Data-driven short-circuit fault critical inertia prediction method for power system

Abstract

The application discloses a data-driven short-circuit fault critical inertia prediction method for a power system, and relates to the technical field of power system inertia prediction. The method comprises the following steps: constructing a typical day multi-period simulation model of a node system, setting different short-circuit fault scenes and obtaining a system frequency response curve; adjusting the inertia constant of a synchronous unit, respectively making the system frequency change rate reach a frequency change rate constraint value and the system frequency deviation reach a frequency minimum point constraint value, obtaining critical inertia under the two constraint conditions, and taking the larger value as the critical inertia under the fault condition; traversing all period steady-state operation conditions, constructing a typical day full-period critical inertia data set; inputting the constructed critical inertia data set into a long short-term memory network for training and testing, establishing a data-driven short-circuit fault critical inertia prediction model, and realizing accurate prediction of the short-circuit fault critical inertia of the power grid. The prediction method can accurately predict the critical inertia required to ensure frequency safety based on the constructed critical inertia data set, and provides an effective prediction means for preventing frequency accidents induced by short-circuit faults.

Description

Technical Field

[0001] This invention relates to the field of power system inertia prediction technology, specifically to a data-driven method for predicting the critical inertia of power system short-circuit faults. Background Technology

[0002] As the penetration rate of new energy sources in the power system continues to rise, the system's equivalent inertia level is constantly decreasing, significantly weakening its frequency disturbance immunity. In the event of sudden situations such as short-circuit faults, the system may experience frequency stability problems induced by power imbalances, potentially even leading to frequency accidents. Therefore, it is urgent to proactively predict frequency security risks triggered by short-circuit faults, especially to quickly and accurately predict the system's critical inertia, in order to ensure the safe operation of the power grid.

[0003] Currently, online assessment methods for critical inertia are lacking, with existing methods primarily relying on time-domain simulation and analytical calculation. Time-domain simulation utilizes advanced simulation tools to model the frequency dynamics of a system under the most severe fault scenarios and determines the critical inertia value that meets frequency safety requirements by gradually adjusting the system's inertia level. However, this method is computationally slow, making it difficult to rapidly assess the critical inertia during system transients. Analytical calculation methods mainly include the rate of change of frequency constraint method and the minimum frequency constraint method. The rate of change of frequency constraint method, based on the negative correlation between system inertia and the rate of change of frequency in the rotor motion equations, calculates the required critical inertia of the system under the premise of satisfying the maximum rate of change of frequency limit and the worst fault conditions. However, this method does not fully consider the impact of the minimum frequency constraint, which may lead to the system's frequency response meeting the rate of change of frequency limit in some fault scenarios, but still resulting in a frequency drop exceeding the safety limit. In contrast, the minimum frequency constraint method, based on the rotor motion equations, comprehensively considers multiple constraints such as the rate of change of frequency, the minimum frequency, and the quasi-steady-state frequency, thereby systematically deriving the critical inertia of the power system. However, because this method uses a linearized approximation for the primary frequency regulation response of the equivalent generator set, there is a certain deviation between the theoretical calculation result and the actual value of the critical inertia.

[0004] Therefore, there is an urgent need to develop a critical inertia prediction method that can adapt to changing operating modes and take into account frequency safety constraints. Essentially, this method uses a pre-constructed critical inertia dataset to quickly and accurately predict the critical inertia of a system under short-circuit faults, thereby effectively predicting whether the system frequency remains within a safe range after a fault, and providing crucial decision-making support for scheduling operations and safety control. Summary of the Invention

[0005] This invention proposes a data-driven method for predicting the critical inertia of short-circuit faults in power systems. Based on a pre-built critical inertia dataset, it can accurately predict the critical inertia required to ensure frequency safety. This method provides an effective means of prediction for preventing frequency accidents induced by short-circuit faults.

[0006] The technical solution adopted in this invention is as follows:

[0007] A data-driven method for predicting the critical inertia of short-circuit faults in power systems includes the following steps: Step 1: Construct a typical daily multi-period simulation model of the node system, set different short-circuit fault scenarios, and obtain the system frequency response curve; Step 2: Adjust the inertia constant of the synchronous generator unit to make the system frequency change rate reach the frequency change rate constraint value and the system frequency deviation reach the minimum frequency point constraint value respectively. Obtain the critical inertia under the two constraint conditions and take the larger value as the critical inertia under the fault condition. Step 3: Traverse all steady-state operating conditions for all time periods to construct a typical daily all-time critical inertia dataset; Step 4: Input the critical inertia dataset constructed in Step 3 into the Long Short-Term Memory network for training and testing, establish a data-driven short-circuit fault critical inertia prediction model, and achieve accurate prediction of the critical inertia of power grid short-circuit faults.

[0008] In step 1, an improved simulation model of the New England 10-unit 39-bus system is built in the power system analysis and synthesis program, and the steady-state operating conditions during a typical day of 96 hours are determined; the synchronous units connected to nodes 34 and 37 in the original 39-bus system are replaced with wind farms and photovoltaic power stations. 1.1: The output power of wind farms and photovoltaic power plants in each time period was determined based on actual wind speed and solar irradiance data over 96 time periods. The expression for the output power of wind farms in relation to wind speed is: (1); In formula (1): P w ( v )and P wr These are the output power of the wind farm and the output power of the wind farm at rated wind speed, respectively. v , v c , v r and v co These are the actual wind speed, cut-in wind speed, rated wind speed, and cut-out wind speed of the wind farm, respectively.

[0009] 1.2: For photovoltaic power plants, their output power is directly proportional to the light intensity. Assuming the operating temperature of the photovoltaic array has a negligible impact on the output power, the output power of a photovoltaic power plant can be approximated as: (2); In formula (2): P v This is expressed as the output power of a photovoltaic power station; η , S , I These represent the photoelectric conversion efficiency, total area, and light intensity of the photovoltaic array composed of solar panels, respectively.

[0010] Within a single time period, short-circuit faults are applied to the buses of each synchronous generator unit and the load bus, causing adjacent synchronous generator units and loads to disconnect from the grid. The frequency response curve of the system's center frequency of inertia is obtained through time-domain simulation, and its dynamic characteristic parameters, including the rate of frequency change and the minimum frequency value, are extracted. Figure 1 As shown, this provides a data basis for the subsequent determination of critical inertia.

