Communication delay compensation method for real-time simulation of spatially distributed power system

Abstract

The invention provides a communication delay compensation method for real-time simulation of a spatially distributed power system, and the method comprises the steps: obtaining the communication delay time between a transmitting end simulation host and a receiving end simulation host, and the current electric quantity data received by the receiving end simulation host at the current simulation step length; according to the communication delay time, the current electrical quantity data and historical electrical quantity data of the receiving end simulation host, an electrical quantity predicted value of the next simulation step length is generated by utilizing a target fitting function, and the electrical quantity predicted value serves as input data of the receiving end simulation host at the next simulation step length and is used for compensating data vacancy caused by communication delay; and calculating a prediction error value according to the next electrical quantity data and the electrical quantity prediction value received by the receiving end simulation host at the next simulation step length, and optimizing the target fitting function by adopting the prediction error value so as to continuously generate the electrical quantity prediction value by adopting the optimized target fitting function. According to the method, the time consistency of cross-node data and the stability of the whole system are ensured.

Description

Technical Field

[0001] This application relates to the field of real-time simulation technology for power systems, and in particular to a communication delay compensation method for real-time simulation of spatially distributed power systems. Background Technology

[0002] With the expansion of power system scale and the increase in the proportion of renewable energy integration, the dynamic characteristics of power systems are becoming increasingly complex, placing higher demands on the real-time performance and accuracy of control strategy verification, power electronic device testing, and system-level simulation. Real-time digital simulation, due to its high fidelity and real-time response capabilities, has become an important tool for dynamic analysis of power systems. However, the computing and interface capabilities of a single simulation platform are limited, making it difficult to meet the needs of large-scale collaborative simulation. To address this, researchers have proposed constructing a spatially distributed real-time simulation architecture by connecting simulation nodes distributed across different regions through a communication network, thereby achieving cross-platform resource sharing and collaborative operation.

[0003] Existing spatially distributed real-time simulations mostly rely on wide area networks (WANs) or dedicated communication links to achieve data exchange and time synchronization between nodes. They typically employ methods such as data caching, timestamp alignment, linear extrapolation, or asynchronous step size coordination to mitigate the impact of communication latency. Some systems improve timing accuracy through precise clock synchronization or high-speed networks to enhance overall stability and real-time performance. However, because WAN communication latency is generally higher than the real-time simulation step size, existing methods often only maintain approximate synchronization under stable operating conditions. This makes it difficult to accurately reflect the nonlinear changes in power systems during high-speed dynamic processes such as faults and disturbances, easily leading to data misalignment, numerical divergence, or amplified simulation errors, thus affecting system stability and accuracy.

[0004] As a result, existing spatial distributed real-time simulation technology cannot effectively capture the trend of variable changes in high-speed dynamic processes under the condition of communication delay, thus making it difficult to guarantee the time consistency and overall stability of cross-node simulation. Summary of the Invention

[0005] The purpose of this application is to at least address one of the aforementioned technical deficiencies, particularly the fact that existing spatial distributed real-time simulation technology cannot effectively capture the trend of variable changes in high-speed dynamic processes under conditions of communication delay, thus making it difficult to guarantee the time consistency and overall stability of cross-node simulations.

[0006] In a first aspect, this application provides a communication delay compensation method for real-time simulation of spatially distributed power systems, the method comprising:

[0007] To obtain the communication delay time between the transmitting simulation host and the receiving simulation host in the spatial distributed power system, and the current electrical quantity data received by the receiving simulation host at the current simulation step;

[0008] Based on the communication delay time, the current electrical quantity data, and the historical electrical quantity data received by the receiving simulation host, the target fitting function is used to generate the predicted electrical quantity value of the receiving simulation host in the next simulation step. The target fitting function is obtained by fitting the historical electrical quantity data. The predicted electrical quantity value is used as the input data of the receiving simulation host in the next simulation step to compensate for the data gap caused by the communication delay.

[0009] Based on the electrical quantity data received by the receiving simulation host in the next simulation step and the predicted electrical quantity value in the next simulation step, the prediction error value is calculated, and the prediction error value is used to optimize the target fitting function, so as to continue to generate electrical quantity prediction values ​​using the optimized target fitting function.

[0010] In one embodiment, the step of generating the predicted electrical quantity values ​​for the receiving simulation host in the next simulation step, based on the communication delay time, current electrical quantity data, and historical electrical quantity data received by the receiving simulation host in the past, using a target fitting function, includes:

[0011] Based on the historical electrical quantity data received by the receiver simulation host, determine the fitting parameters of the target fitting function;

[0012] Based on the fitting parameters of the target fitting function and the communication delay time, the current electrical quantity data is linearly extrapolated along the trend to obtain the predicted electrical quantity value of the receiving simulation host in the next simulation step.

[0013] In one embodiment, the step of determining the fitting parameters of the target fitting function based on historical electrical quantity data received by the receiving simulation host includes:

[0014] At the receiving end, the simulation host selects the latest N simulation step sizes of data points from the historical electrical quantity data received in the past, and forms a data sequence with the time point corresponding to each data point, where N is a positive integer.

[0015] Based on the data sequence, linear fitting is used to determine the fitting parameters of the target fitting function.

[0016] In one embodiment, the step of linearly extrapolating the current electrical quantity data along the trend according to the fitting parameters of the target fitting function and the communication delay time to obtain the predicted electrical quantity value of the receiving simulation host in the next simulation step includes:

[0017] Calculate the predicted electrical quantities for the next simulation step using the following formula:

[0018]

[0019] in, This represents the predicted electrical quantity for the next simulation step. This indicates the current electrical quantity data. The fitting parameters represent the target fitting function. Indicates the communication delay time.

[0020] In one embodiment, the step of calculating the prediction error value based on the next electrical quantity data received by the receiving simulation host in the next simulation step and the predicted electrical quantity value in the next simulation step includes:

[0021] Calculate the prediction error value using the following formula:

[0022]

[0023] in, This represents the prediction error value. This indicates the next electrical quantity data received in the next simulation step. This represents the predicted electrical quantity value in the next simulation step. This represents the steady-state value used to normalize the prediction error.

