risk-based design of transmission lines for hurricane winds

Peer-reviewed by international ex-perts and accepted for publication by SEI Editorial Board

Paper received April 24 2013Paper accepted August 6 2013

Structural Engineering International 22014 Scientific Paper 275

transmission line is greater than the exceedance probability at a single point The study in Ref [5] showed that the transmission lines designed using the National Electrical Safety Code (NESC) criterion will experience extreme wind speeds more frequently than implied by the NESC criterion The study in Ref [6] developed a tor-nado risk model that takes into account the length of a transmission line and the damage length of a tornado Similar studies78 were performed on the risk of ice storms to transmission lines

The ldquoGuidelines for Electrical Transmission Line Structural Loadingrdquo published by the American Society of Civil Engineers (ASCE)9 recognizes that the likelihood of failure is a func-tion of the transmission line length and that the length of a transmission line should be a factor in selecting the design criterion but the guidelines do not offer any firm recommendations regarding the influence of length on the design criterion Up to this point the effect of aggregation has been gen-erally ignored in practice although it is an active field of research in sys-tem reliability The objective of this paper was to demonstrate through a costndashbenefit analysis that it is more economical in the long run to consider the effect of aggregation in the design of transmission lines The selection of a risk-based design criterion will be illustrated for a 1076 km (669 mi) long transmission line in hurricane-prone coast of the USA The scope of this paper is limited to the selection of a risk-based wind design criterion Detailed design of the transmission line is outside its scope

Data Used in Analysis

The hurricane wind speed data used in this study were developed as described in Ref [10] to generate the design wind speed maps in ASCE 7-0511 The same data are also used in the Federal Emergency Management Agencyrsquos (FEMArsquos) multi-hazard loss assess-ment model HAZUS12 Hurricane events were simulated by sampling

provides some measure of the risk to a building from wind loads

Unlike buildings power transmission lines (such as the one shown in Fig 1) are not entirely located at single sites Transmission lines are long continu-ous structures that are simultaneously located in many sites They can be dam-aged by wind speeds anywhere along their length resulting in a disruption of the power supply hence losses to the operators and the consumers of the electricity During a hurricane the entire transmission line is not expected to experience the same wind speed Also different parts of a transmission line can be damaged by different hur-ricanes Therefore the probability of damage to a transmission line is not same as the probability of exceeding the design wind speed at any specific location The design criterion for a transmission line can be evaluated by accumulating (aggregating) the risk along the entire length of the transmis-sion line

The effect of aggregation has been discussed before The study in Ref [3] showed that the wind speed any-where along the Dade County FL coastline is higher than the wind speed at a point in Miami FL The study in Ref [4] showed that the tornado wind speed exceedance probability along a

Introduction

Power transmission lines in the USA are expected to meet the minimum design requirements of the National Electrical Safety Code NESC C21 The objective of the NESC C2 require-ments is to reduce the risk of injury and death to humans from construc-tion operation and maintenance of transmission lines1 As per NESC C21 the wind speeds for the design of con-ductors (wires) towers and founda-tions of a transmission line can be read from the loading standard for build-ings ASCE 7-102 The design wind speeds in ASCE 7-102 were derived from the site-specific hazard analy-sis3 ASCE 7-102 wind speeds have certain probabilities of exceedance at specific locations Assuming that the damage occurs when the design wind speed is exceeded the probability of wind damage to a building designed per ASCE 7-102 can be deduced In other words the design based on the site-specific criterion in ASCE 7-102

Abstract

The design requirements for electric power transmission lines in the USA address only the risk of injury and death from construction operation and maintenance They do not explicitly address the risk to operators (owners) and consumers from the disruption of power supply Like most structures transmission lines are designed for wind speeds with ldquolowrdquo probability of exceedance at specific locations Unlike most structures transmission lines can be damaged by winds anywhere along their length As a result the probability of disruption to a trans-mission line can be significantly greater than the probability of exceeding the design wind speed at any specific location In this paper it is shown that a 1076 km (669 mi) long transmission line designed for 700-year mean return period (MRP) wind speeds is damaged with an MRP of only 54 years Hence the design based on site-specific criterion provides a low perception of the risk to a trans-mission line A risk-based approach is proposed to evaluate and select the design criterion for transmission lines It is more economical in the long run to design a longer transmission line to a higher criterion than a shorter transmission line

