Nominal T model of a transmission line

Nominal T model of a medium transmission line has two components- series impedance and shunt admittance. In this post, we shall discuss the nominal T model of a medium transmission line. In a nominal T model of a transmission line;

• The series impedance is divided into two equal parts.
• The shunt admittance is concentrated at the center of the line.

Nominal-T Representation:

The nominal T model of a medium transmission line is as shown below.

Where,

Series impedance of the line Z = R + jX
Shunt admittance of the line Y = jwc
Receiving end voltage = V_r
Receiving end current = I_r
Current in the capacitor = I_ab
Sending end voltage = V_s
Sending end current = I_s

By KCL and KVL rules, We can calculate the sending end voltage and current. The voltage across the capacitors is ;

The current flowing through capacitor is

From above equations, we can calculate the sending end voltage and current.

The sending end voltage is ;

Sending end voltage and current is as written in matrix form;

The A,B,C and D constant of medium transmission line is.

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Classification of Transmission Line

The phasor diagram of the nominal T-circuit for a lagging power factor is as shown below.

Abbreviation in Phasor Diagram

OA = V_r – receiving end voltage to neutral, as reference voltage
OB = I_r – load current lagging V_r by an angle ∅. Where, cos∅ is the power factor of the load.
AC = I_rR/2 – Voltage drop in the reactance of the right-hand half of the line. It is 90 degree to OB, i.e., Ir.

OD₁ = V_ab – voltage at the midpoint of the line across the capacitance C.
BE = I_ab – current in the capacitor. It leads the voltage V_ab by 90.
OE = I_s -sending-end current, the phasor sum of load current and capacitor current.
D₁C₁ = I_sR/2 – voltage drop in the resistance on the left-hand side of the lines.It is perpendicular to Is.
C₁D = I_s X/2 – voltage drop in the reactance in the left half of the line. It is perpendicular to Is
OD = V_s – sending end voltage. It is the phasor sum of the of V_ab and the impedance voltage drop in the left-hand half of the line.
∅_s – phase angle at the sending end. cos∅_s is the power factor at the sending end of the line.

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