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Draft Investigation of Effects of Unbalanced Snow Loads 1992
FILE CORY DRAFT INVESTIGATION OF EFFECTS OF UNBALANCED SNOW LOADS on THE ANCHORAGE-FAIRBANKS INTERTIE Prepared for: ALASKA ENERGY AUTHORITY P.O.Box 190869 Anchorage,Alaska 99519-0869 Prepared by: DRYDEN &LaRUE,INC. P.O.Box 111008 Anchorage,AK 99511 July 7,1992 Table of Contents Page SUMMARY ...-2eccceee ccc eee weemmemereer ee re ese reeeeeeeeses 1-1 BACKGROUND ...cccsccsccsccccecs weeccece eee reeceeeeccne 1-1 SHIELD WIRE -PHASE CONFLICTS .......c ccc ccc cc cc cvcce 1-1 REDUCING CONDUCTOR SAGE UNDER UNBALANCED SNOW LOADS ..1-2 OPTIONS paeeeveeesneveeevoeaeeeeene Ce eeee22erer 1-3 +Options 1,2,3.eaenreoe eeoeveveneee Pa a a ee a ee ee ee ry 1-4 +Options 4,5 .....occ eee eee eee eee eee reece en eeee 1-5 LIMITATIONS Cr ee ee ee ee ee eearer oneeeveens 1-6 INTRODUCTION .ccccccvccsecccssesevrccsceses ecm cee ewer cece eens 2-1 OUTAGES eeeeeeeeaneanes eneeevnvneees re ee ee ee eeer 3-] AREAS AFFECTED BY UNBALANCED SNOW LOADS ........0ccccccvccvce 4-1 SNOW AMOUNT AND DENSITY ...-.ccecscvcvvccece we cceee cece reece 5-1 LIGHTNING PERFORMANCE ......cc.8 eee ee eee weer error weer nen sees 6-1 TOWER ANALYSIS AND RESPONSE TO LONGITUDINAL LOADS .........7-1 MECHANICS OF UNBALANCED SNOW LOADS ..ceecceversnanscesccvece 8-1 RESULTS OF ANALYSIS ..ccccccccc cen cnn nsccvccece eee eee eee ee 9-1 +Sag of the Phase Conductors ........weer ecw ecw eee 9-2.)Shield Wire Conflict with Phases .....cece eee eee 9-7 ¢Tower Loading eeonevneevrevneevrevreev eevee eeeee er a ee ee 9-9 COST ESTIMATES 2...ccc ccc ccc ccc ere cnc e sneer cece ceees wee ee wces 10-1 EXCERPTS FROM THE NESC ...ccccccecccvscccvrccceerssesccessces 11-1 FIGURES APPENDIX 1 -Previous Reports APPENDIX 2 -Ground Snow Densities APPENDIX 3 -"ICE.BAS"Computer Program 9 Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table List of Tables Page 1-1 -Options for Improving Ground Clearance ........1-7 1-2 -"A"Tower Crossarm Utilization End or 2 Spans Loaded ...........eee ecw e ee ee men wren e enn ceene 1-8 1-3 -Comparision of End or 2 Spans Loaded Ground ClEALTANCYSS 2.ewe ewer eee wee e ee naar enerceccccces 1-8 3-1 -Summary of Anchorage-Fairbanks Intertie Outages 3-2 5-1 -Range of Snow DensSitieS .....cece cece cece ce ecee 5-2 6-1 -Comparison of Lightning Outage Rates for South 60 Miles of Line 2...ccc ccc ee eee ec ce ee cere net eee 6-3 7-1 -Comparison of Analytic and Test Deflections ...7-3 7-2 -Deflections and Stiffnesses Under Torsional Loads 7-5 8-1 -Left -Unloaded Span 2...ccc cere cnc nec cre ccccccs 8-5 8-2 -Right -Loaded Span 2...ccc ccc ccc c cc cre cc rece ccee 8-6 9-1 -Tower Spring Constants 80 ft."A"Tower ........9-1 9-2 -Effect of Tower Stiffness on 345-kV I-String ...9-3 9-3 -Comparison of I-String Insulators ..............9-3 9-4 -Comparison 230-kV I-String and Inverted V-String INSULACOLFS 2...eee cece cree e cece scarce scceces eeeese 9-5 9-5 -Comparison of 230-kV I-String and Inverted V-String Insulators with Conductor Resagged ....9-5 9-6 -Conductor Sag CompariSOn ......eee eee cers een cee 9-6 9-7 -Phase to Ground Clearance Comparison............9-7 9-8 -Data on Summary Options ......rr 9-8 10-1 -Estimated Crew HourS ......cece rece cece eens eee 10-2 10-2 -Estimated Material CostS ........2..cc ceeceeees 10-3 ii Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 18 19 List of Figures Fault and Snow Loading Locations 80'"A"Tower 80'"A"Tower with Shield Wire Arms Reversed and 138- kV Insulators Alternatives for Guy Yoke Removal 345-kV I-String Modified I-String Insulator I-String Insulators 230-kV Inverted V-String Insulator Isokeraunic Map of Alaska Percentage Frequency of Thunderstorm Days for the Talkeetna Mountains Sector Sectors and Neighboring Stations Chosen for Presenta- tion of Time Distributions of Thunderstorm Days Plan View of Guys Guys Under Longitudinal Loads Evolution of Finite Element Model of Yoke and Guys Two Span Model of Unbalanced Snow Loads Detail of Tower and Insulator Movement Multiple Spans with Unbalanced Snow Loads in One Span Sag,Crossarm Loads and Tower Movement Crossarm Loads iii DRAFT 1 -SUMMARY BACKGROUND The Anchorage-Fairbanks Intertie has had several extended outages during snow storms caused by phase-to-ground faults.Both the phase conductors and shield wires have been observed to sag well in excess of design sag during these snow storms.The increased sags are due to several factors including the effects of span-to-spandifferencesintheamountofsnowclingingtothewires. Figure 1 shows the locations where faults and increased sags have been reported.The area extends from Douglas Substation,the southern terminus of the Intertie,to the Susitna River Crossing,a distance of 80 miles.Eyewitness reports of increased sag due to unbalanced snow loads appear to be confined to the southern 35 miles. There have been four outages for which there is information from the Sweitzer Relays about location and type of fault.All four were phase-to-ground faults on the outside phases. At least one outage,at Caswell Lakes Road,has been tied to con- tact between a phase and a tree on the right-of-way.Contacts between the shield wire and outside phases are also suspected. This study has focused on methods of reducing the possibility of the phase conductors sagging to the ground or coming in contact with the shield wires. SHIELD WIRE -PHASE CONFLICTS Contact between the phases and the shield wire can be reduced or eliminated by either reversing the support arms for the shield wire and shortening the attachment link or removing the shield wire completely.Figure 2 shows the present shield wire attachment (on the "A"tower).Figure 3 shows the shield wire arms reversed.The extension link shown in Figure 2 has to be shortened to keep the shield wire from banging against the tower in high winds.The horizontal clearance from the outside phase is increased from 5.4 to 9.9 feet. Shielding performance will be practically unchanged by reversing the shield wire arms.In either case,the shield wires prevent any lightning strikes to the phases.Removing the shield wires on the southern 60 miles of line will result,on average,in 3 to 4 light- ning strikes to the phases each year.Each of these strikes can be expected to cause an outage;however,reclosing after the energy of the lightning stroke has dissipated should be effective.There is 1-1 also a small possibility of the lightning flashover damaging an insulator string sufficiently to require its replacement before the line can be reenergized.Almost all thunderstorms occur between May and August with the majority in June and July. REDUCING CONDUCTOR SAG UNDER UNBALANCED SNOW LOADS The conductor sag increases in a span loaded with snow surrounded by bare spans because the insulator string swings and pulls the tower along towards that span until the force on the tower and the tension in the unloaded span balance the tension in the loaded span.Reducing the amount of sag increase depends on reducing the movement of the tower and the swing of the insulator.A corollary of this is that as the tower movement and insulator swing is re- duced,the load on the tower is increased and the chances of damag- ing or destroying the tower are increased. As the basis of our analyses,we have assumed 4 inches of radialsnowwithadensityof5lb/ft®.While there is circumstantial evidence that this assumption is reasonable,there is no hard evi- dence to prove it.As the discussion progresses,we will offer options for improving the ground clearances under unbalanced snow loads.It should be kept in mind that the improvements are rela- tive.The actual values for the ground clearances which are given are valid only for the assumed size,density and distribution of snow loads.Heavier snow loads due to either larger buildups of snow or higher densities will reduce the ground clearances,lighter loads will increase them. Two cases were used for comparing the effects of changes to the insulators and structures.For the first,4 inches of radial snow was assumed to be on one span of wire in the middle of a long tan- gent with all the rest of the spans bare;i.e."one span loaded". For the second,one span of a long tangent adjacent to a deadend tower was assumed to have 4 inches of radial snow with all the rest of the spans bare.The second case is identical to one half of a tangent with "two spans loaded"in the middle.This is because the tower in the center will have equal loads on either side with no movement of the tower or insulators at the center -making the center tower equivalent to a deadend loaded on one side. The standard tangent tower on the southern section of the intertie is an "X-tower"as shown in Figure 2.The resistance to movement of this tower,particularly of the outside phases,can be substan- tially increased by removing the yokes and tensioning the guys. Figure 4 shows the proposed modification.The yoke and single guy are replaced by a scissors assembly with extension links to pick up the existing pair of guys.The scissors assembly has a shear bolt to provide slack in the guys when the force exceeds the shear strength of the bolt.This is necessary to prevent damage to the tower should one or both of the leg foundations jack because of frost action.It also can help the tower survive an unusually large longitudinal load. The movement of the insulator can be reduced by shortening it or by changing it to an inverted V-string or both.Figure 5 shows the original I-strings used on the outside phases,Figure 6 shows the same insulator string modified for operation at 230 kV,161 kV,or 138 kV.The hotline link and shackle at the tower end have been replaced with an oval eye tongue and shackle to minimize the over- all length of the assembly. Figure 7 shows the effects of changing the I-string insulator length on the ground clearance.The straight sloping line at the top represents the ground clearance with all spans evenly loaded. The changes in ground clearance represented by this line are due to the change in length.The other curved lines show the ground clearance with different tower stiffnesses (resistance to movement under longitudinal load).A tower stiffness of 1500 lb/ft repre- sents the outside phase without any modifications.4500 lb/ft is an outside phase with the yoke removed,9500 lb/ft has the yoke removed and the guys pretensioned.23,000 lb/ft represents the center phase of the tower.Shortening the insulator increases ground clearance both by raising the attachment point of the con- ductor and by reducing the swing into the loaded span. Figure 8 shows a 230 kV inverted V-string.The inverted V-strings are more resistant to swing along the line than the standard I- strings. OPTIONS Table 1-1 shows five options for addressing the reduced ground clearances under unbalanced snow loads.The options range from living with the problem (Option 1)to removing the shield wire, changing the guy yokes,resagging the wire and replacing the insu- lator strings (Option 5).The first column of figures is the clea- rance calculated for an outside phase with one span loaded with snow towards the middle of a long section of tangent towers.The calculations are based on all the spans being 1225 feet long with 80 ft.(measured from ground to conductor at the tower)"A"towers. These are average values for the first ruling span section north of Douglas Substation.The second column has the clearance calculated if either two spans are loaded or one end span -the span adjacent to a deadend -is loaded.The next column has the resultant load on the crossarm which is the vector sum of the vertical and longi- tudinal loads.For the "A"tower,which is the typical tangent tower,the critical member under combined vertical and longitudi- nal conductor loads is the crossarm.The crossarm is a round tube with a capacity of 17,700 lbs.in any direction applied at an out- side phase attachment point.The next column gives the crossarmresultantloadaspercentageofthe17,700 lb.capacity.The last column gives the estimated cost to modify one type "A"tower. Option 1: This option is the "do nothing option". With one span loaded in the center of a long tangent,the conductor in that span is on the ground and should cause a fault.The reduced line clearances as snow builds up and falls off spans would become an operational problem.The line may have to be shut down during periods of severe snow buildup until it can be patrolled and any snow buildup is removed from the line. Option 2: With this option,the center V-string insulator is changed to an I-string with a lower insulation level.The outer I- strings have bells removed and the hardware modified as shown in Figures 5 and 6.This increases the attachment height and reduces the movement of the conductor clamp into the loaded span resulting in more ground clearance.A new attachment for the center phase insulator must be fabricated and either bolt- ed or welded to the crossarm. The tower movement under longitudinal loads is reduced by taking out the yokes and pretensioning the guys. The ground clearance under the assumed snow load is increased by 9 to 15 feet depending on the insulation level.The load on the crossarm under the assumed loads is increased by 28 percent. Impact loads from broken wires or other catastrophes will be increased,particularly if the impact is on an outside phase. This will increase the chances of damaging a tower should that occur. The shield wire arms are reversed to more nearly center the shield wires between the phases and increase the horizontal clearance to the outside phases. If the density or amount of snow increases sufficiently,there is still potential for the conductor to sag to the ground. Option 3: This is essentially the same as option 2 with the addition of resagging the conductor.Because the resagging operation would require two visits to each tower and equipment for sag- ging,the estimate includes removing the shield wire instead of reversing the shield wire arms. Resagging the conductor distributes the unbalanced loads from the loaded span to more towers,slightly reducing the crossarm loads. The clearances in Table 1-1 are based on resagging to tighten the conductor up as much as possible and still being able to protect the conductor from vibration damage with stockbridge dampers.The sag is reduced 5 to 6 feet under all normaldesignconditions.This reduction in sag carries over to the unbalanced snow conditions.Resagging the wire this amount increases the tension loads on the angle and deadend struc tures about 10%over the initial tensions for which the towers were designed.This requires either accepting some increased risk of failure of the angles and deadends or strengthening them.It also increases the risk if snow loads an entire tangent in excess of the design loads. Resagging to bring the conductor back to the initial stringing tensions would increase the clearances approximately 3.5 feet over option 2 without requiring any changes in the angles and deadends. The estimated cost does not include the cost of strengthening the angles and deadends.This cost is highly dependent upon how much of the line is changed because the percentage of angles and deadends is not uniform. Option 4: In this option,the existing center V-string and outside I- strings are replaced with 230 kV Inverted V-strings (Figure 8).As with options 2 and 3 a new insulator attachment brack- et would need to be added for the center phase. The inverted V-strings are much more resistant to movement than I-strings.The load on the crossarm is increased 45 percent under the assumed unbalanced snow load.The capacity to absorb impact loads is lowered because of the increased stiffness of the insulator and tower. Option 5: Option 5 is essentially the same as option 4 with the addition of resagging the conductor.As with option 3,angle and dead- end towers may need some attention to get a 5 to 6-foot reduc- tion in sag.A smaller sag reduction of 3.5 feet can be made without increasing the loads on the angle and deadend struc- tures. The cost estimate is based on removing the shield wire rather than reversing the arms. LIMITATIONS The options shown in Table i-1 and discussed above cover the range of possibilities (short of raising or insetting structures)for im- proving the ground clearances under unbalanced snow loads.As can be seen,a substantial improvement in ground clearance can be gained through changing the insulator strings and modifying the yokes and guys on the towers.The biggest unknown here is what the design weight and distribution of snow should be.To our knowl- edge,there have been no measurements made to provide reliable data on the weight of snow that has accumulated and the frequency at which it can be expected to occur.The snow load used in the com- parisons is our best guess.The amount and distribution of snow fit what facts we have;they are also simple enough to make mean- ingful comparisons between different options. Table 1-2 compares the percentage of the type "A"tower's crossarm strength utilized by Options 1,2c and 3 for different snow densi- ties.There is a tradeoff between improving the ground clearance in the loaded span and increasing the load on the crossarm. Similarly Table 1-3 shows the loaded sags to be expected with high- er snow densities for Options 1,2c and 3 when two spans are load- ed. In summary,there are several ways of improving the performance of the line under unbalanced snow loads.All these methods carry some increased risk of damaging the towers if our estimates of the den- sity or amount of snow are low in terms of the loaded weight per foot.The southern 35 miles or so of the intertie seem to clearly have a problem,whether the rest of the line lying in the Susitna Valley also has a problem is not so clear.The cost of making the modifications could vary by a factor of two depending on the length of line to be modified.The best choice from the options outlined also depends heavily on when or whether the voltage of the line will be increased and if increased,to what level. Table 1-1 Options for Improving Ground Clearance 4"Radial Snow 5 lb/ft? Outside Phase Ground Clearance Estimated One Two Rsltnt Xarm Cost Span Spans Xarm Cpcty Per Loaded Loaded Load Used Structure Options:ft ft kip %$ 1.Leave as is with 345-kV Insulation:-2.09 7.59 6.4 36 -0- 2.Remove yokes,pretension guys, reverse shield wire peaks,shorten insulator strings to: a.230-kV 7.62 17.05 7.5 42 15,300 b.161-kV 9.94 19.22 7.8 44 15,300 c.138-kV 12.52 21.57 8.2 46 15,300 3.Remove yokes,pretension guys,resag conductor,remove shield wire, shorten insulator strings to: a.230-kV 13.80 22.09 7.1 40 21,800 b.161-kV 15.87 24.10 7.3 41 21,800 Cc.138-kV 18.16 26.28 7.7 43 21,800 4.Remove yokes,pretension guys, change insulator strings to 230-kV Inverted V-Strings,reverse shield wire peaks:17.10 24.13 9.3 53 22,400 5.Remove yokes,pretension guys, change insulator strings to 230-kV Inverted V-Strings,remove shield wire,resag conductor:22.84 29.23 9.0 51 27,900 1-7 Table 1-2 "A"Tower Crossarm Utilization End or 2 Spans Loaded Percentage of Xarm Strength Used with 4 in Radial Snow Insltr Table 1 Density (lb/ft?) Insltr Lgth Option 5 10 15 Type Voltage ft No.%%% I-String 345 11.00 1 36 61 86 I-String 138 5.45 2c 46 91 136 Inverted V-String 230 7.60 3 53 95 136 Table 1-3 Comparison of End or 2 Spans Loaded Ground Clearances 2 Spans Loaded Ground Clearance with 4 in Radial Snow Insltr Table 1 Density (lb/ft*) Insltr Lgth Option 5 10 15 Type Voltage ft No.ft £t £t I-String 345 11.00 1 7.59 -6.05 -14.76 I-String 138 5.45 2c 21.57 13.69 8.40 Inverted v-String 230 7.60 3 24.13 15.43 9.49 2 -INTRODUCTION This report discusses an investigation into the effects of unbal- anced snow loads on the Anchorage-Fairbanks Intertie.Unbalanced snow loads are those loads that occur when snow has accumulated on some spans of the transmission line but not all,or when heavier accumulations occur on some spans than on others. The Anchorage-Fairbanks Intertie was built in 1983 and 1984.It was initially energized in December 1984;however,full operation aid not begin until September 1985.Commercial operation began in May 1986.To date (July 1992)the line has been in continuous operation through 7 full winters and one partial winter. Outages that have definitely been tied to unbalanced snow loads occurred in snowstorms in January 1989 and December 1990.On aver- age,a snow storm causing outagages happens every 3 to 4 years. The return period of the storms that have occurred is probably on the order of 2 to 10 years.Storms with a longer return period of 25 or 50 years may be experienced in the future.Such a storm can be expected to last longer.Larger accumulations of snow and larg- er span to span unbalances in loading can also be expected. The investigation consisted of several parts: fe)Determine the section of line affected by unbalanced snow loads. fe)Estimate the amount and density of the snow that accumu- lates on the conductors. fe)Determine the behavior of the towers in response to lon-gitudinal and torsional loads. fe)Calculate the response of the line using the estimated snow amounts and density. fe)Compare the response of the line with various modifica- tions. fe)Estimate the cost of the more promising modifications. The area affected by unbalanced snow loads was determined by com- piling a list of outages,fault locations,twisted conductor bundle locations and places where observations of large buildups of snow and excessive sag have been reported.These locations were plotted on a map of the southern end of the line (See Figure 1). Snow fall records at Talkeetna and Mckinley Park were provided by the Soil Conservation Service.This provided information to esti- mate the snow densities.Measurements from photographs helped establish approximate amounts of snow accumulating on the wires. The 80 ft and 90 ft type "A"towers were analyzed to evaluate their flexibility under unbalanced longitudinal loads. A computer program,ICE.BAS,was written to calculate how the con- ductor,insulator assembly and tower move in response to unbalanced snow loads.Various modifications to the towers and insulator assemblies were evaluated for improvements to the ground clearances and their effect on structure loads. The lightning performance of the existing line and the line with modifications to the shield wire were examined using EPRI's Multi- flash program. Finally,cost estimates were made for the better methods of improv- ing ground clearances. Some previous reports have been made that bear on this problem.In October of 1989 Dryden and LaRue measured the sag at Caswell Lakes Road.This was reported November 1,1989 with a follow up letter January 8,1990.This report concluded that the wire had not stretched beyond the amount expected based on its age,ie it was between initial and final sags,but more towards the final sags. Brian White came to Alaska in January 1991 to investigate and make recommendations about the problems that had occurred as a result of the December 1990 snow storm.His letter reports are dated January 31 and February 18,1991 (See Appendix 1). It should also be pointed out that very similar unbalanced snow loading problems have been experienced on the Tyee Lake 138 -kV Line,particularly on the section between Wrangell and Petersburg. 