Real-Time Simulation and Hardware-in-the-Loop Testing Based on OPAL-RT ePHASORSIM: A Review of Recent Advances and a Simple Validation in EV Charging Management Systems

Abstract

Phasor-domain (RMS) simulations have become increasingly vital in modern power system analysis, particularly as the complexity and scale of these systems have expanded with the integration of renewable energy sources. ePHASORSIM, an advanced phasor-based simulation tool developed by OPAL-RT, plays a crucial role in this context by enabling real-time phasor-domain simulation and hardware-in-the-loop testing. To keep pace with these evolving needs, continuous efforts are being made to further improve the accuracy, efficiency, and reliability of ePHASORSIM-based simulations. These efforts include automating model conversion processes for enhanced integration with ePHASORSIM, extending ePHASORSIM’s simulation range with custom models, developing hybrid co-simulation techniques involving ePHASORSIM and an EMT simulator, enhancing simulation scalability, and refining HIL testing to achieve more precise validation of control and protection systems. This paper provides a comprehensive review of these recent advances. Additionally, the paper discusses the conversion of models from PowerFactory—a widely used and comprehensive modeling environment—to ePHASORSIM through both automated tools and manual methods using Excel workbooks, which has been discussed little in the literature. Furthermore, as ePHASORSIM is a relatively new tool with limited cross-validation studies, the paper aims to contribute to this area by presenting a comparative validation against DIgSILENT PowerFactory, with a specific emphasis on its application in electric vehicle charging management systems.

1. Introduction

The increasing integration of renewable energy sources and advanced power electronic devices, along with their associated fast-acting monitoring, control, and protection schemes and the requirement to maintain system stability under diverse operational conditions demand robust testing and validation methods to ensure the reliability and efficiency of modern power systems [1]. One widely adopted approach is the offline simulation of these systems using software tools such as MATLAB/Simulink [2], PSS/E [3], and DIgSILENT [4], among others, which allow engineers to evaluate these complex systems under various operating conditions before they proceed to the operational or manufacturing stage. This method offers significant advantages, including the ability to test numerous scenarios without the risks associated with physical prototypes, lower costs, and quicker iteration times. However, offline simulations have notable limitations, including the significant runtime due to the mathematical complexity of differential equations involved and discrepancies between simulated and real-time (RT) behaviors. Furthermore, conventional offline simulations cannot encompass every effect of hardware implementation, which can result in less reliable outcomes [5].

To address these limitations, fully digital RT simulation and hardware-in-the-loop (HIL) testing have emerged as essential tools. Fully digital RT simulation involves executing a model of a power system in real-time, where the simulator computes and updates system states within a fixed, short time step [6,7,8,9,10]. The time step required for RT simulation varies depending on the specific power system study. For very large networks, a time step of around 1–10 ms is typically sufficient for transient stability (TS) simulations. However, for systems involving high-frequency switching power electronics, much smaller time steps, often in the range of 1 $\mathsf{\mu }$s to 10 ns, are necessary due to the faster internal dynamics of these components [6]. The time steps required for different simulation studies are shown in Figure 1.

There are, however, several scenarios where a simple RT simulation may not suffice. Examples include systems that involve both fast and slow dynamic behaviors, such as power systems integrated with high-frequency switching power electronics, situations where computational resources are limited for simulating very large-scale power systems, or scenarios involving outages or blackouts where phenomena span from electromechanical to electromagnetic transients. In such cases, a multi-rate RT co-simulation approach can be adopted, where only the critical parts of the power system, such as flexible AC transmission systems (FACTS), high-voltage DC (HVDC), or distributed energy resources (DER) components, are modeled using EMT simulations with time steps on the order of microseconds, while the remainder of the system is modeled using phasor-domain simulations with time steps on the order of milliseconds [11,12,13,14,15].

However, there are scenarios where even fully digital RT simulations are not enough, and HIL testing becomes essential. This is particularly true when it comes to validating the performance and interaction of actual hardware components under simulated operational conditions. For instance, in systems requiring precise control validation, such as inverter control in DERs or protection schemes in HVDC systems, the physical hardware must interact with the simulation environment to ensure accurate and reliable operation. HIL testing can be subdivided into controller hardware-in-the-loop (CHIL) [16,17,18,19,20], where control hardware interacts with a simulated system, and power hardware-in-the-loop (PHIL) [21,22,23,24], which includes power transfer between simulated and physical components, providing a comprehensive and realistic testing platform. The basic concepts of CHIL and PHIL are shown in Figure 2 [6].

To support these advanced simulation techniques, the development of RT simulators has been crucial. The initial RT simulators were built on digital signal processors (DSPs) [25], reduced instruction set computers [26], and complex instruction set computers [27]. In 1991, RTDS Technologies Inc. [28] introduced the first commercial RT digital simulator using DSPs, which combined analog and digital components and was used to evaluate HVDC converter controllers. Subsequent developments led to the introduction of the digital transient network analyzer (DTNA) [29] for small-scale simulations and ARENE by Électricité de France in 1996 [30], which was capable of simulating high-frequency phenomena on standard multipurpose parallel computers. Around the same time, OPAL-RT Technologies [31,32] introduced a general-purpose processor-based simulator using MATLAB/Simulink, followed by similar approaches from other companies like dSPACE [33]. Among these advanced options, OPAL-RT stands out by offering four distinct simulation tools: ePHASORSIM, eMEGASIM, HYPERSIM, and eFPGASIM, each tailored to different applications based on the system size, simulation domain, and simulation step size. ePHASORSIM is specifically used for phasor-domain simulations, while the other tools are used for EMT simulations with different levels of detail (see

Table 1. Feature comparison of ePHASORSIM, eMEGASIM, HYPERSIM, and eFPGASIM simulation tools.

	ePHASORSIM	eMEGASIM	HYPERSIM	eFPGASIM
Application	Power Systems Simulation	Power Systems and Power Electronics Simulation	Power Systems Simulation	Power Electronics Simulation
Simulation domain	Phasor domain	EMT domain	EMT domain	EMT domain
Typical time steps	1–10 ms	10–100 $\mathsf{\mu }$s	5–100 $\mathsf{\mu }$s	200 ns–2 $\mathsf{\mu }$s
Modeling domain	Positive-sequence phasor domain	Three-phase time domain	Three-phase time domain	Three-phase time domain
Size of Study System	10,000 nodes/CPU core (max: 108,000 nodes)	30–40 three-phase nodes/core (max: 900 nodes)	75 three-phase nodes/core (max: 27,000 nodes)	128 switches/FPGA
Compatible modeling environments	Simulink, Excel, ETAP, PSS®E, CYME, Power Factory, FMU (Open Modelica and Dymola)	SPS/Simulink	SPS/Simulink, HYPERSIM	SPS/Simulink, PLECS, PSIM, and NI Multisim
Typical Type of Studies Performed	Wide-Area Monitoring Protection and Control, Power System Controls, Cybersecurity	Protection Systems, Power System Controls, MMC, Microgrid, Onboard Power Systems, Hybrid and Electrical Transportation, Cybersecurity	Protection Systems, Power System Controls, MMC, Wide-Area Monitoring Protection and Control, Cybersecurity, Microgrid, Distribution	Energy Conversion Controls, Hybrid and Electrical Transportation, Power System Controls

for details).

