Blondel's Two Reaction Theory (Theory of Salient Pole Machine) : part 2
We know that, the armature reaction flux ΦAR has two components, Φd along direct axis and Φq along quadrature axis. These fluxes are proportional to the respective m.m.f. magnitudes and the permeance of the flux path oriented along the respective axes.
... Φd = Pd Fd
where Pd = permeance alomng the direct axis
Permeance is the reciprocal of reluctance and indicates ease with which flux can travel along the path.
But Fd = m.m.f. = Kar Id in phase with Id
The m.m.f. is always proportional to current. While Kar is the armature reaction coefficient.
... Φd = Pd Kar Id
Similarly Φq = Pq Kar Iq
As the reluctance along direct axis is less than that along quadrature axis, the permeance Pd along direct axis is more than that along quadrature axis, (Pd < Pq ).
Let Ed and Eq be the induced e.m.f.s due to the fluxes Φd and Φq respectively. Now Ed lags Φd by 90o while Eq lags Φq by 90o .
where Ke = e.m.f. constant of armature winding
The resultant e.m.f. is the phasor sum of Ef, Ed and Eq.
Substituting expressions for Φd and Φq
Now Xard = Equivalent reactance corresponding to the d-axis component of armature reaction
= Ke Pd Kar
and Xarq = Equivalent reactance corresponding to the q-axis component of armature reaction
= Ke Pq Kar
For a realistic alternator we know that the voltage equation is,
where Vt = terminal voltage
XL = leakage reactance
Substituting in expression for ĒR ,
where Xd = d-axis synchronous reactance = XL + Xard .............(2)
and Xq = q-axis synchronous reactance = XL + Xarq .........(3)
It can be seen from the above equation that the terminal voltage Vt is nothing but the voltage left after deducing ohmic drop Ia Ra, the reactive drop Id Xd in quadrature with Id and the reactive drop Iq Xq in quadrature with Id, from the total e.m.f. Ef.
The phasor diagram corresponding to the equation (1) can be shown as in the Fig. 1. The current Ia lags terminal voltage Vt by Φ. Then add Ia Ra in phase with Ia to Vt. The drop Id Xd leads Id by 90o as in case purely reactive circuit current lags voltage by 90o i.e. voltage leads current by 90o . Similarly the drop Iq Xq leads Xq by 90o . The total e.m.f. is Ef.
Read : Part 1 , Part 3
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Read : Part 1 , Part 3
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