Question

Consider the transmission line of Problem 5.18. (a) Find theparameters of the line when uncompensated. (b) For a series capacitivecompensation of $\mathbf{70}\mathbf{\%}$($\mathbf{35}\mathbf{\%}$at the sending end and $\mathbf{35}\mathbf{\%}$at the receivingend), determine the ABCDparameters. Comment on the relative change in the magnitude of the Bparameter with respect to the relative changes in the magnitudes of the A, C, and Dparameters. Also comment on the maximum power that can be transmitted when series compensated.

Short answer

(a)Therefore, the ABCD parameters are $0.8904\angle 1.{34}^0\mathrm{pu}$, $186.78\angle 79.{46}^0\mathrm{\Omega }$, role="math" localid="1655269055572" $1.131\times {10}^{-3}\angle 90.{42}^0\mathrm{S}$ and $0.8904\angle 1.{34}^0\mathrm{pu}$.

(b) Therefore, the new ABCD parameters are $0.97\angle 1.{24}^0\mathrm{pu}$, $60.88\angle 55.{85}^0\mathrm{\Omega }$, $0.00118\angle 90.{41}^0\mathrm{S}$ and $0.97\angle 1.{24}^0\mathrm{pu}$. The maximum power transmission will increase by $300\%$.

Step-by-step solution

Given data.

From problems 5.18, the given data is,

$$\begin{gathered} {\mathrm{Z}}_{\mathrm{C}}=406.4\angle -5.{48}^0\mathrm{\Omega } \\ \cosh \mathbb{y}\mathrm{l}=0.8904\angle 1.{34}^0 \\ \sinh \mathbb{y}\mathrm{l}=0.4597\angle 84.{93}^0 \end{gathered}$$

The $70\%$ series compensation is mentioned.

Determine the formula of ABCD parameters.

Write the formula of equivalent ABCD parameters.

$$\begin{gathered} \mathbf{A}\mathbf{=}\mathbf{D} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{cosh\gamma l} \end{gathered}$$ .............(1)

$\mathbf{B}\mathbf{=}{\mathbf{Z}}_{\mathbf{C}}\mathbf{sin\gamma l}$ ..............(2)

$\mathbf{C}\mathbf{=}\frac{\mathbf{sinh\gamma l}}{{\mathbf{Z}}_{\mathbf{C}}}$ ................(3)

Determine the ABCD parameters.

(a)

Determine the change in ABCD parameters.

(b)