Keywords transmission lines hurricanes wind loads risk aggregate hazard anal-ysis design standards insurance

Risk-Based Design of Transmission Lines for Hurricane WindsPraveen K Malhotra PhD PE President StrongMotions Inc Sharon MA USA Contact PraveenMalhotraStrongMotionscom

DOI 102749101686614X13830790993249

Authors

Cop

y

276 Scientific Paper Structural Engineering International 22014

key hurricane parameters (radius to maximum wind central pressure dif-ference and translational speed) from their respective probability distribu-tions derived from historical data13ndash16 Each hurricane event produces a ldquofootprintrdquo of spatially varying wind speeds Figure 2 shows the footprint of a hurricane event that makes land-fall in South Carolina This is one of the 71 515 hurricane footprints in a ldquo10 000-yearrdquo simulation generated in Ref [10] It was assumed that the hurricanes follow a time-independent (Poisson) process that is the size and frequency of hurricanes do not change with time The potential effect of cli-mate change on the size and frequency of hurricanes was not considered in this simulation The Poisson assump-tion is also made in the generation of ASCE 7-102 wind speed maps The ldquo10 000-yearrdquo simulation of hurricanes was considered reasonable for the purpose of this study because the mean return period (MRP) of design wind speeds for transmission lines is only a few hundred years

Design Based on Site-Specific Hazard Analysis

The design criterion for structures is typically based on site-specific proba-bilistic hazard analysis Site-specific probabilistic hurricane hazard analysis is performed at individual sites with-out giving any consideration to other sites At each site the wind speeds from 71 515 hurricane events were arranged in an ascending order Each wind speed has an associated occur-rence rate that equals the occurrence rate of the hurricane event which pro-duces that wind speed The occurrence rates of wind speeds exceeding specific values (eg 50 55 and 60 ms) were added to generate a plot between the wind speed V and its rate of exceed-ance l (number of times per year) This is known as the wind speed haz-ard curve for the site Figure 3 shows the wind speed hazard curve for a site in South Carolina (34ordm N 801376ordm W) For a Poisson process the reciprocal of the rate of exceedance is the MRP of exceedance17

MRP = 1l (1)

MRP is the average time between suc-cessive occurrences of a Poisson pro-cess it is measured in years In Fig 3 the MRP of exceedance is shown on the right-hand side For a Poisson process the probability of exceedance

100 to 115 mph (447ndash514 ms)

115 to 130 mph (514ndash581 ms)

gt130 mph (gt581 ms)

Fig 2 Footprint of a simulated hurricane event that makes landfall in South Carolina The wind speeds shown in different colors are for 3-second gust at 33 ft (10 m) above ground in Open Terrain2

00002

0001

001

01

Rat

e of

exc

eeda

nce

(

per

year

)

20 30 40 50 60

10

100

1000

5000

Exc

eeda

nce

retu

rn p

erio

d T

(ye

ars)

Wind speed V (ms)

Fig 3 Hurricane wind speed hazard curve for a site in South Carolina (34degN 801376degW)

Fig 1 A 500 kV power transmission near Bowdle South Dakota (image by Gary Christenson Basin Electric Power Cooperative)

Authors

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P during a time-span t is given by the following expression17

P = 1 ndash exp(ndashlt) (2)

Substituting l = 1MRP in Eq (2) gives

P = 1 ndash exp(ndasht MRP) (3)

According to the hazard curve in Fig 3 any wind speed is possible at the site higher wind speeds have longer MRPs (or lower probabilities P) of exceed-ance The wind speeds shown in Fig 2 and 3 are for 3-second gust at 33 ft (10 m) above ground in Open Terrain2 The wind speeds for other terrains and heights can be obtained by applying adjustments specified in the loading standard ASCE 7-102