[0024] In one embodiment, the step of optimizing the target fitting function using the prediction error value includes:

[0025] Based on the prediction error value, calculate the parameter correction amount of the target fitting function;

[0026] The fitting parameters of the target fitting function are adjusted based on the parameter correction amount.

[0027] Secondly, this application provides a communication delay compensation device for real-time simulation of a spatially distributed power system, the device comprising:

[0028] The communication delay time acquisition module is used to acquire the communication delay time between the transmitting end simulation host and the receiving end simulation host in the spatial distributed power system, as well as the current electrical quantity data received by the receiving end simulation host at the current simulation step.

[0029] The prediction value generation module is used to generate the predicted electrical quantity of the receiving simulation host in the next simulation step based on the communication delay time, the current electrical quantity data, and the historical electrical quantity data received by the receiving simulation host in the past, using a target fitting function. The target fitting function is obtained by fitting the historical electrical quantity data, and the predicted electrical quantity value is used as the input data of the receiving simulation host in the next simulation step to compensate for the data gap caused by the communication delay.

[0030] The target fitting function optimization module is used to calculate the prediction error value based on the next electrical quantity data received by the receiving simulation host in the next simulation step and the predicted electrical quantity value in the next simulation step, and to optimize the target fitting function using the prediction error value so as to continue to generate the predicted electrical quantity value.

[0031] In one embodiment, the predicted value generation module includes:

[0032] The fitting parameter determination unit is used to determine the fitting parameters of the target fitting function based on the historical electrical quantity data received by the receiving simulation host.

[0033] The prediction value generation unit is used to linearly extrapolate the current electrical quantity data along the trend according to the fitting parameters of the target fitting function and the communication delay time, so as to obtain the predicted electrical quantity value of the receiving simulation host in the next simulation step.

[0034] Thirdly, this application provides a storage medium storing computer-readable instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of any of the communication delay compensation methods for real-time simulation of spatially distributed power systems described in the above embodiments.

[0035] Fourthly, this application provides a computer device, including: one or more processors, and a memory;

[0036] The memory stores computer-readable instructions, which, when executed by one or more processors, perform the steps of any of the communication delay compensation methods for real-time simulation of spatially distributed power systems as described in the above embodiments.

[0037] As can be seen from the above technical solutions, the embodiments of this application have the following advantages:

[0038] The communication delay compensation method for real-time simulation of spatially distributed power systems provided in this application introduces a prediction compensation mechanism based on communication delay awareness, constructing an adaptive simulation process that maintains data continuity under delayed conditions. This effectively solves the problem that existing spatially distributed real-time simulations struggle to capture variable change trends under high-speed dynamic conditions. The method first utilizes the communication delay between the transmitter and receiver, along with currently received electrical quantity data, and combines historical electrical quantity data to construct a target fitting function that conforms to recent dynamic changes. Based on the fitting results, it generates predicted electrical quantity values ​​for the next simulation step, enabling the receiver to obtain input quantities for calculation in advance before the actual data arrives, thus eliminating data gaps caused by communication delays. The predicted values, on the time axis, are equivalent to pre-completing the actual electrical quantities, ensuring that the receiver and transmitter have logically synchronized input data within the same simulation step. This avoids problems such as inconsistent solution step sizes across nodes, misaligned state update rhythms, and disrupted coupling relationships between sub-networks caused by data lag.

[0039] Subsequently, after receiving the actual electrical quantity data in the next simulation step, the method calculates the prediction error by comparing the actual and predicted values, and adaptively optimizes the fitting function based on this error. This allows the prediction model to promptly correct deviations based on the actual system response, continuously reflecting the high-speed dynamic changes of the power system. Through this closed-loop mechanism formed by prediction generation and error feedback updates, the receiving simulation host can always obtain input quantities that are consistent with the actual trend and are time-continuous, ensuring that the state evolution across nodes remains synchronized in the time dimension. As a result, even under conditions of communication delay, the time consistency of cross-node simulation can still be maintained, further preventing instability phenomena such as numerical divergence, energy imbalance, or system oscillation caused by asynchrony in multi-node simulations. This significantly improves the dynamic response capability and overall stability of distributed simulation. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 A flowchart illustrating a communication delay compensation method for real-time simulation of a spatially distributed power system, provided in an embodiment of this application.

[0042] Figure 2 Example diagram of a communication delay compensation method for real-time simulation of a spatially distributed power system provided in an embodiment of this application;

[0043] Figure 3 A schematic diagram of the communication delay compensation device for real-time simulation of a spatially distributed power system provided in an embodiment of this application;

[0044] Figure 4 This is a schematic diagram of the internal structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0045] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0046] This application provides a communication delay compensation method for real-time simulation of spatially distributed power systems. The following embodiments illustrate this method using a computer device as an example. It is understood that the computer device can be any device with data processing capabilities, including but not limited to a single server, server cluster, personal laptop, desktop computer, etc. Figure 1 As shown, the method may include the following steps:

[0047] S101: Obtain the communication delay time between the transmitting simulation host and the receiving simulation host in the spatial distributed power system, as well as the current electrical quantity data received by the receiving simulation host at the current simulation step.

[0048] In this context, a spatially distributed power system refers to a simulation architecture comprised of multiple geographically dispersed power simulation nodes interconnected via a communication network. Each node, located at a different physical position, undertakes real-time calculation tasks for local power equipment or subsystems. The transmitting simulation host is responsible for generating electrical quantity calculation results and transmitting them to other nodes via the network within the distributed simulation structure. The data generated drives the synchronous calculations of downstream nodes. The receiving simulation host receives data packets from other nodes during the simulation process and performs local real-time simulations based on these data. Communication delay time describes the one-way transmission time experienced by the transmitting simulation host when transmitting electrical quantity data packets to the receiving simulation host via the communication link. This time quantifies the real-time characteristics of the cross-node communication process. The simulation step size represents the discrete calculation cycle of the simulation system in the time dimension, used to limit the updating of the power system state by each node within a consistent time interval. Electrical quantity data refers to the electrical physical quantities such as voltage, current, and power calculated by the simulation host within each simulation step size. This data describes the operating state of the power system at the corresponding moment and serves as the input basis for cross-node coupled simulations.

