Reducing Greenhouse Gas Emissions through Improving the Life Span of Wooden Power Electric Poles of Eucalyptus saligna

The present work deals with reducing greenhouse gas emissions through improving the life span of wooden power electric poles of Eucalyptus saligna. Indeed, in Sub-Saharan African countries, Cameroon in particular, most of the power line networks are made of wooden supports and according to the Cameroon energy distribution company, wooden poles represent 32% of the causes of death linked to the state of the network. The company’s 2019 annual report indicates that 40,000 wooden poles were in critical condition and should be replaced. A significant number of mechanical failures affecting these supports have been observed. For example, on the HVA/LV power line “D17 Nko-abang” in Yaoundé in Cameroon, less than three years old, 10 (ten) cases of poles falling and/or breaking, due to their mechanical loading, were observed over a period of fewer than nine months, causing an average service stoppage for more than 11 hours and affecting an average of 3280 customers. These incidents lead to questions about how the supports are dimensioned and what load capacities they are designed to support. The aim of this work is, there-fore, to suggest a method of dimensioning wooden poles hence reducing greenhouse gas emissions due to the deforestation by reducing the number of wooden poles at risk to be replaced


Introduction
The public and industrial electricity power supply requires efficient production equipment and reliable transmission and distribution networks. In Sub-Saharan Africa, the transmission and distribution networks are mostly constituted of "overhead power lines", which are assemblies of conductor cables held by steel, concrete or wooden supports.
In Cameroon, in particular, a great number of mechanical failures affecting the electric line supports are still observed, causing financial losses, risks to the people's safety and goods, electrical power distribution/supply services interruptions, and increased deforestation. According to the Cameroon energy distribution company, wooden poles account for 32% of causes of death linked to the condition of the grid. The company's 2019 annual report indicates that 40,000 wooden poles were in critical condition and should be replaced [1]. A significant number of mechanical failures affecting these supports have been observed. For example, over a period of fewer than nine months, 10 cases of poles' failures or breakings under the effect of their mechanical loading have been reported on the D17 Nkoabang power line in Yaoundé Cameroon, in electrical power line networks which are less than three years old. It should be noted that these incidents caused an average downtime of more than 11 hours 41 minutes to more than 3280 customers on average [2]. This early replacement of these wooden poles increases deforestation, and therefore, increases greenhouse gas emissions. This state of affairs questions the validity of the dimensioning initially done for those wooden poles, and their ability to support loads. What are the current loads of the supports? How to dimension the wooden power line supports to be more reliable, more sustainable and how to reduce greenhouse gas emissions due to the deforestation? This work attempts to answer these questions. The first section is devoted to the constituent elements and characteristics of power lines, and presents the methods and formulas used to dimension wooden poles. The second section presents the results obtained after applying these methods on the D17 Nkoabang power line supports, and the third section determines the loading state of the differrent columns and proposes dimensioning complements in order to make the line supports more reliable and more sustainable.

Elements of an Electric Power Line
The elements of an electric transmission line are conductors, line's supports and the line's accessories. Modern Mechanical Engineering

The Conductor
The conductor is the piece of hardware through which circulates the electric current. Here, its sizing is essentially to choose/determine: its material, its section area and its structure. This structure reveals how the different strands of conductor have been assembled together, in a smooth or twisted pack, to favour either mechanical resistance or heat dissipation [3]. The most commonly used materials for electrical conductors are copper, aluminium, and alloys produced from one of them. The material met in this study is almelec, and the conductors have the twisted structure. Some useful features of almelec conductors are recorded in Table 1.

The Line Accessories
After the conductor, follow the line accessories. Among these accessories, we find: -Insulators (in the form of a seat): these are insulating elements making the connection between the conductors and the supports. They play role both in mechanical (for fixing the conductor to the support, maintaining a suitable tension) and in electrical (for providing insulation between the conductor and the support). Their choice is made essentially according to the level of voltage carried by the conductor. Insulators are used for currents medium and high voltage; -Suspension and fixing elements (clamps, cross members, uprights, rods, fasteners, plates, fittings…). They are essential to link the conductor to its support; -Some supports are fitted with anti-cascade devices, to protect the line in case of incident; -According to the type of conductor, its length, and the wind speed, vibration absorbers may be required on some lines.