According to Fig 3 the 120 mph (54 ms) wind speed is exceeded with an MRP of 700 years Substituting MRP = 700 years and t = 50 years in Eq (3) gives P = 0069 asymp 7 Therefore 700-year MRP is equivalent to 7 chance of exceedance in 50 years The hazard curves similar to those shown in Fig 3 were generated for 31 140 sites throughout the hurri-cane-prone coast of the USA The map of wind speed for any specific MRP is then generated by first reading the wind speeds (for the specified MRP) from the hazard curves at various locations Figure 4 shows the 700-year MRP wind speed map This map is slightly differ-ent from that shown in Figure 265-1A of ASCE 7-102 because the ASCE 7-10 map was based on the latest hurricane simulations discussed in Ref [18] Wind speed maps similar to Figure 4 can be generated for any MRP

Figure 5 shows a hypothetical trans-mission line between Miami FL and Atlanta GA The total length of the transmission line is 1076 km and it has 3075 spans with average distance between towers of 350 m The design wind speeds along the transmission line were read from the 700-year MRP site-specific hazard map shown in Fig 4 these are shown in Fig 6 If each span (tower conductors and foundation) of the transmission line is designed only for the wind speed shown in Fig 6 then it will be damaged with an MRP of 700 years However wind speeds along the entire length of the transmission line are not the same during a hurricane and different hurricanes can damage different parts of the transmission line Therefore the MRP of any damage to the transmission line should be signifi-cantly shorter than 700 years as dis-cussed in the following section

Aggregate Risk along the Transmission Line

Each of the 71 515 hurricane events produces a ldquofootprintrdquo of spatially varying wind speeds as shown in Fig 2

The objective is to calculate the length of the transmission line damaged by each hurricane event Of course many hurricane events will cause no dam-age to the transmission line The wind load is proportional to the square of

120 mph (54 ms)

130 mph (58 ms)

140 mph (63 ms)

Fig 4 Design wind speeds from site-specific probabilistic hurricane hazard analysis The wind speeds shown on this map are exceeded with an MRP of 700 years

Miami FL

Atlanta GA

Fig 5 A hypothetical transmission line of length 1076 km between Miami FL and Atlanta GA

lt 115 mph (lt 514 ms)

115 to 125 mph (514ndash559 ms)

125 to 135 mph (559ndash604 ms)

gt 135 mph (gt 604 ms)

Miami FL

Atlanta GA

Fig 6 700-year MRP design wind speeds (read from Fig 3) along the transmission line shown in Fig 5

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wind speed The damage occurs when the load exceeds the strength It is assumed that tower-collapse is the dominant mode of failure Other fail-ure modes such as broken conduc-tors or insulators are less common19 Towers designed according to codes20 are likely to have some over strength Ω due to inbuilt conservatism and post-yield strength of towers It has been suggested that ldquoon averagerdquo the actual strength is 25 greater than the design strength1921 or the collapse wind speed is 12 greater than the design wind speed as loads are proportional to the square of wind speed Also there is some uncertainty in over strength Ω due to human errors and differences between as-built and design condi-tions In this study Ω is assumed to fol-low a truncated lognormal distribution shown in Fig 7 Ω ranges from 06 to 2 with a mean of 125 and coefficient of variation of 025 Discrete values of Ω (06 08 1 12 14 16 18 and 2) were assigned weights (probabilities) according to the distribution shown in Fig 7 The weights add up to 1

There is also some correlation in dam-age along the transmission line The loss of one tower results in unbal-anced conductor loads which could collapse adjacent towers like a string of dominos This is known as the cas-cade failure The cascade failure is more common for brittle support structures such as wood poles because they completely collapse (snap) when their strength is exceeded Lattice steel towers are relatively ductile They do not completely collapse when their strength is exceeded because they can bend and twist in a ductile manner Therefore cascade failure is less com-mon for lattice steel towers The cas-cade failure can be reduced by adding dead-end towers for example every