3 -OUTAGES Table 3-1 is a tabulation of the reported Intertie Outages.The list was compiled from copies of reports furnished by AEA and GVEA _and conversations with the ML&P's dispatch staff.There may have been other outages which are not listed here. Two snow storms definitely caused several of the outages.The first was in late December 1988 and early January 1989.Outages 4 to 6 happened in this storm.The second storm was in December 1990.It caused outages 9 to 12.The outage on January 17,1990, No.8 may also have been due to unbalanced snow loads. 10. 11. 12. 13. Table 3-1 Summary of Anchorage -Fairbanks Intertie Outages 12/8/86 2/5/88 10/6/88 1/2/89 1/6/89 1/10/89 4/6/89 1/17/90 12/23/90 12/24/90 12/25/90 12/25/90 5/10/91 Near Healy Substation,no information on phase or duration of outage. Fault was apparently a tree near the Susitna River Crossing which is between Structures 356 and 357. Fault Between Healy and Cantwell,no cause found, no information available on type of fault or phases affected. The outage lasted from 3:27 to 3:56,it was attrib- uted to heavy snow.The Sweitzer relays showed it being 12 miles north of Douglas at one end and 85 miles from Douglas on the other end,another report has it 50 miles from Douglas.It was reported as a phase to ground fault;however the phase was not noted. The outage lasted from 19:24 on the sixth to 13:17 on the seventh.This is attributed to the snow putting the line into trees at Tower 70 at Caswell Lakes Road 16.5 miles north of Douglas and at Tower 128 29 miles north of Douglas Attributed to a tree at Tower 70.This may be the same outage as listed on 1/6/89.The trees were trimmed on 1/11/89. No cause or other information available. Phase to ground fault on A phase 60 miles north of Douglas on A phase Outage from 19:07 to 19:44 35 or 40 miles north of Douglas,Phase to ground on A phase Outage from 12:13 TO 12:21 To check switches that were improperly operated Outage from 12:50 to 12:52 on C phase 46 miles north of Douglas Outage from 15:31 to 23:47 on 12/31/90.Fault was phase to ground on C phase 35 miles north of Doug- las. Intertie breakers opened for unknown reason when one of the Beluga Lines lost a tower. 4 -AREAS AFFECTED BY UNBALANCED SNOW LOADS The section of line which has experienced unbalanced snow loads appears to extend about 80 miles north of Douglas Substation,the southern terminus of the line.Within this area,the first 35 miles from Douglas appear to be more heavily affected.Figure 1 shows the locations where problems have been identified.The data shown on Figures 1 was compiled from a review of correspondence provided by AEA and discussions with staff at AEA,MEA,GVEA and ML&P.The data includes: fe)Fault location information from Sweitzer Relays. fo)Locations where trees were cut or trimmed. ro)Locations reported where low wires were seen or snow was removed from the wires. fe)Locations where the two conductor bundles required un-wrapping. °Observations reported by Brian White. There were four faults that for which information was available from the Sweitzer relays: 1/17/90 Phase to ground fault on A phase 60 miles north of Douglas Substation (Outage 8). 12/23/90 Phase to ground fault on A phase 35 or 40 miles north of Douglas Substation (Outage 9). 12/25/90 Phase to ground fault on C phase 46 miles north of Douglas Substation (Outage 11). 12/25/90 Phase to ground fault on C phase 35 miles north of Douglas Substation (Outage 12). The faults in December 1990 are almost certainly related to the affects of unbalanced snow loads. In response to outages in January 1989 trees were trimmed in the these areas: Twrs 70 to 71 1-11-89 Caswell Lakes Road Twrs 197 to 217 2-16-89 Twrs 197 to 198 2 21-89 Twrs 217 to 218 2 27-89 Twrs 218 to 223 2-28-89 Golden Valley crews worked to clear the outage that started in late December 1990 and extended into January 1991.GVEA reports clear- ing snow from the line in the following areas: Twrs 37 to 48 (intermittent spans in this area) Twrs 63 to 64 Twrs 70 to 71 Twrs 83 to 84 Several pictures were taken at this time showing the snow buildup on the wires and the low ground clearances.Some spans were re- ported to have the conductor bundle twisted while weighted down with snow. GVEA also reported that a patrol after the outage on January 6, 1989 found heavy snow loads caused the conductor to sag excessively at tower 70 and tower 128.They also reported the outage of Febru- ary 5,1989 to be due to a tree at the Susitna River crossing which is between structures 356 and 357. Matanuska Electric Association reported that the problems seem to extend from Douglas Substation to the Talkeetna Area.Some specif- ic locations reported are: Twrs 1 to 2+Shield wire loaded with snow sagged below phase conductor two spans from Douglas Substa- tion approximately 2 years ago. Twr 20 to 22 At Little Willow River 1/1/91 Twrs 50 to 52 Snow unloaded from static and conductor 1/1/91 Twr 57 to 58+At Kashwitna River 1/1/91 Twr 73 to 74+Just north of Sheep Creek 1/1/91 Matanuska Electric Associations maintenance crew unwrapped bundled conductor that was rolled in the following locations: 1991 1992 Twrs 17 to 18 Twrs 22 to 23 Twrs 29 to 30 Twrs 36 to 37 Twrs 36 to 37 Twrs 45 to 46 Twrs 41 to 42 Twrs 52 to 53 Twrs 44 to 45 Twrs 63 to 64 Twrs 45 to 46 Twrs 43 to 54 Twrs 97 to 98 Twrs 120 to 121 During his visit and flight along the line in January 1991 Brian White observed twisted bundles in some spans and rotated shield wire arms at various towers from tower 40 to tower 150. 5 -SNOW AMOUNT AND DENSITY A snow load of 4 inches of radial snow with a density of 5 1b/ft® was assumed for the basic analysis of the unbalanced snow loads. This load was chosen for the following reasons: fe)Ground snow densities tend to be in the range of 2 to 5lb/ft? fe)The snow was reported to be dry,dry snow has densitiesof2to9lb/ft fo)Dry snow accumulations at temperatures below 32°F havebeenreportedintheliteratureat5to6%lb/ft? oO The unit wire load is slightly less than the amount nec- essary to permanently stretch the wire °Measurements from photographs indicated accumulations of 2.9 to 5.3 inches of radial snow oO In the computer model of the line,this load applied to an outside phase is just sufficient to cause the wire to sag to the ground The soil conservation service has stations at Talkeetna and McKin- ley Park.Daily observations of temperature,amount of snowfall for the day and water equivalent of snowfall for the day are made at these stations.This data was used to calculate snow densities during the snow storms which apparently resulted in outages on the transmission line.Appendix 1 contains a tabulation of the densi-ties.The majority of the densities are in the 2 to 5 lb/ft?range.The highest density,10 lb/ft?was measured the day before the outages in December 1991. Roger Kyle of the soil conservation service said that in the fallandwinter,in cold weather,the snow runs 10%moisture (100 kg/n',6.2 lb/ft?)however in March and April the snow can be have as muchas30to35%moisture (300 to 350 kg/m?or 18.7 to 21.8 lb/ft?). According to Perla and Martinelli':"Alpine snow commonly has adensitybetween30kg/m?for light,newly fallen snow and 500 kg/m? for old,highly compressed layers.When measured in areas shel-tered from the wind,newly fallen snow is found to have a densitythataveragesbetween70and120kg/m?,depending on the tempera- ture.In areas exposed to the wind,the average densities areabout250kg/m?-AS a general rule,high densities correlate withwarmairorhighwinds,and low densities correlate with cold air or low winds." 1 Perla,Ronald I.and Martinelli,M.Avalanche Handbook.U.S. Department of Agriculture,Agriculture Handbook 489,WashingtonD.C.U.S.Government Printing Office,(1978)Page 15 5-1 Table 5-1 relates the descriptions of new fallen snow with the range of densities to be expected.The foreman of MEA's line crew which maintains the Intertie described the snow he has seen on the line as falling off the line relatively easily.It could not be packed into snowballs. Table 5-1 Range of Snow Densities Range of Snow Description Density lb/ft> Very Light Powder Snow 2 Powder Snow 3 6 Heavy Powder 7 9 "Snow Ball Snow"10 14 During the Christmas 1990 snow storm,one of the authors observed dry powdery snow accumulated to 4.5 radial inches on a phone wire in the Goldstream area of Fairbanks.The snow was very light and could be easily brushed off.One jerk of the wire was sufficient to clear the entire span. Gland and Admirat*report that "dry sleeves"of snow formed at temperatures below freezing had measured densities of 80 to 100kg/m (5 to 6.24 lb/ft).They also reported "wet snow"which formed on wires at temperatures above freezing had measured densi-ties of 250 to 350 kg/m (15.6 to 21.8 lb/ft). When the clearances at the Caswell Lakes Road crossing were mea- sured,the wire sag was about where it would be expected given the age of the line.The uniform load required over a section of line to produce final sag greater than the design final sag is .89 in of radial glaze ice at a load of 3.3506 lb/ft.Similarly 4 inches ofradialsnowat51b/ft?results in a load of 3.3297 lb/ft. Approximate measurements from pictures furnished by GVEA (from December 1990 -January 1991)and MEA (of the Caswell Lakes Road outage)showed that the conductor overall diameter ranged from 5.9 to 11.7 inches on the conductor,which translates into 2.9 to 5.3 inches of radial snow. Based on the above,4 in.of radial snow at a density of 5 1b/ft® was used as the basis for the analysis. 2 Gland,H.and Admirat,P "Meteorological Conditions for Wet Snow Occurrence in France.Calculated and Measured Results in a Recent Case Study,On March 5 th,1985",Proceedings of the Inter- national Workshop on the Atmospheric Icing of Structures,6-8 May 1986 Vancouver Canada Page 91 to 96.Editors L.E.Welsh and D.J. Armstrong.Canadian Climate Program,1991. 5-2 6 -LIGHTNING PERFORMANCE One of the suspects in the phase to ground faults is the conductor and shield wire coming into contact with one another.This could happen when one or the other sheds its snow load,or when the wind blows one into the other when conditions have caused the shield wire to be sagged below the conductor.The effects of either re- moving the shield wire,or changing its location in relation to the phases were examined. The purpose of the shield wires is to intercept lightning strokesbeforetheyhitthephases.When a line has shield wires,light-ning outages are divided into two categories:"shielding failures" and "back flashovers."A shielding failure occurs when a phase isstruckdirectlybythelightning.When this happens,the relays which trip the line out either operate on the voltage transient caused by the stroke or on the phase to ground fault established by the flashover from the phase to a structure.Back flashovers occur when the lightning strikes a shield wire or a tower.The current passing through the tower causes a rise in potential of the tower itself.The rise in potential is sufficient to cause a flashover from the tower to a phase.This establishes a phase to ground fault. The keraunic level is the starting point for calculations of light-ning outage rates.The keraunic level (sometimes termed the isoke- raunic level)represents the "average number of days per year onwhichthunderwillbeheardduringa24-hour period.'"The ke- raunic levels in Alaska are given in "Thunderstorm Climatology ofAlaska.?"The keraunic level for the Intertie varies from lessthen2atWillowto8atHealy(See Figure 9%).From Willow to the Susitna River Crossing,the area where -to date -snow problems have occurred,the keraunic level varies from less than 2 to 4. Following are the "concluding comments"from the "Thunderstorm Climatology of Alaska"which are appropriate. "From the various thunderstorm time distributions presented,it is clear that maximum thunderstorm activity occurs during or shortly following the most intense solar heating.This was indicated on both the diurnal and the one-third monthly time distributions.It was also shown that Alaska thunderstorms show a strong affinity for the moderately higher terrain.The 'General Electric Company,Transmission Line Reference Book 345 kV and Above /Second Edition.Electric Power Research Insti- tute,Palo Alto,California,(1982)Page 546 2 Grice,Gary K.and Comiskey,Albert L.Thunderstorm Clima- tology of Alaska.Weather Service Regional Headquarters,Anchorage, Alaska (February 1976) 3 Hoop,Robert R.and Morrison,John C.Anchorage -Fairbanks Transmission Intertie,Structure Grounding Study for Alaska Power Authority.Gilbert/Commonwealth Inc.of MI,(July 1985)Figure 3 6-1 Yukon-Tanana Upland,Kuskokwim Mountains,Talkeetna Mountains, Alaska Range,(lower elevations)and the south slopes of the Brooks Range are areas of preferred thunderstorm formation. The general absence of thunderstorms over valleys is notable." Figures 10 and 11 are taken from "Thunderstorm Climatology of Alas- ka."Figure 10 shows the distribution of thunderstorms by month in the Talkeetna Mountain Sector.The sector's location is shown in Figure 11.Practically all the thunderstorms take place between May and August with the majority in June and July. Based on the above,a keraunic level of three was used for the calculations. The Electric Power Research Institute's (EPRI)Multiflash Program (one of the programs in TLWorkstation)was used to evaluate the effects of either reversing the shield wire arms or removing the shield wire. For backflash calculations,the important parameters are the insu- lator length,the line voltage and the ground resistance.Ground resistances were based on measured ground resistances reported in the grounding study.Table 6-1 summarizes the results. The first line in Table 6-1 represents the line as it is operating today -energized at 138-kV with 345-kV insulation (See figure 2, Note that the shield wires for the Intertie are insulated and seg- mented to reduce or eliminate the energy losses due to circulating currents).The second line represents the present line operating at 345-kV.The back flashovers increase slightly because the line potential is higher and the potential across the insulator string during strikes to the shield wire or towers will be higher.The third line represents the shield wire arms reversed (See Figure 3) with the insulator strings shortened to 230-kV insulators.The back flashovers are higher than the two previous cases because the insulation has been reduced.The fourth line is the same as line the second with the shield wire arms reversed,ie 345-kV operation. The strokes to the line are marginally less due to the narrower profile but total outages are the same.The last line shows the effects of removing the shield wire.There are fewer strokes to the line because the phases are lower than the shield wire;but each stroke to the line causes an outage. Table 6-1 Comparison of Lightning Outage Rates for South 60 Miles of Line Strokes Operating to Shielding Backflash-Total Configuration Voltage Line Failures overs Outages Existing Line 138-kV 5.26 0.00 0.15 0.15 Existing Line 345-kV 5.26 0.00 0.17 0.17 Shield Arms Reversed 230-kV 5.25 0.01 0.43 0.43 Shield Arms Reversed 345-kV 5.17 0.00 0.17 0.17 Shield Wire Removed 345-kV 3.44 3.44 0.00 3.44 Two of the original studies made about the line design are of in-terest.They are the "Structure Grounding Study*"and the "Shield-ing and Shield Wire Coordination Study".In the shielding study, which used a keraunic level of 8,the outage rate was calculated as 12.9 per 100 miles per year without any shield wire and .82 with two shield wires.These appear to be consistent with the results obtained for the Southern 60 miles when proportioned for the length and keraunic levels used. 4 Ibid >Hoop,R.R.et al,Anchorage-Fairbanks Transmission Intertie, Shielding and Shield Wire Coordination Study for Alaska Power Au- thority.Commonwealth Associates Inc.,Jackson,MI (1982) 6-3 7 -TOWER ANALYSIS AND RESPONSE TO LONGITUDINAL LOADS In this section,the need for a structural analysis of the towers, how the towers were analyzed,how the towers respond to loads - particularly longitudinal loads,and how the towers can be modified to change their characteristics are discussed.The advantages and disadvantages of using a yoked guying system and tests performed with and without yokes performed on the first X-towers ever in- stalled will be addressed. For assessing the effects of unbalanced ice and snow loads on ground clearances,the most important tower parameter is how much the tower crossarm moves longitudinally when unbalanced tension loads are applied to it.The longitudinal force divided by the movement gives an effective tower spring constant which determines how much of the increased sag of conductors is due to the tower. The "X"towers which are used on a number of transmission lines in Alaska (Tyee Lake,Bradley Lake,Beluga,Willow and Solomon Gulch to Glennallen as well as the Intertie)have a unique system for resisting longitudinal loads.The tower legs are pinned at the base which allows the structure to pivot at the ground.In the longitudinal direction,the tower is supported by two guys each ahead and back of the structure.The guys are attached at the top of the upper legs about midway between the phase attachments.The bottom ends of these guys are attached to a horizontal yoke which is in turn attached to the anchor with a single guy. Figure 2 shows an elevation of the basic tangent tower,Figure 12 shows a plan view of the tower with guys and yokes. When longitudinal loads are applied equally to all three phases, or only to the center phase,the tower is supported at the top by the guys and at the bottom by the pinned connections to the founda- tions.The loads in the guys will be equal on the side opposite the direction of the load.The guys on the other side will slack off (See Figure 13a).The legs of the tower will be mainly in compression from the vertical component of the guy loads. If a twisting load is applied to the tower,for example equal lon- gitudinal loads applied at the outside phases in opposite direc-tions,the tower will twist and the yokes will follow as shown in Figure 13b.This type of load is not resisted by the guys at all but rather by the torsional stiffness of the X-tower itself. As far as the guys are concerned,a longitudinal load at an outside phase is equivalent to a longitudinal load applied at the centerphaseplusatwistingloadappliedtotheoutsidephases.Thebalancedlongitudinalpartisresistedbytheguysandthetwisting part is resisted by the tower.This is true until the twisting issufficienttobringtheyokeinlinewithoneoftheguys. A finite element analysis was made of the basic "A"tower (the tow- ers were named "A","B","Cc"etc in order of strength)to determine the deflection characteristics under longitudinal loads.Modeling the yoke and guys as installed results in an unstable mathematical model that will not run.Figure 14 shows the progression to reach a stable mathematical model which exhibits behavior close to that of the actual structure.Figure 14a shows the actual tower.If the yoke were made as wide as the attachment at the tower,Figure 14b,it would still offer no torsional restraint.Moving the yoke up to the crossarm,Figure 14c would not change the effective loads on the tower itself.Attaching the yoke to the tower and using a single guy equivalent in section to the two guys makes a stable model.The yoke at the crossarm is pin connected to one guy at- tachment point and pin connected to the other attachment point with a sliding connection along the crossarm (joint release).The cross section of the new yoke is chosen to have the same deflection at the ends for a given guy load as the original yoke.This is the model which was used to analyze the towers with the yokes in- stalled. A full scale load test was performed on the 90 foot "A"tower. Table 7-1 compares calculated deflections from the finite element analysis with the deflections recorded during the tower test. The only unbalanced torsional load tested was 3900 lb applied at one shield wire peak in Case 5A.The measured deflection was 22.5 inches.The calculated deflection is 36 inches.The difference may be due the longitudinal rigging needed for the other load cases tested,the tower model may be less torsionally rigid than the actual tower,or the tower may have pulled the yoke parallel with the guy limiting the movement during the test,the test report does not have sufficient information to distinguish between these possi- bilities. For use in the balance of the study,the 80 ft tower was also ana- lyzed for performance with the yokes installed using a model with the yoke moved up to the crossarm level. In order to reduce the movement under twisting loads -longitudinal loads applied to one outside