## DC1 - Two-Quadrant Single-Phase Rectifier 5 HP DC Drive

This example shows the DC1 two-quadrant single-phase rectifier DC drive during speed regulation.

C.Semaille, Louis-A. Dessaint (Ecole de technologie superieure, Montreal)

### Description

This circuit uses the DC1 block of Specialized Power Systems. It models a two-quadrant single-phase rectifier drive for a 5 HP DC motor.

The 5 HP DC motor is separately excited with a constant 150 V DC field voltage source. The armature voltage is provided by a single-phase rectifier controlled by two PI regulators. The rectifier is fed by a 220 V AC 50 Hz voltage source followed by a linear transformer to boost the voltage up to a sufficient value.

The regulators control the firing angle of the rectifier thyristors. The first regulator is a speed regulator, followed by a current regulator. The speed regulator outputs the armature current reference (in p.u.) used by the current controller in order to obtain the electromagnetic torque needed to reach the desired speed. The speed reference change rate follows acceleration and deceleration ramps in order to avoid sudden reference changes that could cause armature over-current and destabilize the system. The current regulator controls the armature current by computing the appropriate thyristor firing angle. This generates the rectifier output voltage needed to obtain the desired armature current.

A 150 mH smoothing inductance is placed in series with the armature circuit to reduce armature current oscillations.

### Simulation

Start the simulation. You can observe the motor armature voltage and current, the rectifier firing angle and the motor speed on the scope. The current and speed references are also shown.

The speed reference is set at 1750 rpm at t = 0 s. Initial load torque is 15 N.m.

Observe that the motor speed follows the reference ramp accurately (+250 rpm/s) and reaches steady state around t = 8.5 s. The armature current follows the current reference very well, and the firing angle stays below 90 degrees, the converter being in rectifier mode (first quadrant operating mode). The lower limit of the firing angle has been set to 20 degrees.

At t = 8.75 s, the load torque passes from 15 N.m to 20 N.m. The motor speed recovers fast and is back at 1750 rpm at t = 10 s. The current reference rises to about 17.5 A to generate a higher electromagnetic torque to maintain the needed speed. As observed before, the armature current follows its reference perfectly.

### Notes

1) The power system has been discretized with a 25 us time step. The control system (regulators) uses a 100 us time step in order to simulate a microcontroller control device.

2) In order to reduce the number of points stored in the scope memory, a decimation factor of 20 is used.

3) A simplified version of the model using an average-value rectifier can be used by selecting 'Average' in the 'Model detail level' menu of the graphical user-interface. The time step can then be increased up to the control system sample time value.This can be done by typing 'Ts = 100e-6' in the workspace in the case of this example. See also dc1_example_simplified model.

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