I still don’t understand. With a battery, less is fed in because more is consumed.
It is about the current power at any given time. With 14.4kWp, a maximum of 70%, i.e. 10.08kW, may be fed in. There are now 2 approaches for this: 1. You install an inverter that only delivers 70%. That is your offer. No matter what your modules deliver, a maximum of 10kW is produced. You consume part of it, the rest is fed in. This corresponds to the "70% hard" regulation. 2. You use a larger inverter, e.g. with 12kW, and regulate the feed-in amount via a measurement control, here e.g. the HomeManager. Then up to 12kW can be produced. So you could consume 2kW at the same time and still feed in 10kW. If you only consume 1kW, the HomeManager throttles the inverter to 11kW so that only 10kW continue to be fed in. This is called "70% soft". A battery can be used as a buffer for peak times. That means the HomeManager charges the battery only up to 50% if the weather forecast predicts overproduction. If then 12kW are available but you only consume 500W yourself at midday, the battery is charged with 1.5kW at this time. This keeps self-consumption at at least 2kW so that the full possible 12kW power and 10kW feed-in are utilized. In the evening the battery is still full, but the solar energy is used in the best possible way.