A string of three suspension insulators is used in a 132 kV overhead line. The insulator string has a voltage distribution ratio of 1:0.8:0.6 (from the top to the bottom). If the system line voltage is 132 kV, calculate:

The voltage across each insulator.
The string efficiency.

In this problem, we are given the following:

- The total line voltage of the system is \( V_{\text{line}} = 132 \, \text{kV} \).
- The voltage distribution ratio across the three suspension insulators is \( 1:0.8:0.6 \) (from top to bottom).

To calculate the voltage across each insulator and the string efficiency, let's break it down step by step.

### Step 1: Determine the Phase Voltage

For a 3-phase system, the line voltage \( V_{\text{line}} \) is related to the phase voltage \( V_{\text{phase}} \) by:

\[
V_{\text{phase}} = \frac{V_{\text{line}}}{\sqrt{3}}
\]

Thus:

\[
V_{\text{phase}} = \frac{132 \, \text{kV}}{\sqrt{3}} \approx 76.21 \, \text{kV}
\]

### Step 2: Express the Voltage Across Each Insulator

Let the voltages across the top, middle, and bottom insulators be \( V_1 \), \( V_2 \), and \( V_3 \), respectively.

Given the voltage distribution ratio is \( 1:0.8:0.6 \), the sum of the ratios is:

\[
1 + 0.8 + 0.6 = 2.4
\]

Therefore, the voltage across each insulator can be calculated as a proportion of the total phase voltage.

#### Voltage across the top insulator:
\[
V_1 = \frac{1}{2.4} \times V_{\text{phase}} = \frac{1}{2.4} \times 76.21 \, \text{kV} \approx 31.75 \, \text{kV}
\]

#### Voltage across the middle insulator:
\[
V_2 = \frac{0.8}{2.4} \times V_{\text{phase}} = \frac{0.8}{2.4} \times 76.21 \, \text{kV} \approx 25.40 \, \text{kV}
\]

#### Voltage across the bottom insulator:
\[
V_3 = \frac{0.6}{2.4} \times V_{\text{phase}} = \frac{0.6}{2.4} \times 76.21 \, \text{kV} \approx 19.05 \, \text{kV}
\]

### Step 3: Calculate String Efficiency

The string efficiency is a measure of how uniformly the voltage is distributed across the insulators in a string. It is defined as:

\[
\text{String Efficiency} = \frac{\text{Voltage across the string}}{\text{Sum of voltages across insulators}} \times 100\%
\]

Since the total voltage across the string is the phase voltage \( V_{\text{phase}} = 76.21 \, \text{kV} \), and the sum of the individual insulator voltages is also \( 76.21 \, \text{kV} \), the string efficiency is:

\[
\text{String Efficiency} = \frac{76.21}{76.21} \times 100\% = 100\%
\]

However, this 100% efficiency is based on perfect conditions where no losses or capacitance exist, but practically, the efficiency might be slightly less.

### Summary of Results

- Voltage across the top insulator \( V_1 \approx 31.75 \, \text{kV} \)
- Voltage across the middle insulator \( V_2 \approx 25.40 \, \text{kV} \)
- Voltage across the bottom insulator \( V_3 \approx 19.05 \, \text{kV} \)
- String efficiency \( \approx 100\% \)

---

Do you want more details or have any questions?

Here are 5 relative questions to expand on this:
1. What factors affect string efficiency in real-world conditions?
2. How does the presence of stray capacitance affect the voltage distribution across insulators?
3. What are methods to improve string efficiency in suspension insulators?
4. How is the voltage distribution affected in a 6-insulator string compared to a 3-insulator string?
5. How would changing the insulator material impact the voltage distribution and efficiency?

**Tip:** Improving string efficiency often involves using grading rings or adjusting the mechanical arrangement of insulators to balance the voltage more evenly.

A string of three suspension insulators is used in a 132 kV overhead line. The insulator string has a voltage distribution ratio of 1:0.8:0.6 (from the top to the bottom). If the system line voltage is 132 kV, calculate the voltage across each insulator and the string efficiency.

This problem calculates the voltage across each insulator in a 132 kV overhead line and the string efficiency using the voltage distribution ratio 1:0.8:0.6. Learn how to apply voltage distribution in suspension insulators and three-phase systems, with step-by-step instructions. Suitable for Grades 11-12.

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