## 1 Introduction  
In recent years, energy systems have undergone substantial changes caused by a host of factors. These are a widespread use of renewable energy resources and energy storage devices, and the presence of active adaptive elements allowing control of branched energy systems in real time. Thus, power systems are nowadays multi-layered and complexly integrated engineering objects. A ramified information structure in the stages of energy generation, transmission, and use made it necessary to use new approaches to control and optimize these systems. This circumstance, in turn, has brought about fundamentally new issues, which can be resolved only within the framework of the fourth industrial revolution. The above factors have led to the development and creation of principally new technical and information systems that are mathematical models. Currently, this approach is being implemented independently in each energy industry. However, there are some energy objects for which the possibility of a quick and economically feasible transformation of various types of energy carriers into each other is essential. Research in this area is conducted based on the multi-energy systems (MES) concept, which relies on the energy hub concept [1]. Traditionally, various channels of energy (heat, gas, electricity) supply are considered independently of each other. At the process level, this affects various approaches to collect process information (data transfer protocols, forms of information storage, data analysis and presentation). Data on various channels are poorly integrated with each other (different data rates, sampling times). The level of analysis involves various mathematical descriptions of objects and various approaches to model such objects. A similar approach is currently being observed in the development of mathematical models in various energy supply applications. Various structural models are built for power, heat, and gas supply systems. For example, this approach cannot be used to create digital twins of multi-energy systems [2; 3; 4]. A distinctive feature of multi-energy systems is the need to consider various energy flows jointly, given their mutual influence. Traditionally, a methodological approach and mathematical tools for the joint use of various energy flows are considered in terms of their capability to convert one type of energy into another and in terms of their storage systems. The mathematical description of such models traditionally consists of their representation in a matrix notation. Such a mathematical description imposes significant restrictions on taking into account the performance characteristics of technical devices that are part of the energy hub. It should be noted that the characteristics of these devices have a non-linear dependence on the load. At the same time, in recent years, methods of simulation modeling of various technological objects have been widely used. Some authors view this approach as one of the promising areas for the creation of mathematical models [5; 6]. It is worth noting that the main issue facing the widespread adoption of the MES concept in practice is the absence of a modeling technique for the analysis of the structure and behavior of an object in all energy supply channels [7]. The paper presents a methodological approach to create mathematical models of integrated energy systems based on simulation modeling. The model rests on the energy hub concept. The novelty of this approach is the combination of the principles of simulation modeling and the concept of an energy hub, which makes it possible to take into account the nonlinearity of the change in characteristics depending on the loads. Also, the novelty of the approach is the use of a universal system of units of measurement for all technical parameters. The proposed approach offers broad prospects for expanding the design and operation capabilities for integrated multi-energy systems. The structure of the article is as follows.