EMT simulations have long been a cornerstone in the analysis of power systems, as they provide detailed representations of fast dynamics and transient events like faults and switching operations. However, as power systems have evolved—especially with the integration of large-scale renewable energy sources—there has been a growing need for simulations that can address broader system-wide challenges more efficiently. Phasor-domain (RMS) simulations, like those enabled by OPAL-RT’s ePHASORSIM tool [34], have become essential in this context. Unlike EMT simulations, which focus on time-domain details, phasor-domain simulations simplify system dynamics by concentrating on steady-state sinusoidal behavior. They represent sinusoidal waveforms as phasors—complex numbers that capture both magnitude and phase—allowing for a significant reduction in computational complexity.

Today, OPAL-RT’s ePHASORSIM, whether used alone or in combination with an EMT simulator, plays a crucial role in real-time simulations and hardware-in-the-loop testing in power systems. However, to keep pace with the evolving needs of modern power systems, efforts to further enhance the accuracy, efficiency, and reliability of these studies are still ongoing. These include automating model conversion processes for enhanced integration with ePHASORSIM, extending ePHASORSIM’s simulation range with custom models, developing hybrid co-simulation techniques involving ePHASORSIM and an EMT simulator, improving simulation scalability, and refining HIL testing for more accurate control and protection system validation.

This paper reviews the latest efforts in these areas and highlights key examples based on OPAL-RT’s ePHASORSIM. Additionally, the paper discusses the practical aspects of converting PowerFactory models, which is one of the most popular modeling environments for power system simulation, to ePHASORSIM, both through automated processes and manual methods using Excel workbooks. Furthermore, given that ePHASORSIM is a relatively new simulation tool with limited cross-validation studies available, this paper aims to contribute to this area by presenting a comparative validation against DIgSILENT PowerFactory, particularly focusing on EV charging management systems.

The rest of this paper is organized as follows. Section 2 provides an overview of ePHASORSIM’s capabilities. Section 3 reviews recent advancements in the field. Section 4 discusses the conversion of PowerFactory models to ePHASORSIM through both automated and manual methods. Section 5 presents a comparative validation of ePHASORSIM against DIgSILENT PowerFactory, focusing on its application in EV charging management systems. Finally, the paper concludes in Section 6.

2. Opal-RT ePHASORSIM

ePHASORSIM is an advanced phasor-based simulation tool developed by Opal-RT for power system analysis and testing. It offers high-resolution simulation with millisecond-level time steps for accurate voltage/current and power measurements, large-scale network simulation for grids with over 100,000 nodes, and broad compatibility with environments like Simulink, Excel, PSS/E, CYME, ETAP, and PowerFactory (see Table 1 for details).

ePHASORSIM supports dynamic simulations in both offline and RT modes. RT simulations require OPAL-RT’s simulator hardware, which consists of a target computer optimized for RT computations and a host computer that serves as the user interface. The target computer, designed for high-performance computing, operates on an optimized Linux OS and is equipped with multiple computational cores and field programmable gate arrays (FPGAs) to handle the intensive calculations required for RT simulation. This setup ensures that each computational step is completed within a fixed time step, typically ranging from 1 to 10 ms, depending on the complexity of the simulation model. The host computer, on the other hand, provides the interface for designing, developing, and evaluating the simulation models before they are deployed on the target computer. The host computer also manages the communication between the simulation environment and physical hardware in HIL setups, which ensures seamless integration and accurate RT data exchange.

The basic method for importing data into ePHASORSIM is through an Excel workbook. A more straightforward approach, though potentially more costly due to the need for expensive licenses, is to import models directly from compatible simulation packages, such as PowerFactory, PSS/E, and CYME. In this way, particular components and controllers are supported. For instance, in PowerFactory, a model including components such as buses, loads, synchronous machines, lines, transformers, switches, and standard machine controllers (governors, automatic voltage regulators (AVRs), and power system stabilizers (PSSs)) can be directly and automatically imported. However, non-standard controllers, such as those defined in DIgSILENT Simulation Language (DSL) scripts in PowerFactory, cannot be automatically imported.

Figure 3 provides an overview of key research trends in the application of ePHASORSIM for power system analysis and testing, as well as in streamlining and enhancing the accuracy and efficiency of simulations with ePHASORSIM. These trends will be discussed in detail in the next section.

3. Review of Recent Advances

3.1. Automated Model Conversion for Enhanced Integration with ePHASORSIM

In [35], the focus is on the development of a reduced-order model of the Great Britain transmission system to enable automated model conversion and facilitate RT simulation and HIL testing using the OPAL-RT ePHASORSIM. The main challenges were that the original reduced-order model developed by National Grid in 2012 using DIgSILENT PowerFactory contained non-standard, user-defined controllers, complex HVDC link models, and a very large number of nodes. To deal with these challenges, replacing non-standard, user-defined controllers (such as AVRs, GOVs, and PSSs) with standard controllers supported by ePHASORSIM, tuning the controller parameters to match the original model’s dynamic response, and substituting complex HVDC link models with simpler static load/generator equivalents were proposed in [35]. Additionally, the number of nodes and the topology of individual zones were simplified to reduce the computational power required for RT simulation. It was demonstrated that with these changes, the reduced-order PowerFactory model of the GB transmission system can be automatically imported into ePHASORSIM for RT simulation and potential HIL studies. Comparative tests using models in PowerFactory and ePHASORSIM also showed that the implemented changes had a minimal impact on accuracy. The work presented in [35] was later expanded and elaborated upon with additional details in [36].

