A market-clearing framework for endogenous carbon pricing in heterogeneous energy systems

Achieving the transition to low-carbon energy systems requires carbon-pricing mechanisms that reflect the technical, economic, and environmental characteristics of energy systems. However, many existing studies either treat the carbon price as an exogenous parameter, embed price formation within joint or bi-level optimization models, or derive it from strategic equilibrium assumptions. As a result, the link between system-level operational constraints and carbon-market price formation is not always represented transparently. This study proposes an optimization-consistent market-clearing framework for endogenous carbon price formation. Seller-side supply curves are derived from the incremental operating costs associated with additional emission reduction or carbon capture. Buyer-side demand curves are derived from the operating-cost savings enabled by access to emission allowances. These marginal cost responses are used to form stepwise carbon supply and demand curves. The aggregated curves are then cleared through a transparent, non-strategic mechanism under a price-taking assumption, allowing the carbon price and traded quantity to be determined endogenously. The resulting cooperative gains are allocated among participating systems using the Shapley value. A four-system case study shows that capture-based crediting reduces operating costs by 12.4% but increases total emissions, whereas emission-based crediting achieves a 5.1% cost saving while maintaining emissions at the baseline level. Seasonal robustness tests based on four 2025 Australian electricity-market operating profiles, together with a probability-weighted scenario analysis under specified electricity-demand and price distributions, demonstrate the framework’s ability to characterize market outcomes under seasonal variation and operating uncertainty across 196 joint scenarios.