### How is the verification of the thermal equivalent Short-Circuit current done in PowerFactory?

Category:
Short-Circuit

The calculation results for the admissible thermal equivalent short-circuit current are the following values:

- Ithr: rated thermal Short-Circuit current with respect to 1 second (entered in the type data).

- Ith: actual thermal Short-Circuit current with respect to 1 second.

- Ithrtk: rated thermal Short-Circuit Current at the specified Short-Circuit Duration (Tk). Then the value can be compared with the threshold value Ithmax.

- Ithmax: actual value of the effective thermal Short-Circuit current by IEC, it applies to the Short-Circuit Duration (Tk) defined on the Short-Circuit calculation dialog.

Ith calculation:

The exact calculation would be considering the short-circuit moving along the line. The maximum partial short-circuit currents are the closest right and left side contributions to the fault. The maximum partial Short-Circuit current is relevant for the design of the cable. The following description shows how the assessment works in Power Factory. The discussed configuration is shown on the attached image.

- It is assumed that largest partial Short-Circuit Currents are for a fault located close to a busbar.

- A short-circuit calculation is performed at busbars/terminals to determine the Short-Circuit current contribution of the branches.

- For the example configuration the Short-Circuit current Ik" is 10 kA = (2 +6 +2) kA.

Ithmax calculation:

Ithmax will consider the worst Short-Circuit current contribution.

- The worst Short-Circuit current contribution is from L3. L3 is just below the bus bar, then the current flowing into the fault from the bottom part of the circuit is Ik"(bus)-I"3 = (10-2) kA. For this reason we have defined Ikmax" = max {Ik"(bus)-Ik3", Ik3"}, hence the name Ikssmax.

- Ikssmax is calculated for each end node of the branch, this maximum is relevant for the thermal design value. Based on the turn-off period of the Short-Circuit Ikssmax is determined and with the corresponding factors m + n, Ithmax is calculated.

1. Worst estimation case of thermal current:

The worst estimation case of thermal current is when the overloading is calculated as the ratio between the terminal Short-Circuit current and the Ithr. In the example that would be 10kA / 5 kA (Ithr (1s) of the line) gives as result a 200% of loading. This approximation is used when the option "Calculate max. Branch Currents = Busbar Currents" is enabled in the Advance Options of the SC Calculation menu.

2. To determine the allowed maximum Short-Circuit duration for a cable.

In the network for each cable the permissible Short-Circuit duration could be determined according to:

- Exact solution

Given that the two factors m + n (thermal effect of the d.c. and a.c. components) are defined in the IEC standard for the Short-Circuit duration, an accurate calculation is only possible after a parameter variation (sweep) of the failure time (e.g. from 100 to 1000 ms, in increments of 20 ms). Then for each cable will be recorded when the maximum load is reached. This sweep should be part of a DPL script.

- Approximate solution

For Short-Circuit durations above of 200 ms, the effect of increase the durations of Ithrtk will introduce generally a very low error. Therefore, usually the approximate equivalent thermal Short-Circuit current for a typical duration of a fault can be determined (e.g. for a 300 ms fault, Ithrtk (300ms) could be calculated). Then: Tk (allowed) = 300 ms * Ithr / Ithtk (300ms). For practical implementation in PowerFactory is recommended that the values of Ithr and Ithrtk were exported into a spreadsheet (e.g. Excel) from the flexible data page. Then the calculation can be performed easily.

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