[0011] In step 2, after the short-circuit fault is cleared and the unit or load is disconnected from the grid, the system's active power balance is disrupted, resulting in a power deficit or surplus, which in turn causes a dynamic shift in the system's inertia center frequency. The speed and amplitude of the system's frequency response are mainly affected by the system's equivalent inertia, unbalanced power, primary frequency regulation response, and damping effect. To characterize the critical inertia and overall frequency behavior after the fault, the system's equivalent inertia and inertia center frequency are introduced as characterizing quantities. The system's equivalent inertia can be expressed as: (3); In formula (3): H G,i , S G,i The first i The inertia constant and rated capacity of the synchronous generator set; H vir,j , S vir,j These are new energy power stations equipped with virtual inertia control technology. j The virtual inertia constant and rated capacity; m and n These represent the total number of synchronous generator sets and the total number of new energy power stations in the system, respectively. The center frequency of inertia is expressed as: (4); In equation (4): f i Represented as the first i The frequency of the synchronous generator set.

[0012] The analytical solution for the critical inertia is obtained by using the primary frequency regulation model and equivalent parameters of the synchronous generators in the aggregated power grid, and by linearizing the primary frequency regulation response of the equivalent generator units in the power grid. The critical inertia is then solved based on the equivalent rotor motion equations of the power grid, combined with RoCoF constraints and minimum frequency point constraints. The equivalent rotor motion equations of the power grid are expressed as follows: (5); In formula (5): f N The system's rated frequency; f ( t ), D and f ( t ) are respectively t The system's inertia center frequency, the damping coefficient of the system's equivalent synchronous generator, and the time-varying inertia center frequency, and the damping coefficient of the system's equivalent synchronous generator. t The frequency offset of the system inertia center at any given moment; P m ( t )and P e ( t ) are respectively t The total mechanical power and total electromagnetic power of the entire system at any given time.

[0013] Since the system's frequency change rate reaches its maximum value at the instant of the fault, and the frequency offset is negligible at this point, and considering the inertia loss caused by the short-circuit fault, the critical inertia under the corresponding frequency change rate constraint is... H 1 is represented as: (6); In formula (6): H loss This refers to the inertia loss caused by a short-circuit fault in the system. P It represents the unbalanced power of the system, which is the difference between the total mechanical power and the total electromagnetic power of the entire system.

[0014] Based on the linearized primary frequency regulation response of the equivalent generator unit in the power grid, it is assumed that when t A short circuit fault occurs at time 0, and the frequency begins to deviate from the rated frequency. f N The equivalent generator set of the power grid has passed through t r Start a frequency modulation after a delay, and in t min The frequency of time drops to its lowest point f min During this period, the equivalent generating units of the power grid are adjusted according to the droop coefficient of the primary frequency regulation. RAdjust the active power output, such as Figure 2 As shown. Therefore, the critical inertia under the constraint of the lowest system frequency point is... H 2 is represented as: (7); However, the linearization of the primary frequency regulation response of the equivalent generator units in the system neglects the continuous dynamic changes in the system frequency change rate and the active power output of the equivalent generator units during transient processes. Furthermore, in complex power grids, the primary frequency regulation response characteristics of each generator are difficult to accurately represent by a single equivalent model, and the actual system frequency response characteristics may differ significantly from those of the equivalent generator unit model. Therefore, the critical inertia obtained analytically inevitably contains errors, especially in structurally complex power grids where the deviation between the analytical results and the actual critical inertia is even more significant.

[0015] 2.1: Therefore, based on the dynamic characteristics of the inertia center frequency response curve under this fault condition, it is necessary to adjust the inertia constants of each synchronous generator unit in the power grid so that the frequency change rate reaches the set frequency change rate constraint value (currently set to 0.5Hz / s), such as... Figure 3 As shown. Because the current power grid is in a critical transient state, the system's equivalent inertia... H sys1 The critical inertia under this constraint. The critical inertia of this constraint Represented as: (8); In equation (8): H G,i,1 , S G,i,1 These are the first two numbers under the given constraints. i The inertia constant and rated capacity of the synchronous generator set; H vir,j,1 , S vir,j,1 These are new energy power stations equipped with virtual inertia control technology under this constraint. j The virtual inertia constant and rated capacity.

[0016] 2.2: Similarly, based on the dynamic characteristics of the inertia center frequency response curve under this fault condition, continue to adjust the inertia constant of each synchronous generator set so that the frequency deviation reaches the set minimum frequency constraint value (currently set to 49Hz). Figure 4 As shown. Because the current power grid is in a critical transient state, the system's equivalent inertia... H sys2 The critical inertia under this constraint. The critical inertia of this constraint Represented as: (9); In equation (9): H G,i,2 , S G,i,2 These are the first two numbers under the given constraints. i The inertia constant and rated capacity of the synchronous generator set; H vir,j,2 , S vir,j,2 These are new energy power stations equipped with virtual inertia control technology under this constraint. j The virtual inertia constant and rated capacity.

[0017] To ensure that the system simultaneously meets the dual safety requirements of frequency change rate and frequency minimum point after a short-circuit fault, the larger of the two calculated critical inertia is taken as the critical inertia that satisfies the frequency safety constraint under this fault condition. Represented as: (10).

[0018] In step 3, the steady-state operating conditions are traversed over 96 time periods to systematically construct a critical inertia dataset covering the entire time period of a typical day. This dataset is stored in tabular form and contains 2400 sets of sample data.

[0019] The input features recorded in the dataset include the inertia constant, primary frequency regulation droop coefficient, primary frequency regulation delay time, damping effect coefficient, active power of each load before disturbance, location of short-circuit fault (numerically represented by bus node number), unbalanced power caused by fault, inertia loss, and output feature value of critical inertia value of short-circuit fault, as shown in Table 1.

[0020] In step 4, to eliminate the impact of differences in feature dimensions on the model training results and improve the model training speed and stability, the input features are normalized. The normalization expression is as follows: (11); In equation (11): x´ and x These are the data after processing and the data before processing, respectively, for this feature quantity; x max and x min These are the maximum and minimum values ​​of the feature in the dataset, respectively.

[0021] In step 4, since the critical inertia has a significant nonlinear coupling relationship with parameters such as system operation mode, fault location, power deficit degree and frequency modulation, it is difficult to accurately describe it through an explicit analytical model. Therefore, a Long Short-Term Memory (LSTM) network is used to establish a nonlinear mapping between input features and critical inertia.

