Nominal T model of a transmission line

In a nominal T model of a medium transmission line, the series impedance is divided into two equal parts, while the shunt admittance is concentrated at the centre of the line. The nominal T model of a medium transmission line is shown in the figure.

Here,

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

Sending end voltage and current can be obtained by application of KVL and KCL. to the circuit shown below

Current in the capacitor can be given as,

By Kirchoff’s current law at node a,

or

By Kirchoff’s voltage law

Equation of Sending end voltage V_s and current I_s can be written in the matrix form asAlso,

Hence, the ABCD constant of the nominal T-circuit model of a medium line are

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

In the phasor diagram:

OA = V_r – receiving end voltage to neutral. It is taken as a reference phasor.
OB = I_r – load current lagging behind V_r by an angle ∅. 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 perpendicular 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.