Method and system for analyzing influence of photovoltaic access current on transformer area voltage based on COPULA function, and storage medium

Abstract

The invention relates to a method and a system for analyzing the influence of photovoltaic access current on transformer area voltage based on a COPULA function, and a storage medium, and solves the problem in the prior art, and adopts the technical scheme that the method comprises the following steps: obtaining current data of a photovoltaic user in a transformer area and voltage data of a corresponding transformer area terminal; performing data quality optimization operation on the current data and the voltage data; establishing a dynamic edge distribution model based on the preprocessed data; based on the dynamic edge distribution model and the obtained dynamic edge distribution, constructing a time-varying Gaussian Copula model so as to capture the dynamic correlation between the photovoltaic current and the transformer area voltage; and adopting a maximum likelihood estimation method to obtain an unknown parameter describing a dynamic dependency relationship between variables in the time-varying Gaussian Copula model. The method has the advantages that the joint distribution and dependency relationship of the photovoltaic current and the transformer area voltage can be described accurately, dynamically and comprehensively, and scientific and practical theoretical support is provided for power grid voltage regulation and risk assessment.

Description

Technical Field

[0001] This invention relates to the field of distributed photovoltaic power generation technology, and in particular to a method, system, and storage medium for analyzing the impact of photovoltaic access current on transformer voltage based on the COPULA function. Background Technology

[0002] With the widespread application of distributed photovoltaic (PV) power generation technology, the number of distributed PV power sources connected to the power grid continues to grow. Compared with traditional power generation methods, distributed PV power sources have significant uncertainties and intermittency, and this characteristic makes its impact on grid operation an increasingly critical issue that cannot be ignored.

[0003] At present, research on the impact of distributed photovoltaic (PV) grid connection on distribution networks has made some progress. Existing studies are mostly based on engineering practice, using continuous power flow calculation methods with different simulation step sizes. They focus on the two core variables of distributed PV grid connection capacity and connection location to explore their impact on distribution system voltage, and finally summarize the basic laws of voltage changes in distribution networks caused by distributed PV grid connection.

[0004] However, current research still has significant limitations and is difficult to adapt to complex scenarios with high proportions of photovoltaic power grid integration: First, the research methods lack innovation and have inherent flaws. Existing research has long relied on traditional simulation methods such as continuous power flow calculations, without introducing new mathematical tools or analytical frameworks. Furthermore, traditional photovoltaic voltage analysis methods themselves have significant shortcomings: 1. Inherent limitations of linear models: Traditional methods often rely on linear regression or equivalent circuit models, assuming a linear relationship between photovoltaic current and transformer voltage. However, in reality, photovoltaic output is affected by random factors such as sunlight and temperature, and its relationship with voltage often exhibits significant nonlinear characteristics. For example, when photovoltaic output is close to the transformer load, it may show a weak correlation, while it may show strong coupling when the output increases or decreases sharply. The linear assumption is difficult to capture this complex relationship.

[0005] 2. The one-sidedness of single-variable analysis: Existing methods often model the marginal distribution of voltage or current separately, ignoring the joint probabilistic characteristics of the two. However, voltage over-limit accidents in photovoltaic power stations are often caused by synergistic effects such as "high current injection accompanied by high voltage rise" and "sudden voltage drop under low current". Extreme value analysis of a single variable alone cannot accurately assess the joint risk and may lead to misjudgment of voltage fluctuation patterns.

[0006] These problems together make it impossible for traditional methods to accurately capture the nonlinear and time-varying correlation between photovoltaic power output and voltage, and make it difficult to effectively characterize the dynamic correlation in real-world scenarios.

[0007] Secondly, there is a lack of systematic summarization of real-world cases. Existing research is either based on purely theoretical derivations with ideal assumptions (such as assuming stable photovoltaic output and fixed grid load) or on scattered simulations or experiments of individual distribution areas. It has not yet compiled and analyzed a large amount of long-term operational data from real distribution areas (covering different weather conditions and load levels), nor has it formed a replicable and scalable engineering application paradigm. This results in a lack of unified answers regarding the impact of photovoltaic access voltage on distribution areas in different regions and with different grid structures.

[0008] In short, existing research can only solve the basic questions of "whether to connect photovoltaics and how much to connect," and it is difficult to cope with the complex needs of "how to accurately predict and dynamically control voltage" in high-proportion photovoltaic access scenarios. This has become the core direction that subsequent research needs to break through.

[0009] In practical operation, the photovoltaic power generation systems installed by photovoltaic users directly affect the current and voltage of the power grid: when photovoltaic power generation is high, the system injects current into the grid, which may lead to a voltage increase; when photovoltaic power generation is insufficient, users need to draw power from the grid, which may cause a voltage drop. It is evident that the relationship between current and voltage is affected by environmental factors such as weather and will dynamically adjust with time and changes in photovoltaic output. This complex dynamic relationship urgently requires a flexible and effective method to resolve. Summary of the Invention

[0010] The purpose of this invention is to solve the above-mentioned problems in the prior art by providing a method, system and storage medium for analyzing the impact of photovoltaic access current on transformer voltage based on the COPULA function. This method can accurately, dynamically and comprehensively characterize the joint distribution and dependence of photovoltaic current and transformer voltage, providing scientific and practical theoretical support for grid voltage regulation and risk assessment.

[0011] The above-mentioned technical objectives of this invention are mainly achieved through the following technical solutions: The technical solution of the first technical subject of this invention is as follows: A method for analyzing the impact of photovoltaic grid connection current on transformer substation voltage based on the COPULA function, comprising the following steps: Data Acquisition: Screen photovoltaic (PV) user areas that meet the requirements for power generation stability, and collect current data of PV users within the areas and voltage data of the corresponding terminals in the areas; Data preprocessing: Perform data quality optimization operations on the current data and voltage data to obtain preprocessed data that meets the modeling requirements; Dynamic marginal distribution modeling: Based on preprocessed data, a dynamic marginal distribution model is established to eliminate autocorrelation and heteroscedasticity, and to obtain the standardized residuals of voltage and current; Time-varying Gaussian Copula modeling (Copula is a connection function or coupling function): Based on the dynamic edge distribution model, the dynamic edge distribution is obtained, and a time-varying Gaussian Copula model is constructed to capture the dynamic correlation between photovoltaic current and transformer voltage. Parameter estimation: The maximum likelihood estimation method is used to first estimate the dynamic marginal distribution parameters of the dynamic marginal distribution model, and then substitute the dynamic marginal distribution parameters into the time-varying Gaussian Copula model to estimate the time-varying Gaussian Copula parameters, thus obtaining the optimal values ​​of the unknown parameters in the Copula function.

