Directional enlargement of attraction domain via HOPE method

Extending the domain of attraction is an intresting topic in nonlinear system's survey. In this paper we focus on extending DA along a spesific direction which is denoted by fault running vector. Directional extension is presented by a nonlinear conditioanal optimization problem. As the proposed cost function includes the initial state, a proper choice of starting point which converges to global minimum is difficult. To overcome this problem we use Homotopy Optimization method(HOM). In this method the algorithm starts from minimizing a simple function with a well defined global minimum and during the next iterations the starting cost function is converges to the actual one by uniform variations of homotopy coefficient. To avoid local minimums we use a combinational algorithm which contains SA and HOM in Homotopy Optimization with Perturbation and Ensembles (HOPE). The simulation results show the eficiency of HOPE method in solving optimization problem of directional enlargement of DA. Moreover, using this idea we effectively increase the critical clearing time of power systems.