A high-permeability distributed photovoltaic system operation safety analysis method and system

Abstract

The application relates to a high-permeability distributed photovoltaic system operation safety analysis method and system, belongs to the technical field of power system safety evaluation and analysis, and solves the problem of how to improve the calculation efficiency and numerical stability of distributed photovoltaic system risk evaluation; the application is based on the data to perform joint probability distribution modeling, extracts samples as original random variables from the joint probability distribution modeling; based on a self-adaptive order-probability weighted moment-polynomial response surface fitting method, the original random variables are mapped into standard normal variables, and the standard normal variables are expressed in a variable order polynomial form; the application automatically optimizes the optimal order according to the fitting error by presetting the order range, and efficiently solves the polynomial coefficients by using the probability weighted moment and the pre-calculated and stored fixed transformation matrix, compared with a traditional method, the fitting method provided by the application greatly improves the calculation efficiency and numerical stability while improving the adaptability to diversified distribution forms.

Description

Technical Field

[0001] This invention belongs to the field of power system safety assessment and analysis technology, and relates to a method and system for analyzing the operational safety of a high-penetration distributed photovoltaic system. Background Technology

[0002] The penetration rate of distributed photovoltaic (PV) power in the power system has been increasing year by year. The large-scale integration of high-penetration distributed PV systems has gradually transformed the power system from a traditional "source follows load" model to a "source interacts with load" model, posing significant challenges to power flow distribution, voltage stability, and operational safety. Distributed PV output exhibits strong randomness, intermittency, and spatiotemporal correlation, with a complex probability distribution. Traditional normal or single-distribution models are insufficient to accurately characterize the actual statistical characteristics of distributed PV, leading to significant biases in risk assessment results.

[0003] Existing technologies, such as the invention patent with publication number CN106972481A, disclose a method for quantitatively assessing the safety of large-scale charging facilities connected to active distribution networks. First, the annual data is processed and analyzed using probability statistics. Then, the three-point estimation method is used to solve the uncertain power flow calculation simulation. Finally, the safety quantitative assessment method based on fuzzy matter-element analysis is used to integrate and assess a single indicator to obtain a quantitative value, thus representing the fuzzy safety issues with specific values. However, the new power system risk assessment method still has the following limitations: (1) The traditional Monte Carlo simulation method has a large computational load and takes a long time, making it difficult to meet the needs of online assessment and rapid decision-making. (2) The traditional probabilistic power flow calculation method based on point estimation or fixed-order semi-invariant method has limited accuracy when dealing with non-normal and multi-peak related variables. (3) Most existing risk assessment methods consider a single risk dimension and have not considered coupling the severity of exceeding the limit as an independent dimension for assessment. The physical meaning of the risk indicators is unclear. (4) Existing assessment methods lack adaptive distribution fitting and correlation conversion mechanisms, resulting in insufficient adaptability of the model to different photovoltaic penetration scenarios.

[0004] In the current construction of new power systems, the operation mode of the power grid is becoming increasingly complex. There is an urgent need for an analytical method that can accurately characterize the complex characteristics of photovoltaic power output, efficiently handle the correlation of variables, and scientifically quantify operational risks. This method has important engineering application value for improving the power grid's carrying capacity for high proportions of new energy sources, preventing voltage overruns and equipment overloads, and ensuring the safe and stable operation of the power system. Summary of the Invention

[0005] The technical problem to be solved by this invention is how to improve the computational efficiency and numerical stability of risk assessment for distributed photovoltaic systems.

[0006] The present invention solves the above-mentioned technical problems through the following technical solutions:

[0007] A method for operational safety analysis of a high-penetration distributed photovoltaic system includes the following steps:

[0008] Historical output data of distributed photovoltaic power generation in different regions were collected and normalized. Based on the data, a joint probability distribution model was performed, and samples were extracted as original random variables. Based on the adaptive order-probability weighted moment-polynomial response surface fitting method, the original random variables were mapped to standard normal variables, and the standard normal variables were expressed as variable order polynomials.

[0009] The Nataf transformation is performed based on the variable-order polynomial form to convert the correlated photovoltaic output random variable set into an independent standard normal random variable set; probabilistic power flow calculation is performed on the standard normal random variable set to obtain the probability distribution of node voltage and line power flow state variables; risk assessment is performed based on the probability distribution to obtain system operation risk indicators;

[0010] The variable-order polynomial is represented using the following logic:

[0011]

[0012] in, For the original random variable, Let be the coefficients of the polynomial of order k with the i-th variable. Let be the i-th variable and be a standard normal variable of order k, where m is the order of the polynomial.

[0013] Furthermore, the method also includes:

[0014] For various pre-defined distributed photovoltaic penetration scenarios, risk assessment results and risk mitigation strategies are output.

