# Documentation

## AC7 - Comparison Between Detailed and Simplified Models

This example shows the AC7 detailed model and the AC7 average model during speed regulation. The comparison is performed for normal condition and for inverter saturation condition.

O.Tremblay, L.-A. Dessaint (Ecole de technologie superieure, Montreal)

### Description

This circuit uses two AC7 blocks of Simscape™ Power Systems™ library. It models a brushless DC motor drive with a braking chopper for a 3HP motor. The first block is set to average value model and the second is set to detailed model.

For the detailed model, the permanent magnet (PM) synchronous motor (with trapezoidal back-EMF) is fed by a PWM voltage source inverter, which is built using a Universal Bridge Block. The average value model uses ideal voltages and currents sources to feed the PM synchronous motor. The speed control loop uses a PI regulator to produce the torque reference for the current control block. The current control block computes the three reference motor line currents, in phase with the back electromotive forces, corresponding to the torque reference and then feeds the motor with these currents using a three-phase current regulator.

Motor currents, voltages, speed, and torque signals are available at the output of the block.

### Simulation

Start the simulation. You can observe the motor stator current, the back EMF, the rotor speed and the electromagnetic torque on the first scope. The speed set point and the torque set point are also shown. On the second scope, the DC bus voltage and the bus current are displayed. Note that all signals are multiplexed to compare the two models.

At time t = 0 s, the speed set point is 2400 rpm and the full load torque is applied to the motor. Observe that the speed follows precisely the acceleration ramp.

At t = 0.6 s, the inverter is saturated due to insufficient inverter voltage. You can observe loss of current tracking which decreases the motor torque. This saturation point occurs when the speed is about 1200 rpm. That's the same point as predicted by the operation region during acceleration (when load torque is 11 Nm) given by the Speed-Torque curve tool (double-clcik on the 'Speed-Torque curve' tool to check the operating regions).

At t = 1.2 s, the speed set point is changed to -2400 rpm.

At t = 1.6 s., the deceleration ramp reaches the motor speed. The inverter comes back to normal mode.

At t = 2 s., the mechanical load passes from 11 Nm to -11 Nm.

At t = 3 s., the inverter is saturated due to insufficient inverter voltage. You can observe loss of current tracking which decreases the motor torque.

Finally, note how the simplified model reacts well compared to the detailed model.

### Notes

To evaluate the speed gain of the average value model, see ac7_example_simplified and compare the simulation speed with ac7_example.

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