Sobol sensitivity analysis method and system for electric vehicle charging station

Abstract

The invention provides a Sobol sensitivity analysis method and system for an electric vehicle charging station, and relates to the technical field of external influence factor analysis of an adjustable load of the electric vehicle charging station, and the method comprises the following steps: building a user charging decision model of various types of electric vehicle users; performing global sensitivity quantitative analysis on the plurality of key influence parameters of the charging station; based on a result of the global sensitivity quantitative analysis, generating a parameter interaction effect matrix by identifying and quantifying a nonlinear coupling relationship among key influence parameters; establishing a standardized mathematical model of various extreme events, and substituting the user charging decision model into the standardized mathematical model; and based on the parameter interaction effect matrix, performing comprehensive risk assessment through a multi-stage pressure test method and a toughness score calculation model. The method has the advantages that accurate parameter interaction effect identification, comprehensive evaluation of extreme scene risks and quantitative evaluation of system toughness are realized.

Description

Technical Field

[0001] This invention relates to the field of external influencing factor analysis technology for adjustable loads of electric vehicle charging stations, and more specifically, to a Sobol sensitivity analysis method and system for electric vehicle charging stations. Background Technology

[0002] The electrical load of electric vehicle charging stations is not only affected by the rated parameters of the equipment, but also significantly dependent on external factors. By systematically analyzing and modeling the external influencing factors, predictable and controllable load change patterns under the influence of external factors can be extracted, providing a reliable basis for power grid dispatching and planning.

[0003] Existing methods for analyzing external influencing factors all have some shortcomings. For example, methods based on single-factor sensitivity analysis can only reflect the local impact of parameters and cannot capture the interactions between parameters; global sensitivity methods based on regression analysis can handle parameter interactions, but their applicability to highly nonlinear systems is limited; parameter importance ranking based on Morris screening is suitable for preliminary parameter screening, but its accuracy is relatively limited; traditional Monte Carlo methods for extreme scenario analysis lack systematic classification and standardized modeling of extreme events, making it difficult to comprehensively assess the impact of different types of extreme scenarios; and there are also limitations in power grid risk assessment based on scenario analysis. In other words, existing technologies mainly target traditional load settings, failing to fully consider the special characteristics of electric vehicle charging stations as adjustable loads, and cannot comprehensively assess the system's performance under various extreme conditions. They also struggle to accurately identify and quantify the complex interactions between multiple influencing factors, especially the coupling effects of factors such as temperature, electricity price, and user behavior. This results in an insufficient understanding of system behavior and a lack of quantitative assessment indicators such as system resilience and risk level, making it difficult to provide accurate numerical basis for decision-making.

[0004] Therefore, it is necessary to optimize the analysis of external influencing factors on the adjustable load of electric vehicle charging stations, so as to achieve accurate identification of parameter interaction effects, comprehensive assessment of extreme scenario risks, and quantitative assessment of system resilience. Summary of the Invention

[0005] The purpose of this invention is to provide a Sobol sensitivity analysis method and system for electric vehicle charging stations, which achieves accurate identification of parameter interaction effects, comprehensive assessment of extreme scenario risks, and quantitative assessment of system resilience.

[0006] This invention is achieved through the following technical solution: The Sobol sensitivity analysis method for electric vehicle charging stations includes the following steps: Establish a user charging decision model for multiple types of electric vehicle users. The types of electric vehicle users include commuter users whose charging behavior is periodic, flexible users who decide their charging time based on changes in electricity prices, nighttime users who charge during off-peak hours at night, and random users whose charging time is irregular. A global sensitivity quantification analysis was performed on several key influencing parameters of the charging station, including constructing a basic sampling matrix A, an independent sampling matrix B, and a parameter perturbation matrix for the i-th key influencing parameter. , N represents the dimension of the key influencing parameters of the charging station, and the first-order main effect of each key influencing parameter is calculated. Based on the results of the global sensitivity quantification analysis, a parameter interaction effect matrix is ​​generated by identifying and quantifying the nonlinear coupling relationship between key influencing parameters. Establish standardized mathematical models for multiple extreme events, substitute the user charging decision model into the standardized mathematical model, and obtain load distribution statistics under multiple extreme scenarios; Based on the parameter interaction effect matrix, a comprehensive risk assessment is conducted using a multi-level stress testing method and a resilience score calculation model.

[0007] Preferably, the user charging decision model includes: The charging time t of the commuter user decision model follows a normal distribution with a mean of 72 and a standard deviation of 4. ; The charging time is represented by a time unit number, with each time unit consisting of 15 minutes. The flexible user decision-making model is based on real-time electricity pricing: ; in, The real-time electricity price is (RMB / kWh). This refers to the charging response coefficient; The charging time t of the nighttime user decision model follows a mean distribution in the interval 4 to 24: ; The charging time t of the stochastic user decision model follows a mean of Standard deviation is Normal distribution: ; in, and All data comes from system parameters.

