# DC Machine

Implement wound-field or permanent magnet DC machine

## Library

Simscape / Electrical / Specialized Power Systems / Electrical Machines

## Description

The DC Machine block implements a wound-field or permanent magnet DC machine.

For the wound-field DC machine, access is provided to the field terminals (F+, F−) so that the machine model can be used as a shunt-connected or a series-connected DC machine. The torque applied to the shaft is provided at the Simulink® input TL.

The armature circuit (A+, A−) consists of an inductor La and resistor Ra in series with a counter-electromotive force (CEMF) E.

The CEMF is proportional to the machine speed.

E = KEω

KE is the voltage constant and ω is the machine speed.

In a separately excited DC machine model, the voltage constant KE is proportional to the field current If:

KE = LafIf,

Laf is the field-armature mutual inductance.

The electromechanical torque developed by the DC machine is proportional to the armature current Ia.

Te = KTIa,

KT is the torque constant. The sign convention for Te and TL is:

Te , TL > 0: Motor mode
Te, TL < 0: Generator mode

The torque constant is equal to the voltage constant.

KT = KE.

The armature circuit is connected between the A+ and A− ports of the DC Machine block. It is represented by a series Ra La branch in series with a Controlled Voltage Source and a Current Measurement block.

In the wound-field DC machine model, the field circuit is represented by an RL circuit. It is connected between the F+ and F− ports of the DC Machine block.

In the permanent magnet DC machine model, there is no field current as the excitation flux is established by the magnets. KE and KT are constants.

The mechanical part computes the speed of the DC machine from the net torque applied to the rotor. The speed is used to implement the CEMF voltage E of the armature circuit.

The mechanical part implements this equation:

`$J\frac{d\omega }{dt}={T}_{e}-{T}_{L}-{B}_{m}\omega -{T}_{f},$`

J = inertia, Bm = viscous friction coefficient, and Tf = Coulomb friction torque.

## Parameters

### Configuration Tab

Preset model

Provides a set of predetermined electrical and mechanical parameters for various DC machine ratings of power (HP), DC voltage (V), rated speed (rpm), and field voltage (V).

The preset models are available only for the wound-field DC machine model.

Select one of the preset models to load the corresponding electrical and mechanical parameters in the entries of the dialog box. Select `No` (default) if you do not want to use a preset model, or if you want to modify some of the parameters of a preset model.

When you select a preset model, the electrical and mechanical parameters in the Parameters tab of the dialog box become unmodifiable (unavailable). To start from a given preset model and then modify machine parameters:

1. Select the preset model that you want to initialize the parameters.

2. Change the Preset model parameter value to `No`. This does not change the machine parameters. By doing so, you break the connection with the particular preset model.

3. Modify the machine parameters as you want, then click .

Mechanical input

Select the torque applied to the shaft or the rotor speed as a Simulink input of the block, or represent the machine shaft by a Simscape™ rotational mechanical port.

Select `Torque TL` (default) to specify a torque input, in N.m, and change labeling of the block input to `TL`. The machine speed is determined by the machine Inertia J and by the difference between the applied mechanical load torque TL and the internal electromagnetic torque Te. The sign convention for the mechanical torque is: when the speed is positive, a positive torque signal indicates motor mode and a negative signal indicates generator mode.

Select `Speed w` to specify a speed input, in rad/s, and change labeling of the block input to `w`. The machine speed is imposed and the mechanical part of the model (Inertia J) is ignored. Using the speed as the mechanical input allows modeling a mechanical coupling between two machines.

The next figure indicates how to model a stiff shaft interconnection in a motor-generator. The speed output of machine 1 (motor) is connected to the speed input of machine 2 (generator), while machine 2 electromagnetic torque output Te is applied to the mechanical load torque input TL of machine 1. The Kw factor takes into account speed units of both machines (rad/s) and gear box ratio. The KT factor takes into account torque units of both machines (N.m) and machine ratings. Also, as the inertia J2 is ignored in machine 2, J2 referred to machine 1 speed must be added to machine 1 inertia J1.

Select `Mechanical rotational port` to add to the block a Simscape mechanical rotational port that allows connection of the machine shaft with other Simscape blocks having mechanical rotational ports. The Simulink input representing the mechanical torque TL or the speed w of the machine is then removed from the block.

The next figure indicates how to connect an Ideal Torque Source block from the Simscape library to the machine shaft to represent the machine in motor mode, or in generator mode, when the rotor speed is positive.

Field type

Select between the wound-field and the permanent magnet DC machine. Choices are `Wound` (default) and `Permanent magnet`.

Use signal names to identify bus labels

When this check box is selected, the measurement output uses the signal names to identify the bus labels. Select this option for applications that require bus signal label to have only alphanumeric characters.

When this check box is cleared (default), the measurement output uses the signal definition to identify the bus labels. The labels contain nonalphanumeric characters that are incompatible with some Simulink applications.

### Parameters Tab

Armature resistance and inductance [Ra La]

The armature resistance Ra, in ohms, and the armature inductance La, in henries. Default is `[ 0.6 0.012]`.

Field resistance and inductance [Rf Lf]

The field resistance Rf, in ohms, and the field inductance Lf, in henries. This parameter is visible only when the Field type parameter on the Configuration tab is set to `Wound`. Default is `[ 240 120]`.

Field armature mutual inductance Laf

The field armature mutual inductance, in henries. This parameter is visible only when the Field type parameter on the Configuration tab is set to `Wound`. Default is `1.8`.

Specify

For a permanent magnet DC machine, select the machine constant that you want to specify for block parameterization. The values are `Torque constant` (default) and `Back-emf constant`. This parameter is visible only when the Field type parameter on the Configuration tab is set to `Permanent magnet`.

Torque constant

The torque per current constant of the permanent magnet DC machine, in N.m/A. This parameter is only visible when the Field type parameter on the Configuration tab is set to `Permanent magnet` and the Specify parameter above is set to `Torque constant`. Default is `1.8`.

Back-emf constant

The voltage per speed constant of the permanent magnet DC machine, in V/rpm. This parameter is only visible when the Field type parameter on the Configuration tab is set to `Permanent magnet` and the Specify parameter above is set to `Back-emf constant`. Default is `1.8`.

Total inertia J

The total inertia of the DC machine, in kg.m2. Default is `1`.

Viscous friction coefficient Bm

The total friction coefficient of the DC machine, in N.m.s. Default is `0`.

Coulomb friction torque Tf

The total Coulomb friction torque constant of the DC machine, in N.m. Default is `0`.

Initial speed

Specifies an initial speed for the DC machine, in rad/s, in order to start the simulation with a specific initial speed. To start the simulation in steady state, the initial value of the input torque signal TL must be proportional to the initial speed. Default is `1`.

Sample time (−1 for inherited)

Specifies the sample time that the block uses. To inherit the sample time specified in the Powergui block, set this parameter to `−1` (default).

## Inputs and Outputs

`TL`

The block input is the mechanical load torque, in N.m.

`w`

The alternative block input (depending on the value of the Mechanical input parameter) is the machine speed, in rad/s.

`m`

The output of the block is a vector containing measurement signals. You can demultiplex these signals by using the Bus Selector block provided in the Simulink library.

Name

Definition

Units

w

Speed wm

iA

Armature current ia

A

iF

Field current if

A

Te

Electrical torque Te

N.m

## Examples

The `power_dcmotor` example illustrates the starting of a 5 HP 240-V DC machine with a three-step resistance starter.

## References

[1] Analysis of Electric Machinery, Krause et al., pp. 89–92.

## Version History

Introduced before R2006a