The effects of backlash on the frequency stability in a hydro based power system

Sammanfattning: The generated and consumed power should always be in balance in a power system. Any energy from a power imbalance will be stored as kinetic energy in the system's rotating mass leading to a changed frequency. To keep the frequency within acceptable limits hydropower plants are used to counteract power imbalances. The hydropower plants are however introduc­ing a nonlinearity, namely backlash. This complicates the behavior of the system, e.g. a limit cycle behavior can arise. A limit cycle is a standing oscillation and will force the system to move away from what is desired. Oscillations will cause extra wear and tear in the machinery and prevents the system from keeping the frequency fixed. This thesis investigates when this phenomenon occurs and how different system parameters affect the outcome. The Nordic power system is considered in this report. The system is modeled as a single generator, scaled to the total regulating capacity, and then connected to a simplified model that focuses on the dynamics of the rotating masses. Two different approaches are used. Describing function analysis is used to predict limit cycles in the frequency domain and a time domain approach is used to determine an invariant set for the system that includes possible limit cycles. The latter approach is easily extendible and does not simplify the nonlinearity in contrast with the describing function method. The analysis concludes that limit cycles can occur in the Nordic power system and in a similar low inertia case. It illustrates the difference between two types of feedback and the relation between and a stability margin and the existence of limit cycles. Furthermore, a numerical robustness analysis is performed to study of the robustness of one limit cycle and limit cycle-free solution of the system.