Wow! That's a bigger point you've made than you might at first suppose.

Let's start by putting your words into a diagram.

Yes, there are storage batteries available where the flow of stored charge can be adjusted according to time of day.

PowerVault have manufactured such systems for many years, and I was on a trial of some administered by OVO for 24-months.
However, the system didn't offer all the possibilities I had expected or hoped for:

• There was no display or menu system on the PowerVault battery. It relies on using an App and the battery being controlled by a centralised system operated by PowerVault's in-house technology. The system must remain 'live' and connected to the internet at all times.
• The trial I was on was active during the 2022 Energy Crisis. On days when there was insufficient solar for any to be stored in the battery, I had to import from the grid (at peak-rate!) in order to keep the PowerVault control system alive. That cost me hundreds of pounds.
• The PowerVault system assumed that any solar generation should first be stored in the battery until it was full. Only then did it allow further generation to be exported to the grid. But the DNO G98 limit was for a maximum export of 3.6kW, which was less than the solar panels were generating. In the afternoon on sunny days that meant excess generation was simply discarded.

The flat top of the graph is due to additional generation being curtailed.

What should've happened was for the solar generation to be shared between 'storage' and 'export to the grid' throughout the day.
If the software was adequately 'smart' it should've calculated the amount of generation anticipated on a sunny day, and exported just enough to still allow the battery to be full by the end of the afternoon.

In hindsight the software system was pretty primitive in its functionality.

Posted by: @homonid

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Are there inverters on the market that enable the amount of energy sent back to the grid from battery storage to be varied?

Do you really mean "to the grid"?

That's an unusual requirement.
It implies that the householder views the battery as profit-making system, importing when prices are lower and exporting when the price per kWh is high.

My personal view is that grid export from domestic sites should be discouraged.
Over 99% of homes have a single-phase feed.
Exporting to the grid creates phase-imbalance at the local substation.
In turn, that means current will be flowing in the Neutral connection...
... which causes thermal stress and can lead to outages.

I've created the graph above from a monitored local substation.
Few have any monitoring because it's a very expensive process.
I'm fortunate in being allowed access to such data.

I've marked points in the graph where the current in the Neutral is so high that it exceeds the three phases!

Let me stop at that point and allow you to clarify what functionality you're looking for.

Thanks for that interesting technical explanation, I certainly donl't want to export to the grid if I can help it, I probably didn't explain myself very well.

My understanding, which may be wrong, is that when the battery sends power back to the house via the consumer unit, if the battery is sending more power back than is being used by the house the rests goes into the grid.

As I am the only person in the house there are times when the only electrical item drawing power is the fridge. If, for arguments sake, I have a 4kw inverter which has sufficient power to charge the battery bank during the overnight cheap rate, then when the battery is supplying the house I don't want it sending power back to the house via the inverter at the rate of 4kw per hour. If only the fridge is on then my stored energy is being sent back to the grid, possibly for only a few pennies per unit.

If I could vary the rate at which the battery sent power back to the house that would be ideal.

Is that possible with current equipment? 

Thanks for your feedback.

Posted by: @homonid

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...

My understanding, which may be wrong, is that when the battery sends power back to the house via the consumer unit, if the battery is sending more power back than is being used by the house the rests goes into the grid.

...

I don’t believe that’s default behaviour, @homonid; it certainly isn’t for mine. I’m not entirely sure what your question is, so I’ll provide an illustration of what my experience is to see if it helps.

Speaking purely for my inverter for the moment, I can choose between three modes; load first (the default), battery first and grid first.

Load first means the inverter will use any solar energy to service the house’s load first, then send any excess solar to charge the battery, then if the battery’s full send any remaining excess solar to the grid. If there isn’t enough solar to service the house’s load, it will pull what it needs from the battery first and only pull from the grid as a last resort. If the battery has charge and there’s only a minimal load, the battery will only provide what’s necessary and won’t discharge anything to the grid.

Battery first means the inverter will prioritise charging the battery, so the house’s load may pull from the grid even if there’s solar pv being produced. Additionally, there’s a “charge from grid” option that will supplement the solar being produced with power being drawn from the grid so the battery is charged at the maximum rate the inverter can manage.

Grid first will send any solar pv straight out as an export and, additionally, there is an option to discharge the battery to export its power. This is the only time the battery is able to send power to the grid.

In all cases it is also possible to vary the rate at which power is moved around. I expect - but don’t know for certain - that most inverters work in a similar way. Does that clarification help or have I misunderstood your question?

Let me echo what @majordennisbloodnok has written about the 'Priorities' configuration which inverters use.

When evaluating such options, it's important to note from which perspective such Priorities are being offered.
In the case of his inverter, those three options are being viewed from the perspective of the solar input.
The configuration settings are asking the user to decide where that solar energy should go.

I have an inverter here which also offers Priorities, but they are viewed from the perspective of the Load.
There are four possible options in this case; the user decides the order in which the load will draw current from three possible sources.

For example, SBU (Solar, Battery, Utility) allows my Load to take what it can from the PV panels first, followed by the battery, and only then resort to drawing power from the Utility Grid.

