On the application of a pre-conditioned conjugate gradient algorithm to power network analysis

Large, sparse systems of linear equations as found in several power system problems are generally solved using direct LU decomposition methods. Although these techniques are considered efficient for most applications, in cases involving repeated solutions such as security analysis or real time control, direct solvers may still not be sufficiently fast. The incomplete Cholesky pre-conditioned conjugate gradient (PCG) algorithm is a very powerful semi-iterative solver which has been proven to have significant speed advantages over direct methods in the area of finite element electromagnetic analysis (ratios of 100 to 1 are not uncommon). In this paper, the PCG algorithm is applied to the fast decoupled load flow and to the DC load flow. The computation time of the new PCG algorithm is compared with that of a standard direct solver for a wide spectrum of power networks up to 5000 buses and 10000 lines. The results of our numerical experiments indicate that for certain classes of large sparse systems or for repeated solutions with matrix modifications, the PCG method is significantly more efficient than direct techniques and offers important savings in CPU time