Stability analysis programs are a primary tool used by power system planning and operating engineers to predict the response of the system to various disturbances. Important conclusions and decisions are made based on the results of stability studies. This paper presents a theoretical foundation of direct methods for both network-reduction and network-preserving power system models. In addition to an overview, new results are offered. A systematic procedure of constructing energy functions for both network-reduction and network-preserving power system models is proposed. An advanced method, called the BCU method, of computing the controlling unstable equilibrium point is presented along with its theoretical foundation. Numerical solution algorithms capable of supporting online applications of direct methods are provided. Practical demonstrations of using direct methods and the BCU method for online transient stability assessments on two power systems are described. Further possible improvements, enhancements and other applications of direct methods are outlined.

Direct stability analysis of electric power systems using energy functions: theory, applications, and perspective

This paper presents an analysis of static stability in electric power systems. The study is based on a model consisting of the classical swing equation characterization for generators and constant admittance, PV bus and/or PQ bus load representations which, in general, leads to a semi-explicit (or constrained) system of differential equations. A precise definition of static stability is given and basic concepts of static bifurcation theory are used to show that this definition does include conventional notions of steady-state stability and voltage collapse, but it provides a basis for rigorous analysis. Static bifurcations of the load flow equations are analyzed using the Liapunov-Schmidt reduction and Taylor series expansion of the resulting reduced bifurcation equation. These procedures have been implemented using symbolic computation (in MASYMA). It is shown that static bifurcations of the load flow equations are associated with either divergence-type instability or loss of causality. Causality issues are found to be an important factor in understanding voltage collapse and play a central role in organizing global power system dynamics when loads other than constant admittance are present.

http://www.pages.drexel.edu/~hgk22/papers/Kwatny%20Pasrija%20Bahar%20IEEE%20TCS%2086.pdf

Static bifurcations in electric power networks: Loss of steady-state stability and voltage collapse

As power systems become more heavily loaded, there will be an increase in the number of situations where the power flow equations have no real solution, particularly in contingency analysis and planning applications. Since these cases can represent the most severe threats to viable system operation, it is important that a computationally efficient technique be developed to both quantify the degree of unsolvability, and to provide optimal recommendations of the parameters to change to return to a solvable solution. Such an algorithm is developed in the paper. The distance in parameter space between the desired operating point and the closest solvable operating point provides a measure of the degree of unsolvability, with the difference between these two points providing the optimal system parameter changes. The algorithm is based upon a Newton-Raphson power flow algorithm, which provides both computational efficiency and compatibility with existing security analysis techniques. The method is demonstrated on systems of up to 118 buses. >

A power flow measure for unsolvable cases

A security measure is defined to indicate vulnerability to voltage collapse based on an energy function for system models that includes voltage variation and reactive loads. The system dynamic model, the energy function, and the security measure are first illustrated in a simple radial system. Application of the security measure and its computational aspects are then examined in a standard 30-bus example (New England System). The security measure captures nonlinear effects such as VAR limits on generators that can influence the systems vulnerability to collapse. The behavior of the index with respect to network load increases is nearly linear over a wide range of load variation, facilitating prediction of the onset of collapse. >

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An energy based security measure for assessing vulnerability to voltage collapse

Complete results are presented on the phase portrait of a class of large nonlinear dynamic systems that includes the power system The connection between the constant energy surface and the stability boundary of the power system is explored This gives valuable insight into classical stability tests, which are based on the constant energy surface An approach to stability monitoring of the power system derived from these results is outlined >

On the phase portrait of a class of large nonlinear dynamic systems such as the power system

In this paper, a concept of strong stability of an equilibrium point of an electric power system is introduced. It is shown that almost all stable equilibria of the standard transient stability model are strongly stable and that strong stability is a necessary and sufficient condition for the existence of a local energy-like Lyapunov function for all small perturbations of the nominal system. Such a Lyapunov function is explicitly constructed. A complete local analysis of the stability of power system equilibria in the presence of transfer conductances is given.

http://www.pages.drexel.edu/~hgk22/papers/Kwatny%20Bahar%20Pasrija%20IEEE%20Trans%20CS%2085.pdf

A. Pasrija

Papers

Energy-like Lyapunov functions for power system stability analysis

Loss of steady state stability and voltage collapse in electric power systems

Energy-like Lyapunov functions for power system stability analysis