# Five-Phase PM Synchronous Motor Drive

Implement five-phase permanent magnet synchronous motor vector control drive

## Library

Electric Drives/AC drives

## Description

The Five-Phase PM Synchronous Motor Drive block implements an electric drive controlling a five-phase permanent magnet synchronous motor with vector control technique.

 Note   The Five-Phase PM Synchronous Motor Drive block is commonly called the `AC8` motor drive.

## High-Level Schematic

The high-level schematic is built from six main blocks. The five-phase PMSM motor, the five-phase inverter, and the three-phase diode rectifier models are provided in the SimPowerSystems™ library. The speed controller, the braking chopper, and the vector controller models are specific to the drive library. You can alternatively use a simplified version of the drive containing an average-value model of the inverter for faster simulation.

## Speed Controller

The speed controller is based on a PI regulator. The output of this regulator is a torque set point applied to the vector controller block.

## Vector Controller

The vector controller contains four main sections:

The angle conversion section computes the electrical rotor angle from the mechanical rotor angle. The dq-abcde section converts two dq current components in the rotor reference frame into abcde phase variables. The current regulator section is a bang-bang current controller with adjustable hysteresis bandwidth. The switching control section limits the inverter commutation frequency to a maximum value you specify.

## Braking Chopper

The braking chopper contains the DC bus capacitor and the dynamic braking chopper, which is used to absorb the energy produced by the motor deceleration.

## Average-Value Inverter

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

On the DC side of the inverter, a controlled current source represents the average DC bus current behavior based on this equation:

Idc = (Pout + Plosses) / Vin

Where

Pout is the output power

Plosses is the losses in the power electronic devices,

Vin is the DC bus voltage.

On the AC side, four controlled current sources represent the average phase currents that fed the motor. Because the regulation is fast, the current values are set equal to the current references of the current regulator. A small current is injected to compensate for the current drawn by the five-phase resistive load connected in series with the motor.

During loss of current tracking, the currents are fed by four controlled voltage sources that 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 sent by the current controller.

## Remarks

The control system has two different sampling times: the speed controller sampling time and the vector controller sampling time.

The speed controller sampling time must be a multiple of the vector controller sampling time and a multiple of the simulation time step. The average-value inverter model has lower time constants, compared to the detailed converter model. Therefore, you can use higher simulation time steps with this type of model. For a vector controller sampling time of 30 μs, good simulation results have been obtained for a simulation time step of 30 μs.

The simulation time step must be lower than the vector controller time step.

The stator currents id1*, iq2*, and id2* are set to 0 inside the vector controller block since only the iq1 current contributes to torque production.

## Dialog Box

### Permanent Magnet Synchronous Machine Tab

Electrical parameters, Mechanical parameters

The Electrical parameters and the Mechanical parameters sections display the parameters of the Synchronous Machine block.

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 `Detailed` and `Average` inverter models.

Mechanical input

Select between `Torque Tm`, ```Speed w```, and the `mechanical rotational port` as the mechanical input.

When you select `Torque Tm`, the block outputs the motor speed according to the following differential equation, describing the mechanical system dynamics:

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

This mechanical system is modeled inside the Synchronous Machine block.

When you select Speed `w` as the mechanical input, the block outputs the electromagnetic torque, allowing you to model the mechanical system dynamics outside the Five-Phase PM Synchronous Motor Drive block. With this setting, the inertia and viscous friction parameters do not appear in the mask of the block.

When you select `mechanical rotational port`, the block shows the connection port S, which counts for the mechanical input and output. It allows a direct connection to the Simscape™ environment. The mechanical system of the motor is modeled inside the drive and is based on the same differential equation.

### Converters and DC Bus Tab

Rectifier

The Rectifier section of the Converters and DC bus tab displays the parameters of the Universal Bridge block.

Inverter

The Inverter section of the Converters and DC bus tab displays the parameters of the Universal Bridge block that is included in the Power Electronics library of the Fundamental Blocks library.

DC bus – Capacitance

Specify the DC bus capacitance, in farads.

Source frequency

Specify the frequency of the voltage source, in hertz. The Source frequency parameter is visible only when the Model detail level parameter is set to `Average`.

On-state resistance

Specify the on-state resistance of the inverter devices, in ohms. The On-state resistance parameter is visible only when the Model detail level parameter is set to `Average`.

#### Braking Chopper Section

Resistance

Specify the braking chopper resistance, in ohms. Use this resistance to avoid bus overvoltage during motor deceleration or when the load torque tends to accelerate the motor.

Chopper frequency

Specify the braking chopper frequency, in hertz.

