Instantaneous harmonic detection based on composite observer for distort grid with DC bias and variable frequency

This paper presents a real-time detection method for harmonic extraction, which can deal with sudden fluctuation of amplitude, phase, and frequency of the fundamental wave, and has advantages of rapid speed and high accuracy. First, using the Least Squares method with forgetting factor to extract phase and frequency of the fundamental wave, then the phase information is used to design a linear time-varying observer, which is based on a state space model constructed from the grid signal and harmonic components, to estimate state variables and realize the extraction of DC bias and harmonics. Taking Lyapunov function and Lasalle invariant set principle to prove stability and convergence of the proposed observer. Additionally, the input observer method and the definition method are given for DC bias. Simulation and experimental results show that even if the power grid signal is distorted, the method can quickly and accurately extract harmonic components, and it is still robust in the case of white noise, inter-harmonics or high-order harmonics.