Inertia probability prediction method and device

Abstract

The embodiment of the invention provides an inertia probability prediction method and device, and the method comprises the steps: constructing a comprehensive feature set containing basic operation features and real-time dynamic features, and enabling the comprehensive feature set to serve as the input of a prediction model; constructing a mixed risk objective function fusing an economic cost item, a decision risk cost item and a physical safety penalty item, wherein the mixed risk objective function is used for training a prediction model; and training a probability prediction model by adopting a risk-guided probability modeling method based on the mixed risk objective function so as to generate inertia probability distribution of the embedded decision risk and the security constraint. Through a risk-guided probability modeling method, complete probability distribution of the embedded decision preference and the security boundary is generated, so that the statistical accuracy of prediction is improved, and the prediction robustness in an extreme risk scene is ensured; and a more reliable inertia uncertainty description which better meets the decision demand is provided for fine scheduling and security defense of the power system in a new energy high-permeability environment.

Description

Technical Field

[0001] The embodiments in this specification relate to the field of power technology, and in particular to a method for predicting the probability of inertia. Background Technology

[0002] With the advancement of global energy transition strategies, the penetration rate of new energy sources, represented by wind power and solar power, in power systems is rapidly increasing. These new energy sources are mainly connected to the grid through power electronic converters, lacking the rotating mass of traditional synchronous generator sets. This results in a significant decrease in the total rotational inertia of the power system and increased volatility. System inertia is the first line of defense against frequency disturbances, and its reduction poses a serious threat to the frequency stability of the system when subjected to power disturbances.

[0003] To ensure power grid security, dispatching and operation departments must accurately predict the system inertia level for the following day during the day-ahead dispatching planning phase. This prediction is crucial for determining unit combination, allocating reserve capacity, and defining frequency security constraints. Currently, power system inertia prediction technologies are mainly divided into two categories: the first is the statistical method based on physical models, which obtains the predicted value by accumulating the inertia of planned online synchronous units based on the day-ahead unit combination plan; the second is the data-driven machine learning method, which uses algorithms such as neural networks to learn historical data and construct a mapping model from operating characteristics to system inertia.

[0004] The aforementioned existing machine learning-based technologies suffer from several significant objective drawbacks in practical applications. These technologies exhibit a degree of disconnect between statistical and decision-making objectives. Machine learning methods typically aim to minimize symmetric statistical indicators such as mean square error, but this ignores the asymmetric economic consequences of prediction errors in power dispatch decisions. Specifically, under-prediction of inertia can trigger severe frequency safety incidents and exorbitant emergency costs, with the economic penalty far outweighing the slight increase in reserve costs caused by over-prediction. Existing methods fail to incorporate this asymmetric decision-making cost into their models, resulting in suboptimal economic performance. These methods often utilize only day-ahead quasi-static forecast data, such as load and renewable energy output forecasts, as model inputs, neglecting high-frequency time-series information from historical operating data, such as second- or minute-level AGC and frequency data, which reflect the true dynamic response characteristics of the system. This leads to insufficient model perception of system dynamic changes, thus limiting prediction accuracy.

[0005] Therefore, a better solution is urgently needed. Summary of the Invention

[0006] In view of this, embodiments of this specification provide an inertia probability prediction method. One or more embodiments of this specification also relate to an inertia probability prediction device, a computing device, a computer-readable storage medium, and a computer program, to address the technical deficiencies existing in the prior art.

[0007] According to a first aspect of the embodiments of this specification, an inertia probability prediction method is provided, comprising: Construct a comprehensive feature set that includes basic operational features and real-time dynamic features, and use the comprehensive feature set as input to the prediction model; A hybrid risk objective function is constructed that integrates economic cost terms, decision risk cost terms, and physical security penalty terms. This hybrid risk objective function is used to train the prediction model. Based on a hybrid risk objective function, a risk-guided probabilistic modeling method is used to train a probabilistic prediction model to generate an inertia probability distribution with embedded decision risks and safety constraints.

[0008] In one possible implementation, constructing a comprehensive feature set that includes basic operational characteristics and real-time dynamic characteristics includes: Obtain the load forecast, renewable energy output forecast, planned nuclear power output, planned switching power of tie lines, ambient temperature forecast, date type identifier, and historical inertia values ​​for the future target time at the forecast time, and normalize or encode them to form a basic feature vector. Within a preset statistical time window, historical high-frequency automatic power generation control signals are statistically analyzed to extract dynamic statistical features, including average frequency deviation, regulation mileage, standard deviation of frequency deviation, and root mean square of frequency change rate, in order to form a dynamic feature vector. The basic feature vector and the dynamic feature vector are concatenated to form a comprehensive feature set.

[0009] In one possible implementation, the hybrid risk objective function is a weighted sum of economic cost, decision risk cost, and physical security penalty; the economic cost is constructed based on the asymmetric economic consequences of prediction errors, the decision risk cost is constructed based on conditional risk value to reflect risk aversion preferences, and the physical security penalty is constructed based on frequency security constraints.

[0010] In one possible implementation, the economic cost item is constructed as follows: The prediction error of a single sample is defined as the difference between the model's predicted value and the actual inertia value. Construct a piecewise asymmetric cost function and apply a unit penalty coefficient higher than that for the over-predicted part of the prediction error to the under-predicted part. Calculate the expected value of the asymmetric cost function over all training samples, and use it as the economic cost term.

[0011] In one possible implementation, the physical security penalty term is constructed as follows: Determine the minimum inertia requirement threshold needed to ensure frequency security based on the frequency response proxy model; When the predicted inertia value output by the prediction model is lower than the minimum inertia requirement threshold, a large penalty term is applied to guide the predicted value to meet physical safety constraints during model training.

[0012] In one possible implementation, training the probabilistic prediction model using a risk-guided probabilistic modeling approach includes: Quantile regression is used as the basic probability modeling framework; A risk-weighted pinball loss function is constructed, which is a linear combination of the traditional pinball loss function and a risk-weighted term. The calculation of the risk-weighted term integrates decision-making and safety considerations in the economic cost term and the physical safety penalty term. A risk-weighted pinball loss function is used to train a quantile regression model to obtain a set of risk-perceived quantile predictions.

