Download Generated Voltage and Electromagnetic Torque

ECEg439:-Electrical Machine II
2.5. Armature Generated Voltage
and Electromagnetic Torque
By Sintayehu Challa
DC Generator
Equivalent Circuit
By Sintayehu Challa
ECEg439:Electrical Machine II
2
DC Generator Equivalent circuit
• The magnetic field produced by the stator poles induces
a voltage in the rotor (or armature) coils when the
generator is rotated.
• This induced voltage is represented by a voltage
source.
• The stator coil has resistance (R A), which is connected
in series.
• The pole flux is produced by the DC excitation/field
current, which is magnetically coupled to the rotor
• The field circuit has resistance(RF) and a source (VF)
• The voltage drop on the brushes represented by a
battery
By Sintayehu Challa
ECEg439:Electrical Machine II
3
DC Generator Equivalent circuit
Rf
Vf
Vbrush
?
max
If
Eag
Mechanical
power in
Ra
Load
Iag
Vdc
Electrical
power out
• Figure Equivalent circuit of a separately excited dc
generator.
By Sintayehu Challa
ECEg439:Electrical Machine II
4
DC Generator Equivalent circuit
• The magnetic field produced by the stator
poles induces a voltage in the rotor (or
armature) coils when the generator is
rotated.
• The dc field current of the poles generates a
magnetic flux
• The flux is proportional with the field
current if the iron core is not saturated:
?
ag
? K1 I f
By Sintayehu Challa
ECEg439:Electrical Machine II
5
DC Generator Equivalent circuit
• The rotor conductors cut the field lines
that generate voltage in the coils.
E ag ? 2 N r B ? g v
• The motor speed and flux equations are :
v?? r??
?
ag
Dg
2
? BA ? B? g? ? B ? g D g
By Sintayehu Challa
ECEg439:Electrical Machine II
6
DC Generator Equivalent circuit
• The combination of the three equation
results the induced voltage equation:
E ag
? Dg ?
? ? N r ?B ? g D g ?? ? N r ?
? 2 N r B ? g v ? 2 N r B ? g ???
?
? 2 ?
ag
?
• The equation is simplified.
Eag ? N r ?
ag
? ? N r K1 I f ? ? K e I f ?
By Sintayehu Challa
ECEg439:Electrical Machine II
7
DC Generator Equivalent circuit
• The generated voltage per conductor
equals E ? flux per pole x No.of poles x rev per sec
C
? 2 p?
N
volts
60
• The number of conductors connected in series per
parallel path or circuit Z/2a,where is the number of
path pairs and Z is the total conductor. The
generated voltage becomes
N
Z
pZ
)x
? (
)? N
60 2 a
60 a
? Ke ? N
E g ? (2 p?
Where K e ?
pZ
60 a
By Sintayehu Challa
ECEg439:Electrical Machine II
8
DC Generator Equivalent circuit
• When the generator is loaded, the load current
produces a voltage drop on the rotor winding
resistance.
• In addition, there is a more or less constant 1–3 V
voltage drop on the brushes.
• These two voltage drops reduce the terminal
voltage of the generator. The terminal voltage is;
E ag ? Vdc ? I ag Ra ? Vbrush
By Sintayehu Challa
ECEg439:Electrical Machine II
9
DC Generator Equivalent circuit
• Assume the load is connected to the machine so
that a current Ia flows in the armature, the
generated power becomes
Generated Power ? Pg ? E g I a
? K e? N I a
• The input Prime Mover torque becomes
? 2? N ?
Pg ? K e? N I a ? Torque x ? ? Tx?
?
? 60 ?
? 60
?
Torque ? T ? ?
K e ?? I a ? K M ? I a
? 2?
?
By Sintayehu Challa
ECEg439:Electrical Machine II
10
DC Motor
Equivalent Circuit
By Sintayehu Challa
ECEg439:Electrical Machine II
11
DC Motor Equivalent circuit
Rf
Vbrush
?
Ra
Electrical
power in
max
Vf If
Eam
Iam
Vdc
DC Power
supply
Mechanical
power out
• Figure above Equivalent circuit of a separately excited dc
motor
• Equivalent circuit is similar to the generator only the current
directions are different
By Sintayehu Challa
ECEg439:Electrical Machine II
12
DC Motor Equivalent circuit
• The operation equations are:
• Armature voltage equation
Vdc ? E am ? I am Ra ? Vbrush
The induced voltage
Eam ? K e ? N
By Ignoring the Brush Voltage Drop, The Speed of the
motor becomes
Vdc ? I a Ra
N?
K e?
By Sintayehu Challa
ECEg439:Electrical Machine II
13
DC Motor Equivalent circuit
• The operation equations are:
• The combination of the equations results in
K e? N ? Eam ? Vdc ? I am Rm
The current is calculated from this equation. The output
power and torque are:
Pout ? E am I am
Pout
T?
? Km ? Ia
?
One of the most important properties of DC Motor is the fact that it
has starting torque which can be calculated from torque equation.
By Sintayehu Challa
ECEg439:Electrical Machine II
14