1336 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 15, NO. 4, OCTOBER 2000

Even though the model retains some assumptions that yield conser-vative ampacity values, the main thrust of the paper is to remove oneconservative assumption that is never fulfilled in practice. That is, theproposed model allows calculation of the cable temperatures whenallcables in the tray do not carry the maximum allowable code ampacity.Therefore, the model can account for the reduction in heat generatedand the corresponding reduction in cable mass temperatures as long asthe distribution of currents in the cables can be determined. To sim-plify the task of quantifying the current distribution, we have selectedthe percentage of cables energized as our measure of current distribu-tion within the cable mass. Obviously this is somewhat of an over-sim-plification, but a more refined model would require knowledge of thecomplete current distribution in all cables which is information that israrely known. Therefore, the proposed ampacity model will utilize arealistic estimate of cable loading and still give a conservative estimateof the temperature distribution in the cable mass.

The results in Fig. 2 show that the increase in ampacity which canbe realized by not energizing all cables to their code allowable currentis very insensitive to the depth of cables in the tray. This result is due toway in which we quantified the fully loaded cables. By using apercentof fully loaded cables rather than a specific number of fully loadedcables, the value forFD becomes relatively insensitive to the cabledepth. Also by defining the diversity factor as aratio of ampacities, (1),the expected decrease in ampacity as the depth increases has alreadybeen considered in the value for the code ampacity. As a result, thevalues forFD in Fig. 2 are practically constant with changes in cabledepth.

As pointed out by Dr. Morgan, the convection of heat across the airlayer that is trapped between the top surface of the cable mass andthe tray cover is strongly dependent on the air layer thickness. We dis-cussed this issue in [4]. As the air layer decreases in thickness, its abilityto insulate the cables increases, because the motion of the air becomesmore restricted. Rather than complicate the selection of a cover factorunnecessarily, we have decided to use the lowest, most conservativecover factor from [4, Fig. 7] and we have used those values as our rec-ommended cover factors in Fig. 3 of this paper.1

The fact that the influence of load diversity is not dependent uponwhether the tray is covered or uncovered is understandable when youconsider the definitions of the diversity factor. The effect of load di-versity on cable mass temperature would appear at first glance to bedifferent for a covered and uncovered tray. However by defining thediversity factor (1) as aratio of currents, the presence of a cover doesnot influence the valve ofFD . In other words, thepercentagereductionin ampacity which results from de-energizing some of the cables in atray is the same for a covered tray as it is for a tray without a cover.

The form of the shape factor in (4) is correct and it evolves from ageometry of an infinite number of equally spaced, parallel, isothermaltubes embedded in a solid of constant thickness. Our problem involvesa single heated cylindrical object which has the same shape factor as thegeometry in [6], because the vertical planes midway between each ofthe cylinders are also planes of symmetry. These planes of symmetryare also adiabatic boundaries corresponding to the insulated sides ofthe tray. Replacing the nomenclature in [6] with that used in our paperresults in (4).

Equation (8) is also correct, but we have taken one additional stepand replaced the thicknesst of the cable layer in the one-dimensionalmodel with an equivalent term which is a function ofD. We have as-sumed that the heavily loaded cables with diameterD located in thecenter of the actual 2-D cable mass are spread into a uniformly thick

1W. Z. Black and B. L. Harshe,IEEE Trans. Power Delivery, vol. 15, no. 1,pp. 3–7, January 2000.

layer with thicknesst to preserve the 1-D nature of the geometry asshown in Fig. 6. Using this assumption gives

D2= tW 0

and this equation can be used to remove thet dependence, resultingin (8). As a result, the ratio ofW 0=W is only a function of two otherdimensionless ratiosD=W andH=W .

Discussion of “Magnetic Field Effects on CRT ComputerMonitors”

Don W. Deno

This paper1 was interesting to compare the data with the two ref-erences of this discussion. Before comparing results it is essential toappreciate the evolution of this technology.

Since 1930 the television rasters were selected to have a vertical scanat the power frequency to minimize the interference from a power fre-quency to minimize the interference from a power magnetic field. TheTV vertical scan in USA is 60 Hz, while in Europe it is 50 Hz. The orig-inal IBM PC monitor used the PGA raster. It had a precise 60 Hz ver-tical scan with a very readable text screen. A vertical power frequencymagnetic field caused an unnoticeable horizontal character displace-ment at a little over 100 mG. The jitter frequency was unnoticeable atonce a minute. It was insensitive to power frequency magnetic field in-terference. The paper being discussed used the currently popular PCSVGA raster. The 1987 paper reference [4] and closure reference (1)was concerned with MDA, EGA, CGA and PGA rasters. It is useful tocompare the data from a few sources and different rasters.

Computer Monitor Perceptible Power Frequency Magnetic

Field Interference DataSource Raster Perceptible mGDeno 1987 [4] (1) PGA, A 60 Hz 125

text screen rasterCGA 44

EGA 16

MDA 10

1997 Ref. (1) SVGA, 5–1075 Hz graphicSVGA, 10–2060 Hz graphic

Presented paper SVGA, 7–1272 Hz graphic

Recent CRT monitor 60 Hz displays have actually been�1 Hz from60 Hz creating an objectionable wavy appearance.

Manuscript received February 11, 1999.D. W. Deno is with Electric Field Measurements Co., 86 Interlaken Road, W.

Stockbridge, MAPublisher Item Identifier S 0885-8977(00)11128-8.

1B. Banfaiet al., IEEE Trans. Power Delivery, vol. 15, no. 1, pp. 307–312,January 2000.

