Fractional derivative-based performance analysis of hybrid thermoelectric generator-concentrator photovoltaic system

Abstract Concentrator photovoltaic systems get the highest conversion efficiencies among all solar applications. However, they need to increase their efficiency even more to compete with traditional photovoltaic systems. The hybridization with thermoelectric generators allows recovering part of the waste heat and converting it to electricity, enhancing the global efficiency. The physical model of hybrid thermoelectric-concentrator photovoltaic module involves five non-linear equations. In this paper, two adapted Newton-Raphson methods using fractional derivatives are developed to solve such non-linear system, one using the conformable derivative operator and the other using the Riemann-Liouville fractional derivative. Both methods are mathematically innovative and are applied within the photovoltaic field for the first time. They can be used in energy prediction or in design optimisation. As an example of application, one month of real atmospheric data from Jaen, Southern Spain, were processed with the help of the developed methods. The performance outputs of the hybrid system were analysed giving interesting findings on their real behaviour, which is largely unknown nowadays. Linear functions dependent on direct normal irradiance can approximate the total generated power with 12.8 W/m2 root mean squared error and, the thermoelectric efficiency with 0.08 % error.