Electrical energy storage could play an important role in decarbonizing the electricity sector by offering a new, carbon-free source of operational flexibility, improving the utilization of generation assets, and facilitating the integration of variable renewable energy sources. Yet, the future cost of energy storage technologies is uncertain, and the value that they can bring to the system depends on multiple factors. Moreover, the marginal value of storage diminishes as more energy storage capacity is deployed. To explore the potential value of energy storage in deep decarbonization of the electricity sector, we assess the impact of increasing levels of energy storage capacity on both power system operations and investments in generation capacity using a generation capacity expansion model with detailed unit commitment constraints. In a case study of a system with load and renewable resource characteristics from the U.S. state of Texas, we find that energy storage delivers value by increasing the cost-effective penetration of renewable energy, reducing total investments in nuclear power and gas-fired peaking units, and improving the utilization of all installed capacity. However, we find that the value delivered by energy storage with a 2-hour storage capacity only exceeds current technology costs under strict emissions limits, implying that substantial cost reductions in battery storage are needed to justify large-scale deployment. In contrast, storage resources with a 10-hour storage capacity deliver value consistent with the current cost of pumped hydroelectric storage. In general, while energy storage appears essential to enable decarbonization strategies dependent on very high shares of wind and solar energy, storage is not a requisite if a diverse mix of flexible, low-carbon power sources is employed, including flexible nuclear power.