Citation: Corti, F.; Laudani, A.; Lozito, G.M.; Palermo, M.; Quercio, M.; Pattini, F.; Rampino, S. Dynamic Analysis of a Supercapacitor DC-Link in Photovoltaic Conversion Applications. Energies 2023, 16, 5864. https://doi.org/10.3390/ en16165864 Academic Editor: Miguel Castilla Received: 15 July 2023 Revised: 30 July 2023 Accepted: 5 August 2023 Published: 8 August 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). energies Article Dynamic Analysis of a Supercapacitor DC-Link in Photovoltaic Conversion Applications Fabio Corti 1 , Antonino Laudani 2, * , Gabriele Maria Lozito 1,3 , Martina Palermo 2 , Michele Quercio 2 , Francesco Pattini 3 and Stefano Rampino 3 1 Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Firenze, 50139 Florence, Italy; fabio.corti@unifi.it (F.C.); gabrielemaria.lozito@unifi.it (G.M.L.) 2 Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Università degli Studi Roma Tre, 00146 Rome, Italy; martina.palermo@uniroma3.it (M.P.); michele.quercio@uniroma3.it (M.Q.) 3 Institute of Materials for Electronic and Magnetism-National Research Council (IMEM-CNR), delle Scienze 37/A, 43124 Parma, Italy; francesco.pattini@cnr.it (F.P.); stefano.rampino@cnr.it (S.R.) * Correspondence: antonino.laudani@uniroma3.it Abstract: In this work, a dynamic analysis describing the charge and discharge process of a superca- pacitor 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. Keywords: photovoltaics; Supercapacitors; DC–DC; dynamic systems; circuit simulation 1. Introduction The power conversion of PV sources for DC and AC applications is almost always re- quired to ensure that their strongly variable voltage and current are regulated in accordance with the electrical and electronic components for which the energy is generated [1–3]. This conversion makes use of DC–DC converters that, in general, adapt the voltage for the next stage of conversion (or the final load). This approach is also valid in the case of discrete PV + Storage hybrid systems, where the DC–DC converters are used for matching the out- put voltage of the solar cell with the charging voltage of the integrated storage device [4]. Since the PV source is a strongly non-linear device based on the photogeneration process [5], it is not only necessary to adapt the voltage to the load, but also to the source, to ensure that the operating point of the PV source is the one where the maximum power is delivered [6–9]. This process, commonly referred to as maximum power-point tracking (MPPT), introduces the necessity for a dedicated DC–DC converter, since a single converter does not have the degrees of freedom to adapt both input (for MPPT) and output (for correct load functioning) voltage. The two converters, usually connected in cascade, are interleaved with a storage element that has the purpose of stabilizing the voltage and decoupling the converter on the PV side from the converter on the load side. This stage is called the DC-link, and according to the applications, it can be implemented with batteries or capacitors. The former allows the DC-link stage to act as an energy-storage stage, which is particularly useful due to the intermittent nature of the PV source. However, a capacitor-based DC-link is much simpler, leaves less overall footprint, and is more durable [10–14]. The development of new technologies for high-capacity capacitors, known as Superca- pacitors (SC), introduced the possibility of achieving a degree of energy-storage capabilities Energies 2023, 16, 5864. https://doi.org/10.3390/en16165864 https://www.mdpi.com/journal/energies