Photovoltaic system air-water heat pump - profitability single-family house KFW55EE

As written earlier, the heat pump consumes the most in winter. However, the days are short, the sun is low, and it is often gray for days. The system is a subsidy, but nothing more.

In addition, 4.5 kWp is really not very large. On a grimy day, you get 200-300 watts. You can easily extend the 14% to 25% with a larger system. With a bit of control (overheating during the day), even more is possible. Much also depends on the house, but the most important thing is to make the system as large as possible. At the latest when you need the electric car, every module is necessary.

This also means, at

15° DN (Dachflächen sind im Norden und Süden).

definitely fully equip both sides. Adjust roof windows in the plan to the module grid right away (otherwise it tends to mess up the space for 4-6 modules), no satellite system on the roof, and take any ventilation short immediately so the solar installer doesn’t have to cut them later.
And of course no battery.

Everything else has already been answered.

Is the north side really worth it? 15 degrees are not particularly steep, but the modules are still almost continuously in the shade.

Is the north side really worth it? 15 degrees is not particularly steep, but the modules are still almost continuously in the shade.

Usually, yes. But it can be recalculated and also depends on other parameters like buildings, chimneys, trees, etc.

Short: Definitely yes. North is currently built from about 25° and flatter.

Long: With a heat pump (and the associated high self-consumption in winter), maybe even steeper. There are websites, which I am not allowed to mention here, that calculate the exact yield depending on location, orientation, and roof pitch. So you can quantify in advance how much the north modules are allowed to cost extra. And that's not that much:
You don't need another inverter, no additional electrical work, grounding, contactors, planning—all that you have already paid for with the south side anyway. For the north, only a few modules are added, which—if the solar guy doesn't rip you off—cost only about two-thirds of what the south modules cost you. And since the yield loss is probably less than one-third, they pay off.
In bad weather, the orientation of the modules hardly matters; only the area counts. So if I want to charge my e-car even in the rain, or wildly, heat with a heat pump in winter, I am happy about every kWp. You have no idea how LITTLE power is available in bad weather... (it's 5-10%). Therefore, especially with an e-car, 50 kWp is actually still much too small...

Ps: I checked briefly for central Germany: south roof 15°: 980 kWh/y, north roof 15°: 750 kWh/y
You should build from 650 kWh/y.

Ps: I quickly checked for Central Germany: South roof 15°: 980 kWh/y, North roof 15°: 750 kWh/y
You should build from 650 kWh/y onwards.

Per module, sqm, or "football field," right? :)