Method and device for evaluating critical inertia of power system, electronic equipment and medium

Abstract

The present application relates to the technical field of power system, discloses a method and device for evaluating critical inertia of power system, electronic equipment and medium, the method comprises: obtaining the real-time operating parameter of power system, and constructing real-time input feature vector according to real-time operating parameter;Real-time input feature vector is input into the probability prediction model constructed in advance, and the mixed Gaussian probability distribution of critical inertia is obtained by single forward inference;The probability prediction model is constructed by taking the critical inertia true value solved based on the physical model as the training target, and taking the conditional probability distribution of the mixed Gaussian distribution modeling critical inertia as the output form for training;According to the mixed Gaussian probability distribution, the evaluation value of critical inertia is obtained.The present application can quantify the uncertainty of evaluation result, provide more comprehensive safety margin information for dispatching operation decision, improve the evaluation precision and calculation efficiency, and solve the problems of insufficient evaluation precision, calculation efficiency and uncertainty quantification in the prior art.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and more specifically to methods, devices, electronic equipment, and media for evaluating the critical inertia of power systems. Background Technology

[0002] The equivalent inertia level of a power system is a key factor determining the frequency response characteristics of a power system under power disturbances. A decrease in inertia affects the rate of frequency change, frequency extremes, and frequency recovery process after a disturbance. Critical inertia is an important indicator for measuring whether a power system can maintain frequency stability under power disturbances. Its physical meaning is the minimum equivalent inertia level required for the system to maintain a frequency within a set safety range. Accurate assessment of critical inertia can provide safety margin information for system dispatching.

[0003] Existing methods for assessing critical inertia fall into two categories: one is based on mathematical models, which constructs a power system frequency response model and combines it with frequency security constraints to obtain the critical inertia value; the other is based on data-driven methods, which use historical operating data to train the model for prediction. However, existing methods still have limitations such as insufficient assessment accuracy, low computational efficiency, and inability to quantify the uncertainty of the assessment results. Summary of the Invention

[0004] This invention provides a method, apparatus, electronic device, and medium for evaluating the critical inertia of a power system, in order to address the shortcomings of existing technologies in terms of evaluation accuracy, computational efficiency, and uncertainty quantification.

[0005] In a first aspect, the present invention provides a method for evaluating the critical inertia of a power system, the method comprising: Obtain real-time operating parameters of the power system and construct a real-time input feature vector based on the real-time operating parameters; The real-time input feature vector is input into a pre-built probability prediction model, and the mixture Gaussian probability distribution of the critical inertia is obtained through a single forward inference. The probability prediction model is constructed by training with the true value of the critical inertia solved based on the physical model as the training target and the conditional probability distribution of the critical inertia modeled by the mixture Gaussian distribution as the output form. The critical inertia is estimated based on the mixture Gaussian probability distribution.

[0006] This invention provides a method for assessing the critical inertia of a power system. By constructing a probabilistic prediction model using the true critical inertia value obtained from a physical model as the training objective, the time-consuming physical model solving process is transformed into a single forward inference, significantly reducing the assessment time while maintaining the accuracy of the physical model solution. Simultaneously, the model outputs the conditional probability distribution of the critical inertia using a Gaussian mixture distribution, which quantifies the uncertainty of the assessment results and provides more comprehensive safety margin information for scheduling and operation decisions. This improves assessment accuracy and computational efficiency, addressing the shortcomings of existing technologies in terms of assessment accuracy, computational efficiency, and uncertainty quantification.

[0007] In one alternative implementation, the probabilistic prediction model is constructed in the following manner: Obtain the operating parameters of the power system under various operating scenarios, and construct the frequency response model of the power system based on the operating parameters under each operating scenario; With the goal of minimizing system inertia and in combination with preset frequency safety constraints, the true values ​​of critical inertia for each operating scenario are solved based on the frequency response model. Based on the operating parameters of each operating scenario, corresponding input feature samples are constructed, and the input feature samples are paired with the corresponding critical inertia ground values ​​to generate a training sample set. The preset initial probability prediction model is trained using a training sample set to obtain the probability prediction model. The preset initial probability prediction model includes a feature extraction network and a hybrid density network output layer. The feature extraction network is used to extract deep representations of the input features, and the hybrid density network output layer is used to map the deep representations to parameters of a mixture Gaussian distribution.

[0008] In the above technical solution, the probabilistic prediction model is constructed by using the true value of the critical inertia obtained from the physical model as the training label. This allows the data-driven model to embed prior information on physical laws and frequency safety constraints during the training phase, resulting in stronger physical interpretability and generalization ability compared to purely data-driven methods. Simultaneously, the model uses a Gaussian mixture distribution as its output, which can characterize the dispersion of the critical inertia under different operating scenarios, providing results containing uncertainty quantification information for subsequent online evaluation. Furthermore, the deployment method of offline training and online single-step forward inference transforms the computation in the online evaluation phase from time-consuming nested optimization solutions into efficient forward computation, balancing evaluation accuracy and real-time performance.

[0009] In one optional implementation, the operating parameters include parameters of each power generation unit, system baseline capacity, and load frequency response coefficient; Constructing a frequency response model for a power system includes: Based on the parameters of each power generation unit, establish the transfer function of each power generation unit; Based on the system baseline capacity and load frequency response coefficient, each power generation unit is modeled as a frequency response model of the power system.

[0010] In the above technical solution, by establishing transfer functions for synchronous generator sets and grid-connected units via converters, the differences in inertia support characteristics and frequency regulation characteristics of different types of power generation units in frequency response can be accurately reflected. On this basis, each power generation unit is modeled as a frequency response model through the system baseline capacity. While retaining the main dynamic characteristics of the system frequency, the model order is reduced, providing a simplified model basis that balances accuracy and computational efficiency for the subsequent optimization solution of the true value of critical inertia.

[0011] In one optional implementation, the power generation units participating in the frequency response include synchronous generator sets and grid-connected renewable energy units with grid-connected converters; the parameters of each power generation unit include the inertial time constant, damping coefficient, and frequency regulation parameters corresponding to each power generation unit. Based on the parameters of each power generation unit, establish the transfer function of each power generation unit, including: Based on the inertial time constant, damping coefficient and frequency regulation parameters of the synchronous generator set, the first transfer function of the synchronous generator set is established. The first transfer function includes the rotor motion equation and the first-order inertial lag element. Based on the inertial time constant, damping coefficient, and frequency regulation parameters of the renewable energy units connected to the grid using grid-connected converters, a second transfer function that is mathematically consistent with the first transfer function is established.

[0012] In the above technical solution, by distinguishing between the power generation units of synchronous generator sets and grid-connected converter units, and establishing corresponding transfer functions according to their different physical characteristics, the frequency response model can accurately reflect the inertia response and primary frequency regulation lag characteristics of synchronous generator sets, and the virtual inertia and virtual frequency regulation characteristics of grid-connected converters. At the same time, the transfer functions of grid-connected converters and synchronous generator sets are consistent in mathematical form, so that the two types of units can be processed uniformly under the same frequency response analysis framework without the need for additional distinction in model structure and solution algorithm, thus simplifying the complexity of subsequent critical inertia optimization solution.

[0013] In one optional implementation, each generation unit is modeled as a frequency response model of the power system based on the system baseline capacity and load frequency response coefficient, including: The equivalent inertia of the system is obtained by weighting the inertial time constants of each power generation unit according to their respective rated capacities and then dividing the sum by the system reference capacity. The equivalent damping coefficient of the system is obtained by weighting the damping coefficients of each power generation unit according to their respective rated capacities, dividing by the system reference capacity, and then superimposing the frequency response characteristics of the load itself. A frequency response model is constructed using the system's equivalent inertia and equivalent damping coefficient as parameters, and the system's equivalent frequency deviation as a state variable.

[0014] In the above technical solution, the equivalent inertia of the system is obtained by weighting and summing the inertial time constants of each power generation unit according to the rated capacity and dividing it by the system reference capacity. The damping coefficients of each power generation unit are also weighted and summed according to their respective rated capacities and divided by the system reference capacity. Then, the frequency response characteristics of the load itself are superimposed. This model transforms the complex system containing multiple types of power generation units into a frequency response model. While fully preserving key frequency response characteristics such as the system inertia level and damping level, the model order and solution complexity are reduced. This allows the subsequent optimization solution of the true value of critical inertia to reduce computational overhead while ensuring the reliability of the results, and meets the training data generation requirements for batch solutions in large-scale operation scenarios.

[0015] In one alternative implementation, constructing a frequency response model of the power system further includes: The system inertial center frequency is used as a unified frequency analysis benchmark, where the deviation of the system inertial center frequency is the average value of the frequency deviation of each power generation unit weighted by inertia. The actual frequency deviation of any node is decomposed into the sum of the system inertial center frequency deviation component and the node local deviation component; the node local deviation component is used to correct the extreme value constraint of the system inertial center frequency in the frequency safety constraint, so as to independently verify the frequency safety margin of each node.

