You might think that the energy collected from a solar thermal panel was:
Light energy x panel efficiency x panel area
Seems reasonable enough, but it's not the case. The reason is that the energy output of a solar thermal system is normally limited by the capacity to store the heat, and if not the storage capacity, then the heat demand.
On a day of high light levels, once the hot water cylinder reaches its maximum safe temperature, the solar panel has to switch off - there's nowhere else to put the energy. A lower efficiency panel might heat your hot water cylinder up to the maximum temperature a little more slowly than a more efficient panel of the same area, but they'll both harvest the same amount of energy on that day.
The same argument applies to a larger area of solar panel compared to a smaller one, and a west-facing panel compared to a south-facing one.
So, you might ask, why not put in a bigger hot water store? Yes, for those sunny days, you'll collect more of the available energy, and you might carry some of it over for the next day (though your standing losses will be higher too). However the carried-over heat is only useful if the next day is not sunny and you wouldn't have been able to make more hot water that day. Unfortunately, good weather days tend to cluster together which reduces the benefit to only the margins between periods of changeover between settled high pressure weather systems and low pressure.
The other problem with using a very large storage volume comes on less bright days. The solar panel will then only achieve a large volume of luke-warm water rather than a smaller volume of water at a useful temperature, and the back-up heater will needlessly fire to heat it up.
An approach that overcomes this is to introduce a control system that preferentially heats only the top part of the hot water store, to produce a smaller amount of hot water on less sunny days. This overcomes the tendency of a large store to require more top-up heating on low light days, but does introduce more complexity.
The fact is that for a solar water heating installation, the relationship between area and useful energy collected follows a curve of diminishing returns.
The graph, showing the results of simulating differing sizes of solar installation against the same heat demand, illustrates the point. It shows how the energy collected from a solar panel varies against the installed panel area. The household demand for this average-sized house is around 2,200 kWh per year, and is shown in blue. The green line is a typical evacuated tube solar panel; the orange is a flat plate panel.
Both show a characteristic curve of diminishing return as you increase the installed area, for the reasons already discussed. The other feature of note is the small difference in performance between the high efficiency evacuated tube, and the flat plate panel, a difference that is normally overcome in practice by the fact that flat plate solar panel installations tend to have a larger area.
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