Under the wide-band limit approximation for electrodes, this research proposes analytical time-dependent non-equilibrium Green's function (TD-NEGF) formulae to investigate dynamical functionalities of quasi-one-dimensional quantum devices, especially for (microwave) photon-assisted transports. Together with a multiscale approach by lumped element model, we also study the effects of transiently-transferring charges to reflect the non-conservation of charges in open quantum systems, and implement numerical calculations in hetero-junction systems composed of functional quantum devices and electrode-contacts (to the environment). The results show that (i) the current calculation by the analytical algorithms, versus those by conventional numerical integrals, presents superior numerical stability on a large-time scale, (ii) the correction of charge transfer effects can better clarify non-physical transport issues, e.g. the blocking of AC signaling under the assumption of conventional constant hamiltonian, (iii) the current in the long-time limit validly converges to the steady value obtained by standard time-independent density functional calculations, and (iv) the occurrence of the photon-assisted transport is well-identified.