phase -the yokes can be removed and the guys attached directly to the anchors.When this is done, instead of the yokes moving in concert with the crossarm,the diag- onally opposite guys tighten up resisting the twisting.The other two guys go slack. The 80 ft tower was reanalyzed with the yokes removed.The deflec- tions were substantially reduced and the corresponding stiffnesses increased.A third analysis was made with the yokes removed and the guys pretensioned to approximately 5,000 lbs.Pretensioning the guys effectively doubles their stiffness.This further reduced the deflections by about 50%. Table 7-1 Comparison of Analytic and Test Deflections NESC Hvy T-Wind L-Wind Hvy Vert Strgng Unbal-L Location _1 Height Case I Case II Case III Case IV Case VA Case VI Transverse Deflections Left Shield Wire Tl 117.60 19.00 21.60 2.80 0.90 1.80 0.602 Peak 3 17.86 17.71 2.77 -0.10 1.05 -0.177 0.94 0.82 0.99 -0.11 0.58 -0.29% Center of Crossarm T2 101.00 14.50 15.10 3.00 3.60 3.00 2.30 17 13.57 11.87 2.76 3.32 2.77 2.16 0.94 0.79 0.92 0.92 0.92 0.94 Center of Waist T5 71.92 2.00 1.80 0.70 0.50 3.10 3.00 18 -1.96 -1.19 -0.42 -0.51 -0.38 -0.33 -0.98 -0.66 -0.60 -1.02 -0.12 -0.11 Longitudinal Deflections Left Shield Wire Li 117.60 0.40 0.80 11.00 0.30 22.50 21.00 Peak 3 0.00 0.00 10.81 0.00 35.94 20.23 0.00 0.00 0.98 0.00 1.60 0.96 Left End of L3 101.00 0.30 0.50 11.50 0.20 17.50 13.40 Crossarm 9 0.00 0.00 12.91 0.00 33.66 12.03 0.00 0.00 1.12 0.00 1.92 0.90 Left side of L10 71.92 0.10 0.30 9.60 0.10 1.90 2.40 Waist 19 0.00 0.00 14.14 0.00 2.23 4.06 0.00 0.00 1.47 0.00 1.17 1.69 |Location Right Shield Wire v2 Peak 4 Right End of v4 Crossarm 10 'Location from test report/analytic model node number Table 7-1 (Continued) Comparison of Analytic and Test Deflections NESC Hvy T-Wind L-Wind Hvy Vert Strgng Unbal-L Height Case I Case II Case III Case IV Case VA Case VI Vertical Deflections 117.60 15.50 12.20 4.50 6.90 6.20 5.20° 17.04 12.34 3.90 6.71 4.79 4.41° 1.10 1.01 0.87 0.97 0.77 0.854 101.00 18.30 13.40 5.50 8.60 8.30 6.20 20.06 14.45 4.91 8.44 6.43 5.71 1.10 1.08 0.89 0.98 0.78 0.92 2 Deflection from test tower 3 Analytic deflection"Ratio analytic/test Table 7-2 shows the calculated deflections and equivalent tower stiffnesses for longitudinal loads applied at either one shield wire attachment or one outside phase attachment on an 80 ft "A" tower. Table 7-2 Deflections and Stiffnesses Under Torsional Loads Rounded wz"uz"Average Average Load Force Movement Movement Stiffness Stiffness Stiffness Jt Case (1b)(in)(ft)(lb/ft)_(lb/ft)(lb/ft) Longitudinal Load on One Outside Phase w/Yoke 8 T1 2,000 15.8610 1.3218 1,513 8 T2 2,000 16.0085 1.3340 1,499 8 T3 2,000 16.1609 1.3467 1,485 1,499 1,500 Longitudinal Load on One Outside Phase w/out Yoke 8 T1 2,000 4.0789 0.3399 5,884 8 T2 2,000 5.5873 0.4656 4,295 8 T3 2,000 7.4998 0.6250 3,200 4,460 4,500 Longitudinal Load on One Outside Phase w/out Yoke and Guys Pretensioned 8 T1 2,000 2.2438 0.1870 10,696 8 T2 2,000 2.2444 0.1870 10,693 8 T3 2,000 2.7934 0.2328 8,592 9,994 10,000 Note 9,500 used Longitudinal Load on One Shield Wire Peak w/Yoke 2 S81 2,000 15.3892 1.2824 1,560 2 S2 2,000 15.5312 1.2943 1,545 2 S83 2,000 15.8372 1.3198 1,515 1,540 1,500 Longitudinal Load on One Shield Wire Peak w/out Yoke 2 Si 2,000 7.0171 0.5848 3,420 2 S2 2,000 7.0998 0.5917 3,380 2 S3 2,000 8.7421 0.7285 2,745 3,182 3,200 Longitudinal Load on One Shield Wire Peak w/out Yoke and Guys Pretensioned 2 Si 2,000 4.9814 0.4151 4,818 2 S2 2,000 5.0443 0.4204 4,758 2 83 2,000 5.1189 0.4266 4,689 4,755 4,800 In each section of Table 7-2 there are three load cases.The lon- gitudinal load was always 2000 1b,however the vertical load was varied to account for the influence of different vertical loads on the tower deflections.The stiffness is calculated by dividing the movement in ft into the 2000 lb applied longitudinal load.Similar calculations showed that the stiffness of the tower for a load applied at a center phase is 23000 lb/ft with or without the yoke and approximately twice that with the guys pretensioned. The first "X"towers ever built were tested with and without yokes installed.One of the load cases tested was an unbalanced longi- tudinal load at a single outside phase -exactly the case discussed above. These "X"towers were installed on Chugach Electric Association's Beluga Transmission Lines on the west side of Cook Inlet.The towers are lattice aluminum towers which were designed and fabri- cated by Reynolds Metals Company from conceptual designs prepared by Robert W.Retherford Associates. For the tests,the guys were pretensioned to an average of about 2500 lb.With the yokes installed a 3000 1b longitudinal load at the outside phase moved the end of the arm .91 feet.This is an effective stiffness of 3300 lb/ft.With the yokes removed,the same point moved .25 ft for an effective stiffness of 12,000 lb/ft. The end of the crossarm when the tower had the yokes installed moved 3.6 times as far as the same tower without the yokes.By way of comparison,in this study a stiffness of 1500 lb/ft was used with the yokes installed,4500 lb/ft with the yokes removed and 9500 lb/ft with the yokes removed and the guys pretensioned. Some interesting excerpts from the test report follow': "Case No.13,Unbalanced Longitudinal at one outer conductor tip,No Ice,No Wind,Tower top raked 2.5 feet longitudinally with guy yoke included.The tower accepted and held 100%of the required loading with no distortion.Deflections in the longitudinal face ran five times that in Case No.8 without the yoke." "The longitudinal loading cases without the guy yoke assembly developed guy tensions very close to the values used in de- signing the structures.After incorporating the yoke assem- bly,the guy loads realigned themselves as the yoke rotated producing lower overall guy loads.The heaviest loaded guy without the yoke shed a portion of its load to the other guys, increasing the load in some and reducing it in others.This 'Reynolds Electrical Division of Reynolds Metals Company Tower Test Report,Type TX-10 138 KV Tangent Suspension Tower for Chugach Electric Association,Inc.Anchorage Alaska.Reynolds Electrical Division of Reynolds Metals Company,Richmond,Virginia, (1967)Pages 4 &5 phenomenon acted to spread the structural loads from the guys such that there was not one point of load concentration (from one high guyload)but an even distribution on both legs." "The structure proved to be inherently much more rigid than anticipated during design.Deflections under all loading cases were very low in magnitude,less than 1/2 of a foot in every instance except when the yoke assembly was placed in the system.At this time,the crossarm tip on the loaded side moved one foot at 100%load." Another interesting point is that with the yokes installed,the transverse loads are carried entirely by the tower itself.When the yokes removed,some of the transverse load is resisted by the guys,reducing the bending moments in the tower legs. The main disadvantages of having yokes are that there is more move- ment under twisting loads and there are slightly higher bending moments in the tower legs under transverse loads.The additional flexibility gained from the yokes also has some significant advan- tages under other circumstances. Now and again,transmission lines are hit by low flying aircraft, have trees fall onto the wires,or are hit by tornados,avalanches and other extremely high localized loads.These suddenly applied loads with lots of kinetic energy pull the wire into one span, similarly to the unbalanced ice and snow loads.With the yokes installed,the tower twists and moves more with the load,lessening the peak impact loads. Much of the land traversed by the Intertie has frost susceptible soils.There is always a risk of the piles frost jacking,and indeed,at least one structure has had both foundation piles and one anchor pile jack.When one leg only jacks,the yoke redistrib- utes the load caused by stretching the guys as the tower is raised. The yoke twists giving an easily recognized sign of the problem for aerial patrols.Since,with severe jacking,this may not provide enough relief of the loads,the yokes on the towers have a shear bolt in them that is supposed to break before the tower is damaged. The tongue to which the single guy is attached slides through the yoke until it hits a stop.This effectively lengthens the guys. If the yokes are removed,the yoke's shear bolt and slider can be replaced with a scissors mechanism.These are shown in Figure 4. If the shear bolt is properly sized,the tower can be protected against frost heaving and also against some of the unusual longitu-dinal impact loads.It should be noted that this is a change intowerdesignphilosophyandanychangeinherentlyinvolvessome risk. In summary,analysis of the 80 ft A tower shows that removing the yokes will reduce the movement of the tower from 15 to 16 inches to 4 to 7 inches under a 2000 1b longitudinal load on the outside phase.Pretensioning the guys to 5000 lb will further reduce the deflection to between 2 and 3 inches.Tests of the first "X"tow- ers built confirm that differences of this order of magnitude are to be expected.Stiffening of the tower also increases the risk of tower damage if longitudinal impact loads should occur. 8 -MECHANICS OF UNBALANCED SNOW LOADS This section covers the mathematics of why and how much the sag increases in a span which is loaded with snow when the surrounding spans are bare.The contributions of the tower flexibility,the type of insulator,and the elasticity of the wire are discussed. Figure 15 shows a line section of two spans.The left span is bare and the right span is loaded with four inches of radial snow (@ 5lb/ft*).If all three towers were very rigid deadends,the dotted lines would represent the conductor sags.The horizontal component of the tension (H)in the left span is 5089 lb.In the right span H is 13,324 lb.The difference in the horizontal tensions of 8,235 lb per subconductor,or 16,470 lb/phase must be carried by the tower. If the center tower is changed to a type "A"suspension tower with an eleven foot long I-string insulator,the solid lines would rep- resent the conductor sags on an outside phase.Figure 16 shows the movement of the tower and the insulator.The conductor attachment point has moved a total of 3.3 ft to the right,.8424 ft of this is due to movement of the tower and 2.4851 ft to swing of the insula- tor. As the conductor attachment point moves to the right,the tension in the right conductor goes down and the tension in the left con- ductor rises.The movement stops when the difference in tensions is balanced by the horizontal component of the tension in the insu- lator string.The horizontal force on the tower crossarm is equal to the horizontal component of the insulator tension. One way of looking at the balancing process is to look at the spring stiffness each element represents.For a linear spring, stiffness is defined as: 1 Where:(1) F-force lbs x=displacement ft k-spring constant lb/ft The stiffness of the tower is of this form.For the outside phase of the "A"tower,k is 1500 1b/ft. For small movements,the stiffness of the insulator string is: Where: k,=equivalent insulator stiffness (2)=1weight of wire =aweight of insulator Moi]length of insulator The support stiffness is the combined stiffness of the insulator and the tower: 14-2 1+-£(3) t i Where: k,=support stiffness5 k,=tower stiffness k,j=insulator stiffness The combined stiffness will always be less than the smaller of the two stiffnesses.In this example,the insulator stiffness is 501 lb/ft,the tower stiffness is 1500 lb/ft and the combined tower and insulator stiffness is 376 lb/ft. The wire has a spring constant also.It is made up of a factor due to the geometry of the catenary and a factor due the elasticity of the wire.The stiffness due the catenary is: c ”"2aH Where: k,=Catenary stiffness (4) a=span w=unit weight H=horizontal tension S,-stressed length of wires S,7 unstressed length of wire A-area of wire FE -modulus of elasticity of wire Note that the catenary stiffness is dependent on the span and hori- zontal tension.It is highly non-linear and changes as the conduc- tor attachment point moves. The stiffness due to the wire's elasticity is: k,-= Where: k,-stiffness due to wire elasticity (5) A -area E =modulus of elasticity S,=unstressed length The overall stiffness of the wire is: nw Keke 6Where:(6) k,=overall wire stiffness If we look at the wire in the left span in combination with the support (tower and insulator),the total stiffness available to balance the loaded conductor is: Keotal -k,+k,(7) Table 8-1 shows the equations for wire stiffness applied in an iterative fashion to the left span.Table 8-2 shows the right span. Checking overall balance of forces,the force on the support,and overall sum of forces are: F-k x =371x3.3005 =1224.5 (8) Yr-2 (9789.60)+1251.33-2(10414.85)=.83 OK As the number of spans is increased,the support stiffness will remain the same.The wire stiffness decreases in proportion to the number of spans.Neglecting the insulators at subsequent towers, the wire stiffness for "n"spans is: kn n Where: k (9)n7 wire stiffness with n spans to deadend n=number of spans to deadend k,=overall wire stiffnessWw 1.0760 1227.59 0.8010 9307448 660.44 Table 8-1 Left -Unloaded Span w Unit weight of wire lb/ft su Unstressed Len A Area of Wire in E Modulus of Elasticity lb/in? w*Su/2 Support Wt lb Ke Elastic Stiffness of Wire lb/ft gth of Wire ft 6073.11 Stressed k k a da H Length Catenary total dh Saq 1225.000 5089.00 1228.43 746.05 664.43 39.66 0.250 166.11 1225.250 5255.11 1228.46 826.37 727.39 38.42 0.250 181.85 1225.500 5436.95 1228.49 920.88 799.63 37.15 0.250 199.91 1225.750 5636.86 1228.52 1033.07 882.89 35.85 0.250 220.72 1226.000 5857.58 1228.56 1167.50 979.25 34.51 0.250 244.81 1226.250 6102.40 1228.60 1330.20 1091.20 33.14 0.250 272.80 1226.500 6375.19 1228.64 1529.25 1221.63 31.74 0.250 305.41 1226.750 6680.60 1228.69 1775.54 1373.87 30.30 0.250 343.47 1227.000 7024.07 1228.75 2083.92 1551.53 28.83 0.250 387.88 1227.250 7411.95 1228.81 2474.69 1758.24 27.33 0.250 439.56 1227.500 7851.51 1228.88 2975.74 1997.16 25.81 0.250 499.29 1227.750 8350.80 1228.97 3625.28 2270.14 24.28 0.250 567.54 1228.000 8918.34 1229.06 4475.12 2576.54 22.74 0.250 644.13 1228.250 9562.47 1229.17 5594.26 2911.93 21.22 0.078 227.13 1228.328 9789.60 1229.20 5985.40 3014.47 20.73 3.3297 1227.59 0.8010 9307448 Table. Right -Loaded Span 8-2 w Unit Weight of Wire lb/ft gth of Wire ftSuUnstressedLen A Area of Wire in E Modulus of Elasticity lb/in? 2043.75 w*Su/2 Support Wt 1b 6073.11 Ke Elastic Stiffness of Wire lb/ft Stressed k k a da H Length Catenary total dh Sag 1225.000 13298.00 1229.80 1400.89 1138.31 46.97 -0.250 -284.58 1224.750 13013.42 1229.76 1317.24 1082.46 47.98 -0.250 -270.61 1224.500 12742.81 1229.71 1240.84 1030.32 48.97 -0.250 -257.58 1224.250 12485.23 1229.67 1170.91 981.65 49.96 -0.250 -245.41 1224.000 12239.81 1229.63 1106.79 936.17 50.95 -0.250 -234.04 1223.750 12005.77 1229.59 1047.85 893.66 51.92 -0.250 -223.42 1223.500 11782.36 1229.56 993.59 853.89 52.88 -0.250 -213.47 1223.250 11568.88 1229.52 943.52 816.65 53.83 -0.250 -204.16 1223.000 11364.72 1229.49 897.25 781.75 54.78 "0.250 -195.44 1222.750 11169.28 1229.46 854.40 749.03 55.71 -0.250 -187.26 1222.500 10982.03 1229.43 814.66 718.30 56.64 -0.250 -179.58 1222.250 10802.45 1229.40 777.73 689.44 57.56 -0.250 -172.36 1222.000 10630.09 1229.37 743.35 662.29 58.47 -0.250 -165.57 1221.750 10464.52 1229.34 711.31 636.74 59.37 -0.078 -49.67 1221.672 10414.85 1229.33 701.70 629.02 59.64 This indicates that as the number of spans to a deadend increases, the wire resists less of the movement and the support (tower and insulator assembly)more.Figure 17a shows the effect of adding unloaded spans symmetrically on both sides of the loaded span. Figure 17b shows the effect of adding unloaded spans on one side of the loaded span which remains adjacent to a deadend. Looking back at equation (3),the most effective place to increase stiffness in the system is the smaller of the tower and insulator stiffnesses. 9 =RESULTS OF ANALYSIS There are two relatively independent problems associated with the occurrence of unbalanced span to span snow loads.They are theincreaseinsagofthephasescausingreducedclearancetothe ground and the possibility of the outside phases coming in contactwiththeshieldwire. The effects of the unbalanced snow loads on the wire sags and ten- sions were analyzed with a computer program written to model the interaction between the wire,insulator assembly and tower.The computer program is called ICE.BAS (Appendix 3 has an input coding form,a sample input,a sample output and a copy of the current version of the program). Based on a maximum number of spans between deadends,the program is used to calculate the movement of the tower and the insulator in each span and the corresponding horizontal tensions and sags.The tower is modeled as a linear spring with the spring constant based on the finite element analysis described in Part 7 "Tower Analysis &Response to Longitudinal Loads".Table 9-1 shows the spring constants used.The change in length of the wire is accounted for as is the movement of the insulator based on its type (the program does not account for the changes in clamp elevation due to move- ments of the support and insulators). Table 9-1 Tower Spring Constants 80 ft "A"Tower Tower Stiffnesses or Spring Constants lb/ft Outside Center Shield Description Phase Phase Wire Original Configuration 1500 23000 1500 With Yokes Removed 4500 23000 3200 With Yokes Removed and and Guys Pretensioned 9500 46000 4800 Over 160 computer runs were made for different combinations of insulator type,structure stiffness and weights of snow on the wires.The results of the analyses allow some general statements to be made: fe)The increase in sag of the loaded span is a function of the combined movement of the tower and the insulator assembly. .o)Even with the conductor deadended,unbalanced snow loads result in an increase in sag in the loaded span due sole- ly to the flexibility of the tower. 9-1 oO The tower and insulator stiffnesses must be considered together.Increasing the stiffness of the insulator is effective only if the tower is stiff enough and vice - versa,increasing the tower stiffness is only effective if the insulator is stiff enough. °Removing the yokes from the fore and aft guys has a sig- nificant effect on the structure stiffness of the outside phases. fe)With the yokes removed,pretensioning the guys approxi- mately doubles the stiffness of the outside phase. fo)Halving the length of the insulator string doubles its effective stiffness. °Reducing the sag in the loaded span increases the loads on the crossarms of the towers at each end of that span. °One span loaded with snow in the middle of a long tangent is the worst case for ground clearance.One span loaded adjacent to a deadend is the worst case for longitudinal loads on the crossarm of the tangent tower. Sag of the Phase Conductors The sag of the conductor in spans evenly loaded with a 4 in.ofradialsnowwithadensityof5lb/ft?is just under 47 ft.This sag increases to almost 82 ft if only one span in the middle of a long tangent is loaded.The following techniques for reducing the sag and increasing the ground clearance in the loaded span were considered: (o)Modifying the tower-guy system fe)Shortening the Insulator strings fe)Changing the insulators to inverted V-strings °Resagging the conductors Modifying the tower-guy system to increase its stiffness will re- duce the combined tower -insulator movement.The stiffness of the outside phase attachments (and the shield wire attachments)can be increased from 1500 lb/ft to 4500 lb/ft by removing the guy yokes (see Figure 4).It can be further improved to 9500 lb/ft by also tensioning the guys. The present I-strings on the outside phases are 11 ft long.They have a very low effective stiffness due to their length.Increas- ing the stiffness of the tower has very little effect on the over- all movement because the insulator swings more to balance the ten- sions between the loaded and unloaded spans.Table 9-2 shows the effect of increasing the tower stiffness with the 11 ft I-strings. 