[0022] An LSTM network consists of multiple LSTM units, and the internal structure of an LSTM unit is as follows: Figure 5 As shown, an LSTM cell consists of four parts: a storage state, a forget gate, an input gate, and an output gate. The storage state includes the cell state. C and hidden state H A gating device is a mechanism that selectively allows information to pass through, achieved through a series of mathematical operations and activation functions. A forgetting gate combines the hidden state of the previous unit. H t-1 and the input sequence data of this unit X t Selectively forget the state of the previous unit. C t-1 The mathematical model of the forgetting gate can be expressed as: (12); in: σ It is an activation function whose output is between 0 and 1; f The output of the forget gate is the cell state of the forgotten cell. Ct-1 The probability of; Wxf , Whf and bf These are the input sequence data for this unit. Xt The previous unit is in a hidden state. Ht-1 The weight matrix and bias matrix of the forget gate. The input gate mainly consists of two activation functions. The first activation function uses the activation function. σ Its mathematical model is: (13); in: i This is the output of the activation function in the first part; Wxi , Whi and bi These are the input sequence data for this unit. Xt The previous unit is in a hidden state. Ht-1 The weight matrix and bias matrix of the first part of the input gate. The activation function of the first part represents the degree to which the output information of the activation function of the second part is preserved. The activation function of the second part uses the hyperbolic tangent activation function tanh, whose mathematical model is: (14); in: C β This is the output of the activation function in the second part; W xc , W hc and b c These are the input sequence data for this unit. X t The previous unit is in a hidden state. H t-1 The second part of the input gate contains the weight matrix and bias matrix. The activation function in the second part represents the creation of an alternative. C β Based on the forget gate and the input gate, the cell state of this unit... C t It has been updated, and its mathematical model is as follows: (15); in: Ct This represents the cell state; ⊙ and + represent element-wise multiplication and addition operations. The output gate also consists of two activation functions. The first activation function uses an activation function. σ Its mathematical model is: (16); in: Ot This is the output of the activation function in the first part; Wxo , Who and bo These are the input sequence data for this unit. Xt The previous unit is in a hidden state. Ht-1 The weight and bias matrices of the first part of the output gate. Similarly, the activation function of the first part represents the degree to which the output information of the activation function of the second part is preserved, and the activation function of the second part uses the hyperbolic tangent activation function tanh. Based on the updated cell states... Ct Update to get the hidden state of this unit. Ht Its mathematical model is: (17); Updated cell status Ct and hidden state Ht The data is then applied to the next unit, thus enabling the LSTM network to efficiently process and analyze the data.

[0023] Long Short-Term Memory (LSTM) networks control information transmission and memory updates through forget gates, input gates, and output gates, effectively extracting the coupling relationships between multiple features and improving prediction accuracy and generalization ability under complex conditions.

[0024] In step 4, 80% of the dataset and 20% of the dataset are randomly divided into training and test sets, respectively, and then input into the LSTM model for training and testing. The training set is used to learn the parameters of the prediction model, and the test set is used to verify the model's predictive ability for unknown samples. The construction process is as follows: Figure 5 As shown.

[0025] To objectively quantify and compare the prediction performance of different deep learning models, LSTM, convolutional neural network (CNN), and artificial neural network (ANN) were selected and validated on the same test set. The performance of the models was comprehensively judged by introducing three major evaluation indicators: root mean square error (RMSE), mean relative error (MRE), and maximum absolute error (MAE). The mathematical expressions for their calculation are shown in equations (18) to (19). (18); (19); (20); In the above formula: M This represents the total number of samples; X i and Y i The first i The simulated values ​​of the critical inertia and the predicted values ​​are given. RMSE is used to measure the overall error level of the model; MRE is used to measure the average error level of the model; and MAE is used to characterize the maximum deviation under the most unfavorable sample.

[0026] Deep learning prediction models are often considered "black box" models due to the opaque nature of their internal decision-making processes. Furthermore, to improve the interpretability of the constructed critical inertia prediction model, the Shapley additive explanation method (SHAP) is introduced into the trained LSTM model to quantify the contribution of each input feature to the model output. For any sample... x =[ x 1, x 2··· x n The output of the trained prediction model can be represented as: (twenty one); In equation (21): H cr ( x ) as a sample x The corresponding predicted critical inertia value for short-circuit faults; 0 represents the model's baseline output value on the background sample set; j For the first j The SHAP contribution of each input feature to the prediction result of this sample. j The SHAP contribution value of each input feature can be expressed as: (twenty two); In equation (22): N ={1,2,…, n} represents the set of indices for all input features; S For any subset of features that does not contain the j-th feature; | S | represents the number of features in the subset; This indicates that only a subset of features is used. S The critical inertia output of the model for the sample; Indicates in subset S Add the first one based on the existing one j The model output after the first feature. The difference between the two represents the first feature. j The marginal contribution of each feature to the predicted critical inertia value under the current feature combination.

[0027] By calculating the SHAP value of each input feature, the influence of different operating modes, fault locations, unbalanced power, inertia loss, primary frequency modulation droop coefficient, primary frequency modulation delay, and damping coefficient on the critical inertia prediction results can be obtained. The global importance of a feature can be obtained by averaging the absolute values ​​of its SHAP values ​​across all samples; its expression is as follows: (twenty three); In equation (23): I j Let be the global importance of the j-th feature; M The total number of samples; For the first i In the nth sample j The SHAP value corresponds to each feature. The higher the global importance, the more significant the impact of that feature on the prediction result of the critical inertia of short-circuit faults.

[0028] Based on the above SHAP analysis results, we can not only explain the reasons for the formation of single sample prediction values, but also identify the key dominant factors affecting the critical inertia of system short-circuit faults from a global perspective, thereby improving the credibility and engineering usability of model prediction results.

[0029] In practical applications, the system characteristics under the current operating conditions are input into the trained prediction model, which can quickly output the critical inertia prediction value under the corresponding short-circuit fault scenario, thereby providing a basis for power grid frequency security early warning and inertia resource allocation.

[0030] This invention provides a data-driven method for predicting the critical inertia of short-circuit faults in power systems, with the following technical advantages: 1) Step 2 of this invention determines the system inertia by simultaneously introducing frequency change rate constraints and frequency minimum point constraints, and takes the larger value that satisfies the two types of constraints as the critical inertia. This effectively avoids the problem of incomplete frequency safety assessment under a single constraint condition, making the critical inertia result more conservative and reliable, and able to more realistically reflect the frequency safety requirements of the system under short-circuit faults.

[0031] 2) Step 3 of this invention constructs a critical inertia dataset covering different time periods, different fault locations, and grid disconnection combinations by traversing the steady-state operating conditions of typical intraday periods. It fully considers the impact of load level and new energy output changes on system inertia demand, improves the comprehensiveness and representativeness of data samples, and provides a reliable data foundation for subsequent data-driven model training.

[0032] 3) Step 4 of this invention trains and tests the prediction model based on the constructed critical inertia dataset, so as to achieve fast and accurate prediction of critical inertia, reduce online computational complexity, and enhance the application value of the method in actual power system operation and scheduling.

