# Researching a Simulation of Real-Time Nonlinear Dynamical Systems for Digital Power Grids in Massive IoT

Authors: Yingbin Zhang; Xiaowei Zhao; Guoshi Wang; Qing Yan; Siming Li; Ying Liu
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

“Digital real-time simulation” refers to the replication of output waveforms with the required accuracy, which duplicates the behavior of a real power system that is being simulated. A variety of problems relating to the functioning of power systems can be effectively solved using real-time simulators. Fortunately, modern state-of-the-art technological advancements have solved the energy problems. When used as a real-time application of electromagnetic transient-type simulation, the real-time digital simulator takes advantage of the traveling wave properties of cables and transmission lines in conjunction with a parallel processing platform. Power Control (PC), Hardware Under Test (HUT), Time Scale of Events (TSE), and Control Action (CA) are used as independent variables and the Real-Time Dynamic Simulation (RTDS) has been used as dependent variables. The objective of study improves the energy production in Digital Power Grids using Real-time Dynamic Nonlinear System Simulation System. The data was collected by using questionnaires based on 5-Likert Scale. The data has been analyzed using smart PLS 3. The questionnaire were filled from 50 technicians of power grids. The results are that Real-Time Dynamic Simulation improves the energy production in Digital Power Grids.


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## Body

## 1. Introduction

Electrical systems planning and design have benefited greatly from electrical system simulators, which have been in operation for decades. In a wide range of applications, virtual reality simulators have proven critical to the successful development [1]. The development of real-time simulators in applications for studying the functioning of power systems has had a noticeable impact on the development of various commercial solutions. Statements that real-time simulators based on personal computers are no longer needed are frequently made based on publications published at the end of the twentieth century, which are inaccurate [2]. The procedure of simulation and structure test of a real-time digital or an analog hybrid simulation system based at the State Grid Simulation Center and its application in simulation research on a high-voltage alternating current/direct current hybrid power grid are described in this article. It is comprised of corresponding digital models, physical simulative devices, and interfacing devices; among these [3], the transition system and analog model of (High-Voltage Direct Current) HVDC power contains such simulative devices whose characteristics are approximately the same as the characteristics of the actual HVDC transmission system, as well as control and protection devices that are identical to those used in the actual High-Voltage Direct Current project [4]. Using the wide-band electromagnetic transient model, the project enables real-time modeling of power systems with hundreds of buses using the wide-band electromagnetic transient model. It is possible to use real-time simulation to study and test Fast-Alternating Current and High-Voltage Direct Current Controllers, excitation controls, relays, and Special Protection Systems. RTDS hardware and financial costs of the system are proportional to the simulation system’s size, which is measured in terms of processing racks [5, 6].The complete nonlinear description, modeling only the network part that is of particular interest (which is related to the internal infrastructure of the system) [7] and constructing a reasonably accurate equivalent (referred to as the external system), is more cost effective than designing the network from scratch (referred to as design). As a result of this motivation, the research reported in the publication was carried out [8]. However, it should be noted that in order to be accurate, the equivalent must accurately represent both high-frequency electromagnetic transient behavior and low-frequency electromechanical transient behavior [9]. Under the most realistic scenarios, it is possible to effectively secure the immediate transient response of an external system using a network equivalent (FDNE) model dependent on the linear frequency [10, 11]. Power grid simulation is widely considered important for grid operation, planning, and maintenance as well as research and development. When modeling complex systems, accuracy time domain simulations in the power grid are possible because of the diverse range of time scales attributed to grid disturbances and control actions. However, accuracy time domain simulations in the power grid are sometimes hampered by slow simulation times when modeling complex systems [12]. When working in real time, there is a problem known as interruption. Because of the huge number of controls that are active, a defect such as a blockage can spread throughout the system in the form of electromechanical or electromagnetic transients, which can eventually cause a change in the stable state to occur [13]. The disruption occurs on a temporal scale with loads ranging from microseconds to hourly changes, depending on the severity of the disruption.One of the most difficult issues in designing an accurate, rapid simulator that can scale to huge systems while remaining computationally efficient is the range of time scales available to it. The grid is, by its very nature, a dynamic system that is always changing as a result of control operations that have a numerous time constraint in their execution [14]. Tools overcome the difficulty of replicating this dynamic system by focusing on a limited number of time scales and, in many cases, by sacrificing speed for accuracy in their calculations. An engineer needs a tool that enables the technician to understand the operations that interact with the independent controllers in the case of these uses and resolves issues in minutes to hours instead of seconds to minutes [15]. Due to the time scale at which they are built, the simulation tools that are now available limit their ability to mimic such situations. A scalable real-time simulator is frequently used in the development of real-time simulation software. Rack-mount machines, which require data transmission across racks, can be used to increase processing power by a factor of two. Individual processing units run in parallel, resulting in a good scaling property; nevertheless, communication adds time delay to the computation process as well [16]. Communication barriers can be reduced by using the wavelength characteristics of radio waves and by connecting network subsystems that are separated by appropriate length transmission lines that correspond to simulation phase intervals [17]. Communication delays are reduced by sharing shared memories or buses between processors when multiple processors work together in parallel or when additional hardware such as general-purpose central processing units (CPUs) are used. Transformers are a common component of electrical grids, and they serve a variety of functions [18].To accurately represent the dynamics of transformer operation, which is primarily due to the nonlinearity of the magnetization characteristics and the core demagnetization process itself, it is necessary to consider several factors [19]. This is especially true when dealing with real-time simulation. This section contains the results of tests conducted to determine the correctness of the simulation of transient states during the operation of a power transformer. New business models geared toward IoT deployment currently call for extremely high levels of connection, privacy and security, full coverage, ultrahigh dependability, and ultralow latency. Increased data rates, improved coverage, and high-throughput capabilities of the 5G-enabled IoT provide solutions for business models and allow IoT for robotics, actuators, and drones.


