True i did forget to take in account that heat pumps move significantly more heat than they consume. But still a block of ice remains very cheep because its just water, all the cost is in the container around it and this is easily expandable. It's not uncommon to have water heaters that hold more than 100kg of water, so the size of such ice storage would not get unpracticaly large just to store one day worth of air conditioning cold.
As for storing heat energy for half a year to cover the summer and winter difference is not easy. This does reach unpracticaly large sizes to store enough of it. Since latent heat can't be used for this, it makes it even worse (Tho molten wax can store heat pretty efficently). If you really wanted to have an advantage in terms of heating/cooling the best solution is to have an underground house. The ground temperature only varies by a few degrees trough the year. Tho in most climates the average ground temperature is too low to be comfortable, but some insulation and the waste heat from all the electrical appliances could bring that up closer to comfortable. But building such a house is expensive and you end up living in a windowless basement so it's not that great of an idea.
Geothermal is also in most cases too cold to be directly useful, but even the cold groundwater in winter is still a much better source for feeding a heatpump rather than the freezing air outside, can work for air conditioning tho. Unless you end up on top of a hot geothermal spring, those are very useful for heating, but are rather rare.
If you're still curious, the back-of-the-envelope is around 40 tonnes H2O.
That's assuming 1MWh for the season (guessing that's an overestimate for most houses? Didn't look it up), no heat loss to environment and no heat pump dissipation, and a temp swing of 20K in the reservoir.
The heat pump I don't think changes anything, as it's always dissipating its heat somewhere, and the house and tank tend to dissipate that heat to the environment in turn. The tank will end up biased on average, some degrees above/below average outdoor temperature, depending on which need is greater overall (cooling/heating). Interesting is the bias is nonlinear, because of course the heat pump is less efficient for greater differences.
Or maybe it doesn't matter because you'd need a thermal time constant over a year to have this make any sense, and that's actually hard to do (not sure). And if a random tank in the yard or ground has a shorter time constant, then that means you have more heat flux available through ambient dissipation, and the reservoir is simply irrelevant -- the solution reduces to a normal in-ground system.
Certainly, it seems it's at least
good enough to do it that way, and you'd only stand to gain a few percentage points by, essentially, putting a bypass capacitor on one side of the heat pump. That is, the ground-to-buried-line impedance acts like ESR, and a capacitor can average it out over some cycles (say, a time constant of one or a few days) -- which could be provided by a more economically sized reservoir. Maybe doing double duty as, say, the water in a water softener brine tank or something, Idunno. Or if you have well water, an oversized surge tank could do, heh.
Tim
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