A nonlinear well-determined model for power system observability using Interior-Point methods

•Interior-Point method is used to solve the optimal phasor measurement unit placement problem.•Placement method can consider any number, type, and position, of pre-existing measurement.•Proposed method delivers the optimal solution in polynomial time, even for large systems. This paper proposes Interior-Point (IP) methods for the solution of the optimal placement of phasor measurement units (PMUs) ensuring complete observability. The optimization problem consists of a quadratic function under a well-determined system of constraints that is, nonlinear equations equal to the number of the design variables defined over the whole search space Rn. A hybrid-optimization technique coupling a branch-and-bound and a local search-procedure based on the (IP) methods is used in solving the model. The (IP) methods detect solution points that yield a minimum objective value as the one obtained by branch-and-bound algorithm. The (IP) methods optimizes the required PMU numbers whereas practical constraints as well as contingency issues as single PMU failure, costs of communication infrastructure (CI) from Phasor Data Concentrator to PMUs and prohibitive installations are satisfied. A large-scale system is also analysed to exhibit the applicability of (IP) methods to practical power system cases.