?Electric Drive, please help. Thanks Under three-phase balanced sinusoidal condi

Question

?Electric Drive, please help. Thanks

Under three-phase balanced sinusoidal condition with no rotor currents, and neglecting the stator winding resistances R, and the leakage inductance L for simplification, What is the speed at which all of the space vectors rotate? (b) How is the peak flux density related to the magnetizing currents? Does this relationship depend on the frequency fof the excitation? If the peak flux density is at its rated value, then what about the peak value of the magnetizing currents? (c) How do the magnitudes of the applied voltages depend on the frequency of excitation, in order to keep the flux density constant (at its rated value for example)? 19. answer the following questions: (al) 20. What is the relationship between space vectors and phasors under balanced sinusoidal operating conditions?

Explanation / Answer

a)The Space vector move with the Synchronous speed.It is the primciple which says that when 3 phase balanced supply is given to balanced windings in space,there is a creation of rotating magnetic field.Which moves at the Synchronous speed.

b)When a single phase is carrying a current that is sinusoidal,an mmf which is sinusoidally distributed in space(if we neglect space harmonics) is established.Similarly the other phases also produce an MMF which are sinusoiadlly distributed in space.Now if the currents in these phases is sinusoidal then individually they create a standinh wave.But when these indivdual standinh waves are added ,we get a rotating magnetic field.If we represent the indivdual mmf wave by Fm(peak value) then the resultant mmf wave of all three phases is 1.5Fm.

Fr=1.5Fm Now Fm =Nph Im.

Flux =MMF/Relucatnce.

Flux=B.A...therefore Peak flux density is directly proportional to the Magnetising currents..This relation doesn't depend upon the frequency of the supply.If the peak flux density is at its rated value then this means that the currents in the phases are at their peak values.

c)If we ignore losses then Vph~(approx equal to)Eph=4.44Nph× (phi)×f×Kd×Kp

This is RMS value equation

Kd and Kp are distribution and pitch factors.

Nph=Nunber of turns in one phase.

After designing Nph is fixed.So are Kd and Kp.

Phi=Flux =Bm.A

Area(A) is also fixed.

So in the equation the only variables are Vph,Bm and f.

Now if Bm has to be constant.Then Vph and f must vary proportionalyy..that is V/f ratio must remain constant for keeping flux density constant.So V directly proportional to f.

20

The space vectora are rotating in space .When seen from the stator they exactly look like phasors.A single phase MMF has a sinuosoidal distribution.With its peak along the axis of the coil.This is represented by Fm Cos (theta) where theta is space angle measured from the axis.This is pusating in nature.When this is rotated it can be treated as a phasor.

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