# Documentation

Implement two-quadrant chopper (buck-boost converter topology) DC drive

## Library

Electric Drives/DC drives

## Description

The high-level schematic shown below is built from four main blocks. The DC motor and the IGBT/Diode devices (within the Universal Bridge block) are provided with the SimPowerSystems™ library. More details are available in the reference pages for these blocks. 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.

 Note   In SimPowerSystems software, the Two-Quadrant Chopper DC Drive block is commonly called the `DC6` 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 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. In order to avoid negative speeds that could induce conduction of the free-wheeling diode, the speed reference has a lower limit of 0 rpm.

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. Meanwhile, at low speeds, when the back-EMF of the motor is not high enough to generate big reverse currents, the lower limit is reduced proportionally to the speed. This improves current regulation.

## 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 duty ratios of the fixed frequency pulses of the two IGBT devices (Pulse Width Modulation). This generates the average armature voltage needed to obtain the desired armature current and thus the desired electromagnetic torque. For proper system behavior, the two IGBT devices have opposite instantaneous pulse values.

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.

The pulse width modulation is obtained by comparison of the PI output and a fixed frequency sawtooth carrier signal (see the figure called Pulse Width Modulation (PWM)).

The average-value converter is shown in the following figure.

It is composed of one controlled current source on the DC source side and one controlled voltage source on the motor side. The current source allows the representation of the average input current value following the next equation:

Iin = αIout,

with α being the firing angle value and Iout the armature current value. The voltage source on the motor side represents the average voltage value following the next equation:

Vout = αVin,

with Vin being the input voltage.

## 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 an IGBT buck-boost converter controlled by two PI regulators. The converter is fed by a constant DC voltage source. Armature current oscillations are reduced by a smoothing inductance connected in series with the armature circuit.

The model is discrete. Good simulation results have been obtained with a 1 µs time step. In order to simulate a digital controller device, the control system has two different sampling times:

• The speed controller sampling time

• The current controller sampling time

The speed controller sampling time has to be a multiple of the current sampling time. The latter sampling time has to be a multiple of the simulation time step.

Pulse Width Modulation (PWM)

## Dialog Box

### DC Machine Tab

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

For the mechanical rotational port, the connection port S counts for the mechanical input and output. It allows a direct connection to the Simscape™ environment. The mechanical system of the motor is also included in the drive and is based on the same differential equation.

### IGBT/Diode Devices Section

The IGBT/Diode section of the Converter tab displays the parameters of the Universal Bridge block of the Fundamental Blocks (powerlib) library. Refer to the Universal Bridge for more information on the Universal Bridge block parameters.

Smoothing Inductance

The smoothing inductance value (H).

Field DC Source

The DC motor field voltage value (V).

### 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.

### 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).

Sampling Time

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

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

Low-Pass Filter Cutoff Frequency

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

Reference Limit

Symmetrical current reference (pu) limit around 0 pu. 1.5 pu is a common value. Keep in mind that the lower limit is automatically reduced for low speeds (see speed controller description).

PWM Switching Frequency

The switching frequency of the two IGBT devices (Hz).

Sampling Time

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

Power and Voltage nominal values

The DC motor nominal power (W) and voltage (V) values. These 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.

## 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). For the mechanical rotational port (S), this input is deleted.

`Vcc, Gnd `

The DC voltage source electric connections. The voltage must be adequate for the motor size.

`Wm`, `Te` or `S`

The mechanical output: motor speed (Wm), electromagnetic torque (Te) or mechanical rotational port (S).

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 IGBT/Diode device measurement vector. This vector includes the converter output voltage. The output current is not included since it is equal to the DC motor armature current. Note that all current and voltage values of the converter can be visualized with the mulimeter block.

`Ctrl`

The controller measurement vector. This vector contains:

• The armature current reference

• The duty cycle of the PWM pulses

• 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

280 V

550 V

Motor Nominal Values

Power

5 hp

200 hp

Speed

1750 rpm

1750 rpm

Voltage

240 V

500 V

## Example

The `dc6_example` example illustrates the two-quadrant chopper drive used with the 200 hp drive parameter set during speed regulation. A 5 hp parameter set is also available in the library.

The buck-boost converter is fed by a 630 V DC bus obtained by rectification of a 460 V AC 60 Hz voltage source. In order to limit the DC bus voltage during dynamic braking mode, a braking chopper has been added between the diode rectifier and the DC6 block. The IGBT switching frequency is 5 kHz.

The speed reference is set at 400 rpm at t = 0 s. Initial load torque is 814 N.m.

Observe that the motor speed follows the reference ramp accurately (+250 rpm/s) and reaches steady state around t = 2 s. The armature current follows the current reference very well, with fast response time and small ripples. Notice that the current ripple frequency is 5 kHz.

At t = 2.1 s, the load torque passes from 814 N.m to 100 N.m. The motor speed recovers fast and is back at 400 rpm at t = 2.75 s. The current reference lowers to about 40 A to generate a smaller electromagnetic torque, the load torque being reduced. As observed before, the armature current follows its reference perfectly.

At t = 2.75 s, the speed reference jumps down to 100 rpm. In order for the motor to decelerate following the negative speed ramp, the armature current reverses down to −160 A to generate a braking electromagnetic torque (dynamic braking mode). This causes the DC bus voltage to increase. The braking chopper limits the voltage value.

At t = 3.4 s, the motor speed reaches 100 rpm and the current reverses back to 40 A.

At t = 4 s, the speed stabilizes around its reference.

The following figure shows the DC bus voltage, armature current, and speed waveforms.

DC6 Example — DC Bus Voltage, Current, and Speed Waveforms (Blue: Detailed Converter, Red: Average-Value Converter)

The next figure shows the duty cycles of the chopper pulses and the corresponding armature voltage and current waveforms during a time interval of 2 ms.

DC6 Example — Duty Cycles, Armature Voltage, and Current Waveforms (Blue: Detailed Converter, Red: Average-Value Converter)

## References

[1] Boldea, Ion, and S.A. Nasar, Electric Drives, CRC Press LLC, 1999.

[2] Séguier, Guy, Electronique de puissance, Dunod, 1999.