Deep Learning-Accelerated Shapley Value for Fair Allocation in Power Systems: The Case of Carbon Emission Responsibility

Abstract

Allocating costs, benefits, and emissions fairly among power system participant entities represents a persistent challenge. The Shapley value provides an axiomatically fair solution, yet computational barriers have limited its adoption beyond small-scale applications. This paper presents SurroShap, a scalable Shapley value approximation framework combining efficient coalition sampling with deep learning surrogate models that accelerate characteristic function evaluations. Exemplified through carbon emission responsibility allocation in power networks, SurroShap enables Shapley-based fair allocation for power systems with thousands of entities for the first time. We derive theoretical error bounds proving that time-averaged SurroShap allocations converge to be $\varepsilon$-close to exact Shapley values. Experiments on nine systems ranging from 26 to 1,951 entities demonstrate completion within the real-time operational window even at maximum scale, achieving 10^4-10^5 speedups over other sampling-based methods while maintaining tight error bounds. The resulting Shapley-based carbon allocations possess six desirable properties aligning individual interests with decarbonization goals. Year-long simulations on the Texas 2000-bus system validate real-world applicability, with regional analysis revealing how renewable-rich areas offset emission responsibility through exports while load centers bear responsibility for driving system-wide generation.