The details of synchronous generators developed so far is applicable to only round rotor or nonsalient pole alternators. In such machines the air gap is uniform through out and hence the effect of mmf will be same whether it acts along the pole axis or the inter polar axis. Hence reactance of the sator is same throughout and hence it is called synchronous reactance.
But in case salient pole machines the air gap is non uniform and it is smaller along pole axis and is larger along the inter polar axis. These axes are called direct axis or d-axis and quadrature axis or q-axis. Hence the effect of mmf when acting along direct axis will be different than that when it is acting along quadrature axis. Hence the reactance of the stator can not be same when the mmf is acting along d – axis and q- axis. As the length of the air gap is small along direct axis reluctance of the magnetic circuit is less and the air gap along the q –axis is larger and hence the along the quadrature axis will be comparatively higher. Hence along d-axis more flux is produced than q-axis. Therefore the reactance due to armature reaction will be different along d-axis and q-axis.
These reactances are
Xad = direct axis reactance; Xaq = quadrature axis reactance.
Hence the effect of armature reaction in the case of a salient pole synchronous machine can be taken as two components - one acting along the direct axis (coinciding with the main field pole axis) and the other acting along the quadrature axis (inter-polar region or magnetic neutral axis) - and as such the mmf components of armature-reaction in a salient-pole machine cannot be considered as acting on the same magnetic circuit. Hence the effect of the armature reaction cannot be taken into account by considering only the synchronous reactance, in the case of a salient pole synchronous machine.
In fact, the direct-axis component Fad acts over a magnetic circuit identical with that of the main field system and produces a comparable effect while the quadrature-axis component Faq acts along the interpolar axis, resulting in an altogether smaller effect and, in addition, a flux distribution totally different from that of Fad or the main field m.m.f. This explains why the application of cylindrical rotor theory to salient-pole machines for predicting the performance gives results not conforming to the performance obtained from an actual test.
Blondel’s Two reaction Theory:
Blondel’s two-reaction theory considers the effects of the quadrature and direct-axis components of the armature reaction separately. Neglecting saturation, their different effects are considered by assigning to each an appropriate value of armature-reaction “reactance,” respectively xad and xaq . The effects of armature resistance and true leakage reactance (XL) may be treated separately, or may be added to the armature reaction coefficients on the assumption that they are the same, for either the direct-axis or quadrature-axis components of the armature current (which is almost true). Thus the combined reactance values can be expressed as : Xsd = xad + xi and Xsq = xaq + xi for the direct-and cross-reaction axes respectively.
In a salient-pole machine, xaq, the quadrature-axis reactance is smaller than xad, the direct-axis reactance, since the flux produced by a given current component in that axis is smaller as the reluctance of the magnetic path consists mostly of the interpolar spaces. It is essential to clearly note the difference between the quadrature and direct-axis components Iaq, and Iad of the armature current Ia, and the reactive and active components Iaa and Iar. Although both pairs are represented by phasors in phase quadrature, the former are related to the induced emf Et while the latter are referred to the terminal voltage V. These phasors are clearly indicated with reference to the phasor diagram of a
(salient pole) synchronous generator supplying a lagging power factor (pf) load, shown in above Fig.
Iaq = Ia cos(δ+Ø); Iad = Ia sin(δ+Ø); and Ia = √[(Iaq)² + (Iad)²]
Iaa = Ia cosØ; Iar = Ia sinØ; and Ia = √[(Iaa)² + (Iar)²]
where δ = torque or power angle and Ø = the p.f. angle of the load.
The phasor diagram below Fig. shows the two reactance voltage componentsIaq *Xsq and Iad * Xsd which are in quadrature with their respective components of the armature current. The resistance drop Ia x Ra is added in phase with Ia although we could take it as Iaq x Ra and Iad x Ra separately, which is unnecessary as Ia = Iad + jIaq.
