Building a single-family house in NRW

The calculation is fundamentally wrong. The savings result from the thermal energy recovered from the room air being ventilated out. With an open window, this energy is lost 100% and heating is required. The controlled residential ventilation returns 84% or, depending on the model, even more of the thermal energy back into the room. But this has nothing to do with the 1.2kWh of electricity needed to run the controlled residential ventilation for one day

Of course, the calculation is fundamentally wrong, but in so many places that, simplified, it is correct again.

Where is the difference now between using x energy to blow air around or using x energy to reheat cold air? x energy is and remains x energy. Heat recovery does not matter at all. The energy is consumed. In both cases.

With the costs mentioned above (300-350 euros), I heat my house (without controlled residential ventilation).

The electricity that the controlled residential ventilation needs to drive the fan has zero nothing nada to do with the thermal energy recovered through the heat exchanger. Your statements are fundamentally wrong and not somehow a little bit right after all. It would be like saying the electricity of a gas boiler for its control would heat the house or the starter of your car would accelerate the vehicle to 100 km/h.

So the comparison is now massively flawed. The electricity for starting the car also comes from gasoline. And you need gasoline for transportation. So I need a total amount of gasoline for the trip from A to B including starting. But let's leave that.

It is about the amount of energy needed to heat a house for one year.

Case 1 (with controlled residential ventilation):
1500 kWh heating
500 kWh controlled residential ventilation

Case 2:
2,000 kWh heating

Now please tell me (on this limited basis) which house is "energetically/ecologically/economically better." (ceteris paribus)

I cannot, because both houses consume the same amount of energy. That's what I've been trying to get at here for hours.

The equation remains incorrect. The supplied auxiliary energy is in no direct correlation to the recovered heat energy, so your statement is nonsense.

It is about whether the controlled residential ventilation saves heating costs compared to window ventilation. What you have been doing for hours is off-topic.

50 watts in 24/7 operation already amount to about 110 euros in electricity costs per year. Plus the costs for 2 filter changes, we are easily at 200 € per year.

Plus financing costs of 100-150 € per year (around 10,000 euros financed at 1-1.5%).

Thus costs of about 300-350 € per year.

Filter costs for 4 filters each F7 and G4, if you buy an empty frame and the filter separately: 25 EUR per year (quarterly filter change). I took the very first offer from Amazon each time, there might be cheaper filters.

A controlled residential ventilation system has an annual performance factor of about 15 to 20. For 1 kWh of electricity consumption, you get 15 to 20 kWh of heat back.

Consumption about 35 watts per hour, so 306 kWh per year. Savings accordingly about 4,599 to 6,132 kWh. This also matches quite well with the empirical value that with a controlled residential ventilation system you can dimension the heating at least 2 kW smaller (with heat pump).

At 4.82 cents gas price like with us, savings are 221.67 to 295.56 EUR per year.
Electricity costs 306 kWh x 26.54 cents (quite expensive for us) = 81.21 EUR.

Electricity 80 EUR, filter 25 EUR and financing 150 EUR make 255 EUR or in other words, it pays for itself quite well at current prices and saves money at future prices. Comfort, time savings, better indoor air, etc. are all free on top.

And with us, the controlled residential ventilation system made solar domestic hot water heating unnecessary anyway. So about 5,000 EUR saved here (otherwise at least 3 collectors would be necessary for us).

Not to forget, if you heat with an air-water heat pump, you have to pay quite a bit more than 4.8 cents per kWh of thermal energy.

Between 10-20% energy losses that a normal house has typically occur due to classic ventilation.

In a classic existing house with double glazing and poor profiles, uninsulated walls, poorly insulated roof, etc., the 20% figure is correct. In a modern house built to the 2016 Energy Saving Ordinance standard with maximum insulation but still normal window ventilation, you can expect at least 30%, but rather up to 50%.