[0012] This technical solution is based on the Copula model (also known as the "connection function model" or "dependency function model") for analysis. By separating the marginal and joint distributions of variables, it accurately captures and quantifies the nonlinear and asymmetric correlation between photovoltaic power output and transformer voltage, thereby revealing the intrinsic driving mechanism of voltage fluctuations under different photovoltaic power output intensities and environmental conditions. The method involved in this invention not only overcomes the shortcomings of traditional linear analysis in adapting to dynamic and complex relationships, but also solves the problem that single-variable analysis is difficult to assess joint risks, providing innovative technical support for overcoming the limitations of existing research that "emphasizes theoretical simulation but neglects practical quantification."

[0013] As a further improvement and supplement to the above technical solution, the present invention adopts the following technical measures: As a preferred method, the analysis of the impact of photovoltaic access current on transformer substation voltage based on the COPULA function further includes the following steps: Model validation and visualization: Synthetic Copula samples with the same distribution as the original data are generated through inverse probability integral transformation. The statistical characteristics of the original data and the synthetic samples are compared to verify the model fitting effect. A three-dimensional surface plot and quantile dependence structure plot of the joint probability density function are generated to analyze the joint distribution characteristics of photovoltaic current and transformer voltage.

[0014] As a preferred option, the data quality optimization operations in the data preprocessing steps include at least: outlier removal, data stabilization, and data standardization. Missing value imputation: Missing values ​​are imputed using the mean of the nearest neighbor samples; Outlier removal: The 3σ criterion is used to remove outlier data and determine the data range; Data stabilization: By calculating the difference between data at adjacent time points, long-term, systematic trends are eliminated, thus stabilizing the data; Data standardization: Transform the variables in a dataset into a standard normal distribution with a mean of 0 and a standard deviation of 1.

[0015] Preferably, in the step of dynamic marginal distribution modeling, the dynamic marginal distribution model is an ARMA-GARCH model. The ARMA part of the ARMA-GARCH model is used to track the dynamic changes of the mean of the voltage and current sequences, and the GARCH part of the ARMA-GARCH model is used to track the dynamic changes of the variance of the voltage and current sequences. Among them, the marginal distribution of voltage is fitted to a normal distribution, and the marginal distribution of current is fitted to a T-distribution.

[0016] ARMA-GARCH was used to establish marginal distribution models for voltage and current time series data. The ARMA-GARCH model captures both the "time-varying mean" and "time-varying volatility" of the time series, jointly addressing the time-varying nature of marginal distributions. ARMA uses historical observations and historical disturbances to predict the current mean, thus tracking the dynamic changes in the mean. GARCH uses historical volatility and the square of historical disturbances to predict the current volatility, thus tracking the dynamic changes in variance. Through a two-layer structure of "mean dynamics (ARMA) + volatility dynamics (GARCH)," ARMA-GARCH ensures that the core parameters of the marginal distribution (mean and variance) are updated with time t, thus fully characterizing time-varying properties and supporting subsequent Copula joint distribution analysis.

[0017] As a preferred method, the construction steps for time-varying Gaussian Copula modeling include: By using the inverse cumulative distribution function of the marginal distribution, the standardized residuals of voltage and current are transformed into uniformly distributed samples; Fisher transform is applied to the correlation coefficients of uniformly distributed samples to convert bounded correlation coefficients into unbounded continuous variables. A first-order autoregressive model is established for the transformed continuous variables, and the model parameters are solved by maximum likelihood estimation. The continuous variable values ​​at the next time step are predicted based on a first-order autoregressive model, and the time-varying correlation coefficients are obtained by restoring them through Fisher inverse transform.

[0018] As a preferred method, the steps of the maximum likelihood estimation method are as follows: First, the unknown parameters in the dynamic marginal distribution model are solved by maximum likelihood estimation to obtain the calibrated dynamic marginal distribution parameters. Then, the calibrated dynamic marginal distribution parameters are substituted into the likelihood function of the time-varying Gaussian Copula model, and maximum likelihood estimation is performed again to solve for the unknown parameters in the time-varying Gaussian Copula model that characterize the dynamic dependence between variables.

[0019] As a preferred method, the steps for drawing the quantile dependency structure diagram are as follows: The current and voltage data are sorted from smallest to largest, and multiple quantile points are selected. The correlation coefficient at each quantile point is calculated, and a line graph is plotted with the quantile as the x-axis and the correlation coefficient as the y-axis to show the dependence of photovoltaic current on transformer voltage at different quantile levels.

[0020] The technical solution of the second technical subject matter involved in this invention is as follows: A modeling and analysis system for the joint distribution of photovoltaic current and transformer substation voltage, comprising: Data acquisition module: Filter photovoltaic user power generation stability areas that meet the requirements, and collect current data of photovoltaic users in the area and voltage data of corresponding terminals in the area; The data preprocessing module is used to perform data quality optimization operations on the current data and voltage data to obtain preprocessed data that meets the modeling requirements. The edge distribution modeling module is used to build a dynamic edge distribution model for the preprocessed data, eliminate autocorrelation and heteroscedasticity, and obtain the standardized residuals of voltage and current. The time-varying Gaussian Copula modeling module is used to capture the dynamic correlation between photovoltaic current and transformer voltage based on a dynamic edge distribution model. The parameter estimation module uses the maximum likelihood estimation method to obtain the unknown parameters that characterize the dynamic dependencies between variables in the time-varying Gaussian Copula model.

[0021] Preferably, the modeling and analysis system for the joint distribution of photovoltaic current and transformer area voltage further includes: The model validation and visualization module is used to generate synthetic Copula samples with the same distribution as the original data through inverse probability integral transformation. The statistical characteristics of the original data and the synthetic samples are compared to verify the model fitting effect. The module also generates a three-dimensional surface plot and quantile dependence structure plot of the joint probability density function to analyze the joint distribution characteristics of photovoltaic current and transformer voltage.

[0022] The technical solution of the third technical subject matter involved in this invention is as follows: A computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device where the computer-readable storage medium is located to execute the aforementioned method for analyzing the impact of photovoltaic access current on transformer voltage based on the COPULA function.

[0023] The beneficial effects of this invention are as follows: 1. Excellent dynamic capture capability, adaptable to the time-varying characteristics of photovoltaics: By using a time-varying ARMA-GARCH dynamic marginal distribution model, the mean and variance of photovoltaic current (T distribution) and transformer voltage (normal distribution) are accurately tracked (e.g., variance increases during peak photovoltaic power generation periods and fluctuates more gently in the morning and evening). Combined with a time-varying Copula model, the dependency parameters between variables are updated in real time, effectively capturing the dynamic dependency strength at different times (e.g., strong correlation at noon and weak correlation in the morning and evening), thus completely solving the core pain point that traditional static models cannot adapt to the photovoltaic power output being "significantly affected by natural factors and exhibiting strong time-varying characteristics".

