Modeling and Stability Analysis of Power Systems with Discontinuous Right Hand Side Differential, Algebraic Equations

Power systems are one of the most complex dynamic systems due to their multi-time scale and non-linear nature. This work focuses in particular on the electromechanical dynamics of power systems which are hybrid (discrete-continuous) and are therefore studied using a set of Hybrid Differential-Algebraic Equations (HDAEs) or Discontinuous Right-Hand Side DAEs (DRHS DAEs). Traditional HDAEs possess several challenges during modeling, implementation, and numerical simulation stages, depending on the nature of the discontinuities arising from different applications. This thesis studies the impact of discontinuities on power system physical stability as well as on the numerical stability of a solver considering two specific discontinuous models. The first model is an under load tap changing transformer, which introduces a discrete variable in the DRHS DAEs due to the physical operation of the transformer. The second model is a proportional-integral controller used in different components of power systems, e.g. voltage source converter and automatic voltage regulators which introduces a discontinuity in the state and algebraic variables of DRHS DAEs. In particular, a thorough discussion of the deadlock and chattering issues during time-domain simulation arise from the latter model is provided. This discussion is based on two time domain simulation techniques widely used in power system tools, namely, time-stepping and event-driven method. To solve the deadlock and chattering issues in both of these simulation techniques, a theoretical approach given by Filippov is proposed. Case studies with small to large sizes, e.g., single machine infinite bus, WSCC 9-bus, IEEE 14-bus, 74-bus Nordic system and all-island Irish system with 1479-buses connected to a simplified 63-bus Great Britain system through a high-voltage direct current link are considered and tested in the thesis. Simulation results indicate the importance of accurate modeling and implementation of discontinuous models for dynamic analysis.