Modelling and Output Power Evaluation of Series-Parallel Photovoltaic Modules

Abstract

Solar energy has received attention in the Middle East given the abundant and free irradiance and extended sunny weather. Although photovoltaic panels were introduced decades ago, they have recently become economical and gained traction. We present a mathematical model for series-parallel photovoltaic modules, evaluate the model, and present the I-V and P-V characteristic plots for various temperatures, irradiance, and diode ideality factors. The power performance results are then analyzed and recommendations are made. Unlike other related work, our evaluation uses standard spreadsheet software avoiding commercial simulation packages and application programming. Results indicate improved power performance with irradiance and parallel connections of cell series branches. Given the hot weather in our region, increasing the number of cells connected in series from 36 to 72 is not recommended. I. INTRODUCTION The push for renewable energy solutions is steady to reduce carbon emissions, protect the environment and population health, and effect climate and sea water level changes. Solar energy has received attention in the Middle East given the abundant and free irradiance and sunny weather. Although photovoltaic (PV) panels were introduced decades ago, they have recently become economical and gained traction. Saudi Arabia recently saw the successful installation of a 3.5 megawatt photovoltaic field, the largest solar power plant built in the country, and has plans to install 41 Gigawatts of solar power over the next 20 years. PV fields geographically distributed can be located near loads and cut down on fuel consumed by power generating plants. PV cells generate DC electricity during the day, which can be immediately consumed or stored in batteries for future consumption. An inverter is used to convert the generated power from DC to AC. The PV panel has a number of solar cells connected in series (typically 36 or 72) with the possibility to connect PV cell series branches in parallel. The solar cell is a p-n junction fabricated in a silicon (or other material) wafer or semiconductor layer. The photovoltaic effect causes the electromagnetic radiation of the solar energy hitting the PV cells to generate electricity. Photons with energy greater than the band gap energy of the wafer's semiconductor material are absorbed, creating electron-hole pairs, which in turn create a photocurrent in the presence of the p-n junction's internal electric field. The photocurrent's magnitude rises with the number of electron-hole pairs created, which is dependent on the irradiance level. Therefore the magnitude of the current generated by the PV module is proportional to the amount of incident solar radiation. PV module models have evolved to include detailed parameters and even multiple piecewise linear regions or better accuracy. However, most have focused on modeling a number of PV cells in series and stopped short of modeling multiple parallel branches of serially connected PV cells. In this paper, we present a mathematical model for series- parallel photovoltaic modules, evaluate the model, and present the I-V (module current vs. module voltage) and P-V (module power vs. voltage) characteristic plots for various temperatures, irradiance and diode ideality factors. The power performance results are then analyzed and recommendations are made. Unlike others' work, we model series-parallel PV cells with multiple parallel branches each consisting of a number of PV cells in series, and evaluate the model with a basic spreadsheet application, avoiding application programming and commercial simulators. This is facilitated by the mathematical technique (i.e. Newton-Raphson) used in the model evaluation which makes the model evaluation possible with a spreadsheet application. Thus, a key advantage of our approach is that our model can be reused by a larger population of researchers with no access to commercial simulator packages.