[0016] In the above technical solution, by introducing the system inertial center frequency as a unified frequency analysis benchmark and decomposing the actual frequency deviation of each node into the sum of the inertial center component and the node local deviation component, the frequency safety margin of any node in the critical inertia solution can be independently verified. This overcomes the limitation of traditional methods that rely solely on the unified inertia level of the system for evaluation and cannot guarantee that the frequency of each node does not exceed the safety limit. It fundamentally eliminates the blind spot in node-level frequency safety assessment and improves the comprehensiveness and reliability of frequency safety assessment for high-proportion renewable energy power systems.

[0017] In one optional implementation, constructing a real-time input feature vector based on real-time operating parameters includes: Physical quantities that affect the critical inertia are extracted from real-time operating parameters at three levels: system level, node level, and frequency response dynamics. System-level sub-vectors are constructed, consisting of system equivalent inertia, system equivalent damping coefficient, renewable energy penetration rate, total output of system synchronous machine, and total capacity of grid-connected converters. Node-level sub-vectors are constructed, consisting of node local equivalent inertia and electrical distance from node to disturbance source. Frequency response dynamics sub-vectors are constructed, consisting of disturbance power and initial frequency change rate. The system-level sub-vectors, node-level sub-vectors, and frequency response dynamic sub-vectors are concatenated into a real-time input feature vector.

[0018] In the above technical solution, physical quantities that affect the critical inertia are extracted at three levels: system level, node level, and frequency response dynamics. These are then constructed into sub-vectors and concatenated into an input feature vector. This allows the model input to simultaneously include multi-dimensional information such as the system's global frequency response characteristics, the node's local frequency support capability, and the transient characteristics of disturbances. Compared to the approach of blindly piling up or arbitrarily selecting features in pure data-driven methods, this approach has clear physical meaning and interpretability, which helps improve the fitting accuracy and generalization ability of the probabilistic prediction model to the variation law of the critical inertia under different operating scenarios.

[0019] In one optional implementation, the real-time input feature vector is input into a pre-constructed probability prediction model, and a mixture Gaussian probability distribution of the critical inertia is obtained through a single forward inference, including: The real-time input feature vector is input into the feature extraction network of the probability prediction model. After forward computation by the feature extraction network, the deep feature representation of the real-time input feature vector is output. The deep feature representation is input into the output layer of the hybrid density network of the probability prediction model. The parameters of the mixture Gaussian distribution are obtained by forward calculation through the output layer of the hybrid density network. The Gaussian mixture probability distribution is determined based on the parameters of the Gaussian mixture distribution.

[0020] In the above technical solution, a feature extraction network is used to perform deep feature extraction on the input feature vector. Then, the deep feature representation is input to the output layer of the mixture density network and mapped to the parameters of the mixture Gaussian distribution. This allows the entire inference process to be completed in only one forward computation. The online evaluation is transformed from the existing nested iterative optimization solution based on mathematical models into an efficient forward pass, which significantly reduces the computation time of a single evaluation. At the same time, the output layer of the mixture density network directly outputs the distribution parameters describing the complete conditional probability distribution of the critical inertia, rather than a single deterministic value. This allows the model to carry the dispersion information of the critical inertia under different operating scenarios in a single forward inference, providing a distribution basis for the subsequent extraction of the prediction mean, prediction variance, and quantiles at different confidence levels. This overcomes the limitation of traditional deterministic evaluation methods that can only output a single value and cannot quantify the uncertainty of the evaluation results.

[0021] In one alternative implementation, the critical inertia is evaluated based on a mixture of Gaussian probability distributions, including: Obtain the mixing weights and mean of each Gaussian component in the Gaussian mixture probability distribution; The predicted mean is obtained by multiplying the mixed weights by their respective means and summing the results. This predicted mean is then used as the evaluation value for the critical inertia.

[0022] In the above technical solution, the predicted mean is obtained by acquiring the mixture weights and mean of each Gaussian component in the mixture Gaussian probability distribution and summing them by weight. This predicted mean is essentially the mathematical expectation of the critical inertia under the conditional probability distribution, representing the most likely value of the critical inertia in the current operating scenario. It can provide a clear and easily usable numerical reference for scheduling. At the same time, since the evaluation value is not directly given by the point estimation model, but is a distribution statistic calculated on the basis of the complete mixture Gaussian probability distribution, the same distribution can further provide information such as the prediction variance and quantiles at different confidence levels while outputting the evaluation value. This provides a safety margin reference with more dimensions than a single value for scheduling operation decisions, overcoming the limitation of traditional deterministic methods that only output a single evaluation value and cannot support risk quantification decisions.

[0023] In one alternative implementation, the method further includes: The prediction variance is extracted from the Gaussian mixture probability distribution and used as a quantitative indicator of the uncertainty of the evaluation value. And / or, based on the Gaussian mixture probability distribution, extract and output the critical inertia quantiles at a specified confidence level. The critical inertia quantiles are used for scheduling operation decisions.

[0024] In the above technical solution, by extracting the prediction variance based on the mixed Gaussian probability distribution of critical inertia, an intuitive quantitative indicator of the credibility of the current assessment results is provided to the scheduling operators. This helps to identify the operational states that need to be focused on in high uncertainty scenarios and reserve additional safety margins accordingly. At the same time, by extracting the critical inertia quantiles at a specified confidence level, the scheduling operators can select critical inertia values ​​with different levels of conservatism for decision-making based on their own preferences for operational risks. This overcomes the limitation of traditional deterministic assessment methods that only output a single value and cannot provide differentiated decision-making basis.

[0025] In a second aspect, the present invention provides an apparatus for evaluating the critical inertia of a power system, the apparatus comprising: The data acquisition and feature extraction module is used to acquire real-time operating parameters of the power system and construct real-time input feature vectors based on the real-time operating parameters. The probability prediction module is used to input real-time input feature vectors into a pre-built probability prediction model and obtain the mixture Gaussian probability distribution of critical inertia through a single forward inference. The probability prediction model is built by training with the true critical inertia solved based on the physical model as the training target and the conditional probability distribution of critical inertia modeled by the mixture Gaussian distribution as the output form. The output module is used to obtain an evaluation value of the critical inertia based on the Gaussian mixture probability distribution.

[0026] Thirdly, the present invention provides an electronic device, comprising: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the computer instructions to perform the power system critical inertia assessment method of the first aspect or any corresponding embodiment described above.

[0027] Fourthly, the present invention provides a computer-readable storage medium storing computer instructions for causing a computer to perform the power system critical inertia assessment method of the first aspect or any corresponding embodiment thereof.

[0028] Fifthly, the present invention provides a computer program product, including computer instructions for causing a computer to execute the power system critical inertia assessment method of the first aspect or any corresponding embodiment thereof. Attached Figure Description

[0029] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0030] Figure 1 This is a schematic diagram of the first process of the method for evaluating the critical inertia of a power system according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the second process for evaluating the critical inertia of a power system according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the overall structure of a simplified closed-loop model of a renewable energy power system according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the overall structure of a simplified open-loop model of a renewable energy power system according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the Transformer-MDN model structure according to an embodiment of the present invention; Figure 6 This is a schematic diagram of Transformer-MDN model training according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the third process of the power system critical inertia assessment method according to an embodiment of the present invention; Figure 8 This is a structural block diagram of a power system critical inertia evaluation device according to an embodiment of the present invention; Figure 9 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] It is understood that before using the technical solutions disclosed in the various embodiments of the present invention, users should be informed of the types, scope of use, and usage scenarios of the personal information involved in the present invention and their authorization should be obtained in accordance with relevant laws and regulations through appropriate means.

[0033] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0034] In renewable energy power systems, existing technologies for critical inertia assessment have significant limitations. Existing assessment methods ignore the spatial differences in frequency response at each node, making it difficult to guarantee that the frequency at all locations does not exceed safety constraints; furthermore, analytical methods use a single exponential decay form to construct frequency difference curves, which cannot characterize the second-order underdamped oscillation characteristics of the system, resulting in insufficient constraint accuracy; mathematical model-based solution methods have significant computational overhead, making it difficult to meet the real-time requirements of online assessment; and purely data-driven methods have poor generalization ability and typically only output deterministic point estimates, making it difficult to reflect the dispersion of critical inertia under different operating scenarios.

[0035] To address the aforementioned issues, this invention proposes an intelligent calculation method for the critical inertia of a high-proportion renewable energy power system. This method consists of two parts: the first part uses a physical model of the power system's frequency response to solve an optimization problem and obtain an accurate value for the critical inertia. The result is reliable, but each solution is time-consuming, making it difficult to meet the real-time requirements of online evaluation. The second part uses the large number of results obtained from the batch solution in the first part as training samples to train an artificial intelligence model to directly predict the critical inertia. This transforms the time-consuming optimization solution into a single forward inference, significantly reducing the computation time while maintaining accuracy, thereby achieving rapid online evaluation of the critical inertia.

[0036] According to an embodiment of the present invention, an embodiment of a method for evaluating the critical inertia of a power system is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0037] This embodiment provides a method for evaluating the critical inertia of a power system, which can be used in the aforementioned electronic equipment. Figure 1 This is a flowchart of a method for evaluating the critical inertia of a power system according to an embodiment of the present invention, such as... Figure 1 As shown, the process includes the following steps: Step S101: Obtain the real-time operating parameters of the power system and construct a real-time input feature vector based on the real-time operating parameters.

