IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010 995

Study of Leakage Current Distribution in WoodenPole Using Ladder Network Model

K. L. Wong and M. F. Rahmat

AbstractA wooden pole is the most popular choice as thephysical support structure for an electrical distribution network.A recent increase in the failures of wooden poles that lead topole fires warrant further investigation into the performance ofwooden poles and pole design. This paper examines the leakagecurrent distributions on the radial, heartwood and sapwoodsection of the wood pole and the effect of the metal insertionin wooden structures using an electrical ladder network model.This paper presents the findings from two wooden pole models:a basic wooden pole and a complete wooden pole with cross-armand supporting bars attached. The results show that the bulk ofthe leakage current flows through the internal section under wetweather conditions and the metal insertion along the radial of thewood increase the magnitude of the leakage current. The modeltakes into consideration the pole dimension, rain parameter, mois-ture content, air resistance, and preservative effect (chromatedcopper arsenate) on the wooden pole.

Index TermsLadder circuits, leakage currents, poles andtowers.

I. INTRODUCTION

W OODEN poles have been commonly used to supportelectrical distribution throughout the world. More than5 million wooden poles are currently in service all around theAustralian distribution network and up to 70% were installedmore than 20 years ago. Based on economic figures, millionsof dollars of capital expenditure is needed for pole replacementover the next decade. Wooden poles, in general, are less expen-sive compared to manufactured alternative poles such as steeland concrete with minimum greenhouse effect [1]. The life ex-pectancy of a wooden pole is within the range of 30 to 40 years.Therefore, it is critical that there are continuous research worksin studying the performance and methods to prolong the life ex-pectancy of the wooden poles.

Most of the researches are concentrated on wooden polespreservation [2], [3], reliability and assessment of woodenpoles [4][8] and leakage current of high voltage insulatorsrelated to wooden poles [9][11]. The impregnated process ofwood with either oil-borne (pentachlorophenol) or water-bornepreservatives [ammonia copper arsenate (ACA) or chromatedcopper arsenate (CCA)] eliminate biological attack by fungi,

Manuscript received October 16, 2008; revised June 19, 2009. First pub-lished December 04, 2009; current version published March 24, 2010. Paperno. TPWRD-00735-2008.

The authors are with the RMIT University/School of Electrical and Com-puter Engineering, Melbourne, Vic., Australia (e-mail: alan.wong@rmit.edu.au;s3172130@student.rmit.edu.au).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRD.2009.2034894

insects, termites and woodpeckers and also increase the me-chanical and insulation strength [2]. The structural reliability ofwooden poles, nondestructive testing of pole measurement andminimizing life-cycle costs of inspection and refurbishment ofwood poles in large distribution networks has been studied in[4], [7] and [8]. It has been understood that leakage currentflow due to surface insulator contamination causes pole topfire and pocket burning during high humidity [11]. Althoughthe number of pole fires is small relative to the total numberof circuit-poles, the resulting damage and service interruptionmake their prevention of prime importance.

Wooden pole fires attributed the causes to several factors.Contamination of the insulator surface due to industrial pollu-tion, sea salt or agriculture spray and dust allows leakage cur-rent to flow on the surface of the insulator and through to thewooden pole. Precipitations such as fog or rain produce unevenwetting on the wood and together with wind provide the cat-alyst for causing ignition of the wood. Natural shrinkage andcracking of the wood loosening the metal and wood connec-tion may allow spark discharge inside the bolt hole with suffi-cient leakage current magnitude and adequate air in the sparkingzone [12]. It is reported that the annual wood pole failures in theWestern Australia network are between 1.88 and 4.34 pole fail-ures per year per 10 000, in comparison with the industry targetof 1 pole failure per year per 10 000 poles [13]. Wooden polesafety is critically important in asset management as it reduceswildfire ignition, protects the public from injury and minimizescostly power outages for power utility companies.