5 km to resist unbalanced conductor loads In this study it is assumed that the cascade failure extends to two additional towers on each side of a damaged section of the transmission line If the damaged section is at the beginning or end of the transmission line then the cascade failure extends only on one side Note that a single hurricane can damage different sec-tions of a transmission line which need not be contiguous Therefore the num-ber of additional towers damaged by cascade failure can be quite high for some hurricanes

First it is assumed that the transmission line is designed for 700-year MRP wind speeds Then specific value of over strength say Ω = 12 is assumed and the number of towers damaged by each hurricane footprint is calculated These towers need not be contiguous they can be anywhere along the transmission line The number of damaged towers is adjusted to include those damaged by cascade failure After performing the analysis for all hurricane footprints the rate of damaging more than a specific number of towers is calculated The analysis is then repeated by assuming other values of Ω between 06 and 2 The weighted average of the rates for different values of Ω is then calculated Figure 8 shows the rate lD of damaging gtN towers The MRP of damaging gt N towers is shown on the right-hand side in Fig 8 This is the damage curve for the MiamindashAtlanta transmission line (shown in Fig 5) designed for 700-year MRP wind speeds according to Fig 6 In Fig 8 only the initial portion of the damage curve is shown the complete damage curve extends further to the rightAccording to Fig 8 the MRP of

damaging at least one tower is only 54 years As the loss of any tower will result in the disruption of service a transmission line designed for 700-year MRP wind speed will be disrupted with an MRP of only 54 years As expected the MRP of damaging gt N towers increases with increase in N The MRP of damaging gt300 towers (approxi-mately 10 of the transmission line) is 189 years In summary the MRP of any (gt0) damage is 54 years and the MRP of significant (gt10) damage is 189 years These results illustrate that the probability of damage anywhere along a transmission line is significantly greater than the probability of dam-age at a specific location If the MRP of design wind speed is increased the MRP of damage should also increase Figure 9 shows the damage curves for three different MRPs of design wind speed (300 700 and 1700 years) Table 1 shows the MRPs of any (gt0) damage and significant (gt10) dam-age to the transmission line for three different MRPs of design wind speed

The damage to the transmission line produces three types of losses (a) structural repair and conductor replacement cost (b) loss of revenue due to unsold power during the time of repair and (c) loss to consumers due to unavailability of power dur-ing the time of repair The structural repair and conductor replacement cost can be assumed proportional to the number of damaged towers N but it is very small compared to the losses resulting from the interruption in gen-eration and delivery of the power and the customer agreements If any tower is damaged it could take a week or so to repair the damage during which

06 08 1 12 14 16 18 20

04

08

12

16

Over strength (Ω)

Pro

babi

lity

dens

ity

Fig 7 Probability distribution of over strength Ω

0001

0002

0005

001

002

005

0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)

Number of damaged towers NR

ate

of e

xcee

danc

e

D (p

er y

ear)

Fig 8 Damage curve for the Miami-Atlanta transmission line showing the rate and the MRP of damaging gt N towers if the transmission line is designed for 700-year MRP wind speeds

Authors

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the service will be interrupted If addi-tional towers are damaged the repair time may not increase significantly because the damaged towers can be simultaneously repaired

The losses (in $) associated with dam-age can vary significantly from one transmission line to another In this study it is assumed that the loss due to any disruption is $50 million this includes loss of income due to inter-ruption in delivery and penalties due to unavailability of power to the con-sumers The loss due to the damage of each tower is $05 million This includes structural foundation and conductor repair costs The loss due to human injury and death is small if the transmission line is in remote areas and warning is issued before hurricanes For this transmission line 86 towers are assumed to be in popu-lated areas where collapse can result in human injury or death The loss due to the damage of each of these tow-ers is assumed to be $10 million The number of damaged towers N in Fig 9 can then be replaced with the loss This

gives the risk curves shown in Fig 10 Note that only the initial portions of the risk curves are shown in Fig 10 The complete curves extend further to the right Next the design criterion for the transmission line will be estab-lished using a risk-based approach