[0038] The real-time operating parameters of the power system include, but are not limited to: System-level parameters: system equivalent inertia, system equivalent damping coefficient, renewable energy penetration rate, total output of system synchronous machine, and total capacity of converter; Node-level parameters: local equivalent inertia of the node, electrical distance from the node to the disturbance source; Frequency response dynamic parameters: disturbance power, initial frequency change rate.

[0039] The real-time input feature vector is the direct input to the probabilistic prediction model, constructed from physical quantities that affect the critical inertia extracted from real-time operating parameters. Specifically, features are extracted at three levels: system-level, node-level, and frequency response dynamics, and sub-vectors are constructed and concatenated after each level. The difference between real-time operating parameters and raw operating parameters lies in the fact that real-time operating parameters are raw data directly collected or calculated from the power system, while the real-time input feature vector is a vector-based input that has been extracted and concatenated, directly received by the model, serving as a bridge between the raw operating parameters and the probabilistic prediction model.

[0040] Specifically, after obtaining the real-time operating parameters of the power system, physical quantities that affect the critical inertia are extracted from the real-time operating parameters, and the extracted physical quantities are organized into vector form in a preset order to obtain the real-time input feature vector.

[0041] Step S102: Input the real-time input feature vector into the pre-constructed probability prediction model, and obtain the mixture Gaussian probability distribution of the critical inertia through a single forward inference; the probability prediction model is constructed by training with the true value of the critical inertia solved based on the physical model as the training target and the conditional probability distribution of the critical inertia modeled by the mixture Gaussian distribution as the output form.

[0042] The Gaussian mixture probability distribution refers to the conditional probability distribution of the critical inertia under a given input feature vector, which is composed of a weighted sum of multiple Gaussian components. Each Gaussian component has its own mean, variance, and mixture weights. This distribution is generated by the output layer of the mixture density network of the probabilistic prediction model based on the mapping of the deep feature representation of the input. The output form is the parameters of the Gaussian mixture distribution (mixture weights, mean, and variance of each component). After the model training is completed, the Gaussian mixture probability distribution can be obtained by inputting the feature vector in the online stage.

[0043] The probabilistic prediction model is constructed by training the critical inertia true value obtained from the physical model as the training objective and using the conditional probability distribution of the critical inertia modeled by the Gaussian mixture distribution as the output. The critical inertia true value obtained from the physical model refers to the critical inertia value used as the training label during the offline training phase of the probabilistic prediction model.

[0044] Specifically, the true value of critical inertia is obtained in the following way: After obtaining the operating parameters of the power system under a certain operating scenario, a frequency response model of the power system is constructed (including the transfer functions of synchronous generator sets and grid-type converters, and modeled as a frequency response model). With the goal of minimizing system inertia, and combined with preset frequency security constraints (such as node frequency security constraints, frequency change rate constraints, multi-fault scenario robustness constraints, etc.), the minimum equivalent inertia value that can maintain system frequency security under this operating scenario is obtained through optimization solution.

[0045] This ground truth differs from the empirical labels or manual annotations used in purely data-driven methods. Its solution process is based on a clear physical model and frequency safety constraints, hence it is called the "critical inertia ground truth based on a physical model." During the training phase, this ground truth is used as the learning target, so that the probabilistic prediction model incorporates prior information about physical laws and frequency safety constraints during the training process, rather than relying solely on statistical correlations in the data for learning.

[0046] Step S103: Based on the Gaussian mixture probability distribution, obtain the evaluation value of the critical inertia.

[0047] The critical inertia assessment value is the critical inertia point estimate output by the probabilistic prediction model during the online application phase, for the current real-time operating scenario.

[0048] Specifically, the evaluation value is obtained by extracting the predicted mean from the Gaussian mixture probability distribution after obtaining the Gaussian mixture probability distribution. The calculation method is to multiply the mixing weight of each Gaussian component in the Gaussian mixture probability distribution with the corresponding mean and then sum them.

[0049] This evaluation value represents the most likely minimum equivalent inertia level required for the system to maintain all node frequencies below their respective safety limits under the current operating scenario. Unlike the "critical inertia ground truth" (the precise value obtained through optimization of the physical model during offline training, used as a training label), the evaluation value is a predicted value output by the model in a single forward inference during the online phase.

[0050] This assessment value can be directly used as a reference for scheduling and operation: compare the assessment value with the current actual inertia of the system. If the actual inertia is higher than the assessment value, it indicates that the current system inertia level meets the frequency safety requirements; otherwise, it indicates that there is a risk of insufficient inertia and corresponding preventive and control measures need to be taken.

[0051] The power system critical inertia assessment method provided in this embodiment is implemented in two phases: offline training and online assessment. In the offline training phase, based on historical operating data and simulation-generated datasets, an initial probabilistic prediction model (such as the Transformer-MDN model) is trained to obtain optimal parameters, resulting in a trained probabilistic prediction model. After training, the model is deployed in the online assessment system as a module for online inference of critical inertia. In the online assessment phase, the system continuously collects real-time operating parameters of the power system. For the current operating scenario, it calculates the required parameter combinations to form the input feature vector of the node. This feature vector is then input into the trained model, and a single forward inference operation yields the mixture Gaussian probability distribution of the critical inertia. The advantage of online assessment lies in transforming the time-consuming computational process of nested optimization model solving into a single forward inference operation. This reduces the computational overhead of a single assessment, meeting the real-time requirements of online assessment. Furthermore, the system can simultaneously output the predicted mean, predicted variance, and critical inertia quantiles at different confidence levels.

[0052] This embodiment provides a method for evaluating the critical inertia of a power system, which can be used in the aforementioned electronic equipment. Figure 2 This is a flowchart of a method for evaluating the critical inertia of a power system according to an embodiment of the present invention, such as... Figure 2 As shown, the process includes the following steps: Step S201: Obtain the real-time operating parameters of the power system and construct a real-time input feature vector based on the real-time operating parameters.

[0053] Specifically, step S201 includes: Step S2011: Extract the physical quantities that affect the critical inertia from the real-time operating parameters at three levels: system level, node level, and frequency response dynamics. Construct system-level sub-vectors consisting of system equivalent inertia, system equivalent damping coefficient, renewable energy penetration rate, total output of system synchronous machine, and total capacity of grid-connected converters; node-level sub-vectors consisting of node local equivalent inertia and electrical distance from node to disturbance source; and frequency response dynamics sub-vectors consisting of disturbance power and initial frequency change rate.

[0054] Specifically, the system-level sub-vectors are constructed based on the system equivalent inertia, system equivalent damping coefficient, renewable energy penetration rate, total output of the system synchronous machine, and total capacity of the converter in the real-time operating parameters; the node-level sub-vectors are constructed based on the node local equivalent inertia and the electrical distance from the node to the disturbance source in the real-time operating parameters; and the frequency response dynamic sub-vectors are constructed based on the disturbance power and the initial frequency change rate in the real-time operating parameters.

[0055] Step S2012: The system-level sub-vectors, node-level sub-vectors, and frequency response dynamic sub-vectors are concatenated into a real-time input feature vector.

[0056] Specifically, the system-level sub-vectors, node-level sub-vectors, and frequency response dynamic sub-vectors are concatenated and combined in the order of system-level first, node-level in the middle, and frequency response dynamic level last to form a one-dimensional real-time input feature vector. This feature vector contains information from three levels: the global frequency response characteristics of the system, the spatial difference characteristics of the nodes, and the dynamic response characteristics of the disturbance, and serves as the input to the probabilistic prediction model.

[0057] The specific embodiments described above can be implemented using the same process as step S23 below.

[0058] Step S202: Input the real-time input feature vector into the pre-constructed probability prediction model, and obtain the mixture Gaussian probability distribution of the critical inertia through a single forward inference; the probability prediction model is constructed by training with the true value of the critical inertia solved based on the physical model as the training target and the conditional probability distribution of the critical inertia modeled by the mixture Gaussian distribution as the output form.

[0059] In one alternative implementation, the probabilistic prediction model is constructed in the following manner: Step S21: Obtain the operating parameters of the power system under various operating scenarios, and construct the frequency response model of the power system based on the operating parameters under various operating scenarios.

[0060] Among them, each operating scenario refers to a different combination of system operating conditions set up during the offline training phase in order to generate training samples covering multiple system operating states.

[0061] Specifically, the sampling of the operating scenario needs to consider the following multiple dimensions: The full range of renewable energy penetration rate; changes in network topology (such as different line switching states); comprehensive coverage of typical fault scenarios (such as three-phase short circuits on lines, grid disconnection of renewable energy power plants, etc.); and the randomness of renewable energy output (such as output fluctuations under different wind speeds and sunlight conditions).

[0062] Step S22: With the goal of minimizing system inertia and in conjunction with preset frequency safety constraints, solve for the true critical inertia values ​​corresponding to each operating scenario based on the frequency response model.

[0063] Specifically, this embodiment first establishes a mathematical model of the frequency response of the renewable energy power system, which serves as the basis for subsequent node-level critical inertia calculations and frequency security constraint derivations. The power generation units of the power system include synchronous generator units, renewable energy units connected to the grid via grid-following (GFL) converters, and renewable energy units connected to the grid via grid-forming (GFM) converters. Each power generation unit is modeled based on a simplified system model, and the concept of the system center of inertia (COI) frequency is introduced.

