Comparators used in static relays

A comparator is the measuring element of a static relay. It compares two input quantities (signals S1 and S2, formed from the relay voltage and current) either in amplitude or in phase, and gives a trip output when a set condition is met. A phase comparator compares only the phase angle between S1 and S2 and operates when the angle lies within a set range (normally −90° ≤ φ ≤ +90°), whatever their magnitudes.

1. Amplitude comparator

Compares only the magnitudes: trip when |S1| > |S2| (operating > restraining), whatever the phase.

S1 ─►[Rectifier B1]─┐
                    ├─►[ |S1| − |S2| ]─►[Level det.]─► trip
S2 ─►[Rectifier B2]─┘    (> 0 ?)

Types:

• Circulating-current type: two rectifier bridges; their currents are compared in a polarised relay/moving-coil element.
• Opposed-voltage type: rectified voltages are opposed across a resistor; there is an output when the operating voltage is larger.
• Averaging type and sampling (instantaneous) type comparators using transistors/op-amps.

Example: impedance relay, |I·Z_r| > |V|.

2. Phase comparator

Compares phase angle only: trip when −90° ≤ arg(S1/S2) ≤ +90°.

Types:

• Vector product type: a Hall-effect or magneto-resistive device gives an output ∝ |S1||S2|cos φ; a positive output means trip.
• Coincidence type: S1 and S2 are converted to square waves, and an AND gate measures the time for which both are positive. Coincidence > 5 ms (a quarter cycle at 50 Hz) means |φ| < 90° → trip.
• Rectifier bridge phase comparator and integrating type.

S1 ─►[Squarer]─┐
               ├─►[AND]─►[Integrator]─►[Level det]─► trip
S2 ─►[Squarer]─┘          (> 5 ms ?)

Example: mho relay, S1 = I·Z_r − V and S2 = V.

Duality

An amplitude comparator with inputs S1, S2 is equivalent to a phase comparator with inputs (S1 + S2) and (S1 − S2), and vice versa. Hence any characteristic can be obtained with either comparator by mixing the inputs suitably.