[0033] 4) In high-proportion renewable energy power systems, the method proposed in this invention can accurately predict the critical inertia required to ensure frequency safety based on the established critical inertia dataset. This method provides an effective predictive tool for preventing frequency accidents induced by short-circuit faults. Attached Figure Description

[0034] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 The inertia center frequency response curve under a short-circuit fault on bus 35.

[0035] Figure 2 A schematic diagram of the linearization of the primary frequency regulation response of the equivalent synchronous generator in the system.

[0036] Figure 3 The frequency response curve of the center of inertia to meet the frequency change rate constraint.

[0037] Figure 4 The frequency response curve of the center of inertia to meet the minimum frequency constraint condition.

[0038] Figure 5 This refers to the internal structure of the Long Short-Term Memory (LSTM) unit.

[0039] Figure 6 This is a flowchart of the construction process for the LSTM network prediction model.

[0040] Figure 7 To improve the network topology of the New England 10-machine 39-node system.

[0041] Figure 8 This is a typical daily power variation curve of the load.

[0042] Figure 9 This is a typical intraday variation curve of wind speed.

[0043] Figure 10 This is a typical intraday variation curve of light intensity.

[0044] Figure 11 The critical inertia prediction diagram for 200 test samples.

[0045] Figure 12 This is a flowchart of an embodiment of the present invention.

[0046] Figure 13 The SHAP values ​​are for each feature that accounts for 80% of the training set. Detailed Implementation

[0047] This invention proposes a data-driven method for predicting the critical inertia of a power system short-circuit fault, which is used to accurately predict the critical inertia of the power grid after a short-circuit fault occurs.

[0048] First, an improved simulation model of the New England 10-unit 39-bus system was constructed based on the power system analysis and synthesis program. The steady-state operating conditions of 96 time periods on a typical day were determined. Different short-circuit fault scenarios were set at each node, and the frequency response curve of the system inertia center frequency was obtained through time-domain simulation. Subsequently, by adjusting the inertia constant of the synchronous generator set in the system, the system frequency change rate was made to reach the preset frequency change rate constraint value and the system frequency deviation was made to reach the minimum frequency point constraint value, respectively. The critical inertia under the two constraint conditions was calculated, and the larger value was taken as the critical inertia that satisfies the frequency safety constraint condition under the corresponding short-circuit fault condition. Next, the steady-state operating conditions of each time period within a typical day are traversed, and a critical inertia dataset covering the entire time period of a typical day, different fault locations, and offline combination conditions is systematically constructed. Finally, the constructed critical inertia dataset is input into a long short-term memory network model for training and testing, establishing a data-driven short-circuit fault critical inertia prediction model, thereby achieving rapid and accurate prediction of the critical inertia of power system short-circuit faults. The overall process is as follows: Figure 12 As shown, it includes the following steps.

[0049] Step a: Build, for example, a power system analysis and integration program. Figure 7 The improved simulation model of the New England 10-unit 39-bus system shown specifically replaces the synchronous turbines connected to nodes 34 and 37 in the original 39-bus system with wind farms and photovoltaic power stations; the load level of the typical daily 96-hour steady-state operating condition is based on actual load data from a certain area in Chongqing, such as... Figure 8 As shown. Based on actual wind speed and solar intensity data for 96 time periods in the region, respectively, as shown below. Figure 9 and Figure 10 As shown, the output power of wind farms and photovoltaic power plants is determined at different times. The expression for the output power of wind farms and wind speed is: (1); In the formula: P w ( v )and P wr These are the output power of the wind farm and the output power of the wind farm at rated wind speed, respectively. v , v c , v r and v co These represent the actual wind speed, cut-in wind speed, rated wind speed, and cut-out wind speed of the wind farm, respectively. For photovoltaic power plants, their output power is directly proportional to the solar irradiance. Assuming the operating temperature of the photovoltaic array has a negligible impact on the output power, the output power of a photovoltaic power plant can be approximated as: (2); In formula (2): P v This is expressed as the output power of a photovoltaic power station; η , S , I These represent the photoelectric conversion efficiency, total area, and irradiance of the photovoltaic array composed of solar panels, respectively. The remaining eight synchronous generator units employ a stepped output regulation strategy based on the average system load level, with eight power levels (80%–95%, 105%–120%, in 5% increments) set to balance the remaining system load and ensure that power generation output precisely matches load demand. The power generation plans for each synchronous unit and station are summarized in Table 2.

[0050] Within a single time period, short-circuit faults are applied to the buses of each synchronous generator unit and the load bus, causing adjacent synchronous generator units and loads to disconnect from the grid. The frequency response curve of the system's center frequency of inertia is obtained through time-domain simulation, and its dynamic characteristic parameters, including the rate of frequency change and the minimum frequency value, are extracted. Figure 1 As shown, this provides a data basis for the subsequent determination of critical inertia.

[0051] Step b: After the short-circuit fault is cleared and the unit or load is disconnected from the grid, the system's active power balance is disrupted, resulting in a power deficit or surplus, which in turn causes a dynamic shift in the system's inertia center frequency. The speed and amplitude of the system's frequency response are mainly affected by the system's equivalent inertia, unbalanced power, primary frequency regulation response, and damping effects. To characterize the critical inertia and overall frequency behavior after the fault, the system's equivalent inertia and inertia center frequency are introduced as characterizing quantities. The system's equivalent inertia can be expressed as: (3); In formula (3): H G,i , S G,i The first i The inertia constant and rated capacity of the synchronous generator set; H vir,j , S vir,j These are new energy power stations equipped with virtual inertia control technology. j The virtual inertia constant and rated capacity; m and n These represent the total number of synchronous generator sets and the total number of new energy power stations in the system, respectively. The center frequency of inertia is expressed as: (4); In equation (4): f i Represented as the first i The frequency of the synchronous generator set.

[0052] The analytical solution for the critical inertia is obtained by aggregating the primary frequency regulation model and equivalent parameters of synchronous generators in the power grid, linearizing the primary frequency regulation response of the equivalent generator units in the power grid, and solving for the critical inertia based on the equivalent rotor motion equations of the power grid, combined with RoCoF constraints and minimum frequency point constraints.

[11] The equivalent rotor motion equation of the power grid is expressed as: (5); In formula (5): f N The system's rated frequency; f ( t ), D and f ( t ) are respectively t The system's inertia center frequency, the damping coefficient of the system's equivalent synchronous generator, and the time-varying inertia center frequency, and the damping coefficient of the system's equivalent synchronous generator. tThe frequency offset of the system inertia center at any given moment; P m ( t )and P e ( t ) are respectively t The total mechanical power and total electromagnetic power of the entire system at any given time.

