THE UNIVERSITY OF HONG KONG
DEPARTMENT OF ELECTRICAL & ELECTRONIC ENGINEERING

Experiment P3: Effects of length on the power-voltage curve of a AC transmission line
(MATLAB Simulation)

Objective:
To study experimentally the effects of the length of a high-voltage AC transmission line on the
voltage profile.

Apparatus:
Transmission line (resistor, inductor, capacitor)
AC power source
Resistive load
Voltmeter, ammeter
LVDAC-EMS software

Introduction:
An AC transmission line can be regarded as an equivalent PI circuit. The value of load required
at the receiver end of an AC transmission line to make receiver voltage equal to sender voltage
is known as the characteristic impedance 0 , which can be calculated in Equation (1). The
natural load 0 of an AC transmission line, which denotes the active power delivered to a resistive
load whose resistance is equal to the characteristic impedance 0 of the AC transmission line is
calculated by Equation (2).
0 = √ (1)
0 = 3

2
0
(2)
where is the inductive reactance of the AC transmission line in Ω/km or Ω/mile; is the
capacitive reactance of the AC transmission line in Ω/km or Ω/mile.

(a) (b)
Fig. 1 Equivalent PI circuits of transmission line with (a) 250 km and (b) 500 km.
Characteristics of transmission lines changes along with line lengths. Fig. 1 shows parameters
of the equivalent PI circuits of transmission lines with 250 km and 500 km, respectively. Comparing
the corrected PI equivalent circuits of these two transmission lines shows that, the equivalent
resistance ′and inductive reactance
′both increase with the line length, while the capacitive
reactance 2
′ decreases with the line length.
The power-voltage curve changes when the line length varies. By solving the circuit equation
of Fig. 1, Fig. 2 represents power-voltage curves of the AC transmission line of different line lengths.
The value of


and

0
can be calculated accordingly given the resistance of the load.

Fig. 2 Power-voltage curves of the 250 km and 500 km (about 155 miles and 310 miles)
high-voltage (315 kV) ac transmission lines.

Simulation model:

(a)

(b)
Fig. 3 Connection diagram of the AC transmission line of (a) 250 km and (b) 500 km.
A
B
C
1. Simulation model shown in Fig. 3 (a) represents one phase of a three-phase power
transmission system. The circuit consists of an AC power source supplying power to a
resistive load via a 250 km AC transmission line represented by an equivalent PI circuit.
2. Calculate the characteristic impedance 0 of the AC transmission line using equation (1).
3. Open-circuit the receiver end of the line: since the MATLAB simulation model does not
support as infinite values, try set its value to 1200 Ω, then run the model and
record the data shown in ER1 and PR1.
4. Gradually increase the load at the receiver end of the line by changing the resistive load
from 314Ω to 880Ω in about 15 steps. Record data shown in ER1 and PR1.
5. Short-circuit the receiver end of the line: since the MATLAB simulation model does not
support as zero, try set = 0.01 Ω, then record the data.
6. Simulation model shown in Fig. 3 (b). represents an AC power source supplying power
to a resistive load via a 500 km AC transmission line represented by two equivalent PI
circuits of a 250 km line having the same fundamental characteristics.
7. Repeat step 2 to step 6.

Reports:
Plot power-voltage curves of circuits with 250 km and 500 km line lengths using collected data,
respectively. Note that three special points A, B, C should be included in each figure. Compare these
two figures and discuss on the following questions: 1) How does increasing the line length affect
the receiver voltage obtained when the line is left open? 2) How does increasing the line length
affect the maximal amount of active power that the line can convey to the load? 3) How does
increasing the line length affect the variation of the receiver voltage produced by a given change
in the amount of active power P conveyed by the line?
Please submit the lab report by Nov. 9, 2020.


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