## 2. Literature Review

On the other hand, the accuracy of the simulation provided by the dynamic simulation is achieved by solving the electromechanical differential algebraic equation at each step [20]. Due to the large number of control actions on the grid, large-scale dynamics and large systems suffer from time constants (varying from milliseconds to minutes) [21], creating a barrier to fast but accurate transient simulation. To protect fast transitions, even during latent periods where slow transitions predominate, dynamic simulations should take small temporary steps to ensure that they are not lost [22]. When modeling hard circuits, such as phase-locked loops, the circuit community faces a similar dilemma. During these hidden periods, dynamic simulation cannot use long-term measures, which would eliminate the need for additional calculations, and is forced to calculate the entire latent period, which is ineffective.Due to local and temporal differences in some areas of the grid, real-time digital simulators are able to parallel temporary simulation across multiple cores, thus eliminating the problem. Even while Redoes represent a significant step forward in scalability, they typically demand the use of a large number of cores to be effective [23]. The matrix structure of dynamic simulation has been used by some other research initiatives to simulate simulation on a large number of nodes and to achieve high levels of simulation performance. However, while temporary simulations are useful for studying duplication and fluctuating moments [24], real interest in system discovery is usually found in the study state that is gained during the study. Researchers have previously developed a model of a semistable state of temporal equation, which examines the parts of time during which the grid reaches a temporarily stable state. This model is now being used to investigate temporal equations, which is a new development. These two alternate formulations are currently at odds with one another [25], and this model has the potential to bridge the gap that now exists. Semistable performance can be maintained under the assumption of zero-time derivatives for the fast-moving state, long-term analysis [26]. Long-term analysis is possible utilizing the semistable state under the assumption of zero-time derivatives for the fast-moving state. There are numerous examples where this trade-off between accuracy and processing efficiency is useful [27]. The term “digital real-time simulation” refers to the replication of output waveforms (current and voltage) with the required accuracy, which duplicates the behavior of a real power system that is being simulated and is used to describe the process of doing so [28]. In order to be regarded successful [29], For a single time step, a digital real-time simulator must be able to solve the model equations in the same amount of time as a real-time simulation does. Because of this, it provides outputs with discrete time intervals in which the system states are computed at specific discrete periods using a set time step, and the outputs are created at discrete time intervals [30]. Digital real-time simulation [31] is utilized in the power system’s transient simulation in order to attain the required results.For example, the use of an electromagnetic transient-type approach makes the use of a digital computer time-domain solution to achieve the necessary results [32]. It replicates the output waveforms (voltage and current) with the required accuracy, mimicking the behavior of a real power system that is being modeled, called “digital real-time simulation” [33]. This requires a digital real-time simulator so that model equations can be solved in one-time steps equal to a real-world clock in order to be considered successful [34]. Thus, it produces discrete time interval outputs, where system conditions are counted in specific discrete periods using a fixed time phase, and outputs are generated at discrete time intervals. In real-time simulation of power systems, digital real-time simulation is used to achieve the desired results [35]. For example, the use of electromagnetic temporal type approaches uses digital computer time domain solutions to achieve the desired results [36]. According to conventional thinking, there are two types of digital real-time triggers that can be used in the power system. The first type can be characterized as follows, using completely digital real-time simulation (for example, model in loop, process in loop, and software in a loop) [37]. The second real-time simulation, on the other hand, is based on hardware-in-the-loop technology. The complete system must be recreated within the simulator’s virtual environment to execute fully digital real-time simulation [38]. It does not require the processing of input or output signals nor does it necessitate the connection of external devices. In contrast to False Discovery Rate Simulation, hardware-in-the-loop simulation refers to a scenario in which the original physical components are employed to totally modify elements of the digital real-time simulation; for example, analog to digital converters, digital to analog converters, signal conditioners, and filters are input-output interfaces that operate with the simulation device, among other things, on the test or under test hardware. The input output interface is used to link the test or the Hardware Under Test [4].The controller hardware in the loop refers to an HIL system that combines real controller hardware that interacts with the rest of the simulation system, such as the computer, in the context of the HIL system (hardware-in-the-loop) [1]. This technology also makes prototype controllers possible in a short time. Since there is no real power transmission, the power system using this technique is viewed as a virtual system inside the simulator and is treated as such [5]. The controller hardware on the outside of the simulator communicates with the system running within the simulator by exchanging controller I/So signals with the system [7]. In most cases, this procedure is used to evaluate a newly designed or manufactured controller. Previous studies have suggested that machines, converters, fault current lemmers, and other electronic devices should be tested in real time. For hardware-in-the-loop testing of safety devices, such as relays [10], it may be necessary to use a voltage or current amplifier. However, there is not a transfer of power in this circumstance, though. The use of an amplifier is generally done to enable real-time monitoring of the device’s current and voltage signals. Generally speaking, a fully digital simulation is frequently used to better understand a system’s behavior under specific conditions caused by external or internal dynamic influences on the system [25]. An alternative approach is to use hardware in the loop simulation to reduce investment risk through a prototype after the underlying theory has been established through a comprehensive digital real-time simulation, which can be found here .According to the findings of earlier studies, a real-time simulator is required to run continuously without interruption or to a scheduled shutdown, as well as to run concurrently with external processes with an appropriate degree of adequacy and with a constant time step [28]. In order to meet these requirements, appropriate numerical methods for approximating differential equations and solving the equation systems of the developed mathematical model should be explored [18]. There are two ways of approximating differential equations proposed in the publications on the real-time simulator that were described above, as well as in key books on mathematical modeling of power systems that were not listed above: the trapezoidal rule and the backward Euler approach [20]. Because the backward Euler approach requires just a short integration step of the order of one us, the real-time simulator must have a large amount of computing capacity in order to be capable to deliver the results of the calculations in a timely manner [1]. It is possible to increase the time step length using the trapezoidal approach, which is one of its main advantages [16]. No matter how careful you are, numerical oscillations can occur on a regular basis and cause the simulator to lose its stability while in operation. These fundamental truths have remained practically unchanged throughout the course of several decades [10]. Due to the application of a novel method of approximating differential equations in mathematical models of power and electromechanical systems, major breakthroughs have been made in the simulation of the operation of power and electromechanical systems.


