Mathematical model analysis of new-type magnetic integrated CRT considering magnetic leakage

A novel magnetic integrated controllable reactor of transformer type(CRT)has the advantages of simple structure,flexible assembly,convenient maintenance and practicability.To analyze its operation characteristics accurately,we establish corresponding equivalent mathematical model considering magnetic leakage based on magnetic circuit and circuit dualistic transformation method.The distribution of magnetic leakage field of each winding is analyzed qualitatively,and the analytical calculation formulas of magnetizing inductance and leakage inductance of each winding are derived.Based on this,the analytical calculation formulas of short-circuit impedance and winding current of CRT under different working conditions are derived.The field-circuit coupling finite element model of the magnetic integrated CRT is established to simulate the current of each winding under different working conditions.The results show that the analytical calculation results of each winding current have good consistency with the finite element calculation results,indicating the validity of CRT equivalent mathematical model and correctness of the analytical formulas of leakage inductance,short-circuit impedance and winding current of CRT.The working winding current of CRT is increasing gradually with the operation of control winding in turn to realise the transition of CRT compensation capacity from zero to a rated value.

PRINCIPLES AND PARAMETER DESIGN FOR AC-DC THREE-DEGREE FREEDOM HYBRID MAGNETIC BEARINGS

To simplify the mechanical structure, decrease the overall system size of the 3-degree freedom axial-radial magnetic bearings and reduce the manufacturing costs as well as operating costs, an innovated AC-DC 3-degree freedom hybrid magnetic bearing is proposed, which is driven by a DC amplifier in axial direction and a 3-phase power converter in radial directions respectively, and the axial and radial bias magnetic fluxes are provided with a common radial polarized permanent magnet ring. The principle producing magnetic suspension forces is introduced. By using equivalent magnetic circuit method, the calculation formulas of magnetic suspension forces and the mathematics models of the system are deduced. Nonlinearities of suspension forces and cross coupling between different degree freedoms are studied further by calculating the suspension forces at different displacements and control currents to validate the feasibility of the mathematics model. Then based on the mathematics models of the bearing, a control method of this novel bearing is designed. Lastly, the methods on parameter design and calculations of the bearing are presented, and an applicable prototype is simulated to analyze the magnetic path by using finite element analysis. The theory analysis and simulation results have shown that this magnetic bearing incorporates the merits of 3-phase AC drive, permanent magnet flux biased and axial-radial combined control, and reduces overall system size and has higher efficiency and lower cost, This innovated magnetic bearing has a wide application in super-speed and super-precision numerical control machine tools, bearingless motors, high-speed flywheels, satellites, etc.