[0015] Furthermore, the joint probability distribution modeling specifically involves:

[0016] First, a two-stage adaptive clustering initialization strategy is adopted to optimize the historical photovoltaic power output data in two stages. Then, the joint probability distribution characteristics of photovoltaic power output are modeled using the SA-GMM model, and the probability density function is output. The two-stage adaptive clustering initialization strategy includes:

[0017] In the first stage, coarse-grained segmentation of historical photovoltaic data was performed based on improved BWP-AP clustering:

[0018] First, construct the sample similarity matrix. M is the total number of samples, and then the preference parameters are defined. Feasible range , This indicates the prior tendency to select this cluster center. These are the lower and upper limits of the preference parameter, respectively. Then, in the parameter... Within the search space, the following adaptive optimization process is performed:

[0019]

[0020] in, For optimal parameter values, Preference parameters For each candidate parameter value, AP clustering is performed based on the corresponding BWP value. By iteratively updating the responsibility matrix R and availability matrix A, the number of clusters K and the set of cluster centers are obtained. Introduce inter-class / intra-class partitioning index As a clustering quality evaluation standard, the inter-cluster / intra-cluster partitioning index is represented by the following logic:

[0021]

[0022] in, These represent the average distances between and within classes, respectively; based on preset preference parameters. search space Within the framework, the optimal parameter values ​​are adaptively determined with the goal of maximizing BWP. The output corresponds to Number of candidate clusters and set of candidate cluster centers ,in For the first Cluster centers;

[0023] In the second stage, starting with the AP clustering results, K-means++ iteration is performed to recalculate the optimal centers. The recalculated optimal data is then modeled using the SA-GMM joint probability distribution.

[0024] Furthermore, the probability density function Using the following logical representation:

[0025]

[0026] in, As weight, The first The mean vector and covariance matrix of each Gaussian component. For the first The probability density function of Gaussian components.

[0027] Furthermore, the adaptive order-probability weighted moment-polynomial response surface fitting method is specifically as follows:

[0028] Calculate the probability weighted moments of each order of the sample; based on the principle of minimizing fitting error, adaptively select the optimal polynomial order within a preset order range; and linearly transform the probability weighted moment vector into a polynomial coefficient vector based on the fixed transformation matrix corresponding to the optimal polynomial order.

[0029] Furthermore, the step of adaptively selecting the optimal polynomial order within a preset order range based on the principle of minimizing fitting error specifically involves:

[0030] The maximum order M is preset.

[0031] The fitting error of polynomial response surfaces of orders 1 to M to the empirical distribution is calculated sequentially.

[0032] The order that minimizes the fitting error is selected as the optimal order.

[0033] Furthermore, the linear transformation of the probability weighted moment vector into a polynomial coefficient vector based on the fixed transformation matrix corresponding to the optimal polynomial order specifically involves:

[0034] For any polynomial order m, there exists a unique 3D fixed transformation matrix This makes the polynomial coefficient vector With probability weighted moment vector The following linear relationship is satisfied:

[0035]

[0036] in, This is the (i+1)-dimensional probability weighted moment vector; there is a recursive relationship between transformation matrices of different orders, with lower-order matrices being submatrices of higher-order matrices; the polynomial coefficient vector is obtained directly through a single matrix multiplication.

[0037]

[0038] in, Let be a vector consisting of all polynomial coefficients corresponding to the i-th variable. It is a vector The m-th element in the polynomial is the coefficient of the i-th variable and the polynomial of order m.

[0039] Furthermore, probabilistic power flow calculations are performed on the standard normal random variable set to obtain the probability distributions of node voltage and line power flow state variables, including the following:

[0040] Based on the linearized power flow equations and the semi-invariant method, probabilistic power flow calculations are performed on the standard normal random variable set to obtain the semi-invariants of each order of node voltage and line power flow state variables.

[0041] The probability distributions of node voltage and line power flow state variables are obtained based on the statistical moment spectrum decomposition distribution reconstruction method.

[0042] Furthermore, based on the linearized power flow equations and the semi-invariant method, probabilistic power flow calculations are performed on the standard normal random variable set to obtain the following semi-invariants of each order for node voltage and line power flow state variables:

[0043] The central theory is used to calculate the semi-invariants of each order of independent standard normal random variables. Then, based on the linearized AC power flow equations, the semi-invariants of each order of random variables under linear transformation are used to obtain the semi-invariants of each order of node voltage and line power flow state variables through convolution operation. The node voltage and line power flow state variables include node voltage magnitude, phase angle, active power flow, and reactive power flow.

[0044] Furthermore, the probability distributions of node voltages and line power flow state variables obtained by the statistical moment spectrum decomposition distribution reconstruction method include the following:

[0045] Substituting the semi-invariants of each order of the obtained state variables into the Cornish-Fisher series expansion, the complete probability distribution information is restored from the semi-invariants of each order of the state variables, and the cumulative distribution function and probability density function of node voltage and line power flow are reconstructed.

[0046] Furthermore, the risk assessment performed based on the probability distribution to obtain system operation risk indicators includes the following:

[0047] Taking node voltage state variables and line power flow state variables as evaluation objects, calculate the independent risk index for each evaluation object, including node voltage overload risk value and line power flow overload risk value, and solve it by integrating the corresponding probability density function and the preset overload severity function.

[0048] The system comprehensive risk index is obtained by weighting and summing the node voltage over-limit risk value and the line power flow overload risk value based on multi-dimensional weights.

[0049] Furthermore, the severity function of the over-limit is in the form of an exponential utility function, derived from the severity function of the over-limit at node voltages. and the function of severity of line power flow overload Composition, using the following logic to represent the severity function of node voltage. :

[0050]

[0051] in, This indicates an exponential operation. For the actual observed or instantaneous value of the node voltage, when It is undervoltage. This is a safe zone. This is an overvoltage. These are the severity sensitivity coefficients for undervoltage and overvoltage, respectively, used to determine the rate at which severity increases with the depth of exceedance. ;

[0052] The severity function of line power flow can be represented using the following logic. :

[0053]

[0054] in, These are the actual observed or instantaneous values ​​of the power flow along the line. This represents the thermal stability limit of the circuit. The sensitivity coefficient for current overload.

