---
title: "Guard ring sizing for 3-unit string at 20 kV"
subject: "Power System Analysis I"
chapter: 2
key: "semester_4/power_system_analysis_i:guard-ring-3-units-20kv"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/guard-ring-3-units-20kv
site: BCT Engineering
---

# Guard ring sizing for 3-unit string at 20 kV

Power System Analysis I · Chapter 2: Overhead and Underground Transmission

- Asked in: 2075 Bhadra, 8 marks
- Video: [L54: Grading Ring in Hindi | Improving String Efficiency | Power System Series](https://www.youtube.com/watch?v=qmI7LRuQ9p8) — TechInsight
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/guard-ring-3-units-20kv
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-2

## Question

In a transmission line, each conductor is at 20 kV and supported by a string of 3 suspension insulators. The air-capacitance between each cap-pin junction and tower is 1/5th of the capacitance C of each insulator unit. A guard ring, effectively only over the line end insulator unit, is fitted so that the voltages on the two units nearest the line-end are equal. (i) Calculate the voltage on the line-end unit. (ii) Calculate the value of capacitance between the ring and pin.

## Short answer

The line-end unit voltage is 7.06 kV (top unit 5.88 kV, middle unit 7.06 kV). The required ring-to-pin capacitance is 0.367C (or 11C/30).

## Answer

The guard ring adds a capacitance $C_x$ between the ring (at line potential) and the link pin at the top of the line-end unit. This capacitance is chosen so that the two units nearest the line share the voltage equally.

```text
 Tower ─[C]─ A ─[C]─ B ─[C]─ Line (20 kV)
             |       |  \
          C/5       C/5  Cx (ring to pin B)
             |       |
           earth   earth
```

Units: 1 (tower end), 2, 3 (line end), with voltages $V_1, V_2, V_3$. The shunt capacitance is $C/5 = 0.2C$, and the condition is $V_2 = V_3$.

#### Junction A (no guard ring capacitance)
$$
\omega CV_2 = \omega CV_1 + \omega(0.2C)V_1 \;\Rightarrow\; V_2 = 1.2V_1
$$

#### Junction B (guard ring capacitance $C_x$ to line)
The voltage of B to earth is $V_1+V_2$, and to the line it is $V_3$:

$$
\omega CV_3 + \omega C_xV_3 = \omega CV_2 + \omega(0.2C)(V_1+V_2)
$$

With $V_3 = V_2$:

$$
C_x V_2 = 0.2C(V_1 + V_2)
\;\Rightarrow\; C_x = 0.2C\left(\frac{1}{1.2} + 1\right) = 0.3667C
$$

#### (i) Voltage on the line-end unit
$$
V = V_1 + V_2 + V_3 = V_1 + 1.2V_1 + 1.2V_1 = 3.4V_1 = 20\ \text{kV}
$$

$$
V_1 = 5.882\ \text{kV},\qquad V_2 = V_3 = 7.059\ \text{kV}
$$

String efficiency $= 20/(3\times 7.059) = 94.44\ \%$.

#### (ii) Capacitance between ring and pin
$$
C_x = 0.3667C \;(= 11C/30)
$$

**Answer:** (i) The line-end unit carries 7.06 kV (top unit 5.88 kV, middle unit 7.06 kV). (ii) The ring-to-pin capacitance is $0.367C$.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What condition fixes the ring capacitance Cx?
   A. The tower unit voltage is zero
   B. All three unit voltages are equal
   C. The ring capacitance equals C
   D. The voltages on the two line-end units are equal (V2 = V3)
   Answer: D. Cx is chosen so V2 = V3 as specified. (Key point: Design condition)

2. What is V2 in terms of V1 (junction A, no ring)?
   A. V2 = 0.8 V1
   B. V2 = 1.2 V1
   C. V2 = 1.4 V1
   D. V2 = V1
   Answer: B. V2 = V1(1 + 0.2). (Key point: Top junction)

3. What is the voltage on the line-end unit?
   A. 5.88 kV
   B. 6.67 kV
   C. 8.5 kV
   D. 7.06 kV
   Answer: D. V = 3.4 V1 = 20 kV, V1 = 5.882, V3 = 1.2 x 5.882 = 7.059 kV. (Key point: Line-end unit voltage)

4. What is the ring-to-pin capacitance?
   A. 0.2 C
   B. 0.5 C
   C. 0.367 C
   D. 0.12 C
   Answer: C. Cx = 0.2C(1/1.2 + 1) = 0.3667C. (Key point: Ring capacitance)

## Related in Power System Analysis I

- [3-unit string with guard ring: redistribution of voltage](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aguard-ring-3-units-redistribution) — Power System Analysis I, chapter 2
- [4-unit string with guard ring (10% and 6%)](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aguard-ring-4-unit-10-6) — Power System Analysis I, chapter 2, asked 2×
- [4-unit string with guard ring (10% and 5%)](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aguard-ring-4-unit-10-5) — Power System Analysis I, chapter 2, asked 2×
- [Greatest working voltage of 3-unit string, 20 kV limit](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Agreatest-working-voltage-3-units) — Power System Analysis I, chapter 2
- [String of 4 insulators at 66 kV, ratio 10](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Astring-4-insulators-66kv-ratio-10) — Power System Analysis I, chapter 2
- [String of 5 insulators on 100 kV, ratio 0.1](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Astring-5-insulators-100kv) — Power System Analysis I, chapter 2

## Related in other subjects

- [Voltage distribution of 3-unit string with guard ring](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Astring-guard-ring-3-unit) — High Voltage Engineering, chapter 5
- [Guard ring capacitances for 5-disc string](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Aguard-ring-five-disc-capacitance) — High Voltage Engineering, chapter 5
- [Insulator discs per string, 180 MW over 200 km](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Ainsulator-discs-180mw-200km) — Transmission and Distribution System Design, chapter 3
- [Classify insulators; string insulator configurations](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Aclassify-insulators-string-configuration) — Transmission and Distribution System Design, chapter 3