## 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**.

**arrow determines the height and strength of the supporting towers**, as well as the

**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.

^{nd}degree safety factor.

**According to Rapson:**

when:

**T** = tensile strength during the construction, in **K _{p}** (is considered constant along the transmission line).

**A**= conductor cross section, in cm

^{2}

**E**= yield strength factor, in Kp/cm

^{2}

**α**= expansion factor per °C.

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

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

_{c}_{p}(T

_{c}obtained half of the breaking load).

By 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”.

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

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

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

_{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 **h2=45.7m** above the water surface. The horizontal distance between the towers is **335.3 m**. The maximum tensile force is **T = 1932.3 Kp** and the weight of the conductor is **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