Small-Signal Stability Techniques for Power System Modal Analysis, Control, and Numerical Integration

Abstract: This thesis proposes novel Small-Signal Stability Analysis (SSSA)-based techniques that contribute to electric power system modal analysis, automatic control, and numerical integration. Modal analysis is a fundamental tool for power system stability analysis and control. The thesis proposes a SSSA approach to determine the Participation Factors (PFs) of algebraic variables in power system dynamic modes. The thesis also explores SSSA techniques for the design of power system controllers. The contributions on this topic are twofold: i) Investigate a promising control approach, that is to synthesize automatic regulators for power systems based on the theory of fractional calculus. ii) Propose a novel perspective on the potential impact of time delays on power system stability. Through SSSA, the thesis systematically identifies the control parameter settings for which delays in PSSs improve the damping of a power system. Both analytical and simulation-based results are presented. Finally, SSSA is utilized in the thesis to systematically propose a delay-based method to reduce the coupling of the equations of power system models for transient stability analysis. The method consists in identifying the variables that, when subjected to a delay equal to the time step of the numerical integration, leave practically unchanged the system trajectories. Such an one-step-delay approximation increases the sparsity of the system Jacobian matrices and can be used in conjunction with state-of-the-art techniques for the integration of DAEs. The proposed approach is evaluated in terms of accuracy, convergence and computational burden. Throughout the thesis, the proposed techniques are duly validated through numerical tests based on real-world network models.