Application of Krylov Subspace methods for solving Continuous Power Flow problem in voltage stability analysis of power system - Jasni, Jasronita (2010)
Continuation Power Flow (CPF) analysis is developed to overcome singularity problem of Jacobian matrix of power flow analysis. This analysis is done by reformulating the power flow equations so that they remain well-conditioned at all possible loading conditions. This allows the solution of the power flow problem for both stable and unstable equilibrium points. However, its effectiveness and efficiency are still in question 8S it needs many continuation steps to solve each problem. This situation will delay the process of corrector in the system. The CPF algorithm has also been found to fail for a system which has a very sharp turning point for the solution curve which can drag the system to have convergence problem. The step cutting technique that is used to improve convergence can lead to slightly incorrect results in the case of sharp turning point. In order to provide continuity of the power flow in both stable and unstable situations. the numerical method chosen in the analysis should be able lo provide predictor and corrector values with minimal computational effort. Therefore, the aim of this work is to introduce new algorithms that can ensure the continuous power flow eliminate the convergence problem for all power systems regardless of the size of the system and improve the existing CPF. This research will focus on static voltage stability analysis where voltage collapse is explained as static bifurcation phenomenon. Three algorithms, which are based on Krylov Subspace method, have been developed in order to overcome the drawbacks of the existing CPF. These developed algorithms are tested on 14, 118 and 300 IEEE bus systems. Furthermore, the real data with 293 buses and 595 lines is used as a practical system for verification of the new algorithms The results show that these new algorithms are able to eliminate the convergence problem faced by the existing CPF algorithm. For IEEE 300 bus system, the iteration has been reduced from 36 to 34 iterations. The CPU time ratio in performing the analysis has also been reduced between three to twenty percent. These new algorithms are also able to produce more reliable results compared to the existing CPF method.