Review of Existing Tools for Software Implementation of Digital Twins in the Power Industry

Abstract

Digital twin technology is an important tool for the digitalization of the power industry. A digital twin is a concept that allows for the creation of virtual copies of real objects that can be used for technical state analysis, predictive analysis, and optimization of the operation of power systems and their components. Digital twins are used to address different issues, including the management of equipment reliability and efficiency, integration of renewable energy sources, and increased flexibility and adaptability of power grids. Digital twins can be developed with the use of specialized software solutions for designing, prototyping, developing, deploying, and supporting. The existing diversity of software requires systematization for a well-informed choice of digital twin’s development tool. It is necessary to take into account the technical characteristics of power systems and their elements (equipment of power plants, substations and power grids of power systems, mini- and microgrids). The reviews are dedicated to tools for creating digital twins in the power industry. The usage of Digital Twin Definition Language for the description data of electromagnetic, thermal, and hydrodynamic models of a power transformer is presented.

1. Introduction

1.1. Definition of a Digital Twin

In 2003, Michael Grieves introduced the concept of a digital twin (DT) [1]. The digital twin is the real projection of all components in the product life cycle using physical data, virtual data, and data in between [2]. In 2010, NASA defined a DT for spacecraft as integrated multiphysics, multiscale modeling of a vehicle or system that uses the best available physics models, regular sensor data streams, historical data, and so on” [3]. This definition served as the basis for the creation of DT concepts in various research fields. According to [4], the DT includes data on the characteristics of the object, a detailed mathematical model, the parameters of which are refined using the actual data.

According to [5], a DT is defined as a set of technologies and solutions for ensuring the life cycle of a product, machine, structure, system, etc. which has powerful potential. In [6], a DT is defined as a concept of a virtual embodiment of production elements, objects, or entire systems. It takes into account not only the physical model of the object but also the relationships between elements, the influence of the human factor, and the learning ability of the system itself. This allows for the description of the digital life cycle of a product or service.

In the research paper [7], a DT was developed utilizing an IoT Framework, with the development process segmented into two distinct phases. Initially, the framework facilitated the establishment of information exchange channels between the digital model and its corresponding physical counterpart. Subsequently, the second phase focused on organizing data preprocessing activities leveraging cloud computing technologies.

Digital twins can be divided into three types [1]:

• Digital Twin Prototype is described as a virtual analog of a real-life element and contains information that describes a specific element at all life cycle stages, from production requirements and technological processes during operation to requirements for the disposal of the element;
• Digital Twin Instance contains information on the description of an element (equipment), i.e., data on materials, components, and information from the monitoring system;
• Digital Twin Aggregate combines a Digital Twin Prototype and a Digital Twin Instance. It collects all available information about the equipment or system.

There is the term “Digital Shadow”. It is a DT that is updated in accordance with data received from a real object, but with its help, it is impossible to perform influences on the object. Although this term is not very widespread, and, in most cases, it is called a digital twin instance. Figure 1 shows the proposed classification of DT types.

1.2. Existing Reviews and the Contribution of This Research

The authors of the article [5] developed a methodology for analyzing a large volume of publications on digital twins of the Scopus bibliographic database. The database consisted of 8693 articles posted in the database from January 1993 to September 2022. According to the analysis, an increase in the number of publications on the topic of “Digital twins of power grids and power distribution systems” was identified, which may continue in the coming years. The technology of digital twins, despite its high importance, does not yet have an established terminology and classification of concepts and methods.

Siemens, General Electric, IBM, Microsoft, and Bosch are offering the concept of digital twins to businesses. For example, General Electric developed a DT platform that predicts the behavior of systems; Siemens developed a DT platform for the simulation of smart product development processes.

The review [8] considers general approaches to the use of digital twins at the levels of data, models, networks, and applications. The articles [9,10] describe examples of using digital twins in many industries with an assessment of their advantages and prospects. In the article [5], the following conclusion about the three most important areas of DT application was made: “digital twins of assembly lines and robots; BIM technology and digital twins in construction; digital twins of power grids and energy distribution”. Moreover, reviews describe the application of DT in specific industries: transport [11], medicine [12], agriculture and forestry [13,14], industry (production lines) [15], construction [16,17], and software development [18].

In the power industry, there are reviews on the use of digital twins, such as [19] (only electric power plants are considered), [4] (the relationship between DT and machine learning in the power industry is shown), [20] (the industry as a whole). According to [21], a DT of electrical networks can be described using an ontological approach.

The task of creating a DT may be faced by a research team studying the efficiency of new technologies during their pilot operation, by an enterprise seeking to improve the observability of its production assets and the quality of their management, by a company engaged in the development and implementation of digital technologies. When developing a DT, the problem of choosing tools for creating DT will arise. The difficulty of choosing the tool for the DT creation is complicated by the lack of literature comparing various solutions. Since existing papers describe issues at a higher level of abstraction, they do not provide recommendations for software implementation. This is confirmed by the conclusions reached by the authors of the review [22]. It states that there are a large number of articles describing models at various levels of DT. However, in the area of software architecture, tools, and specific recommendations for developing digital twins, there are “clear research gaps”.

This review focuses on the tools for creating software implementation of digital twins in the power industry. It covers the most widely used products for developing digital twins in the power industry. The purpose of this review is to solve the problem of making a reasonable choice of a means of creating a digital twin with a sufficient level of versatility and, at the same time, compatibility with other systems. In addition, the availability of tools and the possibility of their flexible configuration for the tasks being solved are considered. The language of description of digital twins of power systems and their elements based on Digital Twin Definition Language (DTDL) was proposed, and its use for electromagnetic, thermal, and hydrodynamic models of an oil-immersed power transformer was presented.