Risk-based Design Criterion

First the average annual hurricane wind loss AAL is defined as the area under the risk curve

AAL = intL middot dlL (4)

The AALs for three different design criteria (MRP of design wind speeds) were obtained for three different risk curves shown in Fig 10 they are listed in the second column of Table 2 As expected the AAL decreases by raising the design criterion Average annual loss is also the fair price of transfer-ring (insuring) the hurricane wind risk or ldquopure-premiumrdquo If the transmis-sion line is fully insured AAL is the yearly cost to the owner If the trans-mission line is self-insured AAL is the

average cost to the owner over many years Insured or self-insured AAL is a real cost to the owner The expected lifetime hurricane wind loss ELL from the transmission line is obtained by multiplying the AAL by the life of the transmission line No adjustments have been made for the current value of future losses but they can be made in a more refined analysis The ELLs for 50- and 100-year life span are listed in the third and fourth columns of Table 2 These were obtained by multi-plying the values in the second column by 50 and 100 respectively For a given life span of the transmission line the ELL decreases by raising the design criterion (MRP of design wind speed) The cost of construction increases by raising the design criteria

For an expected life span of 50 years the ELL decreases from $437 to $223 million if the design criterion is raised from 300- to 700-year MRP wind speed this is a net decrease of $214 million in ELL If the increase in construction cost is less than $214 million it is more economical in the long run to design the transmission line for 700-year MRP wind speed than 300-year MRP wind speed For an expected life span of 100 years the ELL decreases by $202 million if the MRP of design wind speed is raised from 700-year to 1700-year If the increase in construction cost is less than $202 million it is more eco-nomical in the long run to design the transmission line for 1700-year MRP wind speed than 700-year MRP wind speed Expected lifetime loss should be computed for different design cri-teria to select the most cost-effective design criterion

The transmission line considered in this study was in low-to-moderate tornado activity region of the USA22 Although the probability of tornado strike at

0001

0002

0005

001

002

005Design MRP

1700minusyear700minusyear300minusyear

0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)

Number of damaged towers N

Rat

e of

exc

eeda

nce

D

(per

yea

r)

Fig 9 Damage curves for the MiamindashAtlanta transmission line for three different MRPs of design wind speeds

MRP of design wind speed MRP of any damage MRP of gt 10 damage300 years 30 years 93 years700 years 54 years 189 years1700 years 90 years 373 years

Table 1 MRPs of damage to the Miami-Atlanta transmission line for different MRPs of design wind speed

Fig 10 Risk curves for Miami-Atlanta transmission line for three different MRPs of design wind speeds

0001

0002

0005

001

002

005

0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)

Loss L (million dollars)

Rat

e of

exc

eeda

nce

L

(per

yea

r) Design MRP


MRP of design wind speed Average annual lossExpected lifetime loss

50-Year life span 100-Year life span

300 years $875 million $437 million $875 million700 years $446 million $223 million $446 million1700 years $244 million $122 million $244 million

Table 2 Average annual hurricane wind loss AAL and expected lifetime hurricane wind loss ELL for the Miami-Atlanta transmission line for three different MRPs of design wind speed

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any specific location is very low23 the probability of tornado strike anywhere along a long transmission line can be significant5 In this study the tornado wind speeds have not been considered but they can be considered in a more refined analysis

Conclusions

1 The minimum design requirements for transmission lines in the USA address only the risk of injury and death to humans from construc-tion operation and maintenance of transmission lines They do not explicitly address the risk to opera-tors and consumers from the disrup-tion of power supply

2 Design based on site-specifi c hazard analysis provides a low perception of risk to long continuous structures such as transmission lines It has been shown that a 1076 km (669 mi) long transmission line designed for 700-year MRP wind speed is dam-aged with an MRP of only 54 years

3 If long continuous structures such as transmission lines are designed for site-specifi c loads in building codes an aggregate assessment of the risk can be performed using the method discussed in this paper

