I recently decided to look at the business case for batteries and this led me to developing a crude tarrif model which is possibly of more general use.  In case its of any use to others I attach it.

I have modelled tariffs stand alone, with a 9.5kWh battery and a 19kWh battery, for which local prices (fitted) are currently 5K and 7K respectively

The meat of it is to allocate the % consumption for each load type to the various timed tarrifs.  This is a bit of an informed guess in some instances so you should substitute your own numbers.  Where I am modelling with a 19kWh battery it is much less of a guess, as such a battery is large enough to cover a whole day (except car charging) for almost all of the year.  

Toi an extent the conclusions really depend on the assumptions you make about when you operate the high-draw items (which is adjustable in the spreadsheet).  In all my modelling I assumed that no account is taken of the tarrif when deciding to operate equipment, with the exception of car charging where I make more generous assumptions.  I did this because it is the 'lazy' option which I fear many, including me, will default to, and also because it paints batteries in a 'good' light (my initial motivation for the exercise was to prove, or otherwise, that batteries don't make financial sense, so by painting them in a 'good' light any conclusion that they don't make financial sense is relatively robust).  Cosy also might have an un-modelled advantage in the shoulder season when perhaps your heat pump struggles not to cycle.  In this case operating the heat pump only during the cheap periods will likely reduce the electricity cost without materially compromising efficiency (because the heat pump was destined to cycle anyway).  Interestingly Cosy Mk2 (with the three low price periods) is now entering its first winter.

With any ToU tarrif, and a sufficiently capable heat pump controller, there is the opportunity to 'pre-load' the house, warming it up above the desired temperature before a high tarrif period kicks in.  Thats exactly what homely and the like do.  Cosy may be better suited to this than Go because the cheap periods are better distributed, but I didn't build this into my modelling.  TBH I think Agile is even better suited to this behaviour than cosy because there is much more low price time even better distributed still.  Although there is some uncertainty when the low price time will occur, in practice its pretty predictable.  Of course Homely and the like have the advantage of looking ahead a day so they know what the future price and temperature is, and thus can be more intelligent about this optimisation than any timed controller can.

The percentages of each load class assigned to the different prices within any one tarrif are adjustable, so if anyone wants to make radically different assumptions to see how it changes the picture they can.  Even if you dont intend to buy a battery its quite interesting to look at the 19kW battery column where I essentially assume all, or nearly all, the electricity is at the lowest price.  The trick would be to achieve this, or something close, without the upfront cost of a battery.  With Agile, intelligent control and a house with a reasonably high heat capacity I reckon that may be close to do-able for the heat pump which is the dominant load.  Homely, Havenwise, Adia, PassivUK (the four I know of, there may be more) are, I think, targeting more or less exactly that.  In time I imagine energy suppliers will offer remote heat pump control with some sort of guarantee on minimum and maximum house temperature, so they can load balance.  The technology that Havenwise is developing is particularly well suited to this case, as it doesn't require any hardware, just an internet connection.

My conclusion (which apply for me only)

• Dont bother with a battery, it doesn't pay, or doesn't pay by much (I might change my mind with the 'don't bother' bit if there is solid evidence of environmental benefit). 
• If I were to trust Ovo, the Ovo heat pump tarrif is the winner
• Otherwise get Agile or Intelligent Go or Cosy and just be faintly sensible about use during the peak charging periods, without busting a gut.  definitely dont stick with fixed price
• Agile with a bit of intelligent manipulation of the heat pump to use the house as an energy score (as in what Homely, Havenwise, Adi and Passiv purport to do) looks like its well worth exploring and probably the best bet in the short to medium term

(There is also a plot of (UK) carbon intensity vs (Eastern England) Agile pricing, showing v poor correlation.  I need to do this again with East of England carbon intensity which might show better correlation, so at the the current time its a case absence of evidence for correlation carbon intensity<->pricing, which is evidence of absence.)

Criticism (preferably constructive) welcome.