Electric Power Systems · Line Performance

Medium Transmission Lines

Line Performance — Electric Power Systems

Prof. Mithun Mondal BITS Pilani, Hyderabad Campus
Lecture Video
SECTION 01

Medium Transmission line

  • TL length of more than 80 kms but less than 250 kms

  • The parameters (Resistance, Inductance, and Capacitance) are distributed uniformly along the line.

  • Unlike a short transmission line, the line \(I_c\) of a medium transmission line is appreciable and hence the shunt capacitance must be considered (this is also the case for long transmission lines).

  • \(Y\) and \(Z\) are considered as a lumped parameter

  • Lumped parameters can be represented using two different models, namely:

    • Nominal \(\Pi\) representation (nominal pi model)

    • Nominal \(\mathrm{T}\) representation (nominal T model)

SECTION 02

Nominal\(\mathrm{T}\)representation

Nominal t
\[\begin{aligned} V_{c} & =V_{r}+I_{r}\left(Z/2\right)\\ I_{S} & =I_{r}+V_{c}Y\\ &=I_{r}+Y \cdot V_{r}+I_{r}\left(Z/2\right)\cdot Y\\ V_{s} & =V_{c}+I_{s}\left(Z/2\right) \end{aligned}\]
voltage across the capacitor and Let,
\[V_{s}=V_{r}\left(1+\dfrac{YZ}{2}\right)+I_{r}Z\left(1+\dfrac{YZ}{4}\right)\]
in and Substituting
$$\boxed{ \left[\begin{array}{c} V_s \\ I_s \end{array}\right]=\left[\begin{array}{cc} \left(1+\frac{Y Z}{2}\right) & Z\left(1+\frac{Y Z}{4}\right) \\ Y & \left(1+\frac{Y Z}{2}\right) \end{array}\right]\left[\begin{array}{c} V_r \\ I_r \end{array}\right] }$$
\[\begin{aligned} A & = \left(1+\dfrac{YZ}{2}\right) & B & = Z\left(1+\dfrac{YZ}{4}\right)\\ C & = Y & D & = \left(1+\dfrac{YZ}{2}\right) \end{aligned}\]
SECTION 03

Nominal\(\mathrm{Pi}\)representation

\[\begin{aligned} I_{s} & =I_{r}+V_{r}\dfrac{Y}{2}+V_{s}\dfrac{Y}{2}\\ V_{s} & =V_{r}+\left(I_{r}+V_{r}\dfrac{Y}{2}\right)Z\\ &=V_{r}\left(1+\dfrac{YZ}{2}\right)+I_{r}Z \end{aligned}\]

\(\therefore I_{s}=V_{r}Y\left(1+\dfrac{YZ}{4}\right)+I_{r}\left(1+\dfrac{YZ}{2}\right)\)

Hence,

$$\boxed{ \left[\begin{array}{c} V_s \\ I_s \end{array}\right]=\left[\begin{array}{cc} \left(1+\frac{Y Z}{2}\right) & Z \\ Y\left(1+\frac{Y Z}{4}\right) & \left(1+\frac{Y Z}{2}\right) \end{array}\right]\left[\begin{array}{c} V_r \\ I_r \end{array}\right] }$$
\[\begin{aligned} A& = \left(1+\dfrac{YZ}{2}\right) & B& = Z\\ C & =Y\left(1+\dfrac{YZ}{4}\right) & D & = \left(1+\dfrac{YZ}{2}\right)\\ \end{aligned}\]