So you've basically got the same basic system as I have... even though my inverter is only 5kWh (it's a fanless Deye BTW)
It's hard to give someone else advice on this since we're all doing out own thing and have different requirements.
Also, keep in mind I live alone so it's easier to predict my patterns, I'm assuming it gets much harder with a family around... although, it shouldn't be
that much different... I don't know, my mail-order bride got lost in the SAPOS system. Bless her heart.
That said, here's my current time slot config from Solar Assistant:
If you're not familiar with Solar Assistant or these time slots, the Power setting is just how much/fast I allow the battery to be charged from the grid, typical newer 5kWh LFP batteries can take 1C (meaning 5000 Watts charging) but it's typically better to stay below that if you can, the slower you charge it the longer it takes of course, but also improves the battery charge cycles in the long term and it's better to go lower if you can so you don't become a power sucking problem when the grid goes up again. The State of Charge percentage is what you want the battery level to be... meaning if it's below that it'll charge from the grid if the grid is available. If the battery is above that percentage nothing happens. It'll just keep charging for solar as normal if it's available.
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By the way it's probably not optimized, but that's 'cause it works for me right now so saving a buck here or there isn't at the top of my list.
Also, in regards to "losses", meaning times where the battery is full but I'm getting solar energy in, the inverter is hooked up to dump that energy into the geyser as long as the battery level is at or higher than the preferred charge state in the setting I've provided above. I'd assume yours is set up the same, if not, definitely look into that. You can identify an oversized system relatively easily this way, your battery will be full and your solar input will be almost nothing even when the sun is shining (or even if it's cloudy but you see almost no energy coming in). That's all wasted energy (that should have been fed back into the grid). Happens often on mine so that's how I know my system isn't optimized. But until feedback is a viable option I'm prioritizing availability because I work from home and haven't had an issue yet.
Summary:
Let's start after work at night, 9PM
Between 9PM and 1AM I allow the system to "quick charge" from the Grid to 65% if needed. That covers me if there's an outage during a time when there's no solar available and when I'm either asleep, drunk or just chilling in front of the TV, that keeps my fridge, night lights and security system running all night if needed. If the grid isn't available in that slot, well, then I use whatever the battery has to to give. I'd prefer this to be lower but with cable theft in the area it's better to charge if you can before the stealing starts (they usually steal between 1AM and 5AM).
Between 1AM and 7AM I allow the grid to keep the battery at 50% if the grid's available. If not then it's fine, there's enough to let the battery run down to just above it's recommended SOC, mine's set at 15% but 20% is usually the sweet spot with LFP batteries. I'd prefer the SOC to be lower, say 30-40%, but decided on 50% recently due to it being summer and cloudy. Will likely go down in Winter to my preferred setting of 30%.
Then, usually
between 7AM and 9AM is when the sun starts doing its thing. I've adjusted it recently to keep the battery at 50% just because of the weather, but again like the time slot above, I'll take this setting down again when the weather becomes more predictable. This should typically have the lowest preferred SOC setting of the day since you really shouldn't need the grid to kick in at this point while you're waiting for that sweet-sweet solar energy.
From 9AM to 1PM I allow a slower grid charge to keep me at 40%, this is typically also too high since that's the perfect time slot for the batteries to be filled from solar, however I just keep it there now in case there's outages again, and also again, the weather. In Winter this slot will go down to 20-30%, easy 'cause I know the pack will charge fully from only Solar even if I'm using as many appliances as I can while the system is charging. (My max wattage on the panels is usually 2200 Watts between 12PM and 1PM)
Then
from 1PM to 5PM I use grid again to keep the batteries at 85% if possible. This is typically too high as well BUT I keep it there for now sicne if the batteries (as the usually do) were charged fully during the 9AM to 1PM slot then it won't even use the grid, but if they aren't at 85% during this slot then something obviously went wrong (bad weather or outage) so this settings makes sense and works well for me. This is a very important timeslot. You want to go into dusk knowing you have energy. Even if you don't and the weather is crappy, then you can at least switch off some non-critical devices and even switch off the fridge etc. until the next morning to see what happens at dawn.
Then
5PM to 9PM I try to dump as much energy into the battery from grid again to keep it at 90% just in case there's an outage over night
and bad weather the next day... however I think this setting is too high, I keep it because it gives me peace of mind.
Here's my usage for the past 12 Days.
As far as I'm concerned this is worst case scenario... so that's a good measuring stick.
The days where my solar vs. grid power is roughly 50/50 are the days where it's sunnier... the rest you can bet were cloudy days.
It's kind of obvious to me that if I wanted to go "off grid", I need to double my battery capacity and possibly double my panels too... so 10kWh battery storage with 8 X 550Watt panels... that's actually really not that bad. The only issue I have is space. But will figure that out somehow.
The first thing I would do is double my battery capacity, when monitoring the system throughout the day I'm noticing a lot of energy that doesn't have anywhere to go... I think that's where a lot of people get it wrong, they use general calculations to size the system so they add tons of panels but then don't realize that for hours at a time those panels are just idling and doing nothing, fine if you want to cater for cloudy days but you can also increase battery capacity for those situations (granted, panels are cheaper per watt so I'm likely wrong here. not really sure yet)
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Another hard-learned tip I would add for people with smaller solar systems is this: Solar PV voltage.
Dearlord, I literally doubled my PV efficiency and input by changing to slightly higher voltage panels. My previous 4 panels were just licking the bottom of the barrel on my inverter in regards to how much DC voltage it needed from the panels.... sure the the system was still working, but the MPPT controller was working overtime... Once I changed to 50V panels instead of 38V I literally doubled my PV input.