This paper presents new insights into the current distributionalong wooden poles using the ladder network model first pre-sented by Filter and Mintz [14] and the results will help us tobetter understand the causes of pole failure that lead to cata-strophic events such as pole fires. Sections II and III discussthe ladder network model, including the simulation environmentand the simulation results obtained from MATLAB. Section IVpresents a wooden pole model complete with cross-arm andmetal support and the simulation results in both dry and wetconditions followed by the conclusion in Section V.

II. WOODEN POLE MODELThe ladder network model was developed by Filter and Mintz

[14], which could be used to perform whole pole evaluationsand wood stake studies. The model consists of three wood re-sistances i.e., sapwood resistance , heartwood resistanceand radial resistance as shown in Fig. 1. The resistances inthis model are determined by pole species, type of preservativetreatment and moisture content percentage (MC %) of the pole.These three components are interconnected in the ladder net-work. The model provides possible connection points for other

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996 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010

Fig. 1. Resistance of wooden pole with king bolt insertion.

resistance representing pole hardware, cross arm or metal in-sertion. Rain resistance can be added to the model using a suit-able external bridging resistor, connected between the nodesalong the pole length.

The 0.75 m steps are chosen for the ladder model. For ex-ample, a 12 meter pole will be represented by a 16-step model.This step size is sufficient to describe the behavior at the bottom,middle and the top section of the pole. Section 1 represents thesection closest to the ground and section 16 is the highest sec-tion above ground as shown in Fig. 2. and represent theconductor resistance and water resistance on the wood surfacerespectively. However, these parameters are not taken in con-sideration in this study. The moisture content, was limitedto no more than 30% and scaling factor 1.83 was applied for the

reflected to the [15]. The moisture gradient relative tothe sapwood and heartwood along the wood pole is presentedin Table I. In our simulation, a typical 12 meter Red-Pine poleheight without cross-arm configuration was chosen. The top andbottom radius is 11 and 18 cm, respectively, and the top andbottom heartwood radius is 8.15 and 14.2 cm with 0.75 m stepand the pole was assumed to be treated with CCA. As depictedin Fig. 1, a king bolt of 2 resistance was installed at section12. The magnitude of leakage current depends on the degreeof insulator contamination and the overall pole resistance. Theequations for the and as a function of the moisture con-tent and the are shown in (1) and (2)

(1)(2)

III. RESULTS

A. Pole ResistanceIn this paper, the wooden pole is represented by 16 pole sec-

tions, with section 1 at the pole bottom, connected in ladder net-work format. Each pole section consists of radial, heartwood andsapwood components. Figs. 3 and Fig. 4 depict the values of thethree resistances in dry and wet conditions (11.7% and 22.7%moisture content). For dry pole section 16, which is the highest

Fig. 2. Wood pole ladder network model [14].

TABLE IPOLE MODEL MOISTURE GRADIENT RELATIVE TO THE SAPWOOD AND

THE HEARTWOOD ALONG THE WOOD POLE [14]

section above ground, the heartwood, sapwood and radial resis-tances is 2.89 M , 74.91 M and 137.09 M respectively.The value of resistance varies as the diameter of the pole in-creases from bottom to top. The linearity between the pole re-sistance and the pole diameter can be clearly seen, particularlyin pole section 3 to pole section 14 where the moisture contentremains constant. In the proposed model, the metal insertion isrepresented by a 2 resistor connected to the radial resistance

WONG AND RAHMAT: STUDY OF LEAKAGE CURRENT DISTRIBUTION IN WOODEN POLE USING LADDER NETWORK MODEL 997

Fig. 3. Resistance of dry wooden pole.

Fig. 4. Resistance of wet wooden pole.

at pole section 12. The effect of the king bolt insertion is visiblein both Figs. 3 and Fig. 4, especially when the wooden pole issubjected to moisture.

