## 1 Introduction
The ongoing evolution of network topologyand operating parameters within power grids and power supply systems of industrial consumers necessitates the advancement of new mathematical models and algorithms, which are crucial for making informed decisions on managing electricity consumption, tailored to the specific features of technological processes. The study [30] focuses on a model for forecasting energy consumption based on the assessment of electricity consumption parameters relying on the Bayesian estimation method and the Markov Monte Carlo method in order to reduce electricity costs. In [31], the authors explore methods to lower the auxiliary consumption of thermal power plants. The study considers various factors, including the types, capacity, and duration of operation of peak electric loads; the fuel used; and the capacity of the power plant; as well as the external conditions. In [32], a statistical analysis based on the probability theory is proposed for analyzing electricity consumption in order to determine the \"energy efficiency index\". This index is used to assess the loss of energy resources during production processes for reducing environmental fines. In [33], a system of energy efficiency indicators is designed to facilitate energy audits in coal mining enterprises. The study also involves systematizing the factors that influence the consumption of energy resources and their reduction and investigating the barriers that hinder the implementation of energy-saving measures. The use of artificial intelligence methods, in particular artificial neural network methods, including the long-short-term memory (LSTM) method, is proposed in [34] to improve the accuracy of forecasting electricity consumption at industrial enterprises. The research also highlights the importance of utilizing the Gaussian distribution principles along with normalization and scaling techniques for primary data processing. In [35], the authors suggest using cluster analysis methods to examine electricity consumption measurement data across various parameters while considering load fluctuations and typical load curves. Electricity consumption is forecast based on the LSTM neural network, factoring in the influence of meteorological data on the accuracy of load forecasting. A system of differentiated tariffs for industrial consumers is proposed in [36] to reduce electricity supply costs by shifting the load curve to off-peak hours across the day. This brings down the cost of production by reducing electricity expenses by at least 1.5 times and enables power grid companies to receive a uniform load on power lines and transformers throughout the day, preventing emergency overloads. A particle swarm optimization algorithm is used in [37] to forecast and analyze the changing trend of industrial electricity consumption, which increases the adaptability of the model. The authors propose utilizing the forecasting results to plan the expansion of energy systems and enhance the operation of the electricity market. In [38], various scenarios for reducing the network load during emergency situations are examined by leveraging advanced information and communication technologies. This approach relies on the methods for optimizing and modernizing the generation of emergency commands. In [39], the problem of positive stabilization of linear continuous singular systems of both proportional and proportional derivatives of state feedback is considered. In [40], a control strategy is presented for an isolated hybrid DC microgrid that includes photovoltaic systems, piezoelectric elements, and storage batteries. An approach to model predictive control supplemented by reinforcement learning is proposed to optimize the performance of a hybrid DC microgrid that can be used in industrial power supply systems. In [41], a new combined method for long-term forecasting of consumer power supply systems development is proposed, which allows taking into account their features when planning the development of power systems.