[0008] Preferably, the method for performing global sensitivity quantification analysis on multiple key influencing parameters of the charging station is as follows: The basic sampling points are generated using an M×N dimensional Sobol low-discrepancy sequence, where M is the number of samples, to obtain the basic sampling matrix A; Generate a quasi-random sampling matrix with the same dimension as the basic sampling matrix A but with completely independent sequences to obtain the independent sampling matrix B; By replacing the i-th column of the independent sampling matrix B with the i-th column of the basic sampling matrix A, the parameter perturbation matrix of the i-th key influencing parameter is obtained. , ; By using a linear transformation function, the standard unit interval [0,1] of the Sobol sequence is scaled to the actual range of values ​​for key influencing parameters; Calculate the Sobol sensitivity index.

[0009] Preferably, the method for mapping the standard unit interval [0,1] of the Sobol sequence to the actual range of key influencing parameters is as follows: ; in, It is a value mapped to the actual range of values ​​for key influencing parameters. and These are the minimum and maximum values ​​of the corresponding key influencing parameters. These are the sampled values ​​of the corresponding key influencing parameters in the Sobol low-difference sequence; The method for calculating the Sobol sensitivity index is as follows: Obtain the first-order main effect of the i-th key influence parameter : ; Obtaining the total effect : ; in, , , These are the basic sampling matrix A, the independent sampling matrix B, and the parameter perturbation matrix, respectively. The charging load model output vector, The mean of all outputs. This is to output the total variance.

[0010] Preferably, the method for generating the parameter interaction effect matrix is ​​as follows: By replacing the i-th and j-th columns of the independent sampling matrix B with the i-th and j-th columns of the basic sampling matrix A, respectively, a two-parameter interaction matrix of the i-th key influence parameter and the j-th key influence parameter is obtained. , , , ; Calculate the second-order interaction effect between the i-th and j-th key influence parameters. : ; in, and The basic sampling matrix is ​​respectively and the two-parameter interaction matrix The corresponding charging load model output vector, and These are the first-order main effects of the i-th and j-th key influence parameters, respectively; Traverse and calculate all In the future, The parameters are placed in the i-th row and j-th column of the parameter interaction effect matrix to form the parameter interaction effect matrix.

[0011] Preferably, the method for establishing a standardized mathematical model for multiple types of extreme events is as follows: Multiple extreme scenarios were set up, and each extreme scenario was modeled separately. The extreme scenarios included concentrated charging extreme scenario, grid constraint extreme scenario, extreme weather scenario, equipment failure extreme scenario, demand surge extreme scenario, and electricity price shock extreme scenario. The method for obtaining load distribution statistics under multiple extreme scenarios is to perform Monte Carlo extreme value statistical analysis for each of the extreme scenarios.

[0012] Preferably, the method for modeling each extreme scenario separately includes: Modeling of extreme scenarios for centralized charging, by setting a simultaneous charging ratio coefficient. and time concentration coefficient Describe the extreme scenario of centralized charging; Modeling extreme scenarios with power grid constraints by setting a power grid capacity reduction factor. and line impedance growth factor Describe the extreme scenario of power grid constraints; Extreme weather scenario modeling is achieved by setting an ambient temperature offset. and the corresponding vehicle energy consumption growth coefficient Describe the extreme weather scenario; Extreme scenario modeling of equipment failure is achieved by setting an initial random failure rate for the charging equipment. Cascade Fault Trigger Probability Describe the extreme scenarios of the equipment failure; Modeling extreme scenarios of surging demand by setting a surge coefficient for the number of electric vehicles. and the growth rate of average mileage per vehicle Describe the extreme scenario of a surge in demand. Modeling extreme scenarios of electricity price shocks by setting a multiplier for electricity market prices. The user behavior response latency parameter describes the extreme scenario of electricity price shock.

[0013] Preferably, the method for performing Monte Carlo extreme value statistical analysis for each of the extreme scenarios is as follows: For each of the extreme scenarios, the following operations are performed: Multiple random samples are performed in the extreme scenario, and the user charging decision model for each type of electric vehicle user is run in each sample to obtain the system peak load sample. The mean, standard deviation, 95th percentile, 99th percentile, 99.9th percentile, and observed maximum value of the load distribution were obtained, thus obtaining the load distribution statistics under multiple extreme scenarios.

[0014] Preferably, the method for comprehensive risk assessment using a multi-level stress testing method and a toughness score calculation model is as follows: Four standardized stress test scenarios of different intensities were set up, including: The double load test, with a load multiplication factor of 2.0 and a duration of 4 hours, is used to simulate peak pressure during daily operation. The triple load test, with a load multiplication factor of 3.0 and a duration of 2 hours, is used to simulate short-term shock pressure. The continuous high-load test, with a load multiplication factor of 1.8 and a duration of 8 hours, was used to simulate the pressure of long-term heavy-load operation. Extreme peak load test, with a load multiplication factor of 4.0 and a duration of 1 hour, is used to simulate the system's ultimate load-bearing capacity pressure. For each standardized stress test scenario with different intensities, a toughness score calculation model is established using a comprehensive toughness evaluation function: ;

[0015] Where R is the toughness score. The basic toughness coefficient is determined based on the system's load-bearing capacity under standardized stress test scenarios of varying intensities. This represents the penalty coefficient for violations. To control the violation rate, is the adaptive adjustment coefficient with a value range of 0.8 to 1.2, and min is the function for finding the minimum value.

