Abstract: Aiming at the demand for high-voltage, large-capacity and cost-effective AC-AC converters in low-frequency power transmission and variable-speed pumped storage, a novel half-cycle variable-frequency AC-AC converter topology is proposed. A complete mathematical model of the topology is established to clarify the internal relationships among circulating current, arm current and voltages of each part, and reveal the core rule that the full-bridge voltage is constituted by the difference of half-wave voltages on both sides. The dynamic characteristics of sub-module capacitor voltage and the harmonic distribution characteristics of circulating current are analyzed in depth, which provides a theoretical basis for the design of hierarchical control strategies. Aiming at the voltage stability and balance of numerous floating capacitors in the converter, a hierarchical energy balance control strategy is proposed. The energy balance between the power-frequency side and the low-frequency side is realized by suppressing the sixth-harmonic component, the voltage balance among three-phase arms is achieved by regulating the second-harmonic circulating current, and the capacitor voltage sharing inside the arm is implemented combined with the sub-module switching logic. Simulation results show that the proposed control strategy can effectively suppress the circulating current harmonics and capacitor voltage fluctuations, quickly converge the voltage deviation between phases and sub-modules, and significantly improve the steady-state operation performance and reliability of the converter. It can provide an efficient and reliable technical solution for flexible low-frequency power transmission, offshore wind power delivery and variable-speed pumped storage systems.