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The paper presents a mathematical model for a series architecture hybrid solar vehicle, based on previous versions. A quasi piecewise linear parameter varying (qPWLPV) model was built, both in continuous and in discrete time. The advantage of the new modeling approach lies in a better handling of nonlinearities and answering model related analytical questions. Controllability and stability of the switching system was studied. The model was tested throughout open loop simulations, it can further be used for developing control strategies for energy optimization.