[0024] 2. The joint distribution accurately characterizes the nonlinearity and heavy-tailed properties: By employing a separate modeling approach combining "dynamic marginal distribution + time-varying Copula," the T-distribution accurately fits the thick-tailed characteristics of the current (probabilistic capture of extreme power output scenarios), while the Copula function purely characterizes the nonlinear and asymmetric dependencies between variables (avoiding the underestimation bias of traditional linear correlation coefficients). Combined with quantile dependency analysis and joint PDF visualization, it achieves a comprehensive and accurate characterization from "overall average correlation" to "local quantile dependency," significantly reducing the fitting error of the joint distribution.

[0025] 3. Parameter estimation is reliable and controllable, supporting practical engineering applications: The method employs a two-step maximum likelihood estimation process. First, it independently calibrates the marginal distribution parameters (AR coefficient, MA coefficient, GARCH volatility coefficient, distribution shape parameters, etc.). Then, it solves for the Copula-dependent parameters based on the calibrated marginal distribution. This avoids mutual interference between the two types of parameters, resulting in highly stable estimation results with clear physical meaning. The parameter solution process has a moderate computational load, making it suitable for real-time modeling and decision-making needs in engineering scenarios. It can directly provide quantitative basis for calculating voltage over-limit probability and formulating control strategies.

[0026] 4. Break through the limitations of traditional modeling and expand the boundaries of application scenarios: Breaking through the triple limitations of traditional linear models (which cannot capture nonlinearity), static Copula (which cannot adapt to time-varying characteristics), and the single distribution assumption (which cannot cover the heavy-tailed characteristics), it achieves simultaneous capture of the three core characteristics of photovoltaic-voltage systems: time-varying, nonlinear, and heavy-tailed. It can support the "long-term risk assessment" in the photovoltaic distribution area planning stage, meet the "real-time voltage regulation" in the grid operation stage, and provide refined analysis tools for scenarios such as setting time-segmented early warning thresholds and optimizing reactive power compensation strategies, significantly expanding its application boundaries. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating one method of the present invention.

[0028] Figure 2 This is a schematic diagram of the current-voltage trend involved in the present invention.

[0029] Figure 3 This is a schematic diagram of the edge accumulation distribution involved in the present invention.

[0030] Figure 4 This is a schematic diagram of the original data involved in the present invention.

[0031] Figure 5 This is a schematic diagram of the Copula involved in the present invention.

[0032] Figure 6 This is a schematic diagram of the joint probability density of the present invention.

[0033] Figure 7 This is a schematic diagram of the quantile-dependent structure involved in the present invention. Detailed Implementation

[0034] The technical solution of the present invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings.

[0035] Example 1: As Figures 1-7 As shown, the technical solution of the first technical subject of this invention is: a method for analyzing the impact of photovoltaic access current on transformer voltage based on the COPULA function.

[0036] When considering the actual situation of photovoltaic users, according to the basic theory of power systems, when the current of photovoltaic users increases, the voltage drop of the line will increase due to the increased current, and the terminal voltage may decrease. However, when photovoltaic power generation is connected to the grid as a distributed power source, in this case, there will be a correlation between the current increment (ΔI) and the voltage increment (ΔV).

[0037] This technical solution utilizes correlation quantification analysis based on the Copula model (a time-varying Gaussian Copula model, also known as a "connection function model" or "dependency function model," referred to as the Copula model in this paper), encompassing model validation, visualization of the joint probability density function (PDF), and quantile dependency structure analysis, to conduct an in-depth investigation into the nonlinear correlation between photovoltaic user current and terminal voltage. The results show that after distributed photovoltaic power is connected to the distribution network, an increase in the absolute value of the distributed photovoltaic power generation current leads to a rise in local voltage.

[0038] Therefore, this technical solution is based on the Copula model. By separating the marginal and joint distributions of variables, it accurately captures and quantifies the nonlinear and asymmetric correlation between photovoltaic power output and transformer voltage, thereby revealing the intrinsic driving mechanism of voltage fluctuations under different photovoltaic power output intensities and environmental conditions. This technical solution not only overcomes the shortcomings of traditional linear analysis in adapting to complex dynamic relationships, but also solves the problem that single-variable analysis is difficult to assess joint risks, providing innovative technical support for overcoming the limitations of existing research that "emphasizes theoretical simulation but neglects practical quantification."

[0039] Therefore, this technical solution provides theoretical support and practical application for the efficient operation and scientific management of photovoltaic systems. It is expected to assist in optimizing the stability and controllability of distribution network voltage in high-penetration distributed photovoltaic scenarios, promote the steady development of the photovoltaic industry, and facilitate engineering applications such as predicting the probability of voltage rise exceeding limits based on photovoltaic current. In practical applications, the method involved in this invention can directly serve the planning, design, operation, and control of photovoltaic power stations. At the planning and design level, it can provide quantitative basis for the configuration of photovoltaic power grid access capacity and the selection of access location, and avoid the risk of voltage exceeding the limit due to improper access in advance; At the operational control level, it can support the optimization and formulation of voltage regulation measures such as switching on and off reactive power compensation devices and adjusting transformer taps, enabling accurate prediction and proactive control of voltage fluctuations.

[0040] Next, a method for analyzing the impact of photovoltaic access current on transformer substation voltage based on the COPULA function is described in detail. The steps include: Data Acquisition: Screen photovoltaic (PV) user areas that meet the requirements for power generation stability, and collect current data of PV users within the areas and voltage data of the corresponding terminals in the areas; Data preprocessing: Perform data quality optimization operations on the current data and voltage data to obtain preprocessed data that meets the modeling requirements; Dynamic marginal distribution modeling: Based on preprocessed data, a dynamic marginal distribution model is established to eliminate autocorrelation and heteroscedasticity, and to obtain the standardized residuals of voltage and current; Time-varying Gaussian Copula modeling (Copula is a connection function or coupling function): Based on the dynamic edge distribution model, the dynamic edge distribution is obtained, and a time-varying Gaussian Copula model is constructed to capture the dynamic correlation between photovoltaic current and transformer voltage. Parameter estimation: The maximum likelihood estimation method is used to first estimate the dynamic marginal distribution parameters of the dynamic marginal distribution model, and then substitute the dynamic marginal distribution parameters into the time-varying Gaussian Copula model to estimate the time-varying Gaussian Copula parameters, thus obtaining the optimal values ​​of the unknown parameters in the Copula function.

[0041] In practical applications, to further improve the analysis method of the impact of photovoltaic access current on transformer voltage based on the COPULA function, the steps also include: Model validation and visualization: Synthetic Copula samples with the same distribution as the original data are generated through inverse probability integral transformation. The statistical characteristics of the original data and the synthetic samples are compared to verify the model fitting effect. A three-dimensional surface plot and quantile dependence structure plot of the joint probability density function are generated to analyze the joint distribution characteristics of photovoltaic current and transformer voltage.

[0042] For model verification and visualization, systematic analysis and verification of actual transformer area data can form a replicable engineering application paradigm, providing technical support for the safe and stable operation of the distribution network in high-penetration distributed photovoltaic scenarios, and promoting the coordinated and efficient development of photovoltaic power generation technology and power system.