[0064] In one optional implementation, the operating parameters include parameters of each power generation unit, system baseline capacity, and load frequency response coefficient; step S22 above includes: Step S221: Establish the transfer function of each power generation unit based on the parameters of each power generation unit.

[0065] In one optional implementation, the power generation units participating in the frequency response include synchronous generator sets and grid-connected renewable energy units with grid-connected converters; the parameters of each power generation unit include the inertial time constant, damping coefficient, and frequency regulation parameters corresponding to each power generation unit.

[0066] A power system with a high proportion of renewable energy comprises three parts: The first is synchronous generator sets, whose rotor rotational kinetic energy directly affects inertia, serving as the primary source of frequency support capability for the power system. Synchronous generator sets respond to frequency deviations through a prime mover speed regulation system, actively adjusting mechanical power output to form the primary frequency regulation link of the system. The second is renewable energy units connected to the grid via grid-connected and grid-connected converters. Grid-connected GFL control algorithms use the grid voltage phase as a reference input. Grid-connected GFL converters do not actively generate inertial response and are considered controlled power sources in frequency stability analysis. Grid-connected GFM converters, through control strategies such as Virtual Synchronous Generators (VSGs), simulate the inertial response and primary frequency regulation characteristics of a synchronous machine on the external characteristics of the converter, thereby providing equivalent frequency support capability to the system under the trend of decreasing inertia. The third is the load and transmission network. The frequency response characteristics of the load are reflected in the load damping coefficient, and the transmission network determines the electrical connections between different nodes through line impedance parameters.

[0067] In system frequency response analysis, disturbances include synchronous generator set tripping, new energy power plant disconnection, and transmission line short-circuit faults, which disrupt the system's power balance and trigger frequency dynamic processes. Each unit responds collectively under the influence of frequency deviations, constituting the system's frequency recovery capability.

[0068] The above step S221 includes: Step a1: Based on the inertial time constant, damping coefficient and frequency regulation parameters of the synchronous generator set, establish the first transfer function of the synchronous generator set. The first transfer function includes the rotor motion equation and the first-order inertial lag element.

[0069] Specifically, firstly, the synchronous generator set is modeled.

[0070] The frequency response of a synchronous generator is dominated by the rotor. Neglecting the effects of the excitation system and damping windings, the rotor motion equation of the synchronous generator can be expressed as: (1); in, Synchronous generator set i The inertial time constant, Synchronous generator set i The angular velocity of the rotor, Synchronous generator set i mechanical power, Synchronous generator set i Output electromagnetic power; Synchronous generator set i The damping coefficient, Synchronous generator seti Angular velocity deviation.

[0071] Frequency and angular velocity satisfy a synchronization relationship at per-unit values, that is... ,in, Synchronous generator set i exist t Frequency deviation at time, and These are the system's rated frequency and rated angular velocity, respectively. Power disturbances are considered. The frequency deviation process under action can be transformed into a form where the frequency deviation is the state variable: (2); in, and These are the deviations of mechanical power and electromagnetic power relative to the initial operating point, respectively. The deviation is also called the increment.

[0072] Establish the first transfer function: The primary frequency regulation process of a synchronous generator unit involves the governor's detection of frequency deviation signals, the adjustment of the prime mover valve opening, and the hysteresis characteristics of steam or water flow dynamics. The entire process can be approximated as a first-order inertial element on the time scale of frequency dynamic analysis, with its first transfer function... for: (3); in, Synchronous generator set i The power frequency characteristic coefficient, Synchronous generator set i The equivalent time constant of the governor and prime mover system; the negative sign indicates that the synchronous generator set increases mechanical power output when the frequency decreases. For the Laplace operator, For the first Laplace transform of the mechanical power increment of a synchronous generator set. For the first The Laplace transform of the frequency deviation of the synchronous generator set.

[0073] Transforming equation (3) into time-domain form, synchronous generator set i exist t The increase in mechanical power at time t can be expressed as the convolution integral of the frequency deviation from the initial time to the current time: (4); in, For integration variables, is the base of the natural logarithm.

[0074] Step a2: Based on the inertial time constant, damping coefficient, and frequency regulation parameters of the renewable energy units connected to the grid using the grid-connected converter, establish a second transfer function that is mathematically consistent with the first transfer function.

[0075] Specifically, when renewable energy units are connected to the grid via two types of converters, namely grid-connected and grid-connected, only renewable energy units connected to the grid-connected converter participate in the frequency response, and their frequency response models are established.

[0076] The grid-connected converter employs a virtual synchronous machine (VSG) control to simulate the oscillation equations of a synchronous generator, enabling the converter to exhibit inertial response and primary frequency regulation characteristics similar to those of a synchronous generator in its external characteristics. The control system introduces a virtual synchronous machine control loop above the voltage and current inner loop. By embedding virtual inertia and virtual damping terms, the converter's output power exhibits a delayed response to changes in system frequency, thus simulating the mechanical inertia effect of a synchronous machine rotor. Under this control strategy, renewable energy units can provide instantaneous power support through virtual inertia in the early stages of frequency disturbances, and subsequently generate power regulation similar to the primary frequency regulation of a synchronous machine through a virtual speed governor, thereby compensating for the system's inertia deficit.

[0077] For grid-type renewable energy units Its power response equation is mathematically consistent with the swing equation (2) of the synchronous machine, and can be expressed as: (5); in, To utilize grid-type renewable energy units j The virtual inertial time constant, For grid-type renewable energy units j The virtual damping coefficient, For grid-connected renewable energy units j The primary frequency modulation power increment, For grid-type renewable energy units j The increase in electromagnetic power output to the power grid, For grid-type renewable energy units j The frequency deviation obtained from the measurement.

[0078] The virtual primary frequency regulation element of a grid-type converter can also be described by a first-order inertial element, i.e., the mathematical expression of the second transfer function: (6); in, and These are grid-type renewable energy units j The virtual power frequency characteristic coefficient and the virtual primary frequency regulation time constant are both determined by the control parameters and can be flexibly adjusted according to the control objectives.

[0079] Since Equation (5) is completely consistent with Equation (2) in mathematical form, and Equation (6) is completely identical with Equation (3) in transfer function structure, grid-type renewable energy units and synchronous generator sets can be uniformly processed under the same frequency response analysis framework. In subsequent modeling, the two types of equipment will no longer be structurally distinguished, but their physical attribute differences will be reflected only through their respective inertia parameters and frequency regulation parameters.

[0080] Step S222: Based on the system baseline capacity and load frequency response coefficient, model each power generation unit as a frequency response model of the power system.

[0081] In an optional implementation, step S222 includes: Step b1: The inertial time constant of each power generation unit is weighted and summed according to its rated capacity, and then divided by the system reference capacity to obtain the system equivalent inertia; the damping coefficient of each power generation unit is weighted and summed according to its rated capacity, and then divided by the system reference capacity, and then superimposed with the frequency response characteristics of the load itself to obtain the system equivalent damping coefficient; using the system equivalent inertia and the system equivalent damping coefficient as parameters, and the system equivalent frequency deviation as the state variable, a frequency response model is constructed.

[0082] Specifically, since the frequencies of each generating unit in a power system exhibit a certain spatiotemporal distribution due to differences in unit location, capacity, damping characteristics, etc., this embodiment adopts a simplified system model to facilitate the analytical derivation of the critical inertia, using the system's equivalent frequency deviation. The frequency dynamics of the entire network can be described as follows: (7); in, The system's equivalent inertia time constant, The equivalent damping coefficient of the system is... n The total number of all power generation units (synchronous generator sets and grid-connected renewable energy units with grid-connected converters) participating in the frequency response. For power generation unit i The primary frequency modulation power increment, This represents the initial power disturbance of the system.

[0083] System equivalent inertia The formula for calculating the contribution of both the physical inertia of the synchronous generator unit and the virtual inertia of the grid-type converter to the overall inertia level of the system is as follows: (8); in, It is a collection of synchronous generator sets in the system. It is a collection of grid-type renewable energy units in the system. Synchronous generator set i Rated capacity, For grid-type renewable energy units j Rated capacity, This represents the system's baseline capacity.

[0084] The synchronous generator, through its inertia, and the grid-connected renewable energy units, through their virtual inertia controlled by parameters, jointly determine the total level of the system's equivalent inertia. When the grid-connected renewable energy units occupy the power generation share originally belonging to the synchronous generator units, the system... The total contribution of the set decreases, resulting in The value decreased.

[0085] The damping contribution of each synchronous generator set and the frequency response characteristics of the load itself are combined to form the system's equivalent damping coefficient. Its expression is: (9); in, This is the system's equivalent load frequency response coefficient.

[0086] The overall structure of the simplified closed-loop model of a renewable energy power system can be derived from... Figure 3 express.

