9th International Conference on Probabilistic Methods Applied to Power SystemsKTH, Stockholm, Sweden - June 11-15, 2006 1

Reliability Assessment of Electrical OverheadDistribution Wood Poles

Hong Li, Jiansen Zhang and Gouri Bhuyan

designed using deterministic design practices [5,6]. In thisAbstract-Wood poles are widely used for overhead paper, an evaluation of the achieved reliability of distribution

distribution system, and constitute an important component of wood poles selected according to the CSA C22.3 No.1utilities' assets. Since they are usually designed based on deterministic design requirement (both linear and non-linear)deterministic approach stipulated by utility's own design practiceor relevant nation standard, the reliabilities achieved are often spesented Thre typical referece strtue wr firsunknown. This paper presents a study on structural reliability of specified and pole classes were selected at the 15 locationsdistribution wood poles selected according to the Canadian across Canada for CSA C22.3 Grade 1, Grade 2 and Grade 3deterministic design requirement. Structural reliability of constructions. The reliabilities of the reference structures weretangent wood poles selected at 15 locations across Canada are then calculated using structural reliability method consideringevaluated and discussed. actual weather statistics of the locations.

Index Terms-Wood poles; Tangent pole; Wind; Ice; II. TYPICAL REFERENCE STRUCTURESStructural reliability, CSA C22.3 No.1

To calculate the reliability implied by the design practicesof the national standard CSA C22.3 design requirement, the

I. INTRODUCTION following three typical wood pole structures were chosen forD eterministic design approaches stipulated by several the analysis:

national standards, such as CSA C22.3 No. I [I] have * tangent three-phase pole - reference structure No. Ibeen used by utilities for designing overhead structures * tangent three-phase pole with communication cable -

for many years. These approaches utilize specified load reference structure No. 2factors and strength factors in combination with specified * tangent three-phase pole with secondary conductor,relevant zonal loading maps. The load factors and strength transformers and communication cable - referencefactors, for different grades of construction, have been structure No. 3selected based on subjective criteria. Although a long history III. POLE SELECTED AS PER THE GSA G22.3 DETERMINISTICof satisfactory performance of the overhead structuresprovides a reasonable basis for these factors, the actualperformance (or reliability) level achieved remains unknown. Using the standard engineering procedure the pole classSince 1990, reliability-based design methods (RBD) were was selected based on deterministic approach stipulated in theintroduced and incorporated in several national design CSA C22.3 standard and the recent updated load factors forstandards [1,2,3]. Before using reliability-based design, it is each of the three reference structures, each grade ofimportant to have some understanding of the performance that constructions and each of the four typical loading zones. Thecan be achieved using deterministic design practices. This CSA C22.3 load factors modified in 2003 [7] are shown inknowledge allows the design to be improved or a target Table 1 and the load intensity for the four loading zones isreliability to be established. Towards this end, ASCE/SEI shown in Table 2. Based on the assumption that wood speciesPole RBD Committee carried out a calibration study, in are interchangeable which is the basis of the size classificationwhich, three tangent poles were designed to 100% utilization according to CSA 015-05 [8], only western red cedar wasacross 40 U.S. locations according to NESC C2 deterministic considered in the pole selection. For the tangent poledesign approach (both Grade B and Grade C constructions) selection, both linear and non-linear (considering the P-Deltaand the structural reliabilities of these poles were effect) approaches were used with the corresponding loadcalculated [4]. Based on the study, the target reliabilities for factors. It should be noted that to reflect the general practicereliability-based design were established, used by utilities, the poles are selected based on pole

Similar efforts have been made in Canada to evaluate the classification, thus they are not designed for lOO0% utilization.achieved reliability of transmission and distribution structures

All three authors are in the Civil Infrastructures & Alternative EnergyTechnologies Department at Powertech Labs Inc., 12388-88th Avenue, Surrey,B.C. Canada

©C Copyright KTH 2006

9th International Conference on Probabilistic Methods Applied to Power SystemsKTH, Stockholm, Sweden - June 11-15, 2006 2

