__The Equivalent Circuit and a Simplified Phasor Diagram for a Phase of a Synchronous Generator __

The equivalent circuit answering the equation of electric slate of a stator phase of a synchronous generator is shown in Fig 4 a. Now we will construct a phasor diagram for a phase of a synchronous generator. To do this, we choose as reference the main flux linkage vector Ψ̇_{0} which is directed to the left along the axis of abscissae .

(Fig 4 b). The phasor of *Ė*_{0} induced by Ψ̇_{0} is in quadrature lagging with Ψ̇_{0 }.The phasor of the stator (armature) current *İ* is lagging £0 by an angle φ_{0} determined by the relative magnitudes of the reactances and resistances

φ_{0 }= arc tan ( + _{load})/(*r*_{w} + *r*_{load}) (15.4)

where _{load} and *r*_{load} are the reactance and resistance of the generator load.

The phasor of voltage *r*_{w}* İ* is aligned with the current phasor *İ *, and the voltage phasor *j**İ* is in quadrature leading with it. The phasor of the terminal voltage per phase* V̇*, can be located by subtracting the sum of the voltage phasors across the resistance and reactance per phase from *E*_{0} :

*V̇* = *Ė _{0}* -

*j*

*İ*-

*r*

_{w}

*İ*

On joining the tips of the phasors *E*_{0} and *V̇ *, we obtain a triangle of voltages across the resistance and inductive reactance per phase , with __Z___{w}* İ *as hypotenuse.

The phasor *r*_{w}* İ* is shown on an exaggerated scale to make the diagram more instructive.