ENGNG2024 Electrical Engineering
 E Levi, 2001
1
STEADY STATE OPERATION OF DC MACHINES
1. INTRODUCTION
Electric DC machines, as indeed any other type of electric machine, can be used to
either produce electric energy from the input mechanical energy, or to convert electric energy
into output mechanical energy. These two possible operating regimes are called generation and
motoring. As already mentioned, DC machines used to be in the past the major source of DC
power. In order to produce electric power DC machines were operated as generators.
Nowadays, however, use of DC generators is becoming more and more rare. DC power is
obtained instead by means of power electronic converters. The remaining applications of DC
machines are today restricted to motoring. In this operating regime a DC machine is operated
as a DC motor: it consumes DC power, while delivering at its shaft mechanical power. The
shaft drives a certain load, that is characterised with the load torque.
A DC machine consists of stationary part, called stator, and rotating part, called rotor.
Both stator and rotor are equipped with one winding. Stator winding is supplied from a DC
voltagesourceandtheroleofthiswindingistoproducemagneticfluxintheairgapofthe
machine. This flux is stationary in space. Rotor winding is again supplied from a DC voltage
source (for motoring): DC supply is connected to the rotor winding through a special
assembly, that is composed of brushes and commutator. Brushes are stationary, while
commutator is fixed to the rotor and hence rotates together with the rotor. This assembly
enables supply of electric power from stationary power supply to rotating winding on rotor.
Principle of operation of this assembly is illustrated by means of Fig. 1. Rotor winding is shown
in a very simplified manner, as consisting of just one coil, connected to two segments of the
commutator. Motoring action is assumed and the current is therefore delivered to the rotor
winding through the stationary brushes and rotating commutator. Two positions of the rotor
winding are shown in Fig. 1. Terminal current (current brought to the brushes) and the winding
current are illustrated in Fig. 2. As can be seen from these two figures, current inside the rotor
winding is reversed (commutated) after each half-revolution of the rotor. Current inside the
rotor is therefore AC, while the terminal current is DC. Frequency of the current inside the

a
iI
a
0 θ = ωt0π 2πθ=ωt
−
I
a
Fig. 2 - Terminal current and current through rotor coil.
Note that such a situation regarding frequencies in the two windings is the only possible
one that satisfies the condition of average torque existence. Since the stator winding is supplied
with pure DC current of zero frequency, the machine can develop an average torque if and
only if the rotor winding frequency equals the frequency of rotation. This means that it is not
possible to realise an electric machine with DC currents flowing in both stator and rotor
windings. Such a situation would result in the possibility of developing an average torque at
zero speed only. At zero speed however converted power equals zero and therefore such a
machine could not do the process of electromechanical energy conversion.
Let the stator winding, which is called excitation or field winding as well, be supplied
with constant DC voltage equal to V
f
. Current that flows through this winding is in steady-
state operation determined with
I
f
=V
f
/R
f
(1)
Flux produced in the air gap of the machine is, neglecting saturation of the magnetic circuit,
proportional to this current. Hence

the voltage equilibrium equation for the armature winding (index a)is
V
a
=R
a
I
a
+E (4)
According to the basic law of electromagnetic force creation, if a conductor that carries
current I moves in the flux of flux density B, then an electromagnetic force F=BIlacts on
the conductor. As rotor winding rotates in the flux density produced by the excitation winding,
an electromagnetic torque is produced, equal to
T
e
=c
2
Φ
f
I
a
=kI
f
I
a
(5)
This electromagnetic torque is the reason why the rotor rotates. If there is load connected to
the shaft of the machine, then this load opposes rotation with its torque, called load torque T
L
.
ENGNG2024 Electrical Engineering

P
in
=V
a
I
a
+ V
f
I
f
(8)
P
out
=T
e
ω (9)
The difference of the two powers represents power loss in the machine, which includes
mechanical loss, iron loss and loss in the windings. In what follows mechanical loss and iron
loss will be frequently neglected, but copper loss will always be accounted for. Power loss in
the machine and the efficiency are given with
P
loss
=P
in
-P
out
(10)
η
=P
out

T
L
=const.
T
L
=kω
2
ω
Fig. 4 - Illustration of various types of load torques.
2. SEPARATELY EXCITED DC MOTOR
Excitation winding and armature winding of a separately excited DC motor are
supplied from two independent DC power sources. A separately excited DC motor is described
in steady-state operation with the following set of equations, that essentially only summarise
again (1)-(6)
VERI
VRI
cI
Ec kI
Tc I kII
TT
aaa
fff
ff
ff
efafa
Le
=+
=
=
==

a
f
a
f
e
fn fn f
an
fn
a
fn
e
=+ = +
Þ
=−
== −
=−
=
=−
ωω
ω
ω
ω
()
()
2
2
If both voltages have rated values then
(13)
Speed-torque characteristic, with rated voltages applied to both windings, is the so-called
natural operating characteristic and is shown in Fig. 5 with bold trace. Equation (13) enables

nenn
nnin
=+
Þ
=− =− =
==
Þ
== =
== =
== =
== += =
500 0 5 100 450
2
60
2
60
30 450 1000 4.3
4.3 100 430
430
2
60
1000 45030
45030 50000 5000) 4503 55
.
/( )
//( ./
V
Rated torque is then
Nm
Rated power is mechanical (output)power,

EkI n n
E
kI
x
TkII x
an a a an
fn fn
an
nanaan
nfnnn
n
fn
en fn an
00
00
0
00
2
60
2
60
2
60
30 230 1200 183
230 0 2 40 222
2
60
2
60
30 222 183 1150