### What is the difference between source impedance (Rs,Xs,Zs and phizs), fault impedance (Zf and phizf,Z and phiz and Zl and phizl) and relay impedance (Rfrel,Xfrel,Zfrel and phizfrel) results from the short circuit calculations?

Category:
Short-Circuit

When a short circuit calculation is successfully executed, the user can select the following impedance values in the result box of each branch element:

* Source Impedance Rs,Xs,Zs and phizs (available for balanced faults and per phase for unbalanced faults)

These represent an equivalent impedance seen from the considered branch location looking back to the source of the short circuit current. For all but very simple networks there is no definitive method for deriving Zs and therefore different methods can be found in the literature. In PowerFactory, the following equations are used:

For Line to ground faults:

Zs = (Ua_prefault – Ua) / (Ik”a+3*I0*K0 – Ia_prefault) (for the case of a A phase fault)

For Line to Line faults:

Zs =((Ua_prefault-Ub_prefault)  – (Ua-Ub)) / (Ik“a-Ik“b – (Ia_prefault-Ib_prefault ) ) (for the case of a B-C fault)

For three phase faults:

Zs = (U_prefault – U) / ( Ik“ – I_prefault )

Where the IEC60909 method is used, prefault voltages and currents are not available, therefore I_prefault is specified as zero and U_prefault = c*Un are used where c is the c factor as defined in the standard and Un is the nominal voltage at the point of fault.

* Fault impedance R,X,Z and phiz (available for balanced faults), Line to ground fault loop impedance Z and phiz (available per phase for unbalanced faults only), Line to line fault loop impedance Zl and phizl (available per phase for unbalanced faults only)

For balanced faults these represent the postive sequence impedance to the fault location, for unbalanced faults the loop impedances traverse the considered branch location to the fault location and back. For line to line fault loops the loop impedance is effectively divided by 2 owing to the equal impedances of the two faulted phases of the line and to therefore provide the impedance to the fault. For line to ground fault loops the impedance of the whole loop is provided.

A pfd file and xlsx file have been attached which illustrate the manual calculation of these fault impedance values as seen from Bus 4 looking into Line L2 for 3ph, 2ph and 1ph short circuits on Bus 3.

* Measured fault impedance Zf and phizf (single quantities available for unbalanced faults ony)

This is calculated as the minimum impedance of the line to ground and line to line fault loops. i.e. Min(Z:A,Z:B,Z:C,Zl:A,Zl:B,Zl:C)

* Relay Fault Impedance Rfrel, Xfrel, Zfrel and phizfrel (available for unabalanced faults only)

This is calculated as as per Zf and phiZf, except in considering the ground loops standard zero sequence compensation is considered (Z = U / (I + k * 3 * I0)) to calculate the impedance up to the fault position instead of the full loop impedance.

The measured fault impedance and relay fault impedance parameters are intended to give a simplified measure of the minimum impedance a distance relay at the associated location would likely see in the event of the specifed fault. The loop with the minimum impedance is likely to be the one to cause the fastest tripping of the distance relay and can therefore be considered the critical case.

Some relays use the full line to ground fault loops for ground distance calculations, whilst others use the compensated impedance up to the fault location. The calculation of both measured fault impedance and Relay fault impedance parameters allows both kind of relaying technique to be considered.

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