  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.