[0013] In one possible implementation, the method also includes: Based on the specific high and low quantile values ​​output by the trained quantile regression model, the threshold for tail fitting is dynamically determined. Tail modeling is performed using a generalized Pareto distribution for samples below the low threshold and above the high threshold, respectively; The cumulative distribution function fitted to the quantile regression model in the main body is concatenated with the generalized Pareto distributions in the left and right tails to form a complete conditional cumulative distribution function as the final prediction output.

[0014] According to a second aspect of the embodiments of this specification, an inertia probability prediction device is provided, comprising: The feature construction module is configured to build a comprehensive feature set containing basic operational features and real-time dynamic features, which serves as the input to the prediction model. The model training module is configured to construct a hybrid risk objective function that integrates economic cost, decision risk cost, and physical security penalty. This hybrid risk objective function is used to train the prediction model. The output module is configured to train a probabilistic prediction model based on a hybrid risk objective function and a risk-guided probabilistic modeling method to generate an inertia probability distribution with embedded decision risks and safety constraints.

[0015] According to a third aspect of the embodiments of this specification, a computing device is provided, comprising: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions, which, when executed by the processor, implement the steps of the above-described inertia probability prediction method.

[0016] According to a fourth aspect of the embodiments of this specification, a computer-readable storage medium is provided that stores computer-executable instructions that, when executed by a processor, implement the steps of the above-described inertia probability prediction method.

[0017] According to a fifth aspect of the embodiments of this specification, a computer program is provided, wherein when the computer program is executed in a computer, it causes the computer to perform the steps of the above-described inertia probability prediction method.

[0018] This specification provides an inertia probability prediction method and apparatus. The inertia probability prediction method includes: constructing a comprehensive feature set containing basic operational characteristics and real-time dynamic characteristics, which serves as the input to a prediction model; constructing a hybrid risk objective function that integrates economic cost terms, decision risk cost terms, and physical security penalty terms, which is used to train the prediction model; and training the probability prediction model based on the hybrid risk objective function using a risk-guided probabilistic modeling method to generate an inertia probability distribution with embedded decision risks and security constraints. By using the risk-guided probabilistic modeling method, a complete probability distribution with embedded decision preferences and security boundaries is generated, which not only improves the statistical accuracy of the prediction but also ensures the robustness of the prediction under extreme risk scenarios. This provides a more reliable and decision-oriented description of inertia uncertainty for the refined scheduling and security defense of power systems in environments with high penetration of new energy sources. Attached Figure Description

[0019] Figure 1 This is a flowchart of an inertia probability prediction method provided in one embodiment of this specification; Figure 2 This is a schematic diagram of an inertia probability prediction method provided in one embodiment of this specification; Figure 3 This is a schematic diagram illustrating the asymmetric cost impact of prediction error in an inertia probability prediction method provided in one embodiment of this specification. Figure 4 This is a schematic diagram of the structure of an inertia probability prediction device provided in one embodiment of this specification; Figure 5 This is a structural block diagram of a computing device provided in one embodiment of this specification. Detailed Implementation

[0020] Many specific details are set forth in the following description to provide a full understanding of this specification. However, this specification can be implemented in many other ways than those described herein, and those skilled in the art can make similar extensions without departing from the spirit of this specification. Therefore, this specification is not limited to the specific implementations disclosed below.

[0021] The terminology used in one or more embodiments of this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of the one or more embodiments of this specification. The singular forms “a” and “the” as used in one or more embodiments of this specification and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in one or more embodiments of this specification refers to and includes any or all possible combinations of one or more associated listed items.

[0022] It should be understood that although the terms first, second, etc., may be used to describe various information in one or more embodiments of this specification, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, first may also be referred to as second without departing from the scope of one or more embodiments of this specification, and similarly, second may also be referred to as first. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to a determination."

[0023] This specification provides a method for predicting the probability of inertia. It also relates to a device for predicting the probability of inertia, a computing device, and a computer-readable storage medium, which will be described in detail in the following embodiments.

[0024] See Figure 1 , Figure 1 A flowchart of an inertia probability prediction method according to an embodiment of this specification is shown, which specifically includes the following steps.

[0025] Step 101: Construct a comprehensive feature set containing basic operational features and real-time dynamic features. The comprehensive feature set is used as the input to the prediction model.

[0026] For details, see Figure 2 This step involves constructing a comprehensive feature set that integrates multi-dimensional information and extracting system dynamic features across time scales. By building a comprehensive feature set containing basic operational information and real-time dynamic information, this step provides the model with more comprehensive input, thereby improving the model's predictive performance. Specifically, this step includes the construction and formal definition of basic feature vectors, as well as the extraction and modeling of dynamic features of AGC signals.

[0027] In one possible implementation, constructing a comprehensive feature set that includes basic operational characteristics and real-time dynamic characteristics involves: acquiring the predicted load value, predicted renewable energy output value, planned nuclear power output, planned switching power of tie lines, predicted ambient temperature value, date type identifier, and historical inertia value for the same period at the predicted time, and normalizing or encoding them to form a basic feature vector; performing statistical analysis on historical high-frequency automatic generation control signals within a preset statistical time window to extract dynamic statistical features including average frequency deviation, regulation mileage, standard deviation of frequency deviation, and root mean square of frequency change rate to form a dynamic feature vector; and concatenating the basic feature vector and the dynamic feature vector to form a comprehensive feature set.

[0028] In practical applications, the construction and formal definition of the basic feature vector are as follows: To establish a basic predictive capability for the system inertia level of the next day, we first collect and integrate various pre-dated information known at the prediction time t and related to the system inertia at the future time t+k, and organize them into a basic feature vector X. b (t). The formal definition of this vector is shown in equation (1): (1) In the formula, each component represents the information about the future that can be obtained at the prediction time t. t + k The predictive or deterministic information for a given time is detailed below: P load ( t + k Predicted time t + k The total system load forecast value. This data usually comes from the load forecasting system of the power grid dispatch center and is a continuous numerical variable.

[0029] P wind on ( t + k Predicted time t + k The predicted total output of onshore wind power.

[0030] P wind off ( t + k Predicted time t + k The total offshore wind power output is predicted. Both of these wind power forecast data are usually obtained from new energy power forecasting systems and are continuous numerical variables.

