A primitive electromechanical impedance relay design for detecting faults along long-distance transmission lines uses a simple balance-beam mechanism to sense when the ratio of line current to line voltage (I/V) becomes excessive. It will trip if ever the impedance became too small (i.e. too much I and too little V ):
This relay’s operating coil (OC) is energized by a current transformer signal, while the restraint coil (RC) is energized by a potential transformer signal. During normal and unloaded operation, when voltage is high and current is moderate-to-low, the attractive force exerted on the beam by the restraint coil’s magnetic field exceeds the attractive force exerted on the beam by the operating coil’s magnetic field, and the trip contact remains open. If, however, a fault condition occurs on the transmission line, current will dramatically increase while voltage decreases. This combination of changes causes the operating coil’s magnetic attraction to exceed that of the restraint coil, causing the beam to tilt in a clockwise rotation, closing the trip contact to send a DC tripping signal to the circuit breaker’s trip coil.
An important characteristic of this crude impedance relay design is that it is insensitive to phase shift between voltage and current. In other words, it does not discriminate between line impedance values having different phase angles, but will trip based solely on a minimum impedance magnitude.
The “reach” of this impedance relay may be plotted on an R-X phasor diagram as a circle centered around the origin of the graph:
Any line condition placing the impedance phasor tip within this circle will cause the relay to trip. Any line condition placing the impedance phasor tip outside this circle will cause the relay to be restrained (i.e. it will not trip). Thus, the reach of this relay is represented by the radius of the circle sketched on the R-X diagram.
As you can see, this design of distance relay will trip for reverse-power conditions just as easily as it will trip for forward-power conditions. Since we generally wish to de-sensitize distance relays from “reaching backward” into a reverse protection zone, we must find some way to limit the impedance relay’s tripping sensitivity in the reverse direction.
For the primitive balance-beam design, one solution to the problem of reverse-power sensitivity is to use a directional relay in conjunction with the distance relay to block the distance relay’s action during reverse-power conditions. The trip contact of a directional relay could be wired in series with the trip contact of the impedance relay, such that the only way to trip the breaker is if both the impedance relay and the directional relay agree. We may represent this blocking behavior by drawing a line called a blinder on the R-X diagram showing a threshold beyond which the impedance relay cannot operate:
Phase-shifting components inside the directional relay mechanism tilt its blinder characteristic slightly clockwise from its natural (horizontal) characteristic. As you can see, the blinder prevents all operation in the lower-left quadrant, restricting operation of the impedance relay primarily to the upper-right and upper-left quadrants, with only a small portion of the lower-right quadrant active.
Blocking the impedance relay’s action using a directional relay is a crude solution for a crude relay design. Much better distance relay characteristics have been developed since.
A major breakthrough in distance relay design came with the advent of the induction cup mechanism. This is similar in design to the induction disk mechanism explained in the section on time-overcurrent relays, but designed to operate very quickly rather than very slowly. An induction cup mechanism closely resembles a two-phase induction motor, where a small cup-shaped metal rotor is surrounded by two sets of electromagnet poles. Maximum torque will be induced on the rotor when the stators’ magnetic fields are 90 degrees phase-shifted from one another in time. When a positive torque is applied to the cup, it rotates on its axis to close a trip contact, sending DC power to the circuit breaker’s trip coil:
The amount of torque induced on the rotor (cup) is described by the following formula:
Algebraically solving for the relay constant K at a point of zero torque (the pick-up value for the relay) yields units of mho, or inverse ohms, which is why this mechanism is called a “mho element”:
With no phase-shifting capacitor, this mechanism will be maximally sensitive to impedance values of +90°, with a characteristic resembling a circle passing through the origin of an R-X diagram:
This relay’s reach is defined as any impedance falling within the circle, just as we defined the reach of the impedance relay. The difference here, of course, is that the “mho” distance relay is entirely insensitive to conditions within the lower quadrants of the R-X diagram.
With the addition of the phase-shifting capacitor to the induction cup polarizing coil circuit, the circular characteristic becomes tilted. Ideally, the angle of this tilt is set to match the impedance phasor angle of the transmission line so as to make the relay maximally sensitive to faults along the line.
With a tilted axis, the longest chord within the circle beginning at the origin of the R-X diagram is one matching the axis of tilt. Therefore, the highest impedance value capable of operating the relay and tripping the circuit breaker is one where the phase angle matches the tilt: indicative of a low-resistance fault at the end of a transmission line, assuming the circle’s diameter is proportional to the length of that line. Measured impedances at any other angle must be lower (i.e. a “heaver” loading condition) in order to operate the distance relay and trip the breaker.
If we compare circle characteristics for the simple impedance relay versus the “mho” relay capable of tripping at the same end-of-line fault condition, we see a remarkable contrast:
Both relays have the exact same reach at the transmission line’s impedance angle, but the impedance relay’s reach extends omnidirectionally for all phase angles and power flow directions, while the mho relay’s reach is optimized for the forward power direction and the line’s impedance, making it far more selective to faults along that line.
In some applications it is desirable to have the distance relay sensitized to certain values of reverse impedance (i.e. the lower-left quadrant on the R-X diagram). The induction cup relay mechanism is capable of having its circular reach characteristic “offset” with additional components so that the circle covers part of every quadrant like this:
Another variation on the “mho” characteristic is to equip the distance relay with multiple elements, each one with a different reach. The purpose of this is to provide backup protection for other zones by allowing the distance relay to overreach its primary protection zone:
Since distance relays trip whenever the tip of the impedance phasor falls within the prescribed area on the R-X diagram, at first it may seem as though zones 1 and 2 are pointlessly redundant to zone 3, since any fault lying within one of the inner zones will certainly be within the reach of the furthest zone. Indeed, this would be the case if all three distance elements operated at the same speed. However, if the zone 2 reach is purposely delayed in its action to be slower than zone 1, and zone 3 purposely delayed to make it slower than zone 2, the distance relay will serve to provide remote backup protection for the substation bus and transformer zones in the event the protective relays and/or breakers for those zones fail to properly clear a fault.
The following photograph shows a pair of Westinghouse electromechanical distance relays mounted next to a pair of time-delay units, each timer providing a different amount of delay for each of the two zones of protection afforded by the distance relays:
In the age of microprocessor relays, this design philosophy of physically wiring time-delay relays to the outputs of electromechanical protective relays for multi-zone protection may seem archaic, but it represents standard practice in distance relaying for a number of decades. Of course, modern microprocessor-based distance relays are able to perform all the necessary zone timing functions along with distance-sensing fault detection within the same unit, and do so with a degree of precision unthinkable with electromechanical relays.
Modern microprocessor-based distance relays are not constrained to circular reach characteristics either, and thus may be programmed to implement a variety of interesting reach functions. Although the traditional “mho” characteristic is still available as an option within digital distance relays, another form of reach called the quadrilateral (or “quad” for short) is often provided, whereby the distance relay may be configured to trip for any impedance phasor lying within a four-sided boundary:
Another common option within digital distance relays is the load encroachment blocking characteristic, designed to prevent relay tripping on heavy (legitimate) loads that might otherwise fall within the reach of the distance relay’s characteristic:
