Coordinated Bidding and Profit Sharing of Microgrid Clusters in Day-Ahead Spot Markets: A Multi-Agent System Approach

Coordinated participation of interconnected microgrids in day-ahead spot markets requires dispatch and profit allocation to be evaluated under a common modeling convention. This study develops an evidence-bounded multi-agent coordination and bidding framework that combines a repaired mixed-integer scheduling model, empirical best-response diagnostics, model-consistent standard Shapley allocation, and a post-dispatch settlement layer. The scheduling model uses aggregate internal exchange and a common-cyclic terminal state-of-charge condition; the allocation is computed from seven independently solved non-empty coalitions. For the deterministic three-microgrid case, the cooperative value is CNY 49,037.9741, compared with CNY 45,293.9055 for the unified non-cooperative baseline, corresponding to an 8.2662% increase. The nominal cooperative case has a recorded maximum power-balance residual of approximately 1.46 × 10−13, while photovoltaic (PV) curtailment is 2.3258 source units. The Gauss–Seidel best-response procedure reaches an empirical fixed-point diagnostic after 18 iterations with a maximum unilateral deviation gain of approximately 3.64 × 10−12; this is not a theoretical pure-strategy Nash result. Varying θ ∈ {0.1, 0.5, 0.9} changes settlement outcomes without changing physical dispatch. Synthetic 5- and 10-microgrid tests characterize computational behavior, with the 10-microgrid case returning a feasible time-limited incumbent rather than a proven optimum. The results support the proposed integration under the tested deterministic settings, while uncertainty-aware, network-constrained, and real-time validation remain future work.