We investigate well-accepted formulations describing charge transport in composite cathodes of batteries. Our upscaling of carefully selected microscopic equations shows three main features: (i) a novel set of six equations equipped with nine effective parameters which systematically couple the microscale to the macroscale; (ii) the coupling of transport and flow equations allows to account for three scales: pore scale, Darcy scale, and macroscale; (iii) the upscaled equations take phase separation during Li-intercalation into account as well as specific particle configurations. The wide range of applications and interest in energy storage devices make these results a promising tool to study the influence of the microstructure on current-voltage characteristics and to optimize cathode designs.