A hybrid ANN-transfer function framework for multi-dimensional PV tilt angle optimization

• Complex variable framework improves PV system modelling methodology. • Hybrid multicriteria analysis identifies optimal solar panel orientations. • Transfer functions strengthen PV energy output prediction capabilities. • Mathematical modelling advances photovoltaic system efficiency analysis. • Verification approach confirms accuracy of complex PV performance algorithms. The manuscript focuses on the application of optimization techniques and decision-making processes in photovoltaic energy systems, supported by data analysis methods aimed at solving energy-related modelling problems. This study applies an integrated framework for the analysis, modelling, and evaluation of a photovoltaic system’s energy balance, combining transfer-function methods with neural networks with Monte Carlo simulation to optimise panel tilt, grid interaction, self-consumption, and economic payback. The work presents a mathematical model and a multi-step calculation algorithm for determining the optimum tilt angle of a photovoltaic system, with the tilt angle ranging from 0° to 90°. The model describes the system’s energy balance and enables its analytical identification under varying conditions. 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. A complex simulation procedure was carried out for a tilt angle of 25°, including statistical evaluation of the relationship between the parameters of the analytical model and those of the model defined in a complex variable domain, across different time periods. Statistical significance of the observed differences in key quantification indices was assessed. The results confirmed a high level of validity 93.9% of the original model and demonstrated the practical applicability of the proposed modelling procedure and verification method using complex variable. Furthermore, the framework integrates economic assessment, revealed that tilt angles around 25° provide the highest energy yield (5230 kWh/year) and best net present value (€14,707), whereas vertical panels reduce energy yield by up to 16.2%. The proposed framework therefore provides a rigorous technical basis and economic justification for optimised PV system design under Central European climatic conditions.