## Introduction to the designing principles

When designing an overhead transmission line, we should pay attention to ensure that the * tension force* does not exceed, in any case, the limit of the

*.*

**mechanical strength of the conductor**The maximum stress occurs at the lower temperature,when the line is subjected to contraction, and a possible ice coating. Moreover, it should be considered that can simultaneously be and wind pressure on the line. To address these conditions, a requirement, is knowledge of the * arrow of the conductor*.

*, as well as the*

**arrow determines the height and strength of the supporting towers***(*

**span length***distance between two towers*).

### 1. Static vision of the transmission line

*Even:*

**l** = span length in m (distance between two support points).

**L** = conductor length in m, corresponding to the opening l.

**w** = conductor weight in Kpper meter.

**T** = tensile strength of the transmission line, in Kp.

**D** = maximum arrow, in m.

### 2. Transmission line coated with ice & under the effect of wind

*Even:*

**d** = conductor diameter in cm.

**i** = radial ice thickness in cm.

**w _{i}**= ice weight per meter.

**P**= wind pressure at speed of 80 km/hr.

**W**= resultant force (weight and wind pressure).

The vertical component of the arrow:

### 3. Calculation of the arrow (transmission line construction)

**We accept as unfavorable conditions the following:**

- Ambient temperature -10°C
- Radial ice coating 1 cm
- Wind speed 80 km/hr

With these conditions, we choose * 2^{nd} degree safety factor*, so that the tension force should not exceed half the breaking load of the conductor.

*higher temperature and without ice*), the tension must be done in such a way that, at the most unfavorable conditions, the transmission line to have a 2

^{nd}degree safety factor.

**According to Rapson:**

*when:*

* T* = tensile strength during the construction, in

*(*

**K**_{p}*is considered constant along the transmission line*).

*= conductor cross section, in cm*

**A**^{2}

*= yield strength factor, in Kp/cm*

**E**^{2}

*= expansion factor per °C.*

**α***= ambient temperature above -10°C.*

**t***= tensile strength in adverse conditions, in K*

**T**_{c}_{p}(

*T*).

_{c}obtained half of the breaking loadBy solving the above formula, we obtain the value of * T*. Then, the arrow, during the construction, is:

### 4. Transmission line based on different levels

**Consider “O” the imaginary lowest point of the transmission line.**

* x_{1}* = is the horizontal distance between the lowest support point and the “O”.

*= is the horizontal distance between the highest support point and the “O”.*

**x**_{2}*= is the imaginary arrow from the lowest support point.*

**D**_{1}*= is the imaginary arrow from the highest support point.*

**D**_{2}*With these data, we have:*

*We observe that:*

*From the above, we have:*

With the values of x1, x2, the arrows D1, D2 can be calculated, as well as the height of any point on the transmission line from the ground.

### Example //

An overhead transmission line crosses a river and it is based on the two banks by two towers at height * h1=91.4m* and

*above the water surface. The horizontal distance between the towers is*

**h2=45.7m***. The maximum tensile force is*

**335.3 m***and the weight of the conductor is*

**T = 1932.3 Kp***.*

**w = 0.884Kp/m**Determine the * height “h”* of the line over the water, midway between the two towers.

Consider “* O*” the imaginary lowest point of the transmission line and D1, D2 the arrows from the lower and the tallest tower respectively.

*However:*

*Therefore:*

#### Reference:

* Vasilios N. Xanthos* – Generation, Transmission, Distribution, Measurement and saving of Electrical Energy

Teemu Juvakka

Kp? I think you mean kP?

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