Online Energy Price Matrix Factorization for Power Grid Topology Tracking

Grid security and open markets are two major smart grid goals. Transparency of market data facilitates a competitive and efficient energy environment. But it may also reveal critical physical system information. Recovering the grid topology based solely on publicly available market data is explored here. Real-time energy prices are typically calculated as the Lagrange multipliers of network-constrained economic dispatch; that is, via a linear program (LP) typically solved every 5 min. Since the grid Laplacian matrix is a parameter of this LP, someone apart from the system operator could try inferring this topology-related matrix upon observing successive LP dual outcomes. It is first shown that the matrix of spatio-temporal prices can be factored as the product of the inverse Laplacian times a sparse matrix. Leveraging results from sparse matrix decompositions, topology recovery schemes with complementary strengths are subsequently formulated. Solvers scalable to high-dimensional and streaming market data are devised. Numerical validation using synthetic and real-load data on the IEEE 30-bus grid provide useful input for current and future market designs.