  We develop an analytic model to quantitatively describe the evolution of
superconducting cosmic string networks. Specifically, we extend the
velocity-dependent one-scale (VOS) model to incorporate arbitrary currents and
charges on cosmic string worldsheets under two main assumptions, the validity
of which we also discuss. We derive equations that describe the string network
evolution in terms of four macroscopic parameters: the mean string separation
(or alternatively the string correlation length) and the root mean square (RMS)
velocity which are the cornerstones of the VOS model, together with parameters
describing the averaged timelike and spacelike current contributions. We show
that our extended description reproduces the particular cases of wiggly and
chiral cosmic strings, previously studied in the literature. This VOS model
enables investigation of the evolution and possible observational signatures of
superconducting cosmic string networks for more general equations of state, and
these opportunities will be exploited in a companion paper.
