electronics Article Dirt Loss Estimator for Photovoltaic Modules Using Model Predictive Control Ricardo R. Santos 1 , Edson A. Batista 1 , Moacyr A. G. de Brito 1, * and David D. D. Quinelato 2   Citation: Santos, R.R.; Batista, E.A.; Brito, M.A.G.d.; Quinelato, D.D.D. Dirt Loss Estimator for Photovoltaic Modules Using Model Predictive Control. Electronics 2021, 10, 1738. https://doi.org/10.3390/ electronics10141738 Academic Editors: Moad Kissai, Bruno Monsuez and Barys Shyrokau Received: 5 May 2021 Accepted: 25 May 2021 Published: 19 July 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 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/). 1 Graduate Program in Computer Science and Graduate Program in Electrical Engineering, Federal University of Mato Grosso do Sul—UFMS, Campo Grande 79070-900, Brazil; ricardo.santos@ufms.br (R.R.S.); edson.batista@ufms.br (E.A.B.) 2 Federal Institute of Mato Grosso do Sul—IFMS, Campo Grande 79100-510, Brazil; david.quinelato@ifms.edu.br * Correspondence: moacyr.brito@ufms.br Abstract: The central problem tackled in this article is the susceptibility of the solar modules to dirt that culminates in losses in energy generation or even physical damage. In this context, a solution is presented to enable the estimates of dirt losses in photovoltaic generation units. The proposed solution is based on the mathematical modeling of the solar cells and predictive modeling concepts. A device was designed and developed to acquire data from the photovoltaic unit; process them based on a predictive model, and send loss estimates in the generation unit to a web server to help in decision-making support. The results demonstrated the real applicability of the system to estimate losses due to dirt or electrical mismatches in photovoltaic plants. Keywords: estimates; photovoltaic system; predictive control 1. Introduction Photovoltaic conversion is the direct energy transformation from solar radiation into electrical energy through the photovoltaic effect. The electrical energy obtained can then be injected into the electrical grid by some power electronics converter, giving rise to the mini and micro photovoltaic generation systems. Since the enactment of the resolution of the National Electric Energy Agency (ANEEL), number 482/2012, which regulated the mini and microgeneration distributed systems in Brazil, the usage of photovoltaic solar energy has expanded, achieving thousands of new installations each year [1,2]. It is well-known that photovoltaic solar energy presents financial and ecological benefits associated with the strident reduction in costs for implementing generation systems. The photovoltaic technology has emerged as a trend in the electricity market, once it is a viable solution for the electricity supply by companies and customer. This fact is corroborated by international agencies, which predict that photovoltaic energy increases from 2% of the world energy matrix in 2018 to 25% in 2050 [3]. Despite the many benefits as a source for distributed generation, photovoltaic (PV) modules are sensitive to the accumulation of dust and residues on their surface, causing efficiency reduction common to all generation units. Dirt losses can vary from 2% to 25%, maintaining an average of 5%. The deposit of dirt on the modules’ surface has been a research subject in several aspects: qualitative, quantitative, and economic [4–11]. One study focuses on determining the appropriate time interval for cleaning modules, proposing a preventive solution; that is, clean the modules at pre-established intervals [8]. It turns out that the seasons of the year imply different climatic conditions, as rains, winds, and air humidity, which may require monthly or biannual cleaning, especially if it is considered the location and conditions of the generation unit installation. For instance, a module installed on a building tends to accumulate less dirt than another installed on the ground; in the same sense, summer rainfalls tend to keep the modules cleaner in this Electronics 2021, 10, 1738. https://doi.org/10.3390/electronics10141738 https://www.mdpi.com/journal/electronics