[0055] Furthermore, the node voltage over-limit risk value is represented using the following logic:

[0056]

[0057] in, For the first Risk value of voltage exceeding limit at individual nodes. Let be the probability density function of the node voltage; the line power flow overload risk value is represented using the following logic:

[0058]

[0059] in, For the first Each line has a power flow overload risk value. Let be the probability density function of the power flow of the line.

[0060] Furthermore, the system's comprehensive risk index is represented using the following logic:

[0061]

[0062]

[0063]

[0064] in, These are system voltage and power flow overload risk, respectively. These are the multi-dimensional weights corresponding to the risk values ​​of node voltage exceeding limits and line power flow overload, respectively. For comprehensive system risks, and These represent the weighted sum of the node voltage over-limit risk values ​​for all devices and the weighted sum of the line power flow overload risk values, respectively.

[0065] Corresponding to the above method, the present invention also provides a high-penetration distributed photovoltaic system operation safety analysis system, comprising:

[0066] The probability distribution modeling module is used to collect historical output data of distributed photovoltaic power generation in different regions and perform normalization processing; based on the data, joint probability distribution modeling is performed, and samples are extracted from it as original random variables;

[0067] The polynomial response surface fitting module, based on the adaptive order-probability weighted moment-polynomial response surface fitting method, maps the original random variables to standard normal variables and expresses the standard normal variables in the form of a variable order polynomial.

[0068] The probabilistic power flow calculation module performs Nataf transformation based on a variable-order polynomial form to convert a set of correlated photovoltaic output random variables into a set of mutually independent standard normal random variables; it then performs probabilistic power flow calculation on the set of standard normal random variables to obtain the probability distribution of node voltage and line power flow state variables.

[0069] The risk assessment module performs risk assessment based on the probability distribution to obtain system operation risk indicators;

[0070] The variable-order polynomial is represented using the following logic:

[0071]

[0072] in, For the original random variable, Let be the coefficients of the polynomial of order k with the i-th variable. Let be the i-th variable and be a standard normal variable of order k, where m is the order of the polynomial.

[0073] Furthermore, the system also includes:

[0074] The strategy generation module is used to output risk assessment results and risk mitigation strategies for various preset distributed photovoltaic penetration scenarios.

[0075] The advantages of this invention are:

[0076] (1) This invention proposes a method for analyzing the operational safety of high-penetration distributed photovoltaic (PV) systems that integrates adaptive modeling, probabilistic weighted moment response surface methodology, correlation transformation, and dual-layer coupling risk assessment. First, it improves the ability to characterize complex distribution patterns by fitting the multi-peak non-normal joint distribution of distributed PV output. Second, based on the adaptive order polynomial response surface methodology using probabilistic weighted moments and a fixed transformation matrix, it efficiently and accurately maps probability distribution samples from original random variables to standard normal variables, completely replacing the traditional third-order polynomial normal transformation and overcoming the underfitting or overfitting problems caused by its fixed order. Third, it constructs an efficient probabilistic power flow calculation system by combining the cumulant convolution probabilistic power flow algorithm with statistical moment spectrum decomposition distribution reconstruction. Finally, by performing risk assessment based on the probability distribution, it can clearly separate the probability of risk occurrence from the severity of consequences, making the physical meaning of risk indicators clear and traceable. This invention is particularly suitable for distribution and transmission networks with high-penetration distributed PV access, used to quantitatively analyze their voltage overrun and line overload operation risks, achieving accurate and efficient quantification of power system operational risks under the background of distributed PV access.

[0077] This invention significantly improves the accuracy of risk assessment while ensuring computational efficiency. Compared with existing Monte Carlo simulations, it significantly reduces computation time and can accurately quantify the system operation risks under high-penetration distributed photovoltaic access. It clearly reveals the nonlinear growth law of risk with increasing penetration rate, providing advanced and reliable technical support for power grid planning, operation and risk prevention and control.

[0078] (2) This invention employs an adaptive Gaussian mixture model (SA-GMM) based on improved nearest neighbor propagation clustering to model the joint probability distribution of distributed photovoltaic power output. By introducing the inter-class and intra-class distance partitioning (BWP) index, the clustering process is dynamically optimized, and the optimal number of sub-Gaussian components and initial parameters are adaptively determined. This effectively solves the problems of traditional GMM requiring prior setting of the number of components and being sensitive to initial values, significantly improving the fitting accuracy of complex distribution patterns. In addition, this invention introduces the K-means++ algorithm to perform a single refinement iteration on candidate center points, effectively overcoming the shortcomings of traditional Gaussian mixture models that are sensitive to initial values ​​and require prior setting of the number of clusters, significantly improving the model's fitting accuracy and stability for multimodal, non-normal, and asymmetric distribution functions. Finally, the probability density function of SA-GMM can be expressed as a weighted sum of multiple Gaussian components, enabling it to flexibly approximate joint distributions of arbitrary shapes.