The moisture content has a significant role in wooden polemodeling. In accordance to the original model developed byFilter and Mintz [14], the moisture content increases from 9% atthe central position to 19.5% at 0.75 m to 1.5 m from the groundand eventually 30% at the section just above the ground. Theeffect of moisture content can clearly been seen in Fig. 3. Theheartwood section of a wooden pole has the lowest resistancelevel and this is a result of the higher percentage of moisturecontent level which resides in the heartwood section [15].

When the wooden pole is exposed to rain, the rain effect in-creases the overall moisture content. In this paper, a moisturelevel of 22.7% was chosen to represent the wet condition of thepole and the results can be found in Fig. 4. The moisture contentsignificantly reduces the value of the three resistive componentsof the wood. In comparison to the value of the dry condition,the heartwood, sapwood and radial resistances at pole section16 under the wet conditions is now 5.15 k , 133.22 k , and243.79 k , respectively.

B. Current Distribution of Dry and Wet Wooden PoleIn pole fire study, the insight into the leakage current distri-

bution across various pole sections is critical. Figs. 5, Fig. 6 andFig. 7 depict the current distribution for sapwood, heartwoodand radial resistance for pole section 1 to 16 under both dry andwet conditions. In dry conditions, the sum of the current across

Fig. 5. Current distribution for sapwood resistance.

Fig. 6. Current distribution for radial resistance.

Fig. 7. Current distribution for heartwood resistance.

the three resistances is almost equal to zero or negligible. Thesimulated results show that in the case when the insulation levelof the high voltage insulator reduced significantly due to surfacepollution, the high value of wood resistance limits the total cur-rent flow and the effect of the king bolt insertion at Section 12has minimum effect on the current distribution.

When the moisture level was set to 22.7%, which representstypical damp conditions occurring after rain, the overall leakagecurrent increases to the mA range. In the case of sapwood andheartwood resistance, the highest current of 4.9 mA appearsacross pole section 16, which is the pole top. Under wet con-ditions, the effect of the king bolt insertion can be clearly ob-served. In Fig. 6, we could see a current spike at pole section12 where the king bolt is located. Other observations include

998 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010

Fig. 8. Current distribution of wet radial resistance with different location ofking bolt.

the proportion of current flowing through the heartwood sec-tion. These sections carry most of the current through its heart-wood section down to the ground. Also, the change in currentdistribution at the bottom pole sections (0 to 1.5 m from ground)is contributed to by the higher moisture level. Leakage currentwith the value of 9.5 mA is recorded in the centre sections ofthe pole.

C. Current Distribution Analysis for Radial ResistanceThe damage to the wooden pole due to the pole fires fre-

quently takes place at the cross arm junction where the attach-ment of the king bolt or the insulators metal support is lo-cated. Fig. 8 depicts how the metal insertion affected the cur-rent flow across the radial resistance. In this simulation, threedifferent scenarios are created: the king bolt at pole section 14,pole section 12 and pole section 10. In the first scenario, a cur-rent spike is created at section 14. The leakage current is in-creased from 1.7 mA at pole section 15 to 3.4 mA. As the kingbolt is shifted down to section 12 and 10, the effect becomes lessapparent due to the fact that leakage current drops to approxi-mately 1 mA at pole section 14 for all three scenarios.

IV. COMPLETE WOODEN POLE MODELIn this paper, we extended the wooden pole originally pre-

sented in [14] to include a wooden cross-arm, steel-bar holderand air resistance between the metal and wood interface. Thecomplete wooden pole and the electrical network model areshown in Figs. 9 and Fig. 10. In this section, the followinganalyses were performed.

1. Effect of the steel bar holder.2. Effect of the air resistance.3. Effect of moisture in the wood.The steel bar being used as the cross-arm holder is common

practice in Australia and around the world. It is used to replacethe conventional wooden bar holder for its excellent mechanicalstrength and durability. For comparison, a wooden pole modelwith and without the steel bar is created and the results of the ra-dial current are presented in Fig. 11. The result highlights the ef-fect of the steel bar especially at pole section 13 and pole section14 under dry conditions. The introduction of the steel bar holdercauses the radial current at pole section 14 to increase from 0.04

Fig. 9. Wooden pole with cross-arm and supporting steel bars.

