  We analyze theoretically the properties of the recently introduced and
experimentally demonstrated converter of frequency to power. The system is
composed of a hybrid single-electron box with normal island and superconducting
lead, and the detector of the energy flow using a thermometer on a normal metal
bolometer. Here we consider its potential for metrology. The errors in power
arise mainly from inaccuracy of injecting electrons at the precise energy equal
to the energy gap of the superconductor. We calculate the main systematic error
in form of the excess average energy of the injected electrons and its
cumulants, and due to sub-gap leakage. We demonstrate by analytic and numerical
calculations that the systematic error in detection can, in principle, be made
much smaller than the injection errors, which also, with proper choice of
system parameters, can be very small, < 1 %, at low enough temperature. Finally
we propose a simplified configuration for metrological purposes.
