Mathematical Model for Inverter Power Output in PV Parks

Sammanfattning: Solar photovoltaic (PV) parks have proliferated all over the world as a result of the growing demand for electricity, and especially electricity from renewables. As these parks become larger and complex, it becomes increasingly important to develop accurate and efficient mathematical models that can be used to predict their performance and optimize their design. The inverter is an essential component of a solar PV system that converts the DC power generated by the solar panels into AC power that can be used by the grid or by local loads. This research paper presents a comparative study between a pre-existing reference model and a mathematical model, developed specifically for predicting the AC power output of photovoltaic systems. In addition, a hybrid model is included for comparative analysis. The performance of each model was evaluated using real-world data installed at Glava Energy Centre in Hillringsberg, Sweden. The reference and hybrid models showed similar trends in their calculated versus actual values, but the hybrid model outperformed the reference model slightly. The actual power values were found to be similar to the simulated values in all three models. However, the mathematical model was more specific and sensitive to the inverter under consideration, resulting in a comprehensive and accurate representation of the inverter's behaviour. The models take into account the inverter's characteristics, as well as environmental elements like temperature and solar irradiance that affect its performance. The results showed that the mathematical model outperformed the other models in terms of accuracy and reliability, achieving an R2 score of 0.9226, 0.9936, 0.9789, and 0.9736 for the months of February, April, July, and October, respectively. The mathematical model also had the lowest root mean square error (RMSE) and mean absolute error (MAE) values compared to the other models. The results of this study demonstrate the value of mathematical modelling in the design and optimization of solar PV parks and provide a framework for the development of more complex models in the future.