TABLE 1: LOAD FACTORS (REVISION TO PAGE 85 CSA C22.3 No. 1 2001) [7] (Prob (G < 0)) is called probability of failure. Conversely, theGrade 1 Grade 2 Grade 3 combination of the random variables resulting in G > 0 will

make the system perform as required, i.e. it will survive andl a)|oa-)l@ ^- U ° the corresponding probability (Prob (G > 0)) is termed

Load r;- -o reliability. The situation G = 0 is a limit state between failureoa) a0 D es raD X ( L)a) 0 and survival. To calculate the performance function, we- _ -Jo (xN <)|*: <DC-) - require a computational model, either numerical or analytical,

l: l0 l Zt = tD =, r describing the problem of interest. For example, let G beZ Z z X given as:

Vertical 4 2 2.7 1.5 2.0 1.2 G= M -M( x. )(30| x . ) ....................................... (3)Transversal 2 1.9 1.5 1.3 1.2 1.1Longitudinal 2 1 .9 1 .5 1 .3 1 .2 1.1 MO = bending strength ofwood pole

M =maximum bending moment at groundline, underTABLE 2: DESIGN LOAD INTENSITY AS PER CSA C22.3 No. 1 2001 randmawind andice loads.random wind and ice loads.

Wind pressureLoading zone (N/i2) Ice thickness (mm)The probability of failure termed as Pf can be obtained

Severe 400 19 through the calculation of the probability of the event G < 0.Heavy 400 12.5 As there are a number of random variables involved in G, theMedium A 400 6.5 exact calculation requires the joint probability density

function of all random variables and integration over thefailure region C < 0

According to the CSA C22.3 linear and non-linear design grequirement, pole classes were selected for three grades of Pf = ff.23.n(xIx2...xn)dxldx2...dX n.(4)construction at the 15 locations. It was found that for tangent G<Ostructures (reference Structures 1 to 3), there is a discrepancybetween pole classes selected using CSA C22.3 linear and However, this exact approach can hardly be applied since thenonlinear approaches. The CSA C22.3 nonlinear approach joint probability function f is unknown and very difficult to(considering P-Delta effect) in general yields a pole one class find. An alternative method is the straightforward, standardhigher than that selected using the linear approach for computer simulation (Monte Carlo method) which is simple toStructures 1 and 2, and two classes higher for Structure 3 implement and can converge to the exact solution. However, itwhere heavy equipment is attached. could be very computationally demanding, especially when

dealing with a low probability of failure. For example, if theIV. RELIABILITY AsSESSMENT probability of failure is 10 , the performance function must be

1) Basic Reliability Concepts evaluated 100000 times in order to observe, on average, one

outcome C < 0. A second alternative is the use ofThe reliability of a distribution wood pole structure is approximate methods that have been developed and widely

defined as the probability that it will perform as required in uedring thels three ded,shat FORM/SORMthe given conditions within a specified period of time. In poedures (FirstOrer oecod Od Re Methods)addition to the design parameters such as pole and conductor [9.Tem ore based ontculi oeliabilitysize that are treated as constants, the performance of the [9]. The methods are based on the calculation of the reliabilitystructure is normally affected by several random variables, rel b.FritP ic nbesti e aproximateyoa so in teq

such a poletrengt, windand ic loads reliability P, can be estimated approximately as shown in Equ.suchas pol stegh.id ncod. 5 and 6 by use of the Standard Normal probabilityThe reliability analysis in general is implemented based on y . . '

a performance function G(x) as follows: distribution function DQ.

G(X) = G()X lX2 @..X.) ( l)Pf =(D(- 3) ........................................... (5)

x = (xI, x2, . nx)T is an n-dimensional vector of random andvariables. P =1-D(-p)= 4(D).(6)Some of these may affect the applied loads denoted by D,

while the others may influence the load carrying capacity, To calculate the index ,6, a computer program is required suchdenoted by C. The performance function can be rewritten as: as RELAN [10].

G = CL-LD. .. .(2) 2) Performance Functions

If the combination of the random variables results in G < 0, For reliability assessment of the three reference structures,the structural system will not perform as intended, i.e. it will the bending failure mode at the groundline was considered infail. The corresponding probability of such event establishing the following performance functions.

