Dishwashers aren't very solar-friendly if you don't have net-metering.
They typically have a very powerful 2.5 kilowatt heater they run in bursts - for like 5 mins when prewashing, for like 10 mins when starting the main wash, and like 10 mins again when drying.
In between those times, the machine uses only ~60 watts for pumps.
I have often pondered what a world of machines designed to meet solar output looked like - and for a dishwasher it would involve the heater being modulated to match the solar output (and knowing that sometimes the wash cycle would take longer if a cloud was overhead so heating was delayed by a half hour).
Just have more dishwashers, and use them as storage cabinets: pick from a clean cabinet if you need tableware, deposit in a dirty cabinet when you are done and if you have at least three of them the transition is free to take a lot of time.
I can't imagine a scenario where you've got a large enough solar system that you'd want to be running a dishwasher off it, and you don't already have some battery storage elsewhere in that system.
The money efficiency isn't great - if you had control of the design of the dishwasher, simply having a hot block of concrete inside that you heated when there was spare energy would work out far cheaper.
Concrete costs far fewer $$$'s than batteries do, per kwh of heat stored, it also doesn't require inverters, balancing or safety systems, ad lasts millions of cycles rather than thousands.
I tried to do things like this in my home. It turns out for washers, dryers and dishwashers you should just set a timer to start at noon.
Once you've started an appliance on a cycle it's going to keep running, even if the sun goes behind a cloud. So you don't need to start it when the instantaneous solar power is at its highest, you need to start it when the predicted next two hours of solar power are at their highest.
And it turns out you don't need complex monitoring to figure that out.
That's exactly what I'm using this for. I have a home assistant automation that starts the washing machine when the daily solar peak power (as estimated by a web service for my location) is reached. Of course, I have to prepare everything in the morning. On sunny or even just bright days, no grid power is used.
No, not out of the box. They don't really support any automation, you can build something using Home Assistant or If This Then That, but now we're already past what I care to manage. There isn't even HomeKit integration (which I noticed is a trend, Google Home will be supported, but not HomeKit).
