---
title: "Static MHO relay"
subject: "Switchgear and Protection"
chapter: 8
key: "semester_6/switchgear_and_protection:static-mho-relay"
source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/static-mho-relay
site: BCT Engineering
---

# Static MHO relay

Switchgear and Protection · Chapter 8: Static and Digital Relays

- Asked in: 2076 Bhadra, 8 marks
- Video: [MHO Relay](https://www.youtube.com/watch?v=uDcJXa1lJmc) — Basic Electrical
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/static-mho-relay
- Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-8

## Question

Explain the working of static MHO relay with the help of block diagram.

## Short answer

A static mho relay uses phase comparison of (I·Zr - V) and V; if coincidence exceeds 5 ms, indicating a fault inside the circle through the origin, it trips. It is inherently directional, preferred for long EHV lines, and least affected by power swings.

## Answer

A **static mho (admittance) relay** is a directional distance relay whose characteristic on the R–X diagram is a circle passing through the origin, with diameter Z_r along the line angle. It is realised with a **phase comparator** using the inputs S1 = I·Z_r − V and S2 = V.

#### Principle

```text
 Trip when −90° ≤ angle between (I·Z_r − V) and V ≤ +90°
 i.e. Z = V/I lies inside a circle of diameter Z_r
 through the origin.

        X
        │   .--.
        │  /    \   ← Z_r at line angle θ
        │ |  trip|
        │  \    /
        └──'--'──── R
       origin (directional)
```

#### Block diagram

```text
 PT ─►[Aux PT]────────► V ──────────┐
                        │           │
 CT ─►[Transactor]─► I·Z_r          │
                        │           │
                 [Mixer: I·Z_r − V] │
                        │ S1        │ S2 = V
                   [Squarer]    [Squarer]
                        └──►[AND]◄──┘
                              │
                [Integrator: coincidence > 5 ms?]
                              │
                       [Level detector]
                              │
                  [Zone timer (zones 2, 3)]
                              │
                [Amplifier]─►[Output]─► Trip
```

#### Working

1. **Aux PT** gives V; **transactor** (air-gap transformer) gives a voltage I·Z_r leading the current by the line angle.
2. **Mixing circuit** forms S1 = I·Z_r − V; S2 = V (polarising voltage, sometimes memory-polarised to handle close-in faults).
3. **Squarers** convert S1 and S2 to square waves.
4. **Coincidence (AND) circuit:** output is high while both are positive. If coincidence lasts more than 5 ms (quarter cycle), the angle between S1 and S2 is within ±90° → fault inside the circle.
5. **Integrator and level detector** confirm the coincidence time and reject noise.
6. Zone 1 trips instantly; zone 2 and zone 3 units have timers.
7. **Amplifier and output** relay/thyristor trip the CB.

#### Features

- Inherently directional (no separate directional unit).
- Occupies the smallest area on R–X plane, so it is least affected by **power swings** – preferred for **long EHV lines**.
- Static version is fast, accurate and has low burden.

## Check yourself

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

1. On the R-X diagram, the characteristic of a mho relay is:
   A. A straight line through the origin
   B. A circle passing through the origin with diameter Z_r along the line angle
   C. A circle centred at the origin
   D. A lens-shaped area
   Answer: B. The mho relay is a directional distance relay whose characteristic is a circle through the origin, diameter Z_r. (Key point: Mho characteristic)

2. A static mho relay uses a phase comparator with inputs:
   A. S1 = I Z_r, S2 = V
   B. S1 = I Z_r - V, S2 = V
   C. S1 = V + I, S2 = V - I
   D. S1 = I, S2 = Z_r
   Answer: B. S1 = I Z_r - V (operating) and S2 = V (polarising) are compared in angle. (Key point: Comparator inputs)

3. In the coincidence circuit, what does coincidence lasting more than 5 ms (quarter cycle at 50 Hz) indicate?
   A. The angle between S1 and S2 is within +-90 degrees, so the fault is inside the circle
   B. The fault is outside the zone
   C. The line is healthy
   D. The PT has failed
   Answer: A. Overlap of the square waves for more than a quarter cycle means the angle is within +-90 degrees, i.e. Z lies inside the circle. (Key point: Coincidence timing)

4. Why is the mho relay preferred for long EHV lines?
   A. It needs a separate directional unit
   B. It occupies the smallest area on the R-X plane, so is least affected by power swings
   C. It has the largest operating area
   D. It works without a PT
   Answer: B. Its small circle makes it least affected by power swings; it is also inherently directional. (Key point: Application)

## Related in Switchgear and Protection

- [Directional static overcurrent relay](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Adirectional-static-overcurrent) — Switchgear and Protection, chapter 8, asked 2×
- [Static differential relay](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Astatic-differential-relay) — Switchgear and Protection, chapter 8, asked 3×
- [Static distance relay](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Astatic-distance-relay) — Switchgear and Protection, chapter 8, asked 3×
- [Essential components of a static relay](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Astatic-relay-essential-components) — Switchgear and Protection, chapter 8, asked 5×
- [Static differential relay for two-winding transformer](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Astatic-differential-two-winding) — Switchgear and Protection, chapter 8
- [Short note: Op-amp in static relay](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Ashort-note-op-amp-static-relay) — Switchgear and Protection, chapter 8

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