A Slovak research team has developed a mathematical model for determining the optimum tilting angle of a solar system ranging from 0 ° to 90 °. Their framework was tested for an experimental arrangement in the Czech Republic and achieved 93.9% accuracy in predicting the energy balance of the system.
Researchers from Slovakia Slovak University of Agriculture in Nitra have developed a new framework for optimizing PV tilting corners. It combines transfer function methods with neural networks in addition to Monte Carlo simulation to optimize panel-tilt, grid interaction, self-consumption and economic payback time.
The framework is presented in the research paper A hybrid Ann-Transfer function framework for multidimensional PV-Tilt angle optimizationPublished in Energy conversion and management: X.
“The methodology presented is unique in its ability to verify a wide spectrum of analytical models in various physical parameters, making relevance much further than photovoltaic systems,” the group said. “The algorithm also facilitates reliable long-term prediction and distinguishes it from commercial models that only offer short-term predictions and are not optimized for central European climatic conditions.”
The framework for optimization includes five interconnected modules: a data acquisition function, a pre-processing function, a modeling function, an evaluation function and an adaptive control function. While the data acquisition section collects, standardizes and cleanses the pre-processing section of real-time PV data. The modeling function then builds up a regression model to describe the energy balance and the evaluation resenting calculates performance tricks. Finally, the adaptive control section optimizes tilting settings.
“An extensive modeling algorithm using Laplace transformation was developed to validate the analytical model, with further verification carried out by applying an artificial neural network (Ann),” the team added. “The Ann consists of one hidden layer with two neurons and relu activation functions without data standardization to a standard probability distribution. The inputs were considered every day as data from energy balance, segmented in months. The Ann -Model and Monte Carlo simulation were performed in Python 3.12.3.”
The new framework was trained and tested with data from an experimental PV system in BRNO, Zuid -TSCHechia. The system consists of two sections, one has 48 modules with a total output of 5 kWp installed on a tilt of 90 °, which effectively serves as a building integrated PV (BIPV), while the other section has 288 modules with a total output of 30 kWp placed on a tilt of 25 °. The total surface area of the PV system is 291.4 m2, while the orientation of the PV energy plant southwest is 45 asks.
For economic analysis, the study used use of electricity prices for use, feed-in rates, battery afbra costs and system maintenance schedules. The prices for use time were € 0.24 ($ 0.28)/kWh on peak and € 0.16/kWh at off-peak, while the input rate rates were € 0.08/kWh and the relegation of the battery cycled € 0.02/kWh.
The results found high agreement during a comparative assessment of regression and complex variable models. “The analytical model achieved 93.9% accuracy when predicting the energy balance of the system, while neural network-assisted complex variable verification reached a determination coefficient of 94.38%,” according to the results. “Maximum congruence between approaches took place with a panel tilt of 0), which resulted in an R2 of 0.979. Model robustness was further confirmed via an extensive statistical analysis (R2 = 0.929) and Monte Carlo simulation.”
The results also showed that increasing tilt of the basic line 25 27 to 45 ° and 90 attract reduces the annual energy yield by 11.3% and 16.2% respectively. This corresponds to a net present value reduction of € 1,661 and € 2,382, annual energy shortages of 591 kWh and 847 kWh and sales losses of € 106 and € 153.
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