[0031] P solar ( t + k Predicted time t + k The total photovoltaic power output is predicted. This data also comes from the new energy power prediction system and is a continuous numerical variable.

[0032] P nuc ( t + k Predicted time t + k The planned nuclear power output. Nuclear power is usually used as a baseload power source, and the planned output for the following day is highly deterministic, being a continuous numerical variable.

[0033] P inter ( t + k Predicted time t + k The planned net exchange power of inter-regional power transfer lines. Positive values ​​indicate power reception, and negative values ​​indicate power transmission. This data reflects the power support between regions and is a continuous numerical variable.

[0034] T emp ( t + k Predicted time t + k The predicted ambient temperature. Temperature is an important factor affecting load and indirectly influences the start-up mode of synchronous generator units; it is a continuous numerical variable.

[0035] D day ( t + k Predicted time t + k The corresponding weekday type identifier (1-7 represent Monday to Sunday respectively) or holiday identifier (0 represents weekday, 1 represents holiday). This data is a discrete categorical variable.

[0036] D hour ( t + k Predicted time t + k The corresponding number of hours (0-23). ​​This data is a discrete categorical variable used to capture the periodicity of intraday load and power generation.

[0037] H lag,24 (t Predicted time t The corresponding historical system inertia value (24 hours ago). This lag term provides the model with important information about the time correlation of the inertia itself, and is a continuous numerical variable.

[0038] To ensure that the aforementioned multi-source, heterogeneous features can be effectively utilized by the prediction model, they need to be preprocessed. For continuous numerical variables, to eliminate the influence of different dimensions between features, the max-min normalization method is used to map them to the [0,1] interval, as shown in equation (2): (2) In the formula, x These are the original eigenvalues. x ' is the normalized value, x max and x min These are the maximum and minimum values ​​of the feature in the training set, respectively.

[0039] For discrete categorical variables, such as those for the day of the week, one-hot encoding is used to avoid introducing inappropriate ordinal relationships. This is converted into a 7-dimensional vector, where the value corresponding to the day of the week is 1, and the rest are 0.

[0040] Furthermore, regarding the extraction and modeling of dynamic features of AGC signals: After constructing the basic feature vector, to enable the model to more deeply understand and predict inertia changes driven by the real-time imbalance state of the system, this application innovatively introduces statistical analysis of historical high-frequency automatic generator control (AGC) signals. Most existing inertia prediction methods rely on quasi-static data such as day-ahead plans. While these methods can reflect the static operating baseline of the system the following day, they neglect high-frequency information that characterizes the true dynamic characteristics of the system, resulting in insufficient model perception of dynamic changes. This application, through a cross-scale feature extraction method, extracts statistical features reflecting the slow dynamic characteristics of the system from high-frequency real-time control signals, achieving effective input of dynamic information into the day-ahead prediction model.

[0041] The underlying physical mechanism for introducing these historical high-frequency dynamic characteristics lies in the fact that a power system that has recently required frequent and significant AGC adjustments typically indicates that the system is operating under conditions of high volatility or low system damping. This operating state is often strongly correlated with low synchronous generator online rates and high asynchronous power source penetration rates, the latter being key factors determining the system inertia level the following day. Therefore, these historical dynamic characteristics can be considered effective proxy variables characterizing the dynamic health of the system, providing incremental information about the system's dynamic margin that is not available in existing quasi-static inputs for day-ahead inertia prediction models, thereby improving prediction accuracy.

[0042] This process obtains high-frequency time-series data related to historical AGC from the scheduling automation system, including system frequency. f ( t ) and AGC adjustment commands P agc ( t ),in t The sampling time is set at high frequencies (on the order of seconds or minutes). Then, within a preset statistical time window T, these high-frequency data are calculated. In one embodiment, the value of T can range from 30 minutes to 2 hours. When T is small, the model is more sensitive to the system's recent dynamic response; when T is large, it reflects longer-term operating trends. A series of low-frequency dynamic statistical features are extracted. These features can characterize the system's dynamic health status over a past period from different physical dimensions.

[0043] In a preferred embodiment of this application, the extracted dynamic features and their mathematical modeling are as follows: Average frequency deviation ( f ave This feature is used to quantify the level of power imbalance that persists in the system within a statistical window T. Its calculation formula is shown in equation (3): (3) In the formula, f N This is the system's rated frequency. f ave If the value of (t) continues to deviate significantly from zero, it indicates that the system has a persistent power surplus or deficit, which reflects that there may be a systematic bias in the basic source load forecast that needs to be corrected.

[0044] Adjusting mileage ( f mile This feature quantifies the total regulating effort exerted by the generator set in response to AGC commands, directly reflecting the degree of regulation resource consumption required by the system to maintain frequency stability. Its calculation formula is shown in equation (4): (4) In the formula, Δτ is the high-frequency sampling time interval. A larger regulation mileage value indicates frequent system frequency fluctuations, increased imbalance, higher regulation requirements for synchronous generators, and suggests increased volatility in system operation.

[0045] Frequency deviation standard deviation ( f std This feature is used to quantify the system frequency within a statistical window. T The degree of fluctuation within the frequency range is a key dynamic indicator for measuring frequency stability. Its calculation formula is shown in equation (5): (5) A higher frequency standard deviation indicates poor system stability, which is usually associated with a lower system inertia level and a higher disturbance level.

[0046] Root mean square rate of change of frequency (RoCoF) rms This characteristic directly reflects the system's ability to resist sudden frequency changes and is closely related to the system's total inertia. According to the rotor motion equations of a power system, the rate of frequency change is approximately inversely proportional to the system inertia. (RoCoF) rms The average fluctuation of RoCoF within the statistical window T was quantified, and its calculation formula is shown in equation (6): (6) RoCoF rms A higher value usually indicates a lower system inertia level and a more vulnerable frequency security.

[0047] Through the above calculations, a dynamic feature vector can be obtained at each prediction time t. X d (t), as shown in equation (7): (7) Finally, the basic eigenvector X defined by equation (1) is... b (t) and the dynamic eigenvector X defined by equation (7) d (t) are concatenated to form the final comprehensive feature vector X used as input to the prediction model. final (t), as shown in equation (8): (8) In this way, this application provides richer and more informative inputs for subsequent prediction models than existing technologies, laying a solid data foundation for improving prediction accuracy and reliability.