In [37], the authors presented a detailed software process for the automatic conversion of distribution network models from a quasi-static time-series tool (OpenDSS) into an ePHASORSIM model. The main challenges addressed in the conversion process include the handling of diverse data formats and ensuring the accuracy of model representation in the RT simulator. To overcome these challenges, the authors developed a Python-based tool that utilizes regular expressions and the Pandas library to parse and convert the OpenDSS files into the format required by ePHASORSIM. This involved creating dictionaries for line configurations, extracting and transforming switch data, and converting load and transformer information into three-phase representations, even when only single-phase data were available. The conversion process also included generating initial conditions for voltage magnitudes and angles from OpenDSS output files. The effectiveness of this conversion was validated by comparing power flow results between OpenDSS and ePHASORSIM for a sample distribution feeder, which showed minimal errors in voltage magnitude and angle.

In [38], the authors extended the work presented in [37] by focusing on overcoming errors encountered during the conversion process when applied to a larger-scale system. They developed a customized Python script (version 3.7) to enhance the efficiency of the conversion process and reduce complexity. Key issues addressed include handling islanded networks, representing full impedance models of transformers and lines, and converting single-phase components to three-phase equivalents. The enhanced conversion process was validated using a feeder model consisting of 2330 buses, 1785 lines, 372 transformers, 347 loads, and 248 PV inverters. The paper demonstrated that with these enhancements, the OpenDSS feeder model could be effectively converted into an ePHASORSIM model. Comparative simulations between OpenDSS and ePHASORSIM showed minimal errors, which validates the accuracy of the conversion process for a large-scale system.

In [39], the process of automatic translation and validation of OpenDSS models into ePHASORSIM spreadsheets using CIMHub was presented. CIMHub is a toolset designed for translating electric power distribution system models between various formats by using the IEC Standard 61970/61968 Common Information Model (CIM) as a central “Hub”. The process begins by exporting the OpenDSS model in CIM XML format, which captures all essential network details. This XML file is processed with CIMHub, which converts the data into a triple-store database for efficient querying. A Python script then translates the data into the format required by ePHASORSIM. To ensure the model’s accuracy, power flow solutions between the original OpenDSS model and the ePHASORSIM model are compared.

3.2. Extending ePHASORSIM’s Simulation Range with Custom Models

ePHASORSIM has certain limitations, particularly in its relatively limited library of built-in models for components such as generators, governors, AVRs, and PSSs, among others. This can be restrictive when simulating complex power systems with advanced or non-standard controllers. To overcome this, ePHASORSIM allows users to create custom models in environments like OpenModelica or Dymola using the Modelica language. These models are then exported as functional mock-up units (FMUs) and linked to ePHASORSIM, which enables accurate simulation of complex power systems with advanced or non-standard controllers. Several works have contributed in this area and validated the effectiveness of these custom models within ePHASORSIM for advanced power system simulations. For instance, in [40,41], a study implemented a virtual synchronous machine (VSM) model using OpenModelica, exported it as an FMU, and successfully integrated it into ePHASORSIM. A benchmarking exercise against DIgSILENT PowerFactory revealed that the two platforms had minimal deviations during transient simulations. In [42], a custom doubly fed induction generator (DFIG)-based wind farm model was developed using OpenModelica, exported as an FMU, and integrated into ePHASORSIM. This development was motivated by the need to address the limitations of commercial software, such as PSS/E [3], including the lack of built-in models for synthetic inertia, the inflexibility in adjusting initial conditions for de-loading, and the absence of real-time simulation and interactive control capabilities. Several other works and contributions in this area can be found in [43,44,45].

3.3. ePHASORSIM-Based RT Simulation

In [46], the focus was on simulating the interactions between transmission and distribution (T&D) networks in RT using OPAL-RT’s ePHASORSIM. The need for such an integrated simulation arises from the increasing influence of dynamic loads and DERs in distribution networks, which significantly impact the operation of transmission systems. Note that traditional tools often model and analyze T&D networks separately, which fails to capture the intricate interactions between them. To address this challenge, inspired by [47], the authors of [46] proposed a method that integrates T&D models using dynamic Thevenin equivalents (see Figure 4). This approach was demonstrated by first modifying a positive-sequence transmission network model created in PSS/E and an unbalanced three-phase distribution network model developed in CYME for compatibility with ePHASORSIM, validating each individually, and then combining them and validating them together using OPAL-RT’s ePHASORSIM simulator in real-time using a fixed step time of 10 ms. The study demonstrates the capability of ePHASORSIM to perform RT dynamic simulations of large-scale, integrated T&D networks. However, it is important to note that a fixed step-time of 10 ms may not always effectively capture the fast dynamics of DERs in distribution networks.

In [48], the authors had the same motivation and research focus as in [46], namely, an integrated approach to studying T&D networks. However, contrary to [46], which relied on a single-simulation platform, a co-simulation framework, as depicted in Figure 5, is employed, in which the transmission system model is imported from PSS/E into OPAL-RT’s ePHASORSIM, and the distribution model is imported from CYME. The integration of T&D models follows a similar approach using dynamic Thevenin equivalents. Communication between the OPAL-RT target servers and the host computers is handled using the legacy Modbus interface, with the TCP/IP protocol facilitating communication between the two host computers conducting the joint simulation. The latency in this communication setup is 21 ms. Compared to [46], the approach proposed in [48] allows for the simulation of larger systems and the use of resources that are geographically distributed. However, it is more expensive and may experience communication delays that impact the simulations.

In [49,50], the research focused on developing an adaptive Kalman filter (AKF)-based dynamic estimator of states (DES) using phasor measurement unit (PMU) measurements and validating it in real-time using OPAL-RT ePHASORSIM. The validation process involves several key steps: first, the network and dynamic data of the test power system are defined and entered into an Excel workbook. Then, the ePHASORSIM solver block is incorporated into the Simulink model to process these data and generate the necessary simulation files. The model is divided into three subsystems to enable efficient parallel processing: the master subsystem includes the solver and handles the generation of system states and PMU measurements, the slave subsystem distributes model elements across different cores and executes the DES using AKF algorithms, and the console subsystem manages real-time monitoring and control sequences. The DES was tested under different disturbances, such as three-phase faults and load changes on a New England 39-bus system. It was confirmed that the DES could complete state estimations well before the arrival of the next set of PMU measurements at both 100 and 25 frames per second refresh rates. However, since the validation was conducted on relatively small test systems, it remains uncertain whether the same performance can be consistently achieved in larger and more complex power systems.

