Mathematical Models of Renewable Energy Sources developed at UPRM useful for Microgrid Analysis

Abstract

This paper intends to provide education in the renewable energy field presenting a summary of mathematical tools developed at the University of Puerto Rico-Mayaguez (UPRM) to characterize renewable energy sources such as fuel cells (FC), photovoltaics (PV), and thermoelectric generators (TEG). To generate these mathematical tools, fractional polynomial and second order polynomial equations, transcendental equations, among others were considered along with boundary conditions and the shape of operating curves. Some of the advantages of the presented models are: 1) suitable for applications in power and renewable energy, 2) emulate the shape of FC, PV or TEG curves, 3) replicate FC, PV or TEG realistic constraints, 4) useful for basic circuit analysis. These models have several educational advantages among of them are 1) help students understand the relevance of mathematical modeling in engineering and sciences, 2) help students acquire competencies for problem-solving, 3) have a better understanding of FC, PV, or TEG performance and 4) attract students to the renewable energy and mathematical modeling research field. Also, it is intended to give engineering students a tool for the characterization of renewable power sources in terms of voltage, current, inductance, and power that can be easily programmed onto Arithmetic Logic Units (ALU) and used for cyber-physical-systems or software like PSpice or Saber.