The alpha-modified quasi-second order Newton-Raphson method for load flow solutions in rectangular form

Abstract

In this thesis a new class of methods for solving power system load flows is developed, which is called the alpha-modified quasi-second order Newton-Raphson (alpha - M.Q.S.O.N.R.) class. · The theory is derived from the Taylor expansion for multivariable functions and is developed using rectangular coordinates. The first part of the theory is actually the Newton-Raphson algorithm. This is expanded by including the second order terms from the Taylor expansion to produce a quasi-second order Newton-Rahpson solution method. The theory is then further modified to yield the more general alpha-modified method. Extensive testing is performed using the new method for seven different power systems. The same systems are rerun with the Newton-Raphson so that a comparison can be made and the new method's relative merit judged. The rate of convergence is studied, as well as the mismatch values which occur during the load flows. This is done for many different values of alpha and for the different systems. The results are analysed and discussed in detail with the main result being that the alpha M.Q.S.O.N.R. method tested, with alpha equal to zero, is superior to the Newton-Raphson.