4 A risk-based design criterion for transmission line can be determined by using the approach presented In the long run it is more economical to design a longer transmission line to a higher criterion than a shorter transmission line

5 Although the discussion in this paper is limited to hurricane damage to transmission lines it is equally appli-cable to earthquake and fl ood dam-age to transmission lines and other long continuous structures such as pipelines canals and high-speed rails

Acknowledgements

The following contributions are gratefully acknowledged Dr Frank Lavelle of Applied Research Associates (ARA) provided the hurricane data used in this study Mr Esam Abraham of Southern California Edison (SCE) provided feedback on the costs associ-ated with structural repairs and interruption of transmission lines Mr Shane Vasbinder of Basin Electric Power Cooperative provided information regarding cascade failure in transmission lines Mr Nicholas Legatos and Dr Martin Koller provided feedback on the paper and two anonymous reviewers of the

manuscript provided several helpful sugges-tions to improve this paper

Nomenclature

l Rate of exceedance of specific wind speed (number of times per year)

lD Rate of exceedance of dam-age to gt N towers

lL Rate of exceedance of specific loss in $

Ω Over strength = actualdesign strength

t Time span (years)

ASCE American Society of Civil Engineers

AAL Average annual loss

ELL Expected lifetime loss

Ft Feet

FEMA Federal Emergency Manage-ment Agency

kV Kilovolt

L Loss (million $)

M Meters

Mph Miles per hour

MRP Mean return period

N Number of damaged towers

NESC National Electrical Safety Code

P Probability of exceedance

S Seconds

USA United States of America

V 3-second gust at 10 m above ground in Open Terrain2

References

[1] IEEE National Electrical Safety Code (NESC) C2-2012 Institute of Electrical and Electronics Engineers Inc New York 2012

[2] ASCE Minimum design loads for buildings and other structures ASCESEI 7-10 American Society of Civil Engineers Reston 2010

[3] Vi ckery PJ Twisdale LA Prediction of hur-ricane wind speeds in the United States J Struct Eng 1995 121(11) 1691ndash1699

[4] Tw isdale LA Dunn WL Probabilistic anal-ysis of tornado wind risks J Struct Eng 1983 109(2) 468ndash488

[5] Tw isdale LA Wind-loading underestimate in transmission line design Trans Distrib 1982 40ndash46

[6] Mi lford RV Goliger AM Tornado risk model for transmission line design J Wind Eng Indust Aerodynam 1997 72(1ndash3) 469ndash478

[7] Go likova TN Golikov BF Savvaitov DS Methods of calculating icing loads on overhead lines as spatial constructions Proceedings of First International Workshop on Atmospheric Icing of Structures CRREL Special Report June 83ndash17 341ndash346 1983

[8] La flamme J Spatial variation of extreme val-ues in the case of freezing rain icing Proceedings of Sixth International Workshop on Atmospheric Icing of Structures Hungarian Electricity Board Budapest 1993 19ndash23

[9] AS CE Guidelines for Electrical Transmission Line Structural Loading ASCE-74 Wong CJ Miller MD (eds) 3rd edn American Society of Civil Engineers Reston 2009

[10] V ickery PJ Skerlj PF Twisdale LA Jr Simulation of hurricane risk in the US using an empirical track model J Struct Eng 126(10) 2000 126(10) 1222ndash1237

[11] A SCE Minimum Design Loads for Build ings and Other Structures ASCESEI 7-05 American Society of Civil Engineers Reston 2006

[12] F EMA HAZUS-MH MR4 Hurricane Model Technical Manual Federal Emergency Management Agency Mitigation Division Washington 2009

[13] B atts ME Cordes MR Russell LR Shaver JR Simiu E Hurricane wind speeds in the United States Rep No BSS-124 US Department of Commerce National Bureau of Standards 1980

[14] H olland GJ An analytic model of the wind and pressure profiles in hurricanes Mon Weather Rev 108 1980 108 1212ndash1218