[0049] In the specific implementation process, after the simulation task starts, the computer equipment first obtains the communication delay time between the sending and receiving simulation hosts through a preset delay management interface. The communication delay time can be calculated in two ways: one is based on network delay measurement, which estimates the round-trip time by sending test data packets and receiving response packets; the other is based on the difference between the two-way timestamps, which obtains the one-way or average delay value by comparing the difference between the local timestamp and the timestamp of the data returned by the node, thereby identifying the current system's communication delay magnitude. At the arrival of each simulation step period, the computer equipment can directly obtain the current valid communication delay time by accessing a third-party delay monitoring module or delay status table, without participating in the specific measurement process. To ensure that the delay information strictly corresponds to the simulation cycle, after obtaining the delay time, the computer equipment binds it to the current simulation step timestamp and stores it in the delay buffer, so that subsequent prediction and compensation steps can accurately reference the delay data of the corresponding cycle.

[0050] After obtaining the communication delay time, the computer device continues to receive electrical quantity data corresponding to the current simulation step size through the integrated network communication module. Upon receipt, the computer device verifies the data content, timestamp, and integrity, and writes the verified electrical quantity data into the local data buffer in the order of the simulation step size. A clear step size index is established in the buffer to ensure data traceability and fast access. By recording and managing the accurate communication delay time together with the currently received electrical quantity data, the computer device can provide a stable and synchronous input basis for subsequent delay compensation predictions. This allows spatially distributed real-time simulation to maintain data continuity and time alignment even under conditions of communication delay, thereby improving the real-time performance, stability, and accuracy of cross-node simulations.

[0051] Acquiring communication delay time enables computer equipment to grasp the timeliness of cross-node data transmission in real time, thereby clarifying the order and lag of information arrival between simulation hosts and ensuring accurate determination of the available time window for data in a delayed environment. Acquiring electrical quantity data received at the current simulation step size allows computer equipment to understand the actual operating status of the system within that cycle, providing the latest input basis for predicting the next change in electrical quantities. Acquiring communication delay time together with the current simulation step size data provides synchronous and complete basic information for delay compensation and prediction generation, thereby avoiding inconsistencies in cross-node simulation time and system response lags caused by data gaps or misalignments, improving the stability and accuracy of spatial distributed real-time simulation, and ensuring the continuity and accuracy of data from each node during the simulation process.

[0052] S102: Based on the communication delay time, the current electrical quantity data, and the historical electrical quantity data received by the receiving simulation host, the target fitting function is used to generate the predicted electrical quantity value of the receiving simulation host in the next simulation step. The target fitting function is obtained by fitting the historical electrical quantity data. The predicted electrical quantity value is used as the input data of the receiving simulation host in the next simulation step to compensate for the data gap caused by the communication delay.

[0053] Historical electrical quantity data refers to the set of electrical quantity status data received by the receiving simulation host in previous simulation steps, reflecting the dynamic changes and trends of the power system over past operating cycles. The target fitting function is a mathematical model established by the computer equipment based on historical electrical quantity data. By fitting historical data, it characterizes the trend relationship of variables changing over time, providing a basis for data prediction in future simulation steps. The predicted electrical quantity value refers to the electrical quantity value for the next simulation step, calculated using the target fitting function based on the system state under current communication delay conditions. It is used to compensate for data gaps caused by communication delays before actual data arrives, serving as input data for the receiving simulation host in the next simulation step.

[0054] In the specific implementation process, the computer equipment first obtains historically received electrical quantity data from the local buffer, and simultaneously receives electrical quantity data from the remote simulation node for the current simulation step, and obtains the communication delay time between the transmitting and receiving simulation hosts. The historical electrical quantity data, current electrical quantity data, and communication delay time are used as inputs to a target fitting function for processing, in order to generate the predicted electrical quantity values ​​for the next simulation step. The target fitting function can establish an initial fitting model based on historical electrical quantity data, and adjust the predictions by incorporating the current received data and communication delay time when generating the predicted values, so that the prediction results can reflect the latest dynamic changes of the system in a timely manner.

[0055] The generated electrical quantity predictions can then be stored in a local buffer and used as input data for the next simulation step. This compensates for data gaps caused by communication delays, ensuring that the receiving simulation host receives continuous input before the actual data arrives. In this way, the objective fitting function can provide dynamic predictions by considering historical trends, current simulation state, and delay information. This ensures consistency between the predicted data and the actual system state trend, providing an accurate basis for subsequent simulation step calculations and cross-node synchronization, thereby improving the time consistency and system stability of spatially distributed real-time simulations.

[0056] Generating predicted electrical quantities for the next simulation step using a target fitting function aims to obtain the necessary input data from the receiving end in advance, even with communication delays, thus eliminating computational gaps caused by data not yet arriving. By using historical electrical quantity data, currently received electrical quantity data, and communication delay time as inputs to calculate the target fitting function, the system's recent dynamic changes can be fully utilized, while considering the current simulation state and network latency, to achieve reasonable predictions of the next electrical quantity. This allows the receiving simulation host to obtain continuous and usable input even before the actual data arrives, ensuring the temporal continuity and synchronization of cross-node simulation calculations, improving the dynamic response capability and overall stability of the distributed real-time simulation system, and reducing the negative impact of communication delays on simulation accuracy, achieving high-fidelity and reliable cross-node collaborative simulation.

[0057] S103: Based on the next electrical quantity data received by the receiving simulation host in the next simulation step and the predicted electrical quantity value in the next simulation step, calculate the prediction error value, and use the prediction error value to optimize the target fitting function, so as to continue to generate the predicted electrical quantity value using the optimized target fitting function.

[0058] The next electrical quantity data refers to the electrical quantity status data or simulation result data received within the next simulation step period, used to reflect the dynamic operation of the power system within that period. The prediction error value refers to the deviation between the actual received next simulation step data and the predicted value, used to measure the consistency between the prediction result and the actual data.

