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Industrial Application of the Shapley value-based Redispatch Cost Allocation to Large-Scale Power Grids requires AC Optimal Power Flow

Rebecca Bauer, Xinliang Dai, Veit Hagenmeyer

TL;DR

The paper tackles fair redispatch cost allocation in congested power grids by evaluating how AC Optimal Power Flow (OPF) affects Shapley-value-based allocations, as opposed to the commonly used DC OPF. It formalizes congestion cost sharing as a cooperative game where congested lines are players, and computes costs via OPF results under coalition-specific line-limit modifications. Across benchmarks from 9 to 2383 buses, AC OPF materially changes congestion patterns, redispatch costs, and Shapley allocations, sometimes increasing congestions yet lowering total costs, with Shapley values not simply proportional to overloads. The work concludes that AC OPF is necessary for accurate CM cost allocation and discusses implications for real-world TSO practice and future research directions, including real-world validation and distributed AC OPF approaches.

Abstract

A burgeoning topic in the current energy transition are the huge costs of redispatch congestion management (CM) in large transmission systems. One of the German transmission system operators (TSOs) raised the critical inquiry of how to allocate the redispatch costs amongst TSOs in an equitable and beneficial way. Previously, a Shapley value-based approach has been introduced on small test grids, using the linear DC approximation of optimal power flow (OPF). However, within the application of CM, its feasibility and accuracy for large-scale power grids and its impact on the computed congestions remain uncertain. Therefore, this study investigates the applicability of the DC OPF compared to the exact AC OPF with regard to the Shapley values, for both small and large-scale grids. Numerical simulation shows significant differences in the congested lines, the overall redispatch costs, and the Shapley values. These findings suggest that for future CM, the TSOs should further investigate AC OPF solutions.

Industrial Application of the Shapley value-based Redispatch Cost Allocation to Large-Scale Power Grids requires AC Optimal Power Flow

TL;DR

The paper tackles fair redispatch cost allocation in congested power grids by evaluating how AC Optimal Power Flow (OPF) affects Shapley-value-based allocations, as opposed to the commonly used DC OPF. It formalizes congestion cost sharing as a cooperative game where congested lines are players, and computes costs via OPF results under coalition-specific line-limit modifications. Across benchmarks from 9 to 2383 buses, AC OPF materially changes congestion patterns, redispatch costs, and Shapley allocations, sometimes increasing congestions yet lowering total costs, with Shapley values not simply proportional to overloads. The work concludes that AC OPF is necessary for accurate CM cost allocation and discusses implications for real-world TSO practice and future research directions, including real-world validation and distributed AC OPF approaches.

Abstract

A burgeoning topic in the current energy transition are the huge costs of redispatch congestion management (CM) in large transmission systems. One of the German transmission system operators (TSOs) raised the critical inquiry of how to allocate the redispatch costs amongst TSOs in an equitable and beneficial way. Previously, a Shapley value-based approach has been introduced on small test grids, using the linear DC approximation of optimal power flow (OPF). However, within the application of CM, its feasibility and accuracy for large-scale power grids and its impact on the computed congestions remain uncertain. Therefore, this study investigates the applicability of the DC OPF compared to the exact AC OPF with regard to the Shapley values, for both small and large-scale grids. Numerical simulation shows significant differences in the congested lines, the overall redispatch costs, and the Shapley values. These findings suggest that for future CM, the TSOs should further investigate AC OPF solutions.
Paper Structure (11 sections, 2 equations, 5 figures, 2 tables)

This paper contains 11 sections, 2 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Notation
  4. Shapley Value for Cost Allocation
  5. AC OPF Formulation
  6. Experiments & Results
  7. DC vs. AC OPF in the Shapley algorithm
  8. Discussion
  9. Conclusion
  10. Appendix
  11. Grid modifications

Figures (5)

  • Figure 1: The Shapley algorithm.
  • Figure 2: The images show the overloaded lines with DC OPF (left) and AC OPF (right).
  • Figure 3: Case39 with congestions from DC and AC OPF.
  • Figure 4: Case118 with congestions from DC and AC OPF.
  • Figure 5: Case2383 with congestions from DC and AC OPF.