Estimate the synchronous impedance for an 11 kV, three-phase, 50 Hz ,20 MVA alternator which develops rated emf on no-load with a field current of 20 A. A field current of 12 A produces a short circuit current equal to rated current.
Question 6.22: Estimate the synchronous impedance for an 11 kV, three-phase...
\begin{array}{l}\text { Rated power }=20 MVA =20 \times 10^{6} VA \\\text { Line voltage, } V_{L}=11 kV =11000 V (\text { three-phase connections) }\end{array}
At field current of 20 A;
No-load e m f E_{(L)}= rated voltage =11000 V (line value)
At field current of 12 A :
\text { Short circuit current = rated full load current }=\frac{20 \times 10^{6}}{\sqrt{3} \times 11000}=1049.73 A
At field current of 20 A;
Short circuit current, I_{s c}=\frac{20}{12} \times 1049.73
(S C C \text { is a straight line curve })=1749.54 A
\begin{array}{l}\text { Phase value of no-load } e m f, E_{0}=\frac{E_{0(L)}}{\sqrt{3}}=\frac{11000}{\sqrt{3}}=6351 V\\\text { Synchronous impedance, } Z_{s}=\frac{E_{0}}{I_{s c}}=\frac{6351}{1749.54}= 3 . 6 3 \Omega\\\text { Solution by using } j \text { -notation (polar method) }\end{array}
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