The Line Support
It is the hardware element that carries and suspends the conductors at the required height, in order to ensure people and environment safety. It must be able to withstand the applied loads/efforts on it in a sustainable way, without breaking and the trunks are smoothly scrolled, with a shape close to that of a cylinder or a low-angle cone trunk. The sizes to be determined for a pole are its cross-section (or its diameter or its circumference), and its height. The latter is broken down into four parts, as shown in Figure 1 below.
The head height h head is the pole's height above the point where the lowest conductor is fixed on the pole. The beam f represents the maximum difference of height between the point where the conductor is fixed on the pole and the lowest point of the suspended conductor. The ground clearance H ground represents the minimum distance to maintain between the ground and the lowest point of the suspended conductor, for security reasons. The implanted height h im is the height of the pole to be buried in the ground, so as to ensure stability.
For further sizing computations, it is necessary to define the anchorage height H a (distance between ground and the point where the conductor is linked to the pole) and the height above ground H r (the pole's height measured from the ground level).
The type of wood used is that of the Eucalyptus, whose mechanical characteristics are noted in Table 2.
Eucalyptus wood poles are divided into 7 classes (A, B, C, D, E, F and G).
They are classified according to their diameters (measured at the poles base and at the poles head), circumferences, average volume, average weight or admissible load [10]. Regardless, the poles are also declined into 3 categories (see Figure 2),   Hence, the sizing to be done for a pole will result in choosing a class, a height and a mode of assembly.

Applied Efforts on the Pole
The wooden pole in service undergoes efforts divided into three (3), according to their direction.
• Vertical effort is made of the conductor's and line accessories weight ( Figure   3).
Conductors weight on one side and the side other of the pole. It doesn't represent the entire weight of the conductors, but only the portion effectively supported by the considered pole.
In the further work, only the resulting force (V) will be considered.   The contact action of the conductor on the pole (Ti) has two components: the vertical is nothing else than the conductor's weight, and the horizontal component (Li) is the tensile strength of the conductor. This is the one counted as longitudinal effort.
In the further work, only (L) will be considered as the resultant of the tensile strengths of the different conductors linked to the pole.
• Transverse effort is due to the action of wind, both on the pole and on the carried conductors ( Figure 5). Wind actions on the conductor (t1) and on the pole itself (t2). In the further work, only (T) will be considered as the resulting transverse effort applied on top of the pole. This will produce the same effect (bending moment) as the two previous extended forces.
• The balance of the applied efforts on the pole is represented on Figure 6.
The forces are used according to the chosen limits of the dimensioning. The permanent effort is used for dimensioning the pole with regards to its elastic limit. It takes into account the loads that the pole must support at all times, and is determined assuming the minimum wind and the minimum tensile strength of  The nominal effort is used for dimensioning the pole with regards to its breaking limits. A value is determined for each of the possible climatic conditions in the area, and the maximum value is used for dimensioning.

Methods
The methodology used for dimensioning wooden poles is the synthesis of four calculation approaches below: 1) The one established by the French "the French Electricity Transmission Network (RTE)" [11]; 2) The one promulgated by the Belgium "the General Regulation on Electrical Installations (RGIE) of Belgium" [12]; 3) The one adopted for the calculation of the American electricity network This approach is articulated around eight main steps: the choice of the conductor and accessories, the evaluation/balance sheet of the loads and efforts directly sustain by the conductor, the verification of the conductor to vibrations, the calculation of the (minimum) height of the support, the efforts (and the moments) which will apply to the support, the choice of the support and the choice of the embedding. Since we are working on an existing network, our work will consist of collecting data on those elements, to evaluate the loads and stresses on the conductors of the line, and to calculate the forces applied to the poles and compare these forces with the nominal forces.

Efforts on the Conductor
To dimension a pole, it is necessary to take into account the conductor's deflection and the forces that the conductor transfers to the pole.

La the Arrow
A conductor suspended between two posts takes the form of a chain with the equation: ( ) y a ch x a = ⋅ [14] and its deflection given by: With f: conductor's beam (m), p: conductor's linear weight (N·m −1 ), T: conductor's horizontal tensile strength (N), and d: distance between the two poles (m).

