Nominal T method

                  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 = Vr
Receiving end current = Ir
Current in the capacitor = Iab
Sending end voltage = Vs
Sending end current = Is

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

first-eq-compressor

Current in the capacitor can be given as,         

second-equ-compressor

By Kirchoff’s current law at node a,

fIfth-equ-compressor

or

By Kirchoff’s voltage law

medium-line-fourth

Equation of Sending end voltage Vs and current Is can be written in the matrix form as
medium-line-sixth
Also,

medium-line-seven

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

medium-line-8

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

medium-8

In the phasor diagram:

OA = Vr – receiving end voltage to neutral. It is taken as a reference phasor.
OB = Ir – load current lagging behind Vr by an angle ∅. cos∅ is the power factor of the load.
AC = IrR/2 – Voltage drop in the reactance of the right-hand half of the line.It is perpendicular to OB, i.e., Ir.
OD1 = Vab – voltage at the midpoint of the line across the capacitance C.
BE = Iab – current in the capacitor. It leads the voltage Vab by 90.
OE = Is -sending-end current, the phasor sum of load current and capacitor current.
D1C1 = IsR/2 – voltage drop in the resistance on the left-hand side of the lines.It is perpendicular to Is.
C1D = Is X/2 – voltage drop in the reactance in the left half of the line. It is perpendicular to Is
OD = Vs – sending end voltage. It is the phasor sum of the of Vab 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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