As renewable energy depends on meteorological shocks and is non-controllable, the overall energy production becomes riskier with the rising renewable share. Although this has led to a renewed interest in storage technologies, not much consideration has been given to energy storage due to precautionary motives. In our study, we look at to what extent a convex marginal utility (prudence) and a convex marginal cost (frugality) can spur precautionary energy storage. We set up a simple theoretical model of energy consumption and production with intermittent renewable sources, dispatchable thermal systems, and energy storage. First, we characterize the optimum and show how prudence and frugality can lead to higher levels of energy storage. Furthermore, we demonstrate how the optimal allocation can be decentralized through competitive markets. Our analysis indicates that prudence and frugality increase the market energy price through higher demand for energy storage and decrease price volatility. The results present important lessons about the direct and indirect impacts precautionary motives can have on electricity prices and energy generation decisions.