## 3. Methodology

In order to study the Real-time Dynamic Nonlinear System Simulation System for Digital Power Grids, this research paper has used Power Control, Hardware Under Test, Time Scale of Events, and Control Actions (as all these variables refers to the durability and quality of Real-Time Dynamics of Digital Power Grids). Figure1 shows the research framework of the study. Therefore, Power Control (PC), Hardware Under Test (HUT), Time Scale of Events (TSE), and Control Action (CA) are used as independent variables and the Real-Time Dynamic Simulation (RTDS) has been used as dependent variables. The data was collected by using questionnaires based on 5-Likert Scale; however, the questionnaire scale was adopted from [5].Figure 1
Dependent variables of Real-Time Dynamic Simulation.


## 4. Discussion and Analysis

### 4.1. PLS Algorithm

This paper has used the SEM PLS 3 software to construct the PLS algorithm of our research model. The PLS algorithm assess the model’s fitness. From the standpoint of organizational management, structural equation modeling is used to analyses cross-national cultural communication. Figure2 shows the path analysis of research model and shows that PC🡺RTDS (0.139), TSE🡺RTDS (0.112), and CA🡺RTDS (0.823) have positive path, whereas, Hardware Under Test HUT🡺RTDS (-0.149) has negative path.Figure 2
The path analysis of research model.


### 4.2. Path Coefficients

The table underneath shows the path coefficients of the variables. The results indicate that CA, PC, and TSE have positive path coefficients of 0.823, 0.139, and 0.112, respectively. However, HUT has negative path coefficient (-0.149) in the research framework as shown in Table1.Table 1
the path coefficients of the variables.
RTDSCA0.823HUT-0.149PC0.139TSE0.112


### 4.3. Latent Variable Correlations

The association between the factors is shown in Table2 on the right. As a result, the findings showed that the components are well connected. The findings suggest that CA and HUT has positive association of 0.199, which means these latent variables create 19.9% impact on each other. However, the results indicate that no other correlation expect TSE🡺CA is negative (-0.022). This substantial negative relationship between TSE🡺CA shows -2.2% of the association.Table 2
The association between the factors.
CAHUTPCRTDSTSECA1.0000.1990.1450.811-0.022HUT0.1991.0000.3970.1250.488PC0.1450.3971.0000.2310.274RTDS0.8110.1250.2311.0000.059TSE-0.0220.4880.2740.0591.000


