Question

A 500 kVA, 2300 V, 3-phase star connected alternator has a full load armature resistance drop of 50 V per phase and an effective reactance drop of 500 V per phase. The percentage regulation at UPF is
1. 1.05
2. 10.5
3. 21.8
4. 28.7

Answer 1

Correct Answer - Option 2 : 10.5

Concept:

Voltage Regulation of a synchronous Generator is the rise in voltage at the terminal when the load is reduced full load rated value to zero, speed and field current remaining constant.

Percentage voltage \( \buildrel \Delta \over = \frac{{\left| {{E_a}} \right| - \left| V \right|}}{{\left| V \right|}} \times 100\)

|E_a| = magnitude of Generated voltage per phase

|V| = magnitude of rated terminal voltage per phase

Calculation:

Armature Resistance drop IR = 50 V per phase

Reactance drop IX = 500 V per phase

Power factor = Unity

Rated voltage per phase \({V_p} = \frac{{2300}}{{\sqrt 3 }}\)

V_p = 1327.9 V

V_p = 1327.9 ∠0 V

Let V_p be taken as Reference

E_p = V_p + I_ap Z_s

∴ Z_s = R_a + jX_s

E_p = V_p + I_ap (R_a +  J X_s)

E_p = V_p + I_ap R_a + J I_ap X_s

E_p = 1327.9∠0 + 50 + 500∠90°

E_p = 1327.9∠0 + 500∠90°

E_p = 1465.81∠19.94

|E_p| = 1465.81 V

Percentage voltage \(= \frac{{\left| {{E_p}} \right| - \left| {{V_p}} \right|}}{{\left| {{V_p}} \right|}} \times 100\)

\(= \frac{{1465.81 - 1327.9}}{{1327.9}} \times 100\)

= 10.38%