International Journal of Photoenergy

Volume 2015, Article ID 824832, 10 pages

http://dx.doi.org/10.1155/2015/824832

## Accurate Maximum Power Tracking in Photovoltaic Systems Affected by Partial Shading

Department of Electrical Engineering and Information Technology (DIETI), University of Naples Federico II, Via Claudio 21, 80125 Naples, Italy

Received 28 November 2014; Accepted 19 January 2015

Academic Editor: Ying Dai

Copyright © 2015 Pierluigi Guerriero et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A maximum power tracking algorithm exploiting operating point information gained on individual solar panels is presented. The proposed algorithm recognizes the presence of multiple local maxima in the power voltage curve of a shaded solar field and evaluates the coordinated of the absolute maximum. The effectiveness of the proposed approach is evidenced by means of circuit level simulation and experimental results. Experiments evidenced that, in comparison with a standard perturb and observe algorithm, we achieve faster convergence in normal operating conditions (when the solar field is uniformly illuminated) and we accurately locate the absolute maximum power point in partial shading conditions, thus avoiding the convergence on local maxima.

#### 1. Introduction

In the last few years photovoltaic (PV) installations have become familiar in the landscape of our countries. Their diffusion was initially encouraged by even aggressive, apparently uneconomical, feed-in tariffs; nevertheless the merit of those policies is now fully appreciable and consists in the impressive prices fall for all components of a PV plant, so much so that less than 2 €/Wp are now required as total investment. According to [1] such low prices led the cost of PV energy to be comparable with conventional energy sources and facilitated self-sustainment of the PV market. However, some limiting factors, which are inherently embedded in the PV technology, still persist. One of them is the large dependence on shadows, as they cause dramatic degradation of energy production. This issue prevents PV diffusion in the urban context where neighbor buildings can likely affect daily irradiance actually available on rooftop sites. The effect of shadowing is the deformation of the power-voltage curve exhibited by affected subfield. As will be shown in the next sections, indeed, the power-voltage (*P-V*) curve of locally shaded strings (with the term string we indicate a group of series connected solar panels) is characterized by the presence of multiple local maxima; the consequence is that maximum power point tracking (MPPT) algorithms often stabilizes the PV system at an output power that is lower than the maximum achievable. This problem can be completely avoided by adopting distributed conversion schemes exploiting either microinverter [2–4] or solar panel optimizers [5–8]. Both of them lead each solar panel working at its own MPP; the drawback is that a complex power electronic circuit is brought on board solar panels, thus inducing a not negligible fault probability. As an alternative some centralized inverters allow a periodic scanning of the whole power-voltage curve which univocally individuates the absolute maximum on the curve; in this case a trade-off exists between the scan frequency and energy production because each time a scan is performed the system is driven far from the MPP; thus, when the string is uniformly irradiated the scan is definitively detrimental [9].

In this paper an approach that first identifies all maxima present in the power voltage curve and then drives the operating point of the solar system to the absolute maximum is described.

The procedure is based on the availability of a distributed sensor network devised to the measurement of the actual short circuit current () and open circuit voltage () for each panel forming the solar field. The algorithm for the tracking of the absolute maximum is based on the* information* achieved by the sensors; thus it is hereafter denoted as information based MPPT. The sensors allow on demand disconnection and by passing of solar panels from the string; electrical parameters are measured during the disconnection time (few milliseconds); thus they are not affected by the operating point of others solar panels belonging to the same string.

The paper is organized as follows. Section 2 reports the analytical model of the proposed approach. In Section 3 the distributed sensor network providing individual panels data is presented. In Section 4 numerical simulation results evidencing the effectiveness of the information based MPPT algorithm are reported. Section 5 shows experimental result concerning the comparison between the proposed approach and the behavior of a standard algorithm. Conclusions are drawn in Section 6.

#### 2. First-Order Algorithm

The idea underlying the proposed MPPT algorithm assumes that it is possible to reconstruct an approximate version of the actual current-voltage (*I-V*) curve of a partially shaded string, formed by series connected solar panels, once the couple and is known for each panel. The algorithm estimates the voltage corresponding to the absolute maximum power point () and set this value as starting point for a standard perturb and observe (P&O) tracking procedure [10–13]. Reconstruction of the string* I-V* curve is performed by superposing a simplified form of the single panels* I-V* curves which are approximated by trapezoidal shapes. Namely, once both and of a given panel are known, the coordinates of the maximum power point are calculated according to the following relations:
where the coefficients and are taken from panel datasheets. Then the trapezoidal* I-V* curve of the solar panel is drawn as shown in Figure 1, where the actual* I-V* curve is also reported for comparison. It is worth noting that a critical point of this procedure is the strong temperature dependence of aforementioned coefficients; this implies that the working temperature of each solar panel is needed; actually and depend (weakly) on the irradiance as well. Both issues will be discussed in detail shortly.