The article is structured as follows. Section 2 provides a brief overview of digital twins in the power industry. Section 3 contains an overview of the software for creating and implementing digital twins in the power industry. Section 4 presents an example. Generalization is provided in the conclusion.

2. Applications of Digital Twins in the Power Industry

2.1. Advantages of Using DTs in the Power Industry

Digital twins are of great significance in the power industry, as they allow for the optimization of processes and increase the efficiency of the industry. They provide the ability to model and predict the behavior of the power system in various scenarios, which helps minimize risks and make informed decisions.

The main advantages of using digital twins in the power industry include the following:

• Improving the reliability and safety of the power system. DTs allow for predicting the possibility of failures and accidents in the power system, which helps to carry out preventive maintenance and equipment maintenance promptly;
• Optimizing operation and planning. DTs provide information on the current state of the power system and its components, which allows for optimizing the operation and planning process;
• Saving resources. Using DTs allows for reducing the costs of equipment maintenance and repair, as well as reducing energy consumption due to more efficient load management;
• Innovation and development. DTs can be used to test new technologies and solutions before their implementation in the real power system, which accelerates the innovation process and promotes the development of the industry.

2.2. Industry Examples

GE Predix is a cloud platform for the Industrial Internet of Things (IIoT) developed by General Electric to analyze big data in the industry with full compliance with cybersecurity requirements [23]. Besides such benefits as reducing risks and increasing reliability, availability, and improving production, it optimizes maintenance costs, as well as time expenditures. This platform was developed using IIoT technologies to analyze large amounts of data in real time. The most powerful part of Predix is big data analytics based on digital twins. In this case, various initial states of physical equipment are collected and stored in a virtual information space, and the equipment is controlled by building accurate models and behavior predictions.

Paladin Gateway has launched and deployed the Power Analytics platform [24]. It enhances asset management by considering the interdependencies of each individual asset with other systems and their impact on different departments. Highlighting critical points enables the rapid creation of an effective virtual model, which facilitates more efficient prioritization of tasks, predictive maintenance, and failure prevention. The system also enables the simulation of various scenarios with minimal risk. In general terms, Paladin is an integrated suite of services that can be cloud-hosted. This platform provides an opportunity to create digital twins, software tools for system management, and the exchange of real-time monitoring data within power systems.

Rotek JSC has introduced the Prana diagnostic system [25]. The hardware and software system is designed to evaluate the technical condition of various power generation and transmission equipment, including steam turbines, generators, transformers, boilers, pumps, and gas piston units. Its main advantage is the ability to predict the possible failure 2–3 months before the incident.

At the heart of the Prana system lies a multidimensional state model that includes data on normal operating conditions that serve as a DT of the equipment. This model continuously analyzes the equipment’s performance over predefined control periods in real time and automatically identifies dependencies and trends. It compares the current state of the equipment with the reference model, identifying deviations. The level of these deviations is displayed through the T2 indicator, which serves as a criterion for the technical condition of the equipment.

The Prana system leverages advanced technologies such as neural networks and big data analytics to enhance its diagnostic capabilities. It calculates the impact of each parameter on the deviation from the reference model and provides experts with information on the 10 most significant causes of deviations. This allows us to obtain a complete understanding of the equipment’s condition and predict its changes.

IoT platform Insight Hub (formerly MindSphere) [26], developed by Siemens, is a solution that allows data to be collected, stored, and processed from various devices and sensors located on power facilities. This system allows for monitoring and diagnosing the condition of equipment, predicting its failures and optimizing the operation modes of the power system, optimizing costs, increasing flexibility and automation of the production process, and improving the design and management of products.

The DT “IBM Engineering Lifecycle Management”, developed by IBM, is aimed at evaluating the technical condition of the equipment [27]. It focuses on eliminating the negative impact of data in silos caused by the challenges of data fragmentation, overloading, and high rework costs. ELM creates a digital thread based on the Open Services for Lifecycle Collaboration (OSLC) architecture, enabling holistic management from requirements to systems design, workflow management, and testing. It helps automate management processes and enables the making of more informed decisions.

2.3. Digital Twins for Power Plants and Renewable Energy Sources Integration

The research [28] provides a review of applications of DTs for improving efficiency and safety in renewable energy systems. The study considers closed-loop digital twins (CLDTs), presenting their main functionalities and advantages of their use in terms of their application for renewables. Nevertheless, despite a number of positive features, to make their use maximum efficient, a formalized approach is needed. In this case, observation, orientation, decision, and action (OODA) processes should be integrated.

Implementations of DT technologies for power plants are described in [29,30] (photovoltaic power plant), [31] (tidal power plants), and [32,33] (wind turbines). DT supports the generation forecasting, operation, and maintenance of the power plant. DTs allow the prediction of failures of turbines [34]. This, in turn, should make the process of management of systems through predictive maintenance solutions represented by the methods of machine learning more easy.

The problem of diagnosing the faults of equipment at the early stages is also important in terms of improving the reliability of nuclear power plants [35]. The article [35] explores the application of a DT of nuclear power plant equipment for predictive analysis. Since the safety of such an object has the highest priority, the data used to develop the DT were sourced not from actual physical components but rather from a simulator.

2.4. Digital Twins for Electrical Equipment

DT for simulation of the power substation in real and quasi-real time is presented in the paper [36]. This substation’s DT uses real-time monitoring data, a 3D model of the electrical equipment, and mathematical models for decision-making. According to the study, there are three main elements that should be considered in terms of creating a digital twin. First is its full lifecycle, within which the DT covers all stages of a product, from its design to its disposal, improving both the manufacturing process and the use of the product. Second is the relevant data—the real time of using a physical object and DT. Third is the both-way data flow from the real object to the DT.

