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It is difficult to determine the input parameters values for equivalent circuit models of photovoltaic modules through analytical methods. Thus, the previous researchers preferred to use numerical methods. Since, the numerical methods are time consuming and need long term time series data which is not available in most developing countries, an improved mathematical model was formulated by combination of analytical and numerical methods to overcome the limitations of existing methods. The values of required model input parameters were computed analytically. The expression for output current of photovoltaic module was determined explicitly by Lambert W function and voltage was determined numerically by Newton-Raphson method. Moreover, the algebraic equations were derived for the shape factor which involves the ideality factor and the series resistance of a single diode photovoltaic module power output model. The formulated model results were validated with rated power output of a photovoltaic module provided by manufacturers using local meteorological data, which gave ±2% error. It was found that the proposed model is more practical in terms of precise estimations of photovoltaic module power output for any required location and number of variables used.

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Abstract-The numerical solution of a computationally intensive model becomes more complex in terms of execution time required by a single processor. To speedup the computation, a suitable parallel computing architecture is required. This paper attempts to achieve a fast finite difference solution of electric potential in an EHD ion-drag micropump. A 2D Poisson's equation is solved on a cluster of low cost computers using MATLAB. Numerical solution is obtained for the different mesh refinements and then the execution time, communication time, speedup and efficiency of parallel system are analyzed. The results showed that the speedup and efficiency of the system increases by increasing the grid points. The results also reveal that for each data size there is an optimum number of workers for obtaining the parallel numerical solution in minimum processing time.

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