[0059] In the specific implementation process, the actual received electrical quantity data and corresponding predicted electrical quantity values ​​for the next simulation step are first obtained from the local buffer. These data are generated by a real-time linear predictor or a previously calculated prediction module. The computer equipment compares the actual received electrical quantity data with the predicted electrical quantity values ​​element by element to quantify the prediction error. The prediction error can be calculated using direct interpolation, mean square error, or other statistical error measurement methods, explicitly representing the deviation between the prediction result and the actual observed value as a numerical index, providing a basis for subsequent adaptive adjustments. After completing the prediction error calculation, the obtained error value is passed as feedback input to the optimization module of the target fitting function. The computer equipment automatically adjusts the parameter weights or correction coefficients of the fitting function according to the magnitude and direction of the error, thereby improving the fitting function's predictive ability for future simulation steps. Parameter optimization can be achieved through incremental adjustment, weighted update, or other programmed algorithms to ensure that the fitting function can respond promptly to dynamic changes in the system and communication delay fluctuations.

[0060] The optimized target fitting function is then used to generate predicted values ​​for subsequent simulation steps, creating a closed-loop adaptive feedback mechanism between the predictions and the actual data. In a large-scale distributed simulation environment, this process can be automatically executed cyclically within the computer equipment. Within each simulation step cycle, prediction error calculation, fitting function parameter updates, and the storage and management of prediction data are completed without manual intervention. Through continuous adaptive optimization, prediction errors can be constantly corrected, improving the prediction accuracy and reliability of data for the next simulation step. This effectively mitigates the impact of communication delays and data lags on cross-node collaborative simulation, thereby ensuring the system maintains time consistency, real-time performance, and high fidelity under high-speed dynamic conditions.

[0061] It is understandable that the reason for calculating the prediction error based on the electrical quantity data and predicted values ​​received at the next simulation step, and then using the prediction error to optimize the target fitting function, is to continuously improve prediction accuracy and correct deviations in a timely manner, even in the presence of communication delays and data fluctuations, ensuring a high degree of consistency between the data and predicted values ​​at each simulation node. This approach can reduce the impact of prediction deviations on cross-node simulation synchronization, improve time consistency and simulation accuracy, enhance the stability and reliability of real-time simulation of spatially distributed power systems, and achieve high-fidelity, continuous, and collaborative cross-node real-time simulation.

[0062] In the above embodiments, by introducing a prediction compensation mechanism based on communication delay awareness, an adaptive simulation process capable of maintaining data continuity under delayed environments is constructed, effectively solving the problem that existing spatial distributed real-time simulations struggle to capture variable change trends under high-speed dynamic conditions. This method first utilizes the communication delay between the transmitter and receiver, along with the currently received electrical quantity data, and combines historical electrical quantity data to construct a target fitting function that conforms to recent dynamic change patterns. Based on the fitting results, it generates predicted electrical quantity values ​​for the next simulation step, enabling the receiver to obtain input quantities for calculation in advance before the actual data arrives, thereby eliminating data gaps caused by communication delays. The predicted values, on the time axis, are equivalent to pre-completing the actual electrical quantities, ensuring that the receiver and transmitter have logically synchronized input data within the same simulation step, avoiding problems such as inconsistent cross-node solution step sizes, misaligned state update rhythms, and disrupted coupling relationships between sub-networks caused by data lag.

[0063] Subsequently, after receiving the actual electrical quantity data in the next simulation step, the method calculates the prediction error by comparing the actual and predicted values, and adaptively optimizes the fitting function based on this error. This allows the prediction model to promptly correct deviations based on the actual system response, continuously reflecting the high-speed dynamic changes of the power system. Through this closed-loop mechanism formed by prediction generation and error feedback updates, the receiving simulation host can always obtain input quantities that are consistent with the actual trend and are time-continuous, ensuring that the state evolution across nodes remains synchronized in the time dimension. As a result, even under conditions of communication delay, the time consistency of cross-node simulation can still be maintained, further preventing instability phenomena such as numerical divergence, energy imbalance, or system oscillation caused by asynchrony in multi-node simulations. This significantly improves the dynamic response capability and overall stability of distributed simulation.

[0064] In one embodiment, the step of generating the predicted electrical quantity values ​​for the receiving simulation host in the next simulation step, based on the communication delay time, current electrical quantity data, and historical electrical quantity data received by the receiving simulation host in the past, using a target fitting function, includes:

[0065] Based on the historical electrical quantity data received by the receiver simulation host, determine the fitting parameters of the target fitting function;

[0066] Based on the fitting parameters of the target fitting function and the communication delay time, the current electrical quantity data is linearly extrapolated along the trend to obtain the predicted electrical quantity value of the receiving simulation host in the next simulation step.

[0067] Here, fitting parameters refer to the adjustable coefficients or weights in the target fitting function. Their optimal values ​​are determined through analysis of historical data so that the function can accurately describe the data change trend. Linear extrapolation refers to extrapolating the data for the next simulation step based on the fitting parameters of the target fitting function and the data received at the current simulation step, in order to predict the changes in data within future steps.

[0068] In the specific implementation process, the historical electrical quantity data received by the receiving simulation host is first read. This data includes a set of electrical quantity status data received by the receiving simulation host within several previous simulation steps. Then, this historical data is used as input to determine the fitting parameters of the target fitting function through a fitting algorithm. The fitting algorithm can be executed programmatically within the computer device. For example, the least squares method can be used to calculate the fitting function parameters, minimizing the sum of squared errors between the function output and the historical data. Alternatively, iterative optimization methods such as gradient descent can be used to gradually adjust the parameter weights, enabling the fitting function to fully capture the changing trends and patterns of the historical data. After the fitting parameters are determined, the fitting function can map the patterns of historical data to the next predicted trend, providing a mathematical basis for subsequent data extrapolation.

[0069] After determining the fitting parameters, the electrical quantity data and communication delay time received at the current simulation step are acquired and input into the target fitting function. The computer equipment linearly extrapolates the electrical quantity data received at the current simulation step along the trend based on the fitting parameters, generating the predicted electrical quantity values ​​for the next simulation step. The linear extrapolation process can be adjusted by multiplying the trend output by the fitting function by a time step correction factor and incorporating the communication delay time, ensuring that the predicted electrical quantity values ​​reflect the dynamic changes of each node in the next simulation step. The generated predicted electrical quantity values ​​are stored in a local buffer and used as reference data for synchronization or delay compensation in the next simulation step, thereby ensuring the temporal consistency of simulation data across nodes.