### 4.4. LV Descriptives

Table3 shows the meanings of descriptive and latent variables related to values. Statistics show that the minimum and maximum values in the descriptive statistics table are between 2 and 5, which is within the acceptable range of 2 to 5. Skewness values vary from 1 to +1, and negatively distorted variables are reasonably symmetric and acceptable, while positively distorted variables are reasonably symmetric and irrational. The value of the variable is likely to be shown as a left line due to the negative skewness, with a median and mean value that is smaller than the mode of the variable.Table 3
The meanings of descriptive and latent variables related to values.
MedianMinMaxExcess kurtosisSkewnessCA-0.035-1.7491.661-0.9590.019HUT0.004-2.4711.931-0.531-0.258PC0.061-1.7482.447-0.5750.270RTDS0.157-2.1791.815-0.544-0.294TSE0.237-1.8631.850-1.055-0.388


### 4.5. Inner Model Residual Correlation

According to the residual correlation of the inner model, RTDS exhibited a high positive correlation, with a degree of 100.0 percent change in the link between the variables, as shown in Table4.Table 4
Inner model residual correlation.
RTDSRTDS1.000


### 4.6. Inner Model Residual Descriptives

The residual descriptive of the inner model is shown in Table5. As indicated in the table, the minimum and maximum values of RTDS are 2 and 5, respectively. A total of 50 persons were questioned about their thoughts. The skewness and kurtosis values were close to zero and in the -1 to 1 range, indicating that the data was accurate and not distorted. When it comes to RTDS, the curve is negatively skewed, which means that the curve’s longer side is on the left.Table 5
Inner model residual descriptives.
MedianMinMaxStandard deviationExcess kurtosisSkewnessRTDS0.005-1.2441.1900.559-0.1180.146


### 4.7.R-Square

Table6 shows the R-square value and adjusted R-square for various scenarios. The RTDS (Real-time Digital Simulation) is influenced positively by Power Control (PC), Hardware Under Test (HUT), Time Scale of Event (TSE), and Control Action (CA). The R-square value is 0.688, the current 68.8 percent values have an adjusted R-square of 0.660, and the 60.6 percent model fit for the RTDS study is demonstrated, according to the findings.Table 6
TheR-square value and adjusted R-square for various scenarios.
R-SquareR-Square adjustedRTDS0.6880.660


### 4.8.f-Square

The following Table7 shows the values for f-square. f-Square shows the variability of R-square in a research model with one endogenous variable. The table below shows that when an endogenous variable changes, the relationship between RTDS changes adversely with a low ratio of 2.030 percent change in CA. However, as shown in the table below, if an endogenous variable affects the association between RTDS and TES, a positive change of 0.030 (3.0 percent) will occur (which is a weak change).Table 7
The values forf-square. f-Square shows the variability of R-square in a research model with one endogenous variable.
RTDSCA2.030HUT0.047PC0.052TSE0.030


### 4.9. Construct Reliability and Validity

The construct reliability and validity of the study are listed in Table8 below. In reliability testing, Cronbach’s alpha is more than 0.70 (this shows that the information gathered for the study was correct and acceptable). The data represent the average variance of all variables collected in the study, and the rho_A values reflect composite reliability rates. As a result, the hidden variable composite dependability rating is similarly satisfactory. The average variation of the retrieved value for RTDS is poor with 0.258, indicating that the data has a 25.8% variance extraction [7].Table 8
Construct reliability and validity.
Cronbach’s alpharho_AComposite reliabilityAverage variance extracted (AVE)CA0.7980.8010.8820.713HUT0.9940.8180.6690.410PC0.7200.7270.8410.638RTDS0.9230.8330.5290.258TSE0.8700.8210.7420.517


### 4.10. Mean, STDEV,T Values, and P Values

The path coefficients of the link between all latent variables are provided in Table9. The t-statistics result is in the range of -2 to 2, which is close to zero, indicating that the data is valid and representative. Acceptable P values suggest that there is a relationship between variables. The results in the table indicate that CA🡺RTDS, HUT🡺RTDS, PC🡺RTDS, and TSE🡺RTDS have significant relationship with P values 0.000, 0.002, 0.003, and 0.0000, respectively.Table 9
Mean, STDEV,T values, and P values.
Original sample (O)Sample mean (M)Standard deviation (STDEV)t-statistics (|O/STDEV|)P valuesCA - > RTDS0.8230.7700.07910.4780.000HUT - > RTDS-0.149-0.0120.1890.7900.002PC - > RTDS0.1390.1530.1301.0690.003TSE - > RTDS0.1120.0230.1650.6820.000


### 4.11. Discriminant Validity

#### 4.11.1. Fornell-Larcker Criterion

The Fornell-Larcker criteria (FLC) used in this study are shown in Table10. It is used to determine how CA, HUT, PC, RTDS, and TES interact with each other. The results show that the variables have a positive dispersity with respect to their relative ratios. In this case, the degree of common variance between the variables is 0.488 (HUT🡺TES). This means that the variance between variables changes by 48.8% per unit of change in HUT (which is a big variation).Table 10
The Fornell-Larcker criteria (FLC).
CAHUTPCRTDSTSECA0.844HUT0.1990.640PC0.1450.3970.799RTDS0.8110.1250.2310.508TSE-0.0220.4880.2740.0590.719


