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

Joseph Voufo^1,2*, Zakari Yaou^2,3, Florent Biyeme^1,2, Rolland Djomi^1,2, Richard Dadji Metangmo^1,4, Théodore Tchotang^1,2

¹National Advanced School of Engineering of Yaoundé (NASEY), Yaoundé, Cameroon.
²Laboratory of Civil and Mechanical Engineering, Yaoundé, Cameroon.
³Higher Technical Teacher Training College of Ebolowa, Ebolowa, Cameroon.
⁴Department of Industrial and Mechanical Engineering, Yaoundé, Cameroon.

DOI: 10.4236/mme.2022.121001                

Abstract

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, therefore, to suggest a method of dimensioning wooden poles hence reducing green- house gas emissions due to the deforestation by reducing the number of woo- den poles at risk to be replaced on Cameroon’s electricity distribution network. And more specifically, to reduce the number of mechanical failures affecting the wooden supports observed by analyzing the current wooden supports with their loads and to make proposals for improving the actual dimensioning me- thods. From the study carried out, it appears that 449 out of 845 supports, i.e., 53% needed to be replaced or monitored because they support the nominal forces ranging from 85% to 150% of their admissible limit and proposals have been made to improve their dimensioning.

Keywords

Electrical Power Line, Dimensioning Wooden Pole, Efforts on Pole, Pole’s Height, Method of Loading, Overload Coefficients

1. 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.

2. Material

2.1. Elements of an Electric Power Line

The elements of an electric transmission line are conductors, line’s supports and the line’s accessories.

2.1.1. 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.

2.1.2. 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.

2.1.3. 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

Table 1. Characteristics of the most common almelec conductors [4] [5] [6].

or significant deformation. Line supports are usually poles, porticos or towers, made of wood, concrete or steel. In this case study, the supports are wooden poles from Eucalyptus saligna wood, which present an advantageous compromise between mechanical characteristics, mass, regrowth period, availability and cost.

2.2. Applied Loads on the Eucalyptus Wooden Poles

2.2.1. Shape and Properties of the Eucalyptus Wooden Poles

The available Eucalyptus wood posts are approximately circular in cross-section, 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),

Figure 1. Characteristic heights of a pole.

Figure 2. Types of poles according to the assembly mode.

Table 2. Mechanical characteristics of Eucalyptus wood poles [7] [8] [9].

according to their assembly mode: (a) simple poles, (b) twin poles and (c) strutted poles.

Hence, the sizing to be done for a pole will result in choosing a class, a height and a mode of assembly.

2.2.2. 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.

· Longitudinal effort is the result of the conductors’ tensile strength (Figure 4).

Figure 3. Vertical effort on the pole.

Figure 4. Longitudinal effort on the pole.

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

Figure 5. Vertical effort on the pole.

Figure 6. Balance of the applied efforts on the pole.

the conductors.

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.

3. 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 [13];

4) The one in force in Cameroon [4].

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.

3.1. 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.

3.1.1. La the Arrow

A conductor suspended between two posts takes the form of a chain with the equation:

$y=a\cdot ch\left(x/a\right)$ [14]

and its deflection given by:

$f=p\cdot d^2/8T$ [15] [16] (1)

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).

3.1.2. 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:

$\frac{p^2\cdot d^2}{24T^2}-\frac{T}{E\cdot S}-\alpha \cdot \theta =\text{constant}$ [17] [18] (2)

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 (mm²), 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.

3.2. The Various Efforts Applied on the Pole by Conductor

These efforts are vertical effort, longitudinal effort and transverse effort.

3.2.1. Vertical Effort

The vertical effort corresponds to the amount of the conductors’ weight effectively supported by the pole. It is worth:

$p=\rho \cdot S\cdot I_p\cdot g$ (3)

With p: conductor’s weight (N), ρ: conductor’s density (kg·m⁻³), S: conductor’s section area (mm²), I_p: weight rang of conductor (m) and g: gravity (N·kg⁻¹).

3.2.2. Longitudinal Effort

The longitudinal effort is the result of mechanical tensile strength of the conductors linked to the pole.

$F=\frac{1}{2}k\cdot {\rho }_a\cdot v^2\cdot C_x\cdot D\cdot l_v$ [19] (4)

With F: wind action on conductor (N), k: dispersive coefficient (no unit), ρ_a: wind density (kg·m⁻³), v: win speed (m·s⁻¹), C_x: aerodynamic coefficient (no unit), D: conductor’s diameter (m) and l_p: weight rang of conductor (m).

The term given by $\frac{1}{2}k\cdot {\rho }_a\cdot v^2$ is called wind dynamic pressure, and often

noted q_dyn.

3.3. 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.

3.3.1. 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]. (Figure 7).

It is given by the formula:

Figure 7. Characteristic heights of a pole.

$h_{im}=0.1H_{ground}+0.5$ (5)

With H: pole height (m), h_im: implanted height (m), H_ground: ground clearance (m), f: conductor’s beam (m) and h_head: pole’s head height (m).

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:

$h_{im}=0.1H_{ground}+0.5$ (in meters) (6)

Conductor’s beam is determined by Equation (1) previously given; here, it is its maximum value.

