Decentralized computation of charging controls for plug-in electric vehicles in the S-adapted information structure

Balmelli, Simone; Moresino, Francesco · 2020 · Crossref

DOI: 10.23919/ecc51009.2020.9143829

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Summary

This paper addresses the challenge of managing plug-in electric vehicle (PEV) charging in smart grids under uncertain electricity demand. The authors formulate the problem as a Generalized Nash Equilibrium (GNE) seeking problem within stochastic aggregative games. The motivation stems from the increasing penetration of PEVs, which can create new demand peaks and strain grid capacity. To mitigate this, the study employs a decentralized control scheme that shifts charging intervals to reduce grid load, incorporating a real-time electricity tariff dependent on instantaneous demand. Crucially, the model accounts for stochastic dynamics affecting non-PEV demand, modeled as a discrete-state process independent of player actions, using an S-adapted information structure. This structure ensures that players make nonanticipative decisions based only on observed historical realizations of the stochastic process, rather than future knowledge. The methodology involves modeling the stochastic process as an event tree, where each node represents a specific realization of the non-PEV demand. The authors introduce a coupling constraint that imposes an upper limit on aggregate PEV demand to prevent grid overloads. To solve the resulting GNE problem in a decentralized manner, the authors employ an extended game reformulation that transforms the problem into a Nash Equilibrium problem with $N+1$ players, where the additional player acts as a central operator enforcing the coupling constraint via penalty prices. The equilibrium is calculated using an extragradient algorithm to solve the corresponding variational inequality. The approach assumes players know the properties of the underlying stochastic process in advance but cannot observe other players' controls, only the aggregate demand and price signals. Numerical experiments were conducted using a population of 10 heterogeneous PEVs over a 24-hour horizon with a two-state Markov process for non-PEV demand. The results demonstrate that the S-adapted structure significantly alters the typical "valley-filling" behavior observed in deterministic models. Instead of perfectly smoothing demand, the stochastic nature causes players to postpone charging during periods of high non-PEV demand, anticipating potential returns to lower demand states. The controls remain nonanticipative, overlapping perfectly for sample paths that share the same history up to a given time. The study also compares the expected charging costs across three information structures: perfect anticipative information, the proposed S-adapted structure, and a deterministic naive approach using average demand. The S-adapted structure resulted in a cost only 0.15% higher than perfect information, while the naive approach was more expensive, highlighting the efficiency of the proposed decentralized stochastic framework. The significance of this work lies in its rigorous treatment of uncertainty in decentralized PEV charging control. By integrating the S-adapted information structure, the paper provides a realistic model where agents react to observed stochastic events without requiring perfect foresight or sampling-based inference. The findings suggest that accounting for stochastic dynamics is essential for accurate grid management, as it fundamentally changes charging strategies compared to deterministic assumptions. The proposed decentralized algorithm offers a computationally efficient way to achieve equilibrium in large-scale systems with coupling constraints, contributing to the development of robust demand-side management strategies for smart grids.

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