### 4.12. Heterotrait-Monotrait Ratio (HTMT)

The Heterotrait-Monotrait Ratio (HTMT) values are used to determine if a variable is discriminately valid (as shown in Table11 and Figure 3). It indicates how similar the latent variables are to each other. If CA (Control Action) and PC (Power Control) are comparable, the link will have 0.205 (20.5%) the same validity, according to the findings. This graph depicts the highest levels of validity between CA and RTDS (74/9%), HUT and PC (46.5%), PC and RTDS (48.2%), and HUT and TSE (1.045).Table 11
Heterotrait-Monotrait Ratio (HTMT).
CAHUTPCRTDSTSECAHUT0.337PC0.2050.466RTDS0.7490.3330.482TSE0.1871.0450.1810.235Figure 3
Heterotrait-Monotrait Ratio (HTMT).In Figure3, the values of various latent variables that correlate with the values in the table are shown. The variables had a positive validity score, indicating that the links between them were recognized. All of the relationships between the variables were confirmed to be legitimate.The relationship between TSE🡺HUT, on the other hand, is proven to be invalid in the graph below. Between TSE and HUT is 1.045.


### 4.13. Construct Cross-Validated Communality

The structural equation modeling (SEM) of a digital power grid system has long been used to forecast future events. Despite the fact that they are considered “niches,” empirical research has showed a notable trend of the technique being applied in an increasingly varied variety of applications. Create Q2 using SEM PLS 3 blindfold technology. This is an example of a reuse strategy that omits each piece of data and uses result guessing to predict missing data. For endogenous latent structures with reflex measurement models, the blindfold strategy applies only in combination with these. To estimate Q2, the RTDS reading of the intrinsic latent structure must be greater than 0.00. This can be interpreted to mean that the importance of predicting or explaining the latent extrinsic structure to the intrinsic structure under consideration must be greater than zero. As stated in Table12 of construct cross-validated communality, only the values of HUT (Hardware Under Test) are less than zero, and hence, their Q2 validation was refused (Wang, R,2021).Table 12
Construct cross-validated communality.
SSOSSEQ2 (=1-SSE/SSO)CA150.00087.9320.414HUT150.000164.718-0.098PC150.000108.2490.278RTDS300.000292.7490.024TSE150.000110.0260.266


### 4.14. Collinearity Statistics (VIF)

#### 4.14.1. Outer VIF Values

Table13 shows the external VIF values ​​for the survey items used to measure variables. The outer VIF value represents a statistical analysis of symmetry between all items used to evaluate the variable. As a result, statistics show that VIF has rate values ​​from 1 to 10 on a scale of 1 to 10. Consider the following examples: The HUT1 (1st Question of Hardware Under Test) has the lowest outer VIF value of 1.023, while the TSE3 has the greatest outside VIF value of 3.532. The correlation between the items and the variables is represented by the outer VIF values. As a consequence, all of the items were positively associated to the hidden variables.Table 13
The external VIF values for the survey items used to measure variables.
VIFVIFVIFVIFCA11.569HUT32.533RTDS31.269TSE23.532CA21.819PC21.598RTDS43.233TSE31.719CA31.796PC31.272RTDS52.769PC11.542HUT11.023RTDS11.232RTDS61.253HUT22.504RTDS21.247TSE13.469


### 4.15. Model Fitness

#### 4.15.1. Fit Summary

The summary of model fitness is shown in Table14, and the results are presented in the table after that; it demonstrates how the saturated model and the estimated model were used to conduct a model fitness assessment. According to the model, the saturated model has an SRMR score of 0.173, indicating that it is 17.3 percent acceptable for analysis (moderate-valid fitness). As a result, the rate in the predicted model is 0.173, indicating that the variables’ fitness analyses are similar. Calculating the d-ULS data reveals that the rate is 5.126 percent. This rate demonstrates that CA, PC, HUT, and TSE all have a beneficial effect on RTDS.Table 14
The summary of model fitness.
Saturated modelEstimated modelSRMR0.1730.173d_ULS5.1265.126d_G1.6471.647Chi-square348.966348.966NFI0.3540.354


#### 4.15.2. RMS Theta

Table15 shows that the RMS theta function is used. The root mean square residual covariance of the residuals of the outer model of the variable is shown in this table as the root mean square residual covariance. Calculations show that an RMS theta equal to 0.253 is the closest match to 25.3% of the external model and is the best match overall.Table 15
The RMS theta.
RMS theta0.253


## 4.1. PLS Algorithm

This paper has used the SEM PLS 3 software to construct the PLS algorithm of our research model. The PLS algorithm assess the model’s fitness. From the standpoint of organizational management, structural equation modeling is used to analyses cross-national cultural communication. Figure2 shows the path analysis of research model and shows that PC🡺RTDS (0.139), TSE🡺RTDS (0.112), and CA🡺RTDS (0.823) have positive path, whereas, Hardware Under Test HUT🡺RTDS (-0.149) has negative path.Figure 2
The path analysis of research model.