[0016] The present invention also provides a Sobol sensitivity analysis system for electric vehicle charging stations, applied to the aforementioned Sobol sensitivity analysis method for electric vehicle charging stations, including: The user behavior modeling module is used to establish user charging decision models for multiple types of electric vehicle users. The types of electric vehicle users include commuter users whose charging behavior is periodic, flexible users who decide their charging time based on changes in electricity prices, nighttime users who charge during off-peak hours at night, and random users whose charging time is irregular. The user behavior module is used to perform global sensitivity quantification analysis on multiple key influencing parameters of the charging station, including constructing a basic sampling matrix A, an independent sampling matrix B, and a parameter perturbation matrix for the i-th key influencing parameter. , N represents the dimension of the key influencing parameters of the charging station, and the first-order main effect of each key influencing parameter is calculated. The parameter interaction analysis module is used to generate a parameter interaction effect matrix by identifying and quantifying the nonlinear coupling relationship between key influencing parameters based on the results of the global sensitivity quantification analysis. The extreme scenario generation module is used to establish standardized mathematical models for multiple extreme events, and then substitute the user charging decision model into the standardized mathematical model to obtain load distribution statistics under multiple extreme scenarios. The system resilience assessment module is used to conduct comprehensive risk assessment based on the parameter interaction effect matrix, through multi-level stress testing methods and resilience score calculation models.

[0017] The technical solution of the present invention has at least the following advantages and beneficial effects: This invention employs an improved Sobol global sensitivity analysis method, which can accurately quantify the first-order effect, total effect, and interaction effect of multiple key parameters. Furthermore, the analysis results based on the multidimensional sampling matrix show that it can accurately identify the ranking of key parameters affecting charging load. Compared with the traditional single-factor perturbation method, it can capture the nonlinear interaction between parameters. This invention establishes a mathematical model for the time flexibility, power controllability, and user responsiveness of electric vehicle charging stations, and considers the differentiated adjustment coefficients of various types of users, which can more accurately reflect the actual characteristics of charging stations as adjustable loads. This invention establishes analytical models for multiple extreme scenarios, provides comprehensive and reliable load distribution through Monte Carlo extreme value statistical analysis, and provides a scientific basis for system optimization through interactive analysis of the coupling relationship between parameters; This invention also conducts a comprehensive risk assessment through a multi-level pressure testing method and a toughness score calculation model, which can quantitatively calculate the system's toughness score under different pressure levels. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating an implementation example of the Sobol sensitivity analysis method for electric vehicle charging stations provided in Embodiment 2 of the present invention. Figure 2 This is a schematic diagram of the Sobol sensitivity analysis system for electric vehicle charging stations provided in Embodiment 3 of the present invention. Detailed Implementation

[0019] 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, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0020] Example 1 This embodiment provides a Sobol sensitivity analysis method for electric vehicle charging stations, including the following steps: First, a user charging decision model can be established for multiple types of electric vehicle users. These users include commuters whose charging behavior is periodic, flexible users whose charging time is determined by electricity price changes, nighttime users who charge during off-peak hours, and random users with irregular charging times. The user charging decision model in this embodiment specifically includes: The charging behavior of commuters is highly regular, so the charging time t of the commuter decision model follows a normal distribution with a mean of 72 and a standard deviation of 4. ; The charging time is represented by time unit numbers, with each unit consisting of 15 minutes. This means that the average time is set at 6 PM according to a normal distribution, with a standard deviation of 1 hour. The model is based on the fixed behavior pattern of commuting users who charge immediately after get off work, which has a high time concentration and accounts for 45% of the total users.

[0021] Flexible users are sensitive to changes in electricity prices, and the flexible user decision-making model is based on real-time electricity prices. ; in, The real-time electricity price is (RMB / kWh). This represents the charging response coefficient. The piecewise function design is based on a threshold effect of user electricity price sensitivity: a strong response at low electricity prices, a linear decrease at medium electricity prices, and significant suppression at high electricity prices. For flexible users, the optimal charging time is determined by calculating the maximum value of the 24-hour electricity price response function; flexible users account for approximately 25% of the total users.

[0022] Nighttime users specifically choose to charge during off-peak hours late at night. The charging time t in the nighttime user decision model follows a mean distribution within the interval of 4 to 24 (corresponding to 1 AM to 6 AM): ; The nighttime user decision-making model reflects the rational economic behavior of users who seek the lowest off-peak electricity prices and avoid peak electricity consumption periods, accounting for 15% of the total users.

