Question

Determine the equivalent ABCDparameters for the line in Problem 5.14 if it has$\mathbf{70}\mathbf{\%}$shunt reactive (inductors) compensation and$\mathbf{40}\mathbf{\%}$series capacitive compensation. Half of this compensation is installed at each end of the line, as in Figure 5.14.

Short answer

Therefore, the equivalent ABCD parameters are

$$\begin{gathered} \left[0.9593\angle 0.401°86.66\angle 82.3° \\ 1.121\times {10}^{-3}\angle 89.89°0.9593\angle 0.396°\right] \end{gathered}$$

Step-by-step solution

Given data.

From problems 5.14,

The ABCD parameters are,

$$\begin{gathered} \mathrm{A}=\mathrm{D} \\ =0.8794\angle 0.{66}^0\mathrm{pu} \\ \mathrm{C}=1.688\times {10}^{-3}\angle 90.2^0\mathrm{S} \\ \mathrm{B}=134.8\angle {853}^0\mathrm{\Omega } \end{gathered}$$

The line reactance is ${\mathrm{X}}^{\text{'}}=\mathrm{j}134.3\mathrm{\Omega }$ and susceptance is $\mathrm{B}=8.981\times {10}^{-4}\mathrm{S}$.

The $40\%$ series capacitive compensation and $70\%$ shunt compensation is given.

Determine the formula of ABCD parameters.

Write the formula of equivalent ABCD parameters.

$\mathbf{\left[}\begin{array}{c}{\mathbf{A}}_{\mathbf{eq}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}{\mathbf{B}}_{\mathbf{eq}}\\ {\mathbf{C}}_{\mathbf{eq}}\mathbf{}\mathbf{}\mathbf{}{\mathbf{D}}_{\mathbf{eq}}\end{array}\mathbf{\right]}\mathbf{=}\mathbf{\left[}\begin{array}{c}{\mathbf{A}}_{\mathbf{S}}\mathbf{}\mathbf{}\mathbf{}{\mathbf{B}}_{\mathbf{S}}\\ {\mathbf{C}}_{\mathbf{S}}\mathbf{}\mathbf{}\mathbf{}{\mathbf{D}}_{\mathbf{S}}\end{array}\mathbf{\right]}\mathbf{\left[}\begin{array}{c}\mathbf{A}\mathbf{}\mathbf{}\mathbf{B}\\ \mathbf{C}\mathbf{}\mathbf{}\mathbf{D}\end{array}\mathbf{\right]}\mathbf{\left[}\begin{array}{c}{\mathbf{A}}_{\mathbf{R}}\mathbf{}\mathbf{}\mathbf{}{\mathbf{B}}_{\mathbf{R}}\\ {\mathbf{C}}_{\mathbf{R}}\mathbf{}\mathbf{}{\mathbf{D}}_{\mathbf{R}}\mathbf{}\mathbf{}\end{array}\mathbf{\right]}\mathbf{}\mathbf{}..........\left(1\right)$

Here, eq is representing equivalent, S is representing sending end, and R is representing receiving end.

Determine the ABCD parameters.

The reactance of each series capacitor with 40% compensation is,

$$\begin{gathered} \mathrm{X}=-\left(\mathrm{j}\frac{134.3}{2}\right)\left(0.4\right)\mathrm{\Omega } \\ =-\mathrm{j}26.86\mathrm{\Omega } \end{gathered}$$

The admittance of each shunt reactor with 70% compensation is,

$$\begin{gathered} \mathrm{X}=-\left(\mathrm{j}\frac{8.981\times {10}^{-4}}{2}\right)\left(0.7\right) \\ =-\mathrm{j}3.143\times {10}^{-4}\mathrm{S} \end{gathered}$$