  Present theories of irreversible energy losses and heat generation within
Li-ion cells are unsatisfactory because they are not compatible with energy
conservation. This work aims to provide a consistent theoretical treatment of
energy transport and losses in such devices. An energy conservation law is
derived from the Doyle-Fuller-Newman (DFN) model of a Li-ion cell using a
rigorous mathematical approach. The resulting law allows irreversible chemical
energy losses to be located to seven different regions of the cell, namely: (i)
the electrolyte, (ii) the anode particles, (iii) the cathode particles, (iv)
the solid parts of the anode (ohmic losses), (v) the solid parts of the cathode
(ohmic losses), (vi) the surfaces of the anode particles (polarisation losses),
and (vii) the surfaces of the cathode particles (polarisation losses).
Numerical solutions to the DFN model are used to validate the conservation law
in the cases of a drive cycle and constant current discharges, and to compare
the energy losses occurring in different locations. It is indicated how cell
design can be improved, for a specified set of operating conditions, by
comparing the magnitude of energy losses in the different regions of the cell.
