Static and Digital Relays

A static relay is a relay in which measurement and comparison are done by electronic circuits (diodes, transistors, ICs, op-amps) with no moving parts; only the output (trip) element may be an electromechanical auxiliary relay or a thyristor.

Block diagram

 CT/PT ┌─────────┐  ┌──────────┐  ┌────────────┐
 ─────►│ Input   ├─►│Rectifier/├─►│ Measuring  │
       │(aux CT, │  │ mixing / │  │ unit       │
       │ PT,     │  │ smoothing│  │(comparator,│
       │ filter) │  └──────────┘  │ level det.,│
       └─────────┘                │ timer)     │
                                  └─────┬──────┘
           ┌─────────────┐        ┌─────▼──────┐
           │ Aux DC      │──────► │ Amplifier  │
           │ supply      │        └─────┬──────┘
           └─────────────┘        ┌─────▼──────┐
                                  │ Output     │──► CB trip
                                  │ (relay/SCR)│     coil
                                  └────────────┘

Function of each block

1. Input (transducer) circuit: auxiliary CTs/PTs and transactors reduce the main CT/PT outputs to small voltages suitable for electronics, isolate the electronics from the power circuit, and allow mixing of phase quantities. Surge-suppression and filters remove transients and harmonics.
2. Rectifier / mixing / smoothing circuit: converts AC to DC (bridge rectifier) for amplitude comparison, or produces square waves for phase comparison; sequence networks extract positive/negative/zero sequence quantities when needed.
3. Measuring unit: the heart of the relay. It contains
   • Comparators (amplitude or phase) that compare operating and restraining quantities,
   • Level detectors that give an output when a quantity crosses a set threshold,
   • Timers / integrators (RC circuits, counters) that provide definite or inverse time delays.
4. Amplifier: raises the low-level output of the measuring unit to a level that can drive the output device; uses transistors or op-amps.
5. Output device: an auxiliary electromagnetic relay (attracted armature) or a thyristor that energises the circuit-breaker trip coil and gives signal/alarm contacts.
6. Auxiliary DC supply: a stabilised supply derived from the station battery (via DC-DC converter) to power the electronics, independent of the fault level.

Features

• Low CT/PT burden, fast operation, no contact bounce or friction.
• Characteristics (inverse, mho, quadrilateral) can be shaped easily with circuits.
• Needs protection against temperature and voltage surges.

Static relays use solid-state electronic components (transistors, diodes, ICs) for measurement and decision, unlike electromagnetic relays that use moving armatures, discs or cups.

Advantages of static relays over electromagnetic relays

Other advantages: high sensitivity (amplifiers), good accuracy, easy to combine several functions, suitable for fast schemes like carrier and distance protection.

Limitations

• Sensitive to voltage spikes/transients – need surge suppressors and screening.
• Characteristics drift with temperature; components age.
• Need an auxiliary DC supply.
• Low overload capacity of semiconductor devices.
• Expensive for simple single-function relays; needs skilled staff for repair.
• Affected by electrostatic discharge and electromagnetic interference.

Main components of a static relay

CT/PT→[Input/aux CT]→[Rectifier/smoothing]
      →[Measuring unit: comparator,
         level detector, timer]
      →[Amplifier]→[Output relay/SCR]→Trip coil
               ▲
        [Aux DC supply]

1. Input circuit: auxiliary CTs/PTs, transactors; scale down signals, isolate electronics, filter surges.
2. Rectifier/smoothing: converts AC to DC or square waves for comparison.
3. Measuring unit: comparators (amplitude/phase), level detectors, timing circuits – decides if a fault exists.
4. Amplifier: strengthens the weak decision signal.
5. Output unit: auxiliary relay or thyristor energises the CB trip coil.
6. Auxiliary supply: stabilised DC for the electronics from station battery.

A static differential relay compares the currents at the two ends of a protected zone (transformer, generator, bus) using electronic circuits. It trips when the difference (spill) current exceeds a set percentage of the through (bias) current.

