IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 22, NO. 6, NOVEMBER 2014 2141 Power Optimization for Photovoltaic Microconverters Using Multivariable Newton-Based Extremum Seeking Azad Ghaffari, Miroslav Krsti´ c, Fellow, IEEE , and Sridhar Seshagiri Abstract—Extremum seeking (ES) is a real-time optimization technique that has been applied to maximum power point tracking (MPPT) design for photovoltaic (PV) microconverter systems, where each PV module is coupled with its own dc/dc converter. Most of the existing MPPT designs are scalar, i.e., employ one MPPT loop around each converter, and all designs, whether scalar or mutivariable, are gradient based. The convergence rate of gradient-based designs depends on the Hessian, which in turn is dependent on environmental conditions, such as irradiance and temperature. Therefore, when applied to large PV arrays, the variability in environmental conditions and/or PV module degradation results in nonuniform transients in the convergence to the maximum power point (MPP). Using a multivariable gradient-based ES algorithm for the entire system instead of a scalar one for each PV module, while decreasing the sensitivity to the Hessian, does not eliminate this dependence. We present a recently developed Newton-based ES algorithm that simultaneously employs estimates of the gradient and Hessian in the peak power tracking. The convergence rate of such a design to the MPP is independent of the Hessian, with tunable transient performance that is independent of environmental conditions. We present simulation as well as the experimental results that show the effectiveness of the proposed algorithm in comparison with the existing scalar designs, and also to multivariable gradient- based ES. Index Terms— Dc/dc microconverters, maximum power point tracking (MPPT), Newton-based extremum seeking (ES), photovoltaic (PV) arrays. I. I NTRODUCTION M AXIMUM power point tracking (MPPT) algorithms for extracting the maximum achievable power from a photovoltaic (PV) system have been studied by several researchers [4], [15], [17]–[19], with detailed comparisons presented in [5], [11], and [12]. Several recent works [2], [3], [14], [16] have focused on the application of gradient-based extremum seeking (ES) [1] to MPPT design. To the best of our knowledge, there are a limited number of multivariable MPPT schemes described in the literature, Manuscript received June 3, 2013; revised October 4, 2013; accepted January 3, 2014. Manuscript received in final form January 15, 2014. Date of publication February 17, 2014; date of current version October 15, 2014. Recommended by Associate Editor M. Guay. A. Ghaffari and M. Krsti´ c are with the Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411 USA (e-mail: aghaffari@ucsd.edu; krstic@ucsd.edu). S. Seshagiri is with the Department of Electrical and Computer Engineering, San Diego State University, San Diego, CA 92182-1309 USA (e-mail: seshagir@engineering.sdsu.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCST.2014.2301172 among which we refer the reader to [15], [18], and [19]. Reference [19] uses a multivariable version of the popular Perturb and Observe (P&O) algorithm. Unlike scalar designs that require one current sensor for each module, the algorithm only requires a single current sensor on the dc bus. The operating point of the dc/dc converters is perturbed asynchro- nously, to minimize the possibility of converter interaction having a detrimental effect on the other modules. Closely related to [19] is the work in [18], where extra variables are employed in the classical P&O algorithm to overcome the limitation of scalar designs, which the authors say fail when the feasibility region is nonconvex. It is unclear how [18] compares with distributed architectures, with respect to power loss recovery in the case of module mismatch. Reference [15] uses particle swarm optimization (PSO), which is an algorithm that employs multiple agents to search for the peak power. This paper does not describe the specific criteria used to select the number of agents and parameters of the PSO, nor the conditions on the voltage and power boundary limits to stop the algorithm at maximum power point (MPP). In addition, in a PV system with a higher number of PV modules, the process of reinitialization and the tracking performance depend strongly on variable conditions, such as environmental factors, the nature of the PV modules, and the shading area. The authors claim that the required number of sensors is reduced to two, but to compute the pulse duration, the output voltage of each boost converter needs to be monitored by a separate sensor. The method also has an adaptation time of the order of 1–2 s. By contrast, the response time in ES-based designs is much smaller, of the order of 0.1 s. Expansion of the conventional P&O MPPT methods to the case of cascade PV modules with microconverters (one dc/dc converter for each module), as presented in [19], requires a step-by-step P&O, namely the core part of the algorithm is a scalar P&O, which finds the MPP of each PV module at a time. This results in a longer convergence time. Furthermore, coupling effects between modules that are exacerbated due to a partial shading and model mismatch cause nonuniform transient responses under different environmental conditions. This problem holds in the PSO method of [15]. Multivariable ES, unlike the other MPPT approaches, treats the entire cascade PV system as a whole and it simply fits every PV sys- tem architecture without any need to redesign the control loop. In [9] and [10], we presented a multivariable gradient-based ES MPPT design for the microconverter architecture, where 1063-6536 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.