Mechanical Tension
The mechanical stress of the conductor is affected by the weather conditions. To take this into account, the following equation of state is to be used: With p: conductor's linear weight (N·m −1 ), T conductor's horizontal tensile strength (N), d: distance between the two poles (m), E: conductor's Young modulus (MPa), S: conductor's section area (mm 2 ), α: conductor's linear expansion coefficient (˚C −1 ) and θ: temperature (˚C).
In practice, the state Equation (2) is used to determine the value of the mechanical tensile strength T in the conductor in different climatic conditions, and Equation (1) then gives the beam.

The Various Efforts Applied on the Pole by Conductor
These efforts are vertical effort, longitudinal effort and transverse effort.

Vertical Effort
The vertical effort corresponds to the amount of the conductors' weight effectively supported by the pole. It is worth: With p: conductor's weight (N), ρ: conductor's density (kg·m −3 ), S: conductor's section area (mm 2 ), I p : weight rang of conductor (m) and g: gravity (N·kg −1 ).

Longitudinal Effort
The longitudinal effort is the result of mechanical tensile strength of the conductors linked to the pole.
The term given by

Wood Pole Computation
In general, the support is similar to a vertical beam embedded at its lower end and subjected, in addition to the effect of its own weight, to two other types of stress: -A compression force, due to the weight of the conductors on either side of the support; -A bending stress, resulting from the action of the wind on the support itself or on the conductors, and possibly from the asymmetry of the conductors.

The Pole's Height
The total height of a support is the sum of: the installation height h im , the ground clearance H ground , the maximum conductor's beam f, and the head height h head [4].  Head height depends on the armament of the pole, and is usually between 0 and 0.5 m for the highest placed conductors. Ground clearance is settled by an inter-ministerial order, and depends on the area [20]. Implanted height approximately worth: Conductor's beam is determined by Equation (1) previously given; here, it is its maximum value.

The Stress on the Pole
The various efforts are calculated individually, and then combined according to the principle of the resulting moment [12].
1) Longitudinal effort The moment of the longitudinal effort, calculated regarding the pole's foot, is given by:
With M 1 : momentum of the longitudinal effort (N·m), T: conductor's horizontal tensile strength (N) and H α : anchorage height of the conductor (m) 2) Transverse effort The transverse effort is made up of the wind action, both on the pole itself and on the conductors. The related moments are calculated using formulas: With M t1 : momentum of the wind action on the pole (N·m), C xp : pole's aerodynamic coefficient (no unit), q dyn : wind dynamic pressure (N·m −2 ), D': pole average diameter (m) and H r : height above ground (m).
With M tα : momentum of the wind on the conductor (N·m), F: wind action on the conductor (N) and H α : anchorage height of the conductor (m).
Transverse effort is then given by: On another hand, the combined resulting moment worth: The resulting head effort applied to the pole is then given by [4]: For the wood poles of the line that have a particular function, it is preferable to check that the permanent effort remains under the value causing plastic deformation. This value is given by the pole's catalogue [10].

Stresses and Deformations
The aim here is to determine the stresses and strains and to check that they remain below the permissible limit values [11]. We have used the "ideal model with the characteristics of the minor fiber" [12] [21]. It will be the model of a vertical straight cylindrical beam, whose diameter is either the head diameter of the pole or the foot diameter, whichever is the most unfavorable, and whose mechanical characteristics will be taken equal to those of the least resistant fibers found in Saligna eucalyptus trunks.
1) Bending stress The bending of the pole is due to horizontal loads.
The bending moment M f at the embedment has the following components: The resulting maximum stress is then determined: This stress must be less than the maximum permissible value (breaking limit for supports in alignment, and elastic limit for the others). Otherwise, a column with a larger diameter is chosen, which will have a greater quadratic moment and a reduced stress.

2) Horizontal beam
Given the horizontal loading of the posts, this maximum deflection has two components, which can be found from the deformation equation: With u pole's beam (m), M: resulting bending moment (N·m), I G : quadratic moment of the seciton (m 4 ) and D p : pole's diameter (m).
To check that it is less than 5% of H r (the dot is times Hr). If not, a pole with a larger diameter is chosen, which will have an enlarged quadratic moment of the section and a reduced deflection.

