  An important monitoring task for power systems is accurate estimation of the
system operation state. Under the nonlinear AC power flow model, the state
estimation (SE) problem is inherently nonconvex giving rise to many local
optima. In addition to nonconvexity, SE is challenged by data integrity and
cyber-security issues. Unfortunately, existing robust (R-) SE schemes employed
routinely in practice rely on iterative solvers, which are sensitive to
initialization and cannot ensure global optimality. A novel R-SE approach is
formulated here by capitalizing on the sparsity of an overcomplete outlier
vector model. Observability and identifiability issues of this model are
investigated, and neat links are established between R-SE and error control
coding. The \emph{convex} semidefinite relaxation (SDR) technique is further
pursued to render the nonconvex R-SE problem efficiently solvable. The
resultant algorithm markedly outperforms existing iterative alternatives, as
corroborated through numerical tests on the standard IEEE 30-bus system.