[0053] Since the system's frequency change rate reaches its maximum value at the instant of the fault, and the frequency offset is negligible at this point, and considering the inertia loss caused by the short-circuit fault, the critical inertia under the corresponding frequency change rate constraint is... H 1 is represented as: (6); In the formula: H loss This refers to the inertia loss caused by a short-circuit fault in the system. P It represents the unbalanced power of the system, which is the difference between the total mechanical power and the total electromagnetic power of the entire system.

[0054] Based on the linearized primary frequency regulation response of the equivalent generator unit in the power grid, it is assumed that when t A short circuit fault occurs at time 0, and the frequency begins to deviate from the rated frequency. f N The equivalent generator set of the power grid has passed through t r Start a frequency modulation after a delay, and in t min The frequency of time drops to its lowest point f min During this period, the equivalent generating units of the power grid are adjusted according to the droop coefficient of the primary frequency regulation. R Adjust the active power output, such as Figure 2 As shown. Therefore, the critical inertia under the constraint of the lowest system frequency point is... H 2 is represented as: (7); However, the linearization of the primary frequency regulation response of the equivalent generator units in the system neglects the continuous dynamic changes in the system frequency change rate and the active power output of the equivalent generator units during transient processes. Furthermore, in complex power grids, the primary frequency regulation response characteristics of each generator are difficult to accurately represent by a single equivalent model, and the actual system frequency response characteristics may differ significantly from those of the equivalent generator unit model. Therefore, the critical inertia obtained analytically inevitably contains errors, especially in structurally complex power grids where the deviation between the analytical results and the actual critical inertia is even more significant.

[0055] 2.1: Therefore, based on the dynamic characteristics of the inertia center frequency response curve under this fault condition, it is necessary to adjust the inertia constants of each synchronous generator unit in the power grid so that the frequency change rate reaches the set frequency change rate constraint value (currently set to 0.5Hz / s), such as... Figure 2 As shown. Because the current power grid is in a critical transient state, the system's equivalent inertia... H sys1 The critical inertia under this constraint. The critical inertia of this constraint Represented as: (8); In equation (8): H G,i,1 , S G,i,1 These are the first two numbers under the given constraints. i The inertia constant and rated capacity of the synchronous generator set; H vir,j,1 , S vir,j,1 These are new energy power stations equipped with virtual inertia control technology under this constraint. j The virtual inertia constant and rated capacity.

[0056] 2.2: Similarly, based on the dynamic characteristics of the inertia center frequency response curve under this fault condition, continue to adjust the inertia constant of each synchronous generator set so that the frequency deviation reaches the set minimum frequency constraint value (currently set to 49Hz). Figure 3 As shown. Because the current power grid is in a critical transient state, the system's equivalent inertia... H sys2 The critical inertia under this constraint. The critical inertia of this constraint Represented as: (9); In equation (9): H G,i,2 , S G,i,2 These are the first two numbers under the given constraints. i The inertia constant and rated capacity of the synchronous generator set; H vir,j,2 , S vir,j,2 These are new energy power stations equipped with virtual inertia control technology under this constraint. j The virtual inertia constant and rated capacity.

[0057] To ensure that the system simultaneously meets the dual safety requirements of frequency change rate and frequency minimum point after a short-circuit fault, the larger of the two calculated critical inertia is taken as the critical inertia that satisfies the frequency safety constraint under this fault condition. Represented as: (10).

[0058] Step c: Repeat steps a and b above, traversing 96 steady-state operating conditions, to systematically construct a critical inertia dataset covering the entire time period of a typical day. This dataset is stored in tabular form and contains 2400 sets of sample data.

[0059] The input features recorded in the dataset include the inertia constant, primary frequency regulation droop coefficient, primary frequency regulation delay time, damping effect coefficient, active power of each load before disturbance, location of short-circuit fault (numerically represented by bus node number), unbalanced power caused by fault, inertia loss, and output feature value of critical inertia value of short-circuit fault, as shown in Table 1.

[0060]

[0061] Through the correspondence between the above multidimensional feature parameters and critical inertia, the constructed dataset can comprehensively reflect the changing characteristics of the system's critical inertia under different operating conditions and different short-circuit fault conditions, providing a sufficient and reliable data foundation for subsequent training and testing of data-driven critical inertia prediction models.

[0062] Step d: To eliminate the impact of differences in feature dimensions on model training results and improve model training speed and stability, the input features are normalized. The normalization expression is: (11); In equation (11): x´ and x These are the data after processing and the data before processing, respectively, for this feature quantity; x max and x min These are the maximum and minimum values ​​of the feature in the dataset, respectively.

[0063] In step d, since the critical inertia has a significant nonlinear coupling relationship with parameters such as system operation mode, fault location, power deficit degree and frequency modulation, it is difficult to accurately describe it through an explicit analytical model. Therefore, a Long Short-Term Memory (LSTM) network is used to establish a nonlinear mapping between input features and critical inertia.

[0064] An LSTM network consists of multiple LSTM units, and the internal structure of an LSTM unit is as follows: Figure 5 As shown, an LSTM cell consists of four parts: a storage state, a forget gate, an input gate, and an output gate. The storage state includes the cell state. C and hidden state H A gating device is a mechanism that selectively allows information to pass through, achieved through a series of mathematical operations and activation functions. A forgetting gate combines the hidden state of the previous unit. H t-1 and the input sequence data of this unit X t Selectively forget the state of the previous unit. C t-1 The mathematical model of the forgetting gate can be expressed as: (12); in: σ It is an activation function whose output is between 0 and 1; f The output of the forget gate is the cell state of the forgotten cell. Ct-1 The probability of; Wxf , Whf and bf These are the input sequence data for this unit. Xt The previous unit is in a hidden state. Ht-1 The weight matrix and bias matrix of the forget gate. The input gate mainly consists of two activation functions. The first activation function uses the activation function. σ Its mathematical model is: (13); in: i This is the output of the activation function in the first part; Wxi , Whi and bi These are the input sequence data for this unit. Xt The previous unit is in a hidden state. Ht-1 The weight matrix and bias matrix of the first part of the input gate. The activation function of the first part represents the degree to which the output information of the activation function of the second part is preserved. The activation function of the second part uses the hyperbolic tangent activation function tanh, whose mathematical model is: (14); in: C β This is the output of the activation function in the second part; W xc , W hc and b cThese are the input sequence data for this unit. X t The previous unit is in a hidden state. H t-1 The second part of the input gate contains the weight matrix and bias matrix. The activation function in the second part represents the creation of an alternative. C β Based on the forget gate and the input gate, the cell state of this unit... C t It has been updated, and its mathematical model is as follows: (15); in: Ct This represents the cell state; ⊙ and + represent element-wise multiplication and addition operations. The output gate also consists of two activation functions. The first activation function uses an activation function. σ Its mathematical model is: (16); in: Ot This is the output of the activation function in the first part; Wxo , Who and bo These are the input sequence data for this unit. Xt The previous unit is in a hidden state. Ht-1 The weight and bias matrices of the first part of the output gate. Similarly, the activation function of the first part represents the degree to which the output information of the activation function of the second part is preserved, and the activation function of the second part uses the hyperbolic tangent activation function tanh. Based on the updated cell states... Ct Update to get the hidden state of this unit. Ht Its mathematical model is: (17); Updated cell status Ct and hidden state Ht The data is then applied to the next unit, thus enabling the LSTM network to efficiently process and analyze the data.

