A Complex Least Squares Enhanced Smart DFT Technique for Power System Frequency Estimation

A complex-valued least-squares (CLS) framework is proposed in order to enhance the accuracy of the smart discrete Fourier transform (SDFT) algorithms for power system frequency estimation in the presence of noise and harmonic pollution. It is first established that the underlying time-series relationship among the consecutive DFT fundamental components employed by the original SDFT algorithms does not hold when noises or unexpected higher order harmonics are present, resulting in suboptimal estimation performances. To eliminate these adverse effects on the frequency estimation, the degree of the relationship breakdown is next quantified via a model mismatch error vector. The CLS technique is then employed to minimize the mean-square model deviation when the SDFT voltage modelling is suboptimal. The proposed CLS-enhanced SDFT (CLS-SDFT) methods are shown to be more accurate than the original ones in heavily noisy and harmonic-distorted environments, typical scenarios in online frequency estimation. The benefits of the SDFT framework are verified by simulations for various power system conditions, as well as for real-world measurements.

I. Introduction

System frequency is a key parameter in the control of generation-load imbalance in power grids; it can be used, for instance, to determine the harmonic contents of currents drawn by nonlinear loads. Accurate frequency estimation is essential, since maintaining the nominal frequency value is a prerequisite for the stability of the grid and normal operation of electrical devices. Considering the power system voltage waveform as a pure sinusoid, the time between two zero crossings is an indication of system frequency [3]. However, in reality, the measured voltages are only available in a noisy or distorted form, and a variety of architectures and algorithms has been developed to cater for these scenarios. These include phase-locked loops (PLLs) [4], [5]; notch filters [6]; least-squares (LS) techniques and their variants [3], [7], [8]; adaptive filtering [9]–[11]; Kalman filtering [12], [13]; Taylor series [14], [15]; and iterative approaches [16]–[18].