Principle Study And Technique Application Of Explicit Solution For Solar Cell I-V Equation

Since the photovoltaic effect was found by the French physicist A. E. Becquerel in 1839, the solar cell I-V equation derived from the solid state physics has been to the foundation in solar cell output characteristics research. But this equation is an implicit transcendental equation, and may not be solved explicitly in general for I or V using common elementary functions. Therefore, when applied to solve some practical problems, various approximate methods are often used to avoid the iterative process of calculation and the cumbersome process of deviation.As the explicit solution of solar cell I-V equation can not be given by elementary function, the transcendental function Lambert W function is applied to the solar cell I-V equation to express the explicit solution of current and voltage in the second chapter. After calculating characteristic points and plotting I-V curves of seven different types of solar cells and solar modules using explicit solution of solar cell I-V equation, respectively, the accuracy and validation of this expression are proofed.Next, based on the explicit expression of solar cell current and voltage, simple solutions for several key issues in practical engineering are presented:Solving the optimum load resistance. The derivations of optimum load resistance made by predecessor are based on the implicit expression of solar cell I-V equation, which leads to a cumbersome derivation process and a need for special math skills. Moreover, their optimum load expressions contain the maximum power current and voltage, and are not able to be used to calculate the value of optimum load resistance directly from the model parameters. But based on the explicit solution of solar cell current and voltage, the expression of optimum load resistance can be derived only using the definition of optimum load in the third chapter. And this expression of optimum load resistance can be used to calculate value of optimum load resistance directly from model parameters. This expression of optimum load resistance not only clearly indicates the property of solar cell as neither current source nor voltage source, but also can be used to study how the model parameters effect on the optimum load resistance.Predicting the module performance. The solar module manufacturers provide only an I-V curve under the standard test condition, but the module actually does not work at the standard testing condition. Thus, the prediction of solar module output characteristics under various working conditions is very necessary. A method can accurately predict the module output characteristics under different working conditions which only needs a measured I-V curve under standard testing conditions is present in the fourth chapter. This method, firstly, extracts the solar module model parameters using an I-V curve under standard testing conditions. Secondly, together with the relationships of model parameters varying with illumination intensity and cell temperature, the prediction of solar module output characteristics under different work condition is made. At last, some significant phenomena of solar module output characteristics under the extreme working conditions are discussed.Analyzing the connected module. When analyzing the characteristics of connected solar module, series connected module need study voltage separately and parallel connected module need study current separately. But the implicit I-V equation expression can not be used to study current and voltage separately, which make the analysis for characteristics of series and parallel connected module difficult. But the explicit expressions of current and voltage which based on the Lambert W function make analyzing current and voltage separately possible. In the fifth chapter, based on the explicit solution of solar cell I-V equation, the criterion of connecting module, the working state of module connected in array, and the effect of model parameters on mismatch loss are discussed. Finally, the output characteristics of photovoltaic array with bypass diodes and block diodes under non-uniform illumination are also studied.