[0065] LSTM controls information transmission and memory updates through forget gates, input gates, and output gates, which can effectively extract the coupling relationship between multiple features and improve prediction accuracy and generalization ability under complex conditions.

[0066] In step d, 80% of the dataset and 20% of the dataset are randomly divided into training and test sets, respectively, and then input into the LSTM model for training and testing. The training set is used to learn the parameters of the prediction model, and the test set is used to verify the model's predictive ability for unknown samples. The construction process is as follows: Figure 6 As shown.

[0067] To objectively quantify and compare the prediction performance of different deep learning models, LSTM, CNN, and ANN were selected and validated on the same test set. The performance of the models was comprehensively judged by introducing three evaluation indicators: root mean square error (RMSE), mean relative error (MRE), and maximum absolute error (MAE). The mathematical expressions for their calculation are shown in equations (18) to (19). (18); (19); (20); In the above formula: M This represents the total number of samples; X i and Y i The first i The simulated values ​​of the critical inertia and the predicted values ​​are given. RMSE is used to measure the overall error level of the model; MRE is used to measure the average error level of the model; and MAE is used to characterize the maximum deviation under the most unfavorable sample.

[0068] Deep learning prediction models are often considered "black box" models due to the opaque nature of their internal decision-making processes. Furthermore, to improve the interpretability of the constructed critical inertia prediction model, the Shapley additive explanation method (SHAP) is introduced into the trained LSTM model to quantify the contribution of each input feature to the model output. For any sample... x =[ x 1, x 2··· x n The output of the trained prediction model can be represented as: (twenty one); Where: H cr ( x ) as a sample x The corresponding predicted critical inertia value for short-circuit faults; 0 represents the model's baseline output value on the background sample set; j For the first j The SHAP contribution of each input feature to the prediction result of this sample. j The SHAP contribution value of each input feature can be expressed as: (twenty two); In the formula: N ={1,2,…, n} represents the set of indices for all input features; S Not including the first j Any subset of features; | S | represents the number of features in the subset; f S ( x S ) indicates that only a subset of features is used. S The critical inertia output of the model for the sample; Indicates in subset S Add the first one based on the existing one j The model output after the first feature. The difference between the two represents the first feature. j The marginal contribution of each feature to the predicted critical inertia value under the current feature combination.

[0069] By calculating the SHAP value of each input feature, the influence of different operating modes, fault locations, unbalanced power, inertia loss, primary frequency modulation droop coefficient, primary frequency modulation delay, and damping coefficient on the critical inertia prediction results can be obtained. The global importance of a feature can be obtained by averaging the absolute values ​​of its SHAP values ​​across all samples; its expression is as follows: (twenty three); In the formula: I j Let be the global importance of the j-th feature; M The total number of samples; j (i) For the first i In the nth sample j The SHAP value corresponds to each feature. The higher the global importance, the more significant the impact of that feature on the prediction result of the critical inertia of short-circuit faults.

[0070] Based on the above SHAP analysis results, we can not only explain the reasons for the formation of single sample prediction values, but also identify the key dominant factors affecting the critical inertia of system short-circuit faults from a global perspective, thereby improving the credibility and engineering usability of model prediction results.

[0071] In practical applications, the system characteristics under the current operating conditions are input into the trained prediction model, which can quickly output the critical inertia prediction value under the corresponding short-circuit fault scenario, thereby providing a basis for power grid frequency security early warning and inertia resource allocation.

[0072] Step e: The above-established data-driven critical inertia prediction method for power system short-circuit faults is analyzed for accuracy through numerical examples.

[0073] Build such a system in the power system comprehensive analysis program Figure 7 The improved simulation model of the New England 10-unit 39-node system is shown. The power generation plans of each synchronous unit and station are summarized in Table 2.

[0074]

[0075]

[0076] To ensure the realism of model training and testing, 80% of the dataset and 20% of the dataset were randomly divided into training and testing sets. The processed data was then input into the LSTM model for training and testing.

[0077] The prediction results of 200 randomly selected test samples are as follows: Figure 11 As shown. From Figure 11 It can be seen that the LSTM model performs well overall in predicting critical inertia. Except for a few critical inertia that are too large or too small, the prediction error is relatively high, while the other critical inertia can be predicted relatively accurately.

[0078] To verify the superiority of the LSTM model in predicting critical inertia, this invention compares and analyzes the prediction performance of the LSTM model with that of the CNN and ANN models. RMSE, MRE, and MAE are introduced to further evaluate the prediction accuracy of each model.

[0079] The processed data was input into each model for training and testing, and the error test performance of the three models was compared. Before conducting the model comparison, the LSTM model, convolutional CNN model, and ANN model were trained and tested multiple times using a grid search method, and their network structure and hyperparameters were adjusted to obtain better prediction performance.

[0080] Based on the above settings, an error test comparison table of the three models is obtained, as shown in Table 3.

[0081]

[0082] As shown in Table 3, the LSTM model performed best in the error test for predicting critical inertia, demonstrating the superiority of LSTM.

[0083] With the training set comprising 80% of the total dataset, the contribution ranking of each feature was obtained by introducing the SHAP analysis method, as follows: Figure 13 As shown. Figure 13As shown, the analytical results of the SHAP feature contribution based on the LSTM model indicate that the contributions of different input features in the critical inertia prediction task vary significantly. The SHAP value of feature 8 is significantly higher than other features, indicating that the unbalanced power caused by the fault plays a dominant role in critical inertia prediction. The SHAP values ​​of features 7 and 9 are also relatively large, indicating that the fault location and inertia loss have a significant impact on the prediction results. The SHAP values ​​of features 2 and 3 are in the third tier, reflecting the contribution of the power generation plan to critical inertia prediction. The SHAP values ​​of features 3, 4, and 5 reflect the impact of primary frequency regulation on critical inertia prediction. Furthermore, since the inertia of synchronous generators and new energy power plants remains constant, the SHAP value of feature 1 is close to zero, indicating that its impact on critical inertia prediction is extremely limited. Therefore, fault-related unbalanced power is the dominant feature in critical inertia prediction, while other features have varying degrees of auxiliary influence.

