Energy price matrix factorization

Statistical learning tools are utilized here to study the potential risks of revealing the topology of the underlying power grid using publicly available market data. It is first recognized that the vector of real-time locational marginal prices admits an interesting decomposition: It can be expressed as the product of a sparse, positive definite matrix with non-positive off-diagonal entries times a sparse vector. A convex optimization problem involving sparse regularizers is formulated to recover the constituent factors under relevant noisy and noiseless scenarios. To tackle the high dimensionality and the streaming nature of real-time energy market data, an online algorithm with efficient closed-form iterates is developed. The grid topology matrix is updated every time a new set of locational marginal prices becomes available. Numerical tests with real demand data used on the IEEE 30-bus grid benchmark justify that the solver can partially track the underlying grid topology.