[0070] The process of generating the predicted value for the next simulation step can be automatically looped within the computer device. Within each simulation step cycle, it completes historical data acquisition, fitting parameter calculation, current step data acquisition, trend extrapolation, and predicted value storage without manual intervention. In a large-scale distributed simulation environment, this automated execution ensures continuous real-time simulation capabilities and high-precision synchronization of data across nodes. Simultaneously, it enables the device to accurately predict the state of the next simulation step under conditions of network latency and data fluctuations, achieving high fidelity, stability, and reliability in real-time simulation of spatially distributed power systems.

[0071] It is understandable that the fitting parameters of the target fitting function are determined based on historically received electrical quantity data. Then, the electrical quantity data received at the current simulation step is linearly extrapolated along the trend according to the fitting parameters and communication delay time to obtain the predicted electrical quantity values ​​for the next simulation step. This allows for the prediction of data changes in future simulation steps by utilizing historical data patterns. Simultaneously, the prediction is corrected based on communication delay, thus ensuring the temporal consistency and continuity of data across nodes. By predicting the data change trend for the next simulation step in advance, data misalignment or synchronization errors caused by communication delays can be mitigated, improving the prediction accuracy of the simulation step and the overall stability of the system. This ensures that the real-time simulation of the spatially distributed power system maintains high-fidelity, reliable, and continuous collaborative operation during high-speed dynamic processes.

[0072] In one embodiment, the step of determining the fitting parameters of the target fitting function based on historical electrical quantity data received by the receiving simulation host includes:

[0073] At the receiving end, the simulation host selects the latest N simulation step sizes of data points from the historical electrical quantity data received in the past, and forms a data sequence with the time point corresponding to each data point, where N is a positive integer.

[0074] Based on the data sequence, linear fitting is used to determine the fitting parameters of the target fitting function.

[0075] Here, the latest N simulation step size data points refer to the data records corresponding to the most recent N simulation step sizes selected in chronological order from the historically received electrical quantity data, where N is a positive integer, used to capture the recent dynamic trend of the system. The data sequence is an ordered set consisting of each data point and its corresponding time point, used to mathematically model the changes in the system state over time.

[0076] In the specific implementation process, firstly, historical electrical quantity data is read. This data includes electrical quantity information received from each distributed simulation node within the previous several simulation step periods. Based on the timestamp information, the historical electrical quantity data is sorted chronologically, and data points from the most recent N simulation step periods are selected, where N is a positive integer, to ensure that the selected data can fully reflect the recent dynamic characteristics of the system. These data points represent the operating status of the system in the most recent N simulation step periods, providing a reliable basis for trend analysis and prediction.

[0077] Subsequently, each data point is combined with its corresponding time point to form an ordered data sequence, ensuring that each data point in the sequence clearly corresponds to its occurrence time, thus mathematically describing the trend of system state changes over time. This data sequence is used as input and fed into a target fitting function established within the computer device for processing. The computer device uses a linear fitting algorithm to analyze and calculate the data sequence to determine the fitting parameters. Linear fitting can be performed programmatically within the device using the least squares method, minimizing the sum of squared errors between the output of the fitting function and the data sequence, thereby obtaining fitting parameters that accurately reflect recent data change trends.

[0078] It is understandable that selecting the most recent N simulation step-size data points from historically received electrical quantity data and combining each data point with its corresponding time point to form a data sequence is to characterize the data change trend using the recent operating state of the system. Determining the fitting parameters of the target fitting function using linear fitting based on the data sequence ensures that the fitting function accurately reflects the recent data change patterns, thus providing a reliable basis for data prediction in the next simulation step. This approach can capture the trend changes in the system state in advance, improve prediction accuracy, mitigate data misalignment and synchronization errors caused by communication delays, and ensure the temporal consistency and continuity of simulation data across nodes, thereby enhancing the stability, reliability, and high fidelity of real-time simulation of spatially distributed power systems.

[0079] In one embodiment, the step of linearly extrapolating the current electrical quantity data along the trend according to the fitting parameters of the target fitting function and the communication delay time to obtain the predicted electrical quantity value of the receiving simulation host in the next simulation step includes:

[0080] Calculate the predicted electrical quantities for the next simulation step using the following formula:

[0081]

[0082] in, This represents the predicted electrical quantity for the next simulation step. This indicates the current electrical quantity data. The fitting parameters represent the target fitting function. Indicates the communication delay time.

[0083] In this embodiment, the predicted electrical quantity for the next simulation step is obtained by linear extrapolating the electrical quantity data received in the current simulation step. During the calculation, the electrical quantity data received in the current step is first acquired, and then, combined with the fitting parameters of the target fitting function and the communication delay time, the data change trend for the next simulation step is calculated through a linear relationship. This method can be executed automatically, storing the predicted electrical quantity values ​​in a local buffer to provide a reference for electrical quantity data synchronization or delay compensation in the next simulation step, thereby ensuring the continuity and consistency of data across nodes.

[0084] The above calculation method can predict the state changes of each distributed node in the next simulation step, alleviating data misalignment and step synchronization problems caused by communication delays, and improving prediction accuracy and overall system stability. This prediction method ensures the temporal consistency of simulation data across nodes, enabling the real-time simulation of spatially distributed power systems to maintain high-fidelity, reliable, and continuous collaborative operation during high-speed dynamic processes.

[0085] In one embodiment, the step of calculating the prediction error value based on the next electrical quantity data received by the receiving simulation host in the next simulation step and the predicted electrical quantity value in the next simulation step includes:

[0086] Calculate the prediction error value using the following formula:

[0087]

[0088] in, This represents the prediction error value. This indicates the next electrical quantity data received in the next simulation step. This represents the predicted electrical quantity value in the next simulation step. This represents the steady-state value used to normalize the prediction error.

