Deep Learning for Scalable Optimal Design of Incremental Volt/VAR Control Rules

Volt/VAR control rules enable distributed energy resources (DER) to autonomously regulate voltage in distribution grids. The Volt/VAR rules provisioned by the IEEE Standard 1547 take on a piecewise-linear shape. However, its maximum slope is upper bounded to ensure stability, and that may hamper its voltage regulation performance. This limitation can be surpassed by adding a memory term to the control rule, and thus, obtaining a so-termed incremental control rule. This letter aims to optimally customize the shape of incremental rules across buses to attain desirable voltage profiles. Albeit this task can be posed as a bilevel program, we pursue a more scalable approach by reformulating it as a deep learning task. The idea is that Volt/VAR dynamics can be captured by a recursive neural network (RNN). Interestingly, the RNN weights correspond to the parameters of the control rule; the RNN input to the grid loading conditions; and the RNN output to the equilibrium voltages. Therefore, the optimal rule parameters can be found upon training the RNN so its output (equilibrium voltages) approach unity. Training is performed by feeding the RNN with representative scenarios of the anticipated grid loading conditions. The RNN depth depends on the settling time of Volt/VAR dynamics. Because the discrete-time Volt/VAR dynamics can be viewed as iterations of a proximal gradient descent (PGD) algorithm, we also leverage Nesterov’s accelerated PGD iterations to reduce the RNN depth. The RNN is never implemented in the field. Training this RNN is equivalent to solving the optimal rule design in a more computationally efficient manner. Analytical findings and numerical tests corroborate that the proposed solution can be neatly adapted to single- and multiphase feeders. The proposed approach could be of general interest in designing piecewise-linear controllers acting on linear plants.