3) Buckling
Here the values are calculated to ensure that the pole does not buckle too much under vertical loading. These are on the one hand the pole's twinge λ and on the other hand the buckling critical load N c .
Let us recall the formulas of the critical buckling load. And critical constraint: We determine: -the limit twinge of Euler of our material, which is around 180: -the current twinge of our pole is: Then, two situations are conceivable.
If 20 λ ≥ , there is safety to buckling, and it is a question of checking that In any case, if buckling safety is not guaranteed, a pole with a larger diameter should be chosen.

Data of Nkoabang D17 Line
The The data of the power line are summarized in Table 3 below.
For conductors, an inter-ministerial decree gives the values of the different ground clearances according to the type of pole [20] (see Appendix 2).
The dimensioning calculation is carried out for each installation canton. Within the same canton, the mechanical tension of the conductors is constant, and the conductors have the same characteristics (except in the case of derivation).

Application to the First Pole of the First Canton
A pole of the first canton is selected for this application. The data collected on the field are recorded in Table 4 below, and explicit calculations follow.

Computation of the Pole's Height
In addition to the scope of data, we must take into consideration: ground clearance, linear weight and minimum mechanical tensile strength of the conductor, at 75˚C [3].
The computation using formula (1) then gives the beam 1.08 m f ≈ .
The attachment methods and the minimum distances to keep between the

Computation of the Vertical Effort
In addition to previous data (Table 4), the conductor's density (Table 1)  The vertical force is the sum of these two loads, i.e., 475.4 N vertical F ≈ .

Computation of the Transverse Effort
In addition to previous data, must be considered: aerodynamic coefficients for the conductors and the pole [2], conductor's diameter [2], wind dynamic pressure in the retained climate hypothesis [3], pole's average diameter [3], anchorage height and height above ground. The data are recorded in Table 5 below, for this pole.

Computation of the Longitudinal Effort
In addition to previous data, it is needed to know: Young modulus and linear expansion coefficient for the conductor (Table 6), tensile strength imposed at the implementation of the conductors [3], linear masses, and section areas.
A computer-based resolution from the state Equation (2)

Computation of the Resulting Effort in Head of the Pole
Considering the previous given data and found results, this effort can be computed from formulas (7), (12) and (13). For this pole, we find 12930 N head F ≈ .

Computation of the Pole's Maximum Bending Stress
The resulting bending moment applied on the pole and its average diameter are known already. Formula (15)

Application on the First Laying Canton
The data collected in the field that have to be taken into account for the calculation. They are compiled in Appendix 4.
Using these data, we determined the spans for the laying canton and the spans for each pole. These spans are given in Appendix 5.

Calculation of Pole Force of the First Canton
By applying the same method of calculating forces applied to the first pole of the first canton, and other the poles of canton, the values of the vertical, transverse, longitudinal and nominal forces applied are determined. Table 7 summarizes the results of these calculations and the nominal allowable stress for each pole.

Forces Calculation of the Column of Particular Function
Poles with particular function in this canton are Pole's Order 1 (stop pole), Pole's Order 5 (deviation pole) and Pole's Order 11 (anchorage pole). For these poles with a special function, it must also be checked that they do not acquire any noticeable plastic deformation. For this checking, the permanent forces have to be calculated (Table 8).

Assessment of the Entire Line
Similar calculations were applied to all columns in all cantons line for vertical, transverse, longitudinal and permanent loads. These calculations were used to establish the loading status of the poles of the entire line.

Height Verification
The height found for this first pole is: 11.75 m H ≈ Calculations confirm that a Green color => the pole suitably withstands the efforts. Yellow color => the pole withstands the efforts, but is close to its limits. Red color => the pole is loaded over its eligible limits.
height of 12 m is well indicated for this pole.

Verification of Nominal Effort at Nominal Allowable Forces
The resulting nominal effort is 12930 N tete F ≈ . This value is compared with the eligible nominal efforts listed in the pole's catalogue. The lowest pole found capable of supporting this effort is the strutted D12.

Checking in Relation to Bending
The maximum bending stress is 7 7.324 10 Pa f σ ≈ × The limit value for this pole (given in Table 2) is 5.5 × 10 7 Pa.
This result leads the need to select a pole with higher bending strength. The closest suitable pole is D12, which is strutted.

