Diseño de medios y Teorías de Aprendizaje

The most important aspect of line design from interference point of view is the choice of conductor size, number of sub-conductors in bundle, line height, and phase spacing. Next in importance is the fixing of the width of line corridor for purchase of land for the right-of-way. The lateral decrement of radio noise measured at ground level as one moves away from the line has the profile sketched in Fig. 6.6. It exhibits a characteristic double hump within the space between the conductors and then decreases monotonically as the meter is moved away from the outer

phase. For satisfactory radio reception, a limit RI_i is determined as explained in the previous section. No receiver should be located within the distance d₀ from the outer phase or d_c from the line centre. Therefore, it becomes essential to measure or to be able to calculate at design stages the lateral profile very accurately from a proposed line in order to advise regulatory bodies on the location of receivers. In practice, many complaints are heard from the public who experience interference to radio broadcasts if the line is located too close to their homesteads when the power company routes an e.h.v. line wrongly. In such cases, it is the engineer's duty to recommend remedies and at times appear as witness in judicial courts to testify on the facts of a case.

Fig. 6.6 Lateral profile of RI at ground level for fixing width of right-of-way of line

We will discuss this lateral profile in great detail and dissect it into several components which belong to different modes of propagation, as discussed in Chapter 3, for the radio-frequency energy on the multi-conductor line. This is the basis for determining the expected noise profile from a chosen conductor size and line configuration in un-transposed and fully-transposed condition. We consider 6 preliminary cases of charge distribution on the line conductors after which we will combine these suitably for evaluating the total noise level of a line. In all these cases, the problem is to calculate the field strength at the location of a noise meter when the r-f charge distribution is known. Here, we consider the vertical component of ground-level field intensity which can be related to the horizontal component of magnetic field intensity by the characteristic impedance of free space. We restrict our attention to horizontal 3-phase line for the present. In every case, only the magnitude is of concern.

Case I: Single Conductor above Ground

Consider the simplest of all cases of a single conductor carrying a charge of q coulombs/

metre at radio frequency above a perfectly-conducting ground surface at height H. Figure 6.7.

As mentioned in Chapter 3, the effect of ground in all such problems is replaced by image charge-– q at depth H below the ground surface. It is desired to evaluate the vertical component of electric field strength at point M at a lateral distance d from the conductor on the ground surface.

Fig. 6.7 Single conductor: (a) Vertical component of ground-level electric field and (b) Lateral profile.

x x

RI

RI dB

d0

S dc

Ground – Level RI Field

H θ

d θ + q

D

M

E E

– q E_V

1

0 1 2 3

d/H

(a) (b)

The vertical component due to +q and –q will be

Case 2: 3-Phase AC Line–Charges (+q, + q, +q)

On a perfectly-transposed line, the line-to-ground mode carries equal charges q of the same polarity as described in Chapter 3, and shown in Figure 6.8(a). These are obtained from the eigen-values and eigen-vector and their properties. Following the procedure for case 1 of a single conductor, the field factor for this case is

F_1a = _{2 2 2 2 2}

where s = phase spacing and d = the distance to the noise meter or radioreceiver from the line centre.

Fig. 6 8 Charge distributions at r-f on 3-phase line:

(a) 1st or line-to-ground mode.

(b) 2nd or line-to-line mode of 1st kind.

(c) 3rd or line-to-line mode of 2nd kind.

Case 3 : 3-Phase AC Line–Charges (+ q, 0, –q).

From Fig. 6.8 (b), the field factor will be

F_2a = _{0 2 2 2 2} The field factor for this case from Fig. 6.8(c) is

F_3a =

Case 5: Bipolar DC Line–Charges (+ q, + q)

On a bipolar dc line, the two modes of propagation yield charge distributions (+ q, + q) and (+ q, – q) on the two conductors in each mode, as will be explained later. Considering the first or line-to-ground mode with charges (+ q, + q), as shown in Fig. 6.9(a). with pole spacing P, the field factor is

F_1d = 0 _{2 2 2 2}

Case 6 : Bipolar DC Line–Charges (+ q, – q)

If the polarity of one of the charges is reversed, the resulting field factor is, see Fig. 6.9(b).

F_2d = _{2 2 2 2}

/ ) 5 . 0 ( 1

1 /

) 5 . 0 ( 1

1

H P d H

P

d − + +

−

+ ...(6.21)

Fig.6.9 Charge distribution in the 2 modes of bipolar dc line:

(a) line-to-ground mode, (b) line-to-line mode.

We will plot these in order to observe their interesting and salient properties. Figure 6.10 shows such plots of only the magnitudes of the field factors since a rod antenna of a noise meter picks up these. For purposes of illustration we take s/H = P/H =1.

Fig. 6.10 Plot of field factors for charge distributions of Figures 6.7 to 6.9.

For cases 1,2 and 5 where the charges on the conductors are of the same polarity, the vertical component of electric field decreases from a maximum under the line centre monotonically as the meter is moved along the ground away from the line. For cases 3 and 6 with charge distributions (+ q, 0, – q) and (+ q, – q), we observe that field is zero at the line centre, reaches a maximum value and then decreases monotonically. A combination of field profiles of cases 2 and 3 (or 5 and 6) yield the characteristic double hump of Figure 6.6. For case

1 2 3

2.00 1.75

1.50 1.25 1.00

0.75 0.50

0.25

q

q – 2q q + q q

q– q q

0 q

q

– q q

AC

AC

DC AC

DC

2 5 31 4 FieldFactorsE/(q/tHπ0

x = d/H

0

+ q + q + q – q

P P

d d

M M

( )a ( )b

4 with the charge distribution (+ q, – 2q, + q), the field commence at a high value under the line centre, reaches zero, and then after increasing to a maximum value decreases monotonically.

These different types of r-f charge distributions occur when corona-generated current, voltage, charge and power propagate on the line conductors which can be resolved into modes of propagation. This has already been discussed in Chapter 3. In the next sections we will give methods of calculating the total RI level of a line from the different modal voltages.