©C Copyright KTH 2006

9th International Conference on Probabilistic Methods Applied to Power SystemsKTH, Stockholm, Sweden - June 11-15, 2006 3

Performance Function 1 - Bending failure at groundline4xunder wind during ice load case xa 3

G=R-S(V,t) .......... (7) a1

Performance Function 2 - Bending failure at groundline A A A A Aunder wind only load case 1

- *~~~~~~~~~~~~~~St ruct ure 2

G=R-S(FS ) ................ (8)0 A _Struct_ure3l0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

LocationsR bending strength of the wood pole at groundlineS groundline bending stress (considering P-Delta effect) Fig. 1: Grade 2 Construction Under Wind Only Loading -LinearVI = wind speed during ice 4V2= extreme wind speed xt = radial ice thickness

3) Strength Statistics Q A A

The statistics of wood pole bending strength were obtained 2from the standard CAN/CSA 015. Lognormal was assumed *7|as the probability distribution of the bending strength. m Structure2

4) Weather Statistics A Structure3

The weather statistics used in the reliability analysis were 2810 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

determined based on 50-year return wind speed and ice Locationsthickness obtained from the weather maps in GSA G22.3.hicknce r bityine fron yea window or cl

C

Annua Fig. 2: Grade 2 Construction Under Wind and Ice Loading -LinearSince reliability in one year window or called annualreliability was chosen for representing the reliability 4 Gassessment results, for each of the 15 locations the statistics of x.Grade2annual maximum wind speed, wind speed during ice and 3 *Grade_3annual maximum radial ice thickness were derived based ona***procedure [5] considering a coefficient of variation of 15% for 2 -A-----.-***-wind speed and 70% for ice thickness. Gumbel (Extreme- - m|Type I) distribution was assumed for above three weather- _- Arelated random variables. It should be noted that if reliability _ _ __l_Efor a specified time span (such as 30 years) is to be calculated, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1the statistics of the variables for that time span should be usedin the reliability analysis. Locations

5) ResultsReliability analyses were carried out for each of the three Fig. 3: Structure 3 Under Wind Only Loading- Linear

reference structures. Annual reliability index was obtained4 * Grade 1

using RELAN [0] for each of the load cases and designx | Grade3*2scenarios. 3I

The annual reliability indexes of the three reference 2 1

-I* * * ~*Astructures selected using linear approach for Grade 2 A

construction were obtained using RELAN [10] and are shown _ z~~~~~~~in Figs. 1 to 2, respectively for wind only and wind during iceAA * A Aload cases. The annual reliability indexes of Structure 3 1A Aselected using linear approach for Grades 1 to 3 constructionsare presented in Figs 3 to 4, respectively for wind only and 0

, ,, , ~~~~01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16wind during ice loadl cases. Figure 5 shows the annual Locationsreliability indexes (under wind only load case) of Structure 3selected using both linear and nonlinear approaches. Fig. 4: Structure 3 Under Wind and Ice Loading -Linear

©C Copyright KTH 2006

9th International Conference on Probabilistic Methods Applied to Power SystemsKTH, Stockholm, Sweden - June 11-15, 2006 4

4 design between the approaches.x * Linear

0 Non-linear REFERENCES_3

2.1 g g * * *[1] CSA C22.3 No. 1 -Overhead System, 2001.* * * [2] IEC 60826 - Design Criteria of Overhead Transmission Lines (Also the

X 2 * previous published guidelines- Loading and Strength of OverheadTransmission Lines IEC-TC11-Publication 826, 1991.

t | * + ** * + [3] ASCE 74 Guidelinesfor Transmission Line Structural Loading, 1991[4] Draft ASCE/SEI, Reliability-Based Design of Utility Pole Structure,

2003.__________________________________________ 1[5] Bhuyan, G., Li, H., and Foschi, R.O. "Assessing Design Approaches for

0!0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Overhead Transmission Lines Under Climatic Loads For New Projects

As Well as for Verification of Lines to be Upgraded", CEATI ReportLocations T003700-3301, 2003.

