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Magnetically controlled reactors (MCRs) are widely used as reactive power compensation equipment owing to their favorable properties of smoothly adjusting their inductance value through dc bias. However, the dc bias and the rotational magnetization at corner and T-joint areas make the cores of MCRs saturated, resulting in high magnetostriction and vibration. Thus, the electromagnetic vibration analysis of MCRs must consider the vector hysteretic magnetostriction effect. In this article, a vector hysteretic magnetostriction model of silicon steel is proposed by combining the quadratic domain rotation model with the vector inverse Jiles–Atherton model firstly. Then, based on the measured magnetization and magnetostrictive characteristics curves of silicon steel, the model’s parameters are optimized by velocity controllable particle swarm optimization (VCPSO). Finally, the vector hysteretic magnetostriction model is combined with the finite element method (FEM) to simulate the vector vibration characteristics of MCR under dc bias. The simulation results show that the vector property of electromagnetic vibration and magnetic field at the T-joint area is higher than that at other areas. And the MCR vibration test results are consistent with the simulation results, which verify the accuracy of the proposed model in simulating electromagnetic vibration. [ABSTRACT FROM AUTHOR]