The article deals with the problem of building Digital Twins and Smart Digital Twins for control and management in power systems. The energy system is understood as a set of energy resources of all types, methods for their production (extraction), transformation, distribution and use, as well as technical means and organizational complexes that ensure the supply of consumers with all types of energy. Integrated intelligent energy systems are analyzed as one of the important trends in the Russian energy sector, and the main directions of digitization of the energy sector are considered. The concept of "digital twins" in technical fields is considered as one of the main digitalization trends, an ontological approach to building digital twins and semantic models for building smart digital twins are proposed. It is proposed to use a fractal approach when performing ontological engineering, which makes it possible to formalize the concepts of the subject area and allows you to build different-scale ontologies using metalevels of ontologies. Formalized models of digital twins and smart digital twins are presented. The developed approaches are illustrated by the example of construction of digital twins of a solar power plant and smart digital twins of a fuel and energy complex. The approach described in the article makes it possible to integrate different levels of digital and smart digital twins into a single digital solution when modeling energy facilities and power systems.