Shapley Value-Based Carbon Emission Responsibility Allocation in Power Systems with Energy Storage

Energy storage systems (ESS) are essential for power system decarbonization, yet their carbon emission responsibilities remain ambiguous under market operations due to their unique bidirectional operation characteristics. This paper develops a multi-period carbon responsibility allocation framework integrating system operation modeling, sequential decoupling simulation, and Shapley-based fairness principles. To address computational intractability of exact Shapley values as participant numbers increase, we employ KernelSHAP to approximate average marginal contributions through weighted regression.  Case studies on IEEE 14-bus and 30-bus systems demonstrate three key findings: (i) KernelSHAP achieves accurate Shapley approximations in the carbon allocation context with relative errors below 0.5\% while enabling scalable allocation; (ii) thermal generators consistently bear positive responsibilities as direct emitters while renewables receive negative allocations; (iii) ESS receive near-zero net responsibilities, with charging costs offset by discharging credits. Sensitivity analysis across renewable penetration levels and seven-day horizons confirms allocation robustness. The framework provides fairness benchmarks for evaluating existing carbon responsibility methods and policy design, supporting ESS exemption from emission penalties while clarifying their carbon-neutral role in decarbonization. This work bridges fairness theory with practical implementation, advancing equitable carbon responsibility distribution in electricity markets.