[0087] Power disturbance The system frequency deviation is obtained by subtracting the sum of the power responses of the summation nodes and the synchronous generator sets, and then inputting the difference into the main circuit. System frequency deviation The transfer function of each unit is input through the feedback loop. Grid-connected renewable energy units, because they do not participate in primary frequency regulation and do not appear in the feedback loop, indirectly contribute by reducing the overall system inertia. For example, Figure 3 As shown, the main loop refers to the integration / transmission path from unbalanced power to the system frequency deviation.

[0088] In the known frequency difference curve Under the circumstances, the unit's power regulation can be analyzed and derived. Figure 3 The closed-loop model is transformed into an open-loop form, such as... Figure 4 As shown.

[0089] The prerequisite for applying the open-loop model is It has already been calculated using other methods. The first transfer function, which is the known input signal, directly acts on each synchronous generator set. The solution is no longer obtained through the main loop.

[0090] Step b2: The system inertial center frequency is used as a unified frequency analysis benchmark. The deviation of the system inertial center frequency is the average value of the frequency deviations of each power generation unit weighted by inertia. The actual frequency deviation of any node is decomposed into the sum of the system inertial center frequency deviation component and the node local deviation component. The node local deviation component is used to correct the extreme value constraint of the system inertial center frequency in the frequency safety constraint, so as to independently verify the frequency safety margin of each node.

[0091] Specifically, to account for the spatial differences in the frequency response of each node in the critical inertia assessment, this paper introduces the frequency of the system's center of inertia (COI) as a unified frequency reference, and decomposes the node frequencies into global and local components accordingly. The frequency deviation of the system's center of inertia is defined as the inertia-weighted average of the frequency deviations of each power generation unit, reflecting the equivalent frequency deviation corresponding to the change in the system's total kinetic energy. (10); in, The system's inertial center frequency deviation, subscript k It covers all power generation units that provide inertia support. For power generation unit k The inertial time constant of the synchronous generator set is taken as... Grid-type converter , For power generation unit k Frequency deviation at that location.

[0092] Under the influence of power disturbances, the instantaneous frequencies of each node fluctuate around the inertial center frequency. m The actual frequency deviation at a given point can be decomposed into the sum of the inertial center component and the nodal local deviation component: (11); in, For nodes m In t The actual frequency deviation at any given moment. For nodes m The local deviation component relative to the center of inertia.

[0093] node m Local deviation components relative to the center of inertia It is closely related to the location of the nodes. Nodes closer to the disturbance source usually have larger deviation component amplitudes and more dramatic frequency responses; nodes farther away have frequency responses that are closer to the overall trend of the system's inertial center frequency.

[0094] In step S22, with the goal of minimizing system inertia and in conjunction with preset frequency safety constraints, the critical inertia true values ​​corresponding to each operating scenario are solved according to the frequency response model, including: This step belongs to the nodal-level critical inertia calculation method, and specifically includes: 2.1 Construction of frequency difference curve: Due to the high-order dynamic model of the system, the solution results and parameters of each unit are highly complex in the case of multiple generating units, making it difficult to provide a satisfactory solution. A concise analytical expression is provided. To facilitate subsequent constraint derivation and critical inertia solution, this embodiment does not directly solve the higher-order dynamic equations, but instead uses an analytical construction method, setting the frequency difference curve as a decaying sinusoidal form: (12); in, A The amplitude parameter of the frequency difference curve; This is the attenuation rate parameter; This is the oscillation angular frequency parameter.

[0095] Equation (12) mathematically corresponds to the impulse response of a second-order underdamped system, reflecting the dynamic characteristics of a power system from its initial decrease to reaching its frequency extremum under power disturbance. Compared to using only a single exponential decay frequency difference curve, introducing a sine term allows the constructed curve to characterize the system's oscillation characteristics, resulting in a more accurate match with the actual frequency response of the power system. The three undetermined parameters in the equation are uniquely determined by three endpoint conditions. The first endpoint condition corresponds to the frequency decrease rate generated by the system relying solely on inertial response at the initial moment of the disturbance; the second endpoint condition is that the derivative at the frequency extremum is zero, denoted as... , which is the moment when the system frequency extremum occurs; the third endpoint condition is determined by the frequency extremum taking a set value. Given, that is, constructing the frequency difference curve in The value at time is The three endpoint conditions can be written as the following system of equations: (13); From the first two equations of the system of equations (13), we can... A and use Express: (14); Substituting equation (14) into the third equation of the system of equations (13), we obtain the following about A single-variable transcendental equation can be expressed in an interval. The solution is uniquely obtained through numerical methods, thus yielding... and AThe specific numerical values ​​are determined. The parameter solution process does not introduce iterative closed loops, resulting in high solution efficiency and facilitating high-frequency calls within the inner loop of critical inertia optimization.

[0096] 2.2 Power Response Calculation: Substituting the constructed frequency difference curve into the time-domain integral form of the primary frequency regulation of the synchronous generator unit described by equation (4), the frequency extreme moments of each generator unit can be calculated. The regulating power of the unit. The expression obtained by integration contains multiple combinations of trigonometric and exponential functions. By simplifying the expression using three endpoint conditions and eliminating the trigonometric terms, the final result is obtained. Analytical expression of power adjustment at different times: (15); (16); in, For power generation units (synchronous generator sets and grid-connected renewable energy units with grid-connected converters). i exist Adjusting power at any time; This is a composite parameter of the dynamic time constant of the synchronous generator set and the system attenuation rate.

[0097] 2.3 Critical Inertia True Value Solution Model: The goal of calculating the true value of the node-level critical inertia is to determine the minimum equivalent inertia level that the system can maintain by ensuring that the frequencies of all nodes do not exceed their respective safety settings. To achieve this goal, six types of constraints need to be considered, namely, the node frequency extreme value constraint, the frequency change rate constraint, the robustness constraint under typical fault scenarios, the renewable energy penetration constraint, the unit dynamic adjustment capability constraint, and the unit reserve capacity constraint. These are the preset frequency safety constraints.

[0098] C1: Node frequency safety constraint, the extreme value of frequency deviation of each node shall not exceed its safety set value. When this constraint is transformed into a constraint on the extrema of the construction curve, the maximum value of the local deviation component at the node must be deducted. .

[0099] Define nodes m Frequency safety margin function for: (17); in, For nodes m Corresponding extreme value constraints For setting value, H and The parameters of the frequency difference curve constructed when the input parameters are used; The extreme value constraint that the COI frequency can be reached is determined by the nodes. m The safety setting value is obtained by subtracting the maximum value of the local deviation component of the node: (18); in, Represents a node m Frequency security constraints at the current location It was established.

[0100] C2: The rate of change of frequency (RoCoF) has different effects on system stability at different time scales. Let the set of window widths be... The corresponding threshold is When the window width approaches zero, it degenerates into the initial RoCoF constraint. This limiting form gives a lower bound on the system's inertia.

[0101] C3: Select two typical fault scenarios where the system can still meet the node frequency safety constraint C1. The first scenario is a three-phase short circuit on the line, and the second is the disconnection of a renewable energy power station from the grid. Let the set of fault scenarios be defined. The node frequency safety constraint C1 must be true in all fault scenarios.

[0102] C4: Renewable energy penetration rate is defined as the ratio of renewable energy output connected to grid-connected / grid-based converters to the total system output, and should not be lower than a set threshold. .

[0103] C5: The power change rate of each power generation unit is limited, and each power generation unit in The absolute value of the internal power change rate does not exceed its maximum permissible rate. .

[0104] C6: The total regulation of each generating unit is limited by the reserve capacity. After a disturbance, the unit has a maximum regulation constraint. Each generating unit is in... The regulating power at any time shall not exceed its reserve capacity. .

[0105] By incorporating the above six types of constraints into the optimization model, the optimization model for the optimization problem can be described as follows: (19); in, N This represents the total number of system nodes. To reduce the inertia of the system, For power disturbance, These represent the total output of the system's synchronous generator units and the total output of renewable energy, respectively.

[0106] Step S23: Construct corresponding input feature samples based on the operating parameters of each operating scenario, pair the input feature samples with the corresponding critical inertia ground values, and generate a training sample set.

[0107] Specifically, such as Figure 6 As shown ( Figure 6 The process includes constructing a training dataset and training an artificial intelligence model. Steps S21 and S22 solve the optimization problem based on a mathematical model, which can obtain an accurate value of the critical inertia (i.e., the true value of the critical inertia). However, a single solution requires nested calculations of frequency deviation curve parameters, unit power response, and multi-constraint optimization iterations, resulting in significant computational overhead and making it difficult to meet the real-time requirements of online evaluation. Therefore, this embodiment transforms the solution of the critical inertia into a data-based probabilistic prediction problem: in the offline stage, a large number of operating scenarios are solved in batches using the optimization model to obtain sample pairs as training data; in the online implementation stage, the mixture Gaussian probability distribution of the critical inertia is directly obtained through a single forward inference using the deployed model, balancing accuracy and speed. This embodiment constructs the dataset required for training.

[0108] Specifically, considering the dispersion of the true value of the critical inertia of the power system under different operating and disturbance scenarios, a single deterministic prediction is difficult to reflect this dispersion. This embodiment adopts a probabilistic prediction approach. The goal of the probabilistic prediction task is to provide critical inertia assessment results under different confidence levels for scheduling, which can be expressed as: (20); in, The conditional probability distribution predicted by the probability prediction model. For parameterized probabilistic prediction models, For nodes m Real-time input of feature vectors, The target for prediction is the critical inertia. This is the set of learnable parameters for a probabilistic prediction model.