[0089] In this embodiment, the prediction error value is obtained by comparing the received data of the next simulation step with the previously calculated prediction value and performing normalization. This process first obtains the actual received data and the corresponding prediction value for the next simulation step, and then normalizes the deviation between the two based on a reference steady-state value, thereby quantifying the difference between the prediction result and the actual data. The calculated prediction error value can be used for subsequent adjustment and optimization of the target fitting function to improve prediction accuracy. The steady-state value used in the prediction error calculation is determined based on the electrical quantities of the power system under normal operation or long-term stable conditions. Specifically, it can be obtained by sampling and averaging electrical quantities such as voltage, current, or power of the system for a period of time under undisturbed conditions to obtain a value representing the steady-state level of the system. This steady-state value is used to normalize the prediction error, making the error calculation comparable and dimensionally consistent, thus accurately reflecting the relative deviation between the prediction value and the actual received data, and providing a reliable quantitative basis for subsequent parameter optimization of the fitting function.

[0090] It should be noted that, This is used to normalize the prediction error, and its value is determined based on the rated or reference steady-state level of the target electrical quantity under normal operating conditions. Since the electrical quantity data is generated by the distributed simulation host based on the system nodes it is responsible for within each simulation step and is exchanged and transmitted between simulation hosts to achieve coupled simulation, when the target electrical quantity is a node voltage, the rated voltage can be directly selected as the steady-state value according to the voltage level of the node to which the simulation host belongs; for example, 220 kV for a 220 kV node and 110 kV for a 110 kV node. By using a steady-state reference value consistent with the magnitude of the target electrical quantity for normalization, the influence of differences in the scale of electrical quantities at different nodes on error evaluation can be effectively eliminated, giving the prediction error a unified measurement standard and providing a stable and reliable reference for subsequent optimization of the target fitting function.

[0091] It is understandable that by calculating the prediction error value, the deviation between the prediction and the actual data can be reflected in a timely manner, identifying the shortcomings of the prediction and making dynamic corrections. This helps to continuously optimize the objective fitting function, improve the accuracy of the next simulation step size prediction, mitigate the impact of communication delays and data fluctuations on cross-node simulations, and thus enhance the stability, reliability, and high fidelity of real-time simulation of spatially distributed power systems.

[0092] In one embodiment, the step of optimizing the target fitting function using the prediction error value includes:

[0093] Based on the prediction error value, calculate the parameter correction amount of the target fitting function;

[0094] The fitting parameters of the target fitting function are adjusted based on the parameter correction amount.

[0095] Among them, the parameter correction amount refers to the adjustable value calculated based on the prediction error value, which is used to correct the fitting parameters of the target fitting function so that the fitting function can more accurately reflect the dynamic changes of the system.

[0096] In the specific implementation process, the latest calculated prediction error value is first obtained. This error value reflects the deviation between the predicted data from the previous simulation step and the actual received data. Then, the fitting parameters of the target fitting function are adjusted according to a pre-set correction algorithm. This correction algorithm can be executed internally, for example, by using an incremental adjustment method, which maps the prediction error proportionally to the correction amount of the fitting parameters, or by using a weighted average method combined with historical errors to smoothly adjust the parameters, thereby effectively converting the deviation information into an operable parameter correction magnitude. This step ensures that the parameter adjustment magnitude matches the actual deviation, avoiding over-adjustment or under-response, and improving the prediction accuracy of the fitting function.

[0097] After calculating the parameter corrections, the computer applies them to the fitting parameters of the target fitting function, dynamically updating the fitting parameters so that the function can promptly correct the prediction results based on changes in actual observed data. The dynamic adjustment of the fitting parameters can be completed automatically within each simulation step cycle, and is executed synchronously with data reception and prediction calculation, thereby achieving continuous optimization and real-time updates of the prediction without manual intervention. Through continuous iterative correction, the target fitting function can continuously adapt to the rapid dynamic changes of the system, improving the accuracy and reliability of the prediction data.

[0098] Therefore, the parameters of the target fitting function can be corrected in a timely manner based on actual observation data, effectively eliminating prediction bias and improving the accuracy and reliability of data prediction for the next simulation step. By dynamically adjusting the fitting parameters, the accuracy of cross-node data prediction can be enhanced, mitigating the impact of communication delays and rapid dynamic changes in the system on simulation results. This improves the stability, continuity, and high fidelity of real-time simulation of spatially distributed power systems, enabling reliable collaborative operation of the system under complex dynamic conditions.

[0099] To facilitate understanding of the scheme in this application, specific examples are provided below.

[0100] In a real-time simulation example of a spatially distributed power system, the system consists of multiple functional modules, including simulation host A and simulation host B. These two geographically distributed real-time digital simulators are interconnected via a wide area network (WAN) to simulate different sub-networks of the power system. Each simulation host is equipped with real-time computing hardware and a digital signal processing interface. The data acquisition and transmission module collects physical quantities such as voltage, current, and switch status of the subsystem in real time and transmits them to the remote simulation host via a standard communication protocol. It also adds timestamps to the data to facilitate communication delay identification using a synchronization clock mechanism. The communication delay perception module identifies the current system's communication delay based on network delay measurement or bidirectional timestamp difference calculation and provides a delay parameter Δt for the prediction module to use. The real-time linear predictor module, as the core module, consists of a linear fitting unit, a parameter update unit, and a prediction output unit. By performing least-squares fitting on N historical data points, it estimates the linear trend for the next simulation step, thereby compensating for data lag caused by communication delay. The error feedback and adaptive update module compares the predicted value with the delayed actual received value in real time, calculates the prediction error, and dynamically adjusts the prediction parameters through weighting factors to improve prediction accuracy and adaptability. The system synchronization clock module utilizes GPS signals or a high-precision network clock to unify the time across all simulation hosts, serving for data synchronization and delay calculation. The interconnections between modules are as follows: data generated by the simulation host is sent via the data acquisition and transmission module; delay parameters are provided by communication delay identification; the real-time linear predictor generates predicted values ​​and transmits them to the target host; and the prediction model is updated via the error feedback module.

