Power System Nonlinear State Estimation Using Distributed Semidefinite Programming

State estimation (SE) is an important task allowing power networks to monitor accurately the underlying system state, which is useful for security-constrained dispatch and power system control. For nonlinear AC power systems, SE amounts to minimizing a weighted least-squares cost that is inherently nonconvex, thus giving rise to many local optima. As a result, estimators used extensively in practice rely on iterative optimization methods, which are destined to return only locally optimal solutions, or even fail to converge. A semidefinite programming (SDP) formulation for SE has been advocated, which relies on the convex semidefinite relaxation (SDR) of the original problem and thereby renders it efficiently solvable. Theoretical analysis under simplified conditions is provided to shed light on the near-optimal performance of the SDR-based SE solution at polynomial complexity. The new approach is further pursued toward complementing traditional nonlinear measurements with linear synchrophasor measurements and reducing computational complexity through distributed implementations. Numerical tests on the standard IEEE 30- and 118-bus systems corroborate that the SE algorithms outperform existing alternatives, and approach near-optimal performance.