Block diagram

 CT1 ─┐                         ┌─ CT2
      ▼                         ▼
 [Aux CT]                    [Aux CT]
      │  i1                  i2 │
      ├────────┬───────────────┤
      │        │               │
 [Bias rect]  [Diff (spill)   [Bias rect]
      │        rectifier]      │
      └──► Σ bias  │ operate ◄─┘
             │     │
        ┌────▼─────▼─────┐
        │ Amplitude       │
        │ comparator      │
        └───────┬─────────┘
           [Level detector]
           [Harmonic restraint]
           [Amplifier]→[Output]→Trip

Circuit (simplified)

 CT1 sec (i1)              CT2 sec (i2)
   │                          │
   ├─[bridge B1]─┐  ┌─[bridge B2]─┤
   │             ▼  ▼             │
   │        R_b ─┴──┴─ R_b        │
   │      bias voltage V_r        │
   │      ∝ (|i1| + |i2|)/2       │
   └────────[bridge B3]───────────┘
            spill |i1 − i2|
                 │
             R_o → V_o (operate)
                 │
 [comparator: V_o − K·V_r > 0 ?] → trip

Working principle

1. Auxiliary CTs step down currents i1 and i2 and correct ratio/phase mismatch.
2. Bias (restraining) circuit: rectifies i1 and i2 and forms V_r ∝ (|i1| + |i2|)/2, the through current.
3. Operating (spill) circuit: rectifies the difference |i1 − i2| to give V_o.
4. Comparator: an amplitude comparator (rectifier bridge or op-amp) compares V_o with K·V_r. Trip when |i1 − i2| > K·(|i1|+|i2|)/2 (percentage bias, K ≈ 10–40%).
5. Harmonic restraint (for transformers): a filter extracts the 2nd harmonic of the spill current; if it is large (inrush), the trip is blocked. 5th-harmonic restraint blocks tripping during over-excitation.
6. Level detector and output: when the comparator output exceeds threshold, a transistor/thyristor switches the trip relay.

Advantages over electromechanical type

Very fast (about 1 cycle), low CT burden, precise bias slope, easy harmonic restraint, and unaffected by vibration. Used for transformer, generator and busbar protection.

A static distance relay measures the impedance between the relay and the fault using electronic comparators instead of moving discs. It trips when the measured impedance Z = V/I is inside its set characteristic (impedance, reactance, mho or quadrilateral).

Block diagram

 PT ─►[Aux PT]─► V ──┐
                     ├─►[Mixing: S1 = I·Zr − V
 CT ─►[Transactor]─► I·Zr   S2 = I·Zr + V ]
                     │         │
                     │   [Comparator: amplitude
                     │     or phase type]
                     │         │
                     │   [Level detector]
                     │         │
                     │   [Zone timers T2, T3]
                     │         │
                     └──►[Amplifier]─►[Output]─►Trip

Working principle

1. Input stage: auxiliary PT gives a voltage proportional to line voltage V. A transactor (air-gap CT) gives a voltage I·Z_r, where Z_r is the replica (set) impedance.
2. Mixing circuit forms two signals from V and I·Z_r. Example for a mho relay: S1 = I·Z_r − V and S2 = V.
3. Comparator:
   • Amplitude comparator (impedance relay): trips when |I·Z_r| > |V| → Z < Z_r.
   • Phase comparator (mho relay): trips when the angle between S1 and S2 is within ±90°, which gives a circle through the origin.
4. Level detector checks the comparator output against a threshold and removes noise.
5. Timers: zone 1 instantaneous; zone 2 and zone 3 outputs pass through timers (e.g. 0.3 s, 1 s).
6. Amplifier and output drive the trip relay/thyristor of the CB.

Characteristics are easily shaped: by changing the mixing networks, the same hardware gives impedance, reactance, mho, offset-mho or quadrilateral shapes.

