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This paper basically concentrates on the impact of a price-maker energy storage unit (PMESU) on the operation of the power system. Recently, energy storage systems (ESSs) have attracted much attention as one of the renewable and pollution-free sources of energy and are applicable due to their exclusive advantages in power systems. In this paper, the ESS considered as a price-maker market player, which attempts to maximize the benefits of its competition in the market environment. The main operation problem of the PMESU represented as a bi-level optimization problem which comprises of nonlinear terms. First, a stochastic-based bidding/offering approach (SBOA) is considered which is less complex and takes lesser time to be solved compared to the MPEC method. Second, conditional Value-at-Risk (CVaR) method is used in order to control the risk of utilizing inoperative scenarios. Finally, the operation problem of the proposed PMESU is formed as a max-min problem in order to analyse the impact of the PMESU in the worst case condition from the perspective of the independent system operator (ISO). In addition, transmission switching (TS) method is utilized to minimize the system operation cost from the ISO point of view. The performance of the proposed method has been evaluated on an IEEE 9-bus test system which shows the authenticity and validity of this work. • Proposing SBOA based method in a stochastic scenario-based framework to model the correlated uncertainty. • Assessing the impact of market participants in a worse-case scenario from the ISO perspective. • Analyzing the mutual effect of risk-based participation procedure and the congestion situation. • Proposing a TS method to reduce the ISO cost considering the price-maker participant. [ABSTRACT FROM AUTHOR]