EFFECTS OF THE SHARPNESS OF SHADOWS ON THE MISMATCH LOSSES OF PV GENERATORS UNDER PARTIAL SHADING CONDITIONS CAUSED BY MOVING CLOUDS Kari Lappalainen, Anssi Mäki and Seppo Valkealahti Tampere University of Technology, Department of Electrical Engineering P.O. Box 692, FI-33101 Tampere, Finland kari.lappalainen@tut.fi, phone: +358401981511 anssi.maki@tut.fi, phone: +358401981513 seppo.valkealahti@tut.fi, phone: +358408490915 ABSTRACT: Photovoltaic (PV) generators are composed of series- and parallel-connected PV modules. PV generators can be exposed to mismatch power losses when operating under nonhomogeneous conditions, such as partial shading due to moving clouds. In this paper, the effects of the sharpness of shadows on the mismatch losses of PV generators are studied under partial shading conditions caused by moving clouds. The effects are studied with three different movement directions of shadows: parallel, perpendicular and diagonal to the strings of PV generator arrays. The studied configurations of PV generators are series-parallel (SP), total-cross-tied (TCT) and multi-string (MS). The sharpness of a shadow is modelled by the width of the transition region on the edge of the shadow where the irradiance decreases from the clear sky to the fully shaded value. The work has been conducted by using an experimentally verified MATLAB Simulink model of a PV module based on the well-known one-diode model of a PV cell. The simulations show that the sharpness of shadows has a substantial effect on the amount of mismatch losses. Mismatch losses were also found to be very sensitive to the direction of the movement of shadows, the array size and the configuration of the generator. Keywords: Mismatch Losses, Shading, PV System 1 INTRODUCTION An interest towards sustainable energy sources, renewable energy technologies and energy efficient solutions has risen because of general concern about the climate change and the limited reserves of fossil fuels. Solar energy is one of the most promising ways to combat the climate change and secure the energy production. Photovoltaic (PV) generators are composed of series- and parallel-connected PV modules which consist of series-connected PV cells. PV modules are connected in series in order to increase the voltage level of a PV generator. In grid-connected applications, high voltage levels are needed for interfacing equipment used for connecting PV generators to the utility grid. If a series connection of PV cells with the identical characteristics is partially shaded, the cell that receives the lowest irradiance level limits the total current of the series connection. When the current of the series connection is larger than the short-circuit current of that cell, part of the power produced by other cells is dissipated as heat in that cell, which can lead to the damaging of the cell. This phenomenon, called the hot- spot heating, is usually avoided by using anti-parallel- connected bypass diodes. Although more power can be extracted from a series connection of PV cells under partial shading due to bypass diodes there can be still problems. For example, multiple maximum power points (MPP) can take place in the characteristics of the series connection. That makes the tracking of the global MPP more complicated. Partial shading has actually several harmful effects on the operation of PV generators and a series connection of modules is more prone to these effects than a parallel connection [1]. Partial shading means conditions under which cells or modules of a PV array are exposed to different irradiances due to shading. Partial shading can be due to, inter alia, passing clouds, surrounding objects or soiling. One of the major effects of partial shading is the occurrence of mismatch losses, which are the difference between the sum of the available maximum power outputs of individual modules and the maximum power output of the PV generator. Mismatch losses can also occur for other reasons such as manufacturing tolerances and unequal operating temperature. In practice, some mismatch losses occur always and the actual power of a PV generator is lower than the rated power. The effects of partial shading have been studied in several papers, e.g. in [1]-[11]. In many of these papers the focus is on the modelling of the operation of PV generators under static partial shading conditions. In [12], [13] some studies on the effects of partial shading caused by moving clouds have been presented. In these papers, it has been found that the operating conditions determine the most efficient configurations and that shadows moving parallel to the strings of the array have more harmful effect on the operation of the generator than shadows moving perpendicular to the strings. However, the effects of the characteristics of moving clouds on the mismatch losses of PV generators under partial shading conditions caused by the moving clouds have not been studied extensively. The general characteristics of moving clouds have been studied in several papers. Also fast changes in the irradiance level caused by moving clouds have been studied e.g. in [14], [15]. Contrary to intuition, it can also occur that solar irradiance peaks up to 1.5 times the clear- sky irradiance, called cloud enhancement, during partially shaded conditions [16]. However, the effect of cloud enhancement is not included in this study. In this paper, the effects of the sharpness of shadows on the mismatch losses of PV generators with different configurations are investigated under partial shading conditions caused by moving clouds by assuming that the irradiance transition on the edge of a shadow is linear. The studied directions of the movement of shadows caused by clouds are parallel, perpendicular and diagonal to the strings of PV arrays. The studied configurations of PV generators are series-parallel (SP), total-cross-tied