Area of application

• Main protection of EHV and HV transmission lines (66–400 kV) with three-zone stepped protection.
• Reactance-type for short lines (arc resistance), mho for long lines (power swings), quadrilateral for lines with high fault resistance.
• Carrier-aided schemes (permissive/blocking) for fast clearance of the whole line.
• Back-up for adjacent lines and busbars; loss-of-field protection of generators (offset mho).
• Out-of-step blocking and power-swing detection.

Static relays are relays whose measuring circuits use solid-state components instead of moving parts.

Types of static relays

1. Static overcurrent relays: instantaneous, definite time, inverse/IDMT, very and extremely inverse.
2. Static directional relays: directional overcurrent and directional earth-fault.
3. Static differential relays: for transformers, generators and busbars (with bias and harmonic restraint).
4. Static distance relays: impedance, reactance, mho, offset-mho, quadrilateral.
5. Static voltage relays: over-voltage, under-voltage, negative-sequence voltage.
6. Static frequency relays: under/over-frequency, rate-of-change of frequency (load shedding).
7. Static negative-phase-sequence relays: generator and motor unbalance protection.
8. Static pilot / carrier relays: phase comparison carrier protection.

Classed by measuring principle: amplitude comparator relays and phase comparator relays; and by devices: transistor, IC/op-amp, Hall-effect, rectifier-bridge relays.

Advantages

• Very low burden on CTs/PTs; smaller CTs can be used.
• Fast operation and quick reset; no overshoot.
• No moving parts – no friction, contact bounce or wear; long life with less maintenance.
• High sensitivity due to amplification.
• Any desired characteristic can be shaped (mho, quadrilateral, inverse).
• Compact; one unit gives several functions.
• Not affected by vibration, shocks or mounting position; suitable for earthquake areas and ships.

Disadvantages

• Sensitive to voltage transients and spikes; need filters and screening.
• Characteristics change with temperature and component ageing.
• Need a reliable auxiliary DC supply.
• Semiconductors have low overload and surge capacity.
• Higher cost than simple EM relays; repair needs trained staff and test equipment.
• Affected by electromagnetic interference and electrostatic discharge.

A digital (numerical) relay samples the analog CT/PT signals, converts them to digital numbers and uses a microprocessor running protection algorithms to decide whether to trip.

Advantages

1. Multi-function: one relay gives overcurrent, earth fault, distance, differential, under/over-voltage, frequency, etc.
2. Self-monitoring of hardware and software; failure gives an alarm.
3. Flexible: characteristics and settings changed by software; several setting groups.
4. Very low CT/PT burden and high accuracy; no drift with temperature.
5. Fault recording: event log, disturbance (waveform) record and fault location.
6. Communication: SCADA/IEC 61850 links, remote setting and reading.
7. Compact, lower cost per function, less panel space and wiring.
8. Adaptive protection possible (settings change with system conditions).

Basic functional blocks

CT/PT
  │
[Isolation & signal conditioning
 (aux CT/PT, surge filter)]
  │
[Anti-aliasing low-pass filter]
  │
[Sample & hold]──[Analog MUX]
  │
[A/D converter]
  │
[Microprocessor / DSP] ◄─► [RAM, ROM/EPROM,
  │  (algorithm)              EEPROM settings]
  ├─► [Digital output → trip relay → CB]
  ├─► [Display, keypad, LEDs]
  └─► [Communication port]
  ▲
[Digital inputs: CB status, etc.]
[Power supply (DC-DC from battery)]

1. Signal conditioning: auxiliary transformers scale CT/PT outputs to low voltages (±10 V) and give isolation; surge filters protect electronics.
2. Anti-aliasing filter: low-pass filter removes frequencies above half the sampling rate (Nyquist).
3. Sample-and-hold and multiplexer: freeze each channel's value at the sampling instant and pass channels one by one.
4. A/D converter: converts each sample to a binary number (12–16 bit).
5. Microprocessor/DSP: runs algorithms (Fourier, Walsh, least-squares) to find phasors, impedance, etc., compares with settings and decides.
6. Memory: ROM for program, RAM for samples, EEPROM for settings and records.
7. Digital inputs/outputs: read CB status; output trip and alarm contacts.
8. HMI and communication: display, keypad, and ports for remote access.
9. Power supply: isolated DC-DC converter from the station battery.

