<p>To reduce the computational burden and enhance the control performance of modular multilevel energy storage converters, an improved three-layer hierarchical control strategy for a five-level modular energy storage converter is proposed in this paper, including a phase current layer, a circulating current layer, and an intra-arm submodule layer. Based on the model predictive control (MPC) concept, an objective function is designed for the first layer to minimize the current tracking error and generate the differential-mode voltage reference. Then, a compensation voltage concept is introduced to integrate circulating current suppression with SOC balancing control, based on which a circulating current objective function is formulated to obtain the arm voltage reference. For the third layer, a strategy extending the update period for arm-average SOC is proposed to determine the switching states. Additionally, prediction compensation and reference value correction are implemented in both the phase current and intra-phase circulating current layers to reduce the number of optimization iterations. Numerous comparative experiments based on hardware-in-the-loop (HIL) demonstrate that this three-layer hierarchical control strategy can reduce computational requirements while maintain effective performance in both SOC balancing and circulating current suppression.</p>