[0023] Random user charging behavior shows no obvious pattern; the charging time t in the random user decision model follows a mean of t. Standard deviation is Normal distribution: ; in, and All data are derived from system parameters. This model simulates the random disturbance effect of irregular charging behavior on system load, representing 15% of total users. Based on the above model settings, a dynamic user type allocation mechanism was established, which can be achieved through probability vectors. Multiple electric vehicles are randomly assigned to different types, and node difference coefficients and random perturbation terms are introduced in each charging decision process to ensure the model's realism and systematicity.

[0024] In addition, a global sensitivity quantification analysis is needed for several key influencing parameters of the charging station, including constructing a basic sampling matrix A, an independent sampling matrix B, and a parameter perturbation matrix for the i-th key influencing parameter. , N represents the dimension of the key influencing parameters of the charging station, and the first-order main effect of each key influencing parameter is used to calculate the effect.

[0025] In this embodiment, the method for performing global sensitivity quantification analysis on multiple key influencing parameters of the charging station is as follows: First, M×N dimensional Sobol low-difference sequences are used to generate basic sampling points, where M is the number of samples, to obtain the basic sampling matrix A. In this embodiment, the dimension of the Sobol low-difference sequence is 512*11, that is, 512 is the number of samples and 11 is the dimension of the key influencing parameters of the charging station. The key influencing parameters may include the average charging start time, the standard deviation of charging start time, the average daily mileage, the standard deviation of daily mileage, the power consumption per 100 kilometers, the slow charging power, the fast charging probability, the fast charging power, the proportion of commuter users, the proportion of flexible users, and the temperature offset.

[0026] Next, a quasi-random sampling matrix with the same dimension as the basic sampling matrix A but with completely independent sequences is generated to obtain the independent sampling matrix B; Then, the i-th column of the independent sampling matrix B is replaced with the i-th column of the basic sampling matrix A to obtain the parameter perturbation matrix of the i-th key influencing parameter. , ; Furthermore, by using a linear transformation function, the standard unit interval [0,1] of the Sobol sequence can be scaled to the actual range of values ​​for key influencing parameters. The preferred method is as follows: ; in, It is a value mapped to the actual range of values ​​for key influencing parameters. and These are the minimum and maximum values ​​of the corresponding key influencing parameters. These are the sampled values ​​of the corresponding key influencing parameters in the Sobol low-difference sequence; Simultaneously, the Sobol sensitivity index can be calculated using the following method: Obtain the first-order main effect of the i-th key influence parameter : ; Obtaining the total effect : ; in, , , These are the basic sampling matrix A, the independent sampling matrix B, and the parameter perturbation matrix, respectively. The charging load model output vector, The mean of all outputs. This is to output the total variance.

[0027] After performing a global sensitivity quantification analysis, based on the results of the global sensitivity quantification analysis, a parameter interaction effect matrix is ​​generated by identifying and quantifying the nonlinear coupling relationship between key influencing parameters. The preferred method is as follows: By replacing the i-th and j-th columns of the independent sampling matrix B with the i-th and j-th columns of the basic sampling matrix A, respectively, a two-parameter interaction matrix of the i-th key influence parameter and the j-th key influence parameter is obtained. , , , ; Calculate the second-order interaction effect between the i-th and j-th key influence parameters. : ; in, and The basic sampling matrix is ​​respectively and the two-parameter interaction matrix The corresponding charging load model output vector, and These are the first-order main effects of the i-th and j-th key influence parameters, respectively; Traverse and calculate all In the future, The parameters are placed in the i-th row and j-th column of the parameter interaction effect matrix to form the parameter interaction effect matrix.

[0028] The parameter interaction effect matrix can identify the coupling relationship between key influencing parameters, especially the nonlinear interaction mechanism of important parameter pairs such as temperature shift and power consumption per 100 kilometers, electricity price change and the proportion of flexible users, and charging power and charging time distribution.

[0029] On the other hand, based on the acquired user charging decision model, it is necessary to establish a standardized mathematical model for multiple extreme events, substitute the user charging decision model into the standardized mathematical model, and obtain load distribution statistics under multiple extreme scenarios.

[0030] As a preferred option, the method for establishing standardized mathematical models for multiple types of extreme events is as follows: Multiple extreme scenarios were set up, and each scenario was modeled separately. These extreme scenarios included concentrated charging, grid constraints, extreme weather, equipment failure, demand surge, and electricity price shock. The methods for modeling each extreme scenario separately included: Modeling of extreme scenarios for centralized charging, by setting a simultaneous charging ratio coefficient. and time concentration coefficient Describe the extreme scenario of centralized charging. This scenario simulates a large number of electric vehicles simultaneously returning to the charging station after a major event. The smaller the value, the more concentrated the charging time, the higher the corresponding load peak, and the greater the system impact.

[0031] Modeling extreme scenarios with power grid constraints by setting a power grid capacity reduction factor. and line impedance growth factor Describe the extreme scenario of power grid constraints. This scenario simulates transmission capacity constraints caused by power grid equipment failure, planned maintenance, or overload. Directly affects the system's maximum transmission capacity. It affects line transmission efficiency and power quality.

