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# Four-Quadrant Three-Phase Rectifier DC Drive

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

## Library

Electric Drives/DC drives

## Description

The high-level schematic shown below is built from six main blocks. The DC motor, the two three-phase full converters, and the bridge firing unit are provided with the SimPowerSystems™ library. More details on these blocks are available in the reference pages for each block. The two other blocks are specific to the Electric Drives library. These blocks are the speed controller and the current controller. They allow speed or torque regulation. A "regulation switch" block allows you to toggle from one type of regulation to the other. During torque regulation the speed controller is disabled. It is possible to use a simplified version of the drive containing an average-value model of the three-phase dual-converter and allowing faster simulation.

 Note   In SimPowerSystems software, the Four-Quadrant Three-Phase Rectifier DC Drive block is commonly called the DC4 motor drive.

## Speed Controller

The speed regulator shown below uses a PI controller. The controller outputs the armature current reference (in pu) used by the current controller in order to obtain the electromagnetic torque needed to reach the desired speed. During torque regulation, the speed controller is disabled.

The controller takes the speed reference (in rpm) and the rotor speed of the DC machine as inputs. The speed reference change rate will follow user-defined acceleration and deceleration ramps in order to avoid sudden reference changes that could cause armature over-current and destabilize the system. The speed measurement is filtered by a first-order low-pass filter.

The current reference output is limited between symmetrical lower and upper limits defined by the user.

## Current Controller

The armature current regulator shown below is based on a second PI controller. The regulator controls the armature current by computing the appropriate thyristor firing angles of the two full converters. This generates the converter output voltages needed to obtain the desired armature current and thus the desired electromagnetic torque.

The controller takes the current reference (in pu) and the armature current flowing through the motor as inputs. The current reference is either provided by the speed controller during speed regulation or computed from the torque reference provided by the user during torque regulation. This is managed by the "regulation switch" block.

The armature current input is filtered by a first-order low-pass filter. An arccosine function is used to linearize the control system. The firing angle can vary between 0 and 180 degrees. You can limit the lower and upper limits to intermediate values.

Both converters operate simultaneously, and the two firing angles are controlled so that the sum of their values stays equal to 180 degrees. This produces opposite average voltages at the converter DC output terminals and thus identical average voltages at the DC motor armature, the converters being connected in antiparallel. One converter is working in rectifier mode while the other is in inverter mode.

## Average-Value Three-phase Rectifier

The simplified converter is shown in the following figure.

Average-Value Three-Phase Rectifier with Circulating Current

It is composed of two controlled current sources on the AC side and one controlled voltage and current source on the DC side. The AC current sources allow the representation of the fundamental three-phase current behaviors according to the following equations

$\begin{array}{c}{I}_{a}=\frac{2\sqrt{3}}{\pi }{I}_{d}\mathrm{sin}\left(2\pi ft+\alpha +{\alpha }_{0}\right)\\ {I}_{b}=\frac{2\sqrt{3}}{\pi }{I}_{d}\mathrm{sin}\left(2\pi ft+\alpha +{\alpha }_{0}+\frac{2\pi }{3}\right),\end{array}$

with α being the firing angle value, α0 the phase angle of phase A, f the AC frequency and Id the rectified output current value. The DC voltage source represents the average voltage value of the rectified voltage waveform according to the next equation:

${V}_{d}=\frac{3\sqrt{6}}{\pi }{V}_{\text{rms}}\mathrm{cos}\alpha -6fL{I}_{d},$

with Vrms being the input phase-to-phase RMS voltage value and L being the source inductance value. The controlled current source represents the circulation current due to the instantaneous voltage difference between both converter outputs of the dual-converter. This current is equal to

${V}_{d}=\frac{3\sqrt{2}}{2{\pi }^{2}f{L}_{\text{circ,tot}}}{V}_{\text{rms}}\left(1-\frac{\pi \sqrt{3}}{6}\mathrm{sin}\alpha +\left(\frac{\pi }{2}-\alpha \right)\mathrm{cos}\alpha \right),$

with Lcirc,tot being the total circulation inductance of the circulation current loop.