9-2 Table 9-2 Effect of Tower Stiffness on 345-kV I-String (Middle Spans) Radial Tower Insltr Movement Max Ground Insulator Snow Stiffness Cond Length No Tower Insltr Total Sag Clearance Type in lb/ft Resag ft Spans ft ft ft ft ft Original I-Strng 4.00 1500 No 11.00 15 1.42 3.96 5.37 81.84 -2.09 Original I-Strng 4.00 4500 No 11.00 15 0.55 4.52 5.08 80.25 -0.50 Original I-Strng 4.00 9500 No 11.00 15 0.27 4.71 4.98 79.74 0.01 Original I-Strng 4.00 23000 No 11.00 15 0.12 4.81 4.93 79.45 0.30 Table 9-3 Comparison of I-string Insulators (Middle Spans) Radial Tower Insltr Movement Max Ground Insulator Snow Stiffness Cond Length No Tower Insltr Total Sag Clearance Type in lb/ft Resaqg ft Spans ft ft ft ft ft I-String 138-kV 4.00 1500 No 5.45 15 1.95 2.57 4.52 77.14 8.16 I-String 161 kV 4.00 1500 No 6.40 15 1.83 2.87 4.70 78.15 6.20 I-String 230 kv 4.00 1500 No 7.35 15 1.77 3.13 4.91 79.04 4.36 Original I-Strng 4.00 1500 No 11.00 15 1.42 3.96 5.37 81.84 -2.09 I-String 138-kV 4.00 9500 No 5.45 15 0.44 3.32 3.76 72.78 12.52 I-String 161 kV 4.00 9500 No 6.40 15 0.40 3.64 4.04 74.41 9.94 I-String 230 kv 4.00 9500 No 7.35 15 0.36 3.91 4.28 75.78 7.62 Original I-Strng 4.00 9500 No 11.00 15 0.27 4.71 4.98 79.74 0.01 The lowest tower stiffness of 1500 lb/ft represents an outside phase as presently constructed.In this case (with 4 inches ofradialsnowat5lb/ft')the end of the arm will move 1.42 ft into the loaded span and the conductor clamps at the end of the insula- tor string will move an additional 3.96 ft (an angle of swing of 20°)for a total movement of 5.38 ft.Increasing the tower stiff- ness to 23,000 lb/ft reduces the tower movement to only 0.12 ft - a change of 1.3 ft.The insulator,however,moves .85 ft more to 4.81 ft (a swing angle of 23.6°)for a total movement of .44 ft less of 4.93 ft.The sag is changed from 81.84 ft to 79.45 ft. The reduction in sag -and improvement in ground clearance is only 2.39 ft.The improvement gained by increasing the tower stiffness from 1500 lb/ft to 9500 lb/ft is 2.1 ft. Shortening the insulator string increases its effective stiffness. Table 9-3 compares different lengths of I-strings for two different tower stiffnesses:1500 lb/ft and 9500 lb/ft.With a constant tower stiffness,shortening the insulator reduces the insulator movement while increasing the tower movement.The total movement and sag are reduced.As the insulator becomes shorter and stiffer, stiffening the tower becomes more effective.The reduction in sag due to stiffening the tower is 4.36 ft for the 138-kV I-strings compared to 2.1 feet for the 345-kV I-strings. Inverted V-strings as shown in Figure 8 have a higher effective stiffness than I-strings,their stiffness is in the range of the tower stiffness.Table 9-4 compares a 230-kV I-string with a 230- kV 20°inverted V string (insulators inclined at 20°from the vertical).The inverted V-string is longer than the I-string because of the additional yoke plate needed at the upper end.With a tower stiffness of 1500 lb/ft,the tower actually would contrib- ute more to the movement than the insulator,2.49 ft vs 1.23 ft.In general,with the stiffer insulator,there is more tower movement, less insulator movement,and less total movement. Resagging the conductor is effective across the board,Table 9-5 has the same insulator and tower parameters as shown in Table 9-4 with the conductor resagged.Table 9-6 compares the sags from Tables 9-4 and 9-5.The first two lines in table 9-6 show the bare and loaded sags for 1225 ft spans with all spans equally loaded.With 4 in.of radial snow (density.5 lb/ft?),the sag would be 46.97 ft,resagging the line would reduce the evenly loaded sag by 4.3 ft to 42.67 ft.With a 230-kV I-string,loading one middle span would increase the sag to 79.04 ft,resagging would reduce this increase to 72.1 ft,a difference of 6.94 ft.This table shows that the amount the sag is reduced pretty much carries through across the board for different tower and insulator stiff- nesses. Table 9-4 Comparison of 230-kV I-String and Inverted V-String Insulators Radial Tower Insltr Movement Max Ground Insulator Snow Stiffness Cond Length No Tower Insltr Total Sag Clearance Type in lb/ft Resag ft Spans ft ft ft ft ft I-String 4.00 1500 No 7.35 15 1.77 3.13 4.91 79.04 4.36 I-String 4.00 4500 No 7.35 15 0.71 3.71 4.42 76.62 6.78 I-String 4.00 9500 No 7.35 15 0.36 3.91 4.28 75.78 7.62 I-String 4.00 23000 No 7.35 15 0.16 4.03 4.19 75.28 8.12 20°Inverted V 4.00 1500 No 7.60 13 2.49 1.23 3.72 72.32 10.84 20°Inverted V 4.00 4500 No 7.60 9 1.15 1.82 2.98 67.78 15.37 20°Inverted V 4.00 9500 No 7.60 15 0.62 2.09 2.70 66.05 17.10 20°Inverted V 4.00 23000 No 7.60 9 0.27 2.25 2.53 64.94 18.21 Table 9-5 Comparison of 230-kV I-String and Inverted V-String Insulators With Conductor'Resagged Radial Tower Insltr Movement Max Ground Insulator Snow Stiffness Cond Length No Tower Insltr Total Sag Clearance Type in lb/ft Resaq ft Spans ft ft ft ft ft I-String 4.00 1500 Yes 7.35 15 1.46 2.72 4.18 72.10 11.30 I-String 4.00 4500 Yes 7.35 15 0.60 3.27 3.87 70.24 13.16 I-String 4.00 9500 Yes 7.35 15 0.31 3.46 3.77 69.60 13.80 I-String 4.00 23000 Yes 7.35 15 0.13 3.57 3.71 69.22 14.18 20°Inverted V 4.00 1500 Yes 7.60 13 2.23 0.98 3.21 65.88 17.27 20°Inverted V 4.00 4500 Yes 7.60 13 1.06 1.54 2.60 61.90 21.25 20°Inverted V 4.00 9500 Yes 7.60 13 0.58 1.79 2.37 60.32 22.84 20°Inverted V 4.00 23000 Yes 7.60 13 0.26 1.96 2.22 59.30 23.85 Table 9-6 Conductor Sag Comparison Sag Radial Tower Insltr Present After Sag Insulator Snow Stiffness Length Sag Resagging Diff Type in lb/ft ft ft ft ft Bare Sag NA NA NA 39.72 34.01 5.71 Loaded Sag 4.00 NA NA 46.97 42.67 4.30 I-String 4.00 1500 7.35 79.04 72.10 6.94 I-String 4.00 4500 7.35 76.62 70.24 6.38 I-String 4.00 9500 7.35 75.78 69.60 6.18 I-String 4.00 23000 7.35 75.28 69.22 6.06 20°Inverted V 4.00 1500 7.60 72.32 65.88 6.44 20°Inverted V 4.00 4500 7.60 67.78 61.90 5.88 20°Inverted V 4.00 9500 7.60 66.05 60.32 5.73 20°Inverted V 4.00 23000 7.60 64.94 59.30 5.64 Table 9-8 presents the detailed information for each of the op-tions discussed in the Summary.In this table,results are also given for "End Span or Two Middle Spans Loaded."An end span loaded means that the only the span adjacent to a very stiff deadend tower (no movement of the deadend support is assumed)is loaded.As far as the action of the wire,this is the same as two spans in the middle of a long tangent being loaded.With two spans loaded and symmetrical bare spans on either side,thetensionsinthetwoloadedspanswillbeidentical.The insula- tor string between them will have only vertical loads and will not swing in either direction.This is the same as fixing the conductor to an immovable deadend structure. Shield Wire Conflict with the Phases Table 9-7 compares clearance requirements for various voltages. The 345-kV clearances are the design clearances for the line. The lower voltage clearances are taken from Table VII-1 in REA62-1°. Table 9-7 Phase to Ground Clearance Comparison Operating Voltage (kV) 138 161 230 345 No Wind Clearance 4.0 5.0 5.9 7.4 6 psf Wind Clearance 2.5 2.9 4.2 6.1 High Wind Clearance 1.0 1.2 1.7 2.5 The following options were considered: fe)Removing the shield wire. °Changing the Shield wire to 1/2"EHS to reduce the sags under unbalanced snow loads fe)Shortening the link attaching the shield wire to the struc- ture oO Reversing the shield wire peak to increase the separation from the phases. 'Engineering Standards Division,Rural Electrification Admin- istration,USDA.Rea Bulletin 62-1 Design Manual for High Voltage Transmission Lines.U.S.Government Printing Office,Washington, D.c.(1980) 9-7 Table 9-8 Data on Summary Options Radial Tower Insltr Movement Max Ground Insulator Snow Stiffness Cond Length No Tower Insltr Total Sag Clear- ance Type in lb/ft Resaq ft Spans ft ft ft ft ft Middle Span Loaded Original I-Strng 4.00 1500 No 11.00 15 1.42 3.96 5.37 81.84 -2.09 138-kV I-string 4.00 9500 No 5.45 15 0.44 3.32 3.76 72.78 12.52 161-kV I-String 4.00 9500 No 6.40 15 0.40 3.64 4.04 74.41 9.94 230-kV I-string 4.00 9500 No 7.35 15 0.36 3.91 4.28 75.78 7.62 138-kV I-string 4.00 9500 Yes 5.45 15 0.38 2.99 3.37 67.14 18.16 161-kV I-String 4.00 9500 Yes 6.40 15 0.34 3.25 3.59 68.49 15.87 230-kV I-string 4.00 9500 Yes 7.35 15 0.31 3.46 3.77 69.60 13.80 20°I-Vstring 4.00 9500 No 7.60 15 0.62 2.09 2.70 66.05 17.10 20°I-Vstring 4.00 9500 Yes 7.60 11 0.58 1.79 2.36 60.31 22.84 End Span or Two Middle Spans Loaded Original I-Strng 4.00 1500 No 11.00 10 2.02 5.30 7.31 72.16 7.59 138-kV I-string 4.00 9500 No 5.45 10 0.62 4.00 4.62 63.73 21.57 161-kV I-String 4.00 9500 No 6.40 10 0.57 4.49 5.05 65.13 19.22 230-kV I-string 4.00 9500 No 7.35 10 0.52 4.91 5.43 66.35 17.05 138-kV I-string 4.00 9500 Yes 5.45 10 0.55 3.75 4.30 59.02 26.28 161-kV I-String 4.00 9500 Yes 6.40 10 0.49 4.16 4.65 60.25 24.10 230-kV I-string 4.00 9500 Yes 7.35 10 0.45 4.51 4.96 61.31 22.09 20°I-Vstring 4.00 9500 No 7.60 5 0.78 2.52 3.29 59.02 24.13 20°I-Vstring 4.00 9500 Yes 7.60 5 0.73 2.20 2.93 53.92 29.23 Removing the shield wire obviously cures any conflicts between with the phases that could result in ground faults.The shield wire is installed for lightning protection.Its removal will increase the probability of lightning induced outages (see Part 6 -Lightning Performance). Increasing the size of the shield wire from 3/8 to 1/2 inch would increase the wind load on the shield wire peaks by 37.5%.The structures do not have sufficient excess capacity to make this change. Figure 2 shows the "A"tower.The horizontal offset between the outside phase and the shield wire is 4.65 ft.(5.9 to center of bundle with 1.5 ft bundle spacing).The vertical spacing is 22.5 ft at the tower.The original design was based on maintaining 20 ft separation between the phase and the shield wire with the con- ductor bare and the shield wire loaded with .75 inches of radial glaze ice.This criteria was based on all spans being evenly loaded with ice.Using the typical 1225 ft ruling span with 4inchesofradialsnowat51b/ft*®,the unit weight is 2.1754 lb/ft compared to 1.3086 lb/ft with .75 inches of glaze ice.The sag with all spans uniformly loaded with snow would be 53.34 ft compared with 31.08 ft bare.The bare conductor sag is 39.72 ft. The vertical offset under these conditions would be 8.88 ft and the total clearance would be 10 ft. If only one span of shield wire is loaded,the sag increases from 52.34 ft to 73.44 ft.The shield wire sags over 11 ft past the conductor reducing the clearance to 4.65 ft.Removing the insu- lator and shortening the extension link can reduce the sag but not enough to increase the clearance. Reversing the shield wire arms as shown Figure 3 increases the clearance by twice the length of the arm to 9.15 ft.This is the most effective way to both keep the shield wire and increase the clearance.If the shield wire arms are reversed,the extension link in the shield wire support assembly must be replaced with a shorter link to keep the shoe from hitting the structure under high wind conditions. Tower Loading As the combined tower -insulator stiffness increases,the sag in the loaded span decreases,and the longitudinal load on the tower increases.Figure 18 shows plots of the longitudinal load on the crossarm and the sag versus the total movement for a middle span loaded and for an end span (or two adjacent spans)loaded.This shows that one middle span loaded is more critical for sag and ground clearance while one end span loaded is more critical for loading on the crossarm. For the Type A tower,the critical member under combined vertical and longitudinal loads is the crossarm.The crossarm is a round tube with equal capacity in any direction perpendicular to its axis.The capacity is 17,700 1b applied at an outside phase at- tachment. Figure 19 shows the resultant load on the crossarm for several different insulator assemblies.With the original 11.0 ft I- strings and with the guy yokes installed,the maximum load on the crossarm would reach 15,100 lb with 4 in of snow with a densityof15lb/ft®.This is 86%of the crossarm's calculated capacity. The rest of the curves are based on removing the yokes and ten- sioning the guys.As can be seen from the graph,stiffening the tower-guy-insulator system to improve the ground clearance under unbalanced snow loads also increases the loads on the tower.If much higher densities of snow,or much larger amounts of snow of the assumed density accumulate on the wires,some towers may be damaged.Xe)(10 10 -COST ESTIMATES The cost estimates were based on using a six man crew with a light helcopter,a Hughes 500D or Bell Jetranger.One man would be sta- tioned at the showup to rig loads for the helicopter,the others would be at the site.A further assumption was that the Helicopter would not be used more than the normal minimum average number of flight hours per day of 3 hours. The crew rate was based on $100 per manhour average including ev- erything,ie direct labor,payroll overheads,all equipment except the Helicopter,subsistance pay etc.Also figured on about a 10 hour day on average. Thus the crew rate is 6 men @ $100/mh =$600/crew hr 1 helicopter @ $700/hr @ 3 hr/day -10 h10crewhr/day $210/crew hr Total =$810/crewhr Table 10-1 shows the estimated number of crew hours for each of the options in the summary. Table 10-2 shows the materials required for each of the options. 10-1 Table 10-1 Estimated Crew Hours Change to 230-kV Inverted V's,Resag,Remove Shield Wire ------- Change to 230-kV Inverted V's,Reverse Shield Wire Peak-- Shorten I-Strings,Resag,Remove Shield Wire ----- Shorten I-strings,reverse Shield Wire Pe--|| Options 1 2 3 4 Remove Yokes &Tension Guys Rig Ladders on Structure New Center Phase Attach Reverse Shield Wire Peaks 2 hrs ea 4.00 4.00 Put Shield Wires in Travelers 1 hr ea 2.00 2.00a)°°PPNS°°e°ro)Poh°°Remove Center Phase -Convert to I-string Shorten 2 outside phases 1 hr ea .00 .00bhNM Remove Center Phase -Convert to I-string rig travelers 2.00 Shorten 2 outside phases,rig travelers 1.5 hrs ea 3.00 Clip All three phases 1 hr ea 3.00 Remove Center Phase -Convert to Inverted V-string 4.00 Convert outside phases to Inverted V-strings 3 hr ea 6.00 Hang Travelers at all three phases l hr per phase 3.00 Remove Center Phase -Convert to Inverted V-string,clip 4.00 Convert outside phases to Inverted V-strings 3 hr ea,clip 6.00 Sagging and Reeling Up the OHGW Assume 5 days of crew time per 3 mile section,10 hour days Assum 12 strs per section 4.50 4.50 .00 1.00 00 1.00 Remove Ladders from Str 1.00 Cleanup 1,00 .00 .00 Subtotal 14.00 20.50 20.00 25.50 Showup &Flight Time @ 25%3.50 _5.13 5.00 6.38 17.50 25.63 25.00 31.88 Cost per Crew Hour 810 810 810 810 Estimated Labor and Equipment Cost 14,175 20,756 20,250 25,819 10-2 Resag per deadend tower Deadend Bodies Alcoa Table 10-2 Estimated Material Costs Qty Qty Cat Cntr Out Mfg No Phs_Phs Remove Yokes and Tension Guys Scissor Assembly Special Anchor Shackle Bethea ASH-45 Extension Links Special Preformed Grips Preformed AWDE-4128 Shorten Insulator Strings Center Phase Brekt Special 1 0 Anchor Shackle Bethea Ash-45 1 1 Oval Eye -tongue Bethea OE5-625 1 1 Clevis-Clevis Bethea C-6825-6 1 0 Yoke Plate Bethea C-0112-1P 1 0 Change to Inverted V's Center Phase Brckt 1 0 Anchor Shackle Bethea ASH-45 2 2 Yoke Plate ??1 1 Clevis-Tongue Bethea YCE-65-625 2 2 Clevis-Clevis Bethea CCR-55 2 2 Yoke Plate Bethea C-0112-1P 2 1 Yelevis-eye Bethea RYCE-65-21 2 2 Suspension Clamp Bethea CF-184-N 2 2 Reverse Shield Wire Peaks Anchor Shackle Bethea ASH-45 1 Oval Eye Tongue Bethea OER-5-625 Ll Qty Per str rPrRwWWwWeEMDDDEDHNWOHEHNh12 100.00 1l-EXCERPTS FROM THE NESC In the preceeding sections the effect of unbalanced snow loads on the sag of the conductors and the ground clearance have been dis- cussed.The National Electrical Safety Code establishes require- ments for ground clearances.The following are excerpts from the Code and published interpretations of the code.These excerpts mayprovidesomeguidanceconcerningtheapplicabiltyofthecodeto ground clearance criteria for the unusual loadings covered in this report. The following code interpretation indicates that the code leaves some situations to the discretion of the Owner of the facility. The interpretation was made by the Interpretations Subcommittee fotheNationalElectricalSafetyCodeCommittee,Ansi C2! "Request (June 25,80)IR 270 ',..currently designing a 345 kV line in the high mountain country where the snow cover can reach a depth of almost 15 ft.Since the National Electrical Safety Code,77th Edition,Rule 232,does not specify any special requirements for this condition,we would ap- preciate any recommendations on this clearance problem.' Interpretation (Sept 30,80) The code does not specifically address the question of clearances where snow accumulation in the vicinity of supply lines may be significant.Rules 200,210 and 211 do,however,provide some general requirements." The following are excerpts from the 1977 Edition of the NESC?which was in effect at the time the above interpretation was made. "200.Purpose of Rules The purpose of these rules is the practical safeguarding of persons from hazards arising from the installation,operation or maintenance of overhead supply and communication lines and their associated equipment.They contain provisions consid- ered necessary for the safety of employees and the public. They are not intended as a design specification or an instruc- tion manual.Construction should be made in accordance with accepted good practice for the given local conditions in all particulars not specified in the rules. 'National Electrical Safety Code Committee,ANSI C2 National Electrical Safety Code Interpretations,1978-1980 inclusive and interpretations prior to the 6th Edition,1961.Institute of Elec- trical and Electronics Engineers,Inc.,New York (1981),Page 77. 2 Secretariat,Institute of Electrical and Electronics Engi- neers,Inc.and National Bureau of Standards.National Electrical Safety Code,1977 Edition.Institute of Electrical and Electronics Engineers,New York (1977)Pages 105 &106. 11-1 210.Design and Construction All electric supply and communication lines and equipment shall be of suitable design and_construction for the service and conditions under which they are to be operated. 211.Installation and Maintenance All electric supply and communications lines and equipment shall be installed and maintained so as to reduce hazards to life as far as is practical." The following is an excerpt from the 1990 edition of the NESC? Part 210 has been changed to "Referenced Sections"and Part 211 is no longer used. "010.Purpose The purpose of these rules is the practical safeguarding of persons during installation,operation or maintenance of elec- tric supply and communication lines and associated equipment. These rules contain the basic provisions that are considered necessary for the safety of employees and the public under the specified conditions.This code is not intended as a designspecificationoraninstructionmanual. 012.General Rules All electric supply and communication lines and equipment shall be designed,operated,constructed and maintained to meet the requirements of these rules.For all particulars not specified in these rules,construction operation,and maninte- nance should be done in accordance with good practice for the given local conditions. 200.Purpose The purpose of Part 2 of this code is the practical safeguard- ing of persons during the installation operation,or mainte- nance of overhead supply and communication lines and their associated equipment." The following quotation from Allen L.Clapp*indicates that that pedestrian clearances are based on the height of a person holding a common object in their hand. 3 Secretariat,Institute of Electrical and Electronics Engi- neers,Inc.and National Bureau of Standards.National Electrical Safety Code,1990 Edition.Institute of Electrical and Electronics Engineers,New York (1989)Pages 45 &200. "Clapp,Allen L.,NESC Handbook,1984 Edition.Institute of Electrical and Electronics Engineers,Inc (distributed in coopera- tion with Wiley Interscience,a division of John Wiley &Sons,Inc) New York (1984)Page 174 11-2 "For conductors of all types less than 300 volts to ground the height above pedestrian thoroughfares was increased from 10 ft to 12 ft in the 3rd Edition because an average person could,with an umbrella,reach wires having only a 10-foot clearance,as when a person raises his umbrella at arm's length above his head to avoid hitting that of another person when passing.This clearance ap- plied only where footways or spaces were provided for pedestirans as a thoroughfare.An exception was made to the rule in case of signal wires of less than 150 volts to ground,where a 10-foot clearance was permitted." 11-3 Figures >=N Caswell Lakes Road-Douglas Substation Trees Trimmed 70-71 \1 4 J12.17 40 64 4eohe|a4 84 87 94rT ;HO mi |103 e Sunshine Fault 12/25/90 - |Intermittant |20 mi Wrapped Conductorlw------Snow Removed -Intermittant Spans Wrapped Cond. /1WrappedCond.97-98 0-121 {3s= 30 mi \145 e Talkeetna Fault 12/23/90 Shield Wire Arms Twisted or Wrapped Conductor 5 3 1 0 SeS Fault 12/25/90 SCALE IN MILES @ Curry Fault 1/17/90 242 258 350 pi-63 335 Tree 5/5/8 / 345318PI-62 I py 56Pi-64 /PI-Sop362 331 Figure 1 Fault and Snow Loading Locations 31.5°+31.5°+LL7 "See Detail 1 25.5|moosFAY|,|aeee80'--XTWR-AEI 06/17/92 09:56 Figure e 80'"A*Tower Lg '{'_|-31.5 31.5 NX see Detail 1 be-9,9' 'o 26° 3S N V , ie) wo w o Figure 3 XTWR-AEI 06/17/92 09:56 80'"A'Tower with Shield Wire Arms Reversed and 138-kKV Insulators cmbemeomeodN+--4atk 4 Ld Lys EXISTING PROPOSED ALTERNATIVE YOKE MODIFICATION MODIFICATION Figure 4 Alternatives for Guy Yoke Removal YOK-ASSE 06/17/92 0923 Sieg BLFOUL 18” Figure 35 345-kV I-StringTSS-AE]06/17/92 09157 Sil?8 8 S29 OL siieg ZL AA-8ELAA-19L AA--OLZ ''G AA-BEL Sb¥,0v'9 AA-L91 FSO'L AA OCZ Figure 6 Modified I-String Insulator1010406/17/92TSSS-AEI GroundClearanceftI-String Insulators Middle Span,4"Snow @ 5 Ib/ft*3 10 oS0 SS"10 SSS -20 T T T T 0 5 |10 15 20138kV|930 kV Insulator Length ft161kV.L_345 kV -m™-Twr 1500 lb/ft -+Twr 4500 lb/ft ->K-Twr 9500 lb/ft --6-Twr 23000 Ib/ft -><-Evenly Loaded Spans 25 Figure 7 ||Figure 8 230-kV Inverted TSSV-AEL 06/17/92 09:53 V-String Insulator oReRUNeRae.a..ISOKERAUNIC MAP OF ALASKA Isolines of average number of thunderstorm days per year for the 6.year period,1969-1974 FIGURE 9 50% 402% 30% 20% 10%f 'ma --mM,/hs Ta . ar T t t T t t t 10 20 10 20 10 20 10 20 MAY JUNE JULY AUGUST Percentage frequency of thunderstorm days for the Talkeetna Mountains Sector (solid line)and neighboring stations:Gulkana,Summit and Talkeetna (broken line). FIGURE10 ee BROOKS RANGE BETTLES INDIAN MIN AFS e GALENA TANANA GALM3,FAIRBANKS YUKON-(s @ ' are TANANA q BG OELTA ING uPtano suit |KUSk °TATALINA APS TALKEETNA worm |KW tate -MTNS UL KAMA og = oo. -oe Sectors and neighboring stations chosen for presentation of time distributions of thunderstorm days. FIGURE 11 Single Guy Yoke Guys J Tower Crossarm Figure 12 Plan View of Guys Guys Slack Guys Slack Guy Loaded Slack Guy 5 Guys Approx.;Guy Lightly LoadedGuysEquallyLoadedEquallyLoadedLKorSlack-YL -Guy Heavily Loaded (a)(b)(c) Tower with Yokes Tower with Yokes Tower without Yokes Evenly Loaded Torsionally Loaded Torsionally Loaded Figure 13 Guys Under Longitudinal Loads | (a)(b)(c) Tower with Yokes Tower with Yokes Tower with Yokes Extended Extended and Moved to Crossarm Figure 14 Evolution of Finite Element Model of Yoke and Guys H=9885.08 Ib H=13324 Ib w=1.076 Ib/ft See Fig 16 =y=3'3297 Ib /ft-span=1228.3005'span=1225' 39.716' "Sen,ae80'Woonona en” seleneH=5089 Ib ;w=1.076 Ib/ft 59.252 \-H=10516.92 Ibspan=1225'w=3.5297 lb/ft CP vee 221.6995'a ee '4°radial snow12251225®5 Ib/ft ') Figure 15 Two Span Model of Unbalanced Snow Loads 3.3005'-=-- 0.8424'=} 2.4581?t=-- TOWER STIFFNESS:1500 Ib/ft Figure 16 Detail of Tower and Insulator Movement Sag if Towers and Insulators are Lockec Against Movement (a)Sag 21 SPANS. MIDDLE SPAN LOADED TO 3.3297 Ib/ft.OTHER SPANS LOADED TO 1.0760 Ib/ft. Deadend we (b) 10 SPANS. END SPAN LOADED TO 3.3297 Ib/ft.OTHER SPANS LOADED TO 1.0760 Ib/ft. Figure 17 Multiple Spans with Unbalanced Snow Load in One Span 20,000 16,000 a a ne) re] re} S 12,000 & Oo 3 x m c ro}-8,000 E re] n 0 re)wa oO 4,000 0 Middle Span Xarm Load Middle Span Sag IN " End Span Sag a End Span Xarm Load Total Movement (ft) Figure Crossarm 100 80 60 40 20 18 Loads Sag(ft) ResultantLoadonCrossarm20,000 16,000 12,000 8,000 4,000 iiBareWire4Snow@5pefSnow@10\Xarm Capacity 1it'iI11|iJ1{1|i° ,3 'Y TUT T [i l l |i T T |T ]}|U I l |J T i]{q Y y |T T T | 0 1 2 3 4 5 6 7 8 Unit Weight in Loaded Span (lb/ft) Notes: 1.Tower Stiffness for 345--kV I-String 1500 Ib/ft All Other Tower Stiffnesses 9500 lb/ft Figure 19 Crossarm Loads ayeeeAppendix 1 Previous Reports F EUe ae awe Ce ree 4.BRIAN WH ITE Conculiing Tranmmission Line Engineer D.O.Box 939 Tol.:514-458-4329 Hadron.Quebez Caneda JOP IHo February 18,1991 Mr.Stanley E.Steczkowski Director/Facilities Operations &Engineering Aliaska Energy Authority P.O.Box 1908659 Anchorage,Alaska 99519-0869 Re:Gacond Report on Problems on A/F Intertie Dear Mr.Steczkowski: we have given further thought to the current probiems on theintertieandnavenonewconceptstoaddtothosegiveninthe renort of January 31,1991. Tnere remains the probdiem of trying to give some sort of priority to tne many options that ware proposed and we will give you ourideasatthistime. 