Ab initio quantum mechanics (QM) and classical molecular dynamics (MD) simulations are employed to model an electrolyte composed of a polyphosphazene (PP), lithium triflate (LiCF3SO3) and water. Structures and energetics are systematically studied by QM for binary complexes of Li+, CF3SO3-, and Li+CF3SO3- with water or PP fragments, and for ternary combinations of Li+CF3SO3-, PP fragments, and water. Li+ interacts most strongly with the backbone nitrogen of PP, somewhat more weakly (and comparably) with ether oxygens on PP side chains and with water oxygens. This indicates that Li+-N interactions should significantly affect migration of Li+ in PP polymer electrolytes. Calculated coordination patterns of Li+ with the poly(ethylene oxide) model (ethylene oxide)(6) [(EO)(6)] agree with experimental results in which Li+ is strongly coordinated with five oxygens in PEO. Binary aggregates of LiCF3SO3 and (EO)(6) are also examined. Both Li+ and LiCF3SO3 coordinate preferentially with neighboring N atoms and a methoxy oxygen near the PP backbone. Classical MD simulations qualitatively reproduce the results of QM calculations, and provide details about the Li+ distribution in a larger system. Results of the QM and classical MD calculations suggest a model for the microstructure of the polyelectrolyte.