6_Wooden Pole Ladder Network Model Development_Wiley

Wooden pole ladder network model development and vericationusing nite element analysis

C. D. Halevidis*,

School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece

SUMMARY

In this article, a new resistive ladder network, describing the electrical behavior of the wooden pole, crossarm, and their interconnection, is developed. The network is developed and veried using the results ofthe nite element analysis of the construction. Good agreement was achieved between the two analyses.In addition, several polecross arm topologies were studied, and the effect of the different elements onthe total resistance of the construction was quantied. Characteristically, it was found that the use of a steelcross arm instead of a wooden one decreases drastically the total resistance. Also, the use of a steel cross armbrace can reduce the total resistance by up to 37.4%. Copyright 2011 John Wiley & Sons, Ltd.

key words: cross arm; nite element model; ladder network model; leakage current; wooden pole

1. INTRODUCTION

Wooden poles are widely used for the support of the overhead middle voltage networks. This is due totheir low cost and their comparatively easier transportation to inaccessible places. It should be notedthat the continuous electricity supply of consumers is directly tied to the middle voltage networkreliability because of its great size [1]. Characteristically, the length of a single line can reach 100 km.Cross arms used in conjunction with wooden poles are made of wood, steel, or berglass. Wooden

cross arms exhibit better dielectric performance as they increase the critical ashover voltage acting asa secondary insulation system [2]. However, wood, when wet (having acquired a high moisture content),loses its insulation capability. In addition, when the insulator is polluted (combined with high humidity orlight rain), great leakage currents are developed. The leakage current can reach tens of milliampere [35].The ow of large leakage currents through the cross arm and the pole leads to a temperature rise andcarbonization of the wood [6]. The carbonization signicantly decreases the mechanical strength of thecross arm and can lead to the cross arm breaking. It should also be noted that the presence of an air-lledgap in the interface between wood and galvanized steel (in the cross armpole or cross arm-steel bracejunction) leads to signicant voltage drops and subsequently to minor arcing, which can cause ignitionof the wood and a pole top re [7].Steel cross arms are used for their superior mechanical strength. On the contrary, wooden cross arms

lose a signicant part of their strength in the course of time [8,9]. Steel cross arms intensify the pole topre danger because of arcing in the king bolt connecting the cross arm and the pole [10].Filter andMintz [11] simulated the wooden pole as a resistive ladder network fromwhich pole resistance,

voltage, and leakage current distribution along its height can be extracted. This pole model can account forthe varying moisture content along the pole height. Wong and Rahmat [12,13] modied this model so as tosimulate the pole, the cross arm, and their interconnection.

*Correspondence to: C. D. Halevidis, School of Electrical and Computer Engineering, National Technical University ofAthens, 9 Iroon Polytechniou Str., GR 15780, Athens, Greece.E-mail: [email protected]

Copyright 2011 John Wiley & Sons, Ltd.

EUROPEAN TRANSACTIONS ON ELECTRICAL POWEREuro. Trans. Electr. Power (2011)Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/etep.643

Ladder network models used to study the current distributions are approximations of the geometric ar-rangement of the cross armpole combination. In addition, the increased wood resistance across its grainis approximated by a lumped resistance. On the other hand, nite element analysis (FEA) uses the exactpole geometry and is capable of modeling the increased wood resistance across the grain as anisotropy ofthe material. Thus, FEA can be used for the verication of the validity of ladder network models.The aim of this article was the analysis and verication of the ladder network model using a nite ele-

ment model. The FEA results are assumed correct, and based on these, a new ladder network is proposed.This assumption is made because of the aforementioned reasons. This analysis is performed for both dryand wet conditions as well as for different polecross arm topologies (such as wooden or steel cross arm,the use or not of cross arm braces, etc.). Finally, the effect of each construction element is quantied.

2. WOODEN POLE

The wooden pole used for the development of the model is 12m in height and truncated cone shaped.The base diameter is 30.8 cm, and the conicity is 1.07 cm/m. The cross section of the wooden and steelcross arm is 10 12 cm and 7.5 10 cm, respectively, while the length is equal to 2.5m. The supportcross arm brace, when present, is made from steel. The pole geometry is shown in Figure 1.

