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Deciding setpoints for distributed energy resources (DERs) via local controlrules rather than centralized optimization offers significant autonomy. TheIEEE Standard 1547 recommends deciding DER setpoints using Volt/VAR rules.Although such rules are specified as non-increasing piecewise-affine, theirexact shape is left for the utility operators to decide and possibly customizeper bus and grid conditions. To address this need, this work optimally designsVolt/VAR rules to minimize ohmic losses on lines while maintaining voltageswithin allowable limits. This is practically relevant as excessive reactiveinjections could reduce equipment's lifetime due to overloading. We consider alinearized single-phase grid model. Even under this setting, optimal ruledesign (ORD) is technically challenging as Volt/VAR rules entail mixed-integermodels, stability implications, and uncertainties in grid loading. Uncertaintyis handled by minimizing the average losses under voltage chance constraints.To cope with the piecewise-affine shape of the rules, we build upon ourprevious reformulation of ORD as a deep learning task. A recursive neuralnetwork (RNN) surrogates Volt/VAR dynamics and thanks to back-propagation, weexpedite this chance-constrained ORD. RNN weights coincide with ruleparameters, and are trained using primal-dual decomposition. Numerical testscorroborate the efficacy of this novel ORD formulation and solutionmethodology.

A Chance-Constrained Optimal Design of Volt/VAR Control Rules for Distributed Energy Resources