Modified phasor diagram by two reaction theory
The equivalent circuit of a salient-pole synchronous generator is shown in Fig. 1 (a). The component currents Id and Iq provide component voltage drops jId Xd and jIq Xq as shown in Fig. 1(b) for a lagging load power factor. The armature current Ia has been resolved into its rectangular components with respect to the axis for excitation voltage E0.The angle ψ between E0 and Ia is known as the internal power factor angle. The vector for the armature resistance drop IaRa is drawn parallel to Ia. Vector for the drop IdXd is drawn perpendicular to Id whereas that for Iq × Xq is drawn perpendicular to Iq. The angle δ between E0 and V is called the power angle. Following phasor relationships are obvious from Fig. 1 (b)
E0 = V IaRa jId Xd jIq Xq and Ia = Id Iq
If Ra is neglected the phasor diagram becomes as shown in Fig. 2 (a). In this case,
E0 = V jId Xd jIq Xq
Incidentally, we may also draw the phasor diagram with terminal voltage V lying in the horizontal direction as shown in Fig. 2 (b). Here, again drop IaRa is || Ia and Id Xd is ⊥ to Id and drop Iq Xq is ⊥ to Iq as usual.
Calculations from Phasor Diagram
In Fig. 3, dotted line AC has been drawn perpendicular to Ia and CB is perpendicular to the phasor for E0. The angle ACB = ψ because angle between two lines is the same as between their perpendiculars. It is also seen that