Harmonic Analysis of Type-3 Wind Turbines Subject to Grid Unbalance

The objective of this paper is to adequately model a doubly-fed induction generator (DFIG)-based type-3 wind turbine under grid unbalance by considering not only positive and negative-sequence circuits but also the 3rd harmonic circuit. This 3rd harmonic is a positive sequence component caused by frequency coupling with the negative-sequence 60-Hz component. It is not a zero-sequence component and cannot be got rid of by delta-connected transformers. Hence, accurate modeling is necessary to capture this harmonic component. In addition to modeling, we design an efficient algorithm for steady-state analysis by formulating the steady-state analysis problem as an optimization problem. A set of equality constraints has been formed to reflect the relationship of voltage, current, and power in the ac circuits, the dc circuit, and the different frames. This formulation is defined in YALMIP, a MATLAB interface for optimization problems. The optimization problem is then solved by a nonlinear optimization solver. The results of the steady-state analysis are phasors of harmonic components at steady state. They have been validated by the phasors obtained from Fourier transforms of electromagnetic transient (EMT) simulation results. The paper contributes to both the sophisticated phasor model of DFIG with consideration of grid unbalance and the efficient computing procedure of steady-state analysis by use of advanced solvers.