Question

Express the no-load receiving-end voltage ${\mathbf{V}}_{\mathbf{RNL}}$in terms of the sending end voltage,${\mathbf{V}}_{\mathbf{S}}$, and the ABCDparameters.

Short answer

Therefore, the answer is ${\mathrm{V}}_{\mathrm{RNL}}=\frac{{\mathrm{V}}_{\mathrm{S}}}{\mathrm{A}}$.

Step-by-step solution

Determine the relation between sending end and receiving end quantities.

Write the relation between sending end and receiving end quantities in terms of transmission parameters.

${\mathbf{V}}_{\mathbf{S}}\mathbf{=}{\mathbf{AV}}_{\mathbf{R}}\mathbf{+}{\mathbf{BI}}_{\mathbf{R}}$ ……. (1)

${\mathbf{I}}_{\mathbf{S}}\mathbf{=}{\mathbf{CV}}_{\mathbf{R}}\mathbf{+}{\mathbf{DI}}_{\mathbf{R}}$ ……. (2)

Here,${\mathrm{V}}_{\mathrm{S}}$and ${\mathrm{V}}_{\mathrm{R}}$ are sending end and receiving end voltages, ${\mathrm{I}}_{\mathrm{S}}$ and ${\mathrm{I}}_{\mathrm{R}}$ are sending end and receiving end currents.

Here, $A$, $B$, $C$ and $D$ are parameters that depends on transmission line parameters.

Determine the relation in no-load receiving end voltage in terms of the sending end voltage and the ABCD parameters

For the no-load receiving end voltage, the output terminal will be open, so receiving end current will be zero, that is,

${\mathrm{I}}_{\mathrm{R}}=0$

Substitute $0$for ${\mathrm{I}}_{\mathrm{R}}$ and ${\mathrm{V}}_{\mathrm{RNL}}$for${\mathrm{V}}_{\mathrm{R}}$in equation (1).

$\begin{array}{l}{\mathrm{V}}_{\mathrm{S}}={\mathrm{AV}}_{\mathrm{RNL}}+\mathrm{B}\left(0\right)\\ {\mathrm{V}}_{\mathrm{RNL}}=\frac{{\mathrm{V}}_{\mathrm{S}}}{\mathrm{A}}\end{array}$

Therefore, theno-load receiving-end voltage${\mathrm{V}}_{\mathrm{RNL}}$in terms of the sending end

voltage,${\mathrm{V}}_S$, and the ABCDparameters is ${\mathrm{V}}_{\mathrm{RNL}}=\frac{{\mathrm{V}}_{\mathrm{S}}}{\mathrm{A}}$.