Permanent Magnet Synchronous Machine (Power System Blockset)

Model the dynamics of a three-phase permanent magnet synchronous machine with sinusoidal flux distribution

Library

Description

The Permanent Magnet Synchronous Machine (PMSM) block operates in either motoring or generating mode. The mode of operation is dictated by the sign of the mechanical torque (positive for motoring, negative for generating). The electrical and mechanical parts of the machine are each represented by a second-order state-space model. The model assumes that the flux established by the permanent magnets in the stator is sinusoidal, which implies that the electromotive forces are sinusoidal.

The block implements the following equations expressed in the rotor reference frame (qd frame):

Electrical System

where (all quantities in the rotor reference frame):

L_q, L_d: q and d axis inductances
R: resistance of the stator windings
i_q, i_d: q and d axis currents
v_q, v_d: q and d axis voltages
: angular velocity of the rotor
: amplitude of the flux induced by the permanent magnets of the rotor in the stator phases
p: number of pole pairs
T_e: electromagnetic torque Mechanical System

where:

J: Combined inertia of rotor and load
F: Combined viscous friction of rotor and load
: Rotor angular position
T_m: Shaft mechanical torque

Dialog Box

Inputs and Outputs

The first three inputs are the electrical connections of the machine's stator. The fourth input is the mechanical torque at the machine's shaft (Simulink signal). This input should ordinarily be positive because the PMSM block is usually used in a motor mode. Nevertheless, you can apply a negative torque input if you choose to use the PMSM block in generating mode.

The block outputs a vector containing the following ten variables (all currents flowing into machine):

1-3: Line currents i_a, i_b and i_c, in A;
4-5: q and d axis currents i_q and i_d, in A;
6-7: q and d axis voltages v_q and v_d, in V;
8: Rotor electrical speed , in rad/sec;
9: Rotor electrical angle , in degrees;
10: Electromagnetic torque T_e, in N.m. These variables can be demultiplexed by using the special Permanent Magnet Synchronous Machine Demux block provided in the powerlib/Machine library.

Assumption

The block assumes a linear magnetic circuit with no saturation of the stator and rotor iron. This assumption can be made because of the large air gap usually found in permanent magnet synchronous machines.

Example

This example illustrates the use of the PMSM block in the motoring mode with a closed-loop control system built entirely in Simulink. The interfacing is done using Controlled Voltage Source blocks from the powerlib/Electrical Sources library. The complete system consists of a PWM inverter built with ideal switches (Simulink Relay blocks). Two control loops are used; the inner loop is used to regulate the motor line currents and the outer loop regulates the motor's speed. The mechanical torque applied at the motor's shaft is originally 3 N.m (nominal) and steps to 1 N.m at t=0.025 sec. The parameters of the machine are those found in the Dialog Box section.

Open the Simulink diagram by typing psbpmmotor or by choosing Permanent Magnet Sync Mach (sim) from the demos group in the powerlib library. Set the simulation parameters as follows:

Integrator type: Stiff, ode15s
Stop time: 0.06
Integration options: Use default options, except for Absolute tolerance which you can set to 1e-3. Run the simulation. Once the simulation is completed, observe the motor's torque and speed.

The torque climbs to nearly 32 N.m when the motor starts but stabilizes rapidly to its nominal value (3 N.m), until the step is applied, at which point the torque oscillates slightly before stabilizing to its new value (1 N.m). As for the speed, you can see that it stabilizes quite fast at start-up and is not affected by the load step. Now, observe the line currents.

As for the torque, the currents are high when the machine starts, but stabilize quickly to their nominal value until the step is applied. Then they oscillate before stabilizing to a lower value, corresponding to the load torque decrease.

[ Previous | Help Desk | Next ]