1)Ground wire te conductor confiicts. Tn18 18 the most difficult of the three problems on which to pass judgement because we have no knowledges of the frequency of occurence of phase to ground outages caused by low ground wires and no data on the impact of such an sutage on syetem behaviour. Wow much cost and effort is justified to reducs the frequency of such cutages or to eliminate thom completly? Are there any data on lightning outages in this line section that would indicates the effectiveness and need of the present shield wire protection cr is the Keraunic level truly so low that the angle of cover could be greatly increased with negligible effect on performance? Heving acknowledged this lack of background data and presuming that the problem justifies some action,we have listed the three cptions in the order of their effect on the problem.This order is also the estimated order of cost. aj Remove the 17”Tink in the ground wire suepension assembly and replace with the shortest practical linkage which should be about 2"> Removing 1 fcot from each assembly will reduce the potential drop cf the ground wires by about 1Z to 15'under @ single span loadingsuchasthatwhichmusthaveexistedatthetimeoftherecent flashover. promos MEU Feb.13.1991 ©1°55 Pm P@s H._BRIAN WHITE 2. This {s the minimum action that can te taken that will make substantial improvement in the prasent situation. b)The cost of doing anything to the ground wire system will be largely that of gatting men and some equipment to the peaks. If there ig the opinion that tne risk of further flashovers is so large that step a)will not be sufficient,then the added step of reversing the ground wire arm to tne inside will give an extra 4.5" of horizontal spacing between the ground wire and the outer phacos. A short temeperary davit clamped to the peak can be used to support the load of the ground wire (about 400 Ibs.)while the link its removec and shortened,the arm removed and rebolted in new position and then the wire reattached to the peak.It becomes evident that something clever will have to be done to both support the wire and move it from the outside te the inside of the peak, cS)The third option would be the removal of the ground wires for the affected or threatsned section. Tnis nae been done in tre past by many utilities but done as a result of structural Camage caused by excessive longitudinal loads. In eacn case it had been demonstrated to be almost impossibie to reintorce tne existing structures to resist anticipated future Josds. Tnts is not the condition cn thea intertia (based on the racant evidence)as the probtem is that of simple distortion of the system ano we do have means of reducing the distortion as discussed above. The proposal cf a)will cause a small increase in loading cf the peek but there appears to be enough flexibility left so that loads snould not break the peake. if cudsequent storms exceed the resent ones and peaks are broken, then the removal of the ground wires may become necessary. Removal of the ground wires would probably have little effect on lightning performance if the Keraunic level is as low as reported but that true situation is beyond our knowledge. Racommendation;:Remove or shorten the suspension Jinks and,as a next step,reverse the ground wire arms. }Cc r ¢ The problem is again caused by too much flexibility in the system and the solutions are a)and b),to shorten the insulator assemblies,c)to take some of the excessive siack out of the conductors or d)to restrain the longitudinal movement of the conductors with inverted ¥insulator arrangemants. 0 Ware be bed Waevo Fil ros H.BRIAN WHITE 3. a)The present suspension assemblies are 12'long and removal of the 12"link would marginally reduce the flexibility of the system. A rough estimate of the reduction in sag under the recent load conditions would be about 1 to 2'if the links were to be removed to which would be added to the link length for an improvement of two or three feet at most. Thus,there is little justification for taking this step by itself as the benefits are almost inconsequential,being within the variaticns of tne snow ioadcings. Db)AN adequate solution could be obtained by removing the linke Dius about 6 inavilator unite.The immediate result would be a raising of the conauctors by about 4'and a reduction of the sag increase caused by differential snow or ice loading of another 4 to 5'for a total improvement of 8 to 3'. Our information is that the outer phases got within 4 to 6°of the snow and the snow thickness was ostimated at 4'. 12 to 14'above the snow snoulid be much more than enough to preventaccidentsaslongastheloadscausingthesystemdistortionsare about the came as those recently encountered. All of thie leads to the queations of whether an intermediate voltage such as 220 kV could be the final voltage or whether a reduced insulation ievel at 345 kY could be countenanced. Complete conversion to 138 kV clase insuiation is not necessary to solve the current problems. If the links and some insulator units are removed,then the V assemdlies of the center phase will have to be changed to 1 s. (To be noted in ali of thie discussion is the fact that completely normal and typical line desicns can take on very dangerous postures or positions (clearances,etc.)wnen the system is approaching fallure and after a failure there is never any discussion of tha possibly dangerous condition just prior to the fatiura. The racent conditions on the intertie did not appear to be threatening structural failure but the rarity of the unusual Icading event may equate to the frequency of an ultimate failure load and justify a comparable appraical.) c)A significant part of the current problem can be attributed to the relatively low tensions in the conductores. The sag tablee used to inetal the conductors indicate a bare wire final horizontal tension (H)of 4995 1be or 19.3%of RTS giving a sag of 38.8'and elack per 1200'span of 3.365'. S Fed,ld.lveal wile Sy ei roeFrom>HSU H.BRIAN WHITE 4. Having regard for the direction of tha line relative to prevailing winda,the protection given by the tree cover,the uss of dampers and the fact that the line 1s bundled would,in our opinion, justify a 30F final tension of at least 23%with a sag of 32'and a elack reduced to 2.3'., This reduction of sag would improve ground clearance by 36.8'-32'or almost 7'while the reduction of flexibility would reduce the sag shifting under unbalanced ice by about another 4'for a total improvement of more than 10'. Thus a resagging to e&nigher tension limit would give the same measure Of tmprovement as removing the links and about 6 insulator units that 18 discussed in b)}above. A cneck would nave to be made of the effect of higher tensions on the capacities of the angle towars but we would anticipate few serious problems. 0)We have obtained coste of inverted Y insulator arrangemants that could be installed to restrict longitudinal movement of the clamp positions.The lowest estimates work out to about $1500 per phase position to which would have to be added the costs of installation anc moving dampers etc.,the material costs thus excsaaing $5000 por tower, This scheme could be very effective,would not require romoval of the V assemblies at the center phases but has been put aside at present for reasons of high cost of materials and for the fact that the dimensioning ef the V must be cone vary carefully in order to avoic precipitating tower failure. If decisions are made that remeval of insulators as in b)or resagging as inc)ara nov acceptable,then a further lock at d) may be in order. {Subject to further study,a cass might be made that effective restraint of slack shifting might be obtained by inetallinginvertedVrestraintsateverysecondtower,thue cutting costs byenehalf.) Methods of Resagging The resagging ofa long section of tine would be a majorundertakingbutitwouldnotcompromisefutureoperation at 345 KV. A rasagging could te dens in the conventional manner by placingYongsectionsbackintotravellersandretensioning. However there ie a possibility that the resagging could be done byworkingonsectionsoffourorfivespansatatime. Reducing eage by 20%will mean the removal of about 1.3°of conductor from each 1200'span. eron .Hu rer. H.BRIAN WHITE 5. In a 5 span section from A-B-C -D0 -E -F,the conductors could be towered at C and D so that about 6.5'could be cut out near mid-span where the conductor would be close to the ground (the exact amount depending on the span lengths of the section),the clamps elipped about 2.6'at towers C and D and the conductors raised back into position. whether the clamps would have to be slipped at B and E would be a moot point,dependent upon the existing clearance conditions at spans A-3 and E-F. Thus by working only at 2 towers the sags could ba corrected cn ?Tive spans and the work is concentrated in distance s0 that the three phases of more than a mile langth might be completed in a weekend. Seisction of bj or _c) At This point we fear we cannot go further in recommending options regarding improving the conductor behaviour under unbalanced ice or snow loadings. Wa do not know how real the risk is regarding electrical safety for the snow usually is an insulant,the snow events of the past winter may be no more frequent than the storme that could bring down the line,we know not of the coset of the several options nor of the acceptability of limitations on future voltage leveis,nor of the possibility of service outages that might permit or disallow theworkofreseaggingbyeitherofthetwomethods. In summary,the two eignificant options are to remove the links and at Yeast §insulator unite,(preferrably more)or to resag and reduce sags by about 20%and we require some reations from you orothersinAlaskabeforeproceedingfurther. 3)Bundle Twisting We must await examination of a sample spacer before defining the extent of this problem. If the spacers are deficient.then spacers may have to be replaced over ea considerable length of line if not entirely. N.B.Buring an @aritear flyover of this line we noticed and remarked on the very gooc sagging of tre bundies as there appeared to be very few inclined bundles.The line was vary well sagged in. Following the recent storms and not including the @ pormanentiy twisted phase spans,we noticed that there were very many partially twisted spans,avidence of the saverity of the loadinge and givingagocdtndicaticnofthelengthoftheseverlyjioadedsection. H.BRIAN WHITE 4aAll bundled lines suffer sucn indignittes during ice storme but we have never bsfore noticed so much residual distortion. We have given thought as to whether these twists are of réal concern and whether efforts should be made to correct them, especially if any work is dene to resag the wires. We have discussed this with several associates and they all agrees that unless the position 1s more than about 60 degrees from horizontal,notning should be attempted.Cresp and strain theory tells us that the lower conductors have been overloaded compared to the uppers but that the slightly higher tensions in the uppers will cause more 10ng term creep and eventually bring them dewn closer to the lowers. In any event,correcting such uneven sags within a bundle requires the juggling of very vary small amcunts of slack and even if the wires were to be brought back to the flat position,the different stresa histories of the two (one hee alrsady been stretched more than the other)would eventually find them uneven again. Stan,that is as far as we can go at this time. You now have our recommendations for tne ground wire problem of either just removing the Tinks or also reversing the arms;the conductor prcoblem can be resolved by removing the links and some ineulators or by resagging,neither of which ts an easy decision. If we can be of futher help or explain or expand on the above,we remain at your service, With nest regards Yours very truly re ucae p.S.A very late thought about the tilted bundles. There is the possibility that the conductor twisted in the spacer grips during extrames of loading or during other twisting actions and the grips have retained a grip of the conductors in a non neutral poosition,that is,that the spacers are responsible for retaining tha tilt. Tnis could be verified at the time of spacer removal. Such a finding of partial clamp elippage could account for the very large number of tilted spans now in the line. RO Wd GS:7G eet ST Ges LY.BRIAN WH ITE Consulting Transmission |_ine Caaineer DO.Box 939 Tel.:514-458-4329 Ludsen,Quebec January 31,1991CanadaJoPiLto Mr.Stanley E.Sieczkowski Director/Facilities Operations &Engineering Alaska Energy Authority P.0.Box 190869 Anchorage,Alaska 99519-0869 Re:Wet Snow Problems on the Anchorage to Fairbanks Intertie Dear Mr.Sieczkowski: We have made use of all the information and data available to us at this time and arrived at some findings and a few recommendations regarding the current state of the lower part of the Intertie. A few of the issues are clear cut and almost obvious but there are several problem areas where more study,possibly some testing and certainly more discussion of options will be needed. In order to properly organize our thoughts of the total situation, and then to transfer these findings to you,we have to break the subject into the following topics: 1)Discussion of the type of loading 2)Elastic or system distortion? 3a)Flexibility and disortion of the Ground wire system. 3b)Options for improving the Ground Wire system. 4a)Flexibility and distortion of the Conductor system. 4b)Options for improving the Conductor system 5)Twisting and locking of Bundies under ice or snow release. 6)Summary and Suggested Next Actions 1)Type of Loading All evidence and reports verify that the loadings of the several events were of frozen snow,possibly the most destructive,damaging and frustrating type of natural vertical line loading just because of the fact that it strikes unexpectedly and without forewarning or foreknowledge. H.BRIAN WHITE 7 a)Precipitation icing or freezing rain can be a frequent occurence in temperate or cold climes;it falls on roads and sidewalks and recording instruments at airports and few such icing events occur without note and record being taken. Tne data taken by others can be transferred with fair accuracy into radial thicknesses as appropriate wire loadings. Freezing rain will form quite uniformally with few discontinuities and because of reasonably good adhesion.Under melting conditions it will tend to decrease uniformly until a thin shell is left,at which time it may fall off in relatively insignificant chunks. Freezing rain can produce great vertical loads that overstress the wire systems and lower the wires in what is simply an 'elastic distortion'. Freezing rain does not usually produce severe differences in loadings in adjacent spans such as to cause 'system distortions' whereby wires in one loaded span may be lowered very much while those of adjacent spans are lifted. The only recollections that we have of significant 'distortions of the wire systems'have been at times when ice has been large enough to break parts of structures or some of the wires;ie.at very close to ultimate load conditions. NOTE.Throughout all of the discussion of this subject of system distortion and wires down to or close to the ground,we should recognize that the frequency of snowmobiles running up and down and across the rights of way,and the more frequent patrolling by helicopter may just be increasing our awareness of something that has gone unobserved in the past. It is an important part of this work to try to determine if there really are factors in and about this line that are different from other apparently similar lines or is it just that an unusual combination of circumstances has produced the problems of the past month or so. b)'In cloud icing'.It is not necessary to discuss all the 'in cloud'characteristics except to note that 'in cloud'icing can produce great differences in formation of loadings on adjacent spans because the rate of ice deposit is a direct function of exposure to the moisture laden wind.However a line engineer building for exposure to 'in cloud 'can forecast such problems and prepare defences. Stations are frequent where 'in cloud'data can be collected and extrapolations made to comparable sites. H.BRIAN WHITE 3. 'In cloud'icing was an original prime suspect of ours for these Intertie problems but the evidence and reports of all parties nas pointed very definitely to frozen snow and from this point on all discussion will be of that kind of loading. c)Frozen snow.This form of loading has caused many line failures and problems and all are 'unexpected'because there just are no records kept of freezing snow deposits which really is seen simply as wet snow. Children are fond of it for rolling snowballs and making snowmen and it finds little favour with downhil?skiers who would rather have dry powder snow but for all those who have wires in the air, once more it's just a wet snow fall. As we are aware,if the moisture content and temperature are just right,the snow can adhere to almost anything. AS was noted on the X towers of the tie line,the snow fell vertically without wind,building up on the tops of the crossarms and adhering to the inside surfaces of the upper arms of the X and to the steep outer legs of the lower X.There was no snow attached to fore or aft surfaces,a strictly vertical fall of very sticky wet snow. NOTE:In all of the calculations that we have made,an average span and a Ruling Span of 1200'has been used because a check of the Plan and Profiles of the affected section showed a very regular spacing of towers with little variance from 1200'.A temperature of 30 F has been assumed throughout. Furthermore,it should be recognized that Sag Tension calculations are not precise when working tensions exceed 50%of rated strengths.Tne errors involved are of the same order as those produced by the estimate we have made that the density of the frozen snow was about 0.3 compared to the usually used glaze ice value of 0.9. 2)Elastic or System Distortion Attention was first given to the possibility that straight vertical overload could have produced enough stretch in the ground wires to have brought them down to the level of the conductors to produce flashovers,or stretch in the conductors to have brought them close to the ground. H.BRIAN WHITE , 4. The following table gives approximate 6ag values for both ground wires and conductors under a range of loadings,all at 30F. Loading Ground wires Conductors Separation ** Bare 30.”.38.8'33.8' 3/4"ice 43.5'44.6'26.1'Alcoa data 1.5"snow 43'43'25' 2"snow 49'45'21' 2 1/2"snow 54'48'19° 3"snow 60'approx 50'approx 15' 3"snow 60'38.8'(bare)6' *x The ground wires at the towers are suspended 25'above the conductors.The separation shown is this 25'plus or minus the difference in sags. a)Attention is given first to the ground wires and the condition that would have to exist to bring them down to approximate conductor level when slight wind action could bring them close enough for a 60 cycle flashover. On a span of 1200'at 30F and no ice load,the ground wire should be about 33'above the conductors at mid-span and even with 3/4" radial glaze ice on the ground wires,they should not get within 20'of unloaded conductors. Assuming 3"of 0.25 density frozen snow on the wires for a 6.4” overall diameter,(certainly larger than the largest estimate we heard of),the ground wire sag would only get down to within 6'of the unloaded conductors,still not close enough to produce a 60 cycle fiashover. Even a snow thickness of 2.5"on the ground wires and bare conductors would have a vertical separation of about 10',such a snow load taking the ground wires beyond 75%of RTS. There is at least one photo record showing a ground wire below the level of the conductors and even if the conductors were bare (not known),the snow thickness would have to be greater than 3”,a loading of about 4 1b.per foot which would certainly leave permanent extra sag that would be quite evident and would certainly have damaged peaks and fittings. We are not aware of any reports of overall diameters of more than 6",and that is the loading on the ground wires that would have been necessary to bring the ground wires below the conductors by 'elastic stretching'or simple overloading. H.BRIAN WHITE 7 If this line of reasoning,(based as it iS On approximations of loadings and sags)is agreed upon,then the problem becomes that of 'system distortion',whereby the problems are caused by much smaller loads that are unevenly distributed on adjacent spans. The loaded spans pull slack out of adjacent unloaded spans and depending on the flexibility of the support system,sags can increase or even decrease much more than with simple elastic changes. b)In some spans the conductor was reported to be close to the ground. The desigm standard was for a clearance of 30'at 143 F which equates to 37.6'clearance with a sag of 38.8'at 30 F. As noted in the table above,a 2 1/2"thickness of frozen snow will drop the conductors down about 9',a 3"loading about another 3', neither of which bring the conductor closer than about 25'above bare ground. It is evident that 'elastic deformation'will not bring the conductor down to where it was in the recent events. Once more the evidence points to 'system distortion'. 