[0043] Next, the above technical solution will be explained in detail: In practical applications, during the data acquisition process: Determine the data collection period (e.g., the collection period is xxxx year xx month) and sampling interval (e.g., the sampling interval is 15 minutes), select photovoltaic user power generation areas with relatively stable power generation from smart meters or monitoring systems, and obtain time series data of photovoltaic user current I and corresponding transformer terminal voltage V.

[0044] In practical applications, during the data preprocessing steps: During photovoltaic power generation, the combined effect of numerous influencing factors can cause current fluctuations, even resulting in abnormal values ​​deviating from the normal range. Furthermore, electricity meters are highly susceptible to noise interference and data gaps. These data quality and integrity issues can adversely affect the accuracy of subsequent data analysis. Therefore, it is necessary to preprocess the raw data to ensure its statistical standardization and consistency.

[0045] Therefore, data quality optimization operations should include at least: outlier removal, data stabilization, and data standardization. Specifically: Missing value imputation: Missing values ​​are imputed using the mean of nearest neighbor samples. Specifically, the KNN algorithm (also known as the K-Nearest Neighbors algorithm, a supervised learning algorithm) is used to impute missing data. For a sample with a missing value, the K most similar samples in the dataset are searched, and then the average of the feature values ​​corresponding to these K samples is calculated. This average is then used to impute the missing value.

[0046] The KNN algorithm imputes missing values ​​based on the "feature mean of similar samples," which better reflects the actual distribution of the data compared to simple "global mean imputation." This step provides high-quality, complete data for subsequent outlier handling, stabilization, standardization, and Copula modeling, avoiding the interference of missing values ​​on the analysis results.

[0047] Outlier removal: The 3σ criterion was used to remove outliers, and the data range was determined. The range of data to be retained was... and ,in, : Current variation (such as the current difference between adjacent moments, used to eliminate data trends and make the data stable); : The mean; : Standard deviation; Voltage fluctuations (such as the voltage difference between adjacent moments, which can also be used for data stabilization). : The mean; : The standard deviation.

[0048] The principle of the 3σ criterion is based on the statistical characteristics of the normal distribution. It is believed that in a normal distribution, about 99.7% of the data will fall within the range of "mean ± 3 standard deviations"; data outside this range can be identified as outliers and need to be removed.

[0049] Data stabilization: By calculating the difference between data at adjacent time points (i.e., the first-order difference method: the transformation of the time series by subtracting the previous period from the next period) to eliminate long-term, systematic trends and stabilize the data.

[0050] For current, the current difference ( Current change in adjacent time periods: ,in, It is the first Current data at any given time. It is the first The difference between the current data at any given time reflects the instantaneous change in current.

[0051] Regarding voltage, voltage difference ( ): Voltage fluctuation at grid connection point: ,in, It is the first Voltage data at time of day It is the first The voltage data at any given time, the difference reflects the instantaneous fluctuation of the voltage.

[0052] By using first-order difference, the original trending current and voltage sequences are transformed into "variable / fluctuation" sequences, eliminating long-term trends and making the data more stable. This provides high-quality input data for subsequent marginal distribution modeling (such as ARMA-GARCH) and Copula correlation analysis, ensuring that the model can accurately capture the dynamic relationship between current and voltage.

[0053] Data standardization: Transform the variables in the dataset to have a mean of 0 and a standard deviation of 1, so that the data presents a standard normal distribution and eliminates scale differences between different features.

[0054] The goal of data standardization is to: change in photovoltaic current ( ) and voltage fluctuation ( The numerical scales of these variables can vary considerably (the numerical scale mainly refers to the magnitude of exponential values; current may be a single digit, a dozen, or even tens, while voltage is typically 200 to 250). If used directly for modeling, the model will overemphasize the "absolute value" rather than the "relative variation pattern." Standardization transforms features at different scales into a standard normal distribution with a mean of 0 and a standard deviation of 1, eliminating dimensional differences and allowing subsequent analyses (such as correlation modeling) to focus more on the intrinsic relationships between variables.

[0055] Transforming variables in a dataset to have a mean of 0 and a standard deviation of 1 involves subtracting the mean from each original data point and then dividing by its own standard deviation. This maps the data to a standard normal distribution interval with a mean of 0 and a standard deviation of 1, achieved through the following formula:

[0056] , in, This is the standardized change in current; This is the standardized voltage fluctuation. The change in original current The mean; The change in original current The standard deviation. Original voltage fluctuation The mean; Original voltage fluctuation The standard deviation.

[0057] After standardization, the changes in current and voltage are converted into dimensionless "standard scores," both on the same numerical scale (both fluctuating around 0, with the fluctuation amplitude constrained by a standard deviation of 1). This allows subsequent marginal distribution modeling (such as ARMA-GARCH) and Copula correlation analysis to more accurately capture the nonlinear, time-varying correlation between current and voltage, avoiding model bias caused by differences in dimensions, and laying the foundation for the accuracy of the entire analysis process.

[0058] In the dynamic marginal distribution modeling step, the dynamic marginal distribution model is an ARMA-GARCH model. The ARMA part of the ARMA-GARCH model is used to track the dynamic changes of the mean of the voltage and current series, and the GARCH part of the ARMA-GARCH model is used to track the dynamic changes of the variance of the voltage and current series. Among them, the marginal distribution of voltage is fitted to a normal distribution, and the marginal distribution of current is fitted to a T-distribution.

[0059] In other words, the joint distribution of random variables of current and voltage can be decomposed into the marginal distributions of the two variables and a Copula function, thereby separating the randomness and coupling of the variables.

[0060]

[0061] Among them: joint distribution To describe voltage Take "less than or equal to" "and current" Take "less than or equal to" The joint probability of "".

[0062] Marginal distribution and The edge distributions of voltage and current are respectively; Copula function To connect two edge-distributed "couplers", the correlation structure between voltage and current (such as nonlinear and asymmetric dependence) is specifically characterized. The copula parameter represents the strength of the correlation between variables.

[0063] Dynamic edge distribution modeling involves three steps: S1, Fitted Marginal Distribution and Choose appropriate probability distributions (such as normal distribution, T-distribution, etc.) for voltage and current respectively, and estimate the distribution parameters through methods such as maximum likelihood estimation. For example, the marginal distribution of photovoltaic current may be fitted to a T-distribution (to adapt to the thick tail characteristics of power output), and the marginal distribution of voltage may be fitted to a normal distribution (to adapt to the stable characteristics of grid voltage).

[0064] S2. Select and fit the Copula function. Based on the correlation characteristics of voltage and current (such as the presence of nonlinearity or tail dependence), select the Copula type (such as Gaussian Copula, Clayton Copula, etc.), and then estimate the Copula parameters using methods such as marginal inference method (IFM). For example, if the correlation between current and voltage changes with time, a time-varying Gaussian Copula can be selected, and updated through dynamic equations (such as correlation coefficients).

