Electric steam

You can run the gas boiler off the batteries.

Straight electric boiler you'll need a huge battery backup system. No practical.

This. One of the more common problems with solar PV is that people tend to wildly overestimate the power and energy they can get out of a panel system And then compound the problem by not adding up how much power and energy it take to heat a space.

I'll just toss a few number out here… A good modern state of the art solar panel can be expected to deliver around 200 watts per square meter of area in full sun. But… the sun doesn't always shine, particularly in the northeast in the winter, so a not half bad starting point is to assume that you can get that power output for, on the averabe, 3 hours per day. So 600 watt-hours per day.

And you really need to stay warm for three cloudy days in a row.

Now take a moderately sized hourse and suppose that it's heating load is around 70000 BTUh — 24 hours per day. That's around 20 KE, or around 480 KWh per day. For our 3 clouding days, that means your batteries need to store around 1.5 megawatts. And to recharge them you need around 800 square meters of solar panel…

Big system. really big bucks for the batteries… (a Tesla Poerwall is around 15 KW-hours, and runs around 10 grand each… do the math).

not even close

You still have the basic problem of storing enough energy to carry you when the sun isn't shining, and harvesting enough power to fill that storage.

However.

The problem is much reduced, as with low to medium temperature hot water you do have the opportunity to use an air to water or water to water heat pump. This will reduce the energy required by a factor of somewhere around 3 — the COP or the overall heat pump system — which makes it go from really unfeasible to remotely feasible with enough invested in the storage and solar array.

It is still not remotely cost effective — but at least it isn't eye-popping…

Not sure where there has been a discussion — but the overall topic of operating a steam system in a vacuum does come up from time to time.

And it is quite true — the boiling point of water changes, as you would expect, with absolute pressure, so depending on how deep the vacuum is you can run significantly lower temperatures.

There are a couple of problems which kind of complicate things. The first is achieving a vacuum in the first place. In the bad old days we kind of did that in a backwards way: the boiler was brought up to steam and the air allowed to vent out of the system — but these weren't garden variety of vents. Rather, they sealed to hold a vacuum. So as the fire was allowed to die down (we're looking at coal here) the system naturally went into a vacuum and allowed prolonged operation at rather low temperatures. Vacuum type vents are still available — but are pricey. Some folks have experimented with adding check valves to regular vents to accomplish the same purpose. These were generally two pipe systems running on very small differential pressures (what are called vapour systems), but the same principle could be applied to one pipe systems — with the need for the specialized vents or check valves on every radiator.

One can also have systems which have mechanically induced vacuum. This adds a good bit of complexity to the system, particularly if the system isn't perfectly vacuum tight.

I don't see any point in using steam to distribute heat through the house if you're using electricity to create the heat, you may as well bring the electricity where it's needed and create the heat there.

The problem with solar in general is that it produces the most when you need it least and the least when you need it most. There's no good way to store it on a residential level, there are barely good ways to store it on an industrial level although they're getting better. If your utility offers net metering you can let them worry about storing it.

If you produce more electricity than you use, some utilities will pay you cash and some just give you a credit against future use. If solar makes economic sense for you in most cases the best deal is to take the cash if it's offered. If cash isn't offered then you want to use as much of the electricity as you can to avoid having unusable credits.

Note that net metering is fundamentally economically unsustainable, if everyone had a zero electricity bill the power company would go out of business. So as you plan your installation keep in mind that at some point the net metering is not going to be as generous. Most likely you'll have to pay something for use of the grid in the future.

That's OK, @tarik . I dream about a two stage system — a more or less conventional air to water heat pump first stage, and a high temperature second stage heat pump using water/steam as the refrigerant. Nothing wrong with the physics… in theory…