James R. Winkelman

Singular perturbation analysis of large-scale power systems

This paper reviews some recent results in applying singular perturbation theory to obtain simplified power system models for stability analysis and control design. The topics include synchronous machine modelling, slow coherency and dynamic equivalence of large power networks, and transient stability analysis using direct methods. The objective is to introduce power system engineers to singular perturbation methods as a tool for providing additional insights into power system dynamics of different time scales and for analytically deriving reduced models.

Simultaneous generation of sensitivity functions—transfer function matrix approach

Abstract Sensitivity functions are used in many model parameter identification methods and adaptive control algorithms. Since one sensitivity model has to be used for each parameter, the computation requirement is large when many parameters have to be identified or adjusted. This paper proposes a method to reduce the computation requirement by using one sensitivity model suitable for the generation of sensitivity functions for all parameters. Instead of using modal transformations and eigenvector sensitivities as previously proposed, this paper uses an input-output transfer function matrix approach. Several sufficient conditions in terms of controllability are given for the implementation of the method. An estimate of computation savings is provided.

A direct method for transient stability analysis of power systems with detailed models

This paper presents a direct method for studying transient stability of multimachine systems with detailed models. The method uses a differential equation to define a general energy function. An algorithm is given for using the method with detailed models that contain fast dynamics.

Application of integral manifold theory in large scale power system stability analysis

Near identity coordinate transformations are used to decouple the stability problem for a class of non-linear two time scale systems into a stability problem for slow variables and a stability problem for fast variables only. This facilitates the computation of the region of attraction in the slow subspace of much lower dimension. In this paper we describe a technique to decouple the slow dynamics of the system from its fast components. This is the nonlinear counterpart of the decoupling transformation for linear systems existing in the literature. The results are applied to a three-machine power system having strong and weak connections to compute the critical clearing times.