# Self-Controlled Synchronous Motor Drive

Implement Self-Controlled Synchronous Motor Drive

## Library

Electric Drives/AC drives

## Description

This block models a wound field synchronous motor (WFSM) vector control drive model. The high-level schematic shown below is built from six main blocks. The WFSM motor, the three-phase inverter, and the three-phase rectifier models are provided with the SimPowerSystems™ library. More details are available in the reference pages for these blocks. The speed controller, the rectifier controller, and the vector control models are specific to the drive library. It is possible to use a simplified version of the drive containing average-value models of the inverter and rectifier for faster simulation.

 Note   In SimPowerSystems software, the Self-Controlled Synchronous Motor Drive block is commonly called the `AC5` motor drive.

## Speed Controller

The speed controller is based on a PI regulator, shown below. The outputs of this regulator are set points for the torque and the flux applied to the vector control block.

## Rectifier Controller

The rectifier controller is based on a PI regulator of the DC bus voltage. The output of this regulator is the direct (active) component of the AC line current. The reactive component of the AC line current is set to zero in order to operate at unity power factor.

The dq-abc block performs the conversion of the dq current components into abc phase variables.

The current regulator is a bang-bang current controller with adjustable hysteresis bandwidth.

## Vector Controller

The vector control contains five main blocks shown in this figure. These blocks are described below.

The flux estimator block is used to estimate the motor stator flux .

The flux PI controller is used to regulate the flux in the machine.

The dq2abc block performs the conversion of the dq current components into abc phase variables.

The current regulator is a bang-bang current controller with adjustable hysteresis bandwidth.

The magnetization control unit contains the logic used to switch between the magnetization and normal operation mode.

## Average-Value Inverter and Rectifier

The average-value inverter/rectifier internal architecture is shown in the following figure.

It is composed of one controlled current source on the DC side and of two controlled current sources and three controlled voltage sources on the AC side. The DC current source allows the representation of the average DC bus current behavior following the next equation:

Idc = (Pac + Plosses) / Vdc

with Pac being the AC side instantaneous power, Plosses the losses in the power electronics devices, and Vdc the DC bus voltage.

On the AC side, the current sources represent the average phase currents fed to the motor. The regulation being fast, the current values are set equal to the current references sent by the current regulator. A small current is injected to compensate for the current drawn by the three-phase load (needed because of the inverter current sources in series with the inductive motor).

During loss of current tracking due to insufficient inverter voltage, the currents are fed by three controlled voltage sources. These voltage sources represent the square wave mode and allow good representation of the phase currents during inverter saturation. Each voltage source outputs either Vin or 0, depending on the values of the pulses (1 or 0) send by the current controller.

## Remarks

The model is discrete. Good simulation results have been obtained with a 2 µs time step. To simulate a digital controller device, the control system has two different sampling times:

• Speed controller sampling time

• Active rectifier controller and vector controller sampling time

The speed controller sampling time has to be a multiple of the vector controller sampling time. The latter sampling time has to be a multiple of the simulation time step. The average-value inverter and rectifier allow the use of bigger simulation time steps since they do not generate small time constants (due to the RC snubbers) inherent to the detailed converters. For a vector controller and active rectifier controller sampling time of 50 µs, good simulation results have been obtained for a simulation time step of 50 µs. This time step can, of course, not be higher than the smallest controller sampling time.

The torque sign convention of the synchronous machine is different from the one of the asynchronous and PM synchronous machines. That is, the synchronous machine is in the motor operation mode when the electric torque is negative and in the generator operation mode when the electric torque is positive.

## Dialog Box

### Synchronous Machine Tab

The Synchronous Machine tab displays the parameters of the Synchronous 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.

### Converters and DC bus tab

Rectifier section

The rectifier section of the Converters and DC bus 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 parameters.

Inverter section

The inverter section of the Converters and DC bus tab displays the parameters of the Universal Brige block of the Fundamental Blocks (powerlib) library. Refer to the Universal Bridge for more information on the universal bridge parameters.

The average-value rectifier uses the three following parameters.

Source frequency

The frequency of the three-phase voltage source (Hz).

Source Voltage

The RMS line-to-line voltage of the three-phase voltage source (V).

On-state resistance

The on-state resistance of the rectifier devices (ohms).

The average-value inverter uses the two following parameters:

On-state resistance

The on-state resistance of the inverter devices (ohms).

Forward voltages [Device Vf, Diode Vdf]

Forward voltages, in volts (V), of the forced-commutated devices and of the antiparallel diodes. Theses values are needed for startup and for square wave mode.

DC Bus Capacitance

The DC bus capacitance value (F).

### Input Choke section

Input chokes reduce line current harmonics.

Resistance

The input choke resistance value (ohms).

Inductance

The input choke inductance value (H).

### Controller tab

Regulation type

This drop-down menu allows you to choose between speed and torque regulation.

Schematic

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

### Controller — Speed Controller Subtab

Speed cutoff frequency

The speed measurement first-order low-pass filter cutoff frequency (Hz).

Speed controller sampling time

The speed controller sampling time (s). The sampling time must be a multiple of the simulation time step.