Claims

1. A data-driven method for predicting the critical inertia of short-circuit faults in power systems, characterized in that... Includes the following steps: Step 1: Construct a typical daily multi-period simulation model of the node system, set different short-circuit fault scenarios, and obtain the system frequency response curve; Step 2: Adjust the inertia constant of the synchronous generator unit to make the system frequency change rate reach the frequency change rate constraint value and the system frequency deviation reach the minimum frequency point constraint value respectively. Obtain the critical inertia under the two constraint conditions and take the larger value as the critical inertia under the fault condition. Step 3: Traverse all steady-state operating conditions for all time periods to construct a typical daily all-time critical inertia dataset; Step 4: Input the critical inertia dataset constructed in Step 3 into the Long Short-Term Memory network for training and testing, establish a data-driven short-circuit fault critical inertia prediction model, and achieve accurate prediction of the critical inertia of power grid short-circuit faults.

2. The data-driven method for predicting the critical inertia of short-circuit faults in power systems according to claim 1, characterized in that: In step 1, an improved simulation model of the New England 10-unit 39-bus system is built in the power system analysis and synthesis program, and the steady-state operating conditions during a typical day of 96 hours are determined; the synchronous units connected to nodes 34 and 37 in the original 39-bus system are replaced with wind farms and photovoltaic power stations. 1.1: Based on actual wind speed and solar irradiance data for 96 time periods, the output power of wind farms and photovoltaic power stations in each time period was determined; the expression for the output power of wind farms and wind speed is as follows: （1）； In formula (1): P w ( v )and P wr These are the output power of the wind farm and the output power of the wind farm at rated wind speed, respectively. v , v c , v r and v co These are the actual wind speed, cut-in wind speed, rated wind speed, and cut-out wind speed of the wind farm, respectively. 1.2: For photovoltaic power plants, their output power is directly proportional to the light intensity; the output power of a photovoltaic power plant can be approximately expressed as: （2）； In formula (2): P v This is expressed as the output power of a photovoltaic power station; η , S , I These represent the photoelectric conversion efficiency, total area, and light intensity of the photovoltaic array composed of solar panels, respectively. In a single time period, short-circuit faults are applied to the busbars of each synchronous generator unit and the load busbar, causing adjacent synchronous generator units and loads to disconnect from the grid; the frequency response curve of the system's inertia center frequency is obtained through time-domain simulation, and its dynamic characteristic parameters are extracted.

3. The data-driven method for predicting the critical inertia of short-circuit faults in power systems according to claim 2, characterized in that: In step 2, to characterize the critical inertia and overall frequency behavior after a fault, the system's equivalent inertia and center frequency of inertia are introduced as representation quantities; the system's equivalent inertia is expressed as: （3）； In formula (3): H G,i , S G,i The first i The inertia constant and rated capacity of the synchronous generator set; H vir,j , S vir,j These are new energy power stations equipped with virtual inertia control technology. j The virtual inertia constant and rated capacity; m and n These represent the total number of synchronous generator sets and the total number of new energy power stations in the system, respectively. The center frequency of inertia is expressed as: （4）； In equation (4): f i Represented as the first i The frequency of the synchronous generator set.

4. The data-driven method for predicting the critical inertia of short-circuit faults in power systems according to claim 3, characterized in that: The analytical solution for the critical inertia is obtained by using the primary frequency regulation model and equivalent parameters of the synchronous generators in the aggregated power grid, and by linearizing the primary frequency regulation response of the equivalent generator units in the power grid. The critical inertia is then solved based on the equivalent rotor motion equations of the power grid, combined with RoCoF constraints and minimum frequency point constraints. The equivalent rotor motion equations of the power grid are expressed as follows: （5）； In formula (5): f N The system's rated frequency; f ( t ), D and f ( t ) are respectively t The system's inertia center frequency, the damping coefficient of the system's equivalent synchronous generator, and the time-varying inertia center frequency, and the damping coefficient of the system's equivalent synchronous generator. t The offset of the system inertia center frequency at any given moment; P m ( t )and P e ( t ) are respectively t The total mechanical power and total electromagnetic power of the entire system at any given moment; Since the system's frequency change rate reaches its maximum value at the instant of the fault, and the frequency offset is negligible at this point, and considering the inertia loss caused by the short-circuit fault, the critical inertia under the corresponding frequency change rate constraint is... H 1 is represented as: （6）； In formula (6): H loss This refers to the inertia loss caused by a short-circuit fault in the system. P This is the unbalanced power of the system, which is the difference between the total mechanical power and the total electromagnetic power of the entire system. Based on the linearized primary frequency regulation response of the equivalent generator unit in the power grid, let when t A short circuit fault occurs at time 0, and the frequency begins to deviate from the rated frequency. f N The equivalent generator set of the power grid has passed through t r Start a frequency modulation after a delay, and in t min The frequency of time drops to its lowest point f min During this period, the equivalent generating units of the power grid are adjusted according to the droop coefficient of the primary frequency regulation. R Adjusting the active power output, the critical inertia under the constraint of the system's lowest frequency point. H 2 is represented as: （7）。 5. The data-driven method for predicting the critical inertia of short-circuit faults in power systems according to claim 4, characterized in that: Based on the dynamic characteristics of the inertia center frequency response curve under this fault condition, the inertia constants of each synchronous generator unit in the power grid are adjusted so that the frequency change rate reaches the set frequency change rate constraint value. Since the current power grid is in a critical transient state, the system's equivalent inertia... H sys1 The critical inertia under this constraint. The critical inertia of this constraint Represented as: （8）； In equation (8): H G,i,1 , S G,i,1 These are the first three constrained conditions. i The inertia constant and rated capacity of the synchronous generator set; H vir,j,1 , S vir,j,1 These are new energy power stations equipped with virtual inertia control technology under this constraint. j The virtual inertia constant and rated capacity; Similarly, based on the dynamic characteristics of the inertia center frequency response curve under fault conditions, the inertia constants of each synchronous generator unit are further adjusted to bring the frequency deviation to the set minimum frequency constraint value. Since the current power grid is in a critical transient state, the system's equivalent inertia... H sys2 The critical inertia under this constraint. The critical inertia of this constraint Represented as: （9）； In equation (9): H G,i,2 , S G,i,2 These are the first three constrained conditions. i The inertia constant and rated capacity of the synchronous generator set; H vir,j,2 , S vir,j,2 These are new energy power stations equipped with virtual inertia control technology under this constraint. j The virtual inertia constant and rated capacity; To ensure that the system simultaneously meets the dual safety requirements of frequency change rate and frequency minimum point after a short-circuit fault, the larger of the two calculated critical inertia is taken as the critical inertia that satisfies the frequency safety constraint under this fault condition. Represented as: （10）。 6. The data-driven method for predicting the critical inertia of short-circuit faults in power systems according to claim 5, characterized in that: In step 3, the steady-state operating conditions of 96 time periods are traversed to systematically construct a critical inertia dataset covering the entire time period of a typical day. This dataset is stored in tabular form and contains 2,400 sets of sample data. The input features recorded in the dataset include the inertia constant, primary frequency regulation droop coefficient, primary frequency regulation delay time, damping effect coefficient, active power of each load before disturbance, location of short-circuit fault, unbalanced power caused by the fault, inertia loss, and output feature: critical inertia value of short-circuit fault.

