Traditionally, power systems have been operated to minimize cost while maintaining reliability. However, extreme weather and demand events can affect traditional thermoelectric power generation operations due to their reliance on water for cooling. This paper contributes a novel multi-objective formulation of the optimal power flow (OPF) problem where cost, water withdrawal, and water consumption are minimized. Through this formulation, we assign optimization weights to water withdrawn and consumed, which can be directly incorporated into existing OPF formulations. We apply this formulation with a global mapping sensitivity analysis to a realistic case study to first demonstrate its general effectiveness under extreme climatic, hydrologic, and operational scenarios. Then, we apply a global ranking sensitivity analysis to determine the most influential generators for system performance. Through this operational scenario analysis framework, analysts can gain insights into potential system-level and component-level vulnerabilities within power systems. Such insights can be useful for informing both short-term operations as well as long-term power system planning.