A directional static overcurrent relay trips only when (a) the current exceeds the set value and (b) the power (fault current) flows in the tripping direction. It combines a static overcurrent unit with a static phase comparator that checks the angle between the current and a reference (polarising) voltage.

Block diagram

     CT                      PT
      │                       │
  [Aux CT]                [Aux PT]
      │                       │
      ├──────────┐     [Phase shift τ]
      │          │            │
 [Rectifier] [Squaring]   [Squaring]
      │          └────┬───────┘
 [Level det.]  [Phase comparator]
      │        (coincidence > 5 ms)
  [Timer]             │
      └──────┬────────┘
           [AND]
             │
        [Amplifier]
             │
     [Output relay] ──► CB trip coil

Function of the blocks

1. Auxiliary CT and PT: reduce current and voltage to electronic levels and isolate the circuit.
2. Phase-shift network: shifts the polarising voltage by the relay characteristic angle (e.g. 30° or 45°) so that maximum sensitivity occurs at the typical fault angle.
3. Squaring (zero-crossing) circuits: convert current and voltage to square waves.
4. Phase comparator (coincidence circuit): an AND gate measures the time for which both square waves are positive. If coincidence > 5 ms (in a 50 Hz system, i.e. angle within ±90°), the fault is in the forward direction and a directional output is given.
5. Overcurrent unit: the current is rectified and compared by a level detector with the plug setting; an RC/digital timer gives definite or inverse time delay.
6. AND logic: a trip signal is given only when both the directional and the overcurrent conditions are true.
7. Amplifier and output: drive the auxiliary relay/thyristor which energises the CB trip coil.

Principle

Forward fault: −90° < (θ − τ) < +90° → operate
Reverse fault: angle outside ±90°  → block

Applications

Ring mains, parallel feeders, and lines fed from both ends; generator and transformer reverse-power or back-feed protection; directional earth-fault protection.

In a microprocessor-based line protection scheme, the voltages and currents of the transmission line are sampled, converted to digital form and processed by a microprocessor that computes the apparent impedance (or other quantities) and issues a trip when a fault lies inside a protected zone. Usually it works as a distance (impedance/mho/quadrilateral) relay with three zones.

Block diagram

 Transmission line ══CB══════════════════
        │ CT (Ia,Ib,Ic)     │ PT (Va,Vb,Vc)
        ▼                   ▼
 ┌──────────────────────────────────┐
 │ Aux CTs/PTs, surge suppressors   │
 │ (isolation, scaling to ±10 V)    │
 └───────────────┬──────────────────┘
          [I→V converters]
                 │
       [Anti-aliasing LP filters]
                 │
       [Sample & hold circuits]
                 │
       [Analog multiplexer] ◄─ control
                 │
          [A/D converter]
                 │
 ┌───────────────▼──────────────────┐
 │  MICROPROCESSOR / DSP            │
 │  ROM: program  RAM: samples      │
 │  EEPROM: zone settings           │
 └──┬────────┬────────┬────────┬────┘
    │        │        │        │
 [Timer] [Output   [Display/ [Comm.
         interface]  keypad]  port]
             │
     [Driver + aux relay]──► CB trip coil
 [Digital inputs: CB status, carrier]
 [DC-DC power supply from battery]

