Solve the relaxed OPF problem by generalized gradient smooth Newton methods

Optimal Power flow (OPF) problem is a nonlinear nonconvex optimization problem. It faces three challenges when solving the algorithm based on traditional optimization methods, namely, global convergence, solving efficiency and global optimization. For complex and large-scale power systems, global optimization of algorithms is more difficult to achieve than global convergence and solution efficiency. Therefore, this paper proposes a method for finding the global optimal solution to the OPF problems. This method first transforms the OPF problem into a relaxed OPF problem. Then, by using the transformation function max{ & sdot; } , the relaxed OPF problem is decomposed into two subproblems. Finally, the global optimal value and solution of the OPF problem are obtained by solving two sub problems using the generalized gradient Newton method and the smooth Newton method, respectively. Numerically in the experiments, we compare the proposed method with the interior-point method, the commercial solver SNOPT, NLP(KNITRO) and ESLP2. The results show that under the same order of magnitude of computational efficiency, the method proposed in this paper has more advantages.