Power System Harmonic State Estimation and Observability Analysis via Sparsity Maximization

Harmonic state estimation (HSE) is used to locate harmonic sources and estimate harmonic distributions in power transmission networks. When only a limited number of harmonic meters are available, existing HSE methods have limited effectiveness due to observability problems. This paper describes a new system-wide harmonic state estimator that can reliably identify harmonic sources using fewer meters than unknown state variables. Note there are only a small number of simultaneous harmonic sources among the suspicious buses. Traditional observability analysis is extended to general underdetermined estimation when considering the sparsity of state variables. It is shown that the underdetermined HSE can become observable with proper measurement arrangements by applying the sparsity of state variables. The HSE is formulated as a constrained sparsity maximization problem based on L1-norm minimization. It can be solved efficiently by an equivalent linear programming. Numerical experiments are conducted in the IEEE 14-bus power system to test the proposed method. The underdetermined system contains nine meters and 13 suspicious buses. The results show that the proposed sparsity maximization approach can reliably identify harmonic sources in the presence of measurement noises, model parameter deviations, and small nonzero injections

I. Introduction

In recent years, the proliferation of power electronic devices and nonlinear loads in power systems has led to increasing concern about the distortion of the sinusoidal waveform of voltage and current in transmission networks due to harmonic pollution. Harmonic pollution is recognized as an important factor in the degradation of power quality, which may shorten equipment life and interfere with communication and control devices [1]. In consequence, the IEEE Recommended Practice [2] recommends practices for utilities and customers to limit the harmonic contents in power networks. To effectively alleviate harmonic pollution, it is important to identify harmonic sources and estimate the distribution of harmonic voltages and currents by real-time measurements.