[15] T wisdale LA Vickery PJ Hardy MB Uncertainties in the prediction of hurricane wind speeds Proceedings of ASCE Conference on Hurricanes of 1992 1993 706ndash715

[16] D eMaria M Kaplan J An updated statisti-cal hurricane intensity prediction scheme SHIPS for the Atlantic and eastern north Pacific basins Wea Forecast 1999 14 326ndash337

[17] N owak AS Collins KR Reliability of Structures International edn McGraw-Hill New York 2000

[18] V ickery PJ Wadhera D Twisdale LA Jr Lavelle FM US Hurricane wind speed risk and uncertainty J Struct Eng ASCE 135(3) 2009 135(3) 301ndash320

[19] E idinger JM Kempner L Jr Reliability of transmission towers under extreme wind and ice loading CIGRE Session 2012 International Council on Large Electrical Systems Paris France

[20] A SCE Design of Latticed Steel Transmission Structures ASCE 10 American Society of Civil Engineers Reston 1997

[21] P aschen R Pezard J Zago P Probabilistic Evaluation on Test Results of Transmission Line Towers 22-13 CIGRE Session 1988 International Council on Large Electrical Systems Paris France

[22] F EMA Tornado Activity in the United States Federal Emergency Management Agency httpwwwfemagovplanpreventsaferoomtsfs02_torn_activityshtm 11 August 2010

[23] M acDonald A Wind Loading on Buildings John Wiley amp Sons Inc New York

Authors

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key hurricane parameters (radius to maximum wind central pressure dif-ference and translational speed) from their respective probability distribu-tions derived from historical data13ndash16 Each hurricane event produces a ldquofootprintrdquo of spatially varying wind speeds Figure 2 shows the footprint of a hurricane event that makes land-fall in South Carolina This is one of the 71 515 hurricane footprints in a ldquo10 000-yearrdquo simulation generated in Ref [10] It was assumed that the hurricanes follow a time-independent (Poisson) process that is the size and frequency of hurricanes do not change with time The potential effect of cli-mate change on the size and frequency of hurricanes was not considered in this simulation The Poisson assump-tion is also made in the generation of ASCE 7-102 wind speed maps The ldquo10 000-yearrdquo simulation of hurricanes was considered reasonable for the purpose of this study because the mean return period (MRP) of design wind speeds for transmission lines is only a few hundred years

Design Based on Site-Specific Hazard Analysis

The design criterion for structures is typically based on site-specific proba-bilistic hazard analysis Site-specific probabilistic hurricane hazard analysis is performed at individual sites with-out giving any consideration to other sites At each site the wind speeds from 71 515 hurricane events were arranged in an ascending order Each wind speed has an associated occur-rence rate that equals the occurrence rate of the hurricane event which pro-duces that wind speed The occurrence rates of wind speeds exceeding specific values (eg 50 55 and 60 ms) were added to generate a plot between the wind speed V and its rate of exceed-ance l (number of times per year) This is known as the wind speed haz-ard curve for the site Figure 3 shows the wind speed hazard curve for a site in South Carolina (34ordm N 801376ordm W) For a Poisson process the reciprocal of the rate of exceedance is the MRP of exceedance17

MRP = 1l (1)

MRP is the average time between suc-cessive occurrences of a Poisson pro-cess it is measured in years In Fig 3 the MRP of exceedance is shown on the right-hand side For a Poisson process the probability of exceedance

100 to 115 mph (447ndash514 ms)

115 to 130 mph (514ndash581 ms)

gt130 mph (gt581 ms)

Fig 2 Footprint of a simulated hurricane event that makes landfall in South Carolina The wind speeds shown in different colors are for 3-second gust at 33 ft (10 m) above ground in Open Terrain2

00002

0001

001

01

Rat

e of

exc

eeda

nce

(

per

year

)

20 30 40 50 60

10

100

1000

5000

Exc

eeda

nce

retu

rn p

erio

d T

(ye

ars)

Wind speed V (ms)