Figure 1. Drawing of a wooden polecross arm.

Table I. Moisture content along pole height.

Height Sapwood (%) Heartwood (%)

Top 10.512m M M+ 5Central 1.510.5m+ cross arm M M+ 9Bottom 0.751.5m M+ 5 0.5M+ 19.5Bottom 00.75m M+ 5 30

C. D. HALEVIDIS

Copyright 2011 John Wiley & Sons, Ltd. Euro. Trans. Electr. Power (2011)DOI: 10.1002/ete

The pole is treated with chromate copper arsenate (CCA), a waterborne treatment, used to halt fungigrowth, responsible for the mechanical strength deterioration of the pole [14]. This treatment reaches adepth equal to 30% of the pole radius [11]. Consequently, heartwood is untreated while sapwood is im-pregnated. The wooden cross arm is considered entirely impregnated because of its small cross section.Sapwood and heartwood volume resistivity (rCCA and runtreated respectively) as a function of the

moisture content M.C. is given as follows [11]:

rCCA 10 0:25 %M:C: 9:12 m (1)runtreated 10 0:137 %M:C: 7:27 m (2)

Resistivity and physical dimensions determine the resistance of the wood along the grain (longitudinalresistance). Wood resistance to radial current ow (across the grain) is increased by a factor of 1.83 [15]

Figure 2. Part of the geometry and its tetrahedral discretization.

Figure 3. The topologies under consideration.

WOODEN POLE LADDER NETWORK MODEL AND FINITE ELEMENT ANALYSIS


(radial resistance). Sapwoodmoisture content in themiddle of the pole is 11.7% and 22.7% in the dry andwet condition, respectively. Using as basis, the moisture content for the entire pole is shown in Table I[11]. The maximum moisture content is 30%. Finally, the moisture content of the cross arm is consideredequal to .

3. FINITE ELEMENT MODEL

The mathematical model describing the electric eld of the pole arises directly from the Maxwellequations. As the frequency is very small, the electric and magnetic elds are uncoupled. Therefore,

r!E 0 (3)As

!J s !E (4)

jorC r!J (5)

re!E rC (6)!E rV (7)

where rC is the space charge (due to the time variant conduction current),!J is the current density, o is

the angular frequency, e is the relative permittivity of the medium, and V is the potential. Finally, theelectric eld is

Table II. FEA results.

No.construction Rcon (M) Vapp (V) Ileak (m)

Iheart (%),basemiddle

Isap (%),basemiddle

Vpole,sap(%)

Vpole,heart(%)

1 0.510 4700 9222 8.3 64.9 91.7 35.1 63.7 64.02 0.642 4700 7326 8.3 64.9 91.7 35.1 53 53.23 0.285 4700 16522 8.3 64.9 91.7 35.1 99.5 1004 0.300 4700 15682 8.3 64.9 91.7 35.1 99.7 1005 105.283 8660 82.25 98.1 95.7 1.9 4.3 10.2 10.26 168.252 8660 51.47 98.1 95.7 1.9 4.3 6.8 6.87 10.734 8660 806.83 98.1 95.7 1.9 4.3 99.7 1008 11.443 8660 756.81 98.1 95.7 1.9 4.3 99.9 100

Figure 4. Voltage along the cross arm.

C. D. HALEVIDIS


r e jso

!E

r e js

o

rV

0 (8)

In FEA, the differential equation, describing the phenomena, is solved in the space geometry. ANSYS13.0 was used for the nite element modeling. Part of the geometry and the performed tetrahedraldiscretization is shown in Figure 2.The following boundary conditions were used: the pole base is grounded and the top of the insulator

mounting bolt is at potential equal to Vapp. The increased wood resistance across the grain was modeledas anisotropy of the conductivity (decreased conductivity by a factor of 1.83 for the x- and y-axis).FEAwas performed for eight different polecross arm topologies. The topologies and their numbering are

shown in Figure 3. The mesh consisted of 148610, 104657, 143250, and 99297 tetrahedral elements fortopologies 1 and 5, 2 and 6, 3 and 7, and 4 and 8, respectively. Further renement of the mesh did not resultin altered results. The sapwood voltage at the height of the cross armpole junction (or the cross arm- bracejunction if applicable) was used to quantify the mesh renement effect on the results.Assuming a 20-kV line and a polluted insulator (whose resistance is in the order of 1), the voltage

Vapp applied to the construction in the wet condition is approximately 4700V. As the construction resistanceis greater in the dry condition, the applied voltage is assumed equal to 8660V. Although the applied voltagevaries between different topologies (as the construction resistance Rcon is different), it was deemed desirable

Figure 5. Sapwood voltage along the pole height.

