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Pronounced variability due to the growth of renewable energy sources, flexible loads, and distributed generation is challenging residential distribution systems. This context, motivates well fast, efficient, and robust reactive power control. Optimal reactive power control is possible in theory by solving a non-convex optimization problem based on the exact model of distribution flow. However, lack of high-precision instrumentation and reliable communications, as well as the heavy computational burden of non-convex optimization solvers render computing and implementing the optimal control challenging in practice. Taking a statistical learning viewpoint, the input-output relationship between each grid state and the corresponding optimal reactive power control (a.k.a., policy) is parameterized in the present work by a deep neural network, whose unknown weights are updated by minimizing the accumulated power loss over a number of historical and simulated training pairs, using the policy gradient method. In the inference phase, one just feeds the real-time state vector into the learned neural network to obtain the ‘optimal’ reactive power control decision with only several matrix-vector multiplications. The merits of this novel deep policy gradient approach include its computational efficiency as well as robustness to random input perturbations. Numerical tests on a 47-bus distribution network using real solar and consumption data corroborate these practical merits. 

Power system state estimation (PSSE) aims at finding the voltage magnitudes and angles at all generation and load buses, using meter readings and other available information. PSSE is often formulated as a nonconvex and nonlinear least-squares (NLS) cost function, which is traditionally solved by the Gauss-Newton method. However, Gauss-Newton iterations for minimizing nonconvex problems are sensitive to the initialization, and they can diverge. In this context, we advocate a deep neural network (DNN) based “trainable regularizer” to incorporate prior information for accurate and reliable state estimation. The resulting regularized NLS does not admit a neat closed form solution. To handle this, a novel end-to-end DNN is constructed subsequently by unrolling a Gauss-Newton-type solver which alternates between least-squares loss and the regularization term. Our DNN architecture can further offer a suite of advantages, e.g., accommodating network topology via graph neural networks based prior. Numerical tests using real load data on the IEEE 118-bus benchmark system showcase the improved estimation performance of the proposed scheme compared with state-of-the-art alternatives. Interestingly, our results suggest that a simple feed forward network based prior implicitly exploits the topology information hidden in data.