The DT of high-voltage power transmission lines is proposed in the paper [37] because the problem of cable insulation breakdown is still quite common. As power failures bring huge economic losses, online monitoring is one of the effective tools to prevent power outages.

IoT technologies allow the aggregation of a large amount of different data. The application of DT for the detection of equipment defects is described in [38]. The paper pays special attention to the different machine learning methods such as Logistic Regression, Random Forest, Extreme Gradient Boosting, and ensembles of these algorithms. The assessment of the technical condition of the equipment is described in [39,40,41,42,43].

Study [39] shows the possible methods of modeling the energy processes, which include the ones of both physical and chemical nature. Further transformation of the controlled parameters into the mathematical model provides an opportunity to widely use this approach.

Research [40] discusses the main problems of data storage and acquisition as well as the issue of the responding time of the DT. The authors have developed a preparation model that should raise the efficiency of the whole system in terms of equipment management. Study [41] also emphasizes the importance of DT models for predictive maintenance and proposes a method to access the power grid equipment.

Study [42] presents the model based on the operational behavior of equipment that simulates certain specific effects that might not be measured directly. Two examples of DT are considered by the authors: first, it is realized for the 500 MW electric drive train, and second, for the synchronous motors with DOL start. Finally, the [43] study introduces the problems of unstructured telemetry, the qualitative processing of which should provide great opportunities for the development of the power industry in the future.

The forecasting of the technical condition of power equipment described in [44] discusses the recent developments of control center technology and the implementation of DT. The operational management of power systems is described in [45] and shows the collaborative structure of power grids’ management, showing that the DT-based technology is capable of effective management of it. The review [46] shows how DT improves the reliability of electrical machines due to predictive maintenance and realizes the concept of Industry 4.0. The authors of [46] emphasize that DT technology creates conditions for the application of artificial intelligence techniques, which will ultimately lead to increased decision-making efficiency in the operation of electric machines.

The article [47] discusses the requirements for creating a DT of an oil-immersed power transformer, taking into account the high computational complexity of mathematical modeling of physical processes in it. Comparing various aspects of different approaches, such as calculation time and complexity of implementation, successful examples of DT implementation are provided in the study. This paper shows that modeling individual electromagnetic, thermal, or hydrodynamic processes taking into account the spatial distribution of output values may require significant computational resources. It also indicates the relevance of the correct choice of software for creating the DC of electrical equipment.

3. Software Tools for Digital Twins Development

There are many software solutions for creating and working with digital twins. During the development process, different programming languages and specialized tools such as Python, C++, Java, C#, and MATLAB can be used. The choice of language depends on the specific requirements of the project, the developer’s preferences, and available resources.

Software implementation tools for DT development may include the following approaches and technologies:

• Simulation (MATLAB/Simulink, PSS-E (Power System Simulator for Engineering), DIgSILENT PowerFactory, etc.);
• Cloud platforms and infrastructure (Microsoft Azure Digital Twins, AWS IoT TwinMaker, etc.);
• Data collection and processing tools, Internet of Things (IoT) (SCADA (Supervisory Control and Data Acquisition), IoT sensors and devices, etc.);
• Analytics and machine learning (ML) (Python and machine learning libraries (TensorFlow, PyTorch, sci-kit-learn), R, MATLAB, etc.);
• Visualization tools and 3D modeling (Tableau and Power BI, web-based interfaces, etc.);
• Data integration platforms (Apache Kafka, Apache NiFi, etc.);
• Database management systems (DBMSs);
• Cyber–physical systems.

The development of an intelligent system for creating DT of power systems and their elements is a complex scientific and technical task that requires the use of various tools and advanced experience in creating such systems. The important point is the choice of the language of description and creation of the DT and the programming language in which the software will be implemented. The existing digital platforms and services are reviewed below.

3.1. Ansys Twin Builder

The Ansys Twin Builder platform allows for the creation of digital twins based on digital models of assets (or objects) and updates them by receiving data from measuring devices [48]. Ansys Twin Builder offers the possibility to develop systems using multi-domain models, elements, 3D resolvers, and reduced-order models (ROMs).

The solution provides functionality for creating virtual prototypes of large systems, allowing the combination of pre-installed basic and industry component libraries with custom ones. Users can choose programming languages, including C/C++, and standard-modeling languages. The system model can also be used at the operational stage to organize predictive maintenance of the real product/object and optimize its performance characteristics.

It is mainly used for modeling individual electrical devices such as turbines, engines [49], charging stations [50], and others. Ansys Twin Builder is a commercial product, not open-source, and integrating it with third-party software or systems outside the Ansys ecosystem is complex and requires additional effort and customization.

3.2. COMSOL Multiphysics

The COMSOL Multiphysics platform [51] allows for the analysis of individual and interrelated physical processes. COMSOL Multiphysics is a model builder environment that allows going through all stages, from building a geometric model, setting material properties, and describing the physics of the problem to solving and visualizing the simulation results.

The COMSOL Multiphysics platform allows for the creation of simulation applications with a specialized interface for solving typical problems. A model administration system is used to control versions and manage files. In order to expand the functionality of the platform, additional modules can be used. It provides 2D and 3D finite element analysis, molding electromagnetics, fluid dynamics, heat transfer, and structural mechanics.

The Application Builder allows for the development of applications with a user interface. Application Builder contains two tools: the Form editor and the Method editor. The Method editor is a programming environment that allows changing the model based on an object-oriented representation of data. The code in the Method editor is written in the Java programming language.