3.3.2. 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:

$M\_1=T.H\_\propto$ (7)

With M₁: momentum of the longitudinal effort (N·m), T: conductor’s horizontal tensile strength (N) and H_α: anchorage height of the conductor (m)

And $H_a=H-h_{im}-h_{head}$ (in meters) (8)

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:

$M_{t1}=0.5C_{Xp}\cdot q_{dyn}\cdot D^{\prime }\cdot H_r^2$ [12] (9)

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).

$M_{t2}=F\cdot H_a$ (10)

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:

$F_{transversal}=\left(M_{t1}+M_{t2}\right)/H_r$ (11)

On another hand, the combined resulting moment worth:

$M=M_l+M_{t1}+M_{t2}$ (12)

The resulting head effort applied to the pole is then given by [4]:

$F_{tete}=M/H_r$ (13)

This effort, and the height previously determined, is the basis on which the convenient pole is chosen among the common poles listed in the catalogue (see Appendix 1).

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].

3.3.3. 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:

$\left(H_r-h_{head}\right)\cdot F+0.5\cdot q_l\cdot H_r^2\text{et}\left(H_r-h_{tete}\right)\cdot T$ [22] (14)

The resulting maximum stress is then determined:

${\sigma }_f=\frac{M}{I_G}\cdot D_p$ (15)

With σ_f: maximum flexion stress, M: resulting bending moment (N·m),I_G: quadratic moment of the seciton (m⁴) and D_p: pole’s diameter (m).

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:

$\frac{u^{″}}{{\left(1+{u^{\prime }}^2\right)}^{3/2}}=\frac{M}{E_b\cdot I_G}$ [23] (16)

With u pole’s beam (m), M: resulting bending moment (N·m), I_G: quadratic moment of the seciton (m⁴) 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.

$N_c=\frac{{\pi }^2\cdot E_b\cdot I_G}{4\cdot H_r^2}$ [21] (17)

With λ: pole’s twinge (no unit), λ_lim: pole’s limit twinge (no unit), N_c buckling critical load (N), I_G: quadratic moment of the section (m⁴), E_b eucalyptus young module (Pa), H_r: height above the ground, (m), S_p pole’s section area (m₂) and R_e pole’s stress limit (Pa).

And critical constraint:

${\sigma }_c=\frac{{\pi }^2\cdot E_b\cdot I_G}{4\cdot S\cdot H_r^2}=\frac{{\pi }^2\cdot E}{{\lambda }^2}$ [24] (18)

We determine:

- the limit twinge of Euler of our material, which is around 180:

${\lambda }_{lim}=\pi \cdot \frac{E}{R}$ [21] (19)

- the current twinge of our pole is:

$\lambda =2\cdot H_r\cdot \sqrt{\frac{S}{I_G}}$ [21] (20)

Then, two situations are conceivable.

➢ If $\lambda \ge {\lambda }_{lim}$, Euler’s considerations apply, and it must be verified that:

$\frac{u^{″}}{{\left(1+{u^{\prime }}^2\right)}^{3/2}}=\frac{M}{E_b\cdot I_G}$

P: conductor’s linear weight (N·m⁻¹).

(3 is the buckling safety coefficient used in this hypothesis).

If ${\lambda }_{lim}>\lambda \ge 20$, Rankine’s empirical considerations apply, and it is a question of verifying that:

$p\le \frac{{\pi }^2\cdot E\cdot S}{2\cdot \left({\lambda }_{lim}^2+{\lambda }^2\right)}$ [21] (21)

If $20\ge \lambda$, there is safety to buckling, and it is a question of checking that

$p\le \frac{2}{3}\cdot R_e\cdot S$ (22)

In any case, if buckling safety is not guaranteed, a pole with a larger diameter should be chosen.

4. Results

4.1. Data of Nkoabang D17 Line

The voltage at the start of the line is set at 15 kV, and transformers are installed at the points where it is necessary to lower the voltage. The line is divided into 76 laying cantons. A canton is a continuous portion of the line, at the ends of which anti-cascade devices are fitted. The poles placed at the ends of a canton are therefore dimensioned to support the entire canton in the event of an incident.

The poles are divided into 4 categories, according to their position and function on the line. The stop poles are at the ends of the line. Corner poles are those where the line deviates by more than 10˚. This deviation is the angle measured between the direction of the conductor arriving at the poles and the direction of the conductor leaving the post on the other side. The anchor poles are at the ends of the installation cantons. The other poles, which are neither at particular points nor have a particular function, are called alignment or suspension poles.

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).

4.2. 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.

4.2.1. 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 $f\approx 1.08\text{m}$.

The attachment methods and the minimum distances to keep between the

Table 3. Characteristics of the D17 Nkoabang power line.

Table 4. Data concerning the first pole of the first canton.

NB: The writing “3xalm54” indicates the presence of three conductors (three-phased line), made of almelec, with a section area of 54 mm². The same logic is extended to similar designations.

conductors and the way they are linked to this pole impose a minimum value for the head height $h_{head}\approx 0.8\text{m}$.