[0109] Input feature vector The design is based on a physical model, extracting physical quantities that affect the critical inertia from three levels: system, node, and frequency response dynamics, and constructing system-level sub-vectors accordingly. Node-level subvectors With frequency response dynamic subvector The three sub-vectors are defined as follows: (twenty one); (twenty two); (twenty three); in, The system's equivalent inertia time constant, The equivalent damping coefficient of the system is... This represents the initial power disturbance of the system. It is a collection of synchronous generator sets in the system. This refers to the collection of renewable energy generation units connected to the grid via GFM converters (Grid-Forming Converters). Synchronous generator set i Rated capacity, For grid-type renewable energy units j Rated capacity, For the total output of the synchronous generator set, For total renewable energy output, A grid-connected renewable energy generation unit is a collection of renewable energy generation units in the system that are connected to the grid via a GFL (Grid-Following Converter). For mesh unit k Rated capacity, The local equivalent inertia of the node. The electrical distance from the node to the disturbance source. The amplitude parameter of the frequency difference curve. The attenuation rate parameter is the frequency difference curve. The angular frequency parameter of the frequency difference curve is... The moment when the frequency extremum occurs. Let be the frequency difference value of node m at the frequency extremum. For peak values / extreme values.

[0110] The training dataset is generated through batch scene simulation and solving the optimization model. Each training sample corresponds to a complete running scenario, consisting of an input feature vector and the corresponding critical inertia ground truth value. The training dataset can be represented as: (twenty four); in, For the training dataset, The total number of samples.

[0111] The sample generation process involves randomly sampling operating scenarios, calculating parameters based on the sampled scenarios, solving the optimization model to obtain the true value of the critical inertia, and finally constructing the input feature vector. To ensure the training dataset's coverage of real-world operating scenarios, the sampling of operating scenarios needs to consider multiple dimensions, including the full range of renewable energy penetration, the diversity of network topology changes, comprehensive coverage of typical fault scenarios, and the randomness of renewable energy output. Multi-dimensional sampling of operating scenarios can improve the generalization ability and uncertainty quantification ability of the data-driven model when facing unknown operating scenarios. After the training dataset is generated, it is divided according to the standard ratio of training-validation-test.

[0112] Step S24: Train the preset initial probability prediction model using the training sample set to obtain the probability prediction model. The preset initial probability prediction model includes a feature extraction network and a hybrid density network output layer. The feature extraction network is used to extract the deep representation of the input features, and the hybrid density network output layer is used to map the deep representation to the parameters of a mixture Gaussian distribution.

[0113] Specifically, the initial probability prediction model uses a Transformer encoder as the feature extraction backbone and processes the global correlation between physical quantities within the input feature vector in parallel through a self-attention mechanism. The model output layer adopts a Mixture Density Network (MDN) to map the feature representation output by the encoder to parameters of a mixture Gaussian distribution to achieve probability prediction.

[0114] Step S241, Transformer encoder: Input feature vector First, a linear projection layer is used to map to a high-dimensional embedding space, unifying heterogeneous features of different dimensions and scales to the same representation dimension. Since there are implicit hierarchical relationships between the physical quantities within the input feature vector, learnable positional encoding is used and added element-wise to the embedding vector, enabling the model to distinguish semantic information at different feature locations.

[0115] Transformer encoder is composed of N l The network consists of stacked encoding layers with identical structures. Each encoding layer contains a multi-head self-attention sub-layer and a feedforward neural network sub-layer. Each sub-layer is followed by residual connections and layer normalization. Residual connections alleviate the vanishing gradient problem during deep network training, while layer normalization stabilizes the output distribution of each layer to accelerate training convergence. The multi-head self-attention mechanism calculates the correlation weights between features through scaled dot product attention, achieving context-weighted fusion of input features. Scaled dot product attention can be represented as: (25); in, QFor query matrix, K For the key matrix, V For value matrices, Let be the dimension of the key vector. This represents the softmax function.

[0116] Multi-head attention mechanism will Q , K , V Attention is computed in parallel by projecting the data onto multiple independent subspaces. The outputs of each head are then concatenated and linearly transformed again, enabling the model to simultaneously capture feature association patterns at multiple scales. The feedforward neural network sublayer consists of two linear transformations and an intermediate nonlinear activation function, introducing nonlinear expressive power and allowing the model to fit complex feature mapping relationships. N l After layers of encoding are stacked, the encoder output reflects a contextual representation that reflects the deep associations between the input features. This serves as the input to the output layer of the subsequent hybrid density network (MDN).

[0117] Step S242, Hybrid density network output layer: To predict the probability distribution of critical inertia, a hybrid density network (MDN) is used as the output layer of the model. The MDN models the probability density function of the target through a parameterized Gaussian mixture distribution, and can simultaneously output the prediction mean, uncertainty range, and critical inertia quantiles at different confidence levels.

[0118] Encoder output The output layer of the Mixed Density Network (MDN) is mapped to a mixture of Gaussian components as weights. mean With variance The activation functions are given by three sets of fully connected layers and their corresponding activation functions: (26); in, L Number of mixed components , , These are the learnable parameter vectors for the corresponding outputs.

[0119] Number of mixed components L It is a key hyperparameter of hybrid density network (MDN). If it is too small, it may not be able to fit the complex multimodal distribution, while if it is too large, it may cause training instability and overfitting. In practical applications, it is usually determined by performance tuning on the validation set and is a variable between 3 and 10.

[0120] Critical inertia in input characteristics The predicted probability distribution is expressed as a weighted sum of the Gaussian components: (27); in, The mean ,variance The Gaussian probability density function.

[0121] Compared to a single Gaussian distribution, the mixture Gaussian distribution can more flexibly reflect the dispersion pattern of critical inertia under different operating and disturbance scenarios. The predicted mean of critical inertia can be analytically calculated using equation (27). With prediction variance : (28); The predicted mean gives the most likely value of the critical inertia; the predicted variance quantifies the level of uncertainty of the prediction results. A large variance indicates that the critical inertia has a large dispersion in the current operating scenario, and a higher safety margin should be reserved in the scheduling decision.

[0122] Furthermore, the critical inertia quantiles at different confidence levels can be extracted from the mixture Gaussian distribution of equation (27). Given a confidence level... A lower confidence level provides a median estimate of the critical inertia; a higher confidence level provides a higher quantile estimate, allowing for a larger safety margin and corresponding to conservative decision-making. The quantile of the critical inertia at this confidence level... Values ​​that satisfy the following formula: (29); In the formula, Let be the cumulative distribution function of the standard normal distribution, and let the left side of the equation represent the mixture Gaussian distribution. The cumulative distribution function value at point .

[0123] A schematic diagram of Transformer-MDN model training is shown below. Figure 5 As shown, the Transformer-MDN probabilistic prediction model consists of two cascaded main parts. The left side is the Transformer encoder, where the input feature vector is mapped to a high-dimensional embedding space via an input embedding layer, then element-wise added to the positional encoding, and input into the encoding layer, which consists of a multi-head self-attention sublayer and a feedforward neural network sublayer. Each sublayer has residual connections and normalization operations, and the encoding layer structure is stacked multiple times within the encoder. The right side is the hybrid density network (MDN) output layer, where several fully connected neural networks transform the hidden representation, ultimately outputting three sets of parallel probability distribution parameters. These three sets of parameters together constitute a mixture of Gaussian probability distributions for the critical inertia.

[0124] Step S243, Loss Function and Training: Model parameters during model training The optimal value should maximize the log-likelihood of the predicted distribution on the training samples, and the loss function is defined as the negative log-likelihood on the training samples: (30); in, , , For the model in the first s The mixed distribution parameters of the output given a training sample input.

[0125] Before training, the input feature vectors are standardized and preprocessed, transforming each feature dimension to zero mean and unit variance to eliminate the impact of scale differences between different physical quantities on training convergence speed and stability. Model training uses the Adam optimizer to optimize the parameters. Iterative updates are performed. After setting an initial learning rate empirically, cosine annealing and other learning rate decay strategies are used to prevent training oscillations in later stages. The training process employs mini-batch gradient descent. In each batch, the model output and loss function values ​​are calculated forward, and the gradient is calculated and parameters are updated backward.

[0126] To prevent overfitting, Dropout regularization is introduced between each layer of the encoder and the output layer of the Mixture Density Network (MDN) to randomly suppress the output of some neurons. An early stopping strategy is employed: after each training epoch, the negative log-likelihood of the model is evaluated on the validation set. Training is terminated early when the validation loss no longer decreases after several consecutive epochs, and the model parameters with the best validation performance are retained as the final probabilistic prediction layer model. The probabilistic prediction layer model has the same structure as the preset initial probabilistic prediction model, i.e., it uses a Transformer encoder as the feature extraction backbone and processes the global correlations between various physical quantities within the input feature vector in parallel through a self-attention mechanism. The model output layer uses a Mixture Density Network to map the feature representation output by the encoder to parameters of a Gaussian mixture distribution to achieve probabilistic prediction.

