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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.