## 4.2. Path Coefficients

The table underneath shows the path coefficients of the variables. The results indicate that CA, PC, and TSE have positive path coefficients of 0.823, 0.139, and 0.112, respectively. However, HUT has negative path coefficient (-0.149) in the research framework as shown in Table1.Table 1
the path coefficients of the variables.
RTDSCA0.823HUT-0.149PC0.139TSE0.112


## 4.3. Latent Variable Correlations

The association between the factors is shown in Table2 on the right. As a result, the findings showed that the components are well connected. The findings suggest that CA and HUT has positive association of 0.199, which means these latent variables create 19.9% impact on each other. However, the results indicate that no other correlation expect TSE🡺CA is negative (-0.022). This substantial negative relationship between TSE🡺CA shows -2.2% of the association.Table 2
The association between the factors.
CAHUTPCRTDSTSECA1.0000.1990.1450.811-0.022HUT0.1991.0000.3970.1250.488PC0.1450.3971.0000.2310.274RTDS0.8110.1250.2311.0000.059TSE-0.0220.4880.2740.0591.000


## 4.4. LV Descriptives

Table3 shows the meanings of descriptive and latent variables related to values. Statistics show that the minimum and maximum values in the descriptive statistics table are between 2 and 5, which is within the acceptable range of 2 to 5. Skewness values vary from 1 to +1, and negatively distorted variables are reasonably symmetric and acceptable, while positively distorted variables are reasonably symmetric and irrational. The value of the variable is likely to be shown as a left line due to the negative skewness, with a median and mean value that is smaller than the mode of the variable.Table 3
The meanings of descriptive and latent variables related to values.
MedianMinMaxExcess kurtosisSkewnessCA-0.035-1.7491.661-0.9590.019HUT0.004-2.4711.931-0.531-0.258PC0.061-1.7482.447-0.5750.270RTDS0.157-2.1791.815-0.544-0.294TSE0.237-1.8631.850-1.055-0.388


## 4.5. Inner Model Residual Correlation

According to the residual correlation of the inner model, RTDS exhibited a high positive correlation, with a degree of 100.0 percent change in the link between the variables, as shown in Table4.Table 4
Inner model residual correlation.
RTDSRTDS1.000


## 4.6. Inner Model Residual Descriptives

The residual descriptive of the inner model is shown in Table5. As indicated in the table, the minimum and maximum values of RTDS are 2 and 5, respectively. A total of 50 persons were questioned about their thoughts. The skewness and kurtosis values were close to zero and in the -1 to 1 range, indicating that the data was accurate and not distorted. When it comes to RTDS, the curve is negatively skewed, which means that the curve’s longer side is on the left.Table 5
Inner model residual descriptives.
MedianMinMaxStandard deviationExcess kurtosisSkewnessRTDS0.005-1.2441.1900.559-0.1180.146


## 4.7.R-Square

Table6 shows the R-square value and adjusted R-square for various scenarios. The RTDS (Real-time Digital Simulation) is influenced positively by Power Control (PC), Hardware Under Test (HUT), Time Scale of Event (TSE), and Control Action (CA). The R-square value is 0.688, the current 68.8 percent values have an adjusted R-square of 0.660, and the 60.6 percent model fit for the RTDS study is demonstrated, according to the findings.Table 6
TheR-square value and adjusted R-square for various scenarios.
R-SquareR-Square adjustedRTDS0.6880.660


## 4.8.f-Square

The following Table7 shows the values for f-square. f-Square shows the variability of R-square in a research model with one endogenous variable. The table below shows that when an endogenous variable changes, the relationship between RTDS changes adversely with a low ratio of 2.030 percent change in CA. However, as shown in the table below, if an endogenous variable affects the association between RTDS and TES, a positive change of 0.030 (3.0 percent) will occur (which is a weak change).Table 7
The values forf-square. f-Square shows the variability of R-square in a research model with one endogenous variable.
RTDSCA2.030HUT0.047PC0.052TSE0.030


## 4.9. Construct Reliability and Validity

The construct reliability and validity of the study are listed in Table8 below. In reliability testing, Cronbach’s alpha is more than 0.70 (this shows that the information gathered for the study was correct and acceptable). The data represent the average variance of all variables collected in the study, and the rho_A values reflect composite reliability rates. As a result, the hidden variable composite dependability rating is similarly satisfactory. The average variation of the retrieved value for RTDS is poor with 0.258, indicating that the data has a 25.8% variance extraction [7].Table 8
Construct reliability and validity.
Cronbach’s alpharho_AComposite reliabilityAverage variance extracted (AVE)CA0.7980.8010.8820.713HUT0.9940.8180.6690.410PC0.7200.7270.8410.638RTDS0.9230.8330.5290.258TSE0.8700.8210.7420.517


