Multi-area state estimation using distributed SDP for nonlinear power systems

State estimation (SE) is an important task allowing power networks to monitor accurately the underlying system state, while multi-area SE is becoming increasingly popular as the power grid comprises multiple interconnected “subgrids.” For nonlinear AC power systems, SE per subgrid amounts to minimizing a nonlinear least-squares cost that is inherently nonconvex, thus giving rise to many local optima. Despite the non-convexity, a recent SE approach based on semidefinite programming (SDP) has been effective in approaching globally optimal performance at the price of higher computational cost. A novel reduced-complexity algorithm is developed in this paper for local control areas to solve the centralized SDP-based SE problem in a distributed fashion. It leverages results on positive semidefinite matrix completion to split a global state matrix constraint into local ones, which further allows for parallel implementation using the alternating-direction method of multipliers (ADMM). With minimal data exchanges among neighboring areas, each control center can efficiently perform local updates that scale with each area´s size (number of buses). Numerical simulations using the IEEE 14-bus system demonstrate the asymptotic convergence of local state matrices, and desirable estimation accuracy attainable with a limited number of exchanges.