Activation voltage

The dynamic braking is activated when the bus voltage reaches the upper limit of the hysteresis band. The figure Chopper Hysteresis LogicChopper Hysteresis Logic shows the braking chopper hysteresis logic.

Shutdown voltage

Specify the shutdown voltage, in volts. This value is the point at which the dynamic braking shuts down when the bus voltage reaches the lower limit of the hysteresis band. The chopper hysteresis logic is shown in the following figure.

Chopper Hysteresis Logic

### Controller Tab

Regulation type

Specify the type of regulation, `Speed regulation` or ```Torque regulation```.

Schematic

Open a diagram showing the speed and vector controllers schematics.

#### Speed Controller Section

Acceleration

Specify the maximum acceleration allowed for the motor, in rpm/s. An excessively large positive value can cause DC bus undervoltage. This parameter is used only in speed regulation mode.

Deceleration

Specify the maximum change of speed allowed during motor deceleration, in rpm/s. An excessively large negative value can cause DC bus overvoltage. This parameter is used only in speed regulation mode.

Speed cutoff frequency

Specify the speed measurement first-order low-pass filter cutoff frequency, in hertz. This parameter is used only in speed regulation mode.

Speed controller sampling time

Specify the speed controller sampling time, in seconds. The sampling time must be a multiple of the simulation time step.

Proportional gain

Specify the speed controller proportional gain. This parameter is used only in speed regulation mode.

Integral gain

Specify the speed controller integral gain. This parameter is used only in speed regulation mode.

Negative

Specify the maximum negative torque, in newton-meters, applied to the motor by the vector controller (N.m).

Positive

Specify the maximum positive torque, in newton-meters, applied to the motor by the vector controller.

#### Vector Controller Section

Sampling time

Specify the vector controller sampling time, in seconds. The sampling time must be a multiple of the simulation time step.

Current controller hysteresis band

Specify the current hysteresis bandwidth, in amperes. This value is the total bandwidth distributed symmetrically around the current set point. The following figure shows a case where the current set point is Is* and the current hysteresis bandwidth is set to `dx`.

This parameter is ignored when using the average-value inverter.

 Note   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 might exceed the hysteresis band.
Maximum switching frequency

Specify the maximum inverter switching frequency, in hertz. This parameter is ignored when using the average-value inverter.

## Inputs and Outputs

`SP`

Outputs the speed or torque set point. The speed set point can be a step function, but the speed change rate follows the acceleration and deceleration ramps. When the load torque and the speed have opposite signs, the accelerating torque is the sum of the electromagnetic and load torques.

`Wm`, `Tm`, or `S`

The mechanical input of the drive: motor speed (Wm), mechanical torque (Tm), or mechanical rotational port (S).

`A, B, C `

The three phase terminals of the motor drive.

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 five-phase converter measurement vector. This vector contains:

• The DC bus voltage

• The rectifier output current

• The inverter input current

You can visualize all current and voltage values of the bridges using the Multimeter block.

`Ctrl`

The controller measurement vector. This vector contains:

• The torque 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 4.4 kW drive parameter set. The table shows the specifications of the 4.4 kW drive.

 Drive Input Voltage: Amplitude 160 V (L-L) Frequency 60 Hz Motor Nominal Values: Power 4.4 kW Speed 900 rpm Voltage 160 V (L-N)

## Example

The `ac8_example` model shows the simulation of the Five-Phase PM Synchronous Motor Drive block under standard load condition. The `ac8_example_simplified` model shows the simulation of the average-value model under the same load conditions.

The simulation of the two models shows that the motor speed follows precisely the acceleration ramp reference signal.

• At t = 0.5 s, the nominal load torque is applied to the motor.

• At t = 1 s, the speed set point changes to 0 rpm and the speed decreases to 0 rpm.

• At t = 1.5 s, the mechanical load passes from 11 N.m to −11 N.m.

The average voltage, current, torque, and speed values are identical for both models. Notice that the higher frequency signal components are not represented with the average-value converter.

## References

[1] Bose, B. K., Modern Power Electronics and AC Drives, Upper Saddle River, NJ, Prentice-Hall, 2002.

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

[3] Toliyat, H. A., Analysis and Simulation of Multi-Phase Variable Speed Induction Motor Drives Under Asymmetrical Connections, Applied Power Electronics Conference and Exposition, Vol. 2, 1996, pp. 586–592.

[4] Beaudart, F., F. Labrique, E. Matagne, D. Telteux, and P. Alexandre, Control under normal and fault tolerant operation of multiphase SMPM synchronous machines with mechanically and magnetically decoupled phases, International Conference on Power Engineering, Energy and Electrical Drives, 2009, pp. 461–466.