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Modelling and simulation of automotive electrical power systems is indispensable. For the purpose of system-level large-signal transient studies and small-signal frequency-domain analysis, the very fast switching transients can be neglected resulting in computationally efficient average-value modelling. Although most existing/traditional models do not consider the machine and rectifier losses, the analytical derivation of average-value models for a wide range of operating conditions and taking the systems' losses into account is very challenging. This study extends the recently developed parametric approach and presents a new dynamic average modelling and accelerated characterisation of the most common type of automotive power systems including claw-pole alternator, rectifier and energy-storage subsystems. Such alternator/rectifier systems are particularly known to have significant losses and are difficult to represent using conventional models that are available in the literature. The new model takes into account the rectifier conduction losses as well as the rotational and core losses of the alternator, while avoiding laborious analytical derivations and crude approximations. The final model is verified against the experimental results and a detailed switch-level implementation of the system in time and frequency domains. Very significant computational gains and excellent accuracy of the new model are demonstrated.