Figure 6. Current ow at the pole top (denoted as arrows). (a) Including steel brace. (b) Without steel brace.



to use one voltage level for the dry condition model and one for the wet condition model in order for theresulting leakage currents to be comparable. Furthermore, the choice of the applied voltage does not alterthe construction resistance Rcon.From the results of the analysis, the leakage current distribution between heartwood and sapwood (Iheart

and Isap, respectively) at the pole base and the middle (at a height of 6m) of the pole and the total resistanceof the construction Rcon were calculated. In addition, the voltages applied to the pole sapwood Vpole,sap andheartwood Vpole,heart at the height of the bolt junction were quantied. The heartwood voltage Vpole,heart isequal to Vapp minus the voltage drop on the cross arm and can be used for the determination of the poleand cross arm resistances. The results are shown in Table II.The voltage at the centre of the cross arm cross section along its length, for the topologies under consid-

eration is shown in Figure 4. In addition, the voltage of the pole sapwood along a line following the poleconicity (the line does not cross the bolts) is shown in Figure 5.The spans of the wooden cross arm behind the insulator bolt and after the king bolt (or brace bolt if

present) are not subject to any current ow and thus are at the same potential as the respective bolts(Figure 4). Following the same reasoning, the pole voltage does not vary at a height greater than theheight of the king bolt junction (or brace bolt if present) (Figure 5). The current ow at the pole topis shown qualitatively in Figure 6. Finally, it should be noted that as the insulator mounting bolt fullypenetrates the cross arm, negligible radial current ow is observed. In addition, in the dry condition,negligible radial current ow is observed along the pole. On the contrary, when the pole is wet, signif-icant radial ow from the heartwood toward the sapwood at the height where the moisture contentchanges (1.5m from the base) is observed.

4. RESISTIVE LADDER NETWORK

A resistive ladder network with 24 steps of 0.5m each was used for the pole analysis. For the entire length ofthe wooden cross arm, ve steps of variable length were used so as to approximate with good precision theposition of the king and brace bolts without using a large number of steps. The number of steps was chosenso as to be equal with those used by Wong and Rahmat [13]. Specically, the rst step represents the crossarm length between the insulator mounting bolt and the rst brace bolt, the second step represents the lengthbetween the rst brace bolt and the king bolt, and the third step represents the length between the king bolt

Figure 7. The cross arm lengths represented by the ve variable-length steps.

Figure 8. Ladder network model step.

C. D. HALEVIDIS


and the second brace bolt. The fourth and the fth step represent the length between the second brace boltand the second insulator mounting bolt at the end of the cross arm. The cross arm lengths represented bythe ve steps of variable length are shown in Figure 7.

A ladder network model step is shown in Figure 8. R i h ; Ri s ; and R

i r are the heartwood, sapwood,

and radial resistances of the ith step, respectively.

Figure 9. Cross arm and pole ladder networks and their interconnection as presented byWong and Rahmat [13].

Figure 10. Proposed cross arm and pole ladder networks and their interconnection.



The ladder network is used to calculate the construction resistance Rcon, the total leakage current Ileak, andthe current owing through the heartwood Iheart and the sapwood Isap. The voltage along the pole height iscalculated as well.Next, a comparison of the results from the FEA and the ladder network as described byWong and Rahmat

[13] will be made. In addition, a new ladder network is proposed. This network incorporates the conclusionsgathered from the FEA.The pole and cross arm networks as well as their interconnection as described by Wong and Rahmat

[13] are shown in Figure 9. The proposed ladder network is shown in Figure 10. RS,CAi and Rr,CAi arethe sapwood and radial resistances of the ith step of the cross arm ladder network, respectively, RB isthe resistance of the brace bolts, RST is the resistance of the support braces, and RKB is the resistance ofthe king bolt.The following changes have been made:

First, the resistances Rr,CA are removed as there is negligible radial current ow in the cross armbecause of the full penetration of the cross arm by the bolts.

