The Continuation Power Flow: A Tool for Parametric Voltage Stability and Security Analysis

This paper considers a toll for assessing voltage related
instability problems due to slow load variations, based
on power flow formulation. Most conventional power flow tools
break down when used to analyze voltage stability problems.
This paper deals with a class of methods for solving nonlinear
equations known as path-following (or continuation) methods,
i.e. with a continuation power flow as a robust power flow method
capable of dealing with sometimes difficult mathematical
problems encountered during the analysis of voltage problems
in power systems. In particular, the paper presents a simplified
continuation power flow with the next four basic elements: first
order polynomial predictor (secant predictor), physical parameterization
(bus, area or total system load as a continuation
parameter), an ordinary Newton-Raphson solver based on the
constant imp€dance load model and well-conditioned Jacobian
matrix in that case throughout solution process, and appropriate
step length control. It is well known that constant power load
mod€l is the most conservative in voltage stability analyses, add
four slightly different algorithms which are combination of the
constant power and constant impedance load models during a
continuation process, are investigated and presented in the paper. In addition, the application of the proposed continuation
power flow to compute the saddle node bifurcation points and
security margins in the load parameter space of an electric
power system, with appropriate eigenvalue and eigenvector calculations,
is also presented in the paper. All examples, included in
the report are based on the CIGRE 31-bus Test System which
originates from the CIGRE Task Force that investigated voltage
collapse indices, and real-life Bosniatr Electric Power System
(configuration in 1996.).