[0032] Extreme weather scenario modeling is achieved by setting an ambient temperature offset. and the corresponding vehicle energy consumption growth coefficient The extreme weather scenario is described. The modeling method is based on the physical mechanism of temperature's influence on battery electrochemical performance and vehicle energy consumption: at extremely low temperatures, the discharge capacity of lithium batteries decreases significantly, while at extremely high temperatures, the energy consumption of vehicle air conditioning increases dramatically, both leading to a non-linear increase in charging demand.

[0033] Extreme scenario modeling of equipment failure is achieved by setting an initial random failure rate for the charging equipment. Cascade Fault Trigger Probability The extreme scenarios of equipment failure are described. This modeling method considers the cascading effect of a single-point equipment failure propagating to adjacent charging devices, simulating the randomness of charging pile hardware failures and the systemic risk propagation mechanism.

[0034] Modeling extreme scenarios of surging demand by setting a surge coefficient for the number of electric vehicles. and the growth rate of average mileage per vehicle Describe the extreme scenario of a surge in demand. This scenario simulates a sudden and significant increase in charging demand caused by factors such as concentrated travel during holidays, large-scale events, or severe weather.

[0035] Modeling extreme scenarios of electricity price shocks by setting a multiplier for electricity market prices. The user behavior response latency parameter describes the extreme scenario of electricity price shock. This scenario simulates the differentiated impact of drastic fluctuations in electricity market prices on the charging time selection behavior of different types of users.

[0036] Meanwhile, the method for obtaining load distribution statistics under multiple extreme scenarios involves performing Monte Carlo extreme value statistical analysis for each of the extreme scenarios. The method involves performing the following operations for each of the extreme scenarios: At least 1000 random samples were taken in the extreme scenario, and user charging decision models for various types of electric vehicle users were run in each sample to obtain system peak load samples. The final statistics yielded the mean, standard deviation, 95th percentile, 99th percentile, 99.9th percentile, and observed maximum value of the load distribution, providing statistical data on load distribution under multiple extreme scenarios.

[0037] Finally, to assess system resilience, this embodiment uses a multi-level stress testing method and a resilience score calculation model based on the parameter interaction effect matrix to conduct a comprehensive risk assessment. The method is as follows: Four standardized stress test scenarios of different intensities were set up, including: The double load test, with a load multiplication factor of 2.0 and a duration of 4 hours, is used to simulate peak pressure during daily operation. The triple load test, with a load multiplication factor of 3.0 and a duration of 2 hours, is used to simulate short-term shock pressure. The continuous high-load test, with a load multiplication factor of 1.8 and a duration of 8 hours, was used to simulate the pressure of long-term heavy-load operation. Extreme peak load test, with a load multiplication factor of 4.0 and a duration of 1 hour, is used to simulate the system's ultimate load-bearing capacity pressure. For each standardized stress test scenario with different intensities, a toughness score calculation model is established using a comprehensive toughness evaluation function: ;

[0038] Where R is the toughness score. The basic toughness coefficient is determined based on the system's load-bearing capacity under standardized stress test scenarios of varying intensities, such as double load testing. A value of 0.65 indicates that the system can maintain 65% of its normal function under double load impact, 0.30 corresponds to triple load test, 0.45 corresponds to continuous high load test, and 0.15 corresponds to extreme peak test.

[0039] This represents the penalty coefficient for violations. In the calculation, To constrain the violation rate, its function is to indicate that when safety constraints such as line overload, node voltage exceeding the limit, and system frequency deviation occur during system operation, it indicates that the system's carrying capacity is insufficient under the pressure level, and the resilience assessment results need to be penalized accordingly. The coefficient 0.4 is the weighting factor of the severity of the violation on the resilience, and the upper limit of 0.3 is set to ensure that the penalty does not exceed 30% of the basic resilience. This is the adaptive adjustment coefficient, ranging from 0.8 to 1.2. This coefficient is used to quantify the system's dynamic adjustment and self-recovery capabilities. When the charging station system possesses adaptive adjustment functions such as intelligent load management, distributed energy storage regulation, user demand response, and load transfer, The value is greater than 1.0; when the system lacks flexible adjustment methods and emergency response capabilities, The value is less than 1.0. min is a function for finding the minimum value.

[0040] The above scheme establishes a resilience assessment method based on four levels of stress testing (double load, triple load, continuous high load, and extreme peak load), which can quantitatively calculate the system's resilience score under different pressure levels. Test results show that the system's resilience score is approximately 0.58 under the double load test and approximately 0.16 under the extreme peak load test, providing objective quantitative indicators for system performance evaluation.

[0041] In particular, this embodiment can employ vectorized parallel computing algorithms and the MATLAB parallel computing toolbox to improve computational efficiency through parallel processing when processing a 512×11 dimensional parameter matrix and generating 100 basic scenarios, providing an efficient technical means for large-scale sensitivity analysis.

