With the increasing proportion of new energy, the inertia support, voltage support, and frequency regulation ability are obviously weakened in current power system. The development of energy storage system with synchronous condenser and flywheel (ESSSCF) is of great significance to improve the regulation capability of new energy power generation and enhance the stability of new power systems. This article briefly describes the principle and different operation states of the magnetic-geared speed regulator (MGSR) for ESSSCF, and focuses on the design optimization of its electromagnetic structure. The electromagnetic finite element model of the MGSR is established. The shape of the flux barrier is selected for the inner rotor with V-shaped permanent magnet by calculating and analyzing the no-load leakage flux factor. The geometric parameters of the V-shaped permanent magnets and stator slots and the pole-arc coefficient of the modulating ring are optimized for multiple objectives, respectively, using genetic algorithm, under the conditions of a constant amount of permanent magnet and a constant area of stator slot. In addition, the correlation of the target performances with the geometric parameters is analyzed. The results of the design optimization and correlation analysis can direct the structural design of the magnetic-geared speed regulator for improvement of the torque and efficiency performances.