[0079] (3) This invention proposes an adaptive order-probability weighted moment-polynomial response surface fitting method, which achieves efficient analytical expression of complex distributions and serves subsequent Nataf transforms. By pre-setting the order range and automatically selecting the optimal order based on the fitting error, and by using probability weighted moments combined with a pre-calculated and stored fixed transformation matrix to efficiently solve the polynomial coefficients, this method avoids the complex numerical integration or solving ill-conditioned equations process in traditional polynomial chaotic expansion and other methods. While retaining the efficiency advantages of traditional polynomial normal transform (TPNT), this method significantly improves its fitting ability and flexibility for diverse distribution forms through an adaptive order mechanism, achieving performance improvement and complete replacement of the traditional TPNT method. Compared with traditional methods, the fitting method proposed in this invention greatly improves computational efficiency and numerical stability while enhancing adaptability to diverse distribution forms.

[0080] (4) The probability-severity dual-layer coupled risk assessment architecture constructed in this invention achieves accurate quantification of equipment-level risks by integrating a piecewise exponential severity function with a state variable probability density function in the first layer. In the second layer, it integrates factors such as equipment importance, photovoltaic penetration rate, and voltage sensitivity through a multi-dimensional weight system including the analytic hierarchy process, achieving an objective assessment of system-level comprehensive risks. This method clearly separates the probability of risk occurrence from the severity of its consequences, overcoming the limitations of traditional methods with their single risk dimension and ambiguous physical meaning. It can intuitively identify high-risk areas and weak links, and generate targeted risk mitigation strategies such as reactive power compensation and line expansion, directly supporting power grid operation control decisions. Attached Figure Description

[0081] Figure 1 This is a flowchart of the high-penetration distributed photovoltaic system operation safety analysis method according to Embodiment 1 of the present invention;

[0082] Figure 2 This is a schematic diagram of the execution logic of steps S1 to S7 in Embodiment 1 of the present invention;

[0083] Figure 3 This is a schematic diagram of step S3 of embodiment one of the present invention, which involves polynomial response surface transformation and independence conversion;

[0084] Figure 4 This is a schematic diagram of power flow calculation in steps S4-S5 of Embodiment 1 of the present invention;

[0085] Figure 5 This is a schematic diagram of step S6 of Embodiment 1 of the present invention, which involves a two-layer coupling risk assessment.

[0086] Figure 6 This is a comparison chart of the sample data of distributed photovoltaic power output and the joint probability density distribution of the SA-GMM model in Embodiment 2 of the present invention;

[0087] Figure 7 This is a schematic diagram of the risk indicators of each load node under different distributed photovoltaic penetration scenarios in Embodiment 2 of the present invention. Detailed Implementation

[0088] 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 in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0089] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0090] Example 1

[0091] like Figure 1 , Figure 2 As shown, specifically, a method for analyzing the operational safety of a high-penetration distributed photovoltaic system is disclosed, including the following steps:

[0092] S1, Data Acquisition and SA-GMM Joint Probability Distribution Modeling: Historical output data of distributed photovoltaic power generation in different regions is collected and normalized; an adaptive Gaussian mixture model (SA-GMM) based on improved nearest neighbor propagation clustering (AP clustering) is used to model the joint probability distribution, fitting the multi-peak non-normal joint probability distribution characteristics of photovoltaic output, and utilizing the probability density function. express.

[0093] Compared to existing technologies, such as the invention patent with publication number CN117977596A, which only uses the BWP (between-intra-class distance) index to adjust the reference degree to determine the cluster center and directly uses the AP clustering result as the initial value of GMM (Gaussian Mixture Model), the number of clusters is entirely determined by the AP clustering adaptively, which belongs to single AP clustering guidance. In step S1 of this embodiment, historical output data is first collected from distributed photovoltaic monitoring platforms in different regions and normalized to eliminate the difference in dimensions between data. Then, considering the multi-peak, non-normal, and complex characteristics of photovoltaic output, an SA-GMM model is established to model the joint probability distribution of photovoltaic output. First, a two-stage adaptive clustering initialization strategy is used to optimize the historical photovoltaic output data in two stages. Then, the SA-GMM model is used to model the joint probability distribution characteristics of photovoltaic output and output the probability density function. .

[0094] In this embodiment, the two-stage adaptive clustering initialization strategy includes:

[0095] In the first stage, historical photovoltaic data was coarsely partitioned based on improved BWP-AP clustering, and preference parameters in AP clustering were automatically optimized. The adaptive determination of the number and centers of clusters is carried out through the following steps:

[0096] First, construct the sample similarity matrix. M is the total number of samples, and then the preference parameters are defined. Feasible range , This indicates the prior tendency to be selected as a cluster center, which directly affects the number of clusters and the quality of the centers. These are the lower and upper limits of the preference parameter, respectively. Then, in the parameter... Within the search space, the following adaptive optimization process is performed:

[0097]

[0098] in, For optimal parameter values, Preference parameters For each candidate parameter value, AP clustering is performed based on the corresponding BWP value. By iteratively updating the responsibility matrix R and availability matrix A, the number of clusters K and the set of cluster centers are obtained. Introduce inter-class / intra-class partitioning index As a clustering quality evaluation standard, the inter-cluster / intra-cluster partitioning index is represented by the following logic:

[0099]

[0100] in, The average distances between and within classes are calculated using the following logic:

[0101]

[0102]

[0103] Where K is the number of clusters, The first , , Cluster center, For the first The cluster sample set, M is the total number of samples, representing the total number of historical photovoltaic power output data points used for clustering, and x is a single sample vector, representing a photovoltaic power output observation data point at a specific moment after normalization, which is a multi-dimensional vector.

