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Formulas

Shunt Generator
For a shunt generator with armature induced voltage Ea, armature current Ia and armature resistance Ra, the terminal voltage V is:
V = Ea – IaRa
The field current I f for a field resistance R f is:
I f = V / R f

The armature induced voltage Ea and torque T with magnetic flux F at angular speed w are:
Ea = k fFw = kmw
T = k fFIa = kmIa
where k f and km are design coefficients of the machine.

Note that for a shunt generator:
– induced voltage is proportional to speed,
– torque is proportional to armature current.

The airgap power Pe for a shunt generator is:
Pe = wT = EaIa = kmw Ia

Shunt Motor
For a shunt motor with armature induced voltage Ea, armature current Ia and armature resistance Ra, the terminal voltage V is:
V = Ea + IaRa
The field current I f for a field resistance R f is:
I f = V / R f

The armature induced voltage Ea and torque T with magnetic flux F at angular speed w are:
Ea = k fFw = kmw
T = k fFIa = kmIa
where k f and km are design coefficients of the machine.

Note that for a shunt motor:
– induced voltage is proportional to speed,
– torque is proportional to armature current.

The airgap power Pe for a shunt motor is:
Pe = wT = EaIa = kmw Ia

Series Motor
For a series motor with armature induced voltage Ea, armature current Ia, armature resistance Ra and field resistance R f, the terminal voltage V is:
V = Ea + IaRa + IaR f = Ea + Ia(Ra + R f)
The field current is equal to the armature current.

The armature induced voltage Ea and torque T with magnetic flux F at angular speed w are:
Ea = k fFw Ia = kmw Ia
T = k fFIa2 = kmIa2
where k f and km are design coefficients of the machine.

Note that for a series motor:
– induced voltage is proportional to both speed and armature current,
– torque is proportional to the square of armature current,
– armature current is inversely proportional to speed for a constant induced voltage.

The airgap power Pe for a series motor is:
Pe = wT = EaIa = kmw Ia2

NOTATION
The symbol font is used for some notation and formulae. If the Greek symbols for alpha beta delta do not appear here [ a b d ] the symbol font needs to be installed for correct display of notation and formulae.
B
E
f
G
I
j
k
m
N
n
P
p
R
susceptance
induced voltage
frequency
conductance
current
j-operator
coefficient
number of phases
number of turns
rotational speed
power
pole pairs
resistance
[siemens, S]
[volts, V]
[hertz, Hz]
[siemens, S]
[amps, A]
[1Ð90°]
[number]
[number]
[number]
[revs/min]
[watts, W]
[number]
[ohms, W]
S
s
T
V
X
Y
Z
d
F
f
h
q
w
voltamperes
slip
torque
terminal voltage
reactance
admittance
impedance
loss angle
magnetic flux
phase angle
efficiency
temperature
angular speed
[volt-amps, VA]
[per-unit]
[newton-metres, Nm]
[volts, V]
[ohms, W]
[siemens, S]
[ohms, W]
[degrees, °]
[webers, Wb]
[degrees, °]
[per-unit]
[centigrade, °C]
[radians/sec]

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