3a)Fiexibility and Distortion of the Ground Wire System. It is of benefit to note several basic relationships of a supported wire in which: The slack,the difference between the length of the wire and the straight line distance between support points = 2 3 2 Slack =8 x Sag /3 x Span =Span /24 xC where C is the Catenary or Parabolic value of H/w. 2 Note that with constant span,the slack is a function of Sag or as expressed another way,with constant tension the slack is a 3 function of Span. Of more significance to this study is the first order relationship that the Sag will change by (3 x C /2 x Span)x change of slack. For the ground wire with 30'of sag in a 1200'span at 30F,and ac value of 1640 lbs./0 273 or 6000',the change of sag to change of stack ratio will be about 3 x 6000 /2 x 1200 =7.5 /1. If the suspension clamp at each end of a span moves inward by 1' for a total slack increase of 2',the span will drop by almost 15'. H.BRIAN WHITE 7 The actual drop will be a little less than this because the reduction of tension will decrease the wire length but the 15' value is a fair number for this kind of study. Coincident with the drop in this span would be a lifting of the wire in the adjacent spans. The sags of the ground wires of this line are very consistent with usual practice,higher tensions would threaten vibration performance. The line is unusual in that the ground wires are suspended on an insulator assembly of 21"length that will readily permit almost 1.5 'of wire to move from one span to another. Most ground wires are clamped firmly at each tower or at most with a very short swing linkage of possibly 6”. The only reason for the long linkage that we can imagine is that the designers were copying a trial insallation on a secton of Hydro Quebec line where unbalanced 'in cloud'loadings had broken several peaks.They added links of about 24"in an attempt to reduce the loads (and prevent structural damage and a permanent outage with the wires down between the conductors)but they recognized that there would be more movement span to span. The flexibility of the ground wire system is furtner increased by the torsionally flexible ground wire peaks and the support arm of about 24"that carries the wire. Reference to the report of the load tests carried out in Korea in 1983 shows that a longitudinal load of 3900 lbs.moved the support point longitudinaly some 22.5 ” It is difficult to separate the part of the movement attributed to the twisting of the peak from the overall deflection of the tower due to stretch of the guys but we will assume that most comes fron the peak itself. The differential loads that exist with the unbalanced ice loads of the recent events certainly were of the order of 4000 lbs.so that an assumption of total clamp movement into a loaded span of 3'or more at each end (from adjacent unloaded or lightly loaded spans) is easy to visualize. If we start with the 2”snow load condition with 49°of sag (see table above)when the sag to stack ratio will be about 2 =3x C /2 Span and with C =H /w =Span /8 x sag or 3673', Change of sag =3 x 3670 /2 x 1200 =4.6 x Change of slack. If 3'were to be added at each end,the sag would increase by 6'x 4.6 or 27'which when added to the 49'gives a total of 76'. H.BRIAN WHITE !This is much more than enough to bring the wires down into the bare or even lightly loaded conductors and far more than enough to bring them below conductors that may be higher than normal because there may be snow on the adjacent conductor spans. We have concluded by this point that the ground wire system has more than the usual amount of longitudinal flexibility and this is a major contributor to the flashover problem. Another contributor to the same problem is that in an attempt to provide almost perfect shielding with a cover angle of 15 degrees, the ground wire has been placed with only about 5.2',a small spacing if the wire drops below the conductor level at which time the smallest cross wind would bring them close enough for a flashover. 3b)Options for Improvingthe Ground Wire System a)The 21"suspension linkage as shown on Dwg.2007/2 can be shortened by about 12”while retaining the insulator but this reduction would be accompanied by a modest increase in the ioad applied to the peak support point. Tne cost and effort to reduce the link length (each tower and peak must be climbed)would not be justified if it were to be done by itself but might be combined with 2). b)The suspension arm is unnescessarily long and the length adds greatly to the torque on the peak and the subsequent longitudinal movement. The best adjustment that could be made with this arm would be to remove them and shorten them or simply replace with a new plate drilled to fit the holes in the top of the present peak and accommodating a longitudinal U bolt offset 4 or 5"from the peak member. There is no need to worry about the 85 degree clearance condition that is shown on the concept drawing 2005/3. This reduction of the torque arm should reduce longitudinal movement by about 15"out of that 22.5"measurement although the overall longitudinal tower movement will not be changed. Combining 1)and 2)could produce a reduction of clamp movement of 2 to 3'at each end of a single loaded span which would lessen the midspan drop by from 4'x 4.6 or 18'to as much as 6'x 4.6 or 26'. We must be aware that this reduction in flexibility would result in an increase in the loads that unbalanced spans would apply to the peaks. H.BRIAN WHITE 8. Without benefit of a detailed analysis (an actual pull test might be needed),our best estimate of the longitudinal capacity of the peak with reduced arm length would be between 5000 and 6000 Ibs. Such a load would be reached with from 2 to 2 1/2”of 0.3 density frozen snow on the span on one side and bare wire on the other. This would be a little more load than the original design target value of 3/4"radial glaze ice on but one span. c)A more modest improvement in the problem of conflict between ground wires and conductors can be had by increasing the horizontal separation or offset of the two. The shortening of the arm could increase the present offset of 5.2'to maybe 7'but an even greater improvement would result from turning the arm to the inside while using the same bolting arrangement. Moving to the inside would increase the present 5.2'to about 10' if the arm were not shortened and might be enough to prevent clashes under modest winds if the wire does drop down to conductor level. The increase in shield angle would not have measureable effect on lightning performance as several recent studies have demonstrated that the shield angle is but a very minor factor in aa rathercomplexrelationship. d)One frequently used solution to ground wire/heavy ice problems is to remove the wires in the affected line sections. The Bonneville Power Administration and B.C.Hydro tong ago adopted a general policy of no ground wires in most heavy ice zones,relying on a low Keraunic level and with ground wires for but a few miles out from stations. We Know of several other utilities in both N.A.and S.A.that have removed .the wires after operations began but these were actions taken because the ice loads were causing structural failures of the peaks and permanent outages. We do not Know of any who have removed the wires simply because of distortion problems. It may be noted that the problems with distortion of the ground wire system of this line seem to have resulted first of all from unequal span loads aggravated by several line characteristics that were introduced in an effort to make the line 'super safe'with regard to other matters. H.BRIAN WHITE 5. The 15 degree shield angle (a conservative value for an icing area) brings the wires almost on top of the conductors,the long suspension arm provides much more than needed swing clearance for the wires (85 degrees)but increases longitudinal flexibility and the suspension string itself (possibly introduced to reduce peak loads)adds to the movement. 4a)Flexibility and Distortion of the Conductor system. The conductor system contains two design factors that make it somewhat more flexible than normal while the tower type seems to be a major contributor to the flexibility. Attention is given first to the conductor system. a)The suspension assemblies are longer than have been used on some similar 345 kV lines but this extra length plays only a small part in the overall problem. However,if the line were to be insulated for 138 kV operation,a reduction from the current 11'string length to possibly 5'or less would reduce the flexibility significantly. b)The conductors have been installed with the controlling tension of 25%RTS at -40F which results in a tension level at 60F Initial of 20%. The NESC control is set at 25%Initial at 60F. Thus the conductors have 25%more sag than called for by the Code and this 25%means an increase in slack of 56%. There is no argument that cold temperature conditions should not have influenced the tension level but having regard to the facts that the line is bundled,that two dampers are used per span and, above all,that prevailing winds are almost parallel to the line, the application of the NESC at -40F was not justified in our opinion. The benefit of hindsight shows that the conductors are also well sheltered from any transverse winds so that reducing sags should be a technical possibility.Slack would be reduced and everyday ground clearances would be increased. 'c)Our interpretation of the few photos at hand shows that the conductors that have dropped the most have been outer phases and it may be that twisting of the towers contributes to the outer phase problem. The guying system is yoked at the ground level (4'yoke)so that the tower has little initial resistance to the twisting that could be caused by an outside phase longitudinal load. WH.BRIAN WHITE 10. Because of the flexibility of the ground wire system as built,we doubt that there is the restraint that was allowed in the tower load schedule of Dwg 2005/2 for load case V.Thus,longitudinal deflections greater than those of the test report can be expected. 4b)Options forImproving the Conductor System The possibly excessive sags and the tower flexibility under torque loading certainly add to the system distortions under single span loadings. A resagging would greatly improve the situation by reducing system slackness and increasing basic ground clearances but would be expensive,even if done by cut out methods. There is not much to be done with the yoking system in the guys for although it may contribute somewhat to the problem,too many other good and valuable characteristics of this X tower are dependent on this same yoke arrangement. There remains the major problem of the flexibility of the suspension system,an 11'(or 10')linkage that just allows too much slack to pass from one span to another. If the insulation can be reduced to that of 138 kV,the conductor to ground problem would be solved but there would remain the ground wire to conductor problem that would have to be taken care of as in 3)above. If the insulation system were to be changed,the center phases could be converted to I strings. Another possible solution would involve conversion of the present suspension assemblies to inverted longitudinal V's by straight replacement or by adding the V's to the present strings. As presently envisaged,each leg of the V's would consist of a 2 section low strength non ceramic insulator at about 45 degrees,one or the other of the strings would pick up the load and restrict movement while the other one would go slack. This change would in effect convert the tower into a semi-strain type and could not be attempted without checking on the capacity of the towers to resist the changed loading conditions. A conversion to or the addition of V's would be expensive. The ground wire to conductor problem is potentially a serious one but its real impact on operations will only be known with passage of time.What will be the real frequency of outages caused by contacts or near contacts? Ly BRIAN WHITE ll. The conductor to ground problem is the more serious problem and possibly should receive first attention although,as a large part of the costs of any modification will be those of access to the tops of the towers,there may be value in trying to solve both problems at once. HW.BRIAN WHITE 2. 5)Twisting of Bundles During the inspection by helicopter on January 23,it was noted that at least 9 phase spans were twisted and remained locked,2 spans having either double or triple twists. This is a potentially dangerous condition for even modest wind action can cause the conductors to abrade at the crossover points. Furthermore it may be found quite difficult to bring the bundles back to their normal states. We have never seen more than the occasional single twisted span following a storm so that the large number on this occasion indicates that the ice (snow load)and accompanying activity was truly exceptional or that there is a serious design deficiency in the conductor system. At this time and with only limited knowledge of the spacer system (design and spacings)we tend to suspect that although the loadings were severe,the spacer system is not adequate for tha conditions of this line. Background From 1955 to 1958 we were responsible for the design and construction of twin 345 kV lines north of Lac St.Jean in Quebec, lines using twin bundles for about the first time in N.A. Experiences and tests in Sweden,where bundles had been recently introduced,alerted us to this problem of twisted phases to the extent that we joined in a test program being carried out by the BPA at a site at Pullman,Wa. The BPA had the same concerns regarding bundie behaviour under ice loads and specially with ice release and,on the test span,sand bags were loaded and then released by electrical fusing to simulate ice dropping. With some spacer designs and some spacings,the bundles would remain twisted and with others,the phase might first twist but immediately return to the flat position. The secret to success was found to be that the clamps of the spacers must grip the conductors securely and not permit slipping or rotation which would release the torque that is needed to restore the conductors to their flat positions.This grip must be retained after many years and many temperature cycles and at the low temperatures coincident with ice on the conductors. To our best knowledge ,the 345 kV lines built more than 30 years ago in Quebec have had many ice loadings but have never remained with twisted spans,the result of giving proper attention to the qualities of the spacers that ensure retention of the torque in the conductor. H.BRIAN WHITE :13. The potential problem of bundle twist becomes even more serious with quad bundles so that,during the design studies of the many long crossings of the Hydro Quebec 735 kV system,a very involved study was made of the spacer system and of the needed qualities of the proposed spacers. As consultant to H.Q@.on the design of these lines,we performed the studies of spacer specifics and spacings,basing our work on theory developed by engineers of Sumitomo of Japan. This problem of bundle twist also arose on the large crossing of the Kooteney Lake in Western Canada several decades ago and the problems of restoring the heavy long spans of wires to neutral position made us aware that prevention is much better than constant attempts at repairing the situation.As much as is reasonable must be done to prevent occurances. Spacer Design The torque capacity of the clamps is a major item and it is usually one of the two prime matters in any specifications for spacers for lines subject to icing,the second being the strength or stiffness of the spacer body itself. The specifics usually refer to the needed torque capacity of the spacers which will vary with the J value or torsional stiffness of the proposed conductor and with the anticipated spacing of the spacers because the possible limit of torque will vary inversely as the length of the subspans.This torque capacity can be measured by clamping the spacer to a length of conductor and applying a torque sufficient to rotate a sub span length by a half turn. Our suspicions regarding the adequacy of the current spacer system (spacers and spacings)arise from a look at the design drawing of the spacers used on the intertie (dwg.no.2012/1)in which they appear to have very little if any method for tightning the grip on the conductor. Furthermore the Design Specifications accompanying the Invitation to Bid NO APA-83-R-0011 make no reference to required torque strength or gripping strength other than that 'they shall have sufficient bearing area so that in gripping the subconductor, there is no deformation of the aluminum strands'. There appeared to be no concern for the problems of spacer behaviour under icing activity and chat lack of specifics, combined with the many recent twisted spans and the mere appearance of the spacer as in the design drawing,force the conclusion that the spacer system requires attention. H.BRIAN WHITE a. Recommendations. A program of tests is suggested for the spacer units,including testing of some units taken from the ends of some of the twisted sub spans of the recent event. The grip of these units is enforced through an elastomer insert of some material,rubber or neoprene or a relatively soft compound of some kind.The cold temperature behaviour,stiffness and especially the creep characteristics of this substance must be appraised as well as the method of bonding the two interfaces. Following this detailed study,the ability of the spacer as a whole to restore a flat position should be studied. If it appears that the spacers are not adequate for the needs, then the current units could be moved down closer to midspans and new more effective spacers applied near the ends of the spans where the duty is more severe. If our suspicions of inadequacy prove to be correct,modifications to the line will be costly (access and installation costs)and some judgements will be needed regarding the severity of the revisions and,above all,on the sections of line that snould be modified. Vertical Bundles Some utilities use vertical twin bundles and the suggestion has been made that conversion to a vertical bundle might reduce or remove this twisting problem. The installation of a vertical bundle requires a bit greater sag in the lower conductor so that it in effect is slightly supported by the upper conductor.An icing or frozen snow event will still produce unequal wire loadings with the 'upper'sometimes brought below the 'lower'and there will still be about the same tendency to twist upon release of the ice. However if the 'lower'is now on the wrong side of the 'upper', the work of returning to the correct position will be greatly increased (almost impossible). We know of no one who has used a vertical bundle with success through a significant ice event. H.BRIAN WHITE Span twists as 1 =meztenenmMhETEhumOOphase phase phase phase phase phase phase phase phase noted Jan.23,1991.(e &o e) 37-38 in the end sub span. 41-42 at about 150'from ends. 44-45 45-46 posssibly double or triple wrap 47-48 63-64 at about 150'from ends 70-71 83-84 150-151 appears to be a double twist 15. H.BRIAN WHITE 16. 