Estimation of symmetrical components and their orthogonal components under unknown frequencies and unknown biases

An algorithm to estimate symmetrical components, orthogonal components and amplitudes of each sinusoidal component in three-phase power system signal under unknown frequencies and unknown biases is presented. The algorithm consists of a signal transformation, a biased adaptive orthogonal decomposition (BAOD) and a symmetrical component estimation. The BAOD can be regarded as a combination of a low pass filter and a number of three-phase frequency estimators in parallel. The symmetrical component estimation employs addition and multiplication rather than operations of trigonometry, division and phase shift. The decomposition property and the convergence property were investigated by Lyapunov theorem, integral manifold of slow adaptation and average method. Two design parameters, bandwidth parameter and frequency adaptive gains, give different effects on the convergence property of frequency adaptation and amplitude estimation independently. Simulation results demonstrate the performance of the method.