Concerns about climate change have spurred governments to reduce carbon emissions by supporting adoption of renewable energy (RE) technologies. Due to the intermittent and location-specific nature of RE technologies, energy storage has become important because it could be used to smooth out temporal disparities in residual demand. Thus, carbon policy has made storage-enabled RE generation more critical to the power sector, and this enhanced position could be exploited by firms to exert market power. Using an equilibrium model, we examine the implications of policy interventions and technological change on the marginal value of energy storage in a power market with RE and thermal generation. In particular, we specify the market conditions under which RE producers with storage strategically shift deployment of their resource to the off-peak period and outline its implications for the marginal value of RE storage. Moreover, we find that even price-taking RE producers may actually increase off-peak RE production as storage efficiency increases. Consequently, the RE producer's profit decreases with storage efficiency, which conflicts with the social objective of improving storage efficiency. These private and social incentives can be better aligned via a carbon tax, however. Hence, our results may inform the regulatory process governing market design of a power sector with increasing capacities of RE generation and storage.