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.

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 ).




electro mechanical system


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)

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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 ( dWf  )

       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.


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. 
doubly excited system

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.




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