[0127] Specifically, step S202 includes: Step S2021: Input the real-time input feature vector into the feature extraction network of the probability prediction model. After forward computation by the feature extraction network, output the deep feature representation of the real-time input feature vector.

[0128] Specifically, the real-time input feature vector is first linearly projected into a high-dimensional embedding space through the input embedding layer, unifying heterogeneous features of different dimensions and scales into the same representation dimension. It is then added element-wise with the learnable positional encoding to distinguish the semantic information of different feature positions. Subsequently, it is computed forward through multiple encoding layers. In each encoding layer, the global correlation weights between features are calculated through a multi-head self-attention sub-layer to perform context-weighted fusion of the input features. Then, a non-linear expression is introduced through a feedforward neural network sub-layer. Each sub-layer is followed by residual connections and layer normalization operations, and finally, a deep feature representation that integrates the deep correlation information of the input features is output.

[0129] Step S2022: Input the deep feature representation into the output layer of the hybrid density network of the probability prediction model, and obtain the parameters of the hybrid Gaussian distribution through the forward calculation of the output layer of the hybrid density network; determine the hybrid Gaussian probability distribution based on the parameters of the hybrid Gaussian distribution.

[0130] Specifically, the output layer of the hybrid density network takes the deep feature representation output by the encoder as input. This input is computed in parallel by multiple independent fully connected networks, and outputs three sets of parameters: hybrid weights, mean, and variance. The hybrid weights are processed by the softmax activation function to ensure that the sum of the weights of each component is 1, the variance is processed by exponentiation to ensure that it is always positive, and the mean is directly output by linear mapping. The three sets of parameters together constitute the complete parameter set of the hybrid Gaussian distribution.

[0131] Based on the obtained mixing weights, mean, and variance of each Gaussian component, each set of mean and variance parameters is substituted into the Gaussian probability density function to form the probability density function of each Gaussian component. Then, the mixture is weighted and summed according to the corresponding mixing weights to obtain the mixture Gaussian probability distribution of the critical inertia under given input characteristics.

[0132] Step S203: Based on the mixture Gaussian probability distribution, the critical inertia evaluation value is obtained.

[0133] Specifically, step S203 includes: Step S2031: Obtain the mixing weights and mean of each Gaussian component in the Gaussian mixture probability distribution.

[0134] From the probability density function expression of the Gaussian mixture probability distribution, the mixture weight parameter and mean parameter corresponding to each Gaussian component are directly extracted. The mixture weight parameter is used to characterize the proportion of the Gaussian component in the mixture distribution, and the mean parameter is used to characterize the position of the most likely value range of the critical inertia corresponding to the Gaussian component.

[0135] Step S2032: Multiply the mixed weights by the corresponding means and sum them to obtain the predicted mean, and use the predicted mean as the evaluation value of the critical inertia.

[0136] The mixture weights of each extracted Gaussian component are multiplied by the mean one by one. The resulting product represents the weighted contribution of the component to the final predicted value. All products are then summed, and the summation result is the expected value of the mixture Gaussian distribution. This expected value is then output as the final evaluation value of the critical inertia.

[0137] Step S204: Extract the prediction variance from the Gaussian mixture probability distribution and use the prediction variance as a quantitative indicator of the uncertainty of the evaluation value; and / or, extract and output the critical inertia quantile at a specified confidence level based on the Gaussian mixture probability distribution, and use the critical inertia quantile for scheduling operation decision.

[0138] Specifically, the mixture weights, mean, and variance of each Gaussian component are extracted from the Gaussian mixture probability distribution. The prediction variance is calculated based on these weights, mean, and variance, and is used as a quantitative indicator of the reliability of the current assessment value. A larger variance indicates a greater dispersion of the critical inertia in the current operating scenario, and a higher risk that the most likely value represented by the assessment value deviates from the actual requirements. Therefore, schedulers need to reserve a higher safety margin. At the same time, a specified confidence level is selected in the Gaussian mixture probability distribution. The critical inertia quantile corresponding to this confidence level is obtained by taking the inverse function of the distribution function and output. This quantile represents the inertia threshold required for the system to maintain frequency safety at the current confidence level. Schedulers make differentiated decisions based on the quantiles of different confidence levels.

[0139] It should be noted that the implementation of this embodiment is divided into two stages: offline training and online evaluation. In the offline training stage, the Transformer-MDN model is trained based on historical operating data and simulation-generated datasets to obtain optimal parameters. After training, the model is deployed in the online evaluation system as a module for online inference of critical inertia. In the online evaluation stage, the system continuously collects the real-time operating status of the power system. For the current operating scenario, it calculates the input feature vector of the node based on the required parameter combinations. This feature vector is then input into the trained model, and a single forward inference operation yields the mixture Gaussian probability distribution of the critical inertia. The advantage of online evaluation lies in transforming the time-consuming computational process of nested optimization model solving into a single forward inference operation. This reduces the computational overhead of a single evaluation, meeting the real-time requirements of online evaluation. Furthermore, the system can simultaneously output the predicted mean, predicted variance, and critical inertia quantiles at different confidence levels.

[0140] The method for assessing the critical inertia of a power system provided in this embodiment describes the second-order underdamped oscillation characteristics of the system by constructing a frequency difference curve in the form of a decaying sinusoidal curve, deriving the expression of the regulating power of the generating unit, and establishing an optimization model for calculating the critical inertia that covers six types of operating constraints. The problem of solving the critical inertia is transformed into a single forward inference by using the Transformer-MDN probabilistic prediction model, and the conditional probability distribution of the critical inertia is modeled with a Gaussian mixture distribution. Then, the critical inertia quantiles at different confidence levels are extracted, enabling rapid assessment of the critical inertia in renewable energy power systems.

[0141] As one or more specific application embodiments of the present invention, combined with Figure 7 The method for evaluating the critical inertia of a power system provided by this invention will be further described in detail, such as... Figure 7 As shown ( Figure 7 It does not contain any content using artificial intelligence models (i.e., Transformer-MDN), but only the calculation method for critical inertia. The specific process is as follows: Step 1: Construct a simplified system model for a high-proportion renewable energy power system; the specific implementation details are as described in steps S201, S21, and S22 above.

[0142] Step 2: Construct a decaying sinusoidal frequency difference curve as an approximate solution to the system-level oscillation equation, and establish an optimization model for calculating critical inertia under six types of constraints; the specific implementation details are as described in step S22 of step S202 above.

[0143] Step 3: Construct the input feature vector and generate a training dataset through batch scene simulation; the specific implementation details are as described in step S23 of step S202 above.

[0144] Step 4: Train the Transformer-MDN model; the specific implementation details are as described in step S24 of step S202 above.

[0145] Step 5: Deploy the trained model online and output the critical inertia evaluation results at different confidence levels. Specific implementation details are as described in step S203 above.

[0146] The method for evaluating the critical inertia of a power system provided in this invention achieves rapid online inference while ensuring the reliability of critical inertia calculation, and outputs the critical inertia results at different confidence levels in the form of a probability distribution. Specifically, this invention achieves the following beneficial effects: 1. The spatial differences in frequency response of each node are reflected in the critical inertia assessment, so that the assessment results can ensure that the frequency of all locations in the system does not exceed their respective safety constraints; 2. Construct a frequency difference curve that closely matches the actual frequency response process of the power system to improve the physical fidelity of frequency security constraints; 3. Achieve rapid online inference of critical inertia, overcoming the dual limitations of excessive computational overhead of mathematical model-based methods and lack of generalization of purely data-driven methods; 4. Reflect the dispersion of critical inertia under different operating scenarios, and output critical inertia evaluation results at different confidence levels to support differentiated scheduling decisions.

[0147] This embodiment also provides a device for evaluating the critical inertia of a power system. This device is used to implement the above embodiments and preferred embodiments, and details already described will not be repeated. As used below, the term "module" can be a combination of software and / or hardware that implements a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0148] This embodiment provides a device for evaluating the critical inertia of a power system, such as... Figure 8 As shown, it includes: The data acquisition and feature extraction module 801 is used to acquire real-time operating parameters of the power system and construct a real-time input feature vector based on the real-time operating parameters. The probability prediction module 802 is used to input the real-time input feature vector into the pre-built probability prediction model and obtain the mixture Gaussian probability distribution of the critical inertia through a single forward inference. The probability prediction model is constructed by training with the true value of the critical inertia solved based on the physical model as the training target and the conditional probability distribution of the critical inertia modeled by the mixture Gaussian distribution as the output form. Output module 803 is used to obtain the evaluation value of critical inertia based on the Gaussian mixture probability distribution.

[0149] The power system critical inertia assessment device provided in this embodiment of the invention can execute the power system critical inertia assessment method provided in any embodiment of the invention, and has the corresponding functional modules and beneficial effects for executing the method. Further functional descriptions of the various modules and units described above are the same as in the corresponding embodiments described above, and will not be repeated here.

[0150] Figure 9 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention.

