## 1 Introduction  
Photovoltaic energy is now integral to the world's energy mix, contributing to sustainable development and reducing carbon emissions. The development of small solar photovoltaic (PV) systems, operating both in parallel with the grid and in offline mode, can improve the power supply of household consumers more efficiently and faster than the development of an extensive energy system. They are capable of providing electricity to a household regardless of its geographical location in regions of the country. They are an excellent choice for Southeast regions where solar radiation is high and offer independence from the electricity grid. They are suitable for remote locations where laying electrical cables is expensive and difficult to implement. Here are some of the main advantages and applications of autonomous photovoltaic systems:  
1. Independence from the grid: remote locations like farms, chalets, and guest houses can install them. 2. Economical: in the long run, these systems can reduce electricity and maintenance costs. 3. Sustainability: they are environmentally friendly and reduce the carbon footprint [1; 2; 3]. In the world of solar energy, Germany is a European leader. As of mid-2011, Germany had over 20,000 MWp of installed solar capacity. In Italy, it was around 8000 MWp; in Spain and the Czech Republic, it was between 1500 and 4000 MWp; and in Belgium, it was around 500 MWp. Despite the different speeds of development and the turmoil that these markets have experienced, it must be clearly stated that they have created many jobs and laid the foundations for the development of an innovative economy in the renewable electricity sector. Strengthening production depends on a sustainable local market. Each country has its chance of covering specific niches in component and service production. In many countries, there is a significant shortage of electricity. The level of consumption is high. Populated cities mainly provide a centralized power supply. High levels of solar radiation in southern areas allow solar energy development [4; 5]. Therefore, the work devoted to the study and improvement of small solar equipment is a current task with practical significance. Studies on small PV systems in tropical climates make the topic's level of development relevant. Researchers have not identified any optimization of the structure of a PV system using a non-orientable solar cell (SB) and an inverter at different cell voltages. It is not enough for single-phase inverters to work with low harmonic distortion and fast voltage regulation in the PV system [6; 7; 8]. Each type of mounting system--from roof mounting to ground installation--is characterized by specific advantages and considerations that must be weighed against various factors, such as limited space, structural compatibility, and local weather conditions. Installers can choose the best alternative for their unique design requirements if they know each system's advantages and disadvantages [9]. In addition, the photovoltaic \"climate\" is determined by insolation. An analysis of objective insolation opportunities would provide clarity. Many regions have significant solar radiation potential, yet each region observes relative differences in insolation intensity. In this regard, developing genetic algorithms for predicting PV indicators for household consumers is very appropriate. This allows localizing the PV system and predicting a metric. We use hundreds of indicators, represented by time series (TSs), to assess the dynamics of the development of renewable energy sources. It is challenging to diagnose and make predictions because comparable information is not always reliable. This means that many of the standard methods and algorithms for analysis and prediction cannot be used because they require data sets with a long fundamental part [10]. For instance, the use of time series (TSs) presents a challenge.