Renewable energy is playing a growing role in modern energy systems, while its intermittent characteristics pose significant challenges to the economic and safety operation of power grid. Markov decision process (MDP) models are widely used to study the dynamic scheduling of renewable energy systems, which can capture the stochastic nature of renewable energy and the dynamic characteristics of energy scheduling. In this paper, we propose a steady-state value-at-risk (VaR, also known as quantile)-constrained MDP model for the dynamic scheduling of renewable energy systems, aiming to achieve coordinated economic and safety management. This model optimizes the performance when the system attains steady state. Specifically, the objective is to minimize the long-run average cost for economic performance while ensuring safety by imposing a steady-state VaR constraint, which limits the power fluctuations exchanged between the main grid and the microgrid to below a specified threshold with high probability. Leveraging the duality between VaR and probability constraints, we reformulate the steady-state VaR-constrained MDP as a linear programming problem, which can be solved efficiently. Finally, we validate our approach by using a numerical experiment with real data of a microgrid with wind power.