Question

Two parallel connected, three phase, 50 Hz, 11 kV, star-connected synchronous machines A and B, are operating as synchronous condensers. They together supply 50 MVAR to a 11 kV grid. Current supplied by both the machines are equal. Synchronous reactances of machine A and machine B are 1Ω and 3Ω, respectively. Assuming the magnetic circuit to be linear, the ratio of excitation current of machine A to that of machine B is _________. (Give the answer up to two decimal places.)

Answer 1

Given that,

Machine A: V_A = 11 kV, X_SA = 1 Ω

Machine B: V_B = 11 kV, X_SB = 3 Ω

Grid: 11 kV, 50 MVAR

And I_A = I_B

The reactive power supplied by both machines are equal.

\({Q_A} = {Q_B} = \frac{{50}}{2} = 25\;MVAR\)

\({I_B} = {I_A} = \frac{{{Q_A}}}{{\sqrt 3 \times V}} = \frac{{25 \times {{10}^6}}}{{\sqrt 3 \times 11 \times {{10}^3}}} = 1312.16\;A\)

E_A = V_A - jI_AX_SA

\(= \frac{{\left( {11 \times {{10}^3}} \right)}}{{\sqrt 3 }} - j\left( {1312.16\;\angle 90} \right)\left( 1 \right)\)

⇒ E_A = 7663.05 A

E_B = V_B – jI_BX_SB

\(= \frac{{11 \times {{10}^3}}}{{\sqrt 3 }} - j\left( {1312.16\;\angle 90} \right)\left( 3 \right)\)

⇒ E_B = 10287.33 V

We know that,

E ∝ I_f

\(\Rightarrow \frac{{{I_{fA}}}}{{{I_{fB}}}} = \frac{{{E_A}}}{{{E_B}}} = \frac{{7663.05}}{{10287.33}} = 0.745\)