[0151] The following is a detailed reference. Figure 9The diagram illustrates a structural schematic suitable for implementing an electronic device according to embodiments of the present invention. The electronic device may include a processor (e.g., a central processing unit, graphics processor, etc.) 901, which can perform various appropriate actions and processes according to a program stored in read-only memory (ROM) 902 or a program loaded from memory 908 into random access memory (RAM) 903. RAM 903 also stores various programs and data required for the operation of the electronic device. The processor 901, ROM 902, and RAM 903 are interconnected via bus 904. An input / output (I / O) interface 905 is also connected to bus 904.

[0152] Typically, the following devices can be connected to I / O interface 905: input devices 906 including, for example, touchscreens, touchpads, keyboards, mice, cameras, microphones, accelerometers, gyroscopes, etc.; output devices 907 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; memory devices 908 including, for example, magnetic tapes, hard disks, etc.; and communication devices 909. Communication device 909 allows electronic devices to exchange data via wireless or wired communication with other devices. Although Figure 9 Electronic devices with various devices are shown, but it should be understood that it is not required to implement or have all of the devices shown, and more or fewer devices may be implemented or have instead.

[0153] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device 909, or installed from a memory 908, or installed from a ROM 902. When the computer program is executed by the processor 901, it performs the functions defined in the power system critical inertia evaluation method of the embodiments of the present invention.

[0154] Figure 9 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments of the present invention.

[0155] This invention also provides a computer-readable storage medium. The methods described above according to embodiments of the invention can be implemented in hardware or firmware, or implemented as recordable on a storage medium, or implemented as computer code originally stored on a remote storage medium or a non-transitory machine-readable storage medium and subsequently stored on a local storage medium after being downloaded via a network. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code. When the software or computer code is accessed and executed by the computer, processor, or hardware, the method for evaluating the critical inertia of a power system shown in the above embodiments is implemented.

[0156] A portion of this invention can be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to the invention through the operation of the computer. Those skilled in the art will understand that the forms in which computer program instructions exist in a computer-readable medium include, but are not limited to, source files, executable files, installation package files, etc. Correspondingly, the ways in which computer program instructions are executed by a computer include, but are not limited to: the computer directly executing the instructions, or the computer compiling the instructions and then executing the corresponding compiled program, or the computer reading and executing the instructions, or the computer reading and installing the instructions and then executing the corresponding installed program. Here, the computer-readable medium can be any available computer-readable storage medium or communication medium accessible to a computer.

[0157] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A method for evaluating the critical inertia of a power system, characterized in that, The method includes: Obtain the real-time operating parameters of the power system, and construct a real-time input feature vector based on the real-time operating parameters; The real-time input feature vector is input into a pre-constructed probability prediction model, and the mixture Gaussian probability distribution of the critical inertia is obtained through a single forward inference. The probability prediction model is constructed by training with the true value of the critical inertia solved based on the physical model as the training target and the conditional probability distribution of the critical inertia modeled by the mixture Gaussian distribution as the output form. The critical inertia is evaluated based on the mixture of Gaussian probability distributions.

2. The method according to claim 1, characterized in that, The probability prediction model is constructed in the following manner: Obtain the operating parameters of the power system under various operating scenarios, and construct the frequency response model of the power system based on the operating parameters under various operating scenarios; With the goal of minimizing system inertia and in combination with preset frequency safety constraints, the critical inertia true values ​​corresponding to each operating scenario are solved according to the frequency response model. Based on the operating parameters of each operating scenario, corresponding input feature samples are constructed, and the input feature samples are paired with the corresponding critical inertia true values ​​to generate a training sample set. The preset initial probability prediction model is trained using the training sample set to obtain the probability prediction model. The preset initial probability prediction model includes a feature extraction network and a hybrid density network output layer. The feature extraction network is used to extract a deep representation of the input features, and the hybrid density network output layer is used to map the deep representation to the parameters of a mixture Gaussian distribution.

3. The method according to claim 2, characterized in that, The operating parameters include the parameters of each power generation unit, the system baseline capacity, and the load frequency response coefficient; The construction of the frequency response model of the power system includes: Based on the parameters of each power generation unit, establish the transfer function of each power generation unit; Based on the system's baseline capacity and load frequency response coefficient, each power generation unit is modeled as the frequency response model of the power system.

4. The method according to claim 3, characterized in that, The power generation units participating in the frequency response include synchronous generator sets and grid-connected renewable energy units with grid-connected converters; the parameters of each power generation unit include the inertial time constant, damping coefficient, and frequency regulation parameters corresponding to each power generation unit. The step of establishing the transfer function of each power generation unit based on the parameters of each power generation unit includes: Based on the inertial time constant, damping coefficient and frequency regulation parameters of the synchronous generator set, the first transfer function of the synchronous generator set is established. The first transfer function includes the rotor motion equation and the first-order inertial lag element. Based on the inertial time constant, damping coefficient, and frequency regulation parameters of the renewable energy units connected to the grid using grid-connected converters, a second transfer function is established that is mathematically consistent with the first transfer function.

5. The method according to claim 3, characterized in that, The step of modeling each power generation unit into the frequency response model based on the system baseline capacity and load frequency response coefficient includes: The equivalent inertia of the system is obtained by weighting the inertial time constants of each power generation unit according to their respective rated capacities and then dividing the sum by the system's reference capacity. The equivalent damping coefficient of the system is obtained by weighting the damping coefficients of each power generation unit according to their respective rated capacities, dividing by the system reference capacity, and then superimposing the frequency response characteristics of the load itself. The frequency response model is constructed using the system's equivalent inertia and equivalent damping coefficient as parameters and the system's equivalent frequency deviation as the state variable.

6. The method according to claim 5, characterized in that, The construction of the frequency response model of the power system also includes: The system inertial center frequency is used as a unified frequency analysis benchmark, where the deviation of the system inertial center frequency is the average value of the frequency deviation of each power generation unit weighted by inertia. The actual frequency deviation of any node is decomposed into the sum of the system inertial center frequency deviation component and the node local deviation component; the node local deviation component is used to correct the extreme value constraint of the system inertial center frequency in the frequency safety constraint, so as to independently verify the frequency safety margin of each node.

7. The method according to claim 1, characterized in that, The step of constructing a real-time input feature vector based on the real-time operating parameters includes: Physical quantities that affect the critical inertia are extracted from the real-time operating parameters at three levels: system level, node level, and frequency response dynamics. System-level sub-vectors consisting of system equivalent inertia, system equivalent damping coefficient, renewable energy penetration rate, total output of system synchronous machine, and total capacity of grid-connected converter are constructed respectively; node-level sub-vectors consisting of node local equivalent inertia and electrical distance from node to disturbance source; and frequency response dynamics sub-vectors consisting of disturbance power and initial frequency change rate. The system-level sub-vector, the node-level sub-vector, and the frequency response dynamic sub-vector are concatenated to form the real-time input feature vector.

8. The method according to claim 2, characterized in that, The real-time input feature vector is input into a pre-constructed probability prediction model, and a mixture Gaussian probability distribution of the critical inertia is obtained through a single forward inference, including: The real-time input feature vector is input into the feature extraction network of the probability prediction model. After forward calculation by the feature extraction network, the deep feature representation of the real-time input feature vector is output. The deep feature representation is input into the output layer of the hybrid density network of the probability prediction model. The parameters of the hybrid Gaussian distribution are obtained by forward calculation through the output layer of the hybrid density network. The Gaussian mixture probability distribution is determined based on the parameters of the Gaussian mixture distribution.

9. The method according to claim 1, characterized in that, The process of obtaining the critical inertia assessment value based on the Gaussian mixture probability distribution includes: Obtain the mixing weights and mean of each Gaussian component in the mixture Gaussian probability distribution; The predicted mean is obtained by multiplying the mixed weights by their corresponding means and summing the results. This predicted mean is then used as the evaluation value of the critical inertia.

10. The method according to claim 1, characterized in that, The method further includes: The prediction variance is extracted from the Gaussian mixture probability distribution, and the prediction variance is used as the uncertainty quantification index of the evaluation value. And / or, based on the mixture Gaussian probability distribution, extract and output the critical inertia quantile at a specified confidence level, the critical inertia quantile being used for scheduling operation decisions.

11. A device for evaluating the critical inertia of a power system, characterized in that, The device includes: The data acquisition and feature extraction module is used to acquire real-time operating parameters of the power system and construct a real-time input feature vector based on the real-time operating parameters. The probability prediction module is used to input the real-time input feature vector into a pre-constructed probability prediction model and obtain the mixture Gaussian probability distribution of the critical inertia through a single forward inference. The probability prediction model is constructed by training with the true value of the critical inertia solved based on the physical model as the training target and the conditional probability distribution of the critical inertia modeled by the mixture Gaussian distribution as the output form. The output module is used to obtain an evaluation value of the critical inertia based on the mixture of Gaussian probability distributions.

12. An electronic device, characterized in that, include: A memory and a processor are communicatively connected, the memory storing computer instructions, and the processor executing the computer instructions to perform the method for evaluating the critical inertia of a power system as described in any one of claims 1 to 10.

13. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing the computer to execute the method for evaluating the critical inertia of a power system as described in any one of claims 1 to 10.

14. A computer program product, characterized in that, It includes computer instructions for causing a computer to execute the method for evaluating the critical inertia of a power system as described in any one of claims 1 to 10.

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