Voltage stability modeling and analysis of unbalanced distribution systems with wind turbine energy systems

This paper presents a new method to asses voltage stability of unbalanced distribution systems with wind turbine generation systems (WTGSs). In the voltage tracing process, the Lagrange linear and quadratic interpolations have been applied to predict voltage magnitudes and phase angles. The predicted solutions are then corrected using the unbalanced three-phase forward/backward power flow solver. The solution process continues until the maximum loading conditions of the system under study are reached. The salient advantage of the method is avoiding construction of massive augmented three-phase Jacobian matrix of the classical Newton-Raphson method. The direct connected WTGSs have been modeled with sufficient details to account for distribution system unbalances and slip variations. Substation transformer tap-setting for voltage regulation is also considered. Voltage collapse scenarios are investigated for unbalanced systems using various unbalanced radial feeders. The results show the robustness of the proposed continuous power-flow method for voltage stability of power distribution networks. Assessment of the obtained results shows that WTGSs of synchronous generator types are more robust than those equipped with induction generators from the point of view of voltage stability.