I've just been googling to find descriptions of a TPON network architecture, and everything (not BT specific) generally seems to put the remote electronics into an ONU that is placed in the home - effectively a variant of FTTP. These descriptions do include a passive splitter - which may be the small pillar, rather than the large cabinet.
However, I've come across a 2005 Analysys report for Ofcom, as part of their study into the "cost of the BT local loop network".
It has this to say about TPON:
There have been within BT a number of small trial scale deployments (of order 30,000
lines � approximately 0.1% of all BT lines) of TPON systems. Whilst these trials have
undoubtedly shown that such systems are feasible for either a fibre to the DP architecture
(in the past) or a fibre to the premises solution (in a more recent trial), they have not yet
demonstrated economic viability for the current service set. We understand that a new
build of TPON would use a similar duct layout to the existing network (i.e. a �tree�), and
that it would therefore face very similar costs to the existing network for duct and fibres.
Unfortunately for the economic case for TPON however, there is an additional significant
cost, the CPE (Optical Network Unit, ONU), currently costing several hundred pounds per
line: accordingly significant additional service revenues would be needed to make it
attractive compared to the existing architecture. It is therefore not a modern equivalent
asset we will consider further in this study.
That suggests the ONU has been tried in both the premises, and in a DP-like location.
It also has this to say on power backup:
We understand that the BT TPON deployments with fibre to the cabinet have of order 8hrs of battery backup
power.
Use of battery backup suggests mains power is needed in the first place.