Safe Multi-Agent reinforcement learning with graph neural ODEs for voltage control in Market-Driven distribution networks

Market-driven operation of distribution networks intensifies the autonomous behaviours of photovoltaic generation, electric vehicles and flexible loads, causing rapid source-load fluctuations and challenging real-time voltage control under limited measurements. Existing optimisation and deep reinforcement learning methods either rely on accurate network models and complete state information or enforce safety mainly in expectation, leaving individual actions potentially infeasible under severe conditions. This paper proposes GODE-MASAC-CBF, a multi-agent safe reinforcement learning framework for aggregator-level voltage control in market-driven distribution networks. It combines a constrained Markov decision process- based soft actor-critic policy with a control barrier function projection layer to coordinate long-term voltage-risk reduction and stepwise action feasibility. An AE-GraphODE encoder models topology-aware nodal-state evolution from historical measurements, and a sensitivity prediction head estimates state-dependent voltage-action sensitivities for adaptive CBF projection. Tests on IEEE 33-bus and 141-bus distribution systems validate its effectiveness, robustness and scalability. On the IEEE 33-bus system, the method achieves zero voltage violations in the baseline, measurement-noise and topology-change scenarios, and reduces violations by more than 90 % under rapid source-load fluctuations relative to MASAC, MG-ASTGCN and RASAC. Under high EV penetration, it yields the fewest violations, although voltage limits are not fully maintained at the highest EV penetration level. On the IEEE 141-bus system, it maintains zero violations and reduces cumulative voltage deviation and network losses by 7.7 % and 10.6 % relative to MG-ASTGCN, demonstrating scalable and robust voltage control.