Computational complexity in power systems

The problem of estimating the increase in computational effort as the system size n increases is studied for methods requiring the solution of Ax = b, where A is sparse and topology-symmetric. The expected value of the total number of upper triangular nonzero elements after factorization is assumed to grow as n1+γ. The expected computational effort for the factorization itself is shown to grow as n1+2γ, while the one for each repeat solution is shown to grow as n1+γ. Values of γ for typical power systems are experimentally determined by generating a variety of random networks and ordering the resultant matrices according to "scheme 2". For typical power systems a reasonable value for γ is 0.2. Therefore, methods requiring repeated refactorization of A (such as Newton's method) can be expected to increase as n1.4, while methods requiring merely repeat solutions (such as fast decoupled methods) can be expected to increase as n1.2. Several other important comparisons are included.