The mathematical model of permanent magnet synchronous motor

When the permanent magnet synchronous motor stator flux into the three-phase alternating current (ac),the three phase current produced in the stator winding resistance voltage drop.Rotate the armature magnetomotive force produced by three-phase alternating current (ac) and set up the armature magnetic field,Cutting of the acmotor2.blogspot.com stator winding is on the one hand,and produce inductive electromotive force in stator winding;On the other hand with the electromagnetic drive rotor synchronous speed rotation.The armature current will produce only chain fellowship with the stator winding of the stator winding perkins diesel generator magnetic flux leakage,and in the stator winding The leakage is induced emf.In addition,magnetic fields produced by permanent magnet rotor to the stator winding of synchronous speed cutting.

Resulting in a no-load electromotive force.In order to facilitate analysis,the mathematical model is set up,assume the following parameters:(1) to ignore the iron of the motor Heart saturated;(2) regardless of the motor in eddy current and hysteresis losses;(3) the magnetic field generated by the stator and rotor magnetomotive force along the stator inner circle according to the sine distribution,namely ignoring all space harmonics in the magnetic field;(4) of each phase winding is symmetrical,namely each phase winding of the number of turns and electricity Resistance is the same,each phase axis displacement each other the same Angle.Based on the analysis low rpm generator alternator of  the mathematical model of synchronous motor,often using two phase synchronous rotation (d,q) coordinate system and two-phase static coordinate system (alpha,beta).

Figure 1 shows in permanent magnet synchronous motor (d,q) The mathematical model of rotating coordinate system.(1) of the stator voltage equation is:type:r for stator winding resistance;P for differential operator,p = d/dt;Id,IQ for stator current;Ud,uq for stator

voltage;Bits of d,bits of q respectively flux in d,q axis The component;F the rotor angular velocity

omega (omega = omega FNP);Np for motor logarithmic.(2) of the generator stator

stator flux linkage equations as follows:type:bits of f for the rotor flux linkage.(3) the

electromagnetic torque is:type:J is the moment of inertia of the motor.If the electric Motivation for

non-salient pole motor,the Ld = Lq,select id,IQ and motor mechanical angular velocity omega as state

variables,the available state equation of permanent magnet synchronous motor are as follows:by type

(7) can be seen,three-phase permanent magnet synchronous motor is a multivariable System,and the id,IQ,omega nonlinear coupling relationship between,in order to achieve high performance control of three-phase permanent magnet synchronous motor,is a challenging task.