Aggregated demand response is a constrained sequential-control problem because electric vehicles, distributed batteries, thermostatically controlled loads, flexible industrial demand, and behind-the-meter photovoltaic systems are heterogeneous, uncertain, and connected to voltage- and thermal-limited feeders. We formulate portfolio dispatch as a constrained Markov decision process in which a stochastic policy proposes node-mapped aggregate set-points and a weighted projection corrects each proposal against linearized network constraints and aggregate resource constraints. Feasibility of that projection applies only to the linear surrogate at the current operating point; it is not a hard guarantee for the nonlinear feeder. A conditional-value-at-risk term and the measured projection correction discourage operation near critical margins. In the archived synthetic case study on a modified 33-bus feeder, the reported point estimates reduce daily operating cost from 152.3 to 121.4 USD/day, lower the displayed evening net-load peak from 5.8 to 4.7 MW, and increase reported renewable utilization to 90.1%. The archived constraint table contains two voltage samples outside limits, one branch-overload event, one EV departure shortfall, one comfort event, and no storage-state event for the projected controller. The corresponding opportunity counts, controller-time denominator, seed-level records, and paired linear-versus-nonlinear residuals were not retained; consequently, no violation percentage, confidence interval, or seed-independent performance claim is made. The results are descriptive evidence from the supplied aggregate outputs.
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Liu et al. (2026) studied this question.
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