A framework for analyzing the small-signal dynamic performance of unbalanced power systems

The effect of load and system unbalance is often neglected in the analysis of the small-signal dynamics of power systems, due to the lack of a specialized tool. The main reason for it is the fact that it is not possible to clearly define a steady-state equilibrium point for the power system under unbalanced conditions, since the generators rotor speed oscillate at twice the fundamental frequency of the system due to the effect of the negative sequence torque that appears under these conditions. In other words, the equilibrium conditions of this model are non-stationary, even in Park´s 0dq reference frame. Without a well-defined stationary equilibrium point, it is not possible to linearize the system around it, and thus the existing tools for small-signal stability analysis cannot be applied in this case without large simplifying approximations, which can introduce a significant amount of error if the degree of imbalance in the system is high. This work presents a framework that can overcome this problem, therefore allowing the small-signal stability analysis of power systems under unbalanced operating conditions. This framework consists in simulating small perturbations using a nonlinear power system model and then using a modal estimation technique (based on a rotational invariance approach) to extract the modal characteristics of the simulated signals. The results of the application of the defined framework are presented in a case study, at the end of the paper, comprising an equivalent model of a distribution system with a synchronous generator directly connected to it. From these results, it is possible to conclude that the proposed framework indeed enables the small-signal stability analysis of unbalanced power systems without the approximations needed to apply the traditional tools based on linearized models.