Power flow
The flow of power from mechanical to electrical domain in a generator and electrical to mechanical domain in a motor occurs as shown in the diagram below:
 |
Power Flow Diagram |
For Series and Separately excited machines: I
L = I
a
For Shunt Generator: I
L = I
a - I
f
For Shunt Motor: I
L = I
a + I
f
NOTE:- The amount of conductor and iron materials required for a Machine of given rating ∝
1 / speed of machine
Maximum Power Output
To achieve maximum power output in a DC Machine the following condition must be satisfied.
Motor
Developed Power, P
a = E
aI
a = (V - I
aR
a)I
a = VI
a - I
a^2 R
a
For maximum output,
dP
a/dI
a = V - 2I
aR
a = 0
I
a = V / 2R
a
And E
a = V - 2I
aR
a
E
a = V/2
Efficiency, 𝜂 = P
a / VI
a = E
aI
a / VI
a = 1/2 = 50%
Suppose, R
a = 0.03pu
for maximum output
I
a = 100% / (2*3%) ≈ 17 times full load
Due to such high current, windings will be burnt immediately. Hence, maximum power output is undesirable condition.
Generator
Output Power, P
a = V
aI
a
= (E
a - I
aR
a)I
a
= E
aI
a - I
a^2 R
a
For maximum output power, dP
a / dI
a = E
a - 2I
aR
a = 0
I
a = E
a / 2R
a
V
a = E
a - I
aR
a = E
a/2
Efficiency, 𝜂 = V
aI
a / E
aI
a = 1/2 = 50%
Here, also current will be high due to small Armature Resistance and it can damage the windings.
So, the desirable condition is maximum efficiency so that maximum part of Input Power is converted to Output Power.
Maximum Efficiency
Assuming a Short Shunt Machine with the following parameters:
V
BD = Brush Drop Voltage
P
k = No-Load Rotational Losses
R
a = Armature Resistance
R
f = Shunt Field Resistance
R
se = Series Field Resistance
If Machine operates as a generator,
I
a = I
L + I
f
Where I
L is current delivered to load
I
f is current in Shunt Field Winding
I
a is Armature Current
𝜂 = V
t I
L / (V
t I
a + I
a^2 R
a + V
BD I
a + P
k + I
L^2 R
se + I
f^2 R
f)
For Maximum Efficiency, d𝜂/dI
L = 0
V
t(V
t I
a + I
a^2 R
a + V
BD I
a + P
k + I
L^2 R
se + I
f^2 R
f) - V
t I
L(V
t + 2I
aR
a + V
BD + 2I
LR
se) = 0
Substitute I
a = I
L + I
f
We get, I
L^2
(R
se + R
a) = I
f^2 R
f + P
k + V
BDI
f + I
f^2 R
a
which implies,
Constant Losses = Variable Cu Losses
This can be applied to Shunt Machines by equating R
se to zero and for Series Machines by equating I
f and R
f to zero.
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