That sounds fine...
... except that it makes it difficult to configure the inverter to re-charge the battery from the Grid.
There is no single command to do that.

I haven't yet directly answered the question from @homonid
but I need to first modify a couple of diagrams.

I'll come back to this shortly.

@majordennisbloodnok, thanks for your reply. This is what I wanted to hear. "If the battery has charge and there’s only a minimal load, the battery will only provide what’s necessary and won’t discharge anything to the grid."

I was worried that if I got a 4kw inverter to charge the batteries during the cheap overnight rate, the battery power might leak back to the grid at a rate of 4kw per hour if there were no controls to stop this. But from what you are saying it seems there are such controls and I don't have to worry about losing my stored energy back to the grid.

May I ask which Growatt inverter you are using?

Thanks.

You're welcome, @homonid. I'm using an SPH5000

And yes, you're right. The rating of the inverter, irrespective of brand I believe, will only determine the maximum rate at which power can be transferred rather than transferring at a fixed rate. It is certainly possible to TELL the inverter to dump energy from the battery back to the grid, but that would have to be an explicit decision.

Well worth waiting a short while for @transparent's diagrammatic update, though. As well as making it clearer I have little doubt it'll add more information I wasn't aware of.

It's interesting that @majordennisbloodnok was describing the Priorities system for a Growatt inverter...
... because so was I.

Growatt are using different concepts of Priorities across their own range of solar inverters.
No wonder this subject is tricky to understand!

Let me pick up the first of my diagrams to describe export to the Grid.
Electricity always flows from a higher voltage to a lower

If the Grid in my location is running at 240v AC and the inverter needs to export, then it must raise its output voltage.

An inverter with export capability will most often be required to limit that export to 16A (per phase).
That's the default condition defined in EREC Regulation G98.
It can be overruled by the regional Distribution Network Operator (DNO), who may allow you more current...
... or possibly none at all !

The inverter has to measure the current being sent to the Grid, and then automatically adjust its output voltage to ensure that the 16A limit isn't exceeded.

It most commonly achieves that by using a Current Clamp which surrounds the Live wire at the point where it enters your Consumer Unit (aka Distribution Board).

As you can see above, if there's a storage battery which also has export capability, then it too might require a current clamp.
The number and arrangement of current clamps differs according to each manufacturer and combination of inverter and battery.

A current clamp typically looks like this:

Notice that the clamp is clipped onto the Live supply cable only.
I've moved the Neutral out of the way so that it doesn't magnetically interfere with current measurement on the Live.

I think I need to add another comment to this thread @homonid 

Solar Inverters have two different types of 'mains output' at 240v 50Hz AC.

A: If the Mains Out is synchronised to the 50Hz of the grid then it has the capability to export.
Equally, if there is a power-cut, then your inverter will cease operating (and must do so under its G98 certification).
The inverter cannot synchronise to the grid if there's no 50Hz to synchronise to!

B: If the Mains Out derives its 50Hz signal from its own inbuilt oscillator, then it can't export to the grid.
Any attempt to connect that Mains Output to the grid will blow a protection fuse/trip.
Your tiny domestic inverter cannot possibly fight against the combined forces of the 50Hz frequency being used by the major power generation plants!

In the case of Option-B, such an inverter can continue to supply the house with 'mains power' during a grid outage.
We call that 'off-grid operation'.
That might or might not be an important point for you when deciding what to buy.

Most (but not all) of the solar inverters which I use are off-grid.
The 'Mains Outputs' supply a separate Consumer Unit from which (most of) the household circuits are fed.

Some inverters, such as those from SunSynk or the All-in-One units from GivEnergy, offer both types of Mains Output.

It's up to you to decide which household circuits are connected to which of the two possible outputs.

In the above diagram (bottom-right corner) you will notice that there are some DC devices which I run directly from the storage battery.
That means I don't take the power through the inverters up to 240v AC, and then convert it back to low-voltage DC again.
Those devices will always remain 'alive' even if all my inverters fail, or when I'm doing maintenance work on them.

Please feel free to ask further questions on these choices.

It's better to discuss what you wish to achieve now, before you start buying in equipment.

And to echo what @transparent has said, the H in my inverter's model number (SPH5000) denotes it is a hybrid inverter, hence able to offer both types of mains output.

@majordennisbloodnok Thanks, the SPH5000 seems to retail at a reasonable price too, I will add it to my list of possibles.

As you'd expect me to, I've just checked the spec of that SPH5000 inverter @majordennisbloodnok

Let's note that the off-grid (backup) mains output isn't rated at the full 5kW of the inverter.

It's actually constrained by the discharge current available from the storage battery.

In many cases that wouldn't matter.
If I needed high output to power a larger load, such as a heat-pump, then I'd buy a second inverter and connect them in parallel (as per my diagram above).

But the Growatt SPH range of inverters don't have have a parallel-operation option.
If you later decided that you required more power then the SPH would need replacing.

I thought I'd better mention that before @homonid realises how cheap the SPH-5000 is and orders one.
(He's already responded above before I just posted this warning!)