The non-coherent rate equation approach to the electrical transport in a serial quantum dot system is presented. The charge density in each quantum dot is obtained using the transfer Hamiltonian formalism for the current expressions. The interactions between the quantum dots and between the quantum dots and the electrodes are introduced by transition rates and capacitive couplings. Within this framework analytical expressions for the current and the charge in each quantum dot are presented. The effects of the local potential are computed within the self-consistent field regime. Despite the simplicity of the model, well-known effects are satisfactorily explained and reproduced. We also show how this approach can be extended into a more general case.