Electronics and Electrical Engineering

Power Systems / Electrical Energy Systems Laboratory

The Long Transmission Line

1.   Introduction

Power transmission lines run for up to 1500 km in certain parts of the world where hydro-electric power stations are located far from city load centres. Lines longer

than about 200 km need special “compensating” equipment to control the voltage  along the line, and to ensure the stability of the power transmission. This is because the voltage along an uncompensated line deviates from the ideal “flat voltage

profile”, depending on the load and the length of the line.

2.  Objectives

a.   To demonstrate the  Ferranti effect-voltage rise along a lightly-loaded transmission line;

b.   To demonstrate the flat voltage profile and linear phase-shift along a long transmission line loaded at its natural load or “surge -impedance load” (SIL); and

c.   To demonstrate the effect of line length.

3.  Theory

A transmission line can be represented approximately by a ladder network of LC

branches as shown in Fig. 1. The inductance and capacitance are  distributed along the line, but a ladder network with a large number of lumped elements can provide a fairly accurate model of the actual line. Note that the  resistance of the cable is

considered negligible: the electrical properties are dominated by the series inductance and shunt capacitance.

Fig. 1  Lumped-parameter model of long transmission line

The electrical properties of the line are dominated by two important parameters: the surge impedance and the electrical length.

Surge impedance

The surge impedance Z0 is given by   Z                                                   (1)

where Lis the total line inductance [H] and Cis the total line capacitance [F] (of course, in this case you could use ‘per-unit-length’ or ‘per-section’ values, due to cancellation in the formula). Even though Land Care basically reactive elements, Z0 is a real number: in other words, it has the properties of resistance.

Electrical length

The actual length of a transmission line is measured in km, but the  electrical length θ is measured in radians and is given by

                                                           (2)

Note that here you must use the Land C values for the whole line.   ω = 2πf is the radian frequency of the voltage and current (normally f = 50 or 60 Hz). A line for which  θ = 2π  is said to have a length of one  wavelength at the operating

frequency f, but such lines are impractical and θ rarely exceeds π/6 or 30° .

Key properties

When the receiving-end of a long line is open-circuited, the voltage profile along the line is given by

where x is the distance from the sending end, a is the actual line length, and VS  is the phasor voltage at the sending end. The voltage at the receiving end is given by setting x = a: thus

This equation shows one problem with long lines: the receiving end voltage Vr

exceeds the sending-end voltage VS  by the factor 1/cos θ. For example if θ = 30°,  Vr  = VS  / cos(30°) = 1.155 VS   —an excess voltage of 15% over the nominal or rated value. This is too far outside the acceptable range of voltage.

A line terminated in Z0 has a flat voltage profile, i.e. V (x) = VS  = Vr . The power

corresponding to this load impedance is the surge impedance load (SIL) or natural load. If the load is greater than SIL, the voltage profile tends to sag. If it is less, the voltage profile tends to rise. [At SIL the reactive power requirements at the ends of the line are zero. Below SIL, the line generates excess reactive power at both ends, but above SIL, it absorbs reactive power at both ends.]

4.   Experiments

The model transmission line has ten LC sections. In each section L = 7.29 mH and C = 0.020 µF. If the line is operated at 700 Hz,   ω = 2π × 700 = 4398 rad / s .

a.   Use eqn. (1) to calculate the surge impedance Z0 in ohms.

b.  Use eqn. (2) to calculate the electrical length θ in degrees and

radians. (Remember that Land Care for the whole line, not just one section).

Connect the model transmission line as shown in Fig. 2. Ensure that the function generator is producing a sine wave, and that the 50 Ω output is the one connected. Keep channel 1 of the oscilloscope connected to the sending-end voltage, and use channel 2 as a roving connection. The DVM / Multimeter can also be connected   anywhere along the line.

Fig. 2   Connection of model transmission line. The ground wires to the oscilloscope

and the DVM are not shown in full.

c.   Open-circuit test

Set the frequency to 700 Hz.4 Set the output voltage to about 10 V pk-pk. Set both oscilloscope channels to 2 V/division. Set the DVM to AC volts, 20 V range. The

DVM measures the RMS voltage, i.e.   Vpp /2 × 1/ = 3.5 V approximately.

Using the DVM, measure the voltage Vat each of the 10 points along the line and calculate the ratio V/ VS for each point. Plot a graph showing the variation of

per-unitvoltage v = V/ VS along the line, i.e. v(x). Determine the ratio V/ VS and verify that it agrees with eqn. (4).

Use the oscilloscope to measure the phase angle of the voltage relative to VS  at the mid-point and at the receiving end. Use these phase angles together with the

corresponding voltage values to draw a phasor diagram showing the relationship between VS, Vr  and the mid-point voltage Vm

d.   Surge-impedance load test

Connect a resistive load equal to the surge impedance load Z0 calculated at (a)

above. Re-adjust the sending end voltage so that it has the same value as in

experiment (c), or if you can't reach that voltage, as near to it as possible. Repeat all the measurements of test (c), including the phase angles ofthe voltages at the

mid-point and the receiving end, relative to the sending end. Verify that the

voltage profile is flat, and try to explain any deviations from true flatness. Compare the phase angle between VS  and Vr  with the electrical length of the line, and

comment on the result. Also comment on the phase angle between VS  and Vm  and the phase angle between Vr  and Vm

e.   Line loaded above the surge-impedance load

Connect a resistive load of resistance equal to half the surge impedance load Z0

calculated in (a) above. Re-adjust the sending-end voltage so that it has the same

value as in experiment (c), or if you can't reach that voltage, as near to it as possible. Repeat all the measurements of test (c), including the phase angles ofthe voltages at the mid-point and the receiving end, relative to the sending end. Comment on the voltage profile and the new values of the phase angles between VS  and Vr, between VS  and Vm  and between Vr  and Vm . How would you restore the receiving end

voltage Vr to be equal to VS  without changing the real power transmitted to the load?4

f.    Open-circuit test on double-length line

The line length can be doubled by connecting two model transmission lines in

series. Alternatively, according to eqn. (2), we can simulate the same effect by

doubling the frequency to 1.4 kHz. Do this, and repeat experiment (c). Comment on the differences between the single-length line and the double length line. How

would you restore the receiving end voltage Vr  to be equal to VS?