has the limitation of a linear frequency scale spectrum, which may not be suitable for every system. For example, audio and speech analysis needs a logarithmic frequency scale due to the characteristic of a human’s ear. The Fast Fourier Transform algorithms are not able to efficiently give the desired results and modified techniques have to be used in this case. In the following text a simple technique using the Goertzel algorithm allowing the evaluation of the power spectra on an arbitrary frequency scale will be introduced. Due to its simplicity the algorithm suffers from imperfections which will be discussed and partially solved in this paper. The implementation into real systems and the impact of quantization errors appeared to be critical and have to be dealt with in special cases. The simple method dealing with the quantization error will also be introduced. Finally, the proposed method will be compared to other methods based on its computational demands and its potential speed