you can buy induction cookers that run on 1500w at high heat.
My primary cooktop for the last 10 years has been a portable induction cooktop. I can tell you a few things about them.
Only purchase a unit that has an all glass top where the controls are underneath the glass. I had one that did not have that feature and the plastic on the control panel area fell apart.
Even with an all glass cook top do not use a large skillet or pan that is so wide it overhangs the control panel as that too can cause damage. Not too big of a problem if you are a solo traveler with a smaller fridge freezer as you are not likely to be cooking in large quantities the way people do who like to put stuff into the freezer for eating later.
You can't use really small pans on them, the diameter must be larger than 4" except if you are using one of the plates you put on top of them for using non magnetic cookware. But that comes with the risk of burning yourself on the plate.
Some of the units have a limited number of heat settings. That can be a real pain in the keester for cooking as they tend to be too hot or too cool and it just is not easy to cook on those types. Get one that has a lot of settings and hopefully also gives a readout in degrees of heat versus just numbers such as 1, 2, 3, 4, 5, etc. On my current unit which has a range of 6 settings #3 is the sweet spot for just right for the majority of things such as eggs, pancakes, soups, hamburgers, but sometimes they brown too fast and I have to turn it down to #2. I use #6 for quickly bringing water to a boil and #4 or #5 for a higher heat browning of meat or fast stir fry things. So basically you don't really have to use it above #3 unless you are in a hurry to heat water or brown stuff. So perhaps that means you are generally going to be cooking at about 1,000 watts or less on a 1,500 watt unit which is what I have always owned. I have never had a 1,800 watt unit.
Cast iron pans do work on induction but the rough cast iron pans will scratch the glass top, stainless steel is a better pan for them. You must use pans with a flat bottom that give good contact to the surface. Throw out your old warped pans.
The pans that work best for induction cooking have a thick bottom with a built up core material. You get much better heat distribution and much faster response time for doing things like boiling water. They downside is those pots do weigh more but you are saving on electrical power so that is likely worth the extra weight.
Remember if you use non stick cookware that the biggest enemy for non stick, the thing you do that will completely destroy non stick property, is to use high heat when cooking with them. You want the to last a long time just use medium heat or lower with them. If you want to use high heat then use uncoated stainless steel or carbon steel, or cast iron.
Nice safety features of induction cooking, if you forget and a pan boils dry the cooker will shut itself off. If you take a pan off the burner the cooker will shut off in just a few seconds. I do love having a timer function that shuts off the cooking as it means fewer burned meals or over cooked pasta. It makes things like flipping a burger after the proper number of minutes per side a little easier as an end of time bell goes off reminding you it is time to flip and restart the heat and timer.
I do love using an induction cooker but as I don't have roof top space for a lot of solar I won't be taking one traveling with me. Fortunately I do like cooking with a propane/butane cook top too but it will cost more for cooking fuel.