The rapid growth of the share of energy generated via renewable sources highly challenges grid stability. Flexibility is key to balance the electricity supply and demand. As a relatively new player in the energy market, the Energy Storage System (ESS) is capable of providing such flexibility, acting as both a consumer and producer. Since the Direct. The ongoing energy transition is leading to a substantial increase in the installed capacity of Renewable Energy Sources (RESs) (Hansen, Breyer, & Lund, 2019). In Germany, for example, the installed capacity has more than doubled from 56,545 MW in 2010 to 125,386 MW at the end of 2019 (IRENA, 2020). In total, RESs supplied almost 43 percent of Germany's electricity demand in 2020 (BDEW, 2020). The rapid growth in the share of RESs in the total electricity supply highly challenges grid stability. Due to the intermittent feed-in of RESs, it has become more difficult to maintain the necessary balance of electricity demand and supply in the grid (Fridgen, Keller, Körner, Schöpf, 2020, Ludig, Haller, Schmid, Bauer, 2011). For example, uncertainties in weather forecasts can lead to unexpected peaks in the electricity supplied by RESs. The supply by RESs can only be controlled to a limited extent as, while RESs can be curtailed, upwards adjustments of supply are limited to the respective source of electricity generation, such as solar energy or wind. An increased or decreased feed-in compared to the forecasted one can destabilize the electricity grid and, hence, it requires cost-intensive grid balancing activities such as redispatch measures. For example, German Transmission System Operators (TSOs) spent 207.1 million Euros on redispatch measures in 2019 (Bundesnetzagentur, 2019). In order to be able to adapt both the supply and the demand of electricity to one another as quickly as possible, the system require. In this section, we present the most recent works concerning i.) the basic concepts of market design and congestion management, ii.) the operations of an ESS as a price-taker, iii.) the ESS operations within imperfectly-competitive markets without modeling the transmission grid, and iv.) the operations of an ESS within imperfectly-competitive markets considering physical grid constraints.In contrast to other physical goods, various physical transmission constraints that affect the flow ofIn this section, we introduce the hierarchical structure of the four-stage Stackelberg model that we propose. Afterwards, we introduce the sets, parameters, and variables that are used throughout the paper and present the modeling framework that we rely upon. For the sake of readability, we will refer to the ESS simply as ESS throughout the subsequ. In this section, we formulate the problem of computing an equilibrium in the four-stage Stackelberg game we introduced before as a multilevel mathematical programming problem. Fig. 1 gives an overview of the objective functions and the corresponding constraints in the four levels. For the sake of clarity, we introduce our model under the assumption.