[0048] Step 102: Construct a hybrid risk objective function that integrates economic cost terms, decision risk cost terms, and physical security penalty terms. The hybrid risk objective function is used to train the prediction model.

[0049] For details, see Figure 2 To overcome the shortcomings of existing technologies, such as a single objective function that is disconnected from decision-making, this step, based on the theory of mathematical programming, constructs a hybrid risk objective function to guide the subsequent training of the prediction model. Compared with existing technologies, this application, by constructing an innovative composite objective function, directly links the optimization process of the prediction model with the economic, safety, and risk objectives of downstream scheduling decisions.

[0050] In one possible implementation, the hybrid risk objective function is a weighted sum of economic cost, decision risk cost, and physical security penalty; the economic cost is constructed based on the asymmetric economic consequences of prediction errors, the decision risk cost is constructed based on conditional risk value to reflect risk aversion preferences, and the physical security penalty is constructed based on frequency security constraints.

[0051] In practical applications, the objective function aims to minimize the generalized decision risk. This application formally defines the training process of the prediction model as a mathematical programming problem that minimizes the generalized decision risk. The objective function of this problem is... L total It consists of three weighted components: economic cost, decision risk cost, and physical security penalty. Its complete mathematical programming paradigm is shown in equation (9): (9) In the formula, I This represents the complete set of parameters (weights and biases) of the prediction model (e.g., a neural network) to be optimized. w 1, w 2, w 3 is a non-negative weighting coefficient used to balance the importance of different objectives, and w 1+ w 2+ w 3 = 1; To emphasize security, this can be set... w 3> w 1 and w 3> w 2. To prioritize cost-effectiveness, the following can be set: w 1> w 3, L econ ( I ), L risk ( I ), L sec ( I ) represent the economic cost item, the decision risk cost item, and the physical security penalty item, respectively. The following will provide a detailed mathematical model for them.

[0052] In one possible implementation, the economic cost term is constructed as follows: the prediction error of a single sample is defined as the difference between the model's predicted value and the true inertia value; a piecewise asymmetric cost function is constructed, and a unit penalty coefficient higher than that for the over-predicted part of the prediction error is applied to the under-predicted part; the expected value of the asymmetric cost function over all training samples is calculated as the economic cost term.

[0053] In practical applications, the economic cost item L econ The modeling is as follows.

[0054] To address the disconnect between statistical and decision-making objectives in existing machine learning methods, this application directly models the asymmetric economic consequences of prediction errors. For example... Figure 3 As shown, the economic losses caused by under-prediction of inertia, such as emergency control and load shedding, far outweigh the slight increase in standby costs caused by over-prediction.

[0055] To quantify this asymmetry, we first define the prediction error for a single sample i. e i : (10) In the formula, X i For the first i The input feature vector of each sample, ( I , X i ) represents the model in parameters I The predicted output, H true,i This is the true inertia value for this sample.

[0056] Subsequently, a piecewise asymmetric cost function is constructed. C ( e i Its specific form can be shown in equation (11): (11) In the formula, α and β These are the unit cost penalty coefficients for under-forecasting and over-forecasting, respectively, set based on actual operating experience. α >> β ; p and q An exponential coefficient greater than or equal to 1 is used to adjust the nonlinearity of cost as the error increases. In a preferred embodiment, it can be taken as... p = q =1, which simplifies to linear cost.

[0057] Ultimately, the economic cost item L econ ( I Defined as in all N The expected value of the asymmetric cost on each training sample is shown in Equation (12): (12) By minimizing this term, the model will be guided to produce a prediction that minimizes the expected total economic cost of the system.

[0058] In one possible implementation, the physical safety penalty term is constructed by determining the minimum inertia requirement threshold needed to ensure frequency safety based on a frequency response surrogate model; when the predicted inertia value output by the prediction model is lower than the minimum inertia requirement threshold, a large penalty term is applied to guide the predicted value to meet the physical safety constraints during model training.

[0059] In practical applications, physical security penalties L sec The modeling is as follows.

[0060] While existing technologies have attempted to incorporate frequency security constraints, their approach is indirect and decoupled: that is, they first consider the predicted inertia. Calculate the minimum reserve capacity required to meet various frequency constraints. R min Then R min The input is used to solve a complex economic scheduling optimization problem to obtain the operating cost. C Finally, the cost C The feedback is fed back to the prediction model. This method has drawbacks such as a lengthy computational process, indirect representation of physical constraints, and poor model interpretability.

[0061] To overcome the aforementioned shortcomings, this application proposes a method to directly and explicitly embed physical security constraints into the loss function of the prediction model. The core of this method is to construct a surrogate model at the lowest frequency point. In a preferred embodiment, this surrogate model is constructed based on a two-stage frequency response theory that takes into account the virtual inertial response delay of energy storage, thus representing the system under power deficit disturbances. P loss The subsequent frequency response process is divided into a pure synchronous machine inertial response stage and a multi-resource cooperative response stage. Ultimately, it is derived that the minimum system frequency should not fall below the safety lower limit. f limit (i.e., the maximum frequency deviation does not exceed Δ) f max The minimum total inertia constraint that the system must satisfy. This constraint constitutes the frequency response proxy model of this application, and its specific form is shown in equation (13): (13) The physical meaning of Equation (13) is that, in order to ensure frequency security, the predicted total inertia (left side) must be greater than or equal to an inertia demand threshold (right side) determined by scenario parameters such as frequency security boundary, disturbance size, and frequency modulation resource configuration.

[0062] Besides the preferred embodiment based on the analytical formula described above, the functionality of this surrogate model can also be implemented through a data-driven approach. In another embodiment, extensive offline power system simulations can be used to obtain minimum frequency data under different operating conditions, such as disturbance magnitude, initial inertia, and frequency regulation resource configuration. This data can then be used as training samples to train a neural network model. This trained neural network can then serve as a functionally equivalent surrogate model, taking real-time operating parameters as input and outputting the required minimum inertia threshold. It is also applicable to the physical safety penalty construction framework of this application. Therefore, the scope of protection of this application should not be limited to the specific mathematical implementation of the surrogate model.

