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This paper considers power distribution networks with distributed energy resources and designs an incentive-based algorithm that allows the network operator and customers to pursue given operational and economic objectives while concurrently ensuring that voltages are within prescribed limits. Heterogeneous DERs with continuous and discrete control commands are considered. We address four major challenges: discrete decision variables, non-convexity due to a Stackelberg game structure, unavailability of private information from customers, and asynchronous operation. Starting from a non-convex setting, we develop a distributed stochastic dual algorithm that solves a relaxed problem, and prove that the proposed algorithm achieves the global optimal solution of the original problem on average. Feasible values for discrete decision variables are also recovered. Stability of the algorithm is analytically established and numerically corroborated.
Zhou et al. (Sun,) studied this question.