Constraint-aware multi-agent reinforcement learning with adversarial training for resilience enhancement in multi-microgrid voltage control

The multi-microgrid system faces severe challenges in maintaining voltage stability when subjected to false data injection (FDI) attacks. This paper proposes a constraint-aware multi-agent reinforcement learning (CAMARL) framework, which combines graph neural networks (GNN) to achieve topology-aware state representation, periodic adversarial training, and dynamically adjusted Lagrange multipliers to achieve constraint enforcement. Experiments on IEEE 33-bus, 57-bus, 118-bus, and 300-bus systems show that CAMARL consistently achieves the lowest voltage deviation, both in normal conditions and under attack conditions, outperforming multi-agent soft actor–critic, multi-agent deep deterministic policy gradient, and five other multi-agent reinforcement learning benchmarks. Under normal conditions, CAMARL maintains a 99.8% constraint satisfaction rate on the IEEE 33-bus system, the Lagrange penalty mechanism reduces 94.3% of violations compared to the unconstrained benchmark, and keeps the voltage between 0.95–1.05 p.u. Communication resilience analysis indicates that under a full denial-of-service (DoS) attack, 89.2% of constraints are satisfied, and in the worst-case combination of FDI and DoS threats, this proportion is 87.4%. Ablation studies confirm the necessity of components. Removing GNN and the global state sharing module can increase the voltage deviation by up to 433%, and the removal of any single component alone will lead to a 270% performance degradation.