DC Machine

Purpose

Simple model of DC machine

Library

Electrical / Machines

Description

The machine operates as a motor or generator; if the mechanical torque has the same sign as the rotational speed the machine is operating in motor mode, otherwise in generator mode. In the component icon, the positive poles of armature and field winding are marked with dots.

Electrical System

Fig. 224 Electrical system of a (simple model) DC machine

Electromagnetic torque:

\[T_\mathrm{e} = L_\mathrm{af} \cdot i_\mathrm{f} \cdot i_\mathrm{a}\]

Induced voltage of the armature winding:

\[E_\mathrm{a} = L_\mathrm{af} \cdot i_\mathrm{f} \cdot \omega_\mathrm{m}\]

Mechanical System

\[\dot{\omega}_\mathrm{m}\; =\; \frac{1}{J} \left( T_\mathrm{e} - F\omega_\mathrm{m} - T_\mathrm{m} \right)\]

Parameters

Armature resistance

Armature winding resistance \(R_\mathrm{a}\) in ohms \((\Omega)\).

Armature inductance

Armature winding inductance \(L_\mathrm{a}\) in henries \((\mathrm{H})\).

Field resistance

Field winding resistance \(R_\mathrm{f}\) in ohms \((\Omega)\).

Armature inductance

Field winding inductance \(L_\mathrm{f}\) in henries \((\mathrm{H})\).

Field-armature mutual inductance

Field-armature mutual inductance \(L_\mathrm{af}\) in henries \((\mathrm{H})\).

Inertia

Combined rotor and load inertia \(J\) in \((\mathrm{Nms^2})\).

Friction coefficient

Viscous friction \(F\) in \((\mathrm{Nms})\).

Initial rotor speed

Initial mechanical speed \(\omega_\mathrm{m,0}\) in radians per second \(\left( \frac{\mathrm{rad}}{\mathrm{s}} \right)\).

Initial rotor position

Initial mechanical rotor angle \(\theta_\mathrm{m,0}\) in radians.

Initial armature current

Initial current \(i_\mathrm{a,0}\) in the armature winding in amperes \((\mathrm{A})\).

Initial field current

Initial current \(i_\mathrm{f,0}\) in the field winding in amperes \((\mathrm{A})\).

Probe Signals

Armature current

The current \(i_\mathrm{a}\) in the armature winding, in amperes \((\mathrm{A})\).

Field current

The current \(i_\mathrm{f}\) in the field winding, in amperes \((\mathrm{A})\).

Rotational speed

The rotational speed \(\omega_\mathrm{m}\) of the rotor in radians per second \(\left( \frac{\mathrm{rad}}{\mathrm{s}} \right)\).

Rotor position

The mechanical rotor angle \(\theta_\mathrm{m}\) in radians.

Electrical torque

The electrical torque \(T_\mathrm{e}\) of the machine in \((\mathrm{Nm})\).