[0065] S3. Recombining and Verifying the Joint Distribution: Substituting the marginal distribution of S1 and the Copula function of S2 into the formula yields the complete joint distribution. The effectiveness of the decomposition and recombination can then be verified by generating synthetic samples and comparing statistical properties (such as Kendall's Tau coefficient).

[0066] The core advantage of dynamic marginal distribution modeling is that it decouples the "randomness of a single variable" from the "coupling between variables": Marginal distributions can be flexibly selected based on the characteristics of each variable, without being restricted by the joint distribution; Copula functions are focused on characterizing correlations and can accurately capture the nonlinearity and time-varying dependence of current and voltage in photovoltaic scenarios (such as strong coupling when there are sudden changes in light intensity and weak correlation when the output is stable), which is something that traditional linear models cannot achieve.

[0067] In practical applications, the construction steps for time-varying Gaussian Copula modeling include: By using the inverse cumulative distribution function of the marginal distribution, the standardized residuals of voltage and current are transformed into uniformly distributed samples; Fisher transform is applied to the correlation coefficients of uniformly distributed samples to convert bounded correlation coefficients into unbounded continuous variables. A first-order autoregressive model is established for the transformed continuous variables, and the model parameters are solved by maximum likelihood estimation. The continuous variable values ​​at the next time step are predicted based on a first-order autoregressive model, and the time-varying correlation coefficients are obtained by restoring them through Fisher inverse transform.

[0068] The steps involved in constructing a static Copula model include: Edge distribution modeling: ARMA-GARCH models were established for the voltage and current series respectively to eliminate autocorrelation and heteroscedasticity:

[0069] Similarly defined The model yields standardized residuals. and ; In the formula, The mean of a voltage series; : The order of the autoregressive (AR) term (characterizing the linear relationship between the current value and historical values); Autoregressive coefficient (measures the strength of the influence of historical values ​​on the current value); The order of the moving average (MA) term (characterizing the linear relationship between the current residual and historical residuals); Moving average coefficient (measures the strength of the influence of historical residuals on current residuals); : Residual term (unexplained fluctuations in the model, which will be handled by the GARCH part later).

[0070] GARCH section: Handling "heteroscedasticity" (time-varying volatility at the volatility level): residual The volatility is characterized by the GARCH model, where: The conditional variance (the volatility over time, estimated by the GARCH model). To standardize the residuals ( Divide by time-varying volatility (to stabilize its variance to 1). It is a skewed t-distribution (used to fit the distribution of standardized residuals, because power data often has "thick tails and skewed characteristics, which is more in line with reality than the normal distribution); The degrees of freedom of the distribution (controlling the "thickness of the tail"; the fewer the degrees of freedom, the thicker the tail). This is the skewness parameter of the distribution (controlling the "skewness direction", such as the asymmetric fluctuations when photovoltaic power output changes abruptly).

[0071] GARCH uses "time-varying volatility" "Capture the heteroscedasticity of voltage sequences at the volatility level."

[0072] This allows the standardized residuals of voltage and current to be processed by ARMA-GARCH. and This process eliminates autocorrelation and heteroscedasticity, resulting in a "stationary and variance-stable" sequence. This step lays the foundation for subsequent Copula modeling, allowing Copula to focus solely on characterizing the nonlinear correlation between the two residual sequences without needing to consider the autocorrelation and heteroscedasticity of the original sequence.

[0073] Correlation modeling: Assuming copula parameters Following a dynamic process, taking the time-varying Gaussian copula as an example, according to the inverse CDF transform of the marginal distribution, the copula function expression is:

[0074] in, The cumulative distribution function (CDF) values ​​are the marginal distributions of voltage and current (i.e., the original data is converted into uniformly distributed samples in the [0,1] interval after fitting the marginal distribution). : The joint cumulative distribution function of a multivariate normal distribution, where is the time-varying correlation coefficient, which characterizes the dynamic correlation between two standard normal samples; It is the inverse cumulative distribution function of the standard normal distribution. Let be the joint cumulative distribution function of a multivariate normal distribution; The time-varying correlation coefficient is updated through a dynamic equation:

[0075] In the formula, The Fisher transform maps an unbounded input to an interval, ensuring that the input remains within the effective range of the correlation coefficient (which must satisfy a certain condition). ; For parameters to be estimated, they need to be learned from the data through methods such as maximum likelihood estimation; The voltage and current are the standardized residuals after ARMA-GARCH processing (autocorrelation and heteroscedasticity have been eliminated).

[0076] To ensure the effectiveness of Copula modeling, parameter estimation is required: the maximum likelihood estimation method is used to obtain the unknown parameters in the time-varying Gaussian Copula model that characterize the dynamic dependencies between variables.

[0077] In practical applications, the steps of the maximum likelihood estimation method are as follows: First, the unknown parameters in the dynamic marginal distribution model are solved by maximum likelihood estimation to obtain the calibrated dynamic marginal distribution parameters. Then, the calibrated dynamic marginal distribution parameters are substituted into the likelihood function of the time-varying Gaussian Copula model, and maximum likelihood estimation is performed again to solve for the unknown parameters in the time-varying Gaussian Copula model that characterize the dynamic dependence between variables.

[0078] The core purpose of obtaining the optimal values ​​of the unknown parameters in the Copula function is to enable the Copula function to accurately characterize the true dependency structure among multiple variables (the dependency structure is time-varying, meaning the correlation between the outputs of multiple photovoltaic sites is also time-varying), thus providing a foundation for constructing a reliable multivariate joint distribution. That is: 1. Quantifying the strength and characteristics of dependency: Unknown parameters directly determine the core attributes of the dependency relationship, such as the correlation coefficient of Gaussian Copula and the shape parameter of Clayton Copula. The optimal value can accurately quantify the strength of the dependency between variables and the symmetric / asymmetric characteristics (such as the nonlinear positive correlation strength between photovoltaic current and voltage).

[0079] 2. Adapt to actual data distribution: By solving for the optimal parameters through methods such as maximum likelihood estimation, the dependency structure fitted by the Copula function can be highly consistent with the actual dependency pattern of the original data, avoiding the disconnect between model assumptions and real data.

[0080] 3. Supporting joint distribution applications: Optimal parameters are the key to combining the Copula function with the marginal distribution. Only with optimal parameters can the final constructed joint distribution accurately calculate the probability of multiple variables occurring simultaneously (such as the joint probability of a sudden increase in photovoltaic current and voltage exceeding the limit), providing a reliable basis for subsequent risk assessment and control decisions.

[0081] In other words, after estimating the unknown parameters in the marginal distribution using MLE (Maximum Likelihood Estimation), we substitute them into the likelihood function and perform another maximum likelihood estimation to obtain the unknown parameters in the copula function.