[0104] In preset preference parameters search space Within the framework, the optimal parameter values ​​are adaptively determined with the goal of maximizing BWP. The output corresponds to Number of candidate clusters and set of candidate cluster centers ,in For the first Cluster centers.

[0105] In the second stage, starting with the AP clustering results, K-means++ iteration is performed to recalculate the optimal centers. The recalculated optimal data is then modeled using the SA-GMM joint probability distribution.

[0106] In this embodiment, the second stage uses the candidate centers output from the first stage as the initial center set for the K-means++ algorithm, and performs a single refinement iteration. The iteration process includes sample allocation, center update, covariance initialization, and mixed weight initialization, and iteratively outputs the number of clusters. Using the initial parameter set of the GMM and the above results as input, the probability density function is output through the SA-GMM model. This characterizes the joint probability distribution characteristics of photovoltaic power output. The probability density function described in this embodiment... It can be expressed as a weighted sum of multiple Gaussian components, making the output probability density function... It can flexibly approximate the joint distribution of photovoltaic treatment under arbitrary conditions, using the following logical representation:

[0107]

[0108] in, As weight, The first The mean vector and covariance matrix of each Gaussian component. For the first The probability density function of Gaussian components.

[0109] In this embodiment, an adaptive Gaussian mixture model (SA-GMM) based on improved nearest neighbor propagation clustering is used to model the joint probability distribution of distributed photovoltaic power output. By introducing the inter-class and intra-class distance partitioning (BWP) index, the clustering process is dynamically optimized, and the optimal number of sub-Gaussian components and initial parameters are adaptively determined. This effectively solves the problems of traditional GMM, which requires prior setting of the number of components and is sensitive to initial values, significantly improving the fitting accuracy of complex distribution patterns. In addition, this embodiment introduces the K-means++ algorithm to perform a single refinement iteration on candidate centroids, effectively overcoming the shortcomings of traditional Gaussian mixture models, such as sensitivity to initial values ​​and the need for prior setting of the number of clusters. This significantly improves the model's fitting accuracy and stability for multimodal, non-normal, and asymmetric distribution functions. Finally, the probability density function of SA-GMM can be expressed as a weighted sum of multiple Gaussian components, enabling it to flexibly approximate joint distributions of arbitrary shapes.

[0110] S2, Adaptive order probability weighted moment polynomial response surface fitting: from the probability distribution function Samples were drawn from the original random variable. Based on the adaptive order-probability weighted moment-polynomial response surface fitting method, the original random variables are... Mapped to standard normal variables The standard normal variable can be expressed as a polynomial of variable order using the following logical representation:

[0111]

[0112] in, Let be the coefficients of the polynomial of order k with the i-th variable. Let be the i-th variable and be a standard normal variable of order k, where m is the order of the polynomial.

[0113] like Figure 3 As shown, in this embodiment, the adaptive order-probability weighted moment-polynomial response surface fitting method specifically includes:

[0114] S21, Calculate the probability-weighted moments (PWM) of each order for the samples. Specifically, in this embodiment, the probability-weighted moment vectors of each order are calculated using a sampling point numerical estimation method, including the following:

[0115] First, for the original random variable of The sample values, arranged in ascending order, constitute the order statistic. Define the r-th order probability weighted moment Represented as ,in The cumulative distribution function is raised to the power of r. Represents the original random variable itself. The value of the cumulative distribution function is represented by the power of r. This represents the mathematical expectation operator.

[0116] Next, the unbiased estimator is calculated as the weighted moment vector of each probability order using the sampling point numerical estimation method, and is represented by the following logic:

[0117]

[0118] in, Let be the probability weighted moment vector of order r. , Let be the j-th sample observation value of the i-th random variable.

[0119] S22, based on the principle of minimizing fitting error, adaptively select the optimal polynomial order within a preset order range.

[0120] Specifically, firstly, a maximum order M is preset, and the fitting error of polynomial response surfaces of orders 1 to M to the empirical distribution is calculated sequentially; then, the order that minimizes the fitting error is selected as the optimal polynomial order m.

[0121] In a preferred embodiment, the fitting error can be any one of mean absolute error, mean square error, or mean absolute percentage error.

[0122] S23, based on the fixed transformation matrix corresponding to the optimal polynomial order, linearly transforms the probability weighted moment vector into a polynomial coefficient vector.

[0123] Specifically, for any polynomial order m, there exists a unique 3D fixed transformation matrix This makes the polynomial coefficient vector With probability weighted moment vector The following linear relationship is satisfied:

[0124]

[0125] in, This is the (i+1)-dimensional probability weighted moment vector; there is a recursive relationship between transformation matrices of different orders, with lower-order matrices being submatrices of higher-order matrices; the polynomial coefficient vector is obtained directly through a single matrix multiplication.

[0126]

[0127] in, Let be a vector consisting of all polynomial coefficients corresponding to the i-th variable. It is a vector The m-th element in the polynomial is the coefficient of the i-th variable and the polynomial of order m.