[0042] It is worth noting that in this embodiment, the Extended Fourier Amplitude Sensitivity Test (eFAST) method can be used instead of the Sobol method, which has higher computational efficiency but requires the assumption of parameter independence. Alternatively, the Shapley Additive Explanations (SHAP) method based on machine learning can be used for feature importance analysis, suitable for complex nonlinear models but with relatively weaker interpretability. Furthermore, Latin Hypercube Sampling (LHS) can be used instead of Sobol sequence sampling, which is simpler to implement but has lower convergence than Sobol sequences; Halton sequences or Faure sequences, or other low-discrepancy sequences, can also be used. In addition, a reinforcement learning-based agent model can be used instead of a mathematical analytical model, capable of learning complex user behavior patterns but with poor interpretability; Markov decision processes can also be used to model user charging decisions. Extreme scene generation methods based on deep generative models (such as VAEs and GANs) can also be used, generating more realistic extreme scenes but requiring a large amount of training data; deterministic extreme scene design based on physical constraints can also be employed. Resilience metrics based on network theory (such as spectral radius and algebraic connectivity) can also be used for evaluation. These metrics have a more rigorous mathematical foundation, but their correspondence with actual systems needs further verification. Alternatively, resilience measurement methods based on information entropy can be used.

[0043] Example 2 This embodiment is based on the technical solution of Embodiment 1, see below. Figure 1 This provides an execution flow for a practical analysis case.

[0044] Step 1, System Parameter Configuration and Initialization: Set the number of electric vehicles There are 4 charging station nodes. Key influencing parameters include the average charging start time. Hours, standard deviation Hourly average daily mileage 100 km, standard deviation Electricity consumption per 100 kilometers kWh, slow charging power The fast charging power is 22kW, and the fast charging probability is 0.2.

[0045] Step 2: Establish charging decision models for four types of users: Set the probability distribution of user types as commuter users 45%, flexible users 25%, nighttime users 15%, and random users 15%, and establish charging time decision functions and electricity price response mechanisms for each type of user.

[0046] Step 3: Identification and Range Determination of Key Influencing Parameters: Determine the physical value range of 11 key influencing parameters, including the average charging start time, standard deviation of charging start time, average daily mileage, standard deviation of daily mileage, power consumption per 100 kilometers, slow charging power, fast charging probability, fast charging power, proportion of commuter users, proportion of flexible users, and temperature offset.

[0047] Step 4: Construction of the Sobol three-matrix sampling space: A 512×11-dimensional basic sampling matrix is ​​generated using Sobol low-difference sequences. Independent sampling matrix and 11 parameter perturbation matrices The sampling points are mapped to the actual parameter value range through parameter space scaling transformation.

[0048] Step 5: Parallel computation of the multi-user charging load model: For the fundamental matrix... Independent matrix and parameter perturbation matrix group At each sampling point, four types of user charging decision models are run to calculate the corresponding total system charging load.

[0049] Step 6: Precise calculation of Sobol sensitivity index: Based on the model output corresponding to the sampling matrix, calculate the first-order main effects of 11 key parameters. Total effect The importance of the identification parameters is ranked.

[0050] Step 7: Calculation of the parameter interaction effect matrix: Construct 55 parameter interaction effect matrices. Calculate the complete 11×11 second-order interaction effect matrix and identify the nonlinear coupling relationship between key parameters.

[0051] Step 8: Generation of six types of extreme scenario samples: Based on the standardized modeling method for extreme scenarios, generate samples of six types of extreme scenarios, including centralized charging, grid constraints, extreme weather, equipment failure, demand surge, and electricity price shock, with 50 scenario instances generated for each type.

[0052] Step 9: Monte Carlo extreme value statistical analysis: Perform 1000 random samplings and charging load calculations within the extreme scenario parameter space to statistically analyze the distribution characteristics and confidence intervals of the system load extreme values.

[0053] Step 10, Level 4 Pressure Test and Toughness Assessment: Apply four different intensities of pressure multiplication to the baseline charging load scenario, and calculate the system toughness score and load-bearing capacity assessment at each pressure level.

[0054] Step 11: Generate comprehensive analysis report: output parameter importance ranking report, parameter interaction relationship analysis report, extreme scenario risk assessment report, system resilience analysis report, and operation optimization suggestion report.

[0055] Example 3 This embodiment provides a Sobol sensitivity analysis system for electric vehicle charging stations, applied to the Sobol sensitivity analysis method for electric vehicle charging stations in Embodiment 1. (See attached document.) Figure 2 ,include: The user behavior modeling module is used to establish user charging decision models for multiple types of electric vehicle users. The types of electric vehicle users include commuter users whose charging behavior is periodic, flexible users who decide their charging time based on changes in electricity prices, nighttime users who charge during off-peak hours at night, and random users whose charging time is irregular. These are constructed through commuter user sub-modules, flexible user sub-modules, random user sub-modules, and nighttime user sub-modules, respectively. The user behavior module is used to perform global sensitivity quantification analysis on multiple key influencing parameters of the charging station, including constructing a basic sampling matrix A, an independent sampling matrix B, and a parameter perturbation matrix for the i-th key influencing parameter. , N represents the dimension of the key influencing parameters of the charging station, and the perturbation matrix of all parameters. Form the parameter perturbation matrix set C, and calculate the first-order main effects of each key influencing parameter; The parameter interaction analysis module is used to generate a two-parameter interaction matrix and then obtain the parameter interaction effect matrix based on the results of the global sensitivity quantification analysis by identifying and quantifying the nonlinear coupling relationship between key influencing parameters, thereby characterizing the parameter coupling relationship. The extreme scenario generation module is used to establish standardized mathematical models for multiple extreme events, and then substitute the user charging decision model into the standardized mathematical model to obtain load distribution statistics under multiple extreme scenarios. The system resilience assessment module is used to conduct a comprehensive risk assessment based on the parameter interaction effect matrix, using a four-level stress test method and a resilience score calculation model, and to obtain a risk assessment report.