[0063] Based on this proxy model, physical security penalty items L sec It can be constructed in the form shown in equation (14): (14) In the formula, ( I , X i () represents the model's predicted value for total inertia. RHS (i) is the right side of equation (13) according to the first i The inertia requirement threshold calculated from the parameters of each sample scenario. M The penalty coefficient should be a sufficiently large positive number, and its value should ensure that the physical security penalty term is applied when physical security constraints are violated. L sec The value is at least as high as other items (such as economic cost items). L econ This is an order of magnitude higher than the predicted inertia. The purpose of this term is to: when the model predicts the inertia... When the physical security requirements of equation (13) are not met, L sec This will generate a huge penalty value, thereby directly and explicitly guiding the model parameters during the backpropagation process of model training. I Update towards providing safer predictions.

[0064] Compared to the black-box optimization feedback of existing technologies, the physical information injection method of this application reduces complex external optimization steps, improves computational efficiency, and because the penalty term directly corresponds to the physical constraints, the adjustment direction of the model parameters has a clear physical meaning.

[0065] Furthermore, decision-making risk cost item L risk The modeling is as follows.

[0066] To reflect the risk aversion of power system dispatchers towards extreme events that could lead to significant economic losses in the face of uncertainty, this application introduces Conditional Value at Risk (CVaR) as a risk metric. CVaR measures the conditional expected value of the portion of the cost distribution exceeding Value at Risk (VaR) at a β confidence level, i.e., the average cost under the worst-case (1-β)% scenario. Compared to VaR, which only focuses on a specific quantile, CVaR can more comprehensively characterize the severity of tail risk.

[0067] To facilitate computation within a differentiable optimization model, this application adopts an equivalent optimization form of CVaR. This form introduces an auxiliary optimization variable ζ, whose optimal solution is VaR, transforming the calculation of CVaR into a convex, differentiable functional form, as shown in equation (15): (15) In the formula, ζ is an auxiliary decision variable, representing Value at Risk (VaR).

[0068] β represents the confidence level of CVaR, reflecting the decision-maker's degree of risk aversion. A higher β indicates a greater focus on tail risk. N is the total number of training samples, and the value of β can range from 0.90 to 0.99. Higher β values ​​correspond to a stronger risk aversion preference.

[0069] C ( e i (I , (Xi) ) is defined by equation (11) and is derived from the first i The asymmetric cost incurred by the prediction error of each sample is minimized in the overall objective function. L risk During training, the model not only attempts to reduce the average cost, but also pays special attention to and suppresses predictions that may lead to extremely high costs, thus giving its output predictions a natural risk-averse characteristic.

[0070] Furthermore, the complete mathematical programming model is as follows.

[0071] In summary, the training problem of the inertia prediction model proposed in this application is ultimately constructed as a complete and unified mathematical programming model. The goal of this model is to solve for a set of optimal model parameters. I ^ and optimal value at risk g^ This minimizes the generalized decision risk defined by equation (13). Its complete mathematical form is shown in equation (16): (16) I , g in L econ , L risk , L sec Defined by equations (12), (14), and (15) respectively. This model transforms a complex prediction problem with physical constraints and risk preferences into a mathematical problem that can be solved using standard optimization algorithms.

[0072] Step 103: Based on the hybrid risk objective function, a risk-guided probabilistic modeling method is used to train a probabilistic prediction model to generate an inertia probability distribution with embedded decision risks and safety constraints.

[0073] Specifically, after constructing a unified hybrid risk objective function in step 102, see [link to relevant documentation]. Figure 2 This step aims to select a suitable technical path and design an innovative solution algorithm to train a predictive model capable of generating a risk-aware probability distribution. Unlike existing technologies that only output a single risk-optimized point prediction value, this application aims to provide a panoramic description of inertia uncertainty, i.e., a complete probability distribution. More importantly, through innovative modifications to the solution algorithm, this application ensures that every part of the generated probability distribution deeply embeds the economic, risk, and physical security considerations defined in step 102, achieving a dimensional upgrade from "risk point prediction" to "risk distribution prediction."

[0074] In one possible implementation, training a probabilistic prediction model using a risk-guided probabilistic modeling approach includes: using quantile regression as the basic probabilistic modeling framework; constructing a risk-weighted pinball loss function, which is a linear combination of a traditional pinball loss function and a risk-weighted term, the calculation of which incorporates decision-making and security considerations from both the economic cost term and the physical security penalty term; and using the risk-weighted pinball loss function to train a quantile regression model to obtain a set of risk-perceived quantile prediction values.

[0075] In practical applications, the technical approach chosen for probabilistic modeling is quantile regression, as detailed below.

[0076] To achieve accurate modeling of the inertia probability distribution, this application selects quantile regression as the core technical approach. Compared to traditional mean regression methods such as least squares, quantile regression is nonparametric, making no prior assumptions about the probability distribution of the data. It can flexibly fit distributions of various shapes, and it is insensitive to outliers in the data, making the model training process more stable.

[0077] Furthermore, the principle of traditional quantile regression and the bouncing loss function are described below.

[0078] Traditional quantile regression is achieved by minimizing an asymmetric linear loss function called Pinball Loss. For a given quantile τ (where τ∈(0,1)), the Pinball Loss function ρ... τ (u) is defined as shown in equation (17): (17) In the formula, u is the prediction error, i.e., u = y - , where y is the true value, is the predicted value; I(·) is the indicator function (takes 1 when the condition is true, otherwise takes 0). The loss function applies asymmetric weights τ and 1-τ to positive errors (overprediction, u>0) and negative errors (underprediction, u<0).

[0079] Therefore, for the τth quantile, its prediction model Q τ ( I τ , X )(in I τ The traditional training objective for the parameters (corresponding to this quantile model) is to minimize all N The total bouncing loss over each training sample is shown in Equation (18): (18) Furthermore, the risk-weighted bouncing loss function is as follows.

