Fuel cells are a promising source of clean energy. To find optimal parameters for their operation, modeling is necessary, which is quite difficult to implement taking into account all the significant effects occurring in them. We aim to develop a previously unrealized model in COMSOL Multiphysics that, on one hand, will consider the influence of electrochemical heating and non-isothermal fluid flow on the temperature field and reaction rates, and on the other hand, will demonstrate the operating mode of the Solid Oxide Fuel Cell (SOFC) on carbonaceous fuel. This model incorporates a range of physical phenomena, including electron and ion transport, gas species diffusion, electrochemical reactions, and heat transfer, to simulate the performance of the SOFC. The findings provide a detailed view of reactant concentration, temperature, and current distribution, enabling the calculation of power output. The developed model was compared with a 1-kW industrial prototype operating on hydrogen and showed good agreement in the volt-ampere characteristic with a deviation not exceeding 5% for the majority of the operating range. The fuel cell exhibits enhanced performance on hydrogen, generating 1340 W/m² with a current density of 0.25 A/cm². When fueled by methane, it produces 1200 W/m² at the same current density. Using synthesis gas, it reaches its peak power of 1340 W/m² at a current density of 0.3 A/cm².

The article presents an overview of experimental layout design solutions and the general operation scheme of combined heat and power systems with a high-temperature solid oxide fuel cell (SOFC). This system is an environmentally friendly and energy-saving way to produce electricity and heat. The use of high-temperature SOFCs makes it possible to obtain an electrical efficiency of 45–55%. Combining the electrochemical and mechanical system can increase the total efficiency by up to 60–65% in a hybrid power plant. This article discusses the structure and relationship between the components of a hybrid power plant and various modification options for efficient power generation. The technological schemes for existing and tested hybrid power plants with an SOFC and gas turbine are presented and described in detail. When designing a hybrid power plant, the key factors are the choice of design, heat source, and fuel-reforming method; the design of a solid oxide fuel cell and the number of modules in a stack; selecting devices for generating electricity with the development of cogeneration or trigeneration cycles (for possible use in thermal power plants and for the energy supply of social facilities); the direction of material flows within the system; pressure and tightness; and the interconnection of the hybrid power system elements. Researchers have accumulated and described in scientific papers extensive experience in designing, theoretical research, and numerical modeling of hybrid power plants with high-temperature SOFCs. It is shown that experimental hybrid power plants based on SOFCs of the megawatt class are in operation. Hybrid systems with an SOFC are designed only for the kilowatt power class. Trigeneration systems with a steam turbine exist only in the form of theoretical calculations. Trigeneration systems show the highest electrical efficiency, but the highest construction and service costs. Systems based on high-temperature SOFCs can be used for autonomous systems, and in combination with gas and steam turbines only at thermal power plants. Experimental laboratory studies are limited by the high cost of installations and the difficulties of testing the possibility of using combined heat and power systems on an industrial scale. Therefore, a more detailed study of the relationship between the units of a combined heat and power system is recommended in order to achieve the high efficiency indicators obtained from theoretical studies.

Forecasting electricity consumption is one of the most important scientific and practical tasks in the field of electric power engineering. The forecast accuracy directly impacts the operational efficiency of the entire power system and the performance of electricity markets. This paper proposes algorithms for source data preprocessing and tuning XGBoost models to obtain the most accurate forecast profiles. The initial data included hourly electricity consumption volumes and meteorological conditions in the power system of the Republic of Tatarstan for the period from 2013 to 2025. The novelty of the study lies in defining and justifying the optimal model training period and developing a new evaluation metric for assessing model efficiency—financial losses in Balancing Energy Market operations. It was shown that the optimal depth of the training dataset is 10 years. It was also demonstrated that the use of traditional metrics (MAE, MAPE, MSE, etc.) as loss functions during training does not always yield the most effective model for market conditions. The MAPE, MAE, and financial loss values for the most accurate model, evaluated on validation data from the first 5 months of 2025, were 1.411%, 38.487 MWh, and 16,726,062 RUR, respectively. Meanwhile, the metrics for the most commercially effective model were 1.464%, 39.912 MWh, and 15,961,596 RUR, respectively.

