Power System State Estimation by Phase Synchronization and Eigenvectors

To estimate accurate voltage phasors from inaccurate voltage magnitude and complex power measurements, the standard approach is to iteratively refine a good initial guess using the Gauss–Newton method. But the nonconvexity of the estimation makes the Gauss–Newton method sensitive to its initial guess, so human intervention is needed to detect convergence to plausible but ultimately spurious estimates. This paper makes a novel connection between the angle estimation subproblem and phase synchronization to yield two key benefits: (1) an exceptionally high quality initial guess over the angles, known as a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">spectral initialization</i>; (2) a correctness guarantee for the estimated angles, known as a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">global optimality certificate</i>. These are formulated as sparse eigenvalue- eigenvector problems, which we efficiently compute in time comparable to a few Gauss-Newton iterations. Our experiments on the complete set of Polish, PEGASE, and RTE models show, where voltage magnitudes are already reasonably accurate, that spectral initialization provides an almost-perfect single-shot estimation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> angles from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2n$</tex-math></inline-formula> moderately noisy bus power measurements (i.e. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> pairs of PQ measurements), whose correctness becomes guaranteed after a single Gauss–Newton iteration. For less accurate voltage magnitudes, the performance of the method degrades gracefully; even with moderate voltage magnitude errors, the estimated voltage angles remain surprisingly accurate.