7. The data-driven method for predicting the critical inertia of short-circuit faults in power systems according to claim 6, characterized in that: In step 4, to eliminate the impact of differences in feature dimensions on the model training results and improve the model training speed and stability, the input features are normalized. The normalization expression is as follows: （11）； In equation (11): x´ and x These are the data after processing and the data before processing, respectively, for this feature quantity; x max and x min These are the maximum and minimum values ​​of the feature in the dataset, respectively.

8. The data-driven method for predicting the critical inertia of short-circuit faults in power systems according to claim 7, characterized in that: In step 4, a Long Short-Term Memory (LSTM) network is used to establish a nonlinear mapping between input features and critical inertia. The LSTM network consists of multiple LSTM units, each of which comprises a storage state, a forget gate, an input gate, and an output gate. The storage state includes the unit state. C and hidden state H A gating device is a device that selectively allows information to pass through, achieved through a series of mathematical operations and activation functions; a forgetting gate combines the hidden state of the previous unit. H t-1 and the input sequence data of this unit X t Selectively forget the cell state of the previous cell. C t-1 The mathematical model for the forget gate is as follows: （12）； in: σ An activation function whose output is between 0 and 1; f The output of the forget gate is the cell state of the forgotten cell. Ct-1 The probability of; Wxf , Whf and bf These are the input sequence data for this unit. Xt The previous unit is in a hidden state. Ht-1 The weight matrix and bias matrix of the forget gate; the input gate mainly consists of two activation functions; the first activation function uses the activation function. σ Its mathematical model is: （13）； in: i This is the output of the activation function in the first part; Wxi , Whi and bi These are the input sequence data for this unit. Xt The previous unit is in a hidden state. Ht-1 The first part of the input gate contains the weight matrix and bias matrix; the activation function of the first part represents the degree to which the output information of the activation function of the second part is preserved; and the activation function of the second part uses the hyperbolic tangent activation function tanh, whose mathematical model is as follows: （14）； in: C β This is the output of the activation function in the second part; W xc , W hc and b c These are the input sequence data for this unit. X t The previous unit is in a hidden state. H t-1 The second part of the input gate contains the weight matrix and bias matrix; the activation function in the second part represents the creation of an alternative. C β Based on the forget gate and the input gate, the unit state of this unit is determined. C t It has been updated, and its mathematical model is as follows: （15）； in: Ct This represents the cell state of this unit; ⊙ and + represent element-wise multiplication and addition operations; the output gate also consists of two activation functions; the first part of the activation function uses an activation function. σ Its mathematical model is: （16）； in: Ot This is the output of the activation function in the first part; Wxo , Who and bo These are the input sequence data for this unit. Xt The previous unit is in a hidden state. Ht-1 The weight matrix and bias matrix of the first part of the output gate; similarly, the activation function of the first part represents the degree to which the output information of the activation function of the second part is preserved, and the activation function of the second part uses the hyperbolic tangent activation function tanh; based on the updated cell state Ct Update to get the hidden state of this unit. Ht Its mathematical model is: （17）； Updated cell status Ct and hidden state Ht The data is then applied to the next unit, thus enabling the LSTM network to efficiently process and analyze the data.

9. The data-driven method for predicting the critical inertia of short-circuit faults in power systems according to claim 8, characterized in that: In step 4, 80% of the dataset and 20% of the dataset are randomly divided into training set and test set, and then input into the LSTM model for training and testing. The training set is used to learn the parameters of the prediction model, and the test set is used to verify the model's ability to predict unknown samples. To objectively quantify and compare the prediction performance of different deep learning models, LSTM, convolutional neural network (CNN), and traditional artificial neural network (ANN) were selected and validated on the same test set. The performance of the models was comprehensively judged by introducing three major evaluation indicators: root mean square error (RMSE), mean relative error (MRE), and maximum absolute error (MAE). The mathematical expressions for their calculation are shown in equations (18) to (19). （18）； （19）； （20）； In the above formula: M This represents the total number of samples. X i and Y i The first i The simulated values ​​of the critical inertia and the predicted values ​​of the critical inertia; where RMSE is used to measure the overall error level of the model; MRE is used to measure the average error level of the model; and MAE is used to characterize the maximum deviation under the most unfavorable sample.

10. The data-driven method for predicting the critical inertia of short-circuit faults in power systems according to claim 9, characterized in that: To improve the interpretability of the constructed critical inertia prediction model, the Shapley additive explanation method (SHAP) is introduced into the trained LSTM model to quantify the contribution of each input feature to the model output; for any sample x =[ x 1, x 2··· x n The output of the trained prediction model is represented as follows: （21）； In equation (21): H cr ( x ) as a sample x The corresponding predicted critical inertia value for short-circuit faults; 0 represents the model's baseline output value on the background sample set; j For the first j The SHAP contribution value of the input feature to the prediction result of this sample; j The SHAP contribution value of each input feature can be expressed as: （22）； In equation (22): N ={1,2,…, n } represents the set of indices for all input features; S For any subset of features that does not contain the j-th feature; | S | represents the number of features in the subset; This indicates that only a subset of features is used. S The critical inertia output of the model for the sample; Indicates in subset S Add the first one based on the existing one j The model output after the first feature; the difference between the two represents the first feature. j The marginal contribution of each feature to the critical inertia prediction under the current feature combination; By calculating the SHAP value of each input feature, the influence of features such as different operating modes, fault locations, unbalanced power, inertia loss, primary frequency modulation droop coefficient, primary frequency modulation delay, and damping coefficient on the critical inertia prediction results is obtained. The global importance of a feature is obtained by averaging the absolute values ​​of its SHAP values ​​across all samples, expressed as follows: （23）； In equation (23): I j Let be the global importance of the j-th feature; M The total number of samples; For the first i In the nth sample j The SHAP value corresponding to each feature; the greater the global importance, the more significant the influence of the feature on the prediction result of the critical inertia of short-circuit fault.

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