Documentation

# Four-Quadrant Three-Phase Rectifier DC Drive

Implement three-phase dual-converter DC drive with circulating current

## Library

Simscape / Electrical / Specialized Power Systems / Electric Drives / DC Drives

## Description

The Four-Quadrant Three-Phase Rectifier DC Drive (DC4) block represents a four-quadrant, three-phase, thyristor-based (or phase controlled) drive for DC motors. This drive features closed-loop speed control with two anti-paralleled three-phase thyristor rectifiers. The anti-paralleled rectifiers operate in circulating current mode with the help of circulating current inductors. The speed control loop outputs the reference armature current of the machine. Using a PI current controller, the thyristor firing angles (for the two rectifiers) corresponding to the commanded armature current are derived. These firing angles are then used to obtain the required gate signals for the rectifiers through a thyristor bridge firing unit.

The main advantage of this drive, compared with other DC drives, is that it can operate in all four quadrants (forward motoring, reverse regeneration, reverse motoring, and forward regeneration). However, two anti-paralleled converters along with circulating current inductors are required, which increases the complexity of the drive system.

### Note

In Simscape™ Electrical™ Specialized Power Systems software, the Four-Quadrant Three-Phase Rectifier DC Drive block is commonly called the `DC4` motor drive.

The Four-Quadrant Three-Phase Rectifier DC Drive block uses these blocks from the Electric Drives/Fundamental Drive Blocks library:

• Speed Controller (DC)

• Regulation Switch

• Current Controller (DC)

• Bridge Firing Unit (DC)

## Remarks

The machine is separately excited with a constant DC field voltage source. There is thus no field voltage control. By default, the field current is set to its steady-state value when a simulation is started.

The armature voltage is provided by two three-phase antiparallel-connected converters controlled by two PI regulators. The circulating current produced by the instantaneous voltage difference at the terminal of both converters is limited by inductors connected between these terminals. No smoothing inductance is placed in series with the armature circuit, the armature current oscillations being quite small due to the three-phase voltage source.

The average-value converter represents the average behavior of a three-phase rectifier for continuous armature current in a dual-converter topology. This model is thus not suitable for simulating DC drives under discontinuous armature current conditions. The converter outputs a continuous voltage value equal to the average-value of the real-life rectified voltage. The armature voltage, armature current, and electromagnetic torque ripples are thus not represented. The input currents have the frequency and amplitude of the fundamental current component of the real-life input currents.

The model is discrete. Good simulation results have been obtained with a 10-µs time step. The control system (speed and current controllers) samples data following a user-defined sample time in order to simulate a digital controller device. Keep in mind that this sampling time has to be a multiple of the simulation time step.

The average-value converter allows the use of bigger simulation time steps, since it does not generate small time constants (due to the RC snubbers) inherent to the detailed converter. For a controller sampling time of 100-µs, good simulation results have been obtained for a simulation time step of 100 µs. This time step cannot be higher than the controller time step.

## Parameters

### General

Output bus mode

Select how the output variables are organized. If you select `Multiple output buses` (default), the block has three separate output buses for motor, converter, and controller variables. If you select `Single output bus`, all variables output on a single bus.

Model detail level

Select between the detailed and the average-value inverter. Default is `Detailed`.

Mechanical input

Select between the load torque, the motor speed and the mechanical rotational port as mechanical input. Default is `Torque Tm`.

If you select and apply a load torque, the output is the motor speed according to the following differential equation that describes the mechanical system dynamics:

`${T}_{e}=J\frac{d}{dt}{\omega }_{r}+F{\omega }_{r}+{T}_{m}$`

This mechanical system is included in the motor model.

If you select the motor speed as mechanical input, then you get the electromagnetic torque as output, allowing you to represent externally the mechanical system dynamics. The internal mechanical system is not used with this mechanical input selection and the inertia and viscous friction parameters are not displayed.

Use signal names as labels

When you select this check box, the `Motor`, `Conv`, and `Ctrl` measurement outputs use the signal names to identify the bus labels. Select this option for applications that require bus signal labels to have only alphanumeric characters.

When this check box is cleared (default), the measurement output uses the signal definition to identify the bus labels. The labels contain nonalphanumeric characters that are incompatible with some Simulink® applications.

### DC Machine Tab

The DC Machine tab displays the parameters of the DC Machine block of the Fundamental Blocks (powerlib) library.

### Converters Tab

#### DC Bus and Excitation Circuit Section

Field DC source

The DC motor field voltage value (V). Default is `150`.

Circulating current inductors

The four circulating current inductors inductance value (H). Default is `240`.

#### Converter Sections

The Converter 1 and Converter 2 sections of the Converter tab display the parameters of the Universal Bridge block of the Fundamental Blocks (powerlib) library. For more information on the Universal Bridge block parameters, refer to the Universal Bridge reference page.

Phase-to-phase RMS voltage

Phase-to-phase rms voltage of the three-phase voltage source connected to the A,B,C terminals of the drive (V). This parameter is not used when using the detailed rectifier. Default is `460`.

Frequency

Frequency of the three-phase voltage source connected to the A,B,C terminals of the drive (Hz). This parameter is not used when using the detailed rectifier. Default is `60`.