In [51,52], the research explored the challenges of implementing wind power plant (WPP) voltage control systems using Opal-RT ePHASORSIM in real-time. One of the primary challenges is the selection of appropriate sampling times for different components of the WPP voltage control system, which must balance the need for capturing relevant system dynamics against the computational limitations of the real-time simulator. The study emphasizes that the wind turbine (WT) control system requires a very small sampling time of 1 ms to accurately simulate fast dynamics, while the overall WPP controller can efficiently operate at a slower rate of 100 ms. Managing these multi-rate simulations requires careful use of rate transition blocks in Simulink to ensure data integrity without introducing significant delays that could impair the control system’s performance. The paper also highlights difficulties in distributing computational tasks across multiple CPU cores to prevent overruns and the complexity of choosing suitable discretization methods to ensure system stability and performance. The research found that the forward Euler method resulted in instability, whereas the backward Euler and Tustin methods were more stable, with the Tustin method specifically introducing some overshoot in the dynamic behavior.

3.4. Hybrid RT Simulation Using ePHASORSIM and EMT Simulators

Multi-rate co-simulation enables the simultaneous simulation of multiple interconnected systems operating at different time steps. This approach is particularly useful in power systems, where components such as distribution grids and inverter-based DERs have inherently different dynamic characteristics and computational requirements. In this context, OPAL-RT’s ePHASORSIM can handle phasor-domain simulations of the distribution grid with time steps on the order of milliseconds, while an EMT simulator such as OPAL-RT’s eMEGASIM or Simscape Power Systems toolbox from MathWork can accurately model the fast dynamics of inverter-based DERs with time steps in the microsecond range.

In [53], the research focuses on the challenges and solutions for RT hybrid TS (phasor domain) and EMT simulation of integrated T&D power grids. The study emphasizes the necessity of detailed EMT modeling for components with fast dynamics (e.g., microgrids), typically requiring time steps of a few microseconds, and the complementary need for TS modeling of larger grid sections with longer time steps in the millisecond range to reduce computational load and ensure the feasibility of simulating the entire grid in real-time. Therefore, a hybrid multi-rate simulator that integrates TS and EMT models by using OPAL-RT’s ePHASORSIM for TS simulation and the Simscape Power Systems toolbox from MathWorks for EMT simulation is proposed in [53]. The system is split by modeling zones with power electronic devices using EMT simulators and the rest with TS simulators. These zones are coordinated by parallel communication protocols that update equivalent models at each time step. Two test cases—a transmission grid with 100 nodes and a synthesized T&D system with over 2700 nodes—demonstrate the hybrid simulation’s ability to accurately represent system dynamics and the benefits of detailed EMT modeling in broader TS simulations.

The work in [54,55] is quite similar in nature and motivation to that of [53], as both focus on improving the trade-off between simulation accuracy and computational efficiency. However, a key difference is that [54,55] employ eMEGASIM as the EMT simulator. The interaction between the eMEGASIM and ePHASORSIM solvers in these works is managed through a five-step process, which includes prediction, calculation, and convergence steps to ensure that the results from both solvers are accurately integrated. Time interpolation and phasor extraction techniques are used to translate data between the two solvers. In terms of performance, the hybrid model presented in [54] shows a significant improvement in real-time capabilities over a pure EMT simulation. Specifically, while the EMT model with three inverters required approximately 62% CPU core usage, the hybrid model reduced this to 27.45%, nearly halving the computational load.

In [56], the researchers developed an asynchronous RT co-simulation platform for modeling interactions between transmission, distribution, and microgrid systems. It uses OPAL-RT’s ePHASORSIM to simulate interactions between T&D networks in real-time at a millisecond-level time step, and eMEGASIM to simulate microgrid inverter electromagnetic transients at a 100-microsecond time step. The platform also leverages a MATLAB-based microgrid controller interfacing through Modbus communication to simulate controller logic and its impact on HIL testbeds. For system spatial coupling, at each point of common coupling, an AC source represents the upper system, passing voltage magnitude and phase angles to the lower system, while load consumption from the lower systems are fed back to the upper systems (see Figure 6). Temporal coupling is managed by inserting communication buffers between subsystems to handle calculation delays. The co-simulation platform in [56] couples the simulation of transmission, distribution, and microgrid systems down to the DER level, which allows for precise quantification of the impact of communication errors and delays on system performance.

In [57], the research in [56] was extended by partitioning the entire system into several OPAL-RT simulators and analyzing the effects of communication delays, simulation time step requirements, information exchange frequency, and control sequence design on the performance of a networked HIL test system.

In [58], the research focuses on demonstrating the feasibility of an RT, multi-domain (RMS and EMT), multi-rate (milliseconds and microseconds), and multi-platform (OPAL-RT and RTDS) co-simulation. The goal is to maximize RT simulator computing power for complex power system studies and enable RMS-EMT RT HIL tests of protective relays, with the external power system in an RMS solution and the system of interest in an EMT solution. The method uses ePHASORSIM for RMS simulation and RTDS for EMT simulation, with analog inputs and outputs facilitating communication between the simulators. The interface between the RMS and EMT simulations is established using a transmission line interfacing technique that utilizes the built-in transmission line models available in both simulators. This technique eliminates the need for hybrid RMS-EMT transmission line development and allows the decoupling of large systems for parallel computation by expressing the transmission line as separate resistive Norton or Thevenin circuits using previous time step information. The co-simulation system was validated for HIL testing of protective relays by modeling an electrical system with both simulators—RTDS handling the EMT side and OPAL-RT managing the RMS side—and feeding the amplified RTDS outputs into the protective relay while observing its RT response. Tests showed that the device under test’s behavior in the co-simulation setup was identical to its behavior when the entire system was modeled by RTDS, thus confirming the accuracy of the co-simulation approach. However, the method has limitations, as analog interfaces are susceptible to noise, have scalability issues, and are not optimized for latencies. In [59], these limitations are addressed by developing a low-latency inter-platform fiber-optic communication link using the Xilinx Aurora protocol. This link enables a fast, noise-free, and scalable OPAL-RT-RTDS interface for RMS-EMT co-simulation.