Speed ramps — Acceleration

The maximum change of speed allowed during motor acceleration. An excessively large positive value can cause DC bus under-voltage (rpm/s).

Speed ramps — Deceleration

The maximum change of speed allowed during motor deceleration. An excessively large negative value can cause DC bus over-voltage (rpm/s).

PI regulator — Proportional gain

The speed controller proportional gain.

PI regulator — Integral gain

The speed controller integral gain.

Torque output limits — Negative

The maximum negative demanded torque applied to the motor by the vector controller (N.m).

Torque output limits — Positive

The maximum positive demanded torque applied to the motor by the vector controller (N.m).

### Controller — DC Bus Controller Subtab

PI regulator — Proportional gain

The DC bus voltage controller proportional gain.

PI regulator — Integral gain

The DC bus voltage controller integral gain.

Line current d component limits — Minimum (negative)

The maximum current flowing from the DC bus capacitor towards the AC line (A).

Line current d component limits — Maximum (positive)

The maximum current flowing from the AC line towards the DC bus capacitor (A).

Voltage measurement cutoff frequency

The bus voltage measurement low-pass filter cutoff frequency (Hz).

Active rectifier sampling time

The DC bus voltage controller sampling time (s). The sampling time must be a multiple of the simulation time step.

Current hysteresis bandwidth

The current hysteresis bandwidth. This value is the total bandwidth distributed symmetrically around the current set point (A). The following figure illustrates a case where the current set point is Is* and the current hysteresis bandwidth is set to dx.

This parameter is not used when using the average-value inverter.

 Note   This bandwidth can be exceeded because a fixed-step simulation is used. A rate transition block is needed to transfer data between different sampling rates. This block causes a delay in the gate signals, so the current may exceed the hysteresis band.

### Controller — Vector Controller Subtab

Controller sampling time

The vector controller sampling time (s). The sampling time must be a multiple of the simulation time step.

Machine nominal flux

The motor stator nominal flux (Wb).

Current hysteresis bandwidth

The current hysteresis bandwidth (for details, see the DC Bus Controller subtab).

### Flux Controller Section

PI regulator — Proportional gain

The flux controller proportional gain.

PI regulator — Integral gain

The flux controller integral gain.

Voltage limits — Minimum

The minimum voltage applied to the motor excitation field (V).

Voltage limits — Maximum

The maximum voltage applied to the motor excitation field (V).

Flux estimation lowpass cutoff frequency

The flux estimation first-order filter cutoff frequency (Hz).

### Magnetization Controller Section

When you start the self-controlled synchronous motor, the magnetic flux of the motor must be first established before the motor is allowed to produce an electric torque. Since the motor field time constant is high, a field voltage much higher than nominal is applied in order to accelerate the building of the magnetic flux in the synchronous motor. After the period during which the high voltage is applied, the field voltage is lowered down to its nominal value during a second short period that adds to the latter period giving the total magnetization period. This procedure gives a smooth startup of the self-controlled synchronous motor.

Field magnetization voltage

The field magnetization voltage applied in order to establish the stator flux (V).

High voltage field magnetization time

The field magnetization high voltage application time (s).

Field nominal voltage

The field nominal voltage (V).

Total field magnetization time

The total time before the drive is ready to produce a torque (s).

## 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.

`A, B, C `

The three phase terminals of the motor drive.

`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 allows you to observe the motor's variables using the Bus Selector block.

`Conv`

The three-phase converters measurement vector. This vector contains:

• The DC bus voltage

• The rectifier output current

• The inverter input current

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

`Ctrl`

The controller measurement vector. This vector contains the values for the active rectifier and for the inverter.

For the active rectifier:

• The active component of the current reference.

• The voltage error (difference between the DC bus voltage reference and actual DC bus voltage)

• The DC bus voltage reference

For the inverter:

• The torque reference

• The flux reference

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

• 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 200 hp drive parameter set. The specifications of the 200 hp drive are shown in the following table

14 HP and 200 HP Drive Specifications

14 HP Drive200 HP Drive

Drive Input Voltage

Amplitude

460 V

460 V

Frequency

60 Hz

60 Hz

Motor Nominal Values

Power

14 hp

200 hp

Speed

1800 rpm

1800 rpm

Voltage

460 V

460 V

.

## Example

The `ac5_example` example illustrates an AC5 motor drive simulation with standard load condition for the detailed and average-value models. At time t = 1.5 s, the speed set point is 200 rpm.

As shown below, the speed precisely follows the acceleration ramp. At t = 3 s, the nominal load torque is applied to the motor. At t = 4 s, the speed set point is changed to 0 rpm. The speed decreases along the prescribed deceleration ramp to 0 rpm. At t = 5.5 s., the mechanical load passes from −792 N.m to 792 N.m. Notice that the results of the average-value model are similar to those of the detailed model except that the higher frequency signal components are not represented with the average-value converter.

AC5 Example Waveforms (Blue : Detailed Converter, Red : Average-Value Converter)

## References

[1] Bose, B. K., Modern Power Electronics and AC Drives, Prentice-Hall, N.J., 2002.

[2] Krause, P. C., Analysis of Electric Machinery, McGraw-Hill, 1986.