[0082] 1. Edge Distribution Parameter Estimation: For edge distributions of voltage and current, the goal is to find the parameters. and This maximizes the log-likelihood sum of the voltage and current data: ; ; in: , These are the optimal parameters for voltage edge distribution and current edge distribution (such as the order of ARMA, the volatility parameter of GARCH, etc.). , These are the probability density functions of voltage and current (determined by the type of marginal distribution, such as the density function of ARMA-GARCH). The core of MLE is to maximize the log-likelihood sum in order to find the parameters that best fit the data.

[0083] 2. Copula function parameter estimation: After obtaining the optimal parameters of the marginal distribution and Then, substitute it into the likelihood equation of the Copula function, and use MLE again to estimate the unknown parameters of the Copula. :

[0084] in: For the probability density function of a Copula (such as the density function of a time-varying Gaussian Copula); The cumulative distribution function (CDF) of voltage and current (calculated from the estimated marginal distribution parameters, output as a uniform distribution value in the interval [0,1]); maximize The goal is to find the parameters that maximize the log-likelihood of Copula, thereby characterizing the optimal correlation structure between voltage and current.

[0085] The role of parameter estimation is to ensure that the marginal distribution of a single variable accurately fits its own statistical characteristics through a two-step MLE estimation process of "marginal distribution first, then Copula function," while also ensuring that the Copula function accurately captures the nonlinear and time-varying dependencies between variables. This process is crucial for the model to move from "theoretical framework" to "data adaptation," ultimately enabling the joint distribution model to accurately quantify the dynamic relationship between photovoltaic current and transformer voltage.

[0086] In practical applications, a quantile dependency structure diagram needs to be drawn for easier and more intuitive viewing. The steps for drawing a quantile dependency structure diagram are as follows: The current and voltage data are sorted from smallest to largest, and multiple quantile points are selected. The correlation coefficient at each quantile point is calculated, and a line graph is plotted with the quantile as the x-axis and the correlation coefficient as the y-axis to show the dependence of photovoltaic current on transformer voltage at different quantile levels.

[0087] This technical solution transforms the abstract "joint distribution model" into a visual three-dimensional density surface, upgrading the "joint action mechanism of photovoltaic current and voltage" from a numerical and statistical description to an intuitive graphical understanding. This not only verifies the effectiveness of the previous model but also provides an intuitive basis for subsequent "voltage fluctuation risk identification" and "visual decision-making of control strategies".

[0088] Next, the above technical solution will be applied to actual operation: The current and voltage data are arranged in ascending order, and then a series of different quantile points (such as 0.1, 0.2, 0.3, etc.) are selected. The quantiles represent the values ​​at specific positions after the data is sorted from smallest to largest. For each quantile q, the corresponding correlation coefficient is calculated to measure the dependence of photovoltaic user current and transformer area voltage at that quantile. Figure 7 As shown, the correlation coefficient is plotted at different quantiles with quantiles on the x-axis and correlation coefficients on the y-axis. This plot shows the dependence of variables at different quantile levels and helps researchers discover asymmetric relationships between variables across different data segments.

[0089] pass Figure 7As can be seen, the correlation coefficient curve exhibits a "W"-shaped fluctuation, indicating that the correlation between the two variables fluctuates at different quantile levels. With the increase of the current quantile, the negative correlation between current and voltage strengthens; when the current quantile is between 0.3 and 0.7, the correlation between the two variables is relatively high; after reaching a certain value, the negative correlation between the two variables tends to weaken.

[0090] Photovoltaic power generation is affected by the intensity of sunlight during the day, resulting in a "U"-shaped data characteristic of photovoltaic power generation current throughout the day. Based on the correlation analysis at different quantile levels, it can be seen that as the current generated by photovoltaic users increases during the middle of the day, the voltage in the distribution area will rise accordingly.

[0091] Before plotting the quantile dependence structure, the joint PDF visualization step is completed first. Joint PDF visualization generates a 3D surface plot of the joint probability density function (PDF) based on the fitted Gaussian Copula model. The peak positions and shapes of the surface can provide more information about the joint distribution among variables, helping to deepen the understanding of the interaction mechanism between current and voltage in photovoltaic systems. For example... Figure 6 In the joint distribution diagram of the Copula function, the horizontal axis represents the cumulative probability of the A-phase current Ai-user of the photovoltaic user; the vertical axis represents the cumulative probability of the A-phase voltage Au-ter of the transformer area; and the height represents the joint probability density.

[0092] like Figure 6 As shown in the density map, under different combinations, the combined distribution values ​​of photovoltaic power generation and transformer voltage are significantly concentrated in the upper right corner of the density map. The density peak concentration interval is (I∈[ From a spatial perspective, the probability density of the surface from right to left and from front to back shows a clear upward trend. This phenomenon indicates a strong positive correlation between the variables, that is, as the absolute value of the photovoltaic user current continues to increase, the probability of the transformer area voltage increasing also increases.

[0093] In contrast, in the extreme value region (I < Within 25), the surface exhibits a relatively flat characteristic, and the probability density decreases significantly and approaches 0. This indicates that in this extreme value region, there is no significant tail dependence between current and voltage, and the correlation between them is weak, or even non-existent.

[0094] Next, the steps for model validation and visualization will be explained in further detail: By generating an equal number of synthetic Copula samples with the same distribution as the original data through inverse probability integral transformation, the statistical characteristics of the original data and the generated samples are compared to verify the model's fit to the joint distribution.

[0095] Generate Copula samples and visualize them by comparing them with the original data. Figure 4 This is a scatter plot of the original data. Figure 5 The generated sample is for Copula. The Kendall's Tau coefficient of the generated sample is τgen = -0.523, with an error of Δτ = 0.019 compared to the original data, indicating that the selected Copula model fits the data well and accurately captures the correlation between variables.

[0096] Next, we will further analyze the correlation quantification based on the copula model: Select photovoltaic (PV) user terminals that are stably generating electricity in actual grid operation, and plot a scatter plot of user generation current and substation voltage, such as... Figure 2 As shown. Figure 2 The data can roughly show the degree of overlap between the high and low values ​​of the two sequences and the degree of overlap in the general trend. That is, when photovoltaic users generate a lot of electricity, the voltage of the transformer area will rise accordingly. However, this intuitive judgment has certain limitations when it comes to accurately quantifying the complex relationship between variables.

[0097] The Copula function can delve into the dependency structure between multiple variables, separating the marginal distributions of each variable from their correlations. By fitting the distribution of each variable individually, it can accurately characterize the distribution features of each variable. Then, the Copula function is used to analyze the complex relationships between variables such as user power generation current and transformer voltage, compensating for the shortcomings of trend graph analysis. Specifically: 1. Marginal distribution fitting: An adaptive marginal distribution fitting was performed on the variables. The optimal marginal distribution was automatically selected using the Kolmogorov-Smirnov statistical test and the AIC criterion, and the distribution parameters were output (as shown in Table 1). Current follows a T-distribution, and voltage conforms to a normal distribution. Combined with the cumulative marginal distribution plots of current and voltage (as shown in Table 1), the optimal marginal distribution was determined. Figure 3 As shown in the figure, it can be intuitively observed that the current exhibits a significant thick tail characteristic of T-distribution, while the voltage follows a normal distribution, which conforms to the symmetrical fluctuation characteristics.

