Strategic behavior in TSO-DSO coordinated flexibility markets: A Nash equilibrium and efficiency analysis

This paper investigates the way in which the design of a TSO-DSO coordinated flexibility market can enable strategic behavior by flexibility service providers (FSPs). Multiple flexibility market models are considered for the procurement of flexibility services by transmission and distribution system operators, namely: a common (joint) market, a fragmented market, and a sequential multi-level market. Considering these market models, three non-cooperative games are introduced to investigate the strategic bidding and interaction between FSPs therein. Detailed conclusions are then drawn on the existence and uniqueness of Nash Equilibria (NEs) in the developed games, including derivations of closed-form expressions of the resulting NEs and corresponding price-of-anarchy, capturing the FSPs' strategic bidding impact on the markets' efficiency. The analysis considers - first in a duopoly setting, then with multiple players - three different use cases representing when: (1) a sufficient flexible capacity exists (sufficient flexibility offered from the FSPs and adequate interconnection/grid capacity between systems); (2) participants have a scarce flexibility capacity; and (3) a restrictive interface capacity exists between the systems. A case study considering an interconnected transmission-distribution system and multiple FSPs corroborates the analytical findings. The obtained results show that market participants have incentives to set bid prices greater than their marginal costs, thus decreasing the markets' efficiency. This aspect is shown to be more pronounced when the available flexible capacity is limited, a restrictive line limit is present, or when the market is fragmented, thus supporting the need for additional network investments and the creation of joint flexibility market formats.