Determination of Optimal Tilt and Orientation Angles for Fixed Photovoltaic Systems Using a Three-Dimensional Vector Analysis of Direct Normal Irradiance in Equatorial Regions

Efficient utilization of solar energy in equatorial regions depends on accurately determining the optimal tilt and azimuth angles of fixed photovoltaic (PV) systems. This study presents a three-dimensional vector-based methodology that employs Direct Normal Irradiance (DNI) to estimate the mean direction of incident solar flux. Hourly DNI data from 2020–2024 for the city of Guayaquil, Ecuador, were transformed into spatial vectors and integrated to obtain a resultant vector representing the average orientation and elevation of direct solar radiation. The analysis yielded an optimal tilt angle of 5.73° and an azimuth of 59.15°, values consistent with Guayaquil’s equatorial latitude and previous studies conducted in tropical environments. The low tilt angle reflects the persistently high solar elevation typical of equatorial zones, while the slight northeastward orientation deviation corresponds to the asymmetric diurnal distribution of solar irradiance. The main contribution of this work lies in providing a geometrically rigorous and computationally efficient approach capable of synthesizing the directional behavior of solar flux without relying on complex transposition models. The proposed method enhances the optimization of PV system design, urban energy planning, and renewable microgrid modeling in data-scarce contexts, supporting the sustainable development of solar energy in equatorial regions.