The large variability and unpredictability of energy production from photovoltaic power microinstallations results from the dependence on the current weather conditions. These conditions depend on a number of factors and are variable over the time. Despite this specificity, photovoltaic micro-installations are becoming more and more popular in the world and in Poland. This is mainly due to the fact that the generation of energy from renewable sources has numerous advantages, the energy is free, renewable in time and ecological, and its production on its own gives partial independence from energy supplies from the power grid. In addition, the observed significant prices decrease of solar modules has further accelerated the development of the use of this energy source. Concern for this method of energy production among households has increased significantly in Poland after introducing the prosumer in the legal framework and the use of administrative and financial support. The implemented prosumer mechanisms allowed, for example, the net balancing of the energy consumed and produced by the micro-installation through storage in the power grid. The article describes the problem of balancing sources using solar energy, based on micro-installation used in the household (the so-called prosumer installation). The conducted analyses compared the load profile of a typical household and the energy generation profile from a photovoltaic installation, determining the real balancing formation level of such a system.

This paper provides a method for simplified description of a regional power grid model aimed to deliver a grid reduction, and improve grid performance observability. The derived power grid model can be used to analyze the regional allocation of the decentralized energy generation and consumption. The expansion of wind and solar generation in the power system affects the residual load. The power balance between electricity consumption and generation was calculated and analyzed based on the temporal and spatial scales. The proposed grid clustering method is a useful approach for performance analysis in systems with a growing share of renewable generation.

This paper presents new directions in the modeling of electric arc furnaces. This work is devoted to an overview of new approaches based on random differential equations, artificial neural networks, chaos theory, and fractional calculus. The foundation of proposed solutions consists of an instantaneous power balance equation related to the electric arc phenomenon. The emphasis is mostly placed on the conclusions that come from a novel interpretation of the equation coefficients.