dcmachine
TRANSCRIPT
Direct-Current MachineDirect-Current Machine
Electric Machine Electric machines can be used as motors and
generators Electric motor and generators are rotating energy-
transfer electromechanical motion devices Electric motors convert electrical energy to
mechanical energy Generators convert mechanical energy to electrical
energy
Electric Machine Electric machines can be divided into 2 types:
AC machines DC machines
Several types DC machines Separately excited Shunt connected Series connected Compound connected Permanent magnet
Electric Machine All Electric machines have:
Stationary members (stator) rotating members (rotor) Air gap which is separating stator and rotor
The rotor and stator are coupled magnetically
Schematic representation of a DC Machine
DC Machines
StatorStator
RotorRotor+
VVff
-
If
If
If
NN
ff
22
SS
Electric Machine The armature winding is placed in the rotor
slot and connected to rotating commutator which rectifies the induced voltage
The brushes which are connected to the armature winding, ride on commutator
DC Machines
Elementary two-pole DC Machine
Electric Machine The armature winding consists of identical coils carried in
slots that are uniformly distributed around the periphery of the rotor
Conventional DC machines are excited by direct current, in particular if a voltage-fed converter is used a dc voltage uf is supplied to the stationary field winding
Hence the excitation magnetic field is produced by the field coils
Due to the commutator, armature and field windings produce stationary magnetomotive forces that are displaced by 90 electrical degrees
The field winding is placed on the stator and supplied from a DC Source.
DC Machines
RotorRotor
NN
ff
22SS
xx
xx x
xx
x
ArmatureArmatureWindingWinding
Magnetic Flux in DC machines
f/2
rotor
stator
If
SS
NN
Vf
+
-
.. .. ..xx
x x xx
ArmatureWinding
If
a
The current is induced in the Rotor WindingRotor Winding (i.e. the Armature Armature WindingWinding) since it is placed in the field (Flux Lines) of the Field Winding.
DC Machines
ff
mmf produced by the armature and mmf produced by the field winding are orthogonal.
Orthogonality of Magnetic Fields in DC Machines
B
IL F oILBL 90sin BIF
Magnetic field due to field winding
Magnetic field due to armature winding
90o
The force acting on the rotor, is expressed as
DC Machines
Field the
toDueArmature the
toDue
BLIf
ll
f f
f f
TTeeTTee = xf f ll
The Field winding is placed on the stator and the current (voltage) is induced in the rotor winding which is referred also as the armature winding.
In DC Machines, the mmf mmf produced by the field winding and the mmf mmf produced by the armature winding are at right-angle with respect to each other.
The torque is produced from the interaction of these two fields.
DC Machines
rr
rLsL
srsi
su
ru
ri
stator rotor
axismagneticstator
axism
agneticrotor
0rrr t
er t,
LTmB
Load
Transducer with stator and rotor windings
Equivalent circuit for separately excited DC motors
VOLTAGE SUPPLY
LOAD
rfafa iLE +
-
er T,LT
+
-
ar
ai
arr
aL
frr
fi
fr
fu
fL
auaxisquadrature
axisdirect
armature
field
SEPARATELY EXCITED DC MOTORS
Electric Machine Conventional separately excited DC electric machine
Stator and rotor windings excited by dc current The rotor has the commutator Dc voltage to the armature windings is supplied through the
brushes which establish electric contact with the commutator The brushes are fixed with respect to the stator and they are placed
in the specified angular displacement To maximize the electromagnetic torque, the stator and rotor
magnetic axes are displaced by 90 electrical degrees using a commutator
rrssre iiLT sin
Electric Machine Electric machine can be either a motor or a generator
depending on whether it drives a load or it is driven by a prime mover
The direction of the armature current is reversed when an electric machine changes from motor to generator operation
However line voltage polarity, direction of rotation and field current are the same
a
aaa r
Eui
(MOTOR) If is greater than , the armature current is positive
(GENERATOR) If is greater than , the armature current is negative
aEauai
aE au
Electric Machine Conventional separately excited DC electric machine
Using kirchhoff’s second law and assuming the differential equation of a motor
0 frar rr
dt
diLiriLu a
aaarfafa dt
diLiru f
ffff
In motor application, the output is the angular velocity
Equivalent circuit for separately excited DC generators
LOAD
PRIME MOVER
rfafa iLE +
-
pmr ,pmT
+
-
ar
ai
arr
aL
frr
fi
fr
fu
fL
auaxisquadrature
axisdirect
armature
field
SEPARATELY EXCITED DC GENERATORS
Electric Machine Conventional separately excited DC electric machine
Using kirchhoff’s second law and assuming the differential equation of a generator
0 frar rr
dt
diLiriLu a
aaarfafa dt
diLiru f
ffff
The steady state operating condition for a generator are
In generator application, the output is the voltage induced
aarfafa iriLu fff iru
DC Machines
sin
equation torqueThe,
cos2
1
2
1 22
rafafe
r
ce
rafafaaffc
LiiT
Therefore
WT
LiiiLiLW
constant)90(max
m
afsrMaf
NNLLL
Energy stored in inductor is stored in the magnetic field within the coil
2.2
1ILWm
The mutual inductance between the armature and field windings
90m
The armature and field magnetic axes are displaced by 90 electrical degrees and the magnetizing reluctance is constant
DC Machines The torque equation
aaem iEP
)3(2
e
faf
a
faf
a
faf
aaar T
iL
r
iL
u
iL
iru
remec TP
)1(r
aae
iET
)2( rfafa iLE
afafe iiLT
Electromagnetic power
Given that emmec PP
Therefore
Electromotive force formula is given as
Substituting (2) into (1), yields
aarfafa iriLu afafe iiLT using and
Steady state relationship between the angular velocity end electromagnetic torque
The DC Machine Dynamic Equations for the circuit represented bellow is
DC Machines
dt
dirV f
fff
DC Machines
The flux linkage equations are:
cos
''
'
rfaaf
aaaafafaa
aaafffff
-LLL
iLiL
iLiL
Where Lff = field self-inductance Laa= armature self-inductance Laf = mutual inductance between the field and rotating armature coils
DC Machines - Shunt ConnectedShunt Connected
The Shunt ConfigurationShunt Configuration for a DC DC MachineMachine is as shown below,
DC Machines - Shunt ConnectedShunt Connected
The Dynamic Equations (assuming rrf extf ext = =
0 0 ) are follows,
fafra
afaaaaa
ffffff
iLedt
diLireV
dt
diLirV
Where Lff = field self-inductance Lfa = mutual inductance between the field and rotating armature coils ea = induced voltage in the armature coils (also called countercounter or back emfback emf )
DC Machines - Shunt ConnectedShunt Connected
The torque equation for a Shunt Shunt Connected DC-MachineConnected DC-Machine is
sin
,
cos2
1
2
1 22
rafafe
r
ce
rafafaaafffc
LiiT
Therefore
WT
LiiiLiLW
DC Machines - Shunt ConnectedShunt Connected
For DC MachinesDC Machines, 2
r
mmf fieldmmf field
mmf armaturemmf armature
++
--
2
r
faafe iiLT