# TSO-DSOs Stable Cost Allocation for the Joint Procurement of Flexibility: A Cooperative Game Approach

arXiv: https://arxiv.org/abs/2111.12830 · HTML: https://mlsanity.com/paper/2111.12830/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 50 references that are in the map.
- First posted on arXiv 24 Nov 2021.

## Builds on (most cited first, 7 of 7)

- [QuickFlex: a Fast Algorithm for Flexible Region Construction for the TSO-DSO Coordination](https://mlsanity.com/paper/2107.00114/) (2021)
- [Data Injection Attacks on Smart Grids with Multiple Adversaries: A Game-Theoretic Perspective](https://mlsanity.com/paper/1604.00118/) (2016)
- [Coordination Between TSOs and DSOs: Flexibility Domain Identification](https://mlsanity.com/paper/2009.02088/) (2020)
- [A New Cooperative Framework for a Fair and Cost-Optimal Allocation of Resources within a Low Voltage Electricity Community](https://mlsanity.com/paper/2010.05544/) (2020)
- [Modelling and Characterisation of Flexibilityfrom Distributed Energy Resources](https://mlsanity.com/paper/2107.05144/) (2021)
- [Cyber-physical risk modeling with imperfect cyber-attackers](https://mlsanity.com/paper/2110.00301/) (2021)
- [A Linear Model for Distributed Flexibility Markets and DLMPs: A Comparison with the SOCP Formulation](https://mlsanity.com/paper/2111.02328/) (2021)

## Abstract (arXiv)

In this paper, a transmission-distribution systems flexibility market is introduced, in which system operators (SOs) jointly procure flexibility from different systems to meet their needs (balancing and congestion management) using a common market. This common market is, then, formulated as a cooperative game aiming at identifying a stable and efficient split of costs of the jointly procured flexibility among the participating SOs to incentivize their cooperation. The non-emptiness of the core of this game is then mathematically proven, implying the stability of the game and the naturally-arising incentive for cooperation among the SOs. Several cost allocation mechanisms are then introduced, while characterizing their mathematical properties. Numerical results focusing on an interconnected system (composed of the IEEE 14-bus transmission system and the Matpower 18-bus, 69-bus, and 141-bus distributions systems) showcase the cooperation-induced reduction in system-wide flexibility procurement costs, and identifies the varying costs borne by different SOs under various cost allocations methods.