Second, as the king bolt fully penetrates the cross arm and the pole, its resistance is divided in twoparts: RKB,1 and RKB,2. RKB,1 represents the bolt resistance of the cross arm side part and RKB,2represents the resistance of the pole side part. RKB,2 bridges sapwood and heartwood, shuntingthe radial resistance.

Third, the resistance of the brace bolt that connects the cross arm and the support brace RB isconnected in series with the support brace resistance Rst instead of in parallel. This connectionis in accordance to the observed current ow.

It should be noted that, in the proposed ladder network, two of the ve cross arm sapwood resistances aredangling as no current ows through them (as the current densities due to a single insulator are studied).The results of the proposed ladder network and the ladder network of Wong et al. are shown in Table III.

In addition, assuming the results of the FEA as correct, the percentile error is calculated.

5. DISCUSSION

The results of both the FEA and ladder network models show that the total construction resistance isdrastically reduced because of a wet condition. Namely, in the case of wooden cross arm and steelsupport braces (cases 1 and 5), the wet condition resistance is reduced by 206 times compared withthe dry condition resistance. Correspondingly, in the case of steel cross arm and braces (cases 3 and 7),

Table III. Ladder networks simulation results.

No.construct Method

Ileak(m)

Isap(m)

Iheart(m)

Rcon()

Resistancepercentile error

Vpole(%)

Pole voltagepercentile error

1 Proposed 9151 8287 864 0.514 0.77 66.14 3.83Literature 10395 9414 981 0.453 12.72 75.13 17.94

2 Proposed 7124 6452 672 0.661 2.76 56.06 5.77Literature 8656 7840 816 0.544 18.15 68.36 28.98

3 Proposed 14688 13302 1386 0.320 12.28 100 0Literature 14688 13302 1386 0.320 12.28 100 0

4 Proposed 13823 12518 1305 0.340 13.33 100 0Literature 13544 12266 1278 0.347 15.67 100 0

5 Proposed 80.49 1.78 78.71 107.591 2.15 8.99 11.86Literature 118.73 3.02 115.71 72.939 44.34 13.22 29.61

6 Proposed 49.82 1.16 48.66 173.826 3.21 6.05 11.03Literature 91.31 2.31 89 94.837 77.40 11.06 62.65

7 Proposed 896 20.13 876 9.665 9.96 100 0Literature 899 23.41 876 9.633 10.28 100 0

8 Proposed 824 21.01 803 10.510 8.15 100 0Literature 825 21.23 804 10.497 8.27 100 0

C. D. HALEVIDIS


the wet condition resistance is reduced by 37.7 times compared with the dry condition resistance. It shouldbe noted that, as the resistance of the steel cross arm and brace is negligible and equal in the dry and wetconditions, the aforementioned reduction can be attributed to the reduction of the resistance of the pole by37.7 times from the dry to the wet condition.In the dry condition, the leakage current ows mainly through the heartwood (98.1%). In the wet condi-

tion, the leakage current, at a height greater than 1.5m from the ground, ows approximately two thirdsthrough the heartwood and one third through the sapwood (64.9% and 35.1%, respectively, at a height of6m). Near the pole base, the leakage current ows mainly through the sapwood (91.7%). This can beexplained from the CCA-treated sapwood conductivity, which is more sensitive to moisture contentchanges. Thus, near the pole base where the moisture content is increased, sapwood exhibits smaller resis-tance despite its smaller dimensions.From the results of the FEA, it can be concluded that the wooden cross arm accounts for a great part