By multiphysics modeling, engineers can develop comprehensive digital twins of power industry assets for predictive maintenance, performance optimization, risk assessment, etc. For example, it can be applied for modeling generators [52], elements of wind turbines [53], and other important power industry equipment.

Several license options are available to run COMSOL Multiphysics software and distribute CAE simulation applications through the COMSOL Server platform. Licenses can be commercial or academic, perpetual or term-based. COMSOL licenses can be expensive, especially for commercial use.

The COMSOL Multiphysics supports scripting using its own MATLAB-based language. It is less powerful and flexible than versatile and widely used languages such as C++, Java, or Python. This can make it difficult to automate tasks or integrate COMSOL with other software.

3.3. AnyLogic

AnyLogic is a multifunctional platform for simulation modeling, applied in various industries, and is suitable for solving problems of any complexity [54]. The experience with AnyLogic in large companies makes it easier for developers of DT.

AnyLogic has a unique ability to combine different approaches, including agent, discrete event, and system dynamics modeling. Therefore, it is a powerful tool for accurately representing a real system and flexibly solving a wide range of problems. It supports real-time simulation, allowing users to monitor and interact with digital twins in real time. Advanced visualization tools facilitate the communication of simulation results and insights.

AnyLogic has been used to develop digital twins in different fields of the power industry: smart grids, simulating the interactions between renewable energy sources, energy storage systems, and traditional power generation facilities [55]; power plants, including the scheduling of maintenance activities, the management of fuel supplies, prediction of equipment failures, and optimization of operation mode [56]; demand response simulation; etc.

It is not open-source software. However, AnyLogic allows models to be extended at the code level, including integration with external databases via API. This allows model developers to reuse created objects or modules. In addition, models can automatically adapt their configuration based on incoming data. Models made in AnyLogic are standalone Java applications. It significantly expands the ability to implement custom code to create a digital twin on this platform.

AnyLogic can interact with web services and RESTful APIs, allowing for real-time data exchange with other software applications. It is particularly useful for integrating digital twins with other software systems, such as SCADA, Enterprise Resource Planning (ERP) systems, and Internet of Things devices. These APIs support bidirectional communication; therefore, AnyLogic models can not only receive data but also send commands and updates to external systems.

3.4. SimManager

The SPDM system allows working with engineering modeling objects in their native environment [57]. This system supports automatic access to data from popular commercial PDM systems. In addition, this system can be integrated into the enterprise’s general PLM environment.

SimManager is a system for managing the modeling process and its data at the object level. It allows controlling the sequence of modeling steps and tracking the origin of each result. SimManager is designed to work with large volumes of data obtained in multidisciplinary research. Data may be lost, or it will be impossible to determine which design variant it corresponds to without using such a system. The system allows working with design process templates, automating modeling stages, analyzing and optimizing product designs, and managing engineering analysis data. At present, no examples of its use in the power industry have been found.

SimManager has a standardized user interface that is available for customization to the individual needs of users of the particular enterprise.

Integrating SimManager with other third-party simulation software commonly used in the power industry requires custom scripting or additional plugins. Like many enterprise-level software solutions, SimManager can be expensive, particularly for small- to medium-sized organizations in the power industry.

3.5. Digital Platform CML-Bench

CML-Bench is a digital platform used to develop and implement digital twins of various objects, including industrial constructions, physical and mechanical processes, and production technologies [58].

The CML-Bench digital platform includes a set of services written in Java and Kotlin and a presentation layer in TypeScript. The deployment process uses modern technologies to automate installation, error logging, and performance monitoring, including ELK, Jenkins, Ansible, and Prometheus.

The CML-Bench platform is based on the SPDM class system, which provides links between data from different programs used in the design and simulation process. The system increases the level of automation, ensures transparency and traceability of tests, and improves the simulation and design processes. At present, no examples of its use in the power industry have been found. However, it is used in related fields such as nuclear power and mechanical engineering for the oil and gas industry [58].

The CML-Bench architectural model contains three levels: client, application server, and database server. Clients interact with the CML-Bench digital platform via a web browser. The database server level provides data storage and can be implemented using the Postgres PRO or PostgreSQL database management system. The application server level contains a set of services running under the Tomcat servlet container, written in Java and Kotlin using the Spring Framework. Each service has three main software layers: presentation (controllers), business logic (software model of the subject area), and data access (a set of classes that exchange data between the business logic layer of the application server level and the database level).

It is not open-source software but provides ample opportunities for integrating software created by digital twin developers themselves.

3.6. iTwin and PlantSight Services

Bentley’s iTwins [59] are data warehouses that contain a variety of information types, from drawings and specifications to analytical models and asset management data. iTwin services enable users to work with data warehouses by creating, visualizing, and analyzing them. The company is actively developing these services and adding new capabilities.

iTwin service offers 2D/3D visualization as the primary tool for working with data. It serves as a link between different types of data created using different tools. The service converts data into a single format suitable for visualization and analysis. The obtained data can be viewed and worked with via a web browser. In order to support intelligent design systems, the ProjectWise Bridge service is used, which supports intelligent design systems such as SmartPlant 3D, PDMS, E3D, and OpenPlant, as well as *. RVT, *. DWG, *. DGN, and *. IFC file types.

iModelHub is an iTwin service that stores a history of changes for each digital twin. It allows tracking who made changes to the project and when, moving through the timeline, naming versions, and comparing them with each other.

Digital Twins software contains the following:

• iTwin Capture allows the transformation of physical assets into digital twins;
• iTwin IoT for the connection of physical assets to DT;
• iTwin Experience, a platform that allows users to interact with DT using interactive visualization;
• PlantSight, a service that uses digital twin technology to manage and optimize industrial assets.

