**Subject :**Electrical Machines II (AC Machines)

**Unit :**Alternators

## Analysis by two reaction theory

**Analysis by two reaction theory:**

*Fig: 1 *

The effects of salient poles can be taken into account by resolving the armature current into two components; I_{d} perpendicular to excitation voltage E_{0} and I_{a} along E_{0} as shown in phasor diagram in Fig. (1). Note that this diagram is drawn for an unsaturated salient-pole generator operating at a lagging power factor cos Φ. With each of the component currents Id and I_{q} , there is associated a component synchronous reactance X_{d} and X_{q} respectively.

X_{d} = direct axis synchronous reactance

X_{q} = quadrature axis synchronous reactance

If X_{1} is the armature leakage reactance and is assumed to be constant for direct and quadrature-axis currents, then,

**X _{d} = X_{ad} X_{l} ; X_{q} = X_{aq} X_{l}**

Note that in drawing the phasor diagram, the armature resistance R_{a} is neglected since it is quite small. Further, all values arc phase values. Here V is the terminal voltage phase and E_{0} is the e.m.f. per phase to which the generator is excited.

Referring to Fig. (1).