Therefore, the pole’s height can be extracted from Equation (5): $H\approx 11.75\text{m}$.

Appendix 2 gives the ground clearance equal to 8.2 m and Equation (5) then gives the height of the pole: $H\approx 11.75\text{m}$. This calculation confirms that a 12 m height is correct for this pole.

4.2.2. Computation of the Vertical Effort

In addition to previous data (Table 4), the conductor’s density (Table 1) is to be considered. Formula (3) gives the weight of the conductors effectively supported by the pole: $P\approx 95\text{N}$.

The mass of the various line accessories supported by this pole (isolators, fasteners, armament) is evaluated to 37 kg, which implies an additional load of 362.4 N.

The vertical effort is the direct sum of these two loads, giving $F_{vertical}\approx 475.4\text{N}$.

The total mass of the various accessories supported by the pole (insulators, fixing elements, reinforcement) is evaluated using the data in Appendix 3 is 37 kg, resulting in an additional load of 362.4 N.

The vertical force is the sum of these two loads, i.e., $F_{vertical}\approx 475.4\text{N}$.

4.2.3. 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.

Formulas (4), (9), (10) and (11) enable to find $F_{transversal}\approx 4614.1\text{N}$.

4.2.4. 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) provides the maximum expectable tensile strength in the conductor, in the hypothesis of considered climate. The longitudinal effort is then deducted as the resultant of these tensile strength: $F_{longitunal}\approx 12921\text{N}$.

Table 5. Additional data for the computation of the transverse effort.

Table 6. Additional data for the computation of the transverse effort.

4.2.5. 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 $F_{head}\approx 12930\text{N}$.

4.2.6. 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) provides the value of the maximum bending stress in the pole ${\sigma }_f\approx 7.324\times {10}^7\text{Pa}$.

4.3. 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.

4.3.1. 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.

4.3.2. 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).

4.4. 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.

5. Discussions

5.1. First Pole of the First Canton

5.1.1. Height Verification

The height found for this first pole is: $H\approx 11.75\text{m}$ Calculations confirm that a

Table 7. Applied forces on pole of the first canton and nominal admissible force.

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.

5.1.2. Verification of Nominal Effort at Nominal Allowable Forces

The resulting nominal effort is $F_{tete}\approx 12930\text{N}$.

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.

5.1.3. Checking in Relation to Bending

The maximum bending stress is ${\sigma }_f\approx 7.324\times {10}^7\text{Pa}$ The limit value for this pole (given in Table 2) is 5.5 × 10⁷ Pa.

This result leads the need to select a pole with higher bending strength. The closest suitable pole is D12, which is strutted.

5.1.4. 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.

5.2. First Canton of Installation

5.2.1. 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.

5.2.2. 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.

5.2.3. 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.

5.3. Overall Assessment of the Entire Line

Based on the calculations results of the stress and strain obtained on the 845 poles of the line, we have established the loading status of the posts of the entire line. This state is summarized in Table 10 below.

Table 8. Permanent efforts for the poles with particular function in the first canton.

Table 9. Poles to be replaced on the first canton.

Table 10. Loading status of the supports according to their function on the whole line.

We evaluated the percentages of poles to be replaced along this line. Figure 8 shows these percentages by support loading condition.

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).

6. 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;

Figure 8. Percentage distribution of posts according to their state of loading.

Figure 9. Percentage distribution of poles to be replaced per type of support.

Picture 1. State of the supports of line (TEG picture).

· 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.

6.1. 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:

$k_{overload}=\frac{\text{actualeffortonthe3yearsofusage}}{\text{plannedeffortduringinitialsizing}}$ (23)

The average overload coefficients by direction of effort are summarized in Table 12.

6.2. 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

Table 11. Etude comparative de charges sur les poteaux les plus surchargés.

Table 12. Overload coefficients (empirical determination).

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.

7. 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. From these calculations, it appears that the average overload coefficients by direction of force are: 2.38 for the vertical force, 1.17 for the longitudinal force and 3.70 for the transverse force. The resulting force has an overload coefficient of 2.20.

Face to the difficulties of preventing overloading poles extending the life span of the pole, hence reducing the emission of greenhouse gases by reducing the number of eucalyptus trees to be cut, we propose these overload coefficients which are considered as second safety coefficients for future dimensioning of power line poles in the region and, in addition, the effects of different modes of loading each individual pole should be checked. To this end, for the calculation of:

• The nominal and the permanent resultant force, an additional coefficient of 2.20 will be applied to the force;

• The critical buckling load (buckling check), an additional coefficient of 2.38 will be applied to the stress;

• The maximum resultant stress (verification at bending), an additional coefficient of 3.70 will be applied to the stress.

Appendix 1: Nominal Forces at the Head of the Wooden Poles

1) Simples poles

2) Twin poles

3) Strutted poles

Appendix 2: Ground Guards in Force in Cameroon [20]

Appendix 3: Masses of Line Accessories [2]

Appendix 4: Data from the First Paving Canton

MV (Medium Voltage), LV (Low Voltage).

Appendix 5: Load-Bearing Capacity Values of the First Installation Canton

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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