Estimation of the largest eigenvalue in Chebyshev preconditioner for parallel conjugate gradient method‐based power flow computation

Abstract

An efficient power flow solution is highly important for power system analyses. Traditionally, LU decomposition-based direct method is dominant in solving linear systems in the power flow analysis. However, with the increasing scale and complexity, direct methods may suffer scalability issues, especially under parallel implementation. Therefore, iterative methods such as Conjugate Gradient (CG) are gaining more attention for their scalability and feasibility for parallelisation. To efficiently apply an iterative solver like CG, a preconditioner is usually required. A polynomial-based Chebyshev preconditioner is discussed in this work. An essential parameter in Chebyshev preconditioning is the maximum eigenvalue of the linear system. However, direct calculation of the eigenvalues is too time-consuming to be practical. Therefore, this work proposes a method to estimate the largest eigenvalue to save the time spent on eigenvalue calculation. Thus, Chebyshev preconditioning will be practical to use in power system analyses. This work first proves that the eigenvalues of power system applications range within (0, 2] after a normalisation step, then demonstrates the eigenvalue estimation accuracy, and finally presents the performance improvement. The test shows an average 98.92% runtime saving for the Chebyshev preconditioner, and a 40.99% runtime saving for precondition and iterative solving process.