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

Yuanhao Feng, Tao Sun, Yan Meng, Xuxin Yang, Donghan Feng

TL;DR

The paper addresses the intractability of fair, Shapley-value-based carbon emission allocation in large power networks. It introduces SurroShap, which fuses KernelSHAP sampling with a deep neural network surrogate to rapidly estimate emissions for thousands of coalitions, enabling near real-time Shapley allocations. The authors derive time-averaged, multi-period error bounds showing allocations are $\varepsilon$-close to exact Shapley values, and demonstrate dramatic computational speedups ($10^4$–$10^5$×) across nine systems up to $n_N=1951$, including a year-long Texas 2000-bus analysis that reveals regional emission responsibility patterns. This work provides a scalable, fair CER benchmarking framework for large-scale power systems and offers a blueprint for applying SurroShap to other equilibrium-based allocation problems.

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.

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

TL;DR

The paper addresses the intractability of fair, Shapley-value-based carbon emission allocation in large power networks. It introduces SurroShap, which fuses KernelSHAP sampling with a deep neural network surrogate to rapidly estimate emissions for thousands of coalitions, enabling near real-time Shapley allocations. The authors derive time-averaged, multi-period error bounds showing allocations are -close to exact Shapley values, and demonstrate dramatic computational speedups (–×) across nine systems up to , including a year-long Texas 2000-bus analysis that reveals regional emission responsibility patterns. This work provides a scalable, fair CER benchmarking framework for large-scale power systems and offers a blueprint for applying SurroShap to other equilibrium-based allocation problems.

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 -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.

Paper Structure

This paper contains 21 sections, 23 equations, 7 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Fair allocation of carbon emission responsibility
  3. Problem Formulation
  4. Allocation Properties
  5. The SurroShap Method
  6. KernelSHAP: Sampling-Based Shapley Approximation
  7. Deep Learning Surrogate Model
  8. SurroShap Algorithm
  9. Approximation Error Analysis
  10. Single-Period Error Bound
  11. Multi-Period Error Bound
  12. Practical Error Estimation
  13. Numerical Experiments
  14. Test Systems and Data Sources
  15. Deep Learning Surrogate Training
  16. ...and 6 more sections

Figures (7)

  • Figure 1: Schematic diagram of the SurroShap framework.
  • Figure 2: Estimation of KernelSHAP approximation error bounds via power-law decay function fitting to convergence trajectories. See $\phi_t(m)$ in \ref{['27']}.
  • Figure 3: Convergence of approximation errors on IEEE 30-bus system. (a) Single-period relative error as a function of number of sampled coalitions. (b) Cumulative error evolution across multiple allocation rounds.
  • Figure 4: Validation of allocation properties on IEEE 118-bus system. (a) Baseline CER distribution. (b) Property 3: reduced gas offers decrease CERs. (c) Property 6: profile reshaping benefits. (d) Property 5: load reduction incentive. (e) Property 2: emission intensity improvement rewards.
  • Figure 5: Year-long CER allocation for Texas 2000-bus system showing daily statistics by entity type. Median values (solid lines) with percentile ranges (10th-90th through 40th-60th) demonstrate seasonal patterns and allocation stability.
  • ...and 2 more figures