Researchers from Slovakia’s Slovak University of Agriculture in Nitra have developed a novel framework for optimizing PV tilt angles. It combines transfer-function methods with neural networks alongside Monte Carlo simulation to optimize panel tilt, grid interaction, self-consumption and economic payback.
The framework is presented in the research paper A hybrid ANN-transfer function framework for multi-dimensional PV tilt angle optimization, published in Energy Conversion and Management: X.
“The presented methodology is unique in its ability to verify a broad spectrum of analytical models across various physical parameters, thereby extending its relevance well beyond photovoltaic systems,” the group said. “The algorithm also facilitates reliable long-term prediction, distinguishing it from commercial models that offer only short-term forecasts and are not optimised for Central European climatic conditions.”
The framework for the optimization comprises 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 part collects real-time PV data, the pre-processing part standardizes and cleans the raw data. The modeling function then builds a regression model to describe the energy balance and the evaluation part calculates performance metrics. Finally, the adaptive control section optimizes the tilt settings.
“An extended modelling algorithm using Laplace transform was developed to validate the analytical model, with further verification carried out through the application of an artificial neural network (ANN),” the team added. “The ANN comprises one hidden layer with two neurons and ReLU activation functions without data normalisation to a standard probability distribution. The inputs were considered as data of energy balance on each day, segmented into months. The ANN model and Monte Carlo simulation were performed in Python 3.12.3.”
The novel framework was trained and tested with data from an experimental PV system located in Brno, southern Czechia. The system consists of two sections, one features 48 modules with a total output of 5 kWp that are installed on a tilt of 90◦, effectively serving as building integrated PV (BIPV) while the other section features 288 modules with a total output of 30 kWp placed at a tilt of 25◦. The total area of the PV system is 291.4 m2, while the orientation of the PV power plant is southwest 45◦.
For economic analysis, the study used time-of-use electricity pricing, feed-in tariff rates, battery degradation costs and system maintenance schedules. The time-of-use pricing was €0.24 ($0.28)/kWh at peak and €0.16/kWh at off-peak, while feed-in tariff rates were €0.08/kWh and battery degradation costs were €0.02/kWh cycled.
The results found high concordance during a comparative assessment of the regression and complex variable models. “The analytical model attained 93.9% accuracy in predicting the system’s energy balance, while neural-network-assisted complex-variable verification achieved a coefficient of determination of 94.38%,” according to the results. “Maximum congruence between approaches occurred at a panel tilt of 0◦, yielding an R2 of 0.979. Model robustness was further corroborated via comprehensive statistical analysis (R2 = 0.929) and Monte Carlo simulation.”
The results also found that increasing tilt from the baseline 25◦ to 45◦ and 90◦ reduces annual energy yield by 11.3% and 16.2%, respectively. That corresponds to a net present value reduction of €1,661 and €2,382, annual energy deficits of 591 kWh and 847 kWh and revenue losses of €106 and €153.
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