Estimation of the maximum short-circuit current Ik_max of a transformer.
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22. junio 2021
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Engineering & Services
In practice, the value of the maximum short-circuit current "Isc_max" of a transformer is often needed. On the one hand, to be able to estimate the current carrying capacity of input circuits, such as in the KoCoS fault recorder system SHERLOG. It must also be taken into account that typical protection current transformers used in medium voltage can transmit currents up to 40 times higher than the rated current of the transformer in the event of a short circuit. On the other hand, a typical application is the plausibility check of the parameters of the high current stage of a transformer protection relay during the commissioning or repeat protection test, for example with our relay test system ARTES.
The following formulas are used to estimate the maximum short-circuit current "Ik_max" for three-phase medium-voltage transformers. The determined current value "Ik_max" is in practice somewhat higher than the real short-circuit current "Ik_max_real" which actually occurs. The estimation is therefore made to the "safe side".
The following equations 1 and 2 show that the estimation can be done for the primary as well as for the secondary side. When using equation 1 and equation 2, it should be noted that "usc" must be entered as a percentage in the equations for the relative short-circuit voltage.
If the rated current of the transformer is not explicitly known (for example, only “Srated_transformer” and “uk” are often specified in network calculations for transformers), the tailored quantity equation 3 can be used. Note: This estimation of the maximum short-circuit current applies only to three-phase medium-voltage transformers with a secondary voltage of Unom_sec = 400V. Also, when using equation 3, note that the relative short-circuit voltage "usc" in percent must be inserted into the equation.
When transformers are used, they are often referred to as "voltage-stiff" or "voltage-soft" transformers with regard to the behaviour of the secondary voltage during load changes. Equations 1 and 2 show that the maximum short-circuit current increases with decreasing "uk" (voltage-stiff) and the maximum short-circuit current decreases with increasing "usc" (voltage-soft). The short-circuit voltage “Vsc” and thus also the relative short-circuit voltage “usc” are a measure of the internal resistance of the transformer.
Voltage soft: When loaded, the output voltage of the transformer decreases. The output current hardly changes. The transformer is short-circuit proof (example: welding transformer).
Voltage stiff: Under load, the output voltage of the transformer hardly decreases. The output current increases. The transformer is not short-circuit proof.
As an aid to remembering the behaviour of the transformer's output voltage, a very hard and a soft cushion can be used. If the same amount of pressure is applied to a very hard and a soft pad, the hard pad is depressed significantly less than the soft pad. The depth of the indentation on the cushion is synonymous with the behaviour of the output voltage of the transformer.
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