PlantSight is a joint development of Bentley and Siemens, a specialized iTwin service for the process industry [60].

Cases for which the platform is suitable include designing, analyzing, and operating your infrastructure assets of different types of power plants [61].

Digital twins can be updated in real time with data from the company’s sensors via IIoT. They can be used to create augmented and virtual reality models for training workers, simulating responses, and developing scenarios for refurbishment or restoration.

The DT is created based on data in various formats, as well as maintenance manuals and other documentation. During operation, these data are supplemented with information received from data collection systems to maintain the relevance of the DT. This allows for the creation of a universal digital platform for engineers, which allows them to visualize components, check the condition of assets, conduct analysis, and generate various types of analytical data.

Integration capabilities are inferior to analogs because of the small size of the ecosystem and the lack of tools for interacting with other software.

As with other proprietary software listed above, iTwin and PlantSight Services may be expensive for small- and medium-sized organizations in the power industry.

3.7. Zyfra Industrial IoT Platform (ZIIoT)

Zyfra Industrial IoT Platform (ZIIoT) is an industrial IoT platform developed by the Zyfra Group of Companies for the mining, metallurgy, and engineering industries [62]. The platform is designed to collect, process, and analyze data from production facilities using IoT, machine learning, and artificial intelligence. It positions itself as a platform for creating software in the field of digitalization for the future ecosystem.

Solutions created and operating based on ZIIOT ensure the efficient and uninterrupted operation of industrial enterprises. It supports the integration and adaptation of an existing application with the platform and the development of a new application on the platform. Requirements for creating applications are as follows:

• Application data that should be available to other applications need to be added to the Object Model and provided by the Object Model and Universal Data Bus software interfaces;
• Application must provide authentication for any access to the software or user interface using the OpenID Connect protocol;
• Frontend services of the application need to receive an access token from the authentication service and pass the received token to the backend services, which comply with the identity propagation principle, passing the incoming request token to all outgoing requests;
• Services of the application need to use JSON Web Token Claims for authorization.

Zyfra Industrial IoT Platform supports any solutions on a microservice platform architecture. The platform is new, and the number of successful implementations is still small and related to industry and the oil and gas complex.

3.8. Azure Digital Twins and Digital Twins Definition Language

Digital Twins Definition Language (DTDL) is an open standard, which is based on JSON-LD (a type of JSON) and the RDF (Resource Description Framework) standard [63]. DTDL is used in many commercial solutions offered by Microsoft, such as IoT Hub, IoT Central, and Azure Digital Twins. The main aim of this data presentation format is to ensure simple and flexible integration of models in industry areas of activity while maintaining the complex system of their interrelations, reflecting real objects, processes, and phenomena in the surrounding physical world.

DTDL consists of a set of metamodel classes that are used to define the behavior of all digital twins (including devices). The main metamodel classes that describe this behavior are Interface, Command, Component, Property, Relationship, and Telemetry. The JSON-LD context (operator @context) is used to specify the DTDL version. Also, DTDL provides a set of Geospatial Schemas based on GeoJSON for modeling various geographic data structures.

In order to identify resources and their elements, DTDL uses a special form of URI called a DT modeling identifier (DTMI) of the form <schema>; <path>; <version>. The schema is the lowercase string literal “dtmi”. The path is a sequence of one or more colon-separated segments. The version is a numeric value.

DTDL language follows the syntax of JSON. It allows many text editors to provide basic syntax checking and highlighting of DTDL documents. DTDL extension is also available for Visual Studio Code. Models define semantic relationships between entities so DT can be connected into a knowledge graph that reflects their interactions. Clients can connect external computing resources to manage data processing, extract real-time analytics from the runtime environment using the Azure Digital Twins Query API, or stream data downstream to Azure services for analytics or storage via event routes. Azure Digital Twins is a cloud service from Microsoft that enables the creation of digital twins.

Azure Digital Twins provides developers with tools to create complex models of spaces and objects and interact with them through APIs. Clients can use these models to analyze data, optimize processes, and make decisions.

The repository [64] presents DTDL energy grids, including such parts as Generation and Prosumer. The application of the Azure platform for building long-term maintenance models for wind farms is presented in the paper [65].

3.9. Generalization of Information on Existing Tools

Analysis of existing software tools for DT development allows for the classification shown in Figure 2. Modeling tasks in the power industry can be divided into levels according to the objectives (Figure 3). The most complex modeling is performed at the hardware level since complex physical processes must be considered [47]. Typically, the choice of tools for such modeling is limited. In the field of electrical engineering, COMSOL and Ansys are most commonly used to create mathematical computer models that describe the processes of electricity generation, conversion, transmission, distribution, and consumption. However, such deep detail is not always necessary. For example, creating a digital twin to optimize the topology of an electrical network [66,67] or optimizing reactive power [68,69] does not require the creation of detailed physical models of equipment.

Table 1. Comparison of tools of DT software development.

