Lecture Video
SECTION 01
Short transmission line
TL having its length less than 80 km is considered as a short transmission line.
In short transmission line capacitance is neglected because of small leakage current
Other parameters (resistance and inductance) are lumped in the transmission line.
SECTION 02
Equivalent Circuit of Short TL
\[\begin{aligned}
I_{S} & =I_{R}\\
V_{s} & =V_{R}+I_{R}\cdot Z\\
Z & = R+jX
\end{aligned}\]
SECTION 03
Phasor Diagram
\[\begin{aligned}
OD^{2}&=O G^{2}+G D^{2}\\ &=(O F+F G)^{2}+(G C+C D)^{2}
\end{aligned}\]
\[\begin{aligned} V_{S}^{2}&=\left(V_{r} \cos \phi_{r}+I R\right)^{2}+\left(V_{r}
\sin \phi_{r}+I X\right)^{2} \\ V_{S}&=\sqrt{\left(V_{r} \cos \phi_{r}+I
R\right)^{2}+\left(V_{r} \sin \phi_{r}+I X\right)^{2}} \end{aligned}\]
\[\cos \phi_{s}=\frac{O G}{O D}=\frac{O F+F G}{O
D}=\frac{V_{r} \cos \phi_{r}+I R}{V_{S}}\]
\[V_{r}=V_{r}<0^{\circ}=V_{r}+j
0\]
For lagging PF \(I=I\angle-\Phi_{r}=\operatorname{Icos} \Phi_{r}-j I \sin \phi_{r}\)
For leading PF \(I=I\angle+\Phi_{r}=\operatorname{Icos} \Phi_{r}+j I \sin \phi_{r}\)
For unity PF, \(I=I\angle0^{\circ}=I+j 0^{\circ}\)
The line impedance is given by \(Z=R+j X\)
- Sending end voltage is\[V_{s}=V_{r}+Z I\]
- For lagging power factor,\[\begin{aligned} V_{S}=&\left(V_{r}+j 0\right)+(R+j X)\left(I \cos \phi_{r}-j \operatorname{I\sin} \phi_{r}\right) \\ &=\left(V_{r}+I \operatorname{R\cos} \phi_{r}+I X \sin \phi_{r}\right)+\left(I X \cos \phi_{r}-I R \sin \phi_{r}\right) \\ V_{S}&=\sqrt{\left[\left(V_{r}+I R \cos \phi_{r}+I X \sin \phi_{r}\right)^{2}+\left(I X \cos \phi_{r}-I R \sin \phi_{r}\right)^{2}\right]} \\ \tan \delta & = \frac{I X \cos \phi_{r}-I R \sin \phi_{r}}{V_{r}+I R \cos \phi_{r}+I X \sin \phi_{r}} \end{aligned}\]
SECTION 04
ABCD Constants of Short TL
\[\begin{aligned} I_{S} & =I_{R}\\ V_{s} & =V_{R}+I_{R}\cdot Z\\ Z & = R+jX \end{aligned}\]
$$\boxed{
\left[\begin{array}{c}
V_S \\
I_S
\end{array}\right]=\left[\begin{array}{ll}
1 & Z \\
0 & 1
\end{array}\right]\left[\begin{array}{c}
V_R \\
I_R
\end{array}\right]
}$$
SECTION 05
Voltage Regulation
Rise in \(V_R\) expressed in % of FL voltage, when FL at a specified pf is removed keeping \(V_s\) constant
- At full load,\[\left|V_{R,F.L}\right|=\left|V_{r}\right|\]
- At no load,\[\left|V_{R, N.L}\right|=\left|V_{S}\right|\]$$\boxed{ \% \text { Regulation }=\frac{\left|V_{R, N L}\right|-\left|V_{R, F L}\right|}{\left|V_{R, F L}\right|} \times 100 }$$
greatest for lagging pf
least or -ve for leading pf
SECTION 06
Line Efficiency
\[\text {Efficiency}=\frac{\text {Power
delivered at the receiving end}}{\text {power delieverd at the sending
end }+\text { losses}}\]