3.5. ePHASORSIM-Based HIL Testing

In [60], the research focuses on validating a model of the GB transmission system using PMU data and HIL testing facilitated by the OPAL-RT ePHASORSIM. The study aimed to accurately simulate fast frequency phenomena (F2P)—including electromagnetic, electromechanical, and mechanical phenomena—observed during system disturbances and to ensure the reliability of loss-of-mains (LoM) protection relays. To enable HIL testing, a standard IEEE nine-bus model was adapted to GB conditions and converted to ePHASORSIM. This process involved converting machine and controller models as well as network configurations. The voltage at specific buses was exported to the analog output of the simulator and amplified for LoM relay testing. The HIL tests demonstrated the capability to accurately reproduce system dynamics and evaluate relay performance under various disturbance conditions and inertia scenarios. The results showed clear boundaries for relay tripping based on disturbance severity, which provides valuable insights into LoM relay behavior and overall system stability.

In [36], the OPAL-RT ePHASORSIM-based HIL testing is extended to the reduced GB system model. The study highlights the significant influence of both local and inter-area oscillations on LoM relay sensitivity and reliability, which underscores the necessity of updating protection settings to adapt to the evolving dynamics of power systems, especially with the increased integration of renewable energy sources.

In [61], the research aims to validate the performance of a PMU-based special protection scheme (SPS) for the Colombia–Ecuador interconnection using HIL testing with the OPAL-RT ePHASORSIM. The study focuses on ensuring the SPS can handle various operational scenarios, including generation loss, overloads, and topological changes in the network. To achieve this, a detailed testing architecture was developed, involving the simulation of PowerFactory models of both the Colombian and Ecuadorian power systems in real-time using OPAL-RT ePHASORSIM and interaction with actual protection equipment. The HIL verification in [61] encompassed over 2000 operational scenarios, including real fault events recorded by the previous SPS. Each scenario was first modeled in PowerFactory and then converted to ePHASORSIM. The voltage and current signals at specific substations were up-sampled to create sinusoidal waveforms, amplified, and then fed into the SPS. A Python-based tool was employed to assess the SPS’s performance by grading its response to these scenarios. The results demonstrated the SPS’s capability to maintain system stability and provided valuable insights into its operational effectiveness.

The study conducted in [62] investigates the effects of virtual inertia provided by an HVDC converter terminal on the Nordic power system using HIL testing. The HIL setup includes an RT simulation of the Nordic 44-bus system on OPAL-RT’s ePHASORSIM, with the simulated phasor voltage at a specific node converted to a stationary frame three-phase voltage. This voltage is then used as a reference for a grid emulator, which generates and feeds it into a scaled modular multilevel converter (MMC) prototype representing the HVDC terminal. To provide virtual inertia, the control method uses the derivative of the locally measured grid frequency to adapt the power reference for the converter terminal. The study examines the impact of power injection by the converter on the frequency dynamics of the power system. The results demonstrate that the HVDC converter, equipped with appropriate control strategies, can significantly enhance the power system’s dynamic response during large load transients, specifically by improving the frequency nadir and reducing the rate of change of frequency.

In [63,64,65,66,67], the studies emphasize the critical role of ICT in boosting the reliability, efficiency, and resilience of smart grids with high renewable energy integration. These papers explore various aspects of ICT integration, such as the implementation and management of heterogeneous communication networks that facilitate reliable data exchange between different components of the power grid, the use of advanced data management systems for the collection, processing, and analysis of vast amounts of real-time data generated by distributed energy resources and grid sensors, and the deployment of sophisticated real-time system monitoring and control mechanisms that enable dynamic responses to grid conditions, enhance system observability, and improve decision-making processes in both normal and contingency scenarios. All of these works leverage OPAL-RT’s ePHASORSIM for HIL testing and validation. For instance, the research in [64] specifically explores the impact of communication delays and packet losses on the performance of distributed voltage control schemes. The RT-HIL setup employed in this study is particularly comprehensive, incorporating an aggregator hardware platform based on Bachmann’s M1 controller, which is a widely recognized standard in the renewable energy industry. This platform interfaces with the OPAL-RT system that hosts a real-time model of the benchmark distribution grid, which includes both wind power plants and photovoltaic systems. A critical element of the setup is the RT ICT Emulator, developed with KauNet, which accurately simulates network conditions by introducing realistic delays, packet losses, and other communication impairments. This setup enables a detailed evaluation of how such communication conditions impact the coordination of voltage control across the grid.

3.6. Persistent Challenges

Despite considerable research efforts, some challenges still persist in the application of ePHASORSIM for real-time dynamic simulation and hardware-in-the-loop testing. These challenges require ongoing efforts to improve the tool’s capabilities:

• Limited Support for Non-Standard Components: ePHASORSIM’s built-in library for standard components like generators, governors, AVRs, and PSSs is sufficient for many conventional systems but falls short when more advanced or custom control systems are involved. Although integrating custom models via FMUs has mitigated some issues, the creation, export, and import of these models is still a complex process. More efforts are needed to simplify and improve this process.
• Model Conversion Complexity: While progress has been made in automating model conversions from compatible software environments, non-standard controllers and complex components still present significant challenges. Models with custom controllers, such as those developed using DSL scripts in DIgSILENT PowerFactory, or complex systems like HVDC links, often require manual redefinition, substitution, or simplification—a process that can be both labor-intensive and technically demanding. Moreover, while these simplifications enable real-time simulation, they may compromise the accuracy of the simulations, ultimately limiting seamless integration with ePHASORSIM.
• Limited Data Format Compatibility: Converting models from non-compatible software into ePHASORSIM often requires additional steps to bridge differences in data formats. For example, models from platforms like OpenDSS must be translated into intermediate formats, such as CIM XML, before being processed into ePHASORSIM-compatible spreadsheets using custom scripts. This multi-stage process not only adds complexity but also increases the likelihood of errors during model conversion.
• Time Step Synchronization Challenges: In hybrid multi-rate simulations involving ePHASORSIM and an EMT simulator, temporal synchronization poses a challenge. Specifically, the asynchronous connection between ePHASORSIM and other simulators can lead to delays in data exchange, which affects the overall accuracy of the co-simulation. Reducing the sampling time may alleviate the issue to some extent, but it requires higher computational resources, which may further complicates the simulation setup.

4. PowerFactory Model Conversion to ePHASORSIM

PowerFactory [4] is a widely used software package for the analysis and testing of power systems. Therefore, in this section, the conversion of PowerFactory models to ePHASORSIM will be briefly discussed. Both the automatic conversion and the conversion using an Excel workbook will be covered. This discussion serves as an example for similar conversions from other software packages.

