Since it's not a battery storage setup, the energy being sent into your home circuit alleviates demand by a small amount. Where did they come up with 10 to 25% savings? Factors such as an optimal view of the sun for as much as possible, south-facing or biased East or West, would be the max. payoff. Night would be a zero net gain. At a savings of $7 a month, the panel would pay for itself in maybe 10 years not factoring in government subsidies. You need to keep it clean as well for it to maintain its potential output.
Stuff like your fridge can use a fair chunk of power continuously and a small solar setup can offset that when the sun is out. Same with routers, chargers, standby devices, TVs, etc.
For a 800W setup, 4–5 kWh on a very good summer day is plausible. Over a full year, it's going to be something like 600–900 kWh depending on orientation, shading, and location. So in strong summer months you might get something like 80–120 kWh. But you won't be able to use all of that unless you have a battery.
However, A typical apartment in Germany is not using that much electricity. Roughly speaking, a one-person place might use around 160 kWh a month and a two-person place around 270 kWh. Finding a use for 20–30 kWh a month during sunny periods. That's how you get to 10%. 25% might be harder but doable if you could somehow have a battery soak up the excess power. I don't think there are a lot of plug and play solutions for that yet. But it should not be that hard to do technically.
Power in Germany is relatively expensive 160*0.40 is about 80/month for me. I pay a bit less than that because I use less power somehow. But still, that's is close to 1000 euro per year. Saving 100 per year means the whole setup would earn itself back in 2-4 years (most plug and play setups you find on amazon are between 200 and 400 euro). And depending on where you live you can actually get some of that back via subsidy. But it basically pays for itself even if you don't. Unless like me your balcony faces east and you only get a few hours of sunlight in the morning.
Wow, 160 kWh/month! My family of four uses as much as 790 kWh/month in the high-heat or very cold season, with an annual average of 650 to 700 kWh/month. We pay around 0.13 USD/kWh, however, when you add the taxes and supply charges, it actually averages out to 0.28 USD/kWh...Granted I have two younger children at home, and my wife cooks fresh meals all the time - fresh-baked breads, etc., so we don't eat out much at all. We have an electric oven, electric washing machine and dryer, and electric cooling and heating (split unit HVAC).
I did really rough math and a hypothetical 200W panel getting 100% sun for 5 hours per day (1 kW/hr) would net you a whopping ~$9.30 in savings per month. We're paying something like $0.31 per kW/hr in NYC and it's a lot of money right now.
Did your calculations account for the suboptimal angle of the panels in most balcony solar setups? Most calculators assume the panels are at an optimal angle or on a roof pitch, not vertical like the image in the article.
A setup like the image in the article is going to get much lower than optimal efficiency because the panel is mounted vertically. She could be netting closer to $2-3 dollars per month or even less depending on which way she’s facing.