ArticleScientific reports2026
Spatiotemporal bidding for multi-energy systems with photovoltaic dominance: a scenario-based Stackelberg-Nash game formulation.
Article in Scientific reports, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
0 citing papers in PubMed.
No citing paper in PubMed yet.
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
5 authors.
Funding
Abstract
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.
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.