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In this paper, a transmission-distribution systems flexibility market isintroduced, in which system operators (SOs) jointly procure flexibility fromdifferent systems to meet their needs (balancing and congestion management)using a common market. This common market is, then, formulated as a cooperativegame aiming at identifying a stable and efficient split of costs of the jointlyprocured flexibility among the participating SOs to incentivize theircooperation. The non-emptiness of the core of this game is then mathematicallyproven, implying the stability of the game and the naturally-arising incentivefor cooperation among the SOs. Several cost allocation mechanisms are thenintroduced, while characterizing their mathematical properties. Numericalresults focusing on an interconnected system (composed of the IEEE 14-bustransmission system and the Matpower 18-bus, 69-bus, and 141-bus distributionssystems) showcase the cooperation-induced reduction in system-wide flexibilityprocurement costs, and identifies the varying costs borne by different SOsunder various cost allocations methods.

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