Uniform Conditions
One of the most significant reasons for a reduction in power from a PV module arises due to partial shading [49]. When cells do not receive uniform radiation, the electrical characteristics across the module vary creating a more complex P-V relationship. The configuration of these connected and partially shaded cells, as well as the number of connected cells has a large influence on the power produced under these conditions [24, 34]. As such, configurations could be designed to be able to operate optimally under PSC. The main sources of partial shading are passing clouds and shadow from nearby buildings, trees and telephone poles [24]. Due to the fluctuations in power that could arise as a result of partial shading, there is a financial implication for utilities [24]. As such, predictive models that can quantify the likely power to be available could be invaluable when accompanied by economic analysis to determine feasibility of a PV system before its implementation.
Some models are proposed in the literature to demonstrate the partial shading case [24, 49, 65–70]. Due to the complexity of modelling an individual cell these models are often formed by combining the characteristics of individual cells under different conditions according to how they are connected together. Being able to accurately model the performance and operation of PV systems under PSC is essential for developing and evaluating MPPT techniques under such conditions. As the size of installed PV systems increases and high efficiency operation becomes highly desirable, knowing how the PV system characteristics vary with a change in conditions and under non-uniform conditions is important.
A PSpice model has been developed to evaluate PSC and provide equations for the dual-peak case to predict the voltage and power of each peak [68]. Despite only providing equations to calculate the power and voltage at the MPPs in the case of two peaks on the P-V characteristic, the authors suggest that with some modifications the equations could be extended to deal with multiple MPPs. The DDM is used with parameters determined by curve-fitting to I-V characteristics at three different irradiance levels in this implementation. Validation of the equations for the dual-peak case is provided based on simulation and experimen- tal results.
In [34], a Labview tool is introduced to analyse the I-V and P-V characteristics under PSC. This paper uses terminology introduced in [24] to divide the system into sub-assemblies, series assemblies, groups and an array based on the shading characteristics. Two case studies are presented to demonstrate the performance [34]. The SDM is used to model each cell in a MATLAB model to study the PSC characteristics in [24].
A model in LTSpice is proposed in [65]. In this model, the effects of the bypass diode configuration and number of bypass diodes is explored. Additionally, the impact of a moving shadow across the PV system is investigated. Each cell has its own light generated current which is related to the area of the cell that is shaded and the transmittance of the shadow. The results support that under certain PSC, the configuration of the bypass diodes has a more significant impact on the performance than the number of bypass diodes.
An analytical model based on the SDM is presented in [71] to demonstrate how the characteristics appear when the modules have different orientations. This refers to the case where modules may be located on different surfaces of the same building and subsequently experience different irradiances.
MATLAB is used to model three series-connected cells using the SDM [66]. In this implementation a variety of shading conditions are applied to the system and the results are experimentally validated using Solkar 3712/0507 PV modules. M¨aki et. al. also propose a PSC model developed in MATLAB using the SDM and use their model to assess how system shading and shading strength affect
with a Raloss SR30-36 PV module in an indoor test environment.
Bishops PV cell model is presented as a MATLAB implementation in [69]. Bishops model incorporates an extra term in the SDM to model avalanche breakdown as it affects the shunt resistance term. In this model, cell tempera- ture is determined by using a thermal energy balance that considers the amount of solar power absorbed by the module, that lost by convection and radiation and the electrical power output of the module. Bishops model is also used in [70] to develop a PSC modelling strategy based on describing a system as being composed of strings, blocks and units. Each unit is defined by a series of flags indicating its electrical position and configuration and its physical position and properties. Each string is solved with the damped Newton method by considering the non-linear system of equations and Jacobian matrix. In the paper, the method is implemented using MATLAB, however, it could also be applied on other platforms. Solving for each string provides a solution for the string current, and these currents are combined to obtain the overall system current.
The SSDM is used in a C-language implementation with PSIM to model PSC in [67]. The interface is developed using C++ and allows the user to indicate the shading of the cells, in the module. The PSIM simulator models the module characteristics using a current source which is controlled by the output current of the series connected PV cells.
A MATLAB-based model which considers PSC and electrical mismatch at the cell level is presented in [62]. The Wisconsin 7-parameter SDM is applied in the analysis and 3D shading models are used to map shadows onto the array plane. The method is validated through comparison with the PV*SOL Expert system.
Piecewise linear branches are used to approximate the PV equivalent circuit in [73] and is implemented in Electro-magnetic Transient Program (EMTP). These simulation studies consider the shading percentage, number of shaded cells, bypass cell configuration and overall module configuration.