Working

1. Input stage: CT and PT outputs pass through auxiliary transformers which isolate and scale them; current signals are converted to voltages across precision resistors.
2. Anti-aliasing filter: removes components above half the sampling frequency.
3. Sample-and-hold + multiplexer: all six signals are sampled at the same instant (e.g. 12–20 samples per cycle) and passed one by one to the ADC.
4. ADC: gives 12–16 bit binary numbers to the microprocessor.
5. Microprocessor program:
   • Computes phasors of V and I by Fourier (DFT) or least-squares algorithms.
   • Computes apparent impedance Z = V/I (R and X) for each phase and phase pair, with residual compensation for earth faults.
   • Compares Z with zone 1, zone 2 and zone 3 characteristics (mho or quadrilateral).
   • Zone 1: instantaneous trip; zone 2 and zone 3: trip after timer delays (e.g. 0.3 s and 1 s).
   • Checks power swing, VT fuse failure, and carrier signals.
6. Output interface: opto-isolated drivers operate auxiliary relays to trip the breaker and give alarms.
7. Records events and disturbance data; communicates with SCADA.

Advantages: one hardware for many characteristics, self-checking, fault location, low burden and easy setting changes.

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 is one that 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, currents compared in a polarised relay/moving-coil element.
• Opposed-voltage type: rectified voltages opposed across a resistor; output when 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: Hall-effect or magneto-resistive device gives output ∝ |S1||S2|cos φ; positive → trip.
• Coincidence type: S1 and S2 converted to square waves; an AND gate measures the time both are positive. Coincidence > 5 ms (quarter cycle at 50 Hz) means |φ| < 90° → trip.

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

• Rectifier bridge phase comparator and integrating type.

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 inputs.

For a two-winding power transformer, a static differential relay compares the currents of the HV and LV CTs (after ratio and phase correction) and trips when the spill current exceeds a set percentage of the through current, with harmonic restraint to stay stable during magnetising inrush.

Circuit / block diagram (one phase)

 HV══CT1════[TRANSFORMER]════CT2══LV
      │      (Δ/Y)            │
 [Interposing CT,       [Interposing CT,
  ratio & 30° corr.]     ratio & 30° corr.]
      │ i1                 i2 │
      ├──[Bias rect.]──┬─[Bias rect.]──┤
      │                │ V_r           │
      └──────[Spill CT / summing]──────┘
                   │ i1 − i2
       ┌───────────┼─────────────┐
 [Fundamental] [2nd harmonic] [Unrestrained
  filter →       filter →      high-set
  rectifier]     rectifier]    level det.]
       │ V_o         │ V_h          │
 ┌─────▼─────────────▼──┐           │
 │ Comparator:          │           │
 │ V_o > K·V_r + V_h ?  │           │
 └─────────┬────────────┘           │
           └──────────[OR]──────────┘
                        │
              [Amplifier → thyristor]
                        │
                 Trip HV & LV CBs

Description of the circuit

1. Main CTs and interposing CTs: main CTs on both sides; interposing (auxiliary) CTs match the current magnitudes (inverse of voltage ratio) and correct the 30° phase shift of Δ/Y connection. They also remove zero-sequence currents so that external earth faults do not cause tripping.
2. Bias (restraint) circuit: i1 and i2 are rectified separately and summed across resistors to give V_r ∝ (|i1| + |i2|)/2 – the through current.
3. Operating (spill) circuit: the difference current (i1 − i2) is passed through a filter tuned to 50 Hz and rectified to give V_o.
4. Second-harmonic restraint: a 100 Hz filter extracts the 2nd harmonic in the spill current. During inrush (2nd harmonic > about 15–20% of fundamental) V_h becomes large and blocks tripping. A 5th-harmonic filter may be used for over-excitation restraint.
5. Comparator: an amplitude comparator (op-amp) checks V_o > K·V_r + V_h. K is the bias slope (15–40%) which covers CT mismatch, tap-changer range and CT errors.
6. Unrestrained (high-set) unit: for very heavy internal faults (spill > 8–10 × rating) it trips immediately without waiting for harmonic analysis, because CT saturation may produce harmonics.
7. Output: OR gate, amplifier and thyristor/auxiliary relay trip both HV and LV circuit breakers.

Result: stable for load, external faults and inrush; fast (about 1–2 cycles) and sensitive for internal winding faults.

