# Starter

Starter as a DC motor

Libraries:
Powertrain Blockset / Energy Storage and Auxiliary Drive / Starter

## Description

The Starter block implements a starter assembly as a separately excited DC motor, permanent magnet DC motor, or series connection DC motor. The motor operates as a torque source to an internal combustion engine.

Use the Starter block:

• In an engine model with a front-end accessory drive (FEAD)

• To model engine start and stop scenarios

The Starter block supports only an angular speed input to the DC motor. A load torque input requires engine dynamics.

### Separately Excited DC Motor

In a separately excited DC motor, the field winding is connected to a separate source of DC power.

The relationship between the field winding voltage, field resistance, and field inductance is given by:

`${V}_{f}={L}_{f}\frac{d{i}_{f}}{dt}+{R}_{f}{i}_{f}$`

The counter-electromotive force is a product of the field resistance, mutual inductance, and motor shaft angular speed:

`$EMF={L}_{a}{i}_{f}{L}_{af}\omega$`

The armature voltage is given by:

The starter motor current load is the sum of the field winding current and armature winding current:

The starter motor shaft torque is the product of the armature current, field current, and mutual inductance:

### Permanent Magnet DC Motor

In a permanent magnet DC motor, the magnets establish the excitation flux, so there is no field current.

The counter-electromotive force is proportional to the motor shaft angular speed:

The armature voltage is given by:

The starter motor current load is equal to the armature winding current:

The starter motor shaft torque is proportional to the armature winding current:

### Series Excited DC Motor

A series excited DC motor connects the armature and field windings in series with a common DC power source.

The counter-electromotive force is a product of the field and armature initial series current, field, and armature mutual inductance and motor shaft angular speed:

`$EMF={i}_{af}{L}_{af}\omega$`

The field and armature winding voltage is given by:

The starter motor current load is equal to the field and armature series current:

The starter motor shaft torque is the product of the squared field and armature series current and the field and armature mutual inductance:

For motor stability, the motor shaft angular speed must be greater than the ratio of the series connected field and armature resistance to the mutual inductance:

`$\omega >-\frac{{R}_{ser}}{{L}_{af}}$`

### Power Accounting

For the power accounting, the block implements these equations.

Bus Signal DescriptionVariableEquations

`PwrInfo`

`PwrTrnsfrd` — Power transferred between blocks

• Positive signals indicate flow into block

• Negative signals indicate flow out of block

`PwrMtr`

Mechanical power

Pmot

`PwrBus`

Electrical power

Pbus

Separately excited DC motor

PM excited DC motor

Series excited DC motor

`PwrNotTrnsfrd` — Power crossing the block boundary, but not transferred

• Positive signals indicate an input

• Negative signals indicate a loss

`PwrLoss`

Motor losses

Ploss

`PwrStored` — Stored energy rate of change

• Positive signals indicate an increase

• Negative signals indicate a decrease

`PwrInd`

Electrical inductance

Pind

Separately excited DC motor

PM excited DC motor

Series excited DC motor

${P}_{ind}={L}_{ser}{i}_{af}\frac{d{i}_{af}}{dt}$

The equations use these variables.

 Ra Armature winding resistance La Armature winding inductance EMF Counter-electromotive force Rf Field winding resistance Lf Field winding inductance Laf Field and armature mutual inductance ia Armature winding current if Field winding current Kt Motor torque constant ω Motor shaft angular speed Va Armature winding voltage Vf Field winding voltage Vaf Field and armature winding voltage iaf Field and armature series current Rser Series connected field and armature resistance Lser Series connected field and armature inductance iload Starter motor current load Tmech Starter motor shaft torque

## Ports

### Inputs

expand all

Motor shaft angular speed, in rad/s.

• Armature winding voltage Va and field winding voltage Vf, in V.

• In series excited DC motor, armature and field winding voltage Vaf.

### Output

expand all

Bus signal containing these block calculations.

SignalDescriptionUnits

`ArmCurr`

Armature winding current

A

`FldCurr`

Field winding current

A

`PwrInfo`

`PwrTrnsfrd`

`PwrMtr`

Mechanical power

W

`PwrBus`

Electrical power

W

`PwrNotTrnsfrd`

`PwrLoss`

Motor power loss

W

`PwrStored`

`PwrInd`

Electrical inductance

W

Starter motor load current, in A.

Starter motor shaft torque, in N·m.

## Parameters

expand all

Configuration

Select one of the three motor types.

#### Dependencies

The table summarizes the motor parameter dependencies.

Motor TypeEnables Motor Parameter
```Separately Excited DC Motor```Armature winding resistance, Ra
Armature winding inductance, La
Field winding resistance Rf
Field winding inductance, Lf
Mutual inductance, Laf
Initial armature and field current, Iaf
```Permanent Magnet Excited DC Motor```Armature winding resistance, Rapm
Armature winding inductance, Lapm
Torque constant, Kt
Initial armature current, Ia
```Series Connection DC Motor```Total resistance, Rser
Total inductance, Lser
Initial current, Iafser
Mutual inductance, Lafser

Separately Excited DC Motor

Armature winding resistance, in ohm.

#### Dependencies

To enable this parameter, select ```Separately Excited DC Motor``` for the Motor Type parameter.

Armature winding inductance, in H.

#### Dependencies

To enable this parameter, select ```Separately Excited DC Motor``` for the Motor Type parameter.

Field winding resistance, in ohm.

#### Dependencies

To enable this parameter, select ```Separately Excited DC Motor``` for the Motor Type parameter.

Field winding inductance, in H.

#### Dependencies

To enable this parameter, select ```Separately Excited DC Motor``` for the Motor Type parameter.

Mutual inductance, in H.

#### Dependencies

To enable this parameter, select ```Separately Excited DC Motor``` for the Motor Type parameter.

Initial armature and field current, in A.

#### Dependencies

To enable this parameter, select ```Separately Excited DC Motor``` for the Motor Type parameter.

Permanent Magnet Excited DC Motor

Armature winding resistance, in ohm.

#### Dependencies

To enable this parameter, select ```Permanent Magnet Excited DC Motor``` for the Motor Type parameter.

Armature winding inductance, in H.

#### Dependencies

To enable this parameter, select ```Permanent Magnet Excited DC Motor``` for the Motor Type parameter.

Motor torque constant, in N·m/A.

#### Dependencies

To enable this parameter, select ```Permanent Magnet Excited DC Motor``` for the Motor Type parameter.

Initial armature current, in A.

#### Dependencies

To enable this parameter, select ```Permanent Magnet Excited DC Motor``` for the Motor Type parameter.

Series Connection DC Motor

Series connected field and armature resistance, in ohm.

#### Dependencies

To enable this parameter, select ```Series Excited DC Motor``` for the Motor Type parameter.

Series connected field and armature inductance, in H.

#### Dependencies

To enable this parameter, select ```Series Excited DC Motor``` for the Motor Type parameter.

Initial series current, in A.

#### Dependencies

To enable this parameter, select ```Series Excited DC Motor``` for the Motor Type parameter.

Field and armature mutual inductance, in H.

#### Dependencies

To enable this parameter, select ```Series Excited DC Motor``` for the Motor Type parameter.

## References

[1] Krause, P. C. Analysis of Electric Machinery. New York: McGraw-Hill, 1994.

## Version History

Introduced in R2017a