Multivariable maximum power point tracking for photovoltaic micro-converters using extremum seeking Azad Ghaffari a,n , Sridhar Seshagiri b , Miroslav Krstić c a Joint Doctoral Program (Aerospace and Mechanical) Between San Diego State University and University of California, San Diego, La Jolla, CA 92093-0411, USA b Department of Electrical and Computer Engineering, San Diego State University, San Diego, CA 92182-1309, USA c Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA article info Article history: Received 5 November 2013 Accepted 23 November 2014 Keywords: Photovoltaic systems Maximum power point tracking Extremum seeking DC–DC micro-converters abstract It is well-known that distributed architectures such as micro-converters and micro-inverters for photovoltaic (PV) systems can recover between 10% and 30% of annual performance loss or more that is caused by partial shading and/or module mismatch. In this work, we present a novel multivariable gradient-based extremum-seeking (ES) design to extract maximum power from an arbitrary micro- converter configuration of PV modules, that includes cascade and parallel connections. Conventional maximum power point tracking (MPPT) schemes for micro-converters (where each PV module is coupled to its own DC/DC converter) employ a distributed control, with one peak seeking scheme per each PV module, thereby requiring one control loop and two sensors per module (one each for current and voltage). By contrast, the scheme that we present employs a single control loop with just two sensors, one for the overall array output current and the other one for the DC bus voltage. This multivariable design provides more flexibility in tuning the parameters of the controller, and also takes into account interactions between PV modules. The computational effort of our design is not higher than that of the conventional scheme, and simulation and experimental results show that our proposed design outperforms the conventional one. Thus, our proposed design offers two benefits: (i) the balance- of-system (BOS) cost reduction as a result of the lower number of sensors, and (ii) improved performance, both contributing towards reduced average cost/watt, and enhancing the economic viability of solar. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction Maximum power point tracking (MPPT) is a technique for maximizing the energy extracted from PV modules. Over the years, many MPPT methods have been developed and implemen- ted (Bratcu, Munteanu, Bacha, Picault, & Raison, 2011; Brunton, Rowley, Kulkarni, & Clarkson, 2010; Dhople, Ehlmann, Davoudi, & Chapman, 2010; Esram & Chapman, 2007; Hohm & Ropp, 2003; Jain & Agarwal, 2007; Kadri, Gaubert, & Champenois, 2011; Lei, Li, Chen, & Seem, 2010; Leyva et al., 2006; Miyatake, Veerachary, Toriumi, Fuji, & Ko, 2011; Moura & Chang, 2010; Pai, Chao, Ko, & Lee, 2011; Patel & Agarwal, 2009; Petrone, Spagnuolo, & Vitelli, 2011; Ramos-Paja, Spagnuolo, Petrone, Vitelli, & Bastidas, 2010). These methods vary in complexity, convergence speed, cost, range of effectiveness, implementation hardware, and popularity. Comprehensive comparative analyses of currently available tech- niques can be found in Esram and Chapman (2007), Hohm and Ropp (2003), and Jain and Agarwal (2007). Extremum-seeking (ES) is a non-model-based real-time opti- mization algorithm (Ariyur & Krstić, 2003; Krstić & Wang, 2000; Wang & Krstić, 2000; Wang, Yeung, & Krstić, 1999) for systems with unknown dynamics that has been applied to a wide range of technical applications, including MPPT in PV systems (Bratcu et al., 2011; Brunton et al., 2010; Lei et al., 2010; Leyva et al., 2006; Moura & Chang, 2010). It offers the advantages of fast convergence and guaranteed stability over a range of environmental conditions, and yet is simple to implement, and hence very cost effective in terms of processing/hardware requirements. With the exception of Bratcu et al. (2011), all existing work on ES applies the technique to PV systems whose cells receive the same irradiance level, i.e., have unimodal power characteristics. Recent works (for example, Dhople et al., 2010) concentrate on designing MPPT methods to track multiple peaks (non-unimodal power) under rapidly changing irradiance conditions, and the Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/conengprac Control Engineering Practice http://dx.doi.org/10.1016/j.conengprac.2014.11.007 0967-0661/& 2014 Elsevier Ltd. All rights reserved. n Corresponding author: Tel: þ1 734 763 2227; fax: þ1 734 647 3170. E-mail addresses: aghaffari@ucsd.edu (A. Ghaffari), seshagir@engineering.sdsu.edu (S. Seshagiri), krstic@ucsd.edu (M. Krstić). Control Engineering Practice 35 (2015) 83–91