mathematics Article A Fast Converging Hybrid MPPT Algorithm Based on ABC and P&O Techniques for a Partially Shaded PV System Carlos Restrepo 1,† , Nicolas Yan˜ ez-Monsalvez 1,† , Catalina González-Castaño 2, * ,† , Samir Kouro 3,† and Jose Rodriguez 2,†   Citation: Restrepo, C.; Yan˜ ez-Monsalvez, N.; González-Castaño, C.; Kouro, S.; Rodriguez, J. A Fast Converging Hybrid MPPT Algorithm Based on ABC and P&O Techniques for a Partially Shaded PV System. Mathematics 2021, 9, 2228. https:// doi.org/10.3390/math9182228 Academic Editor: Pedro Beirão Received: 11 August 2021 Accepted: 4 September 2021 Published: 10 September 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 Department of Electromechanics and Energy Conversion, Universidad de Talca, Curicó 3340000, Chile; crestrepo@utalca.cl (C.R.); nyanez16@alumnos.utalca.cl (N.Y.-M.) 2 Department of Engineering Sciences, Universidad Andres Bello, Santiago 7500971, Chile; jose.rodriguez@unab.cl 3 Electronics Engineering Department, Universidad Técnica Federico Santa María, Valparaíso 2390123, Chile; samir.kouro@usm.cl * Correspondence: inv.cet@unab.cl † These authors contributed equally to this work. Abstract: Among all the conventional maximum power point tracking (MPPT) techniques for a photovoltaic (PV) system that have been proposed, incremental conductance (INC) and perturb and observe (P&O) are the most popular because of their simplicity and ease of implementation. However, under partial shading conditions (PSCs), these MPPT algorithms fail to track the global maximum power point (GMPP) and instead converge into local maximum power points (LMPPs), resulting in considerable PV power loss. This paper presents a new hybrid MPPT technique combining the artificial bee colony (ABC) and P&O algorithms named ABC-P&O. The P&O technique is used to track the MPP under uniform irradiance, and only during irradiance variations is the ABC algorithm employed. The effectiveness of the proposed hybrid algorithm at tracking the GMPP, under both uniform and nonuniform irradiance conditions, was assessed by hardware-in-the-loop (HIL) tests employed by a dc–dc boost converter. Then, the ABC-P&O strategy was applied to obtain the voltage reference for the outer PI control loop, which provided the current reference to the discrete-time sliding-mode current control. The ABC-P&O algorithm has a reasonable computational cost, allowing the use of a commercial, low-priced digital signal controller (DSC) with outer voltage and inner current control loops. Many challenging tests validated that the proposed ABC-P&O technique converges fast to the GMPP with high efficiency and superior performance under different PSCs. Keywords: maximum power point tracking; photovoltaic system; artificial bee colony; hardware-in- the-loop testing; partial shading conditions 1. Introduction Photovoltaic (PV) energy is a promising alternative among the renewable sources that offers several advantages, including clean energy generation, using a renewable/essentially permanent energy source that is freely available, and low maintenance and operational costs. However, the low efficiency of PV systems, often due to their nonlinear electricity generation and variable atmospheric conditions, remains a significant challenge. Therefore, to overcome this drawback, a PV system needs to operate at its maximum power point (MPP) regardless of local atmospheric conditions, such as moving clouds, dust, neighboring buildings, and trees [1]. Numerous different maximum power point tracking (MPPT) techniques have been proposed in the literature over the decades [2–62] (see Figure 1), and fascinating recent review articles about them have been published [1,63–68]. These MPPT techniques can operate around the global maximum power point (GMPP) under normal solar irradiance conditions. However, few can operate during partial shading conditions (PSCs) due to Mathematics 2021, 9, 2228. https://doi.org/10.3390/math9182228 https://www.mdpi.com/journal/mathematics