Fig. 10. Electrical model for the wooden pole and cross arm (including steelbar and king bolt).

Fig. 11. Radial current distribution of dry wooden pole.

to 0.12 mA. The steel-bar bolt, existence at pole section 13also creates another current concentration with a magnitude of0.15 mA. The installation of the steel bar causes overall resis-tance changes and results in higher current concentration at theking bolt, as shown in Fig. 11.

Continuous expansion and contraction of the wood influencedby the weather effect and varying air temperature, leads to theloosening of the king bolt, . A loosened bolt creates an airgap in between metal-wood and the wooden pole and woodencross arm junction. Previous reports confirmed that the air gapcreates a high voltage zone across the dry band region whichleads to sparking phenomena across the gap and eventually leadsto pole fire [16]. However, the results in Fig. 12 show that theair gap resistance, does not have much significant effect

WONG AND RAHMAT: STUDY OF LEAKAGE CURRENT DISTRIBUTION IN WOODEN POLE USING LADDER NETWORK MODEL 999

Fig. 12. Radial current distribution of dry wooden pole with cross-arm duringdry condition.

Fig. 13. Comparison of radial current distribution for complete wooden poleconfiguration with .

in terms of causing an increase in current concentration at theradial resistance.

Weather also played an important role in a pole fire event.During the dry season, the moisture content of the wooden polecan be as low as 11.7% and increase up to 22.7% when it isexposed to rain. Fig. 13 shows a large current spike for wetconditions at section 13 and 14 of the wooden pole. The radialcurrent increases from 0.15 to 9 mA in wet conditions at polesection 13. This large magnitude leakage current could lead topole fire phenomena.

V. CONCLUSIONThis paper demonstrates the use of the ladder network model

to study the current distribution in the wooden pole. The modelin this paper was developed based on actual physical detailsof a red-pine CCA-treated 12-meter pole. Since the heartwoodand sapwood resistance are represented by lumped parameters,many different forms of circuit analysis, which could notbe obtained experimentally, can be done using the computersimulation.

Many previous reports described how the loose metal contactbetween the wood and metal insertion contributes to the occur-rence of pole fires [16]. However, the results in Fig. 6 suggestthat higher current concentration occurs at the metal-wood junc-tion regardless of whether air gap exists between the wood andthe metal. The current concentration as shown in this figure is

Fig. 14. Complete leakage current model.

solely due to the reduction in the overall resistance as a result ofthe metal insertion.

The ladder network model also helps us to establish an im-portant fact whereby the bulk of leakage current flows under thesurface of the wood. The heartwood section carries the bulk cur-rent from the pole top to pole bottom and the king bolt insertionsets the upper limit for the amount of current flow. Furthermore,the impact of the king bolt can be clearly seen when it is locatedcloser to the source of the leakage current, in this case, it is adamaged or polluted insulator.

The results in this paper will help us to find new solutions ineliminating the occurrence of pole fires. This work highlightsthe important fact that a complete wooden pole model shouldbe adopted in leakage current studies since the leakage currentis a function of the line voltage and the total resistance con-sists of the insulator resistance and the wood resistance, as de-picted in Fig. 14. In addition, introduction of metal bolts andadditional structure such as a pole-mounted transformer shouldbe thoroughly examined and analyzed. Better pole design thattakes into account the current distribution on the sapwood, ra-dial, and heartwood resistance could provide the answer to thelong-standing pole fire problem.

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[8] S. V. Datla and M. D. Pandey, Estimation of life expectancy of woodpoles in electrical distribution network, Structure Safety, vol. 28, pp.304319, 2006.

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K. L. Wong, photograph and biography not available at the time of publication.

M. F. Rahmat, photograph and biography not available at the time of publica-tion.