## 1. Introduction

A suspension insulator strain consists of a series of * alternately insulators* and

*, which bind each insulator to the next. This constitutes a*

**metal parts***, with each one’s capacitance being created by two successive metal connectors (*

**series of connected capacitors***clips*) with the porcelain as a dielectric.

*between each connector and the support arm or the tower.*

**air capacitances**So let us consider a strain of four suspension insulators, as shown in the figure below, and let C be the same capacitance for each unit and kC the capacitance of each metal connector with earth.

Then, if * V_{1}* is the potential difference between the two metal connectors (

*clips*) of the first insulator, we have:

Even * V1 + V2 + V3 + V4 = E* (phase voltage of the line) →

**E = V1 (4 + 10k + 6k**^{2}+ k^{3})**So, if k = 0,1, we have:**

### 2. Corona rings

The distribution of the potential along the insulators strain can be improved by using a * smoothing ring (Corona ring)* or a

*, which consists of a large metal ring surrounding the last insulator that is electricallyconnected to the line.*

**protective ring**The corona ring inserts capacitances between the metal connectors (*clips*) of the insulators and the line. For these capacitances, special care can be taken in order to compensate the capacitances to earth.

### 3. Cases of insulators strains with or without Corona rings

#### Case 1

Determine the * potential distribution* in a strain of three insulators, if the capacitances of the links to earth and to the line are respectively

*and*

**20%***of the capacitance of the insulators. Also, determine the performance of the strain.*

**10%**#### Case 2

An overhead 3-phase transmission line, which has phase voltage * 30 kV*, is hanging from a

*. The capacitance between the links and the earth is*

**three insulators suspension strain***, where C is the capacitance of an insulator.*

**0,2 C**- Determine the potential distribution along the insulators strain.
- If a
inserts capacitances from the line, with the link of the middle and the lower insulator set at**protective (corona) ring**and the link of the medium and the higher insulator set at**0,4 C**, find the new distribution.**0,1 C**

##### 2.1 Determine the potential distribution along the insulators strain

##### 2.2 Protective (corona) ring inserts capacitances from the line

### 4. Generalized formula of voltage distribution in a suspension insulators strain

The above mathematical formula is the generalized formula we can use to find the voltage Vn of the (n-1) insulator.

E = phase voltage of the line.

The value of ‘a’ is given by the above formula:

#### 4.1 Determine the voltage distribution in a six insulators strain (z=6) with k=0,1

#### 4.2 Determine the voltage distribution of the first, the sixth and the twelfth insulator with z = 12 (12 – insulators strain) and k = 0,1

We have:

###### References:

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