Loss-of-field (field failure) protection of an alternator can be done by a microprocessor that continuously monitors the field (excitation) current. If the field current falls below a set minimum (field open, short-circuited, or AVR/exciter failure), the generator loses synchronism and draws large reactive power from the system; the scheme gives an alarm and trips the generator after a short delay.

Block diagram

 Exciter ──► Field winding of alternator
              │
        [Shunt / Hall-effect current
         sensor in field circuit]
              │ V ∝ I_f
      [Isolation amplifier / filter]
              │
     [Signal conditioner (0–5 V)]
              │
       [Sample & hold] ─► [A/D converter]
                               │
 ┌─────────────────────────────▼─────┐
 │        MICROPROCESSOR             │
 │ ROM: program   RAM: data          │
 │ Set value I_f(min), time delay    │
 └──────┬──────────┬───────────┬─────┘
        │          │           │
  [Output port] [Display]  [Clock/timer]
        │
  [Driver + aux relay]──► Alarm
        └──────────────► Trip gen. CB
                         & field CB

Working

1. Sensing: the DC field current I_f is measured by a shunt (or Hall sensor) giving a small voltage proportional to I_f. An isolation amplifier separates the field circuit from the electronics and filters ripple.
2. Conversion: the signal is scaled to the ADC range (e.g. 0–5 V), sampled and converted to a digital number.
3. Program logic:
   • Read the ADC value at regular intervals and convert to field current.
   • Compare with the stored minimum value I_f(min) (e.g. 20–40% of no-load field current; set from the generator's capability curve).
   • If I_f ≥ I_f(min): healthy, repeat.
   • If I_f < I_f(min): start a timer (about 0.5–2 s) to avoid tripping on transient dips or swings.
   • If the low value persists for the set time: give alarm, then send trip signal to the generator CB and field CB.
4. Output: the output port drives a transistor/auxiliary relay that trips the breakers; the display shows field current and status.

 Start → Read I_f → I_f < I_min ? ─No─► loop
                         │Yes
                   Start/continue timer
                         │
                 t > t_set ? ─No─► loop
                         │Yes
                  Alarm + Trip CBs

Advantages: simple, accurate settings, self-checking, and the same microprocessor can also log data and add an under-voltage or reactive-power check to confirm loss of field.

Amplitude comparator and phase comparator

A comparator in a static relay compares two signals S1 (operating) and S2 (restraining) derived from the relay current and voltage.

• Amplitude comparator: compares magnitudes only. It trips when |S1| > |S2|, irrespective of the phase angle. Example: impedance relay with S1 = I·Z_r, S2 = V → trips when Z < Z_r. Built with rectifier bridges (circulating-current or opposed-voltage type) or op-amps.
• Phase comparator: compares the phase angle φ between S1 and S2 only. It trips when −90° ≤ φ ≤ +90° (or another set range), irrespective of magnitudes. Example: mho relay with S1 = I·Z_r − V, S2 = V. Built with coincidence circuits (AND gate measuring overlap > 5 ms at 50 Hz) or Hall-effect devices.
• They are dual: an amplitude comparator with (S1, S2) acts like a phase comparator with (S1 + S2, S1 − S2).

(i) Time delay circuits

Time delay circuits give an intentional delay between fault detection and trip, for grading and to avoid tripping on transients.

 V_in ─►[R]─┬─────►[Level detector]─► output
            │       (V_c > V_ref ?)
           [C]
            │
           ─┴─ (transistor resets C
                 when input removed)

• RC charging type: a capacitor charges through a resistor; when its voltage reaches a reference, the level detector switches. Delay t = RC·ln[V/(V − V_ref)]. Making the charging current proportional to the fault current gives an inverse characteristic; constant current gives definite time.
• Digital (counter) type: an oscillator and counter count pulses; delay = N × clock period. Very accurate and long delays possible.
• Integrating op-amp type: integrator output rises linearly with time.

(ii) Level detector

A level detector gives an output (logic 1) when its input signal exceeds a set threshold, and no output below it. It acts as the "pick-up" element of a static relay.

