Short Transmission Line

Short Transmission Line

A transmission line having a length of less than 80 km is considered a short transmission line. The operating voltage of this line is in terms of 20kV.

Due to the small length and low operating voltage, the capacitance in a short transmission line is negligible. But in case of Long transmission line and Medium transmission line, we need to consider capacitance.

There is the only effect of resistance and inductance considered while modeling a short transmission line. The equivalent circuit or graphical representation of a short line is as shown below figure.

"Graphical

I = Load Current
R = Line Resistance
XL = Line Reactance
VR = Receiving End Voltage
Vs = Sending End Voltage
cosфR = Receiving End Power Factor
Cosфs = Sending End Power Factor
Z = Line Impedance

When current flows through the circuit, a voltage drop occurs due to resistance and inductance. Due to resistance, IR drops occurs. And due to inductive reactance, IXL drop occurs.

Therefore, some amount of voltage drops in the circuit and the value of receiving end voltage is less than the sending end voltage.

The phasor diagram of this system is as shown in the below figure.

"Phasor

From the above Phasor diagram;

    \[ (OC)^2 = (ON)^2 + (NC)^2 \]

    \[ V_S^2 = (OM + MN)^2 + (NB + BC)^2 \]

    \[ V_S^2 = [ V_R cos \phi_R + IR ] ^2 + [V_R sin \phi_R + IX_L ]^2 \]

    \[ V_S = \sqrt{ (V_R cos \phi_R + IR) ^2 + (V_R sin \phi_R + IX_L)^2 \]

    \[ \% Voltage \, Regulation = \frac{V_S - V_R}{V_R} \times 100 \]

Sending End Power Factor;

    \[ cos \phi_S = \frac{ON}{OC} \]

    \[ cos \phi_S = \frac{OM + MN}{OC} \]

    \[ cos \phi_S = \frac{V_R cos \phi_R + IR}{V_S} \]

Receiving End Power =VR IR cosфR

Losses in Line = I2R

Sending end power = Power at Receiving end + Line losses

    \[ P_s = V_R I_R cos \phi_R + I^2R \]

    \[ \% Transmission \; Efficiency = \frac{Receiving \, end \, power}{Sending \, end \, power} \times 100 \]

    \[ \% Transmission \; Efficiency = \frac{V_R I_R cos \phi_R}{V_R I_R cos \phi_R + I^2 R} \times 100 \]

ABCD Parameter for Short Transmission Line

From the above figure, we can say the sending end current is the same as the receiving end current. And sending end voltage is a summation of receiving end voltage and the drop across the line.

    \[ I_S = I_R \]

    \[ V_S = V_R + I_R Z \]

Now, compare these equations with the equations of ABCD parameters;

    \[ V_S = AV_R + BI_R \]

    \[ I_S = CV_R + DI_R \]

If we compare above equations, we can conclude that;

A=1
B=Z
C=0
D=1

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