4.1. Automatic Conversion Using Built-In Importing Tools

With the appropriate licenses, the conversion of the PowerFactory model to ePHASORSIM can be carried out automatically, as illustrated in Figure 7. The initial step in the conversion process is the creation of the network model using the graphical user interface in DIgSILENT PowerFactory. However, it is important to note that non-standard controllers defined in DSL scripts cannot be automatically converted to ePHASORSIM and require manual redefinition later. Additionally, not all complex components (e.g., power electronics converters) can be directly added to the model; they may need to be replaced by simpler static load/generator equivalents in the model.

Once the model is complete, it is exported using DGS (DIgSILENT Interface for GIS and SCADA) according to the export definitions specified by OPAL-RT. It is important to note that DGS files can be based on various formats, such as MS Access, EXCEL, ASCII, or XML. In Figure 7, the XML format is illustrated to demonstrate the export process. This exported model is then imported, along with a solver/pin configuration, into a Matlab/Simulink environment containing the ePHASORSIM solver.

This conversion process may leverage the Unified Database (UDB) developed by OPAL-RT, which serves as a central repository for network data and supports the automated import of network data, model parameter obfuscation, and domain conversion—essential for creating RT simulation models from offline data [68]. Note that the UDB parses model data from PowerFactory DGS files and other types of power system models (e.g., CYME or PSS/E models) and uses a sophisticated mapping engine to translate components and their attributes into a user-defined intermediate representation. This intermediate representation is stored in a PostgreSQL database and subsequently exported as .opal files for use with the ePHASORSIM solver [69].

Figure 7. Workflow for automatic conversion of PowerFactory models to ePHASORSIM using the Unified Database (UDB) developed by OPAL-RT [69].

Figure 7. Workflow for automatic conversion of PowerFactory models to ePHASORSIM using the Unified Database (UDB) developed by OPAL-RT [69].

4.2. Conversion Using Excel Workbook

Without the appropriate licenses, the conversion can be performed using an Excel Workbook. Additionally, using an Excel workbook for conversion can be advantageous in situations where greater customizability is required. For example, built-in importing tools for PowerFactory only support three-phase balanced sources in the phasor domain. However, describing the entire system with an Excel file allows for modeling unbalanced voltage sources, which is essential for accurately modeling unbalanced power systems [70].

Whether due to a lack of licenses or to benefit from higher customizability, the initial steps—creating the network model in DIgSILENT PowerFactory, redefining non-standard controllers defined in DSL scripts, replacing complex network models with simpler equivalents, and exporting the model using DGS—in the conversion using an Excel Workbook are similar to those described in the automatic conversion process in Section 4.1. However, the DGS file format should be set to Excel.

It is important to note that the DGS file exported from PowerFactory in Excel format is not directly compatible with the Excel file required for import into the ePHASORSIM solver. Thus, an intermediate step is necessary to translate the parameters from the PowerFactory Excel output to the ePHASORSIM Excel file.

Table 2. PowerFactory Excel file sheets and definitions.

Excel Sheet	Definition
General	Basic project information
BLKDef	Definitions for blocks
ElmComp	Component information
ElmDsl	Exciter and governor parameters for generators
TypVt(1)	Information about wind power plants
Elmlne	Line placement, length, and type
ElmLod	Load placement and PQ values
ElmNet	Nominal frequency of the grid
ElmShnt	Capacitor banks and shunt filters
ElmSym	Generator placement, PQ values, and type
ElmTerm	Bus names and nominal voltages
ElmTr2	Transformer placement and type
StaCubic	Connections of elements to buses
StaSwitch	Switch information
TypLne	Line specifications including rated voltage, resistance, and reactance
TypLod	Load types
TypSym	Synchronous machine parameters
TypTr2	Transformer parameters

and

Table 3. Opal-RT ePHASORSIM Excel File Sheets and Definitions.

Excel Sheet	Definition
General	Includes fundamental details of the power system, such as the base frequency and MVA.
Pins	Details the outgoing and incoming data for ePHASORSIM Solver. Outgoing pins monitor measurements or status, while incoming pins send control commands or fed in voltage/current/power signals to the simulator.
Bus	Lists bus IDs along with their voltage and angle information for initializing the simulation.
Vsource Three-Phase	Contains information on the substation bus and voltage, including series impedance.
Current Injector	Describes buses and current source IDs, such as distributed generators and PV. These sources need to be modeled in Simulink and linked to the ePHASORSIM environment.
Load Three-Phase	Specifies three-phase loads, breaking them down into constant impedance, constant current, and constant power components.
Shunt Three-Phase	Used to model shunt devices like capacitor banks and reactors.
Line Three-Phase	Provides details on three-phase lines, including overhead, underground, and service lines, modeled as pi-sections.
Transformer Three-Phase	Includes information on transformers in the feeder, with capabilities for voltage regulation via external tap position signals.
Switch	Describes breakers and disconnects, indicating their open (0) or closed (1) status.
Bus Faults Three-Phase	Used to simulate various types of balanced and unbalanced faults in three-phase systems, allowing faults to be applied at buses through external signals.

provide descriptions of the essential sheets in these Excel files and the information they contain [37].

The translation process from PowerFactory Excel file sheets into ePHASORSIM Excel file sheets requires careful mapping of parameters and conversion of units to ensure compatibility with the ePHASORSIM environment. For instance, in ePHASORSIM Excel file, everything is in system p.u. except for machines (including exciter, Turbine, and Governor), so most values require some transformation. Below is a summary of some key tasks for converting the PowerFactory Excel File to an Opal ePHASORSIM Excel File:

• System Base and Frequency: Set up the system power base in the General sheet. The frequency can be obtained from the ElmNet sheet.
• Buses: Copy bus names from the ElmTerm sheet. Set initial voltage magnitudes and angles using generator rated voltage where applicable.
• Generators: Map generator connections using the object IDs from ElmSym and StaCubic sheets. Transfer parameters from TypSym, while adjusting for the system power base.
• Loads: Transfer load parameters from ElmLod to the Load sheet. For shunt capacitors/filters, use the ElmShnt sheet.
• Lines: Convert line parameters from ElmLne and TypLne to the Line sheet, while adjusting resistance, reactance, and susceptance to per-unit values.
• Transformers: Transfer transformer parameters from ElmTr2 and TypTr2 while adjusting resistance and reactance for the system power base.

Note that the ePHASORSIM Excel file requires fewer sheets as it consolidates information from both Elm and Typ sheets in the PowerFactory Excel File into single sheets.

The transformation from PowerFactory Excel file sheets into ePHASORSIM Excel file sheets can be automated using an m-file or Python script. These scripts systematically read the PowerFactory Excel file, process the data according to the required mappings and unit conversions, and output the correctly formatted ePHASORSIM Excel file. This automation significantly reduces manual effort and ensures accuracy in the conversion process. At the SMART ENERGY SYSTEMS LABORATORY of AAU Energy [71], a software tool based on a MATLAB m-file has been developed to automate this transformation.

