  Variability of the energy output throughout the day/night poses a major
hurdle to the widespread adoption of photovoltaic systems. An integrated
photovoltaic (PV) and electrochemical (EC)-storage system offers a solution,
but the thermodynamic efficiency ({\eta}_sys) of the integrated system and the
optimum configuration needed to realize the limit are known only for a few
simple cases, derived though complex numerical simulation. In this paper, we
show that a simple, conceptually-transparent, analytical formula can precisely
describe the {\eta}_sys of a 'generalized' PV-EC integrated system. An M-cell
module of N-junction bifacial tandem cells is illuminated under S-suns mounted
over ground of albedo R. There are K-EC cells in series, each defined by their
reaction potential, exchange current, and Tafel slope. We derive the optimum
thermodynamic limit of {\eta}_sys(N,M,K,R,S) for all possible combinations of a
PV-EC design. For a setup with optimal-(M,K) and large N, under 1-sun
illumination and albedo = 0, the ultimate limit for {\eta}_sys ~ 52%. The
analysis will unify the configuration-specific results published by diverse
groups worldwide and define the opportunities for further progress towards the
corresponding thermodynamic limit.