Name	Type	Scope of Application in the Power Industry	Features	Integration Ability	License
Ansys Twin Builder	Physical process modeling	Physical modeling for design and analysis of equipment	Combination of pre-installed basic and industry component libraries with custom ones	High	Commercial
COMSOL Multiphysics	Physical process modeling	Physical modeling for design and analysis of equipment	Analysis of individual and interrelated physical processes; multiphysics modeling. Widely used in electrical engineering	Low	Commercial; academic
AnyLogic	Modeling of interactions; platform	Simulation and optimization processes for smart grids, energy storage systems, equipment diagnostics, etc.	Multi-agent approach, dynamic modeling; widely used in the power industry	High	Commercial; personal learning edition (free)
SimManagment	Platform	Data aggregation, processing, and analysis	Designed to work with large volumes of data obtained in multidisciplinary research	Medium	Commercial
CML-Bench	Platform	Integration of various software into a single platform	Focused on the integration of various software in the field of creation and use of digital data	High	Commercial; academic
iTwin	Platform	Integration of various models	Real-time data processing; Support various formats of data for DT creation	Low	Commercial
ZIIoT	Platform	Integration of various software into a single platform	The platform is designed to collect, process, and analyze data from production facilities using IIoT and artificial intelligence	High	Commercial
Azure DTs	Platform	Data aggregation, processing, and analysis	DTDL as a language for DT development; Azure platform for cloud computing and machine learning usage	High	Commercial (Azure); open-source (DTDL)
Own open-source-based software	Any	Any	It is possible to create a product specifically for your needs and not depend on third-party developers	Maximum	Any

summarizes key aspects of the tools analyzed.

In the context of developing digital twins for the electrical grid, it is worth noting simulation tools for electrical networks such as Power Factory, Pandapower, Simscape Electrical, and PYPOWER [70,71]. However, with these tools, it is impossible to model processes at a higher level of the organization, taking into account market relations and other aspects that are usually considered at the level of a multi-agent approach. AnyLogic is primarily used for modeling interactions between various objects, such as power plants, energy storage systems, consumers, etc., rather than physical processes themselves.

A significant portion of software products positioned as DT creation tools are essentially platforms that enable the integration of diverse enterprise data, including 3D models of objects, physical models, monitoring system data, and software for working with models and data. If a company utilizes various software for modeling and analysis but lacks a unified process for their integrated application in building a desired DT, it is advisable to employ the above platforms that enable such integration and establish data exchange processes between applications.

At a theoretical level, a multi-layered architecture for the DT could be considered, where physical processes in the equipment would be modeled using, for example, COMSOL, simulation of electrical networks in PowerFactory, and interactions between objects in AnyLogic. Overall management would be carried out using CML-Bench. However, the cost of such a solution would be very high, and numerous specialists skilled in working with each system would also be required.

For electric power companies, it is crucial to ensure the integration of new software with existing software, such as SCADA, ERP, automated process control systems, internal equipment diagnostics, and electrical network simulation systems. Moreover, electric power facilities are critical infrastructure, making information security a top priority. Governments aim to achieve technological independence [72,73,74], which restricts the use of proprietary software developed by foreign companies. At the same time, the open-source solutions can be analyzed and modified to create a secure certified version.

It is worth noting separately that a digital twin, as a system for aggregating diverse data from a real object or multiple objects, opens up the possibility of applying machine learning methods [4,75,76]. There are many open-source frameworks available in machine learning that can be used to develop custom solutions.

Thus, existing open-source frameworks and libraries in the fields of numerical modeling, data analysis, and machine learning cover many of the tasks required for creating digital twins of power systems and their components. Exceptions may include tasks related to developing high-detail multiphysical models.

Certainly, developing one’s own software also requires significant investment. However, if a company is unsure about the need for a digital twin or it is being developed as part of a research project. It will be more cost-effective to create a prototype on which to conduct necessary experiments to make a final decision.

Thus, developing software for digital twins in the power industry based on open-source technologies can be the most effective choice for the following reasons:

• The ability to provide maximum flexibility and adaptation to the object and requirements;
• Considering legal requirements, industry standards, and company policies;
• Independence from third-party proprietary software;
• Gradual development of own code base and developments that can scale together with the company;
• The ability to use the full power of existing open-source solutions;
• Saving on expensive licenses if it is necessary to test a hypothesis or create only a prototype.

For development software for digital twins in the power industry, it is essential to choose standards to ensure maximum compatibility of solutions. In our view, DTDL is precisely the tool that should be used to design digital twins in this field. It has sufficient adoption, detailed documentation, and the necessary flexibility. Specifically, it is not tied to any programming language, while all major programming languages have tools for processing data in JSON format.

3.10. Current Trends and Challenges

Modern studies show that the development of digital twin technologies is closely linked to the application of artificial intelligence [4,31,33,36,75,76]. Digital twins enable the collection of vast amounts of diverse data, the analysis of which is impractical using traditional statistical methods. It is machine learning algorithms that are typically employed for the aforementioned tasks, such as assessing equipment condition, diagnosing faults, forecasting electricity generation and demand, and more. At the same time, it must be considered that DTs in the power sector result in creating data that are predominantly unlabeled. This causes the use of unsupervised learning methods [77] or semi-supervised learning methods [78]. Another approach is the generation of synthetic data [79]. However, this increases the risks of incorrect model training or misinterpretation of their operation [80].

Moreover, it should be noted that creating fully functional DT requires significant computational power to process and analyze data in real time or near real time [81]. In the power sector, this is particularly crucial for tasks related to relay protection [82], as insufficient decision-making speed can render the implementation of a DT pointless.

Aggregating large volumes of data and processing them quickly necessitates the implementation of cloud technologies. The cloud can be deployed on proprietary servers or those of service providers. Various options are possible:

• Infrastructure as a Service (IaaS). In this scenario, the developer of DT gains access to server resources and maximum flexibility in implementation. They are not dependent on software providers for DT development;
• Platform as a Service (PaaS). This is a common approach where the DT developer implements it on a specialized platform, such as solutions indicated in group #3 in Figure 2;
• Software as a Service (SaaS). Typically, creating DT requires more than just standalone software, so this option may only be suitable for specific tasks. For example, COMSOL can run in a cloud.

However, data transfer in such systems, storage of important information on servers, and the need to provide remote access to it are closely related to the problems of ensuring cybersecurity. These problems are the subject of articles [83,84,85].

