Application of Impedance Diagrams to Characterize Faults

Oscilloscope displays showing the raw voltage and current waveforms are clumsy representations of line impedance. Better visual representations for impedance exist, the most popular being a phasor diagram for line impedance with resistance (R) on the horizontal axis and reactance (X ) on the vertical axis, commonly referred to as an R-X diagram. The three line examples shown in the previous section using the oscilloscope are shown in phasor format here:

Keep in mind that these phasors represent impedance, and as such a short-circuited (faulted) condition is shown as a short phasor, while an unloaded condition is shown as a long phasor. It should also be noted that these impedances, while calculated from measurements of voltage and current, do not change unless the line, load, or fault characteristics change. If the system voltage were to sag due to a generator problem, for example, the impedance phasor representing the combined effects of line and load impedance would not be altered. Any protective relay operating on impedance would therefore ignore such changes, and trip only if the line’s characteristics were to change. This is precisely the behavior we need from a “distance” relay, enabling it to discriminate line faults better than a simple overcurrent relay ever could.

For a normal load condition, the impedance phasor will be significantly longer than that of the line’s full length (i.e. much higher impedance) with an angle significantly less than that of the line impedance alone:

Short-circuit faults at various locations along a transmission line will cause the impedance phasor to vary primarily in magnitude and angle. Recall that during fault conditions, the resistance and reactance of the power line itself is the dominant impedance limiting fault current. The actual fault is predominantly resistive, with a very small impedance value.

For a fault far removed from the relay, the impedance phasor will be long (i.e. relatively high impedance) with angle nearly equal to that of the line impedance alone:

For a fault closer to the relay, the impedance phasor will be short (i.e. low impedance) with angle slightly less than that of the line impedance alone:

The goal of a distance relay (ANSI/IEEE code 21) is to trip its circuit breaker(s) if a fault occurs within its programmed “reach” and to ignore both normal operating loads and faults lying outside its reach.

If additional sources of electrical power are connected to the far end of the transmission line, it is possible for the distance relay to sense reverse power flow. Consider a case where a short-circuit fault occurs on the generator bus shown in this single-line diagram:

A fault to the left of the distance relay manifests as high current and low voltage just like a fault on the transmission line, but since the current waveform is inverted (180o phase shift) due to the opposite direction of fault current, the impedance phasor ends up in an entirely different quadrant of the R-X diagram. If the goal of the distance relay is to protect the transmission line, we need it to ignore such faults, because to operate on such a fault would be an example of overreach, the distance relay “reaching into” the generator bus zone where it should be concerned with the transmission line zone.

Each of the R-X diagram’s quadrants may be labeled in terms of power direction and power factor, either “lagging” (predominantly inductive) or “leading” (predominantly capacitive):

Article text from Lessons In Industrial Instrumentation by Tony R. Kuphaldt – under the terms and conditions of the Creative Commons Attribution 4.0 International Public License

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