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.
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
By Kirchoff’s voltage law
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.