Thus, the use of advanced machine learning methods capable of working with unlabeled data and ensuring comprehensive cybersecurity are the most important trends in the development of digital twins in the electric power industry. When evaluating projects for creating DTs, developers should comprehensively consider not only the development itself but also additional important issues: what methods to use for data processing and extracting valuable information; how to ensure infrastructure for fast data transmission, processing, and analysis; and how to protect the system from cyber threats.

4. Specific Example. Description of Power Transformer Models

As a result of the analysis of the digital platforms and services considered in the previous section, the authors proposed to use the DTDL language at the initial stage of creating digital twins of power systems and their elements. The DTDL format is designed to model and describe digital twins in order to ensure the effective integration of various types of digital twins within a single software solution in a specific subject area. The key objective of this data presentation format is to provide a simple and flexible integration of models in various fields while maintaining a complex system of their interrelations that reflects real objects, processes, and phenomena in the surrounding physical world [86].

The DTDL used the terms Interface, Command, Component, Property, Relationship, and Telemetry.

• Interface describes the contents (commands, components, properties, communication, and telemetry) of any DT. The interface encapsulates the entire model, representing a specialized data schema (dictionary) for the DT;
• Telemetry describes data sent from a real object, whether the data are a regular stream of current sensors or an output data stream such as occupancy, alert, or information message;
• Property describes the read-only and read/write-only state of DT. For example, the serial number of the device may be a read-only property; the desired temperature of the thermostat may be a read/write property. Because DT is used in a distributed system, the property not only describes the state of the DT but also describes the synchronization of this state between the various components that make up the distributed system;
• Command describes a function or operation that can be performed on DT. CommandRequest describes the input data for the command. CommandResponse describes the output data of the command;
• Relationship describes the relationship between DTs and allows the creation of graphics of DTs. Relationship differs from Component because it describes a reference to a single DT;
• Components allow the Interface to be composed of other Interfaces. Component differs from Relationship because it describes the content that is the part of the Interface, whereas Relationship describes the connection between two Interfaces. Component describes the inclusion of Interface in Interface “by value”. This means that cycles in Components are not allowed because the Component value will be infinitely large. The DTDL v3 Component cannot contain another Component;
• Shemas are used to describe the on-the-wire or serialized format of data in the DT interface. A full set of primitive data types and support for many complex schemas (Array, Enum, Map, and Object) are provided. Schemas described using the DTDL are compatible with popular serialization formats, including JSON, Avro, and Protobuf. Primitive schema provides a full set of primitive data types (boolean, date, dateTime, double, duration, float, integer, long, string, time), which can be specified directly as a schema property value in the DT model. Complex schemas are designed to support complex data types consisting of primitive data types. In DTDL v3, complex schemas are Array, Enum, Map, and Object. A complex schema can be specified directly as a schema property value or described in the interface schema set and specified in a schema property;
• Complex schema definitions are recursive. ElementSchema of an array can be Array, Enum, Map, Object, or any of the primitive schema types. The same definition can be applied to the MapValue schema and the Object field schema. The maximum embedding depth of complex circuits for DTDL v3 is five levels.

In order to identify resources and their elements, DTDL uses a special form of URI called a DT modeling identifier (DTMI) of the form <schema>:<path>;<version>. The schema is the lowercase string literal “dtmi”. The path is a sequence of one or more colon-separated segments. The version is a numeric value.

Digital twins that represent things in the physical environment can be defined using metamodels described using a specialized vocabulary in JSON-LD–the Digital Twin Definition Language in the Power Industry (DTDL-PI), which is based on the Digital Twin Definition Language (DTDL). JSON-LD is intended for direct use as JSON, as well as for use in Resource Description Framework (RDF) systems.

Metamodels are universal definitions for each type of entity that exists in the industry under consideration. Metamodels have names (e.g., “Power transformer” or “Temperature Sensor”) and contain elements such as properties, components, and relationships that describe the object’s purpose. Thus, each metamodel describes one type of entity in terms of its properties, relationships, and components.

Metamodels can be described in any text editor due to JSON format. DTDL-PI consists of a set of metamodel classes: Interfaces, Telemetry, Properties, Commands, and data types. Two top-level classes describe digital twins and their capabilities: CapabilityModel and Interface (represent a specialized data schema (dictionary) for the DTDL). Since DTDL-PI is based on JSON-LD, the JSON-LD context (the @context operator) is used to indicate the DTDL version used.

In order to demonstrate the proposed format for describing the DT, the metamodels of an electromagnetic, thermal, and hydrodynamics model of a power transformer were described. The models’ properties were selected based on [44,87,88].

Currently, digital twins in the power industry are not as relevant for power transformers as they are for generators, electric motors, and protection elements. We have chosen a power transformer as an example to demonstrate the syntax and principles of describing digital twins using the proposed DTDL-PI.

The data models for DT of electromagnetic, thermal, and hydrodynamic models of an oil-immersed power transformer are described in

Table 2. Electromagnetic model of an oil-immersed power transformer.

Name	Refresh Rate	Unit	Data Type	Dimension	Input Data	Internal	Output
Type	Constant	ID	Integer	(1)	NO	YES	NO
Phase voltage HV	Constant	kV	Float	(1)	YES	NO	NO
Total power of each phase	Hourly	kVA	Complex	(3)	YES	NO	NO
Geometric parameters	Constant	-	Class “Transformer geometroc parameters”	(1)	NO	YES	NO
Integral value of loss of power	Hourly	kW	Float	(1)	NO	NO	YES
Integral value of electrodynamic forces (axial, radial)	Hourly	N (newton)	Float	(1)	NO	NO	YES
Distributed value of the electric field strength	Hourly	V/m	Float	(n × 6)	NO	NO	YES
Distributed value of the magnetic field strength	Hourly	A/m	Float	(n × 6)	NO	NO	YES

,

Table 3. Thermal model of an oil-immersed power transformer.