Fig 3 Hurricane wind speed hazard curve for a site in South Carolina (34degN 801376degW)

Fig 1 A 500 kV power transmission near Bowdle South Dakota (image by Gary Christenson Basin Electric Power Cooperative)

Authors

Cop

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120 mph (54 ms)

130 mph (58 ms)

140 mph (63 ms)


Miami FL

Atlanta GA



115 to 125 mph (514ndash559 ms)

125 to 135 mph (559ndash604 ms)


Miami FL

Atlanta GA


Authors

Cop

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06 08 1 12 14 16 18 20

04

08

12

16

Over strength (Ω)

Pro

babi

lity

dens

ity


0001

0002

0005

001

002

005

0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)


ate

of e

xcee

danc

e

D (p

er y

ear)


Authors

Cop

y












0001

0002

0005

001

002

005Design MRP


0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)


Rat

e of

exc

eeda

nce

D

(per

yea

r)





0001

0002

0005

001

002

005

0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)


Rat

e of

exc

eeda

nce

L

(per

yea

r) Design MRP






Authors

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Conclusions






Acknowledgements



Nomenclature





t Time span (years)




Ft Feet


kV Kilovolt

L Loss (million $)

M Meters

Mph Miles per hour





S Seconds



References
























Authors

Cop

y












120 mph (54 ms)

130 mph (58 ms)

140 mph (63 ms)


Miami FL

Atlanta GA



115 to 125 mph (514ndash559 ms)

125 to 135 mph (559ndash604 ms)


Miami FL

Atlanta GA


Authors

Cop

y








06 08 1 12 14 16 18 20

04

08

12

16

Over strength (Ω)

Pro

babi

lity

dens

ity


0001

0002

0005

001

002

005

0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)


ate

of e

xcee

danc

e

D (p

er y

ear)


Authors

Cop

y












0001

0002

0005

001

002

005Design MRP


0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)


Rat

e of

exc

eeda

nce

D

(per

yea

r)





0001

0002

0005

001

002

005

0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)


Rat

e of

exc

eeda

nce

L

(per

yea

r) Design MRP






Authors

Cop

y



Conclusions






Acknowledgements



Nomenclature





t Time span (years)




Ft Feet


kV Kilovolt

L Loss (million $)

M Meters

Mph Miles per hour





S Seconds



References
























Authors

Cop

y








06 08 1 12 14 16 18 20

04

08

12

16

Over strength (Ω)

Pro

babi

lity

dens

ity


0001

0002

0005

001

002

005

0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)


ate

of e

xcee

danc

e

D (p

er y

ear)


Authors

Cop

y












0001

0002

0005

001

002

005Design MRP


0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)


Rat

e of

exc

eeda

nce

D

(per

yea

r)





0001

0002

0005

001

002

005

0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)


Rat

e of

exc

eeda

nce

L

(per

yea

r) Design MRP






Authors

Cop

y



Conclusions






Acknowledgements



Nomenclature





t Time span (years)




Ft Feet


kV Kilovolt

L Loss (million $)

M Meters

Mph Miles per hour





S Seconds



References
























Authors

Cop

y












0001

0002

0005

001

002

005Design MRP


0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)


Rat

e of

exc

eeda

nce

D

(per

yea

r)





0001

0002

0005

001

002

005

0 100 200 300 400

20

50

100

200

500

1000

MR

P o

f exc

eeda

nce

(yea

rs)


Rat

e of

exc

eeda

nce

L

(per

yea

r) Design MRP






Authors

Cop

y



Conclusions






Acknowledgements



Nomenclature





t Time span (years)




Ft Feet


kV Kilovolt

L Loss (million $)

M Meters

Mph Miles per hour





S Seconds



References
























Authors

Cop

y



Conclusions






Acknowledgements



Nomenclature





t Time span (years)




Ft Feet


kV Kilovolt

L Loss (million $)

M Meters

Mph Miles per hour





S Seconds



References
























Authors

Cop

y

risk-based design of transmission lines for hurricane winds

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