of the total construction resistance. This can be attributed to its small cross section compared with thatof the pole. As an example, in the dry condition without cross arm braces (case 6), the wooden crossarm consists 93.2% of the total resistance (the pole accounts for 6.8% of the total voltage drop, andthus the rest of the voltage drop can be attributed to the cross arm). In addition, it can be seen thatits relative effect on resistance is smaller in the wet condition.The use of a steel cross arm reduces signicantly the total construction resistance as it replaces the

wooden one. Characteristically, in the dry condition without cross arm braces, it reduces the resistanceby 14.7 times (cases 6 and 8). This agrees with the wooden cross arm consisting 93.2% of the total resis-tance in case 6. Its resistance can be assumed to be negligible compared with the pole resistance. It shouldbe noted that as the steel cross arm reduces the total resistance, when minor arcing manifests between abolt and a wood, the arcing will be more intense. This agrees with the observations by Rahmat andWong[10].The use of a steel cross arm brace reduces the total construction resistance by 5% up to 37.4% in cases 3

and 4 and 5 and 6, respectively (the reduction is given as (Rcon,no barRcon,bar)/Rcon,no bar). Its effect is greaterin the dry condition. The reduced resistance is due to the shunting of a length of the cross arm and the pole(0.5m from the cross arm and 0.5m from the pole). This great reduction can be explained as the brace shuntsthe cross arm and the pole at the cross section minimum. In addition, the brace increases the voltage appliedon the pole.The knowledge of the current paths and densities through a cross armpole combination and the

quantication of its resistance can be useful in the study of the generated heat by partial dischargeand leakage currents inside a pole. This could lead to a better understanding of pole top res and crossarm carbonization (and possible breakage). In addition, the current distribution could be used in thedesign of pole top re mitigation techniques.The proposed ladder network was developed in such a manner so as to simulate the current ow observed

in the nite element model. More specically, the cross arm radial resistances have been removed as noradial current ow was observed. In addition, a part of the king bolt resistance RKB,2 shunts the pole radialresistance between the heartwood and the sapwood. Consequently, at the height of the bolt, sapwood andheartwood are equipotentially connected.The proposed ladder network achieves a close approximation of the results of the FEA in the topologies

containing a wooden cross arm (cases 1, 2, 5, and 6). Themaximum resistance percentile error was 3.21% incase 6. It should be noted that in all cases, the total construction resistance is overestimated. Finally, in thewet condition, the proposed network underestimates the relative cross arm resistance (cases 1 and 2). On theother hand, in the dry condition, it overestimates the relative cross arm resistance.The cross arm and pole ladder network and their interconnection as described byWong and Rahmat [13]

does not achieve good agreement with the results of the FEA in the topologies containing a wooden crossarm (cases 1, 2, 5, and 6). Namely, it underestimates the construction resistance and results in greater leakagecurrents. In addition, it underestimates the contribution of the cross arm to the total resistance as shown bythe increased voltage applied to the pole (Table III). This underestimation can be explained by the presenceof the radial resistances Rr,CA in the cross arm model as these resistances reduce the cross arm resistance.In the topologies containing a steel cross arm (cases 3, 4, 7, and 8), the proposed ladder network and the

ladder network as described by Wong and Rahmat [13] achieve close agreement. This can be explained bythe steel cross arm, which is represented in the same way by both networks. Furthermore, the maximum



percentile error of these cases is now increased to 13.33%. In addition, in the wet condition, the total con-struction resistance is overestimated, whereas in the dry condition, it is underestimated. Finally, it shouldbe noted that the results of the two networks for case 3 are not precisely equal.

6. CONCLUSION

In this article, the FEA of the electrical performance of eight different wooden polecross arm topologies wasperformed. From the results, the effects of the material used for the cross arm (wood or steel), the presence of across arm brace, and themoisture content on the total construction resistance were quantied. It was found thatthe cross arm brace can reduce the total resistance by up to 37.4%, whereas the use of a steel cross arm insteadof awooden one can reduce the resistance up to 14.7 times. In addition, a new ladder networkmodel describingthe cross arm, pole, and their interconnection, was proposed. This proposed network incorporates the results ofthe FEA regarding the current ow. The proposed ladder network results achieve good agreement with theresults of the FEA.

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6_Wooden Pole Ladder Network Model Development_Wiley

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