6)Summary _and Suggested Next Actions It has been found that the flashovers between wires and the very low conductors are the result of system distortions whereby unequal span loadings of frozen snow have moved slack from one span to another. Some conductors have dropped too close to the ground while ground wires have dropped to or below the level of the conductors. There have also been at least 9 cases of span flips with the bundles remaining in a locked position that is conducive to rapid abrasion of the aluminum wires. Some modifications that would reduce or possibly eliminate the problems have been described in the above pages. The next stage of work will be for those who have access to cost data to put some costs to the many options and to start to rate the many options with respect to these costs and their possible effectiveness. Judgements must be made as to which would or would best fit the future operation of the line. After all interested parties have reviewed the above and made these assessments of costs and preferences (related of course to degree of improvement)and then listed questions and requested clarifications,there may be need for further discussion to select and plan the next steps. We remain of course at your service for assistance in any way you need. We shall be away from Hudson until about Feb.16 but will attempt to contact you or Eric about the 10th to learn if there are any immediate problems or questions about this report. This report and the needed calculations have been prepared in rapid order and we trust that you will forgive any errors or lack of syntax that have not been caught. With best regards Yours very truly _fusu lage IDRPYDEN f LalRue,INC.CONSULTING /ENGINEERS 6436 Homer Drive,Anchorage,AK 99518 Mailing Address:P.O.BOX 111008,ANCHORAGE,AK 99511-1008 (907)349-6653 e FAX 522-2534 January 8,1990 Mr.Remy Williams ALASKA ENERGY AUTHORITY P.O.Box 190869 Anchorage,Alaska 99519-0869 Reference:Alaska Energy Authority Anchorage/Fairbanks Intertie Subject:Design Practice for Ground Clearances under Unbalanced Span Loads This letter is a follow up to our brief report of November 1, 1989 regarding conductor ground clearances at Caswell Lakes and Hidden Hills roads.The initial investigation revealed that if only one span in a long tangent section were heavily loaded the resulting ground clearance would be greatly reduced.Also,the report and our discussions concluded that:(1)the conductor has probably not been stretched beyond the elastic limit;(2)this particular line loading condition is not directly addressed as a clearance requirement in the NESC;(3)the design was typical for this voltage line;(4)additional review of the operating records should be conducted to try and determine if the problem could be isolated to a few locations;and (5)research of the design and operating practices from additional outside sources should be made to see how this problem is handled elsewhere.The latter two items are the purpose of this letter. A search of the Anchorage/Fairbanks Intertie records and discus- sions with operations personnel show that low conductor clear- ances resulting in tree contact outages have occurred twice since the line was energized.The first on February 5,1988 when the line was tripped due to a tree near the Susitna River.The second was on January 6,1989 when the conductors near Tower 70 (this is the location of our original investigation)and Tower 128 were sagging lower than existing trees in the right-of-way. This event followed a significant snow storm.At that time oper- ating personnel cleared portions of the right-of-way between Structures 70 and 71 to reduce further outages;additional clear- ing was done between Towers 197 to 223 at a later date.Two out- ages for this period are not particularly significant,but the highly reduced ground clearance is of concern.This specific problem was discussed with other engineers. Alaska Energy Authority January 8,1990 Remy Williams Page 2 We have talked with several engineers in Canada and outside con- cerning design consideration of span to span unbalanced wet snow and ice loads.The following engineers discussed the situation with us: °H.Brian White -an independent consultant and lecturer in transmission line design.Mr.White has a distin- guished international career in the transmission line industry since 1945.He is a recognized authority on transmission line failure analysis throughout the world.He has worked as a special consultant in more than fifteen countries and has published over thirty- five technical papers.Brian recently taught about conductor and movement of slack between spans at the December '89 short course on transmission design held by the University of Wisconsin and has served on a nun- ber of IEEE,CIGRE,and IEC committees concerned with technical standards for transmission lines. fe)Frank Denbrock -a principal of Denbrock and Assoc. Consulting Engineers and Vice Chairman of ANSI Commit- tee C2 which is responsible for the NESC. fe)Robert C.Peters -Director of T &D Engineering for SEGA Engineering and a member of the IEEE Working Group Subcommittee Coordinating Towers,Poles and Conductors Revisions to the NESC fo)Don Nagel -a transmission engineer with Saskatchewan Power fe)Dave Armstrong -a transmission engineer with British Columbia Hydro fe)Jerry Redding -a transmission engineer with Bonneville Power Administration fe)Lee Belfore -Chief ,Transmission Standards Branch of the Rural Electrification Administration fe)Don Heald -Transmission Engineer for the Rural Elec- trification Administration Excerpts from some of their comments are: fe)Brian White related an instance that involved the Kemano-Kitimat line.The span was an 800-foot span with 80 feet of ground clearance adjacent to a 2,200- foot span.Under an unusual loading condition,the 800-foot span was iced and the 2,200-foot span was bare.The 800-foot span lost 40 feet of ground clear- ance by pulling wire out of the 2,200-foot span.The other 40 feet of ground clearance was lost by the Alaska Energy Authority January 8,1990 Remy Williams Page 3 buildup of a snow cornice.Brian found out about this when he was called by people that had been standing on the cornice looking down at the line in the snow. fe)Jerry Redding was not aware of an incidence of this type of loading on the BPA system. fo)Lee Belfore related that heavy ice loads at some Coops in North Dakota have reduced ground clearance on oper- ating lines to 6 or 8 feet. fe)Don Heald of REA stated that he has reviewed hundreds of transmission line designs and never seen a require- ment for ground clearance with unequal span loadings. [o)Dave Armstrong knew of one instance where unbalanced ice loading resulted in reduced ground clearance,but BC does not consider this for ground clearance. fe)Don Nagel stated that the operational personnel watch for normal hoar frost and knock it off. Without exception the above agreed that: fe)Design practice in the U.S.and Canada does not nor- mally address ground clearances when one span is loaded with ice or wet snow and the adjacent spans are not. Several of those noted above knew of isolated instances of low sags that have occurred on other systems under conditions analo- gous to those at Caswell Lakes Road.They would expect it to occur on the typical high voltage line under the same circum- stances. Further,those familiar with the NESC agreed that: fo)The NESC does not address ground clearances when one span is loaded with ice or wet snow and the adjacent spans are not. Based on our discussions with the listed experts,it is apparent that typical design practice does not consider ground clearances under span to span unbalanced snow and ice loading.They also consider their lines to be in conformance with the NESC.The phenomena is known but has not been considered probable enough to change the utilities design. To demonstrate the relationship of slack and sag,we considered a typical Alaskan transmission line with an 800-foot span of Dove conductor with ;inch radial ice.An insulator movement of 6 Alaska Energy Authority January 8,1990 Remy Williams Page 4 inches at each end will cause an increase in sag of 6.4 feet. This would happen with an initial tension before the movement of 8342 lbs.and after the movement of 5925 lbs.An additional 6.4 feet of sag would bring the typical 115 kV line with 23 feet of ground clearance down to less than 17 feet.Six inches of move- ment in a suspension string is easily possible and this is with-out consideration for pole movement.This indicates to us that a typical wood H-frame line could,under the right circumstances, also see a substantial reduction in ground clearance due to un- balanced wet snow or ice loads;i.e.probably many transmission lines in Alaska and elsewhere would not have rule 232 ground clearance if this extreme unbalanced span to span loading were to occur. Given that such a situation can be created,the next step is should the code or a prudent designer consider this condition. Two of the engineers that reviewed this with us are on the NESC committees to consider just this sort of question and they bothstatedthatithasnotnordotheyexpectsuchunusualloadingconditionstobespecificallyaddressedbytheNESC.The reason is that this type of loading is considered rare and not practical for a design parameter.The purpose of the NESC is rules for the "practical safeguarding of persons"Section 1,010.The "NESC Handbook"(by A.L.Clapp,Chairman of the ANSI Committee C2 for the NESC)emphasizes that the term practical is "intended to achieve a reasoned balance between the public's needs for both safe utility service and economical utility service"Section 1, 010.The NESC is a safety code intended to provide a guideline for safe and practical power systems. We do not believe the Anchorage/Fairbanks Intertie is in viola- tion of the guidelines or the intent of the NESC.If there is, however,a local loading condition that has a reasonable prob- ability of recurring,then it must be dealt with.If not already being done,consistent gathering of adequate data to allow evalu- ation and analysis of such problems should be started.The oper- ations staffs can be particularly helpful here by patrolling lines looking for this condition when wet snow and ice storms occur,documenting the incident and removing the ice when found. This would also test one of the responses that has been sug- gested,which is treating this as an operational problem.If, after evaluating the data furnished by the utilities,this is a reasonably probable phenomena,we suggest the railbelt utilities develop an Alaskan design or operating criteria to be applied consistently on all lines in the railbelt area. After gathering the historical data,if any concern remains about whether the Anchorage/Fairbanks Transmission Intertie is designed in accordance with the NESC or whether the code addresses the un- balanced wet snow conditions that resulted in the reduced clear- ance over Caswell Lakes Road,a submission to the Interpretations Committee for the NESC requesting an interpretation should be considered. Alaska Energy Authority January 8,1990 Remy Williams Page 5 Some other things that could be done include analyzing several typical Alaskan lines,including the Anchorage/Fairbanks Inter- tie,to determine the theoretical extent of reductions in clear- ances.This can be done using the "BRODI"computer program available from EPRI. During the interim there are several options that we believe should be considered for the southern section of the Anchorage/Fairbanks Intertie are: fe)Continue to collect as much data as possible on line loading conditions in this particular area,including distribution lines.Try and correlate this data to see if a pattern of specific locations are involved. fe)There are only two road crossings of the Anchorage/ Fairbanks Intertie in this particular area.Consider the installation of short wood pole structures at the crossings to either force a line trip or to provide additional temporary ground clearance. °For the road crossing spans consider the installation of double longitudinal suspension strings to reduce insulator swing. Before any of the above options is implemented,careful consider- ation should be given to the implications of modifying the time proven design criteria applied in the past for transmission lines here in Alaska.Our investigations to date show neither the NESC nor typical utility practice are violated.It would seem prudent to move ahead with the investigation of the phenomenon in Alaska, but leave the question of whether this condition is within the normal operating risks to be answered after more data is collect- ed.This incident offers an opportunity for cooperation between engineering and operations to identify the factors actually affecting system reliability and to search for practical engi- neering and operational solutions. The operational aspects of dealing with this phenomena have not been reviewed with outside experts.Operational procedures tend to be customized to the exact local problem more than is the nor- mal line design.We are designers and have therefore emphasized the design aspect rather than the operations.We suggest that someone from the operational side follow up and inquire as to the procedures used by outside utilities. Based on our original report and subsequent review with outside experts,we believe the reduced ground clearance at Caswell LakesRoadisanexplainableconditionthatcouldoccuronmanylines in Alaska.Severely reduced ground clearance is not reasonable if this condition is a common occurrence.Our conclusion and recommendation is that more data needs to be collected.If the Alaska Energy Authority January 8,1990 Remy Williams Page 6 data shows these loadings are highly probable then they need to be included in a practical Alaskan transmission design criteria. In the interim it appears to be an operational concern that can hopefully be assisted with investigation into other utility prac- tices. DRYD &LaRUE,INC.WWaeDelbertS.LaRue,P.E. DSL:jfancfbk.1tr IDRYDEN j A AIRUE,ENC.CONSULTING /ENGINEERS 6436 Homer Drive,Anchorage,AK 99518 Mailing Address:P.O.BOX 111008,ANCHORAGE,AK 99511-1008 (907)349-6653 e FAX 522-2534 November 1,1989 Mr.Remy Williams ALASKA ENERGY AUTHORITY 701 East Tudor Road P.O.Box 190869 Anchorage,Alaska 99519-0869 Reference:Alaska Energy Authority Anchorage -Fairbanks Transmission Intertie Subject:Ground Clearances at Caswell Lakes Road and Hidden Hills Road CONCLUSIONS: A survey was made on October 19,1989 to determine the clearance of the Anchorage -Fairbanks Transmission Interties above Caswell Lakes Road and Hidden Hills road.At the time the survey was made the clearances were 46 ft.above Caswell Lakes Road and 64 ft.above Hidden Hills Road.The locations where clearances were measured are shown on the attached exhibits A,B,and C. The wire tension at the low point of sag was calculated based on the clearance measurements.The calculated tension was 5,074 lbs.at 32°F.The design tension of the wire at installation (initial tension)was 5,549 lb.The tension which would be expected in the wire after ten years of service (final tension) at 32°F is 5,038 lbs.As most of the change from initial tension to final tension takes place in the first few years after installation,the wire is at about the tension one would expect for its age. The design ground clearance of 30 ft.is typical of 345-kV lines and is in compliance with the NESC code.The existing ground clearances are consistent with the design requirements.The overall design of conductor and hardware appears to follow standard practice for 345-kV lines. Alaska Energy Authusity November 1,1989 Mr.Remy Williams Page 2 BACKGROUND: The Anchorage -Fairbanks Intertie suffered an outage due to contact between the line and trees in the right-of-way below the line where the line crosses over Caswell lakes Road.Dryden & LaRue was asked to determine the present ground clearance in that span and in the crossing over Hidden Hills Road.They were also asked to assess whether the clearances are in conformance with the NESC code. Our understanding is that wet snow had bridged between the two subconductors in the span between Strs.70 and 71.The adjacent spans -as many as six on either side -had bare conductors.The insulator bells from the adjacent bare spans were swung into the span with wet snow still on the wires.The estimated ground clearance was 12 ft.A 12 ft.spruce was used to knock the snow off which allowed line to jump back up to an unloaded position. FIELD MEASUREMENTS: Caswell Lakes Road:(See Drawings A &B) A point "A"was set directly under the center of the east phase between Strs.70 and 71.Sights were taken to the attachment points of the east and west phases of both Strs.70 and 71.A point "B"was set 152 ft.east of point "A"perpendicular to the line.From point "B",sights were taken of each phase.The air temperature was 34°F during when the data was taken.At the start of the day some wet snow was clinging to the conductor. Most of the snow had dropped off by the time the wire elevation sights were made.The conductor temperature has been assumed to be 32°F. Sights were also taken of two of the taller trees,a spruce anda birch.Distances from point "B"to the trees were taken using stadia. While at Point "A"sights were taken to the belly of the sag of the east phase in the spans from 69 to 70 and 71 to 72.Sights were also taken to the east attachment points of the phases at 69 and 72,the west phase at 72 and the shield wire attachments at 69.This data has not been reduced or used in this review. Hidden Hills Road:(See Drawing C) Elevations of trees on either side of the road were estimated using a 25 ft.range pole and a rule to extend the range pole. There was a 31 ft.spruce approximately 20 ft.north of the road and a 38 to 40 ft.spruce approximately 25 ft south of the road. A point was set under the center phase on the north shoulder of the road.A second point was set on the shoulder of the road 127.7 ft.to the west.Sights were then taken on all three phases. Alaska Energy Authority November 1,1989 Mr.Remy Williams Page 3 CALCULATIONS:(See attached calculation sheets) Caswell Lakes Road: The sights to the attachment points at Strs 70 and 71 were used to calculate the location of point "A"in the span.Using the profile for the east phase as a basis of elevation,the attachment elevation at Str.70 was calculated as .5 ft.lower than shown on the P &P sheet.The attachment elevation at Str. 71 was 1 ft.higher.The calculated span was 1030.5 ft.compared to the P &P sheets 1030 ft.Clearances above the road,based on the elevation of the road at Point "A"ranged from 46 ft.to 48 ft.The elevation sights were used,along with the wirepropertiestocalculatethetensioninthewire.This allowed a template to be made (The 32°F Survey curve,dwg.B)to show the wire position over the whole span.Using the provided stringing sags information,we used a computer program to calculate initial and final sag tension data.It appears that the ground clearance curve is based on a 167°F temperature and that the final tensions are governed by long term creep in the wire. Some very rough calculations were done to see if there was sufficient wire in the span to sag within about 12 ft.of the ground if the insulators swung into the span.This was done by calculating the arc length of the wire assuming all spans had wet snow.The wet snow was dropped from the adjacent spans and the insulators were assumed to swing several feet into the span between Strs 70 and 71. The same length of wire was assumed on an effectively shorter span and the tension and sag calculated.These rough calculations show that the wire could sag to about 12 ft from the ground with a snow weight which would not affect the final sag of the wire. Hidden Hills Road: The wire clearances were calculated as from 64 ft.to 66 ft.. As noted above,the line appears to be designed as a normal 345- kV line and is functioning per the design.Please let me know if you need any more information. DRYDEN &LARUE,INC. "los ra LZ.°Lt lta tome. Alan B.Peabody P.E. ABP:dh/aea/survey.ltr Enclosures 90225 >NLINEOFSIGHTFORCLEARANCESCONSULTING /ENGINEERS parE:}/1/99 By:ABP CASWELL LAKES RD PLAN 'Oo 2S i oft jo " 3 i <xXSoc)we +- Es i oy /IDreypen ¢ILalRue DRAWING NO. A 90225 A ,0t=,1'H00t=,1 A1VOS | 7 pT ee QI]x -- O9T NNieAlSyaS bp ONnyd > >Q Houle? - os7 aip aAYND 10Hd}d - OF A314 AAMYS AAUND AAS4ov da -Ott AAs” a ANSNXdhd sle _ _. _ 1=0th "16 Fb509 4 OnE lekOTTIRP EET A S1S)>=&=&i)Cyacvy)Louv=xoso1x - >Ly)LUsscyWwW<C)Lu3gfsa2eo&> Tawf=YyAr7> soHaQsss 90225 x o w 2 4 ot3PLo).