[0128] This invention proposes an adaptive order-probability weighted moment-polynomial response surface fitting method, achieving efficient analytical representation of complex distributions and serving subsequent Nataf transforms. While retaining the efficiency advantages of traditional polynomial normal transform (TPNT), this method significantly improves its fitting ability and flexibility for diverse distribution patterns through an adaptive order mechanism, achieving performance improvement and complete replacement of the traditional TPNT method. Compared with traditional methods, step S2 avoids complex integration operations, significantly improving computational efficiency and numerical stability. This improvement solves the potential underfitting or overfitting problems of traditional TPNT methods due to their fixed order, laying a solid foundation for subsequent high-precision probabilistic power flow calculations.

[0129] S3, Transformation and Independence Transformation Based on Sequence Polynomial Response Surface: Based on the variable-order polynomial of S2, the Nataf transformation is performed to convert the correlated photovoltaic output random variables into a set of mutually independent standard normal random variables.

[0130] In this embodiment, since the input variables are required to be independent when using the semi-invariant method for probabilistic power flow calculation in the subsequent stage, in order to handle the spatial correlation between distributed photovoltaic power output data, this embodiment uses the Nataf transform based on adaptive order-probability weighted moment-polynomial response surface fitting in S2 to replace the traditional fixed third-order polynomial normal estimation method (TPNT).

[0131] Specifically, firstly, a variable-order polynomial is used to map the correlated photovoltaic output random variables into independent standard normal variables. The same steps as in S2 are then used to solve for the optimal polynomial order, probability weighted moments, fixed transformation matrix, and polynomial coefficients. The correlated photovoltaic output random variables are the same as in step S2, specifically derived from the probability distribution function. To illustrate the linear correlation between photovoltaic power output variables in different regions, a correlation matrix of random variables was drawn from the sample. It can be estimated from historical output data samples or pre-set based on the geographical location and meteorological correlation of the photovoltaic cluster.

[0132] The correlation matrix was processed using Cholesky decomposition. For intermediate variable groups Perform a discorrelation linear transformation, where the intermediate variable set It is the set of standard normal variables that has been mapped by the polynomial response surface and has not yet been uncorrelated, i.e., the number of random variables in photovoltaic power output. Let d be a standard normal variable of the d-th dimension, and each standard normal variable is represented by a polynomial response surface. The data consists of standard normal variables that follow a standard normal distribution N(0,1), but the correlation structure between the variables is still maintained as in the original photovoltaic power output data. The lower triangular matrix is ​​obtained by Cholesky decomposition of the correlation matrix. ,satisfy , and then ,but This represents a set of mutually independent standard normal random variables. Let be the d-th dimension standard normal random variable after transformation.

[0133] S4, Cumulative Convolution Probabilistic Power Flow Algorithm: Based on the linearized power flow equation and the semi-invariant method, probabilistic power flow calculations are performed on the standard normal random variable set to obtain the semi-invariants of each order of node voltage and line power flow state variables.

[0134] In this embodiment, using a set of independent standard normal random variables as input, probabilistic power flow calculations are performed on the set of standard normal random variables based on the semi-invariant method and linearized AC power flow equations to solve for the probability distributions of node voltage and line power flow state variables. Specifically, firstly, the semi-invariants of each order of the independent standard normal random variable set are calculated using central theory; then, based on the linearized AC power flow equations, the additivity of the semi-invariants of each order of random variables under linear transformation is utilized. Through convolution operations rather than extensive random sampling, the semi-invariants of each order of node voltage and line power flow state variables are quickly obtained, establishing an efficient probabilistic power flow calculation system that considers the correlation with photovoltaic output. The node voltage and line power flow state variables include node voltage amplitude and phase angle, and active power flow and reactive power flow. This embodiment transforms complex probability distribution convolution operations into simple algebraic operations, resulting in an order-of-magnitude improvement in computational efficiency compared to the Monte Carlo method, while rigorously calculating the impact of photovoltaic output randomness. The specific semi-invariant method and linearized AC power flow equation forms can employ existing technologies and will not be elaborated upon here.

[0135] S5, Statistical Moment Spectrum Decomposition Distribution Reconstruction: Based on the statistical moment spectrum decomposition distribution reconstruction method, the probability distribution of node voltage and line power flow state variables is obtained, including the cumulative distribution function (CDF) and the probability density function (PDF).

[0136] In this embodiment, the statistical moment spectrum decomposition distribution reconstruction method specifically involves substituting the semi-invariants of the state variables obtained in S4 into the Cornish-Fisher series expansion to reconstruct the complete probability distribution information of the state variables from the semi-invariants of each order, thereby reconstructing the cumulative distribution function (CDF) and probability density function (PDF) of node voltage and line power flow. Through this reconstruction method, the quantiles of any non-normally distributed variable are expressed as polynomial functions of the standard normal distribution quantiles, with the coefficients of the polynomial determined by the semi-invariants of the variable. The polynomial expansion of the standard normal quantiles achieves a high-precision approximation of the non-normal distribution. The Cornish-Fisher series expansion can efficiently and accurately reconstruct the cumulative distribution function (CDF) and probability density function (PDF) of system state variables such as node voltage and line power flow, overcoming the limitations of traditional methods that assume a normal distribution of state variables and significantly improving the accuracy of tail probability estimation.

[0137] Furthermore, such as Figure 4 As shown, the Cornish-Fisher series can be used to calculate any quantile of a state variable (such as those of interest in risk analysis). (Quantities). To verify the reconstruction accuracy, the obtained distribution was compared with the Monte Carlo simulation results. If the mean relative error... And the relative error of variance If the accuracy requirement is met, the final probability distribution is output; otherwise, the process returns to adjust the order of the polynomial or the order of the semi-invariant and re-executes the fitting and reconstruction process.