[0056] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A Sobol sensitivity analysis method for electric vehicle charging stations, characterized in that, Includes the following steps: Establish a user charging decision model for multiple types of electric vehicle users. The types of electric vehicle users include commuter users whose charging behavior is periodic, flexible users who decide their charging time based on changes in electricity prices, nighttime users who charge during off-peak hours at night, and random users whose charging time is irregular. A global sensitivity quantification analysis was performed on several key influencing parameters of the charging station, including constructing a basic sampling matrix A, an independent sampling matrix B, and a parameter perturbation matrix for the i-th key influencing parameter. , N represents the dimension of the key influencing parameters of the charging station, and the first-order main effect of each key influencing parameter is calculated. Based on the results of the global sensitivity quantification analysis, a parameter interaction effect matrix is ​​generated by identifying and quantifying the nonlinear coupling relationship between key influencing parameters. Establish standardized mathematical models for multiple extreme events, substitute the user charging decision model into the standardized mathematical model, and obtain load distribution statistics under multiple extreme scenarios; Based on the parameter interaction effect matrix, a comprehensive risk assessment is conducted using a multi-level stress testing method and a resilience score calculation model.

2. The Sobol sensitivity analysis method for electric vehicle charging stations according to claim 1, characterized in that, The user charging decision model includes: The charging time t of the commuter user decision model follows a normal distribution with a mean of 72 and a standard deviation of 4. ； The charging time is represented by a time unit number, with each time unit consisting of 15 minutes. The flexible user decision-making model is based on real-time electricity pricing: ； in, The real-time electricity price is (RMB / kWh). This refers to the charging response coefficient; The charging time t of the nighttime user decision model follows a mean distribution in the interval 4 to 24: ； The charging time t of the stochastic user decision model follows a mean of Standard deviation is Normal distribution: ； in, and All data comes from system parameters.

3. The Sobol sensitivity analysis method for electric vehicle charging stations according to claim 1, characterized in that, The method for global sensitivity quantification analysis of multiple key influencing parameters of charging stations is as follows: The basic sampling points are generated using an M×N dimensional Sobol low-discrepancy sequence, where M is the number of samples, to obtain the basic sampling matrix A; Generate a quasi-random sampling matrix with the same dimension as the basic sampling matrix A but with completely independent sequences to obtain the independent sampling matrix B; By replacing the i-th column of the independent sampling matrix B with the i-th column of the basic sampling matrix A, the parameter perturbation matrix of the i-th key influencing parameter is obtained. , ; By using a linear transformation function, the standard unit interval [0,1] of the Sobol sequence is scaled to the actual range of values ​​for key influencing parameters; Calculate the Sobol sensitivity index.

4. The Sobol sensitivity analysis method for electric vehicle charging stations according to claim 3, characterized in that, The method for mapping the standard unit interval [0,1] of the Sobol sequence to the actual range of key influencing parameters is as follows: ； in, It is a value mapped to the actual range of values ​​for key influencing parameters. and These are the minimum and maximum values ​​of the corresponding key influencing parameters. These are the sampled values ​​of the corresponding key influencing parameters in the Sobol low-difference sequence; The method for calculating the Sobol sensitivity index is as follows: Obtain the first-order main effect of the i-th key influence parameter : ； Obtaining the total effect : ； in, , , These are the basic sampling matrix A, the independent sampling matrix B, and the parameter perturbation matrix, respectively. The charging load model output vector, The mean of all outputs. This is to output the total variance.

5. The Sobol sensitivity analysis method for electric vehicle charging stations according to claim 1, characterized in that, The method for generating the parameter interaction effect matrix is ​​as follows: By replacing the i-th and j-th columns of the independent sampling matrix B with the i-th and j-th columns of the basic sampling matrix A, respectively, a two-parameter interaction matrix of the i-th key influence parameter and the j-th key influence parameter is obtained. , , , ; Calculate the second-order interaction effect between the i-th and j-th key influence parameters. : ； in, and The basic sampling matrix is ​​respectively and the two-parameter interaction matrix The corresponding charging load model output vector, and These are the first-order main effects of the i-th and j-th key influence parameters, respectively; Traverse and calculate all In the future, The parameters are placed in the i-th row and j-th column of the parameter interaction effect matrix to form the parameter interaction effect matrix.

