Static MHO relay

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

 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

 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.