[0138] S6, Probability-Severity Dual-Layer Coupled Risk Assessment: Perform risk assessment based on the probability distribution to obtain system operation risk indicators.

[0139] like Figure 5 As shown, in this embodiment, the risk assessment is a probability-severity dual-layer coupled assessment, including the following:

[0140] The risk layer uses node voltage state variables and line power flow state variables as evaluation objects. It calculates independent risk indicators for each evaluation object, including node voltage overload risk values ​​and line power flow overload risk values, by integrating the corresponding probability density function with a preset overload severity function. The overload severity function adopts an exponential utility function form, derived from the node voltage overload severity function. and the function of severity of line power flow overload Composition; probability density function of node voltage With the probability density function of line power flow Obtained through step S5.

[0141] In this embodiment, the safe operating range of the node voltage is defined as follows: , Let the minimum and maximum values ​​of the node voltage amplitude be represented, and the following logic be used to express the severity function of the node voltage exceedance. :

[0142]

[0143] in, This indicates an exponential operation. For the actual observed or instantaneous value of the node voltage, when It is undervoltage. This is a safe zone. This is an overvoltage. These are the severity sensitivity coefficients for undervoltage and overvoltage, respectively, used to determine the rate at which severity increases with the depth of exceedance. .

[0144] In this embodiment, the line power flow overload severity function is represented by the following logic. :

[0145]

[0146] in, This refers to the actual observed or instantaneous value of the power flow along the line, typically expressed as active power. This represents the thermal stability limit of the circuit. The sensitivity coefficient for current overload.

[0147] In this embodiment, the voltage over-limit risk is used as an example for explanation. The node voltage over-limit risk value is represented using the following logic:

[0148]

[0149] in, For the first Similarly, the risk value of voltage exceeding the limit at each node can be represented using the following logic to indicate the risk value of power flow overload on the line:

[0150]

[0151] in, For the first Each line has a power flow overload risk value.

[0152] The system risk layer, based on a multi-dimensional weighting system considering the importance of integrated equipment nodes, photovoltaic penetration rate, and voltage sensitivity, weights and sums the node voltage exceedance risk value and the line power flow overload risk value to obtain a comprehensive system risk index, which is represented by the following logic:

[0153]

[0154]

[0155]

[0156] in, These are system voltage and power flow overload risk, respectively. These are the multi-dimensional weights corresponding to the risk values ​​of node voltage exceeding limits and line power flow overload, respectively. For comprehensive system risks, and These represent the weighted sum of the node voltage over-limit risk values ​​for all devices and the weighted sum of the line power flow overload risk values ​​for the lines, respectively. In this embodiment, the multi-dimensional weights are determined by scientific methods such as the analytic hierarchy process, taking into account factors such as the importance of the devices, the photovoltaic penetration rate of the nodes, and voltage sensitivity.

[0157] This invention proposes a two-layer coupled assessment architecture that comprehensively considers the risk of each assessment object and the overall system. Compared with traditional methods, which suffer from unclear probability and consequence weights, ambiguous physical meaning, and inability to be optimized specifically, the probability-severity two-layer coupled risk assessment proposed in this invention can clearly separate the assessment of the probability of risk occurrence and the severity of consequences, with clear physical meaning, and has the following advantages:

[0158] (1) The present invention integrates multiple dimensions of objective weights such as equipment importance, photovoltaic penetration rate, and voltage sensitivity, and the design is objective and scientific; (2) Based on the dual-layer coupling risk assessment, a risk spatial distribution map can be generated, which can intuitively identify high-risk areas and weak links, making the risk visible; (3) Four-color risk level can be output to directly guide operation control decisions and make the decision-making efficient; (4) Based on the actual effect of the dual-layer coupling risk assessment, the calculation time of the present invention is more than 90% faster than the traditional Monte Carlo method, the error is controlled within 2.56%, and it can clearly show the trend of node voltage risk increasing by 10 times and power flow risk increasing by 2.4 times when the penetration rate increases from 155% to 235%.

[0159] S7, Multi-scenario Risk Assessment and Strategy Generation: For various preset distributed photovoltaic penetration scenarios, output risk assessment results and risk mitigation strategies.

[0160] In this embodiment, based on the system comprehensive risk index of step S6 Operational risks are divided into four levels; in a preferred embodiment, when the overall system risk... If the risk level is ≤0.1%, the current operational risk level is considered low; if the risk level is <0.1%, the risk level is considered low. When the risk level is ≤0.5%, the current operational risk level is considered medium; when the risk level is <0.5%, the risk level is considered medium. When the risk level is ≤2.0%, the current operational risk level is considered high; when the overall system risk level is... When the risk level is >2.0%, the current operational risk level is considered extremely high. The operational risk level is then correlated with power grid dispatch terminology, and corresponding handling recommendations are formulated as shown in Table 1 below:

[0161] Table 1 System Operation Risk Level Generation Strategy Table

[0162]

[0163] In this embodiment, to analyze the impact of different distributed photovoltaic (PV) access schemes on system security, various distributed PV penetration scenarios are set up. Four typical scenarios based on demand penetration rate (DP) are used as examples. For each typical scenario, steps S1 to S6 are repeated to calculate and compare key indicators such as system voltage exceedance risk and line overload risk, analyzing risk distribution patterns and key weaknesses. Based on the risk assessment results, system weaknesses and high-risk equipment are located, and risk mitigation strategy suggestions are automatically generated. For example, configuring static var generators (SVG) at nodes with high voltage exceedance risk and proposing capacity expansion and modification suggestions for lines with high power flow overload risk. Finally, a comprehensive assessment report is generated, including risk quantification indicators, spatial distribution maps, and an optimization strategy set, providing direct decision support for power grid planning, operation, and upgrades.

