Calculating the Energy Produced by Solar PV Modules: A New Mathematical Model

Abstract

Values for the input parameters of comparable circuit models of solar modules are notoriously difficult to calculate analytically. 
Consequently, prior researchers favoured using numerical approaches. An enhanced mathematical model was created by combining 
analytical and numerical approaches to address the limits of previous methods; this was necessary since numerical methods are time- 
consuming and need long-term time series data that is unavailable in most developing nations. Input parameters for the model were 
determined analytically. The Lambert W function provided an explicit expression for the photovoltaic module's output current, while the 
Newton-Raphson approach provided a numerical value for the module's voltage. In addition, an algebraic model for the power output of 
a single-diode photovoltaic module was developed, including the form factor, which incorporates the idealist factor and the series 
resistance. Using local meteorological data, the results of the created model were compared with the rated power output of a solar 
module given by manufacturers, yielding an inaccuracy of less than 2%. The suggested model was shown to be more applicable in terms 
of accurate predictions of photovoltaic module power output for any given location and set of input variables.