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This paper focuses on pricing Energy Storage as a Service (ESaaS) for Transmission congestion relief (TCR). We consider a merchant storage facility that competes in an electricity market to trade energy and ancillary services on a day-to-day basis. The facility also has the opportunity to provide a firm TCR service to a regional network operator under a long-term contract. Providing the additional TCR service would impose limitations on the facility's ability to fully harvest daily market trade opportunities. Thus, we model the opportunity costs associated with the TCR service and use it in a hybrid cost-value customized pricing technique to determine the risk-constrained optimal price of ESaaS for TCR. Given the long-term nature of the commitment to provide the TCR service, we use the Conditional Value at Risk (CVaR) metric to mitigate the long-term financial risks faced by the facility. The proposed pricing strategy enables the storage owner to estimate the additional financial gains and the associated risks that would likely result from adding the new service to its operation. Numerical simulations are provided to support the proposed methodology.INDEX TERMS Energy storage as a service (ESaaS), transmission congestion relief, storage as transmission asset (SATA).