160405-1902 EDT
JasonCo:
Your first post has inconsistencies that will not produce 24 V output.
Have a question about buck-boost transformers. I'm not sure how they work. But I have a question that says a Supply Circuit is from a 2-pole breaker 277/480v, 3-ph, 4-w panelboard. The load is rated to operate at 24 volts. The transformer is a 120 x 240 - 12/24 volt.
Let's not call this a buck boost transformer to avoid confusion.
Suppose we have an isolation transformer that has four isolated coils consisting of two 120 V coils and two 12 v coils. How can this transformer be wired to produce 24 V output with 264 V input? When connecting windings of a single transformer together the phasing of the coils is important. A typical way of indicating common phasing of windings is to place a large DOT adjacent to and at one end of each coil. If the non dotted ends of each coil are connected together and the transformer is excited, then relative to the non-dotted ends all of the dotted ends will be positive at the same time.
If you take two coils and connect them together with the dotted end of one coil connected to the non-dotted end of the other coil, then the two coils are additive. Thus, if the two 120 V coils are so connected, then that coil combination can be connected to a 240 V source, or if the transformer core was appropriately excited, then this coil combination would supply 240 V, or 120-0-120 V.
It appears that your question wants 24 V output. To get 24 V out you need to additively combine the two 12 V coils. In other words connect the two 12 V coils in series with the correct phasing. This will provide 24 V from a properly excited transformer core. This takes care of how we get 24 V.
We have two remaining coils, each is 120 V. If the coils are connected in parallel and properly phased, meaning DOT to DOT and non-DOT to non-DOT, and if 120 V is applied to this parallel combination, then the voltage from the two 12 V windings in series is 24 V. Further if no connection is made between the 120 V coils and the 12 V coils, then there is electrical isolation between the two different voltage levels.
If instead of connecting the 120 V coils in parallel we connect the 120 V coils in series with proper phasing, then again with electrical isolation we get 24 V output from the seriesed 12 V coils.
Taking the last combination and with correct phasing connect all the coils in series, then we can apply 120 + 120 + 12+ 12 = 264 V across the total series combination and get 24 V out, but now there is not isolation of the two voltages. This combination will be called an auto-transformer.
You do not have 264 V available as a source. Thus, the inconsistency in the initial problem. Available is 277 V. Thus, a possible output is 24*277/240 = 27.7 V. Because of internal impedance in the transformer your output may be somewhat less under load. But also some transformers may be wound with a slightly different ratio to compensate for loaded voltage drop.
If this series combination is connected from a three phase line to neutral with the 12 + 12 V windings to neutral, then your 24 V output will have one side near ground potential under normal conditions, but not isolated so you can not create your ground reference.
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