Direct Methods for Stability Analysis of Electric Power Systems: Theoretical Foundation, BCU Methodologies, and Applications

Chapter 16

Network-Preserving BCU Method and Its Theoretical Foundation

16.1 INTRODUCTION

We present in this chapter a network-preserving BCU method for direct stability analysis of the following generic network-preserving transient stability model:

(16.1)

where u ∈ R^k and w ∈ R^l are instantaneous variables, and x ∈ R^m, y ∈ Rⁿ, and z ∈ Rⁿ are state variables. T is a positive definite matrix, and M and D are diagonal positive definite matrices. Here, the differential equations describe generator and/or load dynamics, while the algebraic equations express the power flow equations at each bus. The function U(u, w, x, y) is a scalar function. The physical limitations of variables are not expressed for the sake of convenience. Existing network-preserving transient stability models can be rewritten as a set of the above general differential and algebraic equations (DAEs) (Chu and Chiang, 2005).

A structure-preserving BCU method (i.e., a BCU method for structure-preserving transient stability models) and its analytical basis will be presented in this chapter. The fundamental ideas behind the development of the BCU method can be explained as follows. Given a power system transient stability model called the original model, which admits an energy function, the BCU method first explores the special properties of the original model to define an artificial, reduced-state model so ...