- The speed of DC motor is related to following equation

N a E

_{b}/ F
N = K ( V – I

_{a}R_{a}) / F
( a ) Supply voltage

( b ) Flux per pole ( Flux control )

( c ) Armature resistance control ( OR Rheostatic control )

### Speed control of DC Shunt Motor

#### ( 1 ) Flux control method

- The speed variation is obtained by inserting variable
resistance is in series with the field circuit. If the supply voltage is kept
constant, back emf E
_{b}is also constant.

N a 1 / F

- It means that an increase in field resistance reduces the field current consequently reduction of field current and increase in speed.
- As the field current is very small the field copper loss is very small.
- Therefore this method is very efficient and economical.
- The maximum speed can be obtained by minimum value of flux which affects the effect of armature reaction.
- At the same time increase in armature current causes over heating of armature, poor commutation and instability.
- Therefore there is some limitation to obtain high speed.
- The maximum to minimum speed can be obtained in the ratio of 6: 1 in the inter polar machine whereas it will be ratio of 2 : 1 in the non inter polar machine.
- This method of speed control is applicable to achieve speed above normal or rated speed.

#### ( 2 ) Armature resistance control

- A variable resistor is inserted in series with the armature winding in this method.
- As the supply voltage is kept constant, voltage across armature is equal to supply voltage minus voltage drop across rheostat.
- As a variable resistor increases, the voltage drop across resistor increases resulting voltage drop across armature decreases.
- This will result in speed of the motor decreases. Greater the value of variable resistor, greater fall in speed.

Let

I

_{a1}= Armature current in first case
I

_{a2}= Armature current in second case
N

_{1}= Speed in first case
N

_{2 }= Speed in second case
V = Supply voltage

R

_{a}= Armature resistance in first case
R

_{a}+ R = Armature + variable resistor in second case
As

( N

_{2}/ N_{1 }) = ( E_{b2}/ E_{b1})
( N

_{2}/ N_{1 }) = [ V – I_{a2 }( R_{a}+ R ) ] / [ V – I_{a1 }R_{a}]
If we consider no load speed N

_{0}
( N / N

_{0 }) = [ V – I_{a }( R_{a}+ R ) ] / [ V – I_{a0 }R_{a}]
Neglecting I

_{a0 }R_{a}as compared to supply voltage V
( N / N

_{0 }) = [ V – I_{a }( R_{a}+ R ) ] / V
N = N

_{0 }[ V – I_{a }( R_{a}+ R ) / V ]
N = N

_{0 }[ 1 – I_{a }( R_{a}+ R ) / V ] …………. ( 1 )- For a given value of ( R
_{a}+ R ) in the armature circuit, the speed is linear function of armature current.

By putting N = 0 in the equation ( 1 )

N

_{0 }[ 1 – I_{a }( R_{a}+ R ) / V ] = 0
I

_{a}= V / ( R_{a}+ R )- This is maximum current and it is known as stalling current.
- This method is employed when speed below the normal speed is required for short period duty i.e. printing machine, crane, hoist etc.

#### Disadvantage

- This method is wasteful because large power loss in the armature circuit.
- Poor voltage regulation is obtained particularly at lower speed

#### ( 3 ) Voltage control ( Ward – Leonard method )

- The field winding is permanently connected to fixed supply voltage and voltage across armature varies by means of either variable supply voltage system or motor – generator set.
- The speed of motor is approximately proportional to voltage across armature.
- The M is main DC shunt motor whose speed control is required as shown in the Figure C.
- The field of the motor is connected to exciter.
- The variable voltage across armature is supplied through induction motor – DC generator set.
- The DC generator is driven by induction motor whose shaft is coupled to an exciter.
- The voltage of the generator is varied from maximum to minimum value by means of a field regulator.
- The generated voltage is given to the DC shunt motor.
- The generator voltage and direction of motor M is reversed by reversing switch RS. The induction motor – generator set always run in the same direction.

Advantages

- Smooth speed control.
- Wide range of speed control from maximum to minimum.
- Good speed regulation is achieved.

#### Disadvantages

- Two extra machines require therefore the initial cost is high.
- Low efficiency of the system particularly at light load.
- More space requires as there are two extra machines require.

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