Optimal phasor measurement unit placement for numerical observability in the presence of conventional measurements using semi-definite programming

This study presents a new approach for optimal placement of synchronised phasor measurement units (PMUs) to ensure complete power system observability in the presence of non-synchronous conventional measurements and zero injections. Currently, financial or technical restrictions prohibit the deployment of PMUs on every bus, which in turn motivates their strategic placement across the power system. PMU allocation is optimised here based on measurement observability criteria for achieving solvability of the power system state estimation. Most of the previous work has proposed topological observability based methods for optimal PMU placement (OPP), which may not always ensure numerical observability required for successful execution of state estimation. The proposed OPP method finds out the minimum number and the optimal locations of PMUs required to make the power system numerically observable. The problem is formulated as a binary semi-definite programming (BSDP) model, with binary decision variables, minimising a linear objective function subject to linear matrix inequality observability constraints. The BSDP problem is solved using an outer approximation scheme based on binary integer linear programming. The developed method is conducted on IEEE standard test systems. A large-scale system with 3120 buses is also analysed to exhibit the applicability of proposed model to practical power system cases.