In recent decades, population growth and industrial evolution have led to a significant increase in the need to produce electricity. Photovoltaic energy has assumed a key role in responding to this need, mainly due to its low cost and reduced environmental impact. Therefore, predicting and controlling photovoltaic power is an indispensable task nowadays. This paper studies how photovoltaic power can be affected under non-uniform irradiance conditions, i.e., when the photovoltaic energy production system is under partial shading. Concretely, the effect of bypass diodes on the current-voltage characteristic curve, according to the shaded area, was studied and the power loss under partial shading was quantified. In addition, electrical characteristics and the temperature distribution in the photovoltaic module were analyzed. Furthermore, we propose a hill climbing neural network algorithm to precisely estimate the parameters of the single-diode and double-diode models under partial shading conditions and, consequently, predict the photovoltaic power output. Different shading scenarios in an outdoor photovoltaic system were created to experimentally study how partial shading of a photovoltaic module affects the current-voltage characteristic curve. Six shading patterns of a single cell were examined, as well as three shading patterns of cells located in one or more strings. The hill climbing neural network algorithm was experimentally validated with standard datasets and different shading scenarios. The results show that the hill climbing neural network algorithm can find highly accurate solutions with low computational cost and high reliability. The statistical analysis of the results demonstrates that the proposed approach has an excellent performance and can be a promising method in estimating the photovoltaic model parameters under partial shading conditions.