## Bridge Firing Unit

The bridge firing unit converts the firing angles, provided by the current controller, to two series of six pulses applied respectively to the thyristor gates of each converter. The bridge firing unit block contains a band-pass filter on voltage measurement to remove voltage harmonics. Two Discrete Synchronized 6-Pulse Generator blocks generate the pulses. Refer to the Synchronized 6-Pulse Generator for more information on this block. When using the average-value converter, the bridge firing unit simply outputs the firing angle value needed by the converter.

## 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.

## Dialog Box

### DC Machine Tab

The DC Machine tab displays the parameters of the DC Machinr block of the powerlib library.

Output bus mode

Select how the output variables are organized. If you select Multiple output buses, 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.

Mechanical input

Select between the load torque, the motor speed and the mechanical rotational port as mechanical input. 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.

### Converter Tab

Field DC Source

The DC motor field voltage value (V).

Circulating Current Inductors

The four circulating current inductors inductance value (H).

### Converter sections

The Converter 1 and Converter 2 sections of the Converter tab display the parameters of the Universal Bridge block of the powerlib library. Refer to the Universal Bridge for more information on the Universal Bridge block parameters.

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.

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.

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.

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.

### Controller Tab

Schematic Button

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

Regulation Type

This pop-up menu allows you to choose between speed and torque regulation.

Sampling Time

The controller (speed and current) sampling time (s). The sampling time has to be a multiple of the simulation time step.

### 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).

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.

Low-Pass Filter Cutoff Frequency

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

Proportional Gain

The proportional gain of the PI speed controller.

Integral Gain

The integral gain of the PI speed controller.

Acceleration

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

Deceleration

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

### Controller — Current Controller Subtab

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).

Proportional Gain

The proportional gain of the PI current controller.

Integral Gain

The integral gain of the PI current controller.

Low-Pass Filter Cutoff Frequency

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

Symmetrical Reference Limit

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

### Controller — Bridge Firing Unit Subtab

Alpha Min

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

Alpha Max

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

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.

Pulse Width

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

## 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

## Example

The dc4_example example illustrates the three-phase dual-converter drive used with the 200 hp drive parameter set during torque regulation. A 5 hp parameter set is also available in the library.

The converters are fed by a 380 V AC 50 Hz voltage source.

The motor is coupled to a linear load, which means that the mechanical torque of the load is proportional to the speed.

The initial torque reference is set to 0 N.m and the armature current is null. No electromagnetic torque is produced and the motor stays still.

At t = 0.2 s, the torque reference jumps to 600 N.m. This causes the armature current to rise to about 180 A. The armature current is supplied by converter 1, and the total current in this converter is the sum of load current and circulating current. Converter 2 simply carries the circulating current. Notice that the armature current follows the reference current quite accurately, with fast response time and small overshooting. Observe also that the firing angles are symmetrical around 90 degrees and that the converter average output DC voltages are equal but of opposite signs.

The electromagnetic torque produced by the armature current flow causes the motor to accelerate. The speed rises and starts to stabilize around t = 4 s at about 560 rpm, the sum of the load and viscous friction torques beginning to equalize the electromagnetic torque.

At t = 4 s, the torque reference is set to 0 N.m and the load torque causes the motor to decelerate. Notice that the four reactors keep the current oscillations quite small.

At t = 8 s, the torque reference is set to −300 N.m. The armature current jumps down to −90 A and is now delivered by converter 2 while converter 1 only handles the circulating current. Converter 2 is now working in rectifier mode and converter 1 in inverter mode.

The negative electromagnetic torque produced allows the motor to accelerate in the negative speed plane.

At t = 12 s, speed starts to stabilize around −290 rpm.

DC4 Example Waveforms (Blue/Green : Detailed Converter, Red : Average- Value Converter)

## References

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