5. Comparative Analysis of EV Charging Management Using ePHASORSIM and PowerFactory

Given the limited cross-validation studies, especially in the domain of demand response control, this section offers a comparative validation of ePHASORSIM against DIgSILENT PowerFactory, with a particular emphasis on its application in electric vehicle charging management systems.

5.1. Background and Context

In Denmark, efforts to reduce transportation-related emissions have driven a significant increase in EV adoption. For example, in the last six months of 2023, 88,720 vehicles were registered, with 41% being EVs and 9% PHEVs [72]. This adoption is even higher in the household sector, where 49% of registered vehicles are EVs and 9% are PHEVs.

Danish households benefit from time-of-use tariffs for electricity consumption, which incentivize them to charge their EVs during periods of lower electricity prices. However, this can lead to a scenario where many users charge their EVs simultaneously when prices are low, potentially overloading the low-voltage distribution network. To prevent this scenario and avoid immediate grid reinforcement needs, implementing an appropriate control system is crucial.

One potential control solution is the use of droop control based on EV’s local terminal voltage. Since the electric distribution network consists of radial feeders with higher resistance, voltage at various nodes of the feeder decreases downstream in proportion to the loading. Hence, a droop coefficient based on the voltage at the common coupling point of the EV charger can be utilized to protect against undervoltage. In the following sections, droop control based on local terminal voltage will be further explained. Then, using a test grid of eight households in a radial feeder, the impacts of this control will be analyzed through simulations from DigSILENT PowerFactory and ePHASORSIM, with the results compared.

5.2. Test Grid

The test system used to study the effects of EV charging under droop control consists of a radial feeder serving eight households. The single-line diagram of this grid is shown in Figure 8, which is the model of the network in the PowerFactory environment. The network features a 0.1 MVA, 10/0.4 kV transformer. Each EV in the system has a rated charging capacity (Prated) of 11 kW and a battery capacity of 62 kWh. The lines and cables connecting the households are all 100 meters in length. Additionally, the system includes two bulk loads, labeled as Other Load 1 and Other Load 2, connected to respective terminals as part of other radial feeders. The daily electricity consumption of the household loads is detailed in

Table 4. Daily Electricity Consumption of Household Loads.

Load Name	Consumption (kWh/day)
H01	15.42
H02	14.03
H03	11.70
H04	11.42
H05	9.23
H06	5.68
H07	12.13
H08	8.75
Other load 1	474.2
Other load 2	124.8

.

5.3. Control Architecture

The architecture for simulating EV charging with droop control is shown in Figure 9. The controller computes the droop coefficient based on the voltage at the EV charger’s connection point and then uses this coefficient to adjust the EV’s charging power to ensure efficient load management on the distribution network. In practice, this controller may communicate information using various human–machine interface technologies, such as mobile applications, hardwired connections, and cloud services, among others.

5.4. EV Modeling

When an EV is connected to the charging station, its electrical load is modeled as a battery with a defined capacity. The initial state of charge (SOC) of the EV is estimated from its depth of discharge (DOD), which reflects the driving profile and distance traveled before charging, as follows:

$$SO{C}_{ini}=100\%-DOD$$

In this study, the DOD values are known and used to accurately determine the SOC. The SOC during charging ($SOC\left(t\right)$) is determined by integrating the charging power ($P_{char}$) over time, relative to the battery capacity ($C_{bat}$):

$$SOC\left(t\right)=SO{C}_{ini}+{\displaystyle \frac{{\int }_0^t{P}_{char}\left(t\right)dt}{C_{bat}\times 3600}}$$

Note that the charging power ($P_{char}$) is proportional to the droop coefficient ($k_t\left(t\right)$) and the rated charging power ($P_{rated}$), as expressed below:

$$P_{char}\left(t\right)=k_t\left(t\right)\times P_{rated}$$

We apply the voltage droop control strategy for managing EV charging power. This approach relies on the terminal voltage at the EV’s coupling point ($V_{poc}\left(t\right)$). As shown in Figure 10, the droop coefficient for voltage control is activated when $V_{poc}\left(t\right)<0.98pu$.

To prevent rapid changes in power output, the droop coefficient ($k_{droop}\left(t\right)$) is filtered using a low pass filter, defined in the Laplace domain as follows:

$$k_t\left(s\right)={\displaystyle \frac{k_{droop}\left(s\right)}{1+sT}}$$

where T is the time constant. This filtering ensures a stable and controlled adjustment of the EV’s charging power based on network conditions.

5.5. Simulation Results from PowerFactory and ePHASORSIM

In this section, we describe the process of carrying out the simulations and present the results. Two scenarios were implemented:

• EV with No Droop Control: EVs are present but without droop control.
• EV with Droop Control: EVs are present, and droop control is applied.

For each scenario, the simulation results from PowerFactory are compared with those from ePHASORSIM. The single-line diagram of the test grid modeled in DIgSILENT PowerFactory is shown in Figure 8, where the EV controllers are implemented using DSL scripts. For the ePHASORSIM simulation, the following procedure needs to be performed to build the model:

• The network model in PowerFactory, excluding EVs, their controllers, and local loads, is exported using the DGS, configured to output data in Excel format according to the export definitions specified by OPAL-RT.
• The exported PowerFactory Excel sheets are then converted to OPAL-RT ePHASORSIM-compatible Excel sheets based on the procedure described in Section 4.2. Note that in the “Pins” sheet of the ePHASORSIM-compatible Excel sheets, the charging power of EVs and local loads needs to be defined as incoming information. Meanwhile, the bus voltages, which are used by the EV charging management system to determine the charging power, along with any other states that may need to be monitored, need to be defined as outgoing information.
• Next, the ePHASORSIM’s solver block is incorporated into the Simulink model, where the Excel workbook is referenced to provide the required network data. These data are then processed by the solver, which produces a *.opal file containing all essential network details.
• Two subsystems are then created: the master subsystem (a computation block) and the console subsystem (a communication block), as depicted in Figure 11a. The master subsystem, which includes the ePHASORSIM solver, is responsible for the power system simulation and encompasses all electrical components, EV controllers, and dynamic models. On the other hand, the communication block handles the specification and visualization of necessary variables and signals within the Matlab graphical environment and may also include events and other parameters for controlling the simulation [36]. Note that all signals exchanged between the master and console subsystems pass through the OpComm block, which simulates the behavior of a real-time communication link. Note also that the EV controllers, which are responsible for managing the charging power of the EVs, are modeled within the Simulink environment, based on the original DSL scripts from PowerFactory.

