LOOP-MAC: Learning-Based Multi-Agent Coordination with Guaranteed Local Feasibility in a Virtual Power Plant

As power systems advance toward net-zero targets, behind-the-meter renewables are driving rapid growth in distributed energy resources (DERs). Virtual power plants (VPPs) increasingly coordinate these resources to support power distribution network (PDN) operation, with EV charging stations (EVCSs) emerging as a key asset due to their strong impact on local voltages. However, in practice, VPPs must make operational decisions with only partial visibility of PDN states, relying on limited, aggregated information shared by the distribution system operator. This work proposes a safety-enhanced VPP framework for coordinating multiple EVCSs under such realistic information constraints to ensure voltage security while maintaining economic operation. We develop Transformer-assisted Lagrangian Multi-Agent Proximal Policy Optimization (TL-MAPPO), in which EVCS agents learn decentralized charging policies via centralized training with Lagrangian regularization to enforce voltage and demand-satisfaction constraints. A transformer-based embedding layer deployed on each EVCS agent captures temporal correlations among prices, loads, and charging demand to improve decision quality. Experiments on a realistic 33-bus PDN show that the proposed framework reduces voltage violations by approximately 45% and operational costs by approximately 10% compared to representative multi-agent DRL baselines, highlighting its potential for practical VPP deployment.

We present a distributed approach for constrained Multi-Agent Reinforcement Learning (MARL) that combines state-augmented policy learning with distributed consensus over dual variables. Our method targets systems where agents have separable dynamics but must coordinate to satisfy global resource constraints, a setting in which, as we demonstrate empirically, independent learning fails to produce feasible solutions because agents cannot determine appropriate individual contributions toward collective constraint satisfaction. The key technical contribution is showing that lightweight neighbor-to-neighbor consensus over Lagrange multipliers suffices for globally coordinated constraint enforcement while preserving the scalability of independent training. Each agent learns a single augmented policy offline, conditioned on both its local state and a dual variable encoding constraint feedback. During execution, agents reach agreement on this dual variable through local communication alone. We prove that under mild connectivity assumptions, the consensus error among agents' multipliers is bounded, and show that this translates to a bounded constraint violation that decreases with graph connectivity and the number of consensus rounds. Unlike centralized training with decentralized execution (CTDE) approaches, whose complexity grows at least quadratically with agent count, our method scales linearly in both training and execution. Experiments on smart grid demand response demonstrate that consensus coordination is essential for feasibility: without it, agents satisfy grid capacity constraints only by indefinitely postponing demand, a degenerate non-solution. With consensus, agents converge to a shared dual variable and satisfy both grid constraints and demand fulfillment, scaling to thousands of agents while CTDE baselines are limited to dozens.

Coordinating large populations of grid-edge devices requires learning methods that remain fully decentralised in deployment while still respecting three-phase AC distribution-network physics. This paper proposes gradient-based multi-agent proximal learning (GradMAP) to address this challenge. GradMAP trains independent neural-network policies for each agent without any parameter sharing, and each agent uses only its own local observation for online decision-making without communication. During offline training, GradMAP embeds a differentiable three-phase AC power-flow model in a primal-dual learning loop and uses implicit differentiation to propagate exact network-constraint violations to update the policy parameters. To speed up training, GradMAP reuses expensive environment gradients through a proximal surrogate within a trust region defined in the more direct policy-output (action) space, instead of the probability distribution space used in other works, such as PPO. In case studies with 1,000 agents managing batteries, heat pumps, and controllable generators on the IEEE 123-bus feeder, GradMAP learns decentralised policies that minimise three-phase AC load-flow constraint violations within 15 minutes of training on a single workstation-class NVIDIA RTX PRO 5000 Blackwell 48GB GPU. This is a 3--5x training speed-up over gradient-based self-supervised learning benchmarks and substantially better training efficiency than multi-agent reinforcement-learning benchmarks. In out-of-sample tests, GradMAP also delivers among the lowest operating cost and constraint violations.