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In this work, a dynamic analysis describing the charge and discharge process of a supercapacitor for the DC-link between a photovoltaic source and a constant power load is presented. The analysis results in a complete nonlinear and dynamic model that can be used for simulation and control for DC–DC converters, achieving fast recharge times and accurate steady-state voltages in the DC link to avoid overcharging the supercapacitor during low power absorption scenarios. The proposed approach includes parasitic elements for the supercapacitor and efficiency effects on the conversion stage, proposing equations useful for design and control. Stability is also discussed for the charge process of the supercapacitor. Validation of the analytical model is performed by comparison with LTSpice simulation, confirming a good agreement between theory and simulation.