[0101] In this example, based on the characteristic that the changes in variables within the short-term dynamic range of a power system can be approximated as linear, a linear regression model is used to fit real-time simulation variables such as node voltage, branch current, and power. When performing spatially distributed real-time simulation with a communication delay Δt, the data received at time t is equal to the data transmitted at time t-Δt. The prediction objective is to minimize the error between the received data and the transmitted data at the previous time. To achieve accurate prediction, a suitable historical data window needs to be selected as input, with a window size of N data points. Voltage changes within each simulation step can be considered linear within a short time range; therefore, the objective function is a linear function y=ax+b, where a and b are fitting coefficients. The optimal fitting coefficients are obtained by minimizing the sum of squared errors between the N historical data points and the fitting function, thus obtaining a target fitting function that accurately reflects the recent data change trend. Subsequently, predicted values ​​are generated based on the calculated slope coefficient a, the current received data Vt, and the communication delay Δt. The predicted values ​​can be obtained using the formula... Significant communication delays may prevent predicted values ​​from perfectly tracking actual values. To enhance the performance of the real-time linear predictor, two real-time simulators are synchronized using a GPS clock signal. The communication delay Δt is obtained by comparing the timestamp of the received data packet with the actual time. The prediction error is calculated by normalizing the difference between the predicted value and the delayed actual received value, quantifying the prediction accuracy and serving as the basis for adjusting the parameters of the target fitting function. This enables dynamic correction and adaptive updates, improving the accuracy, stability, and continuity of spatial distributed real-time simulation.

[0102] like Figure 2 As shown, after the system starts, it enters a real-time loop: first, it reads the latest communication data. If the amount of cached data is insufficient for the window length N, it pushes the data onto the stack in chronological order. Otherwise, it inserts the new data into the bottom of the stack and discards the oldest data to keep N unchanged. Then, it uses these N data points to perform linear regression to obtain the slope a. Then, it calculates the normalized error error based on the current predicted value and the actual delay value. If a is negative, it updates Vt to Vt+(1-error)*a*t. Otherwise, it updates Vt to Vt+(1+error)*a*t. Then, it stores the corrected Vt for the next error calculation. This process is repeated until the simulation stops.

[0103] The following describes a communication delay compensation device for real-time simulation of a spatially distributed power system provided in an embodiment of this application. The communication delay compensation device described below corresponds to the communication delay compensation method described above for real-time simulation of a spatially distributed power system. Figure 3 As shown, this application provides a communication delay compensation device for real-time simulation of a spatially distributed power system. The device includes:

[0104] The communication delay time acquisition module 201 is used to acquire the communication delay time between the transmitting end simulation host and the receiving end simulation host in the spatial distributed power system, as well as the current electrical quantity data received by the receiving end simulation host in the current simulation step.

[0105] The prediction value generation module 202 is used to generate the predicted electrical quantity of the receiving simulation host in the next simulation step based on the communication delay time, the current electrical quantity data and the historical electrical quantity data received by the receiving simulation host in the past, using a target fitting function. The target fitting function is obtained by fitting the historical electrical quantity data. The predicted electrical quantity is used as the input data of the receiving simulation host in the next simulation step to compensate for the data gap caused by the communication delay.

[0106] The target fitting function optimization module 203 is used to calculate the prediction error value based on the next electrical quantity data received by the receiving simulation host in the next simulation step and the predicted electrical quantity value in the next simulation step, and to optimize the target fitting function using the prediction error value, so as to continue to generate the predicted electrical quantity value using the optimized target fitting function.

[0107] In one embodiment, the prediction value generation module 202 includes:

[0108] The fitting parameter determination unit is used to determine the fitting parameters of the target fitting function based on the historical electrical quantity data received by the receiving simulation host.

[0109] The prediction value generation unit is used to linearly extrapolate the current electrical quantity data along the trend according to the fitting parameters of the target fitting function and the communication delay time, so as to obtain the predicted electrical quantity value of the receiving simulation host in the next simulation step.

[0110] In one embodiment, the fitting parameter determination unit includes:

[0111] The data sequence forming sub-unit is used to select the latest N simulation step size data points from the historical electrical quantity data received by the simulation host at the receiving end, and form a data sequence with the time point corresponding to each data point, where N is a positive integer.

[0112] The fitting parameter determination subunit is used to determine the fitting parameters of the target fitting function based on the data sequence using linear fitting.

[0113] In one embodiment, the prediction value generation unit includes:

[0114] The prediction value generation sub-unit is used to calculate the predicted electrical quantities for the next simulation step according to the following formula:

[0115]

[0116] in, This represents the predicted electrical quantity for the next simulation step. This indicates the current electrical quantity data. The fitting parameters represent the target fitting function. Indicates the communication delay time.

[0117] In one embodiment, the objective fitting function optimization module 203 includes:

[0118] The prediction error calculation unit is used to calculate the prediction error value according to the following formula:

[0119]

[0120] in, This represents the prediction error value. This indicates the next electrical quantity data received in the next simulation step. This represents the predicted electrical quantity value in the next simulation step. This represents the steady-state value used to normalize the prediction error.

[0121] In one embodiment, the objective fitting function optimization module 203 includes:

[0122] The parameter correction calculation unit is used to calculate the parameter correction of the target fitting function based on the prediction error value.

[0123] The fitting parameter adjustment unit is used to adjust the fitting parameters of the target fitting function according to the parameter correction amount.

[0124] In one embodiment, this application also provides a storage medium storing computer-readable instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of the communication delay compensation method for real-time simulation of a spatially distributed power system as described in any of the above embodiments.

[0125] In one embodiment, this application also provides a computer device storing computer-readable instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of the communication delay compensation method for real-time simulation of a spatially distributed power system as described in any of the above embodiments.

[0126] Indicatively, such as Figure 4 As shown, Figure 4 This is a schematic diagram of the internal structure of a computer device 300 provided in an embodiment of this application. The computer device 300 can be provided as a server. (Refer to...) Figure 4 The computer device 300 includes a processing component 302, which further includes one or more processors, and memory resources represented by memory 301 for storing instructions, such as application programs, that can be executed by the processing component 302. The application programs stored in memory 301 may include one or more modules, each corresponding to a set of instructions. Furthermore, the processing component 302 is configured to execute instructions to perform the communication delay compensation method for real-time simulation of spatially distributed power systems according to any of the above embodiments.

