Investigating the load flow equations in power systems via LMI-based techniques

Solving the load flow equations is an important problem in power systems. This paper proposes an approach for addressing this problem via a convex optimization with LMI constraints. This approach ensures to find all solutions provided that the dimension of a linear space provided by the optimization is smaller than a known threshold. Then, this paper considers the characterization of the set of admissible power, in particular the computation of the largest admissible power, which amounts to solving a nonconvex optimization problem. It is shown that an upper bound of the sought power can be obtained via convex LMI optimization. Moreover, a necessary and sufficient condition for establishing whether the upper bound is tight or not is provided. Some numerical examples illustrate the proposed approach.