The model can be run in either offline or RT modes. The key difference is that in the RT mode, the computation block is executed on an OPAL-RT Target simulator instead of a standard PC. In both modes, the communication block operates on a host PC.

Figure 12 and Figure 13 present the simulation results, with a focus on the EVs and feeders near to the transformer’s secondary and those at the end of the radial feeder. To evaluate grid conditions, all EVs start charging at the beginning of the simulation, with charging times distributed based on arrival times after 15:00 h to simulate a diverse charging schedule. Based on the obtained results, the following observations can be made:

• Transformer Loading: Figure 12b presents the transformer loading for different scenarios. Charging all EVs without droop control results in a transformer loading of 108%. Conversely, implementing voltage droop control for EV charging reduces the maximum transformer loading to 70.5%.
• Voltage Dip: According to Figure 12c, the voltage dip at terminal T01, which is close to the transformer’s secondary, stays above 0.96 pu across all scenarios. In contrast, Figure 12d illustrates a substantial voltage dip down to 0.9 pu at terminal T08, at the far end of the radial feeder, without droop control. The application of voltage droop control significantly improves the voltage at T08 to 0.95 pu. These findings demonstrate that using droop control for EV charging can address overloading and voltage dip challenges in long radial feeders within the distribution grid.
• Charging Power and SOC: According to Figure 13, When no droop control is applied, all EVs charge at the same power level (11 kW), meaning they equally benefit from electricity prices. In contrast, voltage droop control results in EVs at the end of the radial feeder charging at a lower power level (4.8 kW) than those nearer the transformer (9.8 kW). This demonstrates that voltage droop control enhances terminal voltages but is less economically beneficial for distant consumers.
• In all scenarios, the results from PowerFactory and ePHASORSIM are in excellent agreement, which confirms the reliability of using ePHASORSIM. Additionally, ePHASORSIM offers several benefits over PowerFactory, including the ability to perform RT simulations, which is crucial for validating dynamic control strategies in real-world conditions. Moreover, ePHASORSIM’s integration with MATLAB/Simulink for control design provides greater flexibility in developing and testing control algorithms. In contrast, developing control algorithms in PowerFactory using DSL scripts can be complex and time-consuming. Furthermore, ePHASORSIM’s scalability makes it ideal for large-scale simulations involving multiple distributed energy resources and complex grid configurations. OPAL-RT ePHASORSIM can also be used for CHIL testing real EV control devices.

6. Summary and Conclusions

In this paper, we have reviewed recent advancements and practical applications of OPAL-RT’s ePHASORSIM for RT simulation and HIL testing of power systems. These advancements include:

• Tools and processes for automated model conversion from various simulation environments, such as PowerFactory and OpenDSS, to ePHASORSIM. This automation significantly reduces manual effort and enhances the accuracy and efficiency of model integration.
• Methods to combine transmission network models and distribution network models created in different software packages using OPAL-RT’s ePHASORSIM, which enables investigating interactions between them in real-time. However, due to the millisecond-range step time of OPAL-RT’s ePHASORSIM, this approach may not always effectively capture the fast dynamics of DERs in distribution networks.
• Development of methods for multi-rate RT co-simulation using ePHASORSIM and EMT simulators like eMEGASIM or Simscape Power Systems, which enables the simultaneous simulation of multiple interconnected systems operating at different time steps. These scenarios often involve utilizing ePHASORSIM to handle phasor-domain simulations of the transmission and/or distribution grid with time steps on the order of milliseconds, while an EMT simulator accurately models the fast dynamics of inverter-based DERs, other power electronics devices, or microgrids with time steps in the microsecond range.
• Techniques for ePHASORSIM-based HIL testing, where networks are implemented in the phasor domain using ePHASORSIM, and specific signals such as voltage and current waveforms at specific nodes are amplified and used to interface with physical devices like relays or power converters. This approach allows for the RT evaluation of the device under test performance under simulated operational conditions, ensuring that these components respond accurately to various grid disturbances and dynamic scenarios. Several notable examples were highlighted in the paper, including the simulation of the Great Britain transmission system, focusing on validating LoM protection relays using PMU data to simulate fast frequency phenomena; the Colombia-Ecuador interconnection, concentrating on a PMU-based SPS to handle scenarios like generation loss and overloads; and the Nordic power system, examining the virtual inertia provided by an HVDC converter terminal and its impact on frequency dynamics.

Considering the widespread use of the PowerFactory software package for power system studies, the paper proceeded with detailed discussions about PowerFactory model conversion to ePHASORSIM. Both automatic conversion using built-in importing tools and conversion using an Excel workbook were discussed, with their advantages and disadvantages explained. The automatic conversion leverages appropriate licenses to convert PowerFactory models directly to ePHASORSIM by creating the network model in PowerFactory, exporting it via DGS, and importing it into a Matlab/Simulink environment using ePHASORSIM SOLVER. This method is efficient but requires manual redefinition for non-standard controllers and complex components. On the other hand, the Excel Workbook method, which does not require expensive licenses, involves exporting the model from PowerFactory in Excel format and then translating the parameters to an ePHASORSIM-compatible format. This approach provides greater customizability, particularly for modeling unbalanced power systems, though it is more labor-intensive. However, one may automate this transformation from PowerFactory Excel file sheets into ePHASORSIM Excel file sheets using an m-file or Python script.

In the final part of the paper, a comparative analysis was conducted to cross-validate EV charging management strategies using ePHASORSIM and PowerFactory. The study detailed the implementation of droop control based on EVs’ local terminal voltage to manage charging loads and prevent overloading of the low-voltage distribution network. Simulations in both PowerFactory and ePHASORSIM were used to evaluate this control strategy. The results not only demonstrated the effectiveness of the control strategy but also showed excellent agreement between the PowerFactory and ePHASORSIM simulations, confirming the reliability and effectiveness of ePHASORSIM for demand response controls.

Overall, the advancements and applications discussed in this paper provide useful insights for readers and highlight the versatility and reliability of ePHASORSIM in modern power system analysis and testing, from multi-rate co-simulation methods to sophisticated HIL testing techniques. The comparative studies presented in the paper also underscore its capability and reliability in demand response controls, which have received little attention in the literature.