A solid oxide fuel cell (SOFC) is an electrochemical energy conversion device that provides higher thermoelectric efficiency than traditional cogeneration systems. Current research in this field highlights a variety of mathematical models. These models are based on complex physicochemical and electrochemical reactions, enabling accurate simulation and optimal control of fuel cells. However, these models require substantial computational resources, leading to high processing times. White box and gray box models are unable to achieve real-time optimization of control parameters. A potential solution involves using data-driven machine learning (ML) black-box models. This study examines three ML models: artificial neural network (ANN), random forest (RF), and extreme gradient boosting (XGB). The training dataset consisted of experimental results from SOFC laboratory experiments, comprising 32,843 records with 47 control parameters. The study evaluated the effectiveness of input matrix dimensionality reduction using the following feature importance evaluation methods: mean decrease in impurity (MDI), permutation importance (PI), principal component analysis (PCA), and Shapley additive explanations (SHAP). The application of ML models revealed a complex nonlinear relationship between the SOFC output voltage and the control parameters of the system. The default XGB model achieved the optimal balance between accuracy (MSE = 0.9940) and training speed (τ = 0.173 s/it), with performance capabilities that enable real-time enhancement of SOFC thermoelectric characteristics during system operation.

Thermal power stations (TPS) are the main source of highly mineralized effluents affecting the environment. An analysis of their water systems demonstrates that alkaline effluents prevail at TPSs. Extraction of an alkali from highly mineralized effluents can make the recycling of effluents economically feasible. A method is proposed of electromembrane recycling of liquid alkaline highly mineralized wastes from TPSs. The process includes electromembrane apparatuses of two types, namely, a diffusion dialysis extractor (DDE) intended for extraction of the alkali from a highly mineralized solution having a complex composition and an electrodialysis concentrator for increasing the concentration of the extracted solution to a value suitable for use in water treatment plants at TPSs. For implementation of the first process (i.e. the extraction of alkali from alkaline-salt solution) various membranes from various manufacturers were studied: CM-PAD and AM-PAD (Ralex, Czechia), MK-40, MA-40, MA-41, MA-414, and MB-2 (OOO OKhK “Shchekinoazot”, Russia), AR103-QDF and СR61-CMP (Ionies Inc., USA). The experiments demonstrate that the acceptable degree of separation of the alkali and the salt is achieved in a pair of cation-exchange membranes with the efficiency of separation being higher without an electric field. The highest efficiency was attained with Russian-made membranes (MK-40, OOO OKhK “Shchekinoazot”). A full scale experiment on recycling of highly-mineralized blowdown water from the evaporating water treatment system at the Kazan cogeneration power station No. 3 (TETs-3) was performed in a pilot unit consisting of two electromembrane apparatuses made by UAB “Membraninės Technologijos LT”. In the experiments every ton of blowdown water yielded 0.1 t of concentrated alkaline solution with an alkali content of up to 4 wt % and 0.9 t of the softened salt solution suitable for the reuse in the TPS cycle. The power rate is 6 kWh / ton of blowdown water.

Currently, the process of creating industrial installations is associated with digital technologies and must involve the stage of developing digital models. It is also necessary to combine installations with different properties, functions, and operational principles into a single system. Some tasks require the use of predictive modeling and the creation of “digital twins”. The main processes during the fuel cell modeling involve electrochemical transformations as well as the movement of heat and mass flows, including monitoring and control processes. Numerical methods are utilized in addressing various challenges related to fuel cells, such as electrochemical modeling, collector design, performance evaluation, electrode microstructure impact, thermal stress analysis, and the innovation of structural components and materials. A digital model of the membrane-electrode unit for a solid oxide fuel cell (SOFC) is presented in the article, incorporating factors like fluid dynamics, mass transfer, and electrochemical and thermal effects within the cell structure. The mathematical model encompasses equations for momentum, mass, mode, heat and charge transfer, and electrochemical and reforming reactions. Experimental data validates the model, with a computational mesh of 55 million cells ensuring numerical stability and simulation capability. Detailed insights on chemical flow distribution, temperature, current density, and more are unveiled. Through a numerical model, the influence of various fuel types on SOFC efficiency was explored, highlighting the promising performance of petrochemical production waste as a high-efficiency, low-reagent consumption fuel with a superior fuel utilization factor. The recommended voltage range is 0.6–0.7 V, with operating temperatures of 900–1300 K to reduce temperature stresses on the cell when using synthesis gas from petrochemical waste. The molar ratio of supplied air to fuel is 6.74 when operating on synthesis gas. With these parameters, the utilization rate of methane is 0.36, carbon monoxide CO is 0.4, and hydrogen is 0.43, respectively. The molar ratio of water to synthesis gas is 2.0. These results provide an opportunity to achieve electrical efficiency of the fuel cell of 49.8% and a thermal power of 54.6 W when using synthesis gas as fuel. It was demonstrated that a high-temperature fuel cell can provide consumers with heat and electricity using fuel from waste from petrochemical production.