## 09/09/2017

### Singly Excited - Doubly Excited System

• The electromechanical energy conversion is done through medium of magnetic field.

• It is assumed that there is no loss of energy in the magnetic field. There are two types of the excitation systems.

Singly excited system

• As its name "Singly" suggests that there is only a coil is required to produce the magnetic field.
• There is one set of electrical input terminal and one set of mechanical output terminal in this excitation system.
• The electro – magnetic relay, solenoid coil, hysteresis motor etc are the examples of singly excited system.

Analysis of singly excited system

• Figure shows a force producing device in which single coil acts as an input terminal and a movable plunger serves as an output terminal. The electrical input has two variable : e ( volts ) and I (current ) whereas the mechanical output has two variables : f ( force ) and x ( distance ).

Electrical input energy

Applying Kirchhoff’s voltage Law ( KVL ) to the input side

V = I R + e ………... (1)

As we know that

Induced emf α Rate of change of flux linkage

e  =  d /dt ( NФ )

= N ( dФ / dt )……..(2)

From equation (1) and (2)

V = IR + N ( dФ / dt )

VI = I2R + NI ( dФ / dt )

( VI ) dt = ( I2R ) dt + NI ( dФ )

( V – IR ) Idt = NI ( dФ )

( eI ) dt = NI ( dФ )

dWelect = ( eI ) dt = NI ( dФ )……..(3)

Energy stored in the magnetic field

• If the mechanical output energy or plunger movement is zero ( dWmech = 0 ) therefore the electrical energy input is equal to the energy stored in the magnetic field ( dW)

dWelect = dWf ……… (4)

Mechanical output energy

• If the plunger moves distance dx in the direction of force f, the mechanical work done can be obtained as

dWmech = ( f ) dx ... ... ... (5)

• According to the energy – balance equation for electrical input

Change in stored energy = Electrical input energy – Mechanical output energy

dWf = dWelect – dWmech

from equation (3) and (5)

dWf = N I ( dФ ) – f dx ... ... ... (6)

• It should be noted that equation (6) is used to calculate force and torque in electromechanical system.

Doubly Excited System

• As its name "Doubly" suggests that two coils are required to produce mechanical output force.
• There are two sets of electrical input terminals and one set of mechanical output terminal in this system.
• The synchronous motor, alternators, DC machines etc. are the examples of doubly excited system.

• Figure D shows an example of doubly excited field system.
• There are two windings in the rotating systems.
• One winding is wound on the stator and the other on the rotor.
• The stator and rotor windings are connected to electrical sources V1 and V2 respectively.
• The motor can allow rotating between two poles. The magnetic field depends upon the current I1 and I2 and θ between stator and rotor.

The Doubly Excited system consists of

• Three independent variable I1, I2, θ or λ1, λ2, θ
• The torque is directly proportional to the two electrical signals.
• The mechanical energy conversion does not depend upon change in current.