Question

The series impedance matrix of a short $3-\varphi$ transmission line in phase coordinates is represented by Z,

$where,Z=\left[\begin{array}{ccc}{Z}_s& Z_m& Z_m\\ Z_m& Z_s& Z_m\\ Z_m& Z_m& Z_s\end{array}\right]$

If the positive sequence impedance is $(4+j16)\Omega$ and zero sequence impedance is $(8+j32)\Omega$, then value of imaginary of $Z_m$ is ________$\Omega$

• A. 5.33

Answer 1

The correct option is A 5.33
For $3-\varphi$ transmission line we can use relation,

$X_1=X_s-X_m..\left(1\right)$

$X_0=X_s+2X_m...\left(2\right)$

$Alsogiven,X_0=32\Omega and{X}_1=16\Omega$

$\therefore Solving\left(1\right)and\left(2\right)simultaneously,$
$X_s-X_m=16$

$X_s+2X_m=32$
(-) (-) (-)

$-3X_m=-16$

$X_m=\frac{16}{3}\simeq 5.33\Omega$