[0127] The computer device 300 may also include a power supply component 303 configured to perform power management of the computer device 300, a wired or wireless network interface 304 configured to connect the computer device 300 to a network, and an input / output (I / O) interface 305. The computer device 300 may operate on an operating system stored in memory 301, such as Windows Server™, Mac OS X™, Unix™, Linux™, Free BSD™, or similar.

[0128] Those skilled in the art will understand that Figure 4 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0129] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element. In this document, "a," "an," "the," "the," and "its" may also include plural forms unless the context clearly indicates otherwise. "Multiple" refers to at least two, such as 2, 3, 5, or 8, etc. "And / or" includes any and all combinations of the related listed items.

[0130] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. The various embodiments can be combined as needed, and the same or similar parts can be referred to each other.

[0131] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A communication delay compensation method for real-time simulation of spatially distributed power systems, characterized in that, The method includes: The communication delay time between the transmitting simulation host and the receiving simulation host in the spatial distributed power system is obtained, as well as the current electrical quantity data received by the receiving simulation host at the current simulation step. Based on the communication delay time, the current electrical quantity data, and the historical electrical quantity data received by the receiving simulation host, a target fitting function is used to generate the predicted electrical quantity value of the receiving simulation host in the next simulation step. The target fitting function is obtained by fitting the historical electrical quantity data. The predicted electrical quantity value is used as the input data of the receiving simulation host in the next simulation step to compensate for the data gap caused by the communication delay. Based on the next electrical quantity data received by the receiving simulation host in the next simulation step and the predicted electrical quantity value in the next simulation step, the prediction error value is calculated, and the target fitting function is optimized using the prediction error value, so as to continue to generate electrical quantity prediction values ​​using the optimized target fitting function.

2. The communication delay compensation method for real-time simulation of spatially distributed power systems according to claim 1, characterized in that, The step of generating the predicted electrical quantity value of the receiving simulation host for the next simulation step using a target fitting function based on the communication delay time, current electrical quantity data, and historical electrical quantity data received by the receiving simulation host in the past includes: Based on the historical electrical quantity data received by the receiving end simulation host, the fitting parameters of the target fitting function are determined; Based on the fitting parameters of the target fitting function and the communication delay time, the current electrical quantity data is linearly extrapolated along the trend to obtain the predicted electrical quantity value of the receiving simulation host in the next simulation step.

3. The communication delay compensation method for real-time simulation of spatially distributed power systems according to claim 2, characterized in that, The step of determining the fitting parameters of the target fitting function based on the historical electrical quantity data received by the receiving simulation host includes: The receiving simulation host selects the latest N simulation step size data points from the historical electrical quantity data received in the past, and forms a data sequence with the time point corresponding to each data point, where N is a positive integer. Based on the data sequence, the fitting parameters of the target fitting function are determined by linear fitting.

4. The communication delay compensation method for real-time simulation of spatially distributed power systems according to claim 2, characterized in that, The step of linearly extrapolating the current electrical quantity data along the trend according to the fitting parameters of the target fitting function and the communication delay time to obtain the predicted electrical quantity value of the receiving simulation host in the next simulation step includes: Calculate the predicted electrical quantities for the next simulation step using the following formula: in, This represents the predicted electrical quantity for the next simulation step. This indicates the current electrical quantity data. The fitting parameters of the target fitting function are represented. This indicates the communication delay time.

5. The communication delay compensation method for real-time simulation of spatially distributed power systems according to claim 1, characterized in that, The step of calculating the prediction error value based on the next electrical quantity data received by the receiving simulation host in the next simulation step and the predicted electrical quantity value in the next simulation step includes: The prediction error value is calculated using the following formula: in, This represents the prediction error value. This indicates the next electrical quantity data received in the next simulation step. This represents the predicted electrical quantity value in the next simulation step. This represents the steady-state value used to normalize the prediction error.

6. The communication delay compensation method for real-time simulation of spatially distributed power systems according to claim 1, characterized in that, The step of optimizing the target fitting function using the prediction error value includes: Based on the prediction error value, calculate the parameter correction amount of the target fitting function; The fitting parameters of the target fitting function are adjusted according to the parameter correction amount.

7. A communication delay compensation device for real-time simulation of a spatially distributed power system, characterized in that, The device includes: The communication delay time acquisition module is used to acquire the communication delay time between the transmitting end simulation host and the receiving end simulation host in the spatial distributed power system, as well as the current electrical quantity data received by the receiving end simulation host at the current simulation step. The prediction value generation module is used to generate the predicted electrical quantity of the receiving simulation host in the next simulation step based on the communication delay time, the current electrical quantity data and the historical electrical quantity data received by the receiving simulation host in the past, using a target fitting function. The target fitting function is obtained by fitting the historical electrical quantity data. The predicted electrical quantity is used as the input data of the receiving simulation host in the next simulation step to compensate for the data gap caused by the communication delay. The target fitting function optimization module is used to calculate the prediction error value based on the next electrical quantity data received by the receiving simulation host in the next simulation step and the predicted electrical quantity value in the next simulation step, and to optimize the target fitting function using the prediction error value, so as to continue to generate electrical quantity prediction values ​​using the optimized target fitting function.

8. The communication delay compensation device for real-time simulation of a spatially distributed power system according to claim 7, characterized in that, The predicted value generation module includes: The fitting parameter determination unit is used to determine the fitting parameters of the target fitting function based on the historical electrical quantity data received by the receiving end simulation host in the past. The prediction value generation unit is used to linearly extrapolate the current electrical quantity data along the trend according to the fitting parameters of the target fitting function and the communication delay time, so as to obtain the predicted electrical quantity value of the receiving end simulation host in the next simulation step.

9. A storage medium, characterized in that: The storage medium stores computer-readable instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of the communication delay compensation method for real-time simulation of a spatially distributed power system as described in any one of claims 1 to 6.

10. A computer device, characterized in that, include: One or more processors, and memory; The memory stores computer-readable instructions, which, when executed by the one or more processors, perform the steps of the communication delay compensation method for real-time simulation of a spatially distributed power system as described in any one of claims 1 to 6.

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