The performance of a photovoltaic module is significantly affected by the ambient conditions it is subjected to. For example, the electrical performance and the energy conversion efficiency of a module are directly affected by the module temperature. The temperature of a photovoltaic module changes with changing ambient conditions such as ambient temperature, irradiance, wind speed and wind direction, and the module temperature also depends on the thermal history of the module. Furthermore, non-uniform conditions, such as non-uniform illumination of a photovoltaic module, e.g. due to shadowing effects, strongly affect the electrical performance of a photovoltaic module.
In order to simulate and/or predict the energy production, e.g. the energy yield, of a photovoltaic module or system, a need exists for suitable simulation models that allow the calculation of energy losses within a module while taking optical, thermal and electrical aspects into account, as well as taking changing ambient conditions, e.g. non-steady-state ambient conditions, and non-uniform conditions into account.
Several mathematical and empirical thermal-electrical photovoltaic module models have been developed. These models mostly cover steady-state losses, and often the losses due to non-steady-state conditions and/or non-uniform illumination cannot be addressed by such methods, e.g. due to a limited time granularity and due to particular assumptions made, such as for example a uniform module temperature.
Field measurements and indoor wind tunnel experiments on photovoltaic systems show that there may exist significant inter-module and intra-module temperature differences, e.g. under typical operating conditions. Such temperature differences may for example be caused by spatial variations in forced convection and/or differences in illumination intensity, and may also be influenced by the module mounting method and location, and the electrical operation point of the cells or modules. In non-ideal site locations the module efficiency may be reduced by partial shading losses. Dynamic conditions caused by time-dependent effects, such as the effect of clouds or wind cooling effects, may also have an impact on the energy yield. Furthermore, local variations in illumination and/or temperature, e.g. comprising temporal and/or spatial variations, can cause mismatches between cells connected in series, which may be particularly detrimental for achieving a high yield efficiency.
In “Optical-Thermal-Electrical model for a single cell PV module in non-steady-state and non-uniform conditions build in SPICE”, Proceedings of the 28th EU PVSEC, 2013, page 3291, H. Goverde et al describe an optical-thermal-electrical model for a photovoltaic module that incorporates optical, thermal and electrical aspects and that is suitable for simulating non-steady-state conditions. The disclosed model relates to the simulation of a single cell module, i.e. for a module comprising a single photovoltaic cell. This model is built in SPICE, and is constructed by coupling two equivalent circuits, one circuit describing the electrical behaviour of the single cell module and the other circuit describing the thermal behaviour of the single cell module. Model parameters for the optical, thermal and electrical behaviour are determined from experimental data. However, as the model relates to a single cell module, intra-module differences and intra-module losses are not taken into account.
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