Application of the homotopy method to load flow solution-finding all the multiple solutions

Mathematically, the solution of the non-linear equations of load flow problems may result in multiple solutions. Conventional methods may fail to find all the multiple solutions if the initial guess values are not appropriately located within the convergency region. To overcome this difficulty, the homotopy method is suggested for the solution technique. In this paper, the mathematical performance of the homotopy theorem is discussed and its application to the load flow solution method is approached. By the proposed method, the 'approach load flow solution' can be obtained more systematically using no strict rules to determine the initial guess values. Utilization of the Newton-Raphson method with the approach load flow solutions guarantees all the multiple solutions. In the solution method, extra computation time and additional storage requirements result from the additional step. Nevertheless, the proposed method is highly recommended.