# Two parallel connected, three phase, 50 Hz, 11 kV, star-connected synchronous machines A and B, are operating as synchronous condensers. They together

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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.)

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Given that,

Machine A: VA = 11 kV, XSA = 1 Ω

Machine B: VB = 11 kV, XSB = 3 Ω

Grid: 11 kV, 50 MVAR

And IA = IB

The reactive power supplied by both machines are equal.

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

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

EA = VA - jIAXSA

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

⇒ EA = 7663.05 A

EB = VB – jIBXSB

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

⇒ EB = 10287.33 V

We know that,

E ∝ If

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