The next stage of scientific development in the application of mathematical models has been the consideration of variable parameters of PV installations. The main application concerns the design of hybrid energy systems and off-grid installations, taking into account different parameters. An interesting concept of an off-grid installation designed taking into account results from a neural network model is presented in [PERSON]'s paper [27]. In the study, baseline mathematical variables were defined, namely the electrical load profile, solar radiation, air temperature, and wind speed. Different photovoltaic operating states (on-grid and off-grid), different states related to the angle of tilt of the modules (constant--average annual optimum, variable), and the level of degradation of PV modules over the years were simulated. Another study by [PERSON] et al. [28] applied modeling based on modular blocks to design a stand-alone PV system in an isolated area in Romania. In addition to the PV system, energy storage was used to provide energy at times of low power generation. Another well-known application of ANNs and other mathematical models is the prediction of energy generation and PV panel operation [29; 30]. Some studies focused on optimizing energy generation by varying the operating maximum power point (MPP) of PV modules [31]. Later studies present higher optimization accuracy or consider more variables, e.g., by presenting different selection methods for meteorological variables [32; 33; 34]. A study by [PERSON] et al. [35] presents results for an ANN-performed optimization in a 5 MW solar farm system. On such a large scale, the effects of the model are definitely more visible. A very extensive and at the same time insightful analysis of the use of mathematical models for the design, operation, fault identification, and forecasting of renewable energy generation has been conducted within the framework of monographs [33; 36]. These works summarily present a review of about 150 articles, and this allowed the authors to present new findings in the analyzed field. Additionally, a very broad literature review is presented in the monograph, although it deals with technology that was commercially available before 2017 [37]. Among other things, it presents recommendations for the application of specific computational methods for selected research problems. The research presented in this article is the result of exceedingly high interest in solar energy conversion technology. The literature review prepared confirms the need for and very wide range of advanced mathematical models [38]. This technology is a solution to many problems faced by the energy industry and the increasing population of mankind. In the face of climate change, the need to preserve the environment and improve the quality of life of people is undertaken not only in the professional power industry but also in the transport industry and prosumer energy systems. Photovoltaics as an energy source with a satisfactory return on investment even for very low installed capacity is the most widely developed technology. However, the whole production process must be optimized for both economic and local legal reasons. This paper describes an attempt to systematize the influence of weather conditions on energy production in a temperate climate using artificial neural network (ANN) modeling [39]. The use of basic meteorological data such as predicted insolation, temperature, and humidity is now well established in the literature [35]. Compared to such studies, an element of novelty in this work is the use of additional information such as the day number of the year, corresponding to the intermediate angle of the sun. The use of such custom data allows for improved modeling accuracy, especially for the winter period which is important in temperate climates. The presented methodology is designed to adjust energy consumption based on predictedproduction.