0885–8977/00$10.00 © 2000 IEEE

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 15, NO. 4, OCTOBER 2000 1337

Fig. 1 Magnetic field contours in mG in the IEEE-PES Registration area,January 28, 1992, NY Hilton. Shaded areas are above 5 mG.

The conclusion is that current CRT monitors should be in powerfrequency interference fields of less than 5 of 10 mG today and with thetrend to higher resolution, 5 mG in the future. Solid state displays maybe the monitors of the future. They are insensitive to this interference.

If CRT monitor interference is encountered, the choices for correc-tion are 1) to move the CRT monitor to a location with a lower inter-fering field, 2) change the monitor to a solid state type, or 3) shield theinterfering magnetic field. The preferred choice is to move the com-puter monitor to an area of insignificant interference. The selectionof a computer location is usually a compromise of low interferencefield level area versus convenient office arrangement. Changing froma CRT monitor to a solid state monitor is becoming more appealingwith the rapid improvement in solid state monitors. Shielding practi-cally needs an experienced consultant service, because of the cost inpossibly making a mistake in implementing the expensive shielding.Shielding can be disappointing and is inevitably expensive.

The preferred choice of locating a CRT monitor away from an inter-fering field can be implemented by preparing a map of the area withmagnetic field contour levels. The area of interference is marked bythe magnetic field area exceeding 5 or 10 mG. Point sources usuallyhave high contour levels encircling their location. Interference fromline sources like a power line usually have parallel contour lines ofmagnetic field interference. The data of these papers can then be usedin understanding the compromise of interference level versus office lo-cation convenience on the hand sketched map with contours of inter-ference level. In this way computer monitor interference can usually bealleviated at negligible cost.

An example of a map with magnetic field contours is shown on the1992 registration area (Fig. 1) on the same floor as the paper presen-tation in 1999. Only two areas have field levels above 5 mG. The reg-istration area for the PES 1991 Winter Meeting at the NY Penta hotelhad many electric typewriters in the registration area generating fieldsabove 5 mG. When the typewriters were removed, there were only afew areas above 5 mG. The Oct. 15, 1990 Meeting in the Four SeasonsHotel in Austin, TX had mostly fields above 5 mG on a hot day with airconditioners running and much lower fields on a cooler day. An adja-cent 115 kV line contributed a field level above 30 mG on the hot day.The trend is toward lower fields in newer buildings. There is alwaysthe change in levels over time and use of the building. Finding an areawith a field always lower than 5 mG may be elusive.

The field level map with contour levels is created by measuring ona coarse grid defined on a map of the area of interest. Additional mea-surements are made in areas of changing field level gradients. The datacan be processed in two ways. The elegant procedure is to use a com-puter mapping program to map the area of interest and then computethe interfering field level contours with a suitable algorithm. Unfortu-nately this requires mastering another computer software program and

the measured data may present indeterminate areas for contours thatcompute to incorrect magnitude contours. The less elegant procedureis to prepare a hand sketch map with field measurements noted on themap. The contour lines can then be sketched in by hand. Indeterminateareas are usually obvious and can be filled in with additional measure-ments. These hand sketched magnetic contour maps have been the sub-ject of high school science fair projects. The technical level is the sameas a Boy Scout test of preparing a small geographic contour map. Themain drawback to this hand sketch procedure is that it is too simple.There is no money in it. Research is not sponsored and technical pa-pers are not printed. Then sometimes people in authority unfortunatelyassume the expensive research paper shielding techniques are the wayto start in correcting computer monitor interference.

It is recommended that if computer monitor interference is experi-enced, the hand contour map procedure should be the first approach,simply locate CRT monitors in areas of lower magnetic interferencelevel as indicated in this paper. If relocation is not suitable, then thesubstitution of a solid state monitor should be investigated. Last of allthe expensive shielding techniques should be investigated.

REFERENCES

[1] Baishiki and Deno, Same as paper Ref. [4] with emphasis on the Closureprinted in IEEE Power Engineering Review, pp. 65–66, April 1987.

[2] Hiles, Griffing, Munderloh, and Ziakas, “Field Management ServicesCorp.,” in 1997 Annual Review of Bioeffects Research at San Diego.

Discussion of “Calculation of Spacer Compression forBundle Lines Under Short-Circuit”

C. B. Rawlins

The authors report a comparison between the peak forces imposedon bundled conductor spacers resulting from fault currents, as mea-sured in a test span, and as calculated using the method described in [6]and incorporated in an IEC standard [3].1 They also compare forces ascalculated using Manuzio’s formula [2] with the measured forces, andconclude that Manuzio’s method is less accurate than the IEC method.

It is worth pointing out that there are actually two parts to the IECprocedure. One part calculates an “equivalent” current,I , which is in-tended to represent the symmetrical fault current that would result in thesame peak spacer force as an actual asymmetrical fault. The other partcalculates the peak spacer force that would result from a symmetricalfault of equivalent currentI . Manuzio’s method visualizes symmetricalfaults. In comparing the calculations from that method with the mea-sured forces, the authors used only the symmetrical component of cur-rent rather than the equivalent currentI . In applying the IEC method,however, they did useI .

This difference in treatment seems to account for the apparent lesseraccuracy of Manuzio’s method. When the equivalent current is used,the two methods are of about the same accuracy.

Manuscript received December 13, 1999.C. B. Rawlins is a consultant from Massena, New York.Publisher Item Identifier S 0885-8977(00)11130-6.

1J. L. Lilien and K. O. Papailiou,IEEE Trans. Power Delivery, vol. 15, no. 2,pp. 839–845, April 2000.

0885–8977/00$10.00 © 2000 IEEE