[0098] Table 1:

[0099] 2. Gaussian Copula Model Construction: An elliptic family Gaussian Copula model was constructed based on the marginal distribution, and the applicability of the model was verified by Kendall's Tau statistical test to measure the nonlinear correlation between photovoltaic user current and transformer area voltage.

[0100] 1) Parameter estimation: The Copula covariance matrix Σ is estimated using the maximum likelihood method. The result is:

[0101] The off-diagonal element ρ = -0.4697 initially indicates a negative correlation between the variables.

[0102] 2) Nonlinear correlation test: Kendall's Tau is a statistic used to measure the rank correlation between two variables. It does not depend on the specific distribution of the variables and can effectively capture the nonlinear correlation between variables.

[0103] The Kendall's Tau coefficient τ = -0.542 (p-value < 0.001) for photovoltaic user current and terminal voltage was calculated based on the original data. This coefficient is significantly higher than the linear correlation coefficient (Pearson, sr = -0.3908), confirming that the dependence between the two has nonlinear characteristics.

[0104] Since the current generated by distributed power sources is negative, there is a significant nonlinear positive correlation between the current of photovoltaic users and the voltage of the distribution area; that is, the larger the power generation current, the higher the terminal voltage.

[0105] To further summarize the above technical solutions: In the field of photovoltaic grid connection planning, this technical solution can be used to guide the selection of grid connection locations, capacity configuration, and grid connection scheme optimization for photovoltaic power sources within a distribution area. By accurately characterizing the joint distribution characteristics of photovoltaic grid connection current and distribution area voltage, it provides a scientific basis for planners to avoid voltage over-limit problems caused by improper photovoltaic grid connection. In the field of voltage control strategies, based on the correlation between the two revealed by the Copula function, it can provide quantitative support for the formulation and optimization of photovoltaic distribution area voltage regulation measures (such as switching of reactive power compensation devices, adjustment of transformer taps, etc.).

[0106] Photovoltaic output is affected by natural factors such as light intensity, temperature, and cloud movement, exhibiting significant time-varying characteristics. This is mainly reflected in two aspects: the time-varying nature of peripheral distribution, i.e., the time-varying nature of photovoltaic output caused by light intensity, temperature, etc., received by a single photovoltaic site; and the time-varying nature of structure dependence, i.e., the correlation between the outputs of multiple photovoltaic sites is also time-varying.

[0107] (1) This technical solution uses ARMA-GARCH to establish a marginal distribution model for voltage and current time series data. The ARMA-GARCH model captures the "time-varying mean" and "time-varying volatility" of the time series respectively, and jointly solves the time-varying problem of the marginal distribution. ARMA uses the historical observations and historical disturbance terms of the series to predict the current mean, thereby tracking the dynamic changes of the mean. GARCH uses the historical volatility and the square of the historical disturbances to predict the current volatility, thereby tracking the dynamic changes of the variance. Through the two-layer structure of "mean dynamic (ARMA) + volatility dynamic (GARCH)," ARMA-GARCH ensures that the core parameters (mean and variance) of the marginal distribution are updated with time t, thereby fully characterizing the time-varying nature and supporting the subsequent Copula joint distribution analysis.

[0108] (2) Based on the dynamic modeling of edge distribution, the time-varying Copula captures the time-varying nature of the dependence between the output of multiple photovoltaic sites by dynamically updating the correlation matrix.

[0109] Static Copula assumptions about dependency structure (i.e., the correlation matrix, which refers to the correlation coefficient in this paper) While the correlation coefficient (coefficient of performance) is fixed, in real-world scenarios, the dependencies between variables often change over time. Extending the Gaussian Copula to a time-varying form essentially involves making the correlation coefficient... It dynamically adjusts over time t. The Fisher transform can be used to dynamically update the correlation matrix of a time-varying Gaussian Copula, and is especially suitable for the independent dynamics of a single correlation coefficient in low-dimensional scenarios. It captures the time-varying characteristics of the correlation coefficient through a process of "transformation-dynamic modeling-inverse transformation", converting the correlation coefficient with limited values ​​into a continuous variable that is easy to track dynamically, and finally realizing the time-varying update of the correlation coefficient.

[0110] The steps for dynamically updating the correlation matrix of the time-varying Gaussian Copula using Fisher transform are as follows: Step 1: Obtain standardized residuals Assuming copula parameters Following a dynamic process, taking the time-varying Gaussian copula as an example, according to the inverse CDF transform of the marginal distribution, the copula function expression is:

[0111] in, and It is the inverse cumulative distribution function of the standard normal distribution. Let be the joint cumulative distribution function of a multivariate normal distribution. and This is the standardized residual, denoted as . and The correlation coefficient between the two is the one that needs to be tracked. Let the sliding time window have T time points, according to... and The sample correlation coefficient can be calculated. .

[0112] Step 2: [The sentence is incomplete and requires more context.] Perform the Fisher transform, the formula is as follows: ,when When it approaches 1, Approaching positive infinity, when When approaching -1, Approaching negative infinity, breaking the... Boundary restrictions.

[0113] Step 3: [The sentence is incomplete and requires more context.] Establish a dynamic model, because Unbounded and approximately normally distributed, it can be directly modeled using an autoregressive model, taking AR(1) as an example: Where c is a constant term, Autoregressive coefficient, This is the disturbance term. Historical data (such as the previous 96 time points) is used. The parameters are solved by maximum likelihood estimation.

[0114] Step 4: Based on the estimated AR(1) model, predict the next time step. , The predicted correlation coefficient value is restored using the inverse Fisher transform: = .

[0115] Example 2: The technical solution of the second technical subject matter involved in this invention is as follows: A modeling and analysis system for the joint distribution of photovoltaic current and transformer substation voltage is provided, which is used to perform the analysis method for the influence of photovoltaic access current on transformer substation voltage based on the COPULA function described in Example 1.

[0116] A modeling and analysis system for the joint distribution of photovoltaic current and transformer substation voltage includes: Data acquisition module: Filter photovoltaic user power generation stability areas that meet the requirements, and collect current data of photovoltaic users in the area and voltage data of corresponding terminals in the area; The data preprocessing module is used to perform data quality optimization operations on the current data and voltage data to obtain preprocessed data that meets the modeling requirements. The edge distribution modeling module is used to build a dynamic edge distribution model for the preprocessed data, eliminate autocorrelation and heteroscedasticity, and obtain the standardized residuals of voltage and current. The time-varying Gaussian Copula modeling module is used to capture the dynamic correlation between photovoltaic current and transformer voltage based on a dynamic edge distribution model. The parameter estimation module uses the maximum likelihood estimation method to obtain the unknown parameters that characterize the dynamic dependencies between variables in the time-varying Gaussian Copula model.