## 4.10. Mean, STDEV,T Values, and P Values

The path coefficients of the link between all latent variables are provided in Table9. The t-statistics result is in the range of -2 to 2, which is close to zero, indicating that the data is valid and representative. Acceptable P values suggest that there is a relationship between variables. The results in the table indicate that CA🡺RTDS, HUT🡺RTDS, PC🡺RTDS, and TSE🡺RTDS have significant relationship with P values 0.000, 0.002, 0.003, and 0.0000, respectively.Table 9
Mean, STDEV,T values, and P values.
Original sample (O)Sample mean (M)Standard deviation (STDEV)t-statistics (|O/STDEV|)P valuesCA - > RTDS0.8230.7700.07910.4780.000HUT - > RTDS-0.149-0.0120.1890.7900.002PC - > RTDS0.1390.1530.1301.0690.003TSE - > RTDS0.1120.0230.1650.6820.000


## 4.11. Discriminant Validity

### 4.11.1. Fornell-Larcker Criterion

The Fornell-Larcker criteria (FLC) used in this study are shown in Table10. It is used to determine how CA, HUT, PC, RTDS, and TES interact with each other. The results show that the variables have a positive dispersity with respect to their relative ratios. In this case, the degree of common variance between the variables is 0.488 (HUT🡺TES). This means that the variance between variables changes by 48.8% per unit of change in HUT (which is a big variation).Table 10
The Fornell-Larcker criteria (FLC).
CAHUTPCRTDSTSECA0.844HUT0.1990.640PC0.1450.3970.799RTDS0.8110.1250.2310.508TSE-0.0220.4880.2740.0590.719


## 4.11.1. Fornell-Larcker Criterion

The Fornell-Larcker criteria (FLC) used in this study are shown in Table10. It is used to determine how CA, HUT, PC, RTDS, and TES interact with each other. The results show that the variables have a positive dispersity with respect to their relative ratios. In this case, the degree of common variance between the variables is 0.488 (HUT🡺TES). This means that the variance between variables changes by 48.8% per unit of change in HUT (which is a big variation).Table 10
The Fornell-Larcker criteria (FLC).
CAHUTPCRTDSTSECA0.844HUT0.1990.640PC0.1450.3970.799RTDS0.8110.1250.2310.508TSE-0.0220.4880.2740.0590.719


## 4.12. Heterotrait-Monotrait Ratio (HTMT)

The Heterotrait-Monotrait Ratio (HTMT) values are used to determine if a variable is discriminately valid (as shown in Table11 and Figure 3). It indicates how similar the latent variables are to each other. If CA (Control Action) and PC (Power Control) are comparable, the link will have 0.205 (20.5%) the same validity, according to the findings. This graph depicts the highest levels of validity between CA and RTDS (74/9%), HUT and PC (46.5%), PC and RTDS (48.2%), and HUT and TSE (1.045).Table 11
Heterotrait-Monotrait Ratio (HTMT).
CAHUTPCRTDSTSECAHUT0.337PC0.2050.466RTDS0.7490.3330.482TSE0.1871.0450.1810.235Figure 3
Heterotrait-Monotrait Ratio (HTMT).In Figure3, the values of various latent variables that correlate with the values in the table are shown. The variables had a positive validity score, indicating that the links between them were recognized. All of the relationships between the variables were confirmed to be legitimate.The relationship between TSE🡺HUT, on the other hand, is proven to be invalid in the graph below. Between TSE and HUT is 1.045.


## 4.13. Construct Cross-Validated Communality

The structural equation modeling (SEM) of a digital power grid system has long been used to forecast future events. Despite the fact that they are considered “niches,” empirical research has showed a notable trend of the technique being applied in an increasingly varied variety of applications. Create Q2 using SEM PLS 3 blindfold technology. This is an example of a reuse strategy that omits each piece of data and uses result guessing to predict missing data. For endogenous latent structures with reflex measurement models, the blindfold strategy applies only in combination with these. To estimate Q2, the RTDS reading of the intrinsic latent structure must be greater than 0.00. This can be interpreted to mean that the importance of predicting or explaining the latent extrinsic structure to the intrinsic structure under consideration must be greater than zero. As stated in Table12 of construct cross-validated communality, only the values of HUT (Hardware Under Test) are less than zero, and hence, their Q2 validation was refused (Wang, R,2021).Table 12
Construct cross-validated communality.
SSOSSEQ2 (=1-SSE/SSO)CA150.00087.9320.414HUT150.000164.718-0.098PC150.000108.2490.278RTDS300.000292.7490.024TSE150.000110.0260.266


## 4.14. Collinearity Statistics (VIF)

### 4.14.1. Outer VIF Values

Table13 shows the external VIF values ​​for the survey items used to measure variables. The outer VIF value represents a statistical analysis of symmetry between all items used to evaluate the variable. As a result, statistics show that VIF has rate values ​​from 1 to 10 on a scale of 1 to 10. Consider the following examples: The HUT1 (1st Question of Hardware Under Test) has the lowest outer VIF value of 1.023, while the TSE3 has the greatest outside VIF value of 3.532. The correlation between the items and the variables is represented by the outer VIF values. As a consequence, all of the items were positively associated to the hidden variables.Table 13
The external VIF values for the survey items used to measure variables.
VIFVIFVIFVIFCA11.569HUT32.533RTDS31.269TSE23.532CA21.819PC21.598RTDS43.233TSE31.719CA31.796PC31.272RTDS52.769PC11.542HUT11.023RTDS11.232RTDS61.253HUT22.504RTDS21.247TSE13.469


