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When we perform open circuit test, we measure the core losses and we neglect the copper loss resistance (and also the leakage flux inductance?). But when we perform the short circuit test we measure the copper losses neglecting the core losses. What are the things that make that possible? And also why only apply rated vlota7 only?

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In an open circuit test, the current flowing in the secondary is zero hence copper loss is zero in the secondary. In the primary, the only current is the magnetization current and, it is this current that causes core saturation. It's usually a small fraction of full load primary current hence, those copper losses associated with core saturation current are quite small and can be ignored.

In a short circuit test, the applied voltage on the primary is very much smaller than that applied in proper applications hence, the magnetization current is very much smaller and, because of this, core losses are fairly negligible. Copper losses dominate short circuit testing because the applied voltage to the primary is chosen to produce the equivalent of full-load currents.

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In open circuit test the current in the primary winding is small and the secondary has zero current. Losses happen mainly in the core assuming the primary is properly designed for the voltage.

In short circuit test the voltage is low. The core magnetization is low because the coupled primary and secondary currents cause opposite magnetizations and do not increase the magnetization what's caused by the primary voltage and primary inductance.

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Consider that copper losses are proportional to I^2, while core losses are practically independent of load.

Therefore, for a full load current (referred to the primary) 10x the magnetising current, the copper losses will be 100x greater than in the open circuit case, and for the short circuit test, much greater still. Or, the copper losses in the open circuit test are small enough to be neglected.

The magnetizing loss is about the same in both tests, but it is relatively small when compared to 100x the copper loss so it is much easier to measure in the open circuit case, and there is nothing to be gained from measuring it twice.

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