[0117] In practical applications, the modeling and analysis system for the joint distribution of photovoltaic current and transformer area voltage also includes: The model validation and visualization module is used to generate synthetic Copula samples with the same distribution as the original data through inverse probability integral transformation. The statistical characteristics of the original data and the synthetic samples are compared to verify the model fitting effect. The module also generates a three-dimensional surface plot and quantile dependence structure plot of the joint probability density function to analyze the joint distribution characteristics of photovoltaic current and transformer voltage.

[0118] Example 3: The technical solution of the third technical subject matter involved in this invention is as follows: A computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device where the computer-readable storage medium is located to execute the method for analyzing the impact of photovoltaic access current on transformer voltage based on the COPULA function as described in Example 1.

[0119] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Various modifications and variations can be made to the above embodiments. 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 method for analyzing the impact of photovoltaic access current on transformer substation voltage based on the Copula function, characterized in that, The steps include: Data Acquisition: Screen photovoltaic (PV) user areas that meet the requirements for power generation stability, and collect current data of PV users within the areas and voltage data of the corresponding terminals in the areas; Data preprocessing: Perform data quality optimization operations on the current data and voltage data to obtain preprocessed data that meets the modeling requirements; Dynamic marginal distribution modeling: Based on preprocessed data, a dynamic marginal distribution model is established to eliminate autocorrelation and heteroscedasticity, and to obtain the standardized residuals of voltage and current; Time-varying Gaussian Copula modeling: Based on the dynamic edge distribution model, a time-varying Gaussian Copula model is constructed to capture the dynamic correlation between photovoltaic current and transformer voltage. Parameter estimation: The maximum likelihood estimation method is used to obtain the unknown parameters in the time-varying Gaussian Copula model that characterize the dynamic dependence between variables.

2. The method for analyzing the impact of photovoltaic access current on transformer substation voltage based on the COPULA function according to claim 1, characterized in that, The steps also include: Model validation and visualization: Synthetic Copula samples with the same distribution as the original data are generated through inverse probability integral transformation. The statistical characteristics of the original data and the synthetic samples are compared to verify the model fitting effect. A three-dimensional surface plot and quantile dependence structure plot of the joint probability density function are generated to analyze the joint distribution characteristics of photovoltaic current and transformer voltage.

3. The method for analyzing the impact of photovoltaic access current on transformer substation voltage based on the COPULA function according to claim 1 or 2, characterized in that, In the data preprocessing steps, data quality optimization operations include at least: outlier removal, data stabilization, and data standardization; Missing value imputation: Missing values ​​are imputed using the mean of the nearest neighbor samples; Outlier removal: The 3σ criterion is used to remove outlier data and determine the data range; Data stabilization: By calculating the difference between data at adjacent time points, long-term, systematic trends are eliminated, thus stabilizing the data; Data standardization: Transform the variables in a dataset into a standard normal distribution with a mean of 0 and a standard deviation of 1.

4. The method for analyzing the impact of photovoltaic access current on transformer substation voltage based on the COPULA function according to claim 1, characterized in that, In the dynamic marginal distribution modeling step, the dynamic marginal distribution model is an ARMA-GARCH model. The ARMA part of the ARMA-GARCH model is used to track the dynamic changes of the mean of the voltage and current series, and the GARCH part of the ARMA-GARCH model is used to track the dynamic changes of the variance of the voltage and current series. Among them, the marginal distribution of voltage is fitted to a normal distribution, and the marginal distribution of current is fitted to a T-distribution.

5. The method for analyzing the impact of photovoltaic access current on transformer substation voltage based on the COPULA function according to claim 1, characterized in that, The construction steps of a time-varying Gaussian Copula model include: By using the inverse cumulative distribution function of the marginal distribution, the standardized residuals of voltage and current are transformed into uniformly distributed samples; Fisher transform is applied to the correlation coefficients of uniformly distributed samples to convert bounded correlation coefficients into unbounded continuous variables. A first-order autoregressive model is established for the transformed continuous variables, and the model parameters are solved by maximum likelihood estimation. The continuous variable values ​​at the next time step are predicted based on a first-order autoregressive model, and the time-varying correlation coefficients are obtained by restoring them through Fisher inverse transform.

6. The method for analyzing the impact of photovoltaic access current on transformer substation voltage based on the COPULA function according to claim 1, characterized in that, The steps of the maximum likelihood estimation method are as follows: First, the unknown parameters in the dynamic marginal distribution model are solved by maximum likelihood estimation to obtain the calibrated dynamic marginal distribution parameters. Then, the calibrated dynamic marginal distribution parameters are substituted into the likelihood function of the time-varying Gaussian Copula model, and maximum likelihood estimation is performed again to solve for the unknown parameters in the time-varying Gaussian Copula model that characterize the dynamic dependence between variables.

7. The method for analyzing the impact of photovoltaic access current on transformer substation voltage based on the COPULA function according to claim 2, characterized in that, The steps for drawing a quantile dependency structure diagram are as follows: The current and voltage data are sorted from smallest to largest, and multiple quantile points are selected. The correlation coefficient at each quantile point is calculated, and a line graph is plotted with the quantile as the x-axis and the correlation coefficient as the y-axis to show the dependence of photovoltaic current on transformer voltage at different quantile levels.

8. A modeling and analysis system for the joint distribution of photovoltaic current and transformer substation voltage, characterized in that, include: Data acquisition module: Filter photovoltaic user power generation stability areas that meet the requirements, and collect current data of photovoltaic users in the area and voltage data of corresponding terminals in the area; The data preprocessing module is used to perform data quality optimization operations on the current data and voltage data to obtain preprocessed data that meets the modeling requirements. The edge distribution modeling module is used to build a dynamic edge distribution model for the preprocessed data, eliminate autocorrelation and heteroscedasticity, and obtain the standardized residuals of voltage and current. The time-varying Gaussian Copula modeling module is used to capture the dynamic correlation between photovoltaic current and transformer voltage based on a dynamic edge distribution model. The parameter estimation module uses the maximum likelihood estimation method to obtain the unknown parameters that characterize the dynamic dependencies between variables in the time-varying Gaussian Copula model.

9. The modeling and analysis system for the joint distribution of photovoltaic current and transformer substation voltage according to claim 8, characterized in that, Also includes: The model validation and visualization module is used to generate synthetic Copula samples with the same distribution as the original data through inverse probability integral transformation. The statistical characteristics of the original data and the synthetic samples are compared to verify the model fitting effect. The module also generates a three-dimensional surface plot and quantile dependence structure plot of the joint probability density function to analyze the joint distribution characteristics of photovoltaic current and transformer voltage.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device where the computer-readable storage medium is located to perform the method for analyzing the impact of photovoltaic access current on transformer voltage based on the COPULA function as described in any one of claims 1-7.

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