Modeling the Photovoltaic Power Generation in Poland in the Light of PEP2040: An Application of Multiple Regression

Abstract

This paper presents the results of research on the development of photovoltaic systems in Poland. The authors’ goal was to identify factors that can potentially shape the dynamics of solar energy development in Poland and that will affect the implementation of the PEP2040 goals. The authors also wanted to find a forecasting method that would enable the introduction of many explanatory variables—a set of identified factors—into the model. After an initial review of the literature, the ARMAX and MLR models were considered. Finally, taking into account MAPE errors, multiple regression was used for the analysis, the error of which was 0.87% (minimum 3% for the ARMAX model). The model was verified based on Doornik–Hansen, Breusch–Pagan, Dickey–Fuller tests, information criteria, and ex post errors. The model indicated that LCOE, CO2 emissions, Cu consumption, primary energy consumption, patents, GDP, and installed capacity should be considered statistically significant. The model also allowed us to determine the nature of the variables. Additionally, the authors wrote the WEKR 2.0 program, which allowed to determine the necessary amount of critical raw materials needed to build the planned PV energy generating capacity. Solar energy in Poland currently covers about 5% of the country’s electricity demand. The pace of development of photovoltaic installations has exceeded current expectations and forecasts included in the Polish Energy Policy until 2040 (PEP2040). The built model showed that if the explanatory variables introduced into the model continue to be subject to the same trends shaping them, a dynamic increase in photovoltaic energy production should be expected by 2025. The model indicates that the PEP2040 goal of increasing the installed capacity to 16 GW by 2040 can be achieved already in 2025, where the PV production volume could reach 8921 GWh. Models were also made taking into account individual critical raw materials such as Cu, Si, Ge, and Ga. Each of them showed statistical significance, which means that access to critical raw materials in the future will have a significant impact on the further development of photovoltaic installations.

Predictive Analytics-Based Methodology Supported by Wireless Monitoring for the Prognosis of Roller-Bearing Failure

“…This method is time-series-based and depends on the assumption that the series is stationary. Therefore, the first step of the process is to check whether the assumption is fulfilled using the Dickey-Fuller (DF) stationary test [56]. This test consists of proving the null hypothesis that there is a unit root in an AR model, which implies that the data series is not stationary.…”