6. The Sobol sensitivity analysis method for electric vehicle charging stations according to claim 1, characterized in that, The method for establishing standardized mathematical models for multiple types of extreme events is as follows: Multiple extreme scenarios were set up, and each extreme scenario was modeled separately. The extreme scenarios included concentrated charging extreme scenario, grid constraint extreme scenario, extreme weather scenario, equipment failure extreme scenario, demand surge extreme scenario, and electricity price shock extreme scenario. The method for obtaining load distribution statistics under multiple extreme scenarios is to perform Monte Carlo extreme value statistical analysis for each of the extreme scenarios.

7. The Sobol sensitivity analysis method for electric vehicle charging stations according to claim 6, characterized in that, The methods for modeling each extreme scenario separately include: Modeling of extreme scenarios for centralized charging, by setting a simultaneous charging ratio coefficient. and time concentration coefficient Describe the extreme scenario of centralized charging; Modeling extreme scenarios of power grid constraints by setting a power grid capacity reduction factor. and line impedance growth factor Describe the extreme scenario of power grid constraints; Extreme weather scenario modeling is achieved by setting an ambient temperature offset. and the corresponding vehicle energy consumption growth coefficient Describe the extreme weather scenario; Extreme scenario modeling of equipment failure is achieved by setting an initial random failure rate for the charging equipment. Cascade Fault Trigger Probability Describe the extreme scenarios of the equipment failure; Modeling extreme scenarios of surging demand by setting a surge coefficient for the number of electric vehicles. and the growth rate of average mileage per vehicle Describe the extreme scenario of a surge in demand. Modeling extreme scenarios of electricity price shocks by setting a multiplier for electricity market prices. The user behavior response latency parameter describes the extreme scenario of electricity price shock.

8. The Sobol sensitivity analysis method for electric vehicle charging stations according to claim 7, characterized in that, The method for performing Monte Carlo extreme value statistical analysis for each of the aforementioned extreme scenarios is as follows: For each of the aforementioned extreme scenarios, the following operations are performed: Multiple random samples are performed in the extreme scenario, and the user charging decision model for each type of electric vehicle user is run in each sample to obtain the system peak load sample. The mean, standard deviation, 95th percentile, 99th percentile, 99.9th percentile, and observed maximum value of the load distribution were obtained, thus obtaining the load distribution statistics under multiple extreme scenarios.

9. The Sobol sensitivity analysis method for electric vehicle charging stations according to claim 1, characterized in that, The method for comprehensive risk assessment using multi-level stress testing and a toughness score calculation model is as follows: Four standardized stress test scenarios of different intensities were set up, including: The double load test, with a load multiplication factor of 2.0 and a duration of 4 hours, is used to simulate peak pressure during daily operation. The triple load test, with a load multiplication factor of 3.0 and a duration of 2 hours, is used to simulate short-term shock pressure. The continuous high-load test, with a load multiplication factor of 1.8 and a duration of 8 hours, was used to simulate the pressure of long-term heavy-load operation. Extreme peak load test, with a load multiplication factor of 4.0 and a duration of 1 hour, is used to simulate the system's ultimate load-bearing capacity pressure. For each standardized stress test scenario with different intensities, a toughness score calculation model is established using a comprehensive toughness evaluation function: ； Where R is the toughness score. The basic toughness coefficient is determined based on the system's load-bearing capacity under standardized stress test scenarios of varying intensities. This represents the penalty coefficient for violations. To control the violation rate, is the adaptive adjustment coefficient with a value range of 0.8 to 1.2, and min is the function for finding the minimum value.

10. A Sobol sensitivity analysis system for electric vehicle charging stations, applied to the Sobol sensitivity analysis method for electric vehicle charging stations as described in any one of claims 1-9, characterized in that, include: The user behavior modeling module is used to establish user charging decision models for multiple types of electric vehicle users. The types of electric vehicle users include commuter users whose charging behavior is periodic, flexible users who decide their charging time based on changes in electricity prices, nighttime users who charge during off-peak hours at night, and random users whose charging time is irregular. The user behavior module is used to perform global sensitivity quantification analysis on multiple key influencing parameters of the charging station, including constructing a basic sampling matrix A, an independent sampling matrix B, and a parameter perturbation matrix for the i-th key influencing parameter. , N represents the dimension of the key influencing parameters of the charging station, and the first-order main effect of each key influencing parameter is calculated. The parameter interaction analysis module is used to generate a parameter interaction effect matrix by identifying and quantifying the nonlinear coupling relationship between key influencing parameters based on the results of the global sensitivity quantification analysis. The extreme scenario generation module is used to establish standardized mathematical models for multiple extreme events, and then substitute the user charging decision model into the standardized mathematical model to obtain load distribution statistics under multiple extreme scenarios. The system resilience assessment module is used to conduct comprehensive risk assessment based on the parameter interaction effect matrix, through multi-level stress testing methods and resilience score calculation models.

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