Modern distribution grids are currently being challenged by frequent and sizable voltage fluctuations, due mainly to the increasing deployment of electric vehicles and renewable generators. Existing approaches to maintaining bus voltage magnitudes within the desired region can cope with either traditional utility-owned devices (e.g., shunt capacitors), or contemporary smart inverters that come with distributed generation units (e.g., photovoltaic plants). The discrete on-off commitment of capacitor units is often configured on an hourly or daily basis, yet smart inverters can be controlled within milliseconds, thus challenging joint control of these two types of assets. In this context, a novel two-timescale voltage regulation scheme is developed for distribution grids by judiciously coupling data-driven with physicsbased optimization. On a faster timescale, say every second, the optimal setpoints of smart inverters are obtained by minimizing instantaneous bus voltage deviations from their nominal values, based on either the exact alternating current power flow model or a linear approximant of it; whereas, on the slower timescale (e.g., every hour), shunt capacitors are configured to minimize the longterm discounted voltage deviations using a deep reinforcement learning algorithm. Extensive numerical tests on a real-world 47bus distribution network as well as the IEEE 123-bus test feeder using real data corroborate the effectiveness of the novel scheme.

The dual-channel closed-loop supply chain (CLSC) which is composed of one manufacturer and one retailer under uncertain demand of an indirect channel is constructed. In this paper, we establish three pricing models under decentralized decision making, namely, the Nash game between the manufacturer and the retailer, the manufacturer-Stackelberg game, and the retailer-Stackelberg game, to investigate pricing decisions of the CLSC in which the manufacturer uses the direct channel and indirect channel to sell products and entrusts the retailer to collect the used products. We numerically analyze the impact of customer acceptance of the direct channel (θ) on pricing decisions and excepted profits of the CLSC. The results show that when the variableθchanges in a certain range, the wholesale price, retail price, and expected profits of the retailer all decrease whenθincreases, while the direct online sales price and manufacturer’s expected profits in the retailer-Stackelberg game all increase whenθincreases. However, the optimal recycling transfer price and optimal acquisition price of used product are unaffected byθ.

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To perform any meaningful optimization task, distribution grid operators need to know the topology of their grids. Although power grid topology identification and verification has been recently studied, discovering instantaneous interplay among subsets of buses, also known as higher-order interactions in recent literature, has not yet been addressed. The system operator can benefit from having this knowledge when re-configuring the grid in real time, to minimize power losses, balance loads, alleviate faults, or for scheduled maintenance. Establishing a connection between the celebrated exact distribution flow equations and the so-called self-driven graph Volterra model, this paper puts forth a nonlinear topology identification algorithm, that is able to reveal both the edge connections as well as their higher-order interactions. Preliminary numerical tests using real data on a 47-bus distribution grid showcase the merits of the proposed scheme relative to existing alternatives.