° 5 -_ =x is a © w-|fo) c |* | |LJ |4 <|os; ep) wv | a | o OQ | ©{a hy Ta) e : 2 |=Ss |2&i,a \4)sa ANYS ,$49 NG | | wy - || | ;|* S S g g g g o vy Cy x at nas /DRAWING NO.Devore LalRue |HIDDEN HILLS RD bare:u/1/39 ELEVATION C ay AGP Appendix 2 Ground Snow Densities McKinley Talkeetna kk Mckinley Park kk ANFWNEAnWNPRGround Snow Densities Outage December 8,1986 "Near Healy Sub" Park December 6 to 10,1986 Water Year 1985 Not available Outage February 5,1988 "Tree near Devil's Canyon" February 1 to 6,1988 Water Year 1988 Min Max Water Temp Temp Snowfall Equiv Densit °F °F in in lb/ft -9 25 0.00 0.00 -17 24 0.00 0.00 12 19 0.00 0.00 18 27 0.00 0.00 20 31 0.00 0.00 21 33 0.00 0.00 Outage February 5,1988 "Tree near Devil's Canyon" February 2 to 6,1988 Water Year 1988 Min Max Water Temp Temp Snowfall Equiv Densit °F °F in in lb/ft 5 28 1.70 0.10 3.67 -10 8 0.00 0.00 -20 2 0.00 0.00 -20 17 0.00 0.00 -5 25 0.00 0.00 -7 29 0.00 0.00 A2-1 Outage October 6,1988 "Between Healy and Cantwell" McKinley Park October 3 to 6,1988 Water Year 1989 Not Available Outages January 2,6,and 10,1989 Trees at Tower 70 and 128 and possibly other locations Talkeetna December 30,1988 to January 12,1989 Water Year 1989 Min Max Water Temp Temp Snowfall Equiv Densit Date °F °F in in lb/ft 24 -17 16 0.30 0.01 2.08 25 15 24 2.30 0.10 2.71 26 7 25 0.00 0.00 27 22 26 0.80 0.01 0.78 28 24 27 2.70 0.15 3.47 29 12 28 0.40 0.01 1.56 30 11 21 0.90 0.03 2.08 31 21 27 2.30 0.17 4.61 1 12 30 1.50 0.08 3.33 kk 2 -5 18 0.00 0.00 3 -19 -1 0.00 0.00 4 -24 10 0.40 0.04 6.24 5 -5 15 0.60 0.04 4.16 ek 6 -5 22 1.60 0.11 4.29 7 13 25 0.70 0.02 1.78 8 14 24 0.30 0.01 2.08 9 5 20 1.90 0.12 3.94 **10 5 22 6.40 0.24 2.34 11 22 32 0.90 0.02 1.39 12 13 26 3.30 0.05 0.95 13 -12 13 0.00 0.00 14 -10 10 2.00 0.13 4.06 A2 -2 Talkeetna TalkeetnaANrWHN kk Outage April 6, "No cause found" Outage January 17, April 2 to 6, 1989 19389 Water Year 1989 Max Water Temp Snowfall Equiv Densit °F in in lb/ft 44 0.00 0.00 43 0.00 0.00 43 0.00 0.00 41 0.00 0.00 42 0.00 0.00 1990 "60 miles north of Douglas" January 7 to 24,1990 Water Year 1990 Max Water Temp Snowfall Equiv Density°F in in lb/ft 16 2.30 0.18 4.88 16 0.90 0.04 2.77 24 0.00 0.00 19 0.50 0.02 2.50 29 3.40 0.19 3.49 29 0.60 0.04 4.16 29 1.90 0.10 3.28 28 1.20 0.04 2.08 25 10.00 0.38 2.37 30 19.70 1.56 4.94 33 10.40 0.53 3.18 32 1.50 0.05 2.08 31 1.50 0.10 4.16 30 0.40 0.02 3.12 31 0.00 0.00 23 1.70 0.10 3.67 26 1.20 0.07 3.64 18 1.10 0.07 3.97 A2-3 Outages December 23 and 25 to 31,1990 35,39 and 46 miles north of Douglas Talkeetna December 19 to 31,1990 Water Year 1991 Min Max Water Temp Temp Snowfall Equiv Densit Date °F °F in in lb/ft 19 12 25 5.00 0.29 3.62 20 25 29 7.50 0.69 5.74 21 28 31 0.90 0.10 6.93 22 27 30 7.50 1.21 10.07 kk 23 18 31 0.40 0.03 4.68 24 23 30 7.10 0.52 4.57 ek 25 28 32 9.80 1.14 7.26 xk 26 1 31 0.20 0.00 ek 27 3 15 1.60 0.11 4.29 kk 28 15 21 6.40 0.79 7.70 **k 29 1 23 0.30 0.00 **30 -5 21 0.00 0.00 kk 31 -4 16 0.00 0.00 Snow Statistics Maximum Denisity 10.07 lb/ft? Minimum Density 0.78 Average Density 3.74 Standard Deviation 1.86 Density lb/ft?No. Min Max Samples 0 1 2 1 2 3 2 3 10 3 4 12 4 5 11 5 6 1 6 7 2 7 8 2 8 9 0 9 10 0 10 11 1 Weather Stations: Station 8976 TAlkeetna WSCMO AP Station 5778 McKinley Park A2-4 Appendix 3 "ICE.BAS"Computer Program Le ee ee| bid Lud hed kod kd or|bd kod bd hod | Input Coding for ICE.BAS 1.Client 2.Description 3.End span or Middle Span (E or M) 4.tub)Area (in*2),Diameter (in),Bare Wt (lb/ft),RTS 5.Modulus of Elasticity of Wire (lb/in'*2) 6.Insulator Length (ft),Insulator Weight (lb),Initial movement limit multiplier -1 for long insulators,4 to 10 for short ones If Inverted V-String 7.Insulator Type (V),Angle of leg of V from vertical (deg) If I string 7.Insulator Type (I) If Post Insulator 7.Insulator Type (P),Insulator Diameter (in),Insulator Modulus of Elasticity (lb/in"*2) If Spring 7.Insulator Type (S),Spring Constant (lb/ft) For All Insulator Types 8.Ice/Snow density (lb/ft*3),radial inches of snow/ice (in) Repeat Line 9 up to 20 times 9.Span (ft),elevation difference (ft),unstressed lenght(ft), tower stiffness (lb/ft) A3-1 Sample "ICE.BAS"Input File "ICE.IN" Alaska Energy Authority Conductor M 2,-8010,1.165,1.076,25900 9307448 11,230,2 I 5,4 1225,0,1227.58675,9500 1225,0,1227.58675,9500 1225,0,1227.58675,9500 1225,0,1227.58675,9500 1225,0,1227.58675,9500 1225,0,1227.58675,9500 1225,0,1227.58675,9500 1225,0,1227.58675,9500 1225,0,1227.58675,9500 1225,0,1227.58675,9500 A3 2 Sample ICE.BAS Output File "ICE.OUT" 345-kV I-String with Yokes Removed and Guys Pretensioned ICE8.BAS Version 1,5-12-92 07-06-1992 08:46:02 Alaska Energy Authority Conductor Loaded Span in Center of Tangent Ice or Wet Snow,density:5.00 lb/ft*3 Radial Ice or Wet Snow:4.00 in Number of Subconductors:2 Area:0.8010 in*2 Diameter:1.1650 in Bare Wt:1.0760 lb/ft Iced Wt:3.3297 lb/ft RTS:25,900.lb Modulus of Elasticity of Wire:9,307,448 psi Insulator Length Multiplyer for Iteration Limit:2.00 Insulator Type:I String Length:11.00 ft,weight:230 lb Span Effective Elev Unstressed Unit Sag w/out Tower No Span Span Diff Length Weight Movement Stiffness 1 1,225 1,225.00 0 1,227.5868 3.3297 46.969 9,500 2 1,225 1,225.00 0 1,227.5868 1.0760 39.716 9,500 3 1,225 1,225.00 0 1,227.5868 1.0760 39.716 9,500 4 1,225 1,225.00 0 1,227.5868 1.0760 39.716 9,500 5 1,225 1,225.00 0 1,227.5868 1.0760 39.716 9,500 6 1,225 1,225.00 fe)1,227.5868 1.0760 39.716 9,500 7 1,225 1,225.00 0 1,227.5868 1.0760 39.716 9,500 8 1,225 1,225.00 0 1,227.5868 1.0760 39.716 9,500 9 1,225 1,225.00 0 1,227.5868 1.0760 39.716 9,500 10 1,225 1,225.00 0 1,227.5868 1.0760 39.716 9,500 Results for 3 Spans Tower Insulator Total Horizontal Tension Xarm Span Movement Movement Movement Sag Tension Diff Load No (ft)(ft)(ft)(ft)(ft)(1b)(1b) 1 0.1443 2.6541 2.7983 66.874 9,291.27 0 0 2 0.0000 0.0000 -0.0010 23.571 8,606.06 685 1,370 A3-3 Results for 5 Spans Tower Insulator Total Span Movement Movement Movement No (ft)(ft)(ft) 1 0.2163 3.8419 4.0582 2 0.0508 1.9002 1.9510 3 0.0000 0.0000 -0.0001 Results for 7 Spans Tower Insulator Total Span Movement Movement Movement No (ft)(ft)(ft) 1 0.2500 4.3525 4.6025 2 0.0751 2.7604 2.8355 3 0.0348 1.3121 1.3469 4 0.0000 0.0000 0.0003 Results for 9 Spans Tower Insulator Total Span Movement Movement Movement No (ft)(ft)(ft) 1 0.2647 4.5658 4.8305 2 0.0860 3.1314 3.2174 3 0.0508 1.9005 1.9513 4 0.0236 0.8941 0.9177 5 0.0000 0.0000 0.0005 Results for 11 Spans Tower Insulator Total Span Movement Movement Movement No (ft)(ft)(ft) 1 0.2710 4.6549 4.9259 2 0.0907 3.2888 3.3795 3 0.0579 2.1550 2.2128 4 0.0342 1.2906 1.3249 5 0.0159 0.6022 0.6181 6 0.0000 0.0000 -0.0001 Sag (ft) 74.521 27.823 28.770 Sag (ft) 77.627 29.875 31.523 32.349 Sag (ft) 78.897 30.790 32.814 34.139 34.793 Sag (ft) 79.423 31.183 33.384 34.956 35.957 36.442 A3-4 Horizontal Tension (ft) 8,311.53 7,284.26 7,043.01 Horizontal Tension (ft) 7,968.03 6,780.64 6,424.03 6,258.76 Horizontal Tension (ft) 7,835.29 6,577.93 6,169.43 5,928.14 5,815.96 Horizontal Tension (ft) 7,781.56 6,494.39 6,063.39 5,788.57 5,626.05 5,550.63 Tension Diff (1b) 0 1,027 241 Tension Diff (1b) 0 1,187 357 165 Tension Diff (1b) 0 1,257 408 241 112 Tension Diff (1b) 0 1,287 431 275 163 75 Results for 13 Spans Tower Insulator Total Span Movement Movement Movement No (ft)(ft)(ft) 1 0.2737 4.6925 4.9661 2 0.0928 3.3556 3.4484 3 0.0609 2.2640 2.3249 4 0.0389 1.4626 1.5014 5 0.0229 0.8673 0.8902 6 0.0106 0.4022 0.4128 7 0.0000 0.0000 -0.0002 Results for 15 Spans Tower Insulator Total Span Movement Movement Movement No (ft)(ft)(ft) 1 0.2748 4.7084 4.9832 2 0.0936 3.3841 3.4777 3 0.0622 2.3106 2.3728 4 0.0408 1.5364 1.5773 5 0.0260 0.9821 1.0080 6 0.0152 0.5782 0.5935 7 0.0070 0.2671 0.2741 8 0.0000 0.0000 -0.0001 Results for 17 Spans Tower Insulator Total Span Movement Movement Movement No (ft)(ft)(ft) 1 0.2753 4.7152 4.9905 2 0.0940 3.3962 3.4902 3 0.0628 2.3305 2.3932 4 0.0417 1.5681 1.6098 5 0.0273 1.0313 1.0586 6 0.0173 0.6542 0.6714 7 0.0101 0.3832 0.3933 8 0.0046 0.1765 0.1811 9 0.0000 0.0000 -0.0001 Sag (ft) 79.644 31.352 33.630 35.314 36.480 37.203 37.548 Sag (ft) 79.738 31.424 33.736 35.469 36.708 37.541 38.047 38.286 Sag (ft) 79.778 31.454 33.780 35.536 36.806 37.686 38.266 38.613 38.775 A3-5 Horizontal Tension (ft) 7,759.16 6,459.30 6,018.66 5,729.34 5,544.80 5,436.01 5,385.67 Horizontal Tension (ft) 7,749.73 6,444.46 5,999.69 5,704.15 5,510.12 5,386.81 5,314.40 5,280.99 Horizontal Tension (ft) 7,745.73 6,438.15 5,991.62 5,693.41 5,495.30 5,365.75 5,283.80 5,235.85 5,213.77 Tension Diff (1b) 0 1,300 441 289 185 109 50 Tension Diff (1b) 0 1,305 445 296 194 123 72 33 Tension Diff (1b) 0 1,308 447 298 198 130 82 48 22 Xarm Load (1b) 0 2,600 881 579 369 218 101 Xarm Load (1b) 0 2,611 890 591 388 247 145 67 Results for Span Movement Movement Movement No »COUOANANOPWNPInsulator Total 19 Spans Tower (ft)(ft) 0.2755 4.7181 0.0942 3.4014 0.0630 2.3389 0.0421 1.5815 0.0278 1.0524 0.0181 0.6866 0.0114 0.4331 0.0067 0.2527 0.0031 0.1159 0.0000 0.0000 (ft) 4.9936 3.4955 2.4020 1.6236 1.0802 0.7047 0.4445 0.2593 0.1190 0.0007 Sag (ft) 79.794 31.467 33.800 35.564 36.847 37.749 38.359 38.754 38.988 39.097 A3-6 Horizontal Tension (ft) 7,744.03 6,435.47 5,988.19 5,688.85 5,489.00 5,356.79 5,270.76 5,216.56 5,184.95 5,170.45 Tension Diff (1b) 0 1,309 447 299 200 132 86 54 32 14 "ICE8.BAS -program to calculate the effect of unbalanced ice loads on 'center span of infinite tangent "ICE8.BAS adds the capability of looking at the span next to a deadend 'being the one loaded DECLARE FUNCTION arcsin!(x AS DOUBLE) DECLARE FUNCTION arcsinh!(u AS DOUBLE) DECLARE FUNCTION cosh!(u AS DOUBLE) DECLARE FUNCTION icedwt (diam AS SINGLE,rice AS SINGLE,wbare AS SINGLE,density AS SINGLE) DECLARE FUNCTION sag!(H AS DOUBLE,w AS DOUBLE,a AS DOUBLE) DECLARE FUNCTION sinh!(u AS DOUBLE) DECLARE SUB hcale (H AS DOUBLE,w AS DOUBLE,area AS SINGLE,modulus AS DOUBLE,a AS DOUBLE,b AS DOUBLE,sunstressed AS DOUBLE) DECLARE SUB span (H AS DOUBLE,w AS DOUBLE,area AS SINGLE,modulus AS DOUBLE,a AS DOUBLE,b AS DOUBLE,sunstressed AS DOUBLE) DECLARE SUB teffective (H AS DOUBLE,w AS DOUBLE,S AS DOUBLE,x1 AS DOUBLE,x2 AS DOUBLE,te AS DOUBLE) OIM DIM DIM DIM DIM DIM OIM DIM DIM DIM DIM DIM DIM DIM OIM DIM DIM DIM DIM DIM DIM DIM DIM DIM DIM DIM DIM DIM DIM OIM DIM DIM OIM a(20)AS DOUBLE 'original spans aa(20)AS DOUBLE 'spans after the insulator and tower movement has happened aasum AS DOUBLE 'sum of the spans after insulators move ain(20)AS DOUBLE 'span input before adjusting for inverted V strings affect alpha AS DOUBLE 'angle of inverted v in radians alphad AS DOUBLE 'angle of inverted v in degrees area AS SINGLE 'cross-sectional area of conductor asum AS DOUBLE 'Sum of the spans based on the input spans b(20)AS DOUBLE 'elevation difference between supports biced AS DOUBLE 'elevation difference in iced span client AS STRING 'Client Name d(20)AS DOUBLE 'horizontal movement of the point of attachement of the conductor to the insulator dilower AS DOUBLE 'upper Limit of movement in first span diold AS DOUBLE 'movement in first span from previous iteration diupper AS DOUBLE 'lower limit of movement in first span desc AS STRING 'Description of problem diam AS SINGLE 'wire diameter dins(20)AS DOUBLE 'displacement of insulator dtwr(20)AS DOUBLE 'displacement of tower EorM AS STRING 'Switch for middle or end span loaded etime AS LONG 'elapsed Time flag(20)AS INTEGER 'Flag to set and unset if iterations are used up in Vstring routine flagg AS INTEGER : H(20)AS DOUBLE 'horizontal tension in conductor hdiff AS DOUBLE 'difference in horizontal tensions at a tower hoverw AS DOUBLE 'H/w i AS INTEGER 'counter ii AS INTEGER 'counter iif AS INTEGER 'counter insdiam AS DOUBLE 'Post insulator diameter insE AS DOUBLE 'Modulus of elasticity of insulator ins}AS DOUBLE 'post insulator moment of inertia inslgth AS DOUBLE 'length of insulator string A3-7 DIM instype AS STRING 'type of insulator string I,V,P DIM inswt AS DOUBLE 'insulator string weight DIM j AS INTEGER 'counter DIM k AS DOUBLE 'combined stiffness of post insulator and tower DIM kpost AS DOUBLE 'spring constant of post insulator in lb/ft DIM ktwr(20)AS DOUBLE 'stiffness of tower DIM Linv AS DOUBLE 'spread of bottom of the inverted V string DIM limit AS DOUBLE 'multiplyer on the insulator length for upper bound DIM modulus AS DOUBLE 'modulus of elasticity of wire DIM n AS INTEGER 'counter used to count the number of towers input,20 max DIM ncond AS INTEGER 'number of subconductors DIM pi AS DOUBLE 'pi DIM RTS AS SINGLE 'Rated Tensile Strength of wire DIM sagtest AS DOUBLE 'sag to be compared to unloaded sag to see if adding spans won't make a difference DIM sg(20)AS DOUBLE 'Sag DIM su(20)AS DOUBLE 'unstressed length of wire DIM suin(20)AS DOUBLE 'unstressed length of wire input before adjusting for inverted V DIM teff AS DOUBLE 'effective tension OIM test AS DOUBLE 'test value for calculating change in force due to insulator swing DIM theta AS DOUBLE 'swing angle of insulator of inverted V insulator DIM Va(20)AS DOUBLE 'weight of wire towards ice span DIM Vb(20)AS DOUBLE 'weight of Wire away from iced span DIM w(20)AS DOUBLE 'iced weight of wire DIM whare AS SINGLE 'bare weight of wire DIM x AS DOUBLE 'movement due to swing of the insulator DIM xlower AS DOUBLE 'lower bound of movement DIM xupper AS DOUBLE 'upper bound of movement cLS PRINT "Running ICE8.BAS" etime =TIMER pi =3.14159265# linv =0 OPEN "ice.in"FOR INPUT AS 1 OPEN "ice.out"FOR OUTPUT AS 2 'This section reads in the data from ice.in INPUT #1,client INPUT #1,desc INPUT #1,EorM INPUT #1,ncond,area,diam,wbhare,RTS INPUT #1,modulus INPUT #1,inslgth,inswt,Limit INPUT #1,instype 'Different data is needed depending on the type of insulator A3-8 instype =UCASE$Cinstype) SELECT CASE (instype) CASE IS ="I"CASE IS ="p™INPUT #1,insdiam,insE 'diam in inches,insE,in psi insl =pi *insdiam *4 /64 'psi kpost =3 *jmsE *insI /Cinslgth *3 *144)'kpost in lb/ft CASE IS ="Vv" INPUT #1,alphad alpha =alphad *pi /180 linv =2 *inslgth *TAN(alpha) CASE IS ="Ss" INPUT #1,kpost CASE ELSE PRINT "Incorrect Insulator Type Entered,Execution Stopped" STOP END SELECT INPUT #1,density,rice 'This data is tower by tower,at the same time the insulator loads are calculated "based on the bare weight of the wire FOR n =1 TO 20 IF EOF(1)THEN EXIT FOR INPUT #1,ain(n),b(n),suin(n),ktwr(n) d(n)=0w(n)=wbareVa(n)=ain(n)*win)/2Vb(n)=Van) NEXT 'This completes the input n=n-1 'n is the number of structures input,the counter increments one more than the number input 'this adjusts the span for the spread of the inverted v-string insulators IF instype ="V"THEN FOR i =17T0n a(i)=ainci)-linv su(i)=suinci)-linv NEXT ELSE FOR i=1TOn aci)=ainci) su(i)=suin(i) NEXT END IF A3-9 'this adjusts the weight of the wire in the first span to the iced weight w(1)=icedwt(diam,rice,wbare,density) Va(1)=ain(1)*wl)/2 'This prints out the input data and headers ,"ICE8.BAS Version 1,5-12-92" PRINT #2,DATES,TIMES PRINT #2,client PRINT #2,desc IF EorM ="M"THEN PRINT #2,"Loaded Span in Center of Tangent" PRINT #2,"Loaded Span adjacent to Deadend" PRINT #2,USING "Ice or Wet Snow,density:##.##lb/ft*3";density PRINT #2,USING "Radial Ice or Wet Snow: PRINT #2,USING "Number of Subconductors: PRINT #2,USING "Area:HH HHHH in*2":area PRINT #2,USING "Diameter:##.####in";diam PRINT #2,USING "Bare Wt: PRINT #2,USING "Iced Wt:#H#HHHH Ib/ft"s wC1)PRINT #2,USING "RTS:#8,###.ib":RTS #8.#HHH lb/ft";whare ##.##in";rice ##":ncond PRINT #2,USING "Modulus of Elasticity of Wire:##,###,###psi";modulus PRINT #2,USING "Insulator Length Multiplyer for Iteration Limit:##.4#";Limit SELECT CASE instype CASE IS ="J" PRINT #2,"Insulator Type:I String PRINT #2,USING " CASE IS ="p" PRINT #2,"Insulator Type:Line Post" PRINT #2,USING "Length: PRINT #2,USING "Diameter: PRINT #2,USING " CASE 1S ="y" PRINT #2,"Insulator Type:Inverted Vv" PRINT #2,USING " PRINT #2,USING "Angle: CASE IS ="S" PRINT #2,"Insulator Type:Spring" #4.##deg,Spread: ##.##ft,Weight: ##.##in,Modulus:##,###,###psi";insdiam,insE Stiffness:#,###.##lb/ft";kpost Length:##.##ft,weight:##,###lb";inslgth,inswt #4,#H#Ib":inslgth,inswt Length:##.##ft,Weight:##,###Ib":inslgth,inswt ##HH ft":alphad,linv PRINT #2,USING "Spring Constant:##,###.##":kpost END SELECT A3-10 PRINT #2, PRINT #2,"Span Effective Elev Unstressed Unit Sag w/out Tower" PRINT #2,"No Span Span Diff Length Weight Movement Stiffness" PRINT #2, 'in this section the sag is calculated with the insulators and tower locked against movement FOR i=1TOn CALL healcC(HCi),wi),area,modulus,a(i),bi),suci)) sg(i)=sag(H(i),wi),aci))PRINT #2,USING "###,#4#8,480.88 HHH =HEH HHHH HHH HHH.HHH HA,HHA:i,ain(i):ai),bCi),suci),wi),saci),ktwrCi) NEXT 'initialize some variables sagtest =sg(n) diold =-1 dilower =0 diupper =inslgth *Limit 'Start the main loop 'The main loop starts with 2 spans and increases the number of spans until either the sag in the 'last span is within .1 ft of its locked sag or all the spans have been added FOR j =2 TO n FOR iii =1 TO 20 flag(iii)=0 NEXT flagg =0 d(j)=1 flag =0 'this loop varies the movment d(1)in the first span until the overall length with the 'towers and insulators unlocked equals the overall length locked FOR ii =1 TO 100 'This IF statement sets the first span length depending on whether it is a 'middle span or an end span TF EorM ="M"THEN aa(1)=a(1)-2 *d(1) ELSE aa(1)=a(1)-d(1) END IF H(1)=0 CALL hcalc(H(1),w(1),area,modulus,aa(1),b(1),su(1)) asum =a(1) A3-11 IF EorM ="M"THEN aasum =aa(1)+d(1) ELSE aasum =aa(1) END IF 'This loop steps through the j towers calculating the movements of the insulators and the span lengths "based on the unstressed length of the wire FOR i =2 TO j 'The horizontal tension in the next span is calculated based on the horizontal tension 'jn the previous span and the tower/insulator movement SELECT CASE instype CASE IS ="J" test = xupper xlower FOR iji =1 TO 100 x =(xupper +xlower)/2 test =ktwr(i -1)*2 *(dCi -1)-x)*2 *Cimslgth *2 -x *2)-x *2 *(ncond *(Va(i -1)+VbCi -1))+inswt /2)*2 IF ABS(test)<.01 OR ABSCinslgth -x)<.001 THEN EXIT FOR IF test >O THEN xlower =x ELSE xupper =x NEXT 'This is a warning to check if proper convergence was reached IF iii >99 THEN PRINT #2,"Maximum iterations of iii exceeded for I string,check results" HCI)=HCi -1)-ktweci -1)*(dCi -1)-x)/ncondattd¢i -1) 0 dins(i -1)=x dtwr(i -1)=dCi -1)-x CASE IS ="p" k =kpost *ktwr€i -1)/(kpost +ktwr¢i -1)) H(i)=HCi -1)-k *d¢i -1)/neond dins(i -1)=CHCi -1)-HCi))*ncond /kpost dtwr(i -1)=(HCI -1)-HCI)*ncond /ktwr¢i -1) CASE 1S ="Ss" k =kpost *ktwr(i -1)/(kpost +ktwr(i -1)) H(i)=HCi -1)-k *dCi -1)/ncond dins¢i -1)=CHCi -1)-HCi))*ncond /kpost dtwr€i -1)=CHCi -1)-HCi))*ncond /ktwri -1) CASE IS ="y" xupper =pi /2 -alpha xlower =-pi /2 +alpha FOR iii =1 TO 100 x =(xupper +xlower)/2 HCi)=CHCT -1)*COS(x +alpha)-VaCi -1)*SIN(x +alpha)-VbCi -1)*SIN(x -alpha)-inswt *COSCalpha)*SIN(x)/4)/COS(x -alpha) dtwr(i -1)=CHCi -1)-HCI)*ncond /ktwrci -1) dins(i -1)=inslgth *SIN(x) test =dtwr(i -1)+dins(i -1) A3-12 IF ABS(dC(i -1)-test)<.001 THEN EXIT FOR IF d¢i -1)-test >0 THEN xlower =x ELSE xupper =x NEXT 'This is a warning to check if proper convergence was reached 'It does not necessarily mean the results are bad. IF iif >99 THEN flagci)=1 'PRINT #2,"maximum iterations of iii exceeded for Inverted V,check results" ELSE 'PRINT #2,"normal progression through iii iteration,iii =";iii flag¢i)=0 END IF theta =arcsin(x /inslgth) CASE ELSE PRINT "Not a known insulator type,execution stopped" STOP END SELECT 'If the calculated H is less than 0,this sets it to a small positive value to avoid 'a physically impossible IF HCi)<0 THEN H(i)=100 'this calculates the length of the span given the horizontal tension CALL span(H(i),wi),area,modulus,aa(i),bi),suci)) "here the length based on locked insulators is compared to the length calculated based 'on an assumed movement of the tower/insulator in the first span asum =asum +a(i)+Linv aasum =aasum +aa(i)+linv *COoS(theta) d(i)=asum -aasum NEXT 'If the last insulator has not moved,ie asum =aasum or there is no change 'in movement of the first span,then the results are printed and the number of 'towers ie:j is incremented IF ABS(d(j))<.001 THEN EXIT FOR IF ABS(d(1)-dlold)<.0000001 THEN PRINT #2, PRINT #2, PRINT #2,"Exiting due to no change in d(1)" EXIT FOR END IF 'if the last insulator must have moved,the assumed movement at the 'first tower is adjusted and everything is recalculated dtold =d(1) IF d(j)<=0 THEN dilower =d(1) ELSE Giupper =d(1) END IF d(1)=(dlupper +dilower)/2 A3-13 LOCATE 2,1 PRINT USING "Elapsed Time #,###,###":TIMER -etime; NEXT IF ii >99 THEN PRINT #2,"Maximim iterations reached in MAIN" PRINT #2, IF EorM ="M"THEN PRINT #2,USING "Results for ###Spans";(2 *j -1) ELSE PRINT #2,USING "Results for ###Spans";j END IF FOR iii =1 TO 20 IF flagCiii)=1 THEN flagg =1 NEXT IF flagg =1 THEN PRINT #2, PRINT #2,"Warning!!!,Check Results,Max iterations exceeded in loop iii" PRINT #2, END IF PRINT #2, PRINT #2,"Tower Insulator Total Horizontal Tension PRINT #2,"Span Movement Movement Movement Sag Tension Diff PRINT #2,"No (ft)(ft)(ft)(ft)(ft)(lb) PRINT #2, FOR i =1 T0 j IF i =1 THEN hdiff =0 ELSE hdiff =HCi -1)-HCI) sg(i)=sag(H(i),wi),aaci)) PRINT #2,USING "#4 ##H.HHHH HHA AHHH HHH HHH OHHH HHH OHH RO,NEXT Xarm" Load" (lb)" Ht,HHA";1,dtwe(i),dinsci),dCi),sgCi),HCi),hdiff,ncond *hdiff 'this if the last span has about the same sag unlocked as locked,no more towers are 'added and the program stops IF sagtest -sg(j)<.1 THEN EXIT FOR diupper =inslgth *limit dilower =.8 *d(1) diold =-1 LOCATE 2,1 PRINT USING "Elapsed Time #,###,###":TIMER -etime; NEXT LOCATE 2,1 PRINT USING "ICE8.BAS run finished in #,###,###sec";TIMER -etime END FUNCTION arcsin (x AS DOUBLE) arcsin =ATN(X /SQR(1 -x *2)) END FUNCTION FUNCTION arcsinh (u AS DOUBLE) arcsinh =LOG(u +SQR(u *u +1)) END FUNCTION A3-14 FUNCTION cosh (u AS DOUBLE) cosh =(EXP(u)+EXP(-u))/2 END FUNCTION SUB hcale (H AS DOUBLE,w AS DOUBLE,area AS SINGLE,modulus AS DOUBLE,a AS DOUBLE,b AS DOUBLE,sunstressed AS DOUBLE) 'This subroutine calculates the horizontal tension based on the span 'wire properties and unstressed length DIM ihcale AS INTEGER 'counter DIM hlower AS DOUBLE 'Lower bound of horizontal tension DIM hupper AS DOUBLE 'Upper bound of horizontal tension DIM sdiff AS DOUBLE 'difference in unstressed lengths DIM Strial AS DOUBLE 'trial stressed length of wire DIM sunstresstrial AS DOUBLE 'trial unstressed length DIM tefftrial AS DOUBLE 'trial effective tension DIM x1 AS DOUBLE 'distance from low point of sag to high support DIM x2 AS DOUBLE 'distance from low point of sag to low support DIM z AS DOUBLE 'Ehrenburg's constant sdiff =1 hupper =100000 hlower =0 H =(hupper +hlower)/2 FOR ihcale =1 TO 100 IF ABSChupper -hlower)<.00001 THEN EXIT FOR c =SQR(a *a +b *b) z=(a*w)/(2 *H) Striat =SQR((a *a *sinh(z)*sinh(z))/(z *z)+b *b) x1 =H *Carcsinh(b *z /(a *sinh(z)))+z)/w x2=xl-a CALL teffective(H,w,Strial,x1,x2,tefftrial) sunstresstrial =Strial /(1 +tefftrial /(area *modulus)) sdiff =sunstressed -sunstresstrial IF sdiff >=0 THEN hupper =H H =(H +hlower)/2 ELSE hlower =H H =(H +hupper)/2 END IF NEXT IF ihacalc >99 THEN PRINT #2,"Maximum iterations used in HCALC" END SUB FUNCTION icedwt (diam AS SINGLE,rice AS SINGLE,wbare AS SINGLE,density AS SINGLE) icedwt =3.14159265#*density *rice *(diam +rice)/144 +wbare END FUNCTION A3-15 FUNCTION sag (H AS DOUBLE,w AS DOUBLE,a AS DOUBLE) sag =H *(cosh(a *w /(2 *H))-1)/Ww END FUNCTION FUNCTION sinh (u AS DOUBLE) "PRINT "function sinh" sinh =(EXP(u)-EXP(-u))/2 END FUNCTION SUB span (H AS DOUBLE,w AS DOUBLE,area AS SINGLE,modulus AS DOUBLE,a AS DOUBLE,b AS DOUBLE,sunstressed AS DOUBLE) 'This subroutine calculates the span from the wire properties,horizontal tension 'and unstressed length DIM alower AS DOUBLE 'Lower bound of span length DIM aupper AS DOUBLE 'Upper bound of span length DIM sdiff AS DOUBLE 'difference in unstressed lengths DIM Strial AS DOUBLE 'trial stressed length of wire DIM sunstresstrial AS DOUBLE 'trial unstressed length DIM tefftrial AS DOUBLE 'trial effective tension DIM x1 AS DOUBLE 'distance from low point of sag to high support DIM x2 AS DOUBLE 'distance from low point of sag to low support DIM z AS DOUBLE 'Ehrenburg's constant DIM jj AS INTEGER 'counter jj =1 sdiff =1 aupper =2 *sunstressed alower =.5 *sunstressed a =sunstressed FOR jj =1 TO 100 IF ABSCaupper -alower)<.00000001#THEN EXIT FOR 'PRINT sunstressed,sunstresstrial,sdiff 'PRINT jj,a 'PRINT "Span",jj c =SQR(a *a +b *b) z=(a*w)/(2 *4H) Strial =SQR((a *a *sinh(z)*sinh(z))/(z *z)+b *b) x1 =H *Carcsinh(b *z /(a *sinh(z)))+z)/w x2 =x1l-a CALL teffective(H,w,Strial,x1,x2,tefftrial) sunstresstrial =Strial /(1 +tefftrial /(area *modulus)) sdiff =sunstressed -sunstresstrial IF sdiff >=0 THEN alower =a a =(a +aupper)/2 ELSE aupper =a a =(a +alower)/2 END IF A3-16 NEXT IF jj >99 THEN PRINT #2,"Maximum iterations reached in SPAN" END SUB SUB teffective (H AS DOUBLE,w AS DOUBLE,S AS DOUBLE,x1 AS DOUBLE,x2 AS DOUBLE,te AS DOUBLE) 'this subroutine calculates the uniform tension that would stretch the wire the 'same amount as the varying tension in the span does DIM z1 AS DOUBLE DIM z2 AS DOUBLE zi=xl*w/dk z=x2*w/t te =H *H *(sinh(z1)*cosh(z1)-sinh(z2)*cosh(z2)+(x1 -x2)*w/H)/(2 *w*S) END SUB A3-17