[0080] Traditional pinball loss functions are inherently risk-neutral, focusing only on finding the statistically correct quantile position without considering the decision consequences corresponding to that quantile position. To address this issue, this application proposes an innovative risk-weighted pinball loss function, which incorporates the hybrid risk objective function constructed in step 102. L total The concept is directly integrated into the training process of quantile regression.

[0081] The core idea of ​​this method is to reshape probabilistic prediction into an optimization process directly oriented towards decision-making. The principle is as follows: by adding a risk weighting term directly related to the economic and safety costs of the decision's consequences to the traditional pinball loss function for each quantile, the predicted probability distribution inherently incorporates the asymmetric risk of the decision. This ensures that the predicted distribution behaves more conservatively in key risk areas, achieving a balance between statistical accuracy and decision optimality.

[0082] In terms of specific implementation, firstly, a prediction algorithm for quantile values ​​is constructed. Q τ Risk weighting W ( Q τ The form of the weighted term is the same as that defined in equation (9). L total Similarly, but with the same general prediction value Replaced with the currently optimized quantile predictions Q τ As shown in equation (19): (19) In the formula, C (·) is the asymmetric economic cost function defined by equation (11). L sec (·) is the physical security penalty function defined by equation (14). w 1 and w 3 is the weighting coefficient corresponding to equation (9).

[0083] Then, the risk weighting item W ( Q τ By linearly combining this with the traditional pinball loss function, a completely new, risk-guided loss function is formed. L new ( I τ As shown in equation (20): (20) The hyperparameter λτ in equation (20) controls the statistical fitting accuracy (by... r τ Item representative) and decision risk considerations (by W A balance between items (representatives). In a preferred embodiment, to reflect the decision-maker's focus on extreme risk events, l τ Designed as a quantile t The relevant U-shaped function can be represented by equation (21): (twenty one) In the formula, c is a basic weight coefficient. The model is trained on tail segments representing extremely high and low inertia risks ( or When it comes to ), a huge penalty for decision-making risk will be imposed; while at the training center quantile ( When the risk weight is less than 1, a smaller risk weight is applied.

[0084] By minimizing equation (20), the model achieves end-to-end risk guidance during training. For example, when determining the 5th percentile, if a certain predicted value... It has high statistical accuracy (i.e.) The item is very small, but after being substituted into the proxy model, it was found that it would trigger a huge physical security penalty. The optimization algorithm will automatically adjust the model parameters. To provide a slightly higher, more "safe" one. The predicted value, although this new value may not be optimal for traditional pinball losses.

[0085] Finally, due to the bouncing loss function included in equation (20) r τ The term exhibits a non-differentiable cusp at zero error, making traditional gradient descent methods inapplicable. In embodiments suitable for large-scale deep learning engineering practices, this application employs a smooth approximation method: using the Huber loss function to approximate the cusp near zero in the bouncing loss function. The Huber loss function maintains the linearity of the bouncing loss when the error is large, while transitioning to a quadratic function in the region where the error is close to zero, thus making the entire loss function differentiable everywhere and its gradient continuous. An efficient adaptive gradient optimizer designed for deep neural networks can be directly employed.

[0086] In one possible implementation, the method further includes: dynamically determining the threshold for tail fitting based on specific high and low quantile values ​​output by the trained quantile regression model; performing tail modeling using a generalized Pareto distribution for samples below the low threshold and above the high threshold, respectively; and concatenating the cumulative distribution function fitted by the quantile regression model in the main body with the generalized Pareto distributions of the left and right tails to form a complete conditional cumulative distribution function as the final prediction output.

[0087] In practical applications, the mathematical model for GPD tail fitting is as follows.

[0088] While quantile regression can fit the main body of a distribution well, its prediction results may be unstable in the sparse extreme tail regions. To accurately characterize low-probability, high-impact extreme events, this application uses the over-threshold model from Extreme Value Theory to model the tail of the distribution.

[0089] According to the theory of extreme values, for a sufficiently high threshold u, the conditional probability distribution of the random variable Y exceeding u (i.e., Yu) can be well approximated by the generalized Pareto distribution. The cumulative distribution function (CDF) of GPD is shown in equation (22): (twenty two) In the formula, y is the amount exceeding the threshold, and σ>0 is the scale parameter. x For shape parameters.

[0090] The modeling process is as follows: High and low thresholds: Using the quantile regression model trained in step (3), predict the lower quantiles. u L = Q τL and higher quantiles u H = Q τH As a dynamic threshold.

[0091] Fitting GPD parameters: On the training set, select parameters lower than u. L and higher than u H The excess sample set. Then, using methods such as maximum likelihood estimation, GPD fitting is performed on these two sample sets to solve for the scale parameter σ and shape parameter of the left and right tails, respectively. x .

[0092] Furthermore, the final probability density function (PDF) is concatenated as follows.

[0093] Through the above steps, this application ultimately constructs a piecewise predictive model that can accurately describe the full probability distribution of inertia. For any input features... X Its predicted conditional cumulative distribution function F ( h | X It is composed of three parts, as shown in equation (23): (twenty three) In the formula, G L (·)and G R (·) represent the cumulative distribution functions of GPD for the left and right tails, respectively.

[0094] F QR ( h | X ) represents the cumulative distribution function obtained in the main part of the quantile regression model by performing linear or spline interpolation on the predicted quantiles. L and u H To be based on input X Dynamically determined high and low thresholds. τ L and τ H The quantile level is used to define the threshold.

[0095] This splicing function F ( h |X The final output of this application is the prediction result. It provides a smooth and complete probability distribution, which not only ensures the flexibility and optimal decision-making brought about by the risk-guided quantile regression in the main part, but also ensures the theoretical accuracy of characterizing extreme tail risks through the GPD model.

[0096] This application addresses the problem of separation between prediction and decision-making in traditional prediction methods by constructing and integrating an asymmetric economic cost term, a decision risk cost term (CVaR), and a physical security penalty term into the loss function of the prediction model. This transforms the training process of the prediction model from simply fitting historical data to directly optimizing the comprehensive utility of downstream dispatch decisions, including economic efficiency, safety, and risk levels, through end-to-end optimization. The probabilistic prediction results output by this application not only accurately characterize the uncertainty of inertia at the statistical level through quantile regression and GPD tail fitting techniques, but also embed the dispatcher's risk preference and the physical security boundary of the power grid at the decision level. This provides power system dispatch decisions with more economically efficient, safer, and more comprehensive inertia predictions, thereby improving the precision of power grid dispatching in the context of high-proportion renewable energy grid integration, balancing system operational economy and frequency security risks, and enhancing power system security.