[6] Li, H, Zhang, J.S. and Bhuyan, G. "Assess Structural Reliability ofFig. 5: Structure 3 Under Wind Only Loading -Grade 2 Distribution Overhead Wood Pole Lines" CEATI Report (Draft)

T044700-5047 2005It can be seen from the above results presented that the [7] Revision to CSA C22.3 No. 1 2001, Replace Page 85, December 2003.

reliability achieved by CSA C22.3 deterministic design [8] CAN/CSA 015, Wood Utility Poles and Reinforcing Stubs, 2005.[9] Rackwitz, R. Fiessler, B. "Structural reliability under combined random

requirement varies substantially across the locations for the load sequences." Comp.& Struct. 9, 484-494,1978same grade of construction. The variation mainly results from [10] Foschi, R.O.; Li, H.; Folz, B, Yao, F. and Zhang, J. S. "RELAN:inconsistency between the design loads (loading zone) used Software for Reliability Analysis". Department of Civil Engineering,

and the local weatherconditionsconsideredintheUniversity of British Columbia, Vancouver, B.C., Canada V6T 1Z4,and the local weather conditions considered in the reliability 2000.analysis.

For some locations such as L4, the use of CSA C22.3 VI. BIOGRAPHIESdesign requirement results in ver,y low reliability in Hong Li received his BASc and MASc degrees incomparison to those achieved in other locations for the same Engineering Mechanics from Hohai University,grade of construction. Thus, instead of using the design loads Nanjing China, in 1984 and 1990 respectively. He

defined by loading zone, local weather conditions need to be obtained his Ph.D. degree in Structural Reliabilitydefined by loading zone, local weather conditions need to be Xfrom the University of British Columbia, Canada intaken into account in the design, which is the basis of 1999. Presently, as a Senior Reliability Engineer atreliability-based design approach. Powertech Labs he is working on asset management,

It should be noted that under wind only load case, the structural integrity and reliability, structuralanalysis, and numerical modeling. He has gained

reliabilities of reference structure 3 are the lowest among extensive experience in risk-based assetthose of the three reference structures, suggesting that for a management and reliability analysis of various T&D structures andun-guyed pole with heavy equipments, CSA C22.3 linear components. He is a registered Professional Engineer in the Province ofapproach may not provide adequate reliability in comparison British Columbia, Canada

to that of un-guyed poles without heavy equipment. Jiansen Zhang received his B. Sc. and M. Sc.From Figure 5, it is shown that the nonlinear approach degrees in Structural Engineering from Wuhan

always yields a design with higher reliability than that by the University of Technology, China in 1990 and 1993,linear approach. The differences in reliability between linear respectively, and his Ph. D. degree in

and non-linear approaches can be eliminated by adjusting the University of British Columbia, Canada in 2003.corresponding load factors based on reliability calibration. He is presently a research engineer with Powertech

Labs Inc, Canada, providing services in structural

V. SUMMARY AND CONCLUSIONS safety and reliability assessment, seismic analysis, design and retrofit, andapplication of artificial intelligence in civil infrastructures.

The CSA C22.3 deterministic design approach in generaldoes not produce uniform reliability for poles selected for the Gouri Bhuyan graduated with a Bachelor of Civilsame grade of construction but at different locations. For some Engineering Degree from Bhopal University, India

in 1980. He then obtained his Master in Technologylocations, the reliability achieved by the design practice is degree in Ocean Engineering from IdT. Madras inrather low, indicating that the criteria for loading zones 1982. In 1986, he obtained his Ph.D. degree instipulated in CSA C22.3 may need to be revised or sub-zones Ocean Engineering from the Memorial University of

may need to beadded. ~~~~~~~Newfoundland. At present he is themay needtoeaddedDirector of the Civil Infrastructure & Alternative

The linear and the nonlinear deterministic approaches as EnergyTechnologies Business Unit at Powertechstipulated in the standard are not consistent in terms of Labs. The unit provides consulting services relatedreliability achieved. The nonlinear approach generally yields a to utility asset management. He is also an adjunct professor of Civil

* . . ...........................Engineering at the University of British Columbia. He is a member of thedesign with higher pole class and thus higher reliability. For ASME and a registered Professional Engineer in the Province of Britishan un-guyed structure with heavy equipments, GSA G22.3 Columbia, Canada.linear approach may provides lower reliability in comparisonto that of un-guyed poles without heavy equipment. Effortsshould be made to calibrate the factors to achieved consistent

©C Copyright KTH 2006