Name	Refresh Rate	Unit	Data Type	Dimension	Input	Internal	Output
Type	Constant	ID	Integer	(1)	NO	YES	NO
Distributed heat power density value	On request to execute the calculation	kW/m3	Float	(n × 4)	NO	YES	NO
Transformer oil	Constant	-	Integer	(1)	NO	YES	NO
Hot spot temperature (HST)	On request to execute the calculation	°C	Float	(1)	NO	NO	YES
The maximum oil temperature	On request to execute the calculation	°C	Float	(1)	NO	NO	YES
Temperature field throughout the entire volume of the transformer	On request to execute the calculation	°C	Float	(n × 4)	NO	NO	YES

and

Table 4. Hydrodynamic model of an oil-immersed power transformer.

Name	Refresh Rate	Unit	Data Type	Dimension	Input	Internal	Output
Type	Constant	ID	Integer	(1)	NO	YES	NO
Transformer oil	Constant	-	Integer	(1)	NO	YES	NO
Oil consumption	On request to execute the calculation	m3/s	Float	(1)	NO	NO	YES
Oil velocity field throughout the entire volume of the transformer	On request to execute the calculation	m/s	Float	(n × 6)	NO	NO	YES

, respectively (n is the number of nodes in the computational grid).

The properties presented in Table 2, Table 3 and Table 4 allow for the specification of what data the computational model receives as input and at what frequency, what its internal properties are, and what it produces as a result of calculations. The actual computational model can be implemented in various software. The digital twin management software will wait for input data for this model in the specified format and pass them on to the software responsible for calculations.

The description of the electromagnetic model of a power transformer in the DTDL-PI language looks like this (a fragment of the full description is presented):

{

 “@context”: “dtmi:dtdl:context;3”,

“@id”: “dtmi:example: Transformer;1”,

 “@type”: “Interface”,

 “displayName”: “Transformer”,

 “contents”: [

  {

   “@type”: “Property”,

   “name”: “Type”,

   “refresh_rate”: “constant”,

   “schema”: “integer”,

   “unit”: “ID”,

   “description”: “Transformer type ID”,

   “input”: “False”,

   “internal “: “True”

   “output “: “True”

  },

  {

   “@type”: “Telemetry”,

   “name”: “Phase_voltage_HV”,

   “refresh_rate”: “constant”,

   “schema”: “Float”,

   “unit”: “kV”,

   “description”: “Phase voltage (HV - High voltage)”,

   “input”: “True”,

   “internal “: “False”

   “output “: “False”

  },

  {

   “@type”: “Telemetry”,

   “name”: “ Total_power”,

   “refresh_rate”: “hourly”,

   “schema”: “Complex Array”,

   “unit”: “kVA”,

   “description”: “ Total power of each phase (A, B, C)”,

   “input”: “True”,

   “internal “: “False”

   “output “: “False”

  },

  {

   “@type”: “Property”,

   “name”: “ Electric_field”,

   “refresh_rate”: “hourly”,

   “schema”: “Float Array”,

   “unit”: “kVA”,

   “description”: “ Distributed value of the electric field strength”,

   “input”: “False”,

   “internal “: “False”

   “output “: “True”

  },

 ]

}

5. Conclusions

Digital twins are a powerful tool for monitoring, analyzing, and managing power facilities and power systems. Using digital twins can increase the efficiency of the power system, improve their performance, improve the quality of customer service, reduce equipment-operating costs, and increase power system safety.

The paper presents an overview of tools for software development for digital twins in the power industry.

The following recommendations have been formulated by developers of digital twins in the power sector:

• For modeling complicated physical processes requiring a high level of detail and/or modeling various physical aspects together, it is advisable to use appropriate specialized software for physical simulation, such as COMSOL Multiphysics or Ansys;
• If the company already has a significant amount of software in modeling and digital twins, but integration and automation of the processes of its use are needed, DT platforms can be used, such as SimManager or CML-Bench;
• In the general case, taking into account the variety and power of open-source solutions for electrical engineering and the power industry, as well as the possibility of modifying their code to meet all requirements, it makes sense to develop software based on existing solutions.

In the latter case, there is a need to use some standard for describing digital twins because it is necessary to ensure uniformity in the data models used. This standard should be open, flexible, and suitable for both human understanding and machine processing. A language based on Digital Twin Definition Language can serve as such a standard. It can describe the characteristics and behavior of objects. It is licensed for commercial use under the terms of the MIT license. Introducing models and rules adapted to the industry into the DTDL will make it possible to create a branch specifically for the power industry (DTDL-PI).

As an example, the usage of the description language of digital twins in the power industry for electromagnetic, thermal, and hydrodynamic models of an oil-immersed power transformer was presented. The DTDL-PI does not directly describe mathematical models of equipment or electrical networks. However, it sets a specification that allows us to understand what data the models need and what results the models can produce. Precisely, this is necessary to connect various solutions (software for electrical equipment simulation, power flow calculation, ERP-systems software, data from IIoT and SCADA, etc.) into a unified information system that will serve as the software component of the DT.

Considering only the software part is a limitation of this study. Hardware is also crucial for DT development in the power industry. In the course of further research, it is planned to study and formulate hardware requirements based on the objectives of DT development and publish examples of elements of power systems in a DTDL-PI. In addition, digital twins in the power industry involve handling sensitive data. Therefore, an overview of data security and privacy issues is the additional direction for further research.