[0097] Corresponding to the above method embodiments, this specification also provides embodiments of an inertia probability prediction device. Figure 4 A schematic diagram of an inertia probability prediction device according to one embodiment of this specification is shown. Figure 4 As shown, the device includes: The feature construction module 401 is configured to construct a comprehensive feature set containing basic operational features and real-time dynamic features, which serves as the input to the prediction model. The model training module 402 is configured to construct a hybrid risk objective function that integrates economic cost terms, decision risk cost terms, and physical security penalty terms. The hybrid risk objective function is used to train the prediction model. The output module 403 is configured to train a probabilistic prediction model based on a hybrid risk objective function and a risk-guided probabilistic modeling method to generate an inertia probability distribution with embedded decision risks and safety constraints.

[0098] In one possible implementation, constructing a comprehensive feature set that includes basic operational characteristics and real-time dynamic characteristics includes: Obtain the load forecast, renewable energy output forecast, planned nuclear power output, planned switching power of tie lines, ambient temperature forecast, date type identifier, and historical inertia values ​​for the future target time at the forecast time, and normalize or encode them to form a basic feature vector. Within a preset statistical time window, historical high-frequency automatic power generation control signals are statistically analyzed to extract dynamic statistical features, including average frequency deviation, regulation mileage, standard deviation of frequency deviation, and root mean square of frequency change rate, in order to form a dynamic feature vector. The basic feature vector and the dynamic feature vector are concatenated to form a comprehensive feature set.

[0099] In one possible implementation, the hybrid risk objective function is a weighted sum of economic cost, decision risk cost, and physical security penalty; the economic cost is constructed based on the asymmetric economic consequences of prediction errors, the decision risk cost is constructed based on conditional risk value to reflect risk aversion preferences, and the physical security penalty is constructed based on frequency security constraints.

[0100] In one possible implementation, the economic cost item is constructed as follows: The prediction error of a single sample is defined as the difference between the model's predicted value and the actual inertia value. Construct a piecewise asymmetric cost function and apply a unit penalty coefficient higher than that for the over-predicted part of the prediction error to the under-predicted part. Calculate the expected value of the asymmetric cost function over all training samples, and use it as the economic cost term.

[0101] In one possible implementation, the physical security penalty term is constructed as follows: Determine the minimum inertia requirement threshold needed to ensure frequency security based on the frequency response proxy model; When the predicted inertia value output by the prediction model is lower than the minimum inertia requirement threshold, a large penalty term is applied to guide the predicted value to meet physical safety constraints during model training.

[0102] In one possible implementation, training the probabilistic prediction model using a risk-guided probabilistic modeling approach includes: Quantile regression is used as the basic probability modeling framework; A risk-weighted pinball loss function is constructed, which is a linear combination of the traditional pinball loss function and a risk-weighted term. The calculation of the risk-weighted term integrates decision-making and safety considerations in the economic cost term and the physical safety penalty term. A risk-weighted pinball loss function is used to train a quantile regression model to obtain a set of risk-perceived quantile predictions.

[0103] In one possible implementation, the method also includes: Based on the specific high and low quantile values ​​output by the trained quantile regression model, the threshold for tail fitting is dynamically determined. Tail modeling is performed using a generalized Pareto distribution for samples below the low threshold and above the high threshold, respectively; The cumulative distribution function fitted to the quantile regression model in the main body is concatenated with the generalized Pareto distributions in the left and right tails to form a complete conditional cumulative distribution function as the final prediction output.

[0104] The above is a schematic scheme of an inertia probability prediction device according to this embodiment. It should be noted that the technical solution of this inertia probability prediction device and the technical solution of the inertia probability prediction method described above belong to the same concept. For details not described in detail in the technical solution of the inertia probability prediction device, please refer to the description of the technical solution of the inertia probability prediction method described above.

[0105] Figure 5 A structural block diagram of a computing device 500 according to one embodiment of this specification is shown. The components of the computing device 500 include, but are not limited to, a memory 510 and a processor 520. The processor 520 is connected to the memory 510 via a bus 530, and a database 550 is used to store data.

[0106] The computing device 500 also includes an access device 540, which enables the computing device 500 to communicate via one or more networks 560. Examples of these networks include Public Switched Telephone Network (PSTN), Local Area Network (LAN), Wide Area Network (WAN), Personal Area Network (PAN), or combinations of communication networks such as the Internet. The access device 540 may include one or more of any type of wired or wireless network interface (e.g., a network interface card (NIC)), such as an IEEE 802.11 Wireless Local Area Network (WLAN) wireless interface, a Wi-MAX (Worldwide Interoperability for Microwave Access) interface, an Ethernet interface, a Universal Serial Bus (USB) interface, a cellular network interface, a Bluetooth interface, or a Near Field Communication (NFC) interface.

[0107] In one embodiment of this specification, the above-described components of the computing device 500 and Figure 5Other components, not shown, can also be connected to each other, for example, via a bus. It should be understood that... Figure 5 The block diagram of the computing device shown is for illustrative purposes only and is not intended to limit the scope of this specification. Those skilled in the art can add or replace other components as needed.

[0108] The computing device 500 can be any type of stationary or mobile computing device, including mobile computers or mobile computing devices (e.g., tablet computers, personal digital assistants, laptop computers, notebook computers, netbooks, etc.), mobile phones (e.g., smartphones), wearable computing devices (e.g., smartwatches, smart glasses, etc.) or other types of mobile devices, or stationary computing devices such as desktop computers or personal computers (PCs). The computing device 500 can also be a mobile or stationary server.

[0109] The processor 520 executes the following computer-executable instructions, which, when executed by the processor, implement the steps of the aforementioned inertia probability prediction method. The above is an illustrative scheme of a computing device according to this embodiment. It should be noted that the technical solution of this computing device and the technical solution of the aforementioned inertia probability prediction method belong to the same concept. Details not described in detail in the technical solution of the computing device can be found in the description of the technical solution of the aforementioned inertia probability prediction method.

