Dcmachine 1233234542827948-3-2

Direct-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

ΦΦ 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

ΦΦ ff

22SS

xxxx x

xxx

ArmatureArmatureWindingWinding

Magnetic Flux in DC machines

Φf/2

rotor

stator

If

SS

NN

Vf

+

-

.. .. ..

xx

x x xx

ArmatureWinding

If

Φ a

The current is induced in the Rotor Rotor WindingWinding (i.e. the Armature WindingArmature Winding) since it is placed in the field (Flux Lines) of the Field Winding.

DC Machines

ΦΦ 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 toDue

Armature 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

Transducer with stator and rotor windings

Equivalent circuit for separately excited DC motors

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 θsin−=

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 aaaarfafa +=− ω

dt

diLiru fffff +=

In motor application, the output is the angular velocity

Equivalent circuit for separately excited DC generators

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 aaaarfafa −−=− ω

dt

diLiru fffff +=

The steady state operating condition for a generator are

In generator application, the output is the voltage induced

aarfafa iriLu −=− ω fff iru =

DC Machines

sin

equation torqueThe,

cos2

1

2

1 22

rafafe

r

ce

rafafaaffc

LiiT

Therefore

WT

LiiiLiLW

θ

θ

θ

−=

∂∂=

++=

constant)90(max =

ℜ=== °

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

( )°ℜ 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

iruω

remec TP ω=

)1(−−−−−−−=r

aae

iET

ω

)2(−−−−−= rfafa iLE ω

afafe iiLT =

Electromagnetic power

Given that emmec PP =

Therefore

Electromotive force formula is given as

Substituting (2) into (1), yields

aarfafa iriLu −=− ω 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 ffff

λ+=

DC Machines

The flux linkage equations are:

cos

''

'

rfaaf

aaaafafaa

aaafffff

-LLL

iLiL

iLiL

θλ

λ

==

+=

+=

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

ω=

++=+=

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

θ

θ

θ

−=

∂∂=

++=

DC Machines - Shunt ConnectedShunt Connected

For DC MachinesDC Machines, 2

πθ −=r

mmf fieldmmf field

mmf armaturemmf armature

++

--

2

πθ −=r

faafe iiLT =