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High-temperature superconductors (HTS) exhibit hysteresis, which is the main cause for losses in the subcritical domain. This behavior is well predicted by Bean's critical-state model, which is a subset of the classical Preisach model. We present a parameterized Preisach model that describes the hysteresis of HTS specimens in self-field, where the parameters are identified from electrical lock-in (loss) measurements. That means the model can be used independent of geometry, number of filaments, and other physical measures as long as Bean's model applies. An advantage of the model is that it can predict outputs (flux, voltage) and losses for arbitrary input currents once the HTS has been characterized from measurements. We have further derived exact models for the hysteretic losses in strip and elliptic geometry strips, where the energy losses were calculated by Norris.