## 4.14.1. Outer VIF Values

Table13 shows the external VIF values ​​for the survey items used to measure variables. The outer VIF value represents a statistical analysis of symmetry between all items used to evaluate the variable. As a result, statistics show that VIF has rate values ​​from 1 to 10 on a scale of 1 to 10. Consider the following examples: The HUT1 (1st Question of Hardware Under Test) has the lowest outer VIF value of 1.023, while the TSE3 has the greatest outside VIF value of 3.532. The correlation between the items and the variables is represented by the outer VIF values. As a consequence, all of the items were positively associated to the hidden variables.Table 13
The external VIF values for the survey items used to measure variables.
VIFVIFVIFVIFCA11.569HUT32.533RTDS31.269TSE23.532CA21.819PC21.598RTDS43.233TSE31.719CA31.796PC31.272RTDS52.769PC11.542HUT11.023RTDS11.232RTDS61.253HUT22.504RTDS21.247TSE13.469


## 4.15. Model Fitness

### 4.15.1. Fit Summary

The summary of model fitness is shown in Table14, and the results are presented in the table after that; it demonstrates how the saturated model and the estimated model were used to conduct a model fitness assessment. According to the model, the saturated model has an SRMR score of 0.173, indicating that it is 17.3 percent acceptable for analysis (moderate-valid fitness). As a result, the rate in the predicted model is 0.173, indicating that the variables’ fitness analyses are similar. Calculating the d-ULS data reveals that the rate is 5.126 percent. This rate demonstrates that CA, PC, HUT, and TSE all have a beneficial effect on RTDS.Table 14
The summary of model fitness.
Saturated modelEstimated modelSRMR0.1730.173d_ULS5.1265.126d_G1.6471.647Chi-square348.966348.966NFI0.3540.354


### 4.15.2. RMS Theta

Table15 shows that the RMS theta function is used. The root mean square residual covariance of the residuals of the outer model of the variable is shown in this table as the root mean square residual covariance. Calculations show that an RMS theta equal to 0.253 is the closest match to 25.3% of the external model and is the best match overall.Table 15
The RMS theta.
RMS theta0.253


## 4.15.1. Fit Summary

The summary of model fitness is shown in Table14, and the results are presented in the table after that; it demonstrates how the saturated model and the estimated model were used to conduct a model fitness assessment. According to the model, the saturated model has an SRMR score of 0.173, indicating that it is 17.3 percent acceptable for analysis (moderate-valid fitness). As a result, the rate in the predicted model is 0.173, indicating that the variables’ fitness analyses are similar. Calculating the d-ULS data reveals that the rate is 5.126 percent. This rate demonstrates that CA, PC, HUT, and TSE all have a beneficial effect on RTDS.Table 14
The summary of model fitness.
Saturated modelEstimated modelSRMR0.1730.173d_ULS5.1265.126d_G1.6471.647Chi-square348.966348.966NFI0.3540.354


## 4.15.2. RMS Theta

Table15 shows that the RMS theta function is used. The root mean square residual covariance of the residuals of the outer model of the variable is shown in this table as the root mean square residual covariance. Calculations show that an RMS theta equal to 0.253 is the closest match to 25.3% of the external model and is the best match overall.Table 15
The RMS theta.
RMS theta0.253


## 5. Conclusion

Transformers are a common component of electrical grids, and they are used to perform a range of different tasks and purposes. Especially when considering real-time transformer operation simulation, the riper-sensation of the dynamics of transformer operation, which is principally generated by nonlinearity of the magnetization characteristics and the core demagnetization process itself, is not a minor issue to deal with. The asymmetry of differential equations makes it impossible to solve the long-term dynamics of complex systems for classical temporal simulation without significantly slowing down the simulation time scale. During periods of inactivity, previous steps have dynamically adjusted the time phase to adjust to the situation. Even while they have proved that they can increase speed, they have fell short when it comes to scaling to real-world testing conditions. In order to study the Real-time Dynamic Nonlinear System Simulation System for Digital Power Grids, this research paper has used Power Control, Hardware Under Test, Time Scale of Events, and Control Actions (as all these variables refers to the durability and quality of Real-Time Dynamics of Digital Power Grids). The results shows that the developed relationship was highly significant with acceptable values.


## 6. Recommendations

The following are the recommendations of the study:(i)
The future study can discuss the model base design of Real-Time Dynamic Simulation of Digital Power Grids(ii)
Future studies can indicate the improvement areas of the domain(iii)
Furthermore, the sample size can be increased, and the study can increase the simulation technologies and the impact of system design on the durability of real-time simulation dynamics(iv)
The categories of real-time simulators can be added such as noncommercial and open-source simulators



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*Source: 7153456-2022-08-24.xml*