Transmission LineEPO341 Prepared by Fuad Latip TRANSMISSION LINE
MODELS 1.Short Transmission Line: below 80km (50 miles) 2.Medium
Transmission Line: 80km (50 miles) < Medium TL < 240km (150
miles) 3.Long Transmission Line: above 240km (150 miles)
TRANSMISSION LINE PER-PHASE MODEL Figure 1: General Transmission
Line per-phase model
Thetotalseriesresistance,seriesreactanceandshuntadmittanceoftransmissionlinecanbecalculated
from the following equation. R = rd X = xd Y = yd Wherer =
resistance /km x = reactance /km y = admittance S/km d = length of
transmission line THE SHORT-LENGTH TRANSMISSION LINE
ForShorttransmissionline,thecapacitancecanbeneglected.Thisproducesinaper-phasemodel
consisting of a series resistance and inductance only. Figure 2:
Short-Length Transmission Line per-phase model VS = Sending end
VoltageVR = Receiving end Voltage IS = Sending end Current IR =
Receiving end Current Transmission LineEPO341 Prepared by Fuad
Latip From equivalent circuit it is obvious that I = IS = IR
Applying KVL into the per-phase model, the sending voltage VS is
related to the receiving voltage VR by the equation VS = VR + ZI =
VR + RI + jXLI Or VR = VS - RI - jXLI THE MEDIUM-LENGTH
TRANSMISSION LINE Figure 3: Medium-Length Transmission Line
per-phase model The values R and L are the total resistance and
inductance for the entire line, and the total admittance Y is the
shunt admittance distributed over the entire line. To find the
equation of medium-length transmission line, Two-port network (ABCD
model) analysis has applied. Figure 4: Two port network
Transmission LineEPO341 Prepared by Fuad Latip If the network is
linear, then an elementary circuit theorem (analogous to Thevenins
theorem) states that
therelationshipbetweenthesendingandreceivingendvoltagesandcurrentswillbegivenbythe
following equations: Refer to figure 3, The current in the
receiving end capacitance is given by IC2= IR2 And the current in
the series impedance elements will be Isc=IR2+IR Therefore by KVL,
the voltage on the sending end of the transmission line will be IS=
ZIsc+IR= Z(IC2+ IR) +IR = Z _IR2+ IR] + IR = [z2+1
IR+ZIR----------------------Equation (1) Comparing Equation (1)
with ABCD constant equation A =Z2+ 1 AndB = Z The current following
in the source will be IS= IC1+Isc= IC1+ IC2+ IR = IS2+ IR2+
IR-------------------------------Equation (2) Transmission
LineEPO341 Prepared by Fuad Latip Substituting Equation (1) into
Equation (2), we get IS= [z4+ 1 IR+ [z2+ 1
IR------------------Equation (3) Comparing Equation (3) with ABCD
constant equation C = _Z4+ 1] And =Z2+ 1 Or D = A Medium Length
Transmission Line Constant
Note:Ifweignoretheshuntcapacitanceofatransmissionline,theshuntadmittanceY=0,andthe
ABCD constant reduce to the short transmission line constant i.e.
Short Length Transmission Line Constant A = 1B = ZC = 0D = 1
Transmission LineEPO341 Prepared by Fuad Latip Example A 220kV,
150MVA, 60 Hz three phase transmission line is 140km long. The
characteristic parameters of the transmission line are r = 0.12/kmx
= 0.88/kmy = 4.1 x 10-6 S/km The voltage at the receiving end of
the transmission line is 210kV. Answer the following questions
about this transmission line by assuming 1) Short transmission line
and 2) Medium transmission line a)What the series impedance and
shunt admittance of this transmission line? b)What is the sending
end voltage if the line is supplying rated voltage and apparent
power at 0.85 PF lagging? at unity PF? At 0.85 PF leading? c)What
is the voltage regulation of the transmission line for each of the
cases in (b) d)What is the efficiency of the transmission line when
it is supplying rated apparent power at 0.85 PF lagging? (Answer
will be discussed in class)
