what if we energize 50 Hz h.v side of the transformer with 40Hz, is the transformation ratio don't matter? Suppose 400/200, single phase transformer which is designed to operate at 50Hz. If you provide it 40Hz the output will remain unaffected by frequency?
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\$\begingroup\$ It will saturate. Urms=4.44fNAB. If you decrease f, B will increase. \$\endgroup\$– winnyCommented Feb 5, 2017 at 8:30
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If you supply a transformer with less than the rated frequency, you have to supply it with proportionately less than the rated voltage, otherwise it's likely to saturate. The maximum voltage/frequency ratio (or voltage.period product) you can feed to the transformer is limited by the area of the core.
In this case, your 400/200 50Hz transformer becomes a 320/160 transformer at 40Hz. It will still have the same transformation ratio. It will still handle the same current, so its VA will have dropped to 80% of the 50Hz value.
If the original transformer has been designed conservatively, well clear of saturation, then it will tolerate a slightly higher voltage/frequency ratio. Monitor the magnetising current, that is the current taken by the primary with no load on the secondary, at the correct rated voltage/frequency ratio. Decide a maximum value for this current that you are prepared to tolerate (the limit is mostly \$I^2R\$ heating in copper windings). Now increase the primary voltage slowly, while monitoring the magnetising current. When it's reached your limit, stop increasing the voltage further.
The reason behind this behaviour is the way iron behaves in a magnetic field. As it approaches saturation, its permeability crashes from typically 2000 to something nearer 1. It's the high permeability of the iron that keeps the magnetising current managable. Once it has stopped working as designed, the current rises.
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\$\begingroup\$ What if I still force it to energize at 400Volts? Output will decrease?by what percentage? How do you know that? Meaning if high voltage side is now energized from 400Volts, 40 Hz source, the the no load l.v side voltage would be? Output decrease, increases or remains same at 200Volts? \$\endgroup\$ Commented Feb 5, 2017 at 1:03
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\$\begingroup\$ When a core goes into saturation, the output stays more or less at the correct design voltage of 160, however the primary side magnetising current tends to rise by a factor of 1000. That's correct, I didn't leave my finger on autorepeat, if not interrupted by a fuse, the primary current can rise by a factor of a thousand. That's why we design transformers not to go into saturation. Different transformer irons saturate at different rates, and the original transformer may be been more or less generous with the design, so you may see a smaller increase, but 1000x is possible. \$\endgroup\$– Neil_UKCommented Feb 5, 2017 at 7:09