Synchronizing Power | Expression for Synchronizing Power in salient pole machine

Synchronizing Power(PSY):

Synchronizing Power is defined as the difference between input power to alternator at power angle 𝛿  and input power to alternator at power angle 𝛿 + 𝛿'.Synchronizing Power is denoted by PSY.
          Consider an alternator connected to the infinite bus bar. Let V be the bus bar voltage and E be the e.m.f. induced in the alternator.The excitation of the alternator is adjusted in such a way that E and V are equal in magnitude. In the local circuit, the two voltages E and V are in phase opposition while in the external circuit they are in the same phase.This is represented in the below figure. 
synchronizing-power-expression-salient-pole-machine

 Must Read:


            Consider the alternator to be at no load. If by some means power input to the machine is decreased and it's induced e.m.f. E will then lag behind V by say angle 2𝛿. Due to this difference, E and v will not remain in exact phase opposition but will give rise to resultant e.m.f. Er. This ER will act in the local circuit and a synchronizing current will start flowing in the local circuit. The synchronizing current is given by, 

                                              ISY = Er/Zs

Isy is lagging behind Er by an angle θ given by

                                                θ = tan⁻¹(Xs/R)

R is very very small it can be neglected.

                                            θ ≈ 90°

          The angle 2𝛿 is very very small and θ is approximately equal to 90° so the synchronizing current Isy is almost in phase with V and in phase opposition with E. So infinite bus bar will deliver some power to the alternator. As the current in the local circuit is always opposing to induced e.m.f. E, the alternator will act as a synchronous motor. Thus synchronizing torque will be developed which will try to accelerate the machine. Thus the angle 2𝛿 will go on decreasing and resultant e.m.f. Er also goes on decreasing.Finally the two e.m.f.s E and V will again be in phase opposition and the machine will now act as an alternator in synchronism with the bus bar. 
synchronizing-power-expression-salient-pole-machine

         Thus the power which automatically comes into play and accelerates the machine which was retarding and decelerates the machine which tries to accelerate is called synchronizing power. This power will keep the machine in step with the infinite bus bar. 

Expression for Synchronizing Power(PSY):

Consider an alternator which is operating at a power angle 𝛿 i.e.  E leads V by an angle 𝛿.
synchronizing-power-expression-salient-pole-machine

           Let power input of this alternator be increased suddenly so that it will now operate at a new power angle given by 𝛿 + 𝛿'.So the synchronizing emf ESY
 will come into play and sends a circulating current given by ISY = ESY/Zs.This current produces synchronizing power. Now we will derive the expression for synchronizing power per phase. 
         Before increasing the input of alternator, the power input Pi1 is given by,
            
synchronizing-power-expression-salient-pole-machine

        When power angle 𝛿 has changed to 𝛿±𝛿′ (+ sign indicates acceleration and - sign indicates deceleration) the power input Pi2 is given by


          The difference between these two powers is nothing but synchronizing power PSY.
                                           PSY = Pi2 - Pi1

synchronizing-power-expression-salient-pole-machine

If 𝛿′ is small then 𝛿′/2 is very very small.Therefore sin²(𝛿′/2) can be neglected as it is tending towards zero.
synchronizing-power-expression-salient-pole-machine

For large synchronous machines θ = 90° and Zs = Xs as Ra is neglected 

synchronizing-power-expression-salient-pole-machine

For synchronous generator which is synchronized with bus bar V = E, 𝛿 = 0 and 𝛿′ is very very small.

                                Sin 𝛿′ = 𝛿′    and  Cos 𝛿 = 1

synchronizing-power-expression-salient-pole-machine

The above expression is per phase power.Therefore for the machine having 'm' phases the synchronizing power is given by,

Expression for Synchronizing Power  in salient pole machine:

The same expression is not valid for salient pole machine.The expression for salient pole machine can be obtained as follows:

synchronizing-power-expression-salient-pole-machine


From figure(a), it can be observed that
synchronizing-power-expression-salient-pole-machine

From figure(b), it can be observed that

synchronizing-power-expression-salient-pole-machine
Must Read:

synchronizing-power-expression-salient-pole-machine

synchronizing-power-expression-salient-pole-machine

synchronizing-power-expression-salient-pole-machine



        Thus the total power consists of a fundamental component and a second harmonic component which is present because the armature reaction flux has a tendency to pass through the field structure along its minimum reluctance path i.e. along field pole axis and direct axis.Since  2𝛿 exists because of difference in reluctance along p and q axes and is called reluctance power and the term is called reluctance torque. The first term is identical with that obtained for cylindrical machine and component of power is known as electromagnetic power. 
           Now dP/d𝛿 gives the Synchronizing power.

synchronizing-power-expression-salient-pole-machine

synchronizing-power-expression-salient-pole-machine

Conclusion:
         Now today we have learnt about Synchronizing Power and also derived the expression for Synchronizing Power for salient pole machine.You can download this article as pdf, ppt.If any queries, you can mail @ [email protected]
---------------------------------------------------------------------------------------------------

No comments:

Follow on G+

Followers