Just got my Emon Pi and trying to work out how to connect it all into the system. However, in response to you main question (Does it make financial sense to install a battery?) my response would be an unequivocal YES. The rider to that answer is you have to take everything into consideration.
We have solar PV producing around 3600Kwh per annum, solar thermal HW (which was the first but we installed over 7 years ago), a Tesla Powerwall 2 and replaced our old oil boiler with an ASHP 6 months ago. Our electricity consumption is around 7500Kwh per year (that’s historical still waiting for the first full year of ASHP costs, but we previously ran an electric car for 6 years before deciding it really doesn’t work out here in rural Wales (few public charge points, won’t tow 2 tones of sheep trailer etc! and less expensive to use a but more diesel than run a second vehicle).
We still maintain our Octopus Go tariff (4.5p/unit for 4 hours overnight) and that effectively charges the powerwall (unless Tesla in their infinite wisdom decide it is going to be sunny tomorrow and rely of solar PV instead). This time shifting has a huge impact of the average price per unit - last year (prior to ASHP and the huge energy price rises we averaged about 7.5p per unit over the year. Taking into account the FIT (and allowing for the fact that we export less than 10% of the solar production) our nett energy cost for the year was practically zero - and that was all down to the battery.
This year, trying to work things out is more complex, with greater demand from the ASHP and huge tariff rises makes like for like tough.
With the ASHP working out more effective that anticipated ( we used an average of 20 odd Kwh per month between November and April but that has now fallen to just a few as we hit summer. The Solar thermal feeds into the 300L heat store so provides piping hot water most days meaning the ASHP doesn’t need to, and it is now effectively free energy, long since paid for after 7 years of RHI payments. Electric bills have soared so far, but the time shifting impact of the Powerwall is even more critical now. We had a problem with our solar inverter so lost almost 3 months of production in spring, but that is pushing out up to 25Kwh on a good day so most days we use no peak hours import from the grid. Just had my latest Octopus bill and daily power cost was down below £1 for a good proportion of days. Now you also have to look at the plus side arising from the switch - we have RHI payments amounting to over £1500 per annum, we no longer use oil for heating (previously about £1500 per annum, but on current rates it would have been £4500+ per annum to heat for the six winter months. That saving alone more than pays the electricity bill even with todays rates.
Now of course the elephant in the room is the capital cost of doing all this, but that isn’t always a simple decision. The oil boiler and system needed replacing, so that partly offset the ASHP capital cost and although the RHI payments will barely cover the rest the overall running cost of the system is distinctly lower and much more environmentally sound. The Powerwall 2, set against todays high tariffs looks set to pay for itself fairly quickly and in conversations with our installer they have a massive backlog of orders and a shortage of batteries, solar panels, inverters etc so good luck trying to get anything installed now, which kind of implies people generally think it is a good thing. On top of that the Powerwall/Gateway 2 provides emergency backup power (limited as it may be) in these days of recurrent power cuts.
Bottom line - look at the pluses and minuses, grants, FIT/RHI payments. Choose the right tariff to support time switching. Solar thermal seems to be a low cost way to generate heat for heating and hot water as long as your heat store is big enough. Get the biggest battery storage you can afford (we are seriously considering adding a second Powerwall battery pack if our installer can find one). Having a backup heating option (IMHO) is critical once you run everything from the electricity supply, but we have the log burners to handle that so I am comfortable that we are set fair for the winter to come. Looking forward to having a full years data to make better comparisons in about six months time.