Findings
The pole in place here (type D12 twin) is no longer suitable for the forces to which it is subjected, in particular the nominal force at the head of the pole and the bending stress. It must be replaced by a D12 type pole that is strutted.

Checking the Efforts in Head
By comparing the head stress of each pole with its nominal allowable stress, we find that: three poles from the first canton (Pole's Order 1, 2 and 10), are 27.27% of the poles must be replaced, three other poles (Pole's Order. 4, 5 and 8), are 27.27% of the poles need to be monitored as their head forces are close to their nominal allowable forces five poles are 45.45% of the poles hold the forces perfectly.

Checking the Yield Strength of Poles with Special Functions
By comparing the permanent stress of each pole with its permissible permanent stress from Table 8, we can see that the permanent stress of Pole's Order 1 is above its yield strength, while that of Pole's Order 5 is slightly below its yield strength.

Conclusion
Out the 11 poles in the first canton, three poles (27.27%) need to be replaced.
Three other poles (27.27%) are considered sensitive, but can still be retained. The types of replacement posts are shown in Table 9. This state is summarized in Table 10 below. We evaluated the percentages of poles to be replaced along this line. Figure 8 shows these percentages by support loading condition.

Overall Assessment of the Entire Line
It emerges from this assessment that almost 53% of the poles need to be replaced or monitored, with 20% of the poles to be replaced automatically.
Out the 20% of poles to be replaced, 45% are corner poles, 40% are alignment poles and 15% are anchor or stop poles (Figure 9).

Analysis of the Causes of Poles Overloads and Proposal of Remedial Solutions
The high percentage of supports to be replaced on the network with less than three years of operation led us to carry out an in-depth analysis of the D17 Nkoabang line. This analysis revealed that many poles were overloaded by additional elements during their operation (see Picture 1). Among these elements, we can mention.
• Added Conductors by ENEO to meet the electricity needs of populations, establishments or industries newly established in the area;  • TV cable distribution conductors; • banners and posters; • Unrecognised conductors added by third parties for the purpose of fraudulent supply of electricity from the ENEO network; • Lampposts.

Determination of the Expected Overload Coefficients of the Supports
We carried out an evaluation of the loads initially planned on the supports during the installation of the line (loads used for the initial dimensioning of the poles by ENEO) and the actual loads carried by each of the supports after three years of operation. For these two loads, we determined the vertical, longitudinal and transverse components. These components allowed us to evaluate the resulting loads on each support. The results recorded in Table 11 illustrate these overloads on a few critical supports. We have determined the overload coefficients for the different forces that stress the pole by making the ratios of the different forces. We have: actual effort on the 3 years of usage planned effort during initial sizing The average overload coefficients by direction of effort are summarized in Table 12.

Propositions
In front of the difficulty of preventing these overloads, which are mainly caused by acts of incivility, we propose that these overloads be included in the initial dimensioning of the poles from now. Therefore, these overload coefficients can be considered as second safety coefficients for future dimensioning of power line   poles in the region. For this reason, for:  The calculation of the nominal and permanent resultant stress, an additional coefficient of 2.2 will be applied to the stress;  Buckling verification, and in particular the calculation of the critical buckling load, an additional coefficient of 2.38 will be applied to the stress;  The verification at bending, an additional coefficient of 3.7 will be applied.

Conclusions
After analyzing the current line supports, we found the load of each pole, and compared these current forces to the nominal forces of the poles. The results of this comparison show that: 169 of the 845 poles in the line (20%) must be replaced because they either support nominal forces ranging from 113% to 150% of the admissible limit, or they are stressed beyond the limits in bending or buckling.
Another 280 posts (33%) must be monitored as they are almost at their limit (85% -98% of the permissible limit).
Regarding the overloads of the poles, we carried out an evaluation of the loads initially foreseen on the supports during the installation of the line (loads used for the initial dimensioning of the poles by ENEO) and the actual loads carried by each of the supports after three years of the operation. We then determined the two load cases on each pole, evaluated the resulting loads on each support in both cases and calculated the overload coefficient by reporting the different loads.