[0110] An embodiment of this specification also provides a computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the above-described inertia probability prediction method.

[0111] The above is an illustrative scheme of a computer-readable storage medium according to this embodiment. It should be noted that the technical solution of this storage medium and the technical solution of the inertia probability prediction method described above belong to the same concept. For details not described in detail in the technical solution of the storage medium, please refer to the description of the technical solution of the inertia probability prediction method described above.

[0112] An embodiment of this specification also provides a computer program, wherein when the computer program is executed in a computer, it causes the computer to perform the steps of the above-described inertia probability prediction method.

[0113] The above is an illustrative example of a computer program according to this embodiment. It should be noted that the technical solution of this computer program and the technical solution of the inertia probability prediction method described above belong to the same concept. Details not described in detail in the computer program's technical solution can be found in the description of the technical solution of the inertia probability prediction method described above.

[0114] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0115] The computer instructions include computer program code, which may be in the form of source code, object code, executable file, or certain intermediate forms. The computer-readable medium may include any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium may be appropriately added to or subtracted according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media may not include electrical carrier signals and telecommunication signals.

[0116] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that the embodiments in this specification are not limited to the described order of actions, because according to the embodiments in this specification, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in this specification are all preferred embodiments, and the actions and modules involved are not necessarily essential to the embodiments in this specification.

[0117] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0118] The preferred embodiments disclosed above are merely illustrative of this specification. The optional embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the embodiments described herein. These embodiments are selected and specifically described in this specification to better explain the principles and practical applications of the embodiments, thereby enabling those skilled in the art to better understand and utilize this specification. This specification is limited only by the claims and their full scope and equivalents.

Claims

1. A method for predicting the probability of inertia, characterized in that, include: A comprehensive feature set containing basic operational features and real-time dynamic features is constructed, and the comprehensive feature set is used as the input of the prediction model; A hybrid risk objective function is constructed that integrates economic cost, decision risk cost, and physical security penalty, and the hybrid risk objective function is used to train the prediction model; Based on the aforementioned hybrid risk objective function, a risk-guided probabilistic modeling method is used to train a probabilistic prediction model to generate an inertia probability distribution with embedded decision risks and safety constraints.

2. The inertia probability prediction method based on physical safety constraints and dynamic risk preferences according to claim 1, characterized in that, The constructed comprehensive feature set, which includes basic operational features and real-time dynamic features, includes: Obtain the load forecast, renewable energy output forecast, planned nuclear power output, planned switching power of tie lines, ambient temperature forecast, date type identifier, and historical inertia values ​​for the future target time at the forecast time, and normalize or encode them to form a basic feature vector. Within a preset statistical time window, historical high-frequency automatic power generation control signals are statistically analyzed to extract dynamic statistical features, including average frequency deviation, regulation mileage, standard deviation of frequency deviation, and root mean square of frequency change rate, in order to form a dynamic feature vector. The basic feature vector and the dynamic feature vector are concatenated to form the comprehensive feature set.

3. The inertia probability prediction method based on physical safety constraints and dynamic risk preferences according to claim 1, characterized in that, The hybrid risk objective function is a weighted sum of the economic cost term, the decision risk cost term, and the physical security penalty term; the economic cost term is constructed based on the asymmetric economic consequences of prediction errors, the decision risk cost term is constructed based on conditional value of risk to reflect risk aversion preferences, and the physical security penalty term is constructed based on frequency security constraints.

4. The inertia probability prediction method based on physical safety constraints and dynamic risk preferences according to claim 3, characterized in that, The economic cost item is constructed in the following manner: The prediction error of a single sample is defined as the difference between the model's predicted value and the actual inertia value. Construct a piecewise asymmetric cost function, and apply a unit penalty coefficient higher than that for the over-predicted part to the under-predicted part of the prediction error; Calculate the expected value of the asymmetric cost function over all training samples, and use it as the economic cost term.

5. The inertia probability prediction method based on physical safety constraints and dynamic risk preferences according to claim 3, characterized in that, The physical security penalty items are constructed in the following manner: Determine the minimum inertia requirement threshold needed to ensure frequency security based on the frequency response proxy model; When the predicted inertia value output by the prediction model is lower than the minimum inertia requirement threshold, a large penalty term is applied to guide the predicted value to meet physical safety constraints during model training.

6. The inertia probability prediction method based on physical safety constraints and dynamic risk preferences according to claim 1, characterized in that, The method of training the probabilistic prediction model using risk-guided probabilistic modeling includes: Quantile regression is used as the basic probability modeling framework; A risk-weighted pinball loss function is constructed, which is a linear combination of the traditional pinball loss function and a risk-weighted term. The calculation of the risk-weighted term integrates the decision-making and security considerations in the economic cost term and the physical security penalty term. The risk-weighted bouncing loss function is used to train the quantile regression model to obtain a set of risk-perceived quantile predictions.

7. The inertia probability prediction method based on physical safety constraints and dynamic risk preferences according to claim 6, characterized in that, The method further includes: Based on the specific high and low quantile values ​​output by the trained quantile regression model, the threshold for tail fitting is dynamically determined. Tail modeling is performed using a generalized Pareto distribution for samples below the low threshold and above the high threshold, respectively; The cumulative distribution function fitted to the quantile regression model in the main body is concatenated with the generalized Pareto distribution in the left and right tails to form a complete conditional cumulative distribution function as the final prediction output.

8. An inertia probability prediction device, characterized in that, include: The feature construction module is configured to construct a comprehensive feature set containing basic operational features and real-time dynamic features, which serves as the input to the prediction model. The model training module is configured to construct a hybrid risk objective function that integrates economic cost, decision risk cost, and physical security penalty, and the hybrid risk objective function is used to train the prediction model. The output module is configured to train a probability prediction model based on the hybrid risk objective function using a risk-guided probabilistic modeling method, in order to generate an inertia probability distribution with embedded decision risks and safety constraints.

9. A computing device, characterized in that, include: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions, which, when executed by the processor, implement the steps of the inertia probability prediction method according to any one of claims 1 to 7.

10. A computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the inertia probability prediction method according to any one of claims 1 to 7.

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