MODELING OF A PERMANENT MAGNET SYNCHRONOUS MOTOR

BIBHU PRASAD GANTHIA

Permanent Magnet Synchronous Motor (PMSM)The PMSM is a brushless machine with

sinusoidal flux distribution, for which reason it is also known as a brushless AC (BLAC) machine.

In a PMSM the stator voltage must be sinusoidal. The amplitude and frequency of the stator voltage must be related to the rotor speed, and the sinusoidal waveform must be in tune with the rotor position.

Modeling of a PMSM in SIMULINK

The PMSM is usually modeled in the rotor synchronous rotating frame (q/d frame). A three phase PMSM is electrically described in the rotor synchronous rotating frame by the following equations (Park equations)

(Where Vq,Vd,iq,id are the stator voltage and current quadrature and direct components, Rs is the stator resistance Lqs,Lds are the stator quadrature and direct impedances, λm is the amplitude of the flux linkages established by the rotor permanent magnet, and ωe is the angular speed of the stator electromagnetic field. )

The electromagnetic torque produced by the motor is given by:

(2)

where P is the number of rotor magnetic poles. If the rotor is perfectly round, the quadrature and direct impedances are equal, and in this case the electromagnetic torque only depends on the quadrature stator current.

The mechanical equation of the motor is: (3)

where J is the rotor moment of inertia, TL is the load torque, and F is the friction factor.

As it can be observed in equation (4), the speed is controlled by controlling the electromagnetic torque. This, in turn, is controlled by controlling the quadrature current, as it is indicated by (2). The quadrature and direct currents are controlled by the quadrature and direct applied voltages, according to (1). It can be observed that cross-coupling appears between the two axes currents. This cross-coupling must be compensated in the controller.

The motor is fed by a three phase voltage source inverter (VSI). The VSI is controlled using space vector modulation (SVM) and the SVM algorithm is applied directly to the α/β voltage components.

The PI controllers were discretized using the Tustin approximation, and are described in discrete time by the equation:

Where KI is the integral gain ,Kp is the proportional gain, ε is the controller input, and u is the controller output.

The a/b/c to q/d transform consists of two consecutive transforms, a/b/c to α/β and α/β to q/d:

The SVM algorithm was replaced at this stage of simulation by an α/β to a/b/c transformation and the three phase voltages were fed to the motor model by means of SimPowerSystems controlled voltage sources.

Simulation results

Ia,Ib,Ic CURRENTS

Id,Iq Currents

Torque of pmsm motor

Speed of pmsm motor

ConclusionA novel holistic modeling of speed controller for PMSM was presented, usingMatlab Simulink and System Generator. The approach presented allows the modeling ofthe controller and the controlled system in the same environment.

Future workThe classical PWM method is used to

generate the requested motor voltages. Toimprove the system performance in terms of

torque ripple, power quality and better DCvoltage utilization, space vector modulation

can be employed. The speed is estimated bythe measurement of the position. The speed

estimation can be improved by the use ofKalman lters

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