Source inductance

Source inductance of the three-phase voltage source connected to the A,B,C terminals of the drive (H). This parameter is not used when using the detailed rectifier. Default is `0.1e-3`.

Phase angle of phase A

Phase angle of phase A of the three-phase voltage source connected to the A,B,C terminals of the drive (deg). This parameter is not used when using the detailed rectifier. Default is `0`.

### Controller Tab

Regulation type

This pop-up menu allows you to choose between speed and torque regulation. Default is `Speed regulation`.

Sampling time (s)

The controller (speed and current) sampling time (s). The sampling time has to be a multiple of the simulation time step. Default is `20e-6`.

Schematic

When you click this button, a diagram illustrating the speed and current controllers schematics appears.

#### Controller — Speed Controller Subtab

Nominal speed

The nominal speed value of the DC motor (rpm). This value is used to convert motor speed from rpm to pu (per unit). Default is `1750`.

Initial speed reference

The initial speed reference value (rpm). This value allows the user to start a simulation with a speed reference other than `0` rpm. Default is `0`.

Low-pass filter cutoff frequency

Cutoff frequency of the low-pass filter used to filter the motor speed measurement (Hz). Default is `40`.

Proportional gain

The proportional gain of the PI speed controller. Default is `10`.

Integral gain

The integral gain of the PI speed controller. Default is `50`.

Acceleration

The maximum change of speed allowed during motor acceleration (rpm/s). Too great a value can cause armature over-current. Default is `1000`.

Deceleration

The maximum change of speed allowed during motor deceleration (rpm/s). Too great a value can cause armature over-current. Default is `-1000`.

#### Controller — Current Controller Subtab

Low-pass filter cutoff frequency

Cutoff frequency of the low-pass filter used to filter the armature current measurement (Hz). Default is `500`.

Symmetrical reference limit

Symmetrical current reference (pu) limit around 0 pu. 1.5 pu is a common value. Default is `1.5`.

Power and Voltage nominal values

The DC motor nominal power (VA) and voltage (V) values. The nominal power and voltage values are used to convert armature current from amperes to pu (per unit). Default for Power is `5*746`. Default for Voltage is `440`.

Proportional gain

The proportional gain of the PI current controller. Default is `2`.

Integral gain

The integral gain of the PI current controller. Default is `200`.

#### Controller — Bridge Firing Unit Subtab

Alpha min

Minimum firing angle value (deg). 20 degrees is a common value. Default is `20`.

Alpha max

Maximum firing angle value (deg). 160 degrees is a common value. Default is `160`.

Frequency of synchronization voltages

Frequency of the synchronization voltages used by the discrete synchronized 6-pulse generator block (Hz). This frequency is equal to the line frequency of the three-phase power line. This parameter is not used when using the average-value converter. Default is `60`.

Pulse width

The width of the pulses applied to the thyristor gates (deg.). This parameter is not used when using the average-value converter. Default is `10`.

## Block Inputs and Outputs

`SP`

The speed or torque set point. The speed set point can be a step function, but the speed change rate will follow the acceleration / deceleration ramps. If the load torque and the speed have opposite signs, the accelerating torque will be the sum of the electromagnetic and load torques.

`Tm` or `Wm`

The mechanical input: load torque (Tm) or motor speed (Wm).

`A, B, C `

The three-phase electric connections. The voltage must be adequate for the motor size.

`Wm` or `Te`

The mechanical output: motor speed (Wm) or electromagnetic torque (Te).

When the Output bus mode parameter is set to Multiple output buses, the block has the following three output buses:

`Motor`

The motor measurement vector. This vector is composed of two elements:

• The armature voltage

• The DC motor measurement vector (containing the speed, armature current, field current, and electromagnetic torque values). Note that the speed signal is converted from rad/s to rpm before output.

`Conv`

The three-phase converter measurement vector. It includes:

• The output voltage of converter 1

• The output voltage of converter 2

• The output current of converter 1

• The output current of converter 2

Note that all current and voltage values of the detailed bridges can be visualized with the Multimeter block.

`Ctrl`

The controller measurement vector. This vector contains:

• The armature current reference

• The firing angle computed by the current controller

• The speed or torque error (difference between the speed reference ramp and actual speed or between the torque reference and actual torque)

• The speed reference ramp or torque reference

When the Output bus mode parameter is set to Single output bus, the block groups the Motor, Conv, and Ctrl outputs into a single bus output.

## Model Specifications

The library contains a 5 hp and a 200-hp drive parameter set. The specifications of these two drives are shown in the following table.

5 HP and 200 HP Drive Specifications

5 HP Drive

200 HP Drive

Drive Input Voltage

Amplitude

230 V

380 V

Frequency

60 Hz

50 Hz

Motor Nominal Values

Power

5 hp

200 hp

Speed

1750 rpm

1184 rpm

Voltage

240 V

440 V

## Examples

The `dc4_example` example illustrates the three-phase dual-converter drive used with the 200-hp drive parameter set during torque regulation.

## References

[1] Sen, P.C., Thyristor DC Drives, J.Wiley and Sons, 1981