• Usually an op-amp comparator or a Schmitt trigger with hysteresis so that noise does not cause chattering.
• Threshold set by a reference voltage (potentiometer or Zener).
• Used in overcurrent/over-voltage relays (pick-up), after comparators, and in time-delay circuits.

A level detector is a static relay circuit that compares an input signal with a fixed reference level and gives an output (logic 1) only when the input exceeds that level. It acts as the pick-up element of a static relay.

            +Vcc
             │
 V_in ──►(+)╲
            │ ▷──── V_out → next stage
 V_ref ─►(−)╱   (high when V_in > V_ref)
             │
       (positive feedback R for
        hysteresis – Schmitt trigger)

• Construction: an op-amp (or transistor) comparator; V_ref set by a Zener diode or potentiometer, which fixes the relay setting.
• Hysteresis: positive feedback (Schmitt trigger) gives different pick-up and drop-off levels, so the output does not chatter when the input is near the threshold.
• Input: rectified and smoothed CT/PT signal, or the output of a comparator/timer.
• Uses: pick-up of overcurrent, over/under-voltage and frequency relays; detecting when a timer capacitor voltage reaches its set value; conditioning comparator outputs.
• Requirements: accurate, stable threshold with temperature; high reset ratio (≈ 0.95); fast response.

An operational amplifier (op-amp) is a high-gain DC-coupled differential amplifier IC. Its high input impedance, low output impedance and easy gain control make it the basic building block of modern static relays.

Uses of op-amps in static relays:

 V1 ─R─┐
       ├──(−)╲
 V2 ─R─┘     ▷── V_o = −(V1 + V2)·Rf/R
       ┌─(+)╱
      ─┴─ (Rf from output to (−))

Advantages: high accuracy and sensitivity, very low burden on CTs, compact, characteristics easily shaped, fewer components. Limitations: need a regulated DC supply (±15 V), sensitive to surges and temperature drift (offset), so protection circuits are needed.

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.

A static over-voltage relay trips when the system voltage rises above a set value (e.g. 110–120% of rated), and a static under-voltage relay trips when the voltage falls below a set value (e.g. 70–85%). Both use electronic level detectors in place of electromagnetic coils.

Block diagram

 PT ─►[Aux PT / isolation]
          │
   [Rectifier + smoothing filter]
          │  V_dc ∝ V_system
   ┌──────┴────────┐
 [Level detector] [Level detector]
  OV: V_dc > V_ref1  UV: V_dc < V_ref2
   │                 │
 [Timer t1]        [Timer t2]
   │                 │
 [Amplifier]       [Amplifier]
   │                 │
 [Output relay]    [Output relay]
   └────► Trip CB / alarm ◄────┘
        [Aux DC supply]

Operating principle

1. Input stage: the PT secondary (110 V) is reduced by an auxiliary transformer that also isolates the electronics; surge suppressors remove spikes.
2. Rectification and smoothing: the AC voltage is rectified and filtered to a DC voltage proportional to the rms (or average) system voltage. Some relays use a peak detector.
3. Level detection:
   • Over-voltage: an op-amp comparator (Schmitt trigger) gives output when V_dc > V_ref1.
   • Under-voltage: the comparator inputs are reversed, giving output when V_dc < V_ref2.
   • V_ref is set by a Zener/potentiometer, which gives the plug setting; hysteresis gives a high reset ratio (≈ 0.95–0.98).
4. Timer: an RC or digital timer adds a definite or inverse delay so that short swells, dips or motor-starting do not cause tripping. Instantaneous high-set stages are used for severe over-voltage.
5. Output: amplifier drives an auxiliary relay or thyristor which trips the CB or gives an alarm.

Detecting abnormal conditions and protective action

• Over-voltage stresses insulation and over-fluxes transformers; the relay limits its duration.
• Under-voltage makes induction motors draw high current and stall; the relay disconnects them and prevents dangerous automatic restart when supply returns.
• Advantages: accurate settings, high reset ratio, low PT burden and fast operation.