It sounds to me (so far) that
@Electric-T doesn't have any design specifications. Why does he really want 15 VAC (post #22)? Battery chargers require DC of course. How can you possibly find a vendor without specifying the transformer you "need" and how did you determine what you "need"? In post #13 you state:
Lots of red flags. You can have variable voltage OR variable current, but not BOTH at the same time. All battery chemistries have very specific charging protocols for safe and effective charging. A 12 V lead-acid battery, for example, is typically charged with about 14 VDC using a current-limited power supply. Lithium ion batteries have a more sophisticated (read: complex) charging protocol. None of the battery chargers I have seen have a variable voltage control, but you are free to "design" your own. You will need to specify the voltage range and the current that will be supplied to the load over that range before even beginning to select a transformer with appropriate secondary voltage and current capabilities. Saying you need a 1800 watt transformer, simply because that is the maximum power you can draw from a 15A convenience outlet, is no way to begin a design.
As
@kellys_eye mentioned in post #19, you must work backwards from the load toward the source of power, taking into consideration all the inefficiencies along the way, to arrive at the transformer power capability you need. What if the number that results is greater than 1800 watts? Do you just sigh and say, "Oh, well, I guess it can't be done..." No, you do not. You either plan to use a circuit with a higher current capability, say 20A, or a higher primary voltage, say 240 VAC, or you reduce the load-driving capability to accommodate the power you do have available.
Many years ago I acquired a power transformer whose primary was rated 120 VAC. The transformer weighed in at over seventy pounds dead weight. It came with four 1N3085 stud-rectifier diodes, rated for 100 V and 150 A each, mounted on massive air convection-cooled heat-sinks. The diodes were wired in a full-wave bridge rectifier configuration, connected to TWO 8 VAC center-tapped secondary windings on the transformer connected in series-aiding.
I lugged this treasure home and built a support framework for the transformer and bridge rectifier using slotted angle-iron scraps held together with 1/4-20 bolts, nuts, and washers. As I aged, I became too weak to lift it, so I added four wheels to the framework and a bungee cord to pull it along. Today I plugged it into a wall outlet and measured some volages. Line voltage: 122 VAC, 60 Hz. Secondary voltage: 16.3 VAC. Unfiltered (raw) DC output voltage: 14.185. Output filtered with 16,000 μFd electrolytic capacitor: 20 VDC. Output current capability: enough to turn over the engine in my 2002 Ford Ranger pickup truck. Clearly I "lucked out" in acquiring these parts. All I wanted to do was build a car battery charger. To that end, I installed a 50-0-50 A D'arsenval meter in series with one of the power supply output terminals and a largeish Variac between the convenience outlet and the transformer primary. The Variac allowed me to adjust the output voltage and the analog meter allowed be to monitor the charging current. Good enuf, I told myself, but later I ruined the meter by trying to start the truck without remembering to remove the meter. The Variac was eventually put to use elsewhere, so I used about three feet of heavy gauge nichrome wire, arranged in an air-spaced coil with an alligator clip to select how much to use, as a current limiter for car battery charging.
So bottom line is, if you need a "charger" with variable zero to twenty-volt output capable of delivering 150 amperes, a transformer like mine is what you need. They are available. Just add some "smoothing" filter capacitors, and some electronics to control the output voltage and current, and you are done. Or, as the British say, "And Bob's your uncle!" See photos for possible construction tips.
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