Spatiotemporal bidding for multi-energy systems with photovoltaic dominance: a scenario-based Stackelberg–Nash game formulation

The increasing penetration of photovoltaic (PV) resources and the emergence of Power-to-X (P2X) technologies have fundamentally reshaped the operational and economic dynamics of modern energy systems. This paper develops a unified framework for strategic bidding optimization in distributed multi-energy markets, where decentralized agents equipped with PV, battery storage, electrolyzers, and thermal conversion technologies compete and coordinate across electricity, hydrogen, and heating markets. To account for renewable uncertainty, we formulate the bidding problem as a scenario-based stochastic game, where each agent determines its optimal spatiotemporal bidding strategy under incomplete information and uncertain market conditions. The resulting interactions are modeled using a bilevel Stackelberg-Nash equilibrium structure: the upper level represents the system operator enforcing dispatch feasibility and market rules, while the lower level captures decentralized agent best-responses under a finite scenario tree. Each agent's optimization problem is solved using KKT-based reformulations, allowing the full game to be tractably recast as a mixed complementarity problem. Simulation results demonstrate that intertemporal bidding strategies with cross-market conversion significantly improve profit robustness, system efficiency, and bid clearing rates under high PV variability. Furthermore, the analysis reveals how agent portfolio heterogeneity and market coupling structure influence equilibrium convergence, strategy diversity, and overall coordination performance. This work provides three main contributions: (1) a novel scenario-based stochastic game formulation for multi-energy bidding in sector-coupled PV systems; (2) a bilevel equilibrium modeling and solution framework with realistic intertemporal and inter-market dynamics; and (3) quantitative insights into how flexibility assets, conversion capabilities, and scenario diversity jointly shape system-level outcomes and agent-level profitability in decentralized energy markets.