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

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 approach is based on a new interpretation of the classical modal PFs as eigen-sensitivities, as well as on the definition of adequate inputs and outputs of the system's state-space representation. Both linear and generalized eigenvalue problems are considered for the calculation of PFs and a theorem to cope with eigenvalue multiplicities is presented. SSSA is also ubiquitous in the synthesis of controllers for power systems. The thesis explores SSSA techniques for the design of power system controllers. The contributions on this topic are twofold, as follows: (i) Investigate a promising control approach, that is to synthesize automatic regulators for power systems based on the theory of fractional calculus. In particular, using eigenvalue analysis, a comprehensive theory on the stability of power systems with inclusion of Fractional Order Controllers (FOCs) is provided. Moreover, the software implementation of FOCs based on Oustaloup's Recursive Approximation (ORA) method is discussed. A variety of FOC applications are illustrated, namely, automatic generation control of synchronous machines; frequency control of a converter-interfaced energy storage system; and voltage control through a static synchronous compensator. (ii) Propose a novel perspective on the potential impact of time delays on power system stability. In general, measurement and communication of control signals in electric energy networks introduces significant time delays that are known to be a threat for the dynamic performance of power systems. However, research in control theory has shown that, by nature, delays are neutral and, if properly introduced, can also stabilize a dynamical system. Through SSSA, the thesis systematically identifies the control parameter settings for which delays in Power System Stabilizers (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. Automatic selection of the variables and estimation of the maximum admissible delay are carried out by SSSA-based techniques. 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 Differential-Algebraic Equations (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.