[0164] Example 2

[0165] This embodiment uses a typical high-penetration distributed photovoltaic (PV) grid connection case to illustrate the operational safety analysis method for high-penetration distributed PV systems provided in Embodiment 1. This embodiment employs a modified IEEE 14-node test system, connecting distributed PV clusters at nodes 4, 5, 9, 11, 13, and 14, forming four typical scenarios with penetration rates ranging from 154.97% to 234.98%.

[0166] S1', Data Acquisition and SA-GMM Joint Probability Distribution Modeling: Historical distributed photovoltaic power output data for two regions (Region A and Region B) during the period from March to May 2022, between 11:00 and 14:00, were collected from the power grid monitoring system of a province in eastern China. The sampling interval was 15 minutes. The collected raw data was normalized to eliminate the influence of dimensions.

[0167] To address the multi-peak, non-normal distribution characteristics of photovoltaic (PV) output, PV output data from a target region (e.g., region A) is selected, and joint probability distribution models are established with the output data from two other typical regions in the system (e.g., regions B and C). This comprehensively examines the correlation structure between PV output in the target region and different regions. An adaptive Gaussian mixture model (SA-GMM) based on improved nearest neighbor propagation (AP) clustering is employed. By introducing the BWP index to dynamically adjust the clustering reference degree, the optimal number of sub-Gaussian components for each joint distribution model is adaptively determined (e.g., 4 for the AB joint model and 4 for the AC joint model), as shown below. Figure 6 (a) shows the scatter plot of the original photovoltaic power output data in region AB; (b) shows the correlation coefficient structure diagram of region AB after SA-GMM modeling; (c) shows the joint probability density distribution surface of photovoltaic power output in region AB; (d) shows the scatter plot of the original photovoltaic power output data in region AC; (e) shows the correlation coefficient structure diagram of region AC after SA-GMM modeling; and (f) shows the joint probability density distribution surface of photovoltaic power output in region AC.

[0168] Compared with the traditional Gaussian Copula and the standard GMM, the SA-GMM proposed in Example 1 significantly improves the fitting accuracy in the local probability density range, especially in the low probability density region, and reduces the mean absolute error (MAE) by 3.21%-4.61%.

[0169] S2', Adaptive Order Probability Weighted Moment Polynomial Response Surface Fitting: To establish an accurate mapping relationship between the original output variables and the standard normal variables, this embodiment adopts the adaptive order probability weighted moment polynomial response surface method, setting the maximum order M=3, and using the mean absolute error (MAE) as the evaluation index, calculating the fitting errors of the 1st, 2nd, and 3rd order polynomials to the original distribution. The calculation results show that for the data in this case, the 2nd order polynomial has the smallest fitting error (MAE=0.0221), therefore, the optimal order m=2 is adaptively selected. This is achieved through a pre-calculated 2nd order fixed transformation matrix... Weighted moment vector of sample probabilities Multiplication yields a fast polynomial coefficient vector. Establish mapping relationship .

[0170] S3', based on the sequence polynomial response surface Nataf Transformation and Independence Transformation: Based on the adaptive polynomial response surface obtained from S2', perform... Nataf Transformation is used to convert correlated variables into independent variables. A , B Original related variable set of regional photovoltaic power output Transformed into a group of correlated normal variables through polynomial mapping. Then through Cholesky Decomposition Calculation Nataf Transformation matrix B ultimately yields a set of mutually independent standardized normal variables. Upon testing, the transformed variables... and The correlation coefficient decreased from the original 0.8856 to 0.0023, verifying the effectiveness of the transformation. This allowed step S3' to completely replace the traditional improved third-order polynomial normal estimation (TPNT) method, achieving improved transformation accuracy through an order adaptive mechanism.

[0171] S4', Cumulative Convolutional Probabilistic Power Flow Algorithm: After obtaining independent standard normal input variable sets... Z Based on this, a semi-invariant method is employed for efficient probabilistic power flow calculation. Specifically, firstly, based on the modified IEEE 14-node system, linearization is performed at the convergence point of the deterministic power flow calculation to obtain the Jacobian matrix. and sensitivity matrix Next, the independent normal variables were calculated using the central theory. Z The semi-invariants of each order, specifically the first to fourth orders, are obtained through convolution operations to obtain the semi-invariants of each order of random disturbances of injected power at nodes. Then, the first to fourth orders of semi-invariants of all node voltages and line power flow state variables are quickly calculated according to the linearized power flow equations, and are represented by the following logic:

[0172]

[0173]

[0174] in, The k-th order semi-invariant representing the node voltage deviation (including magnitude and phase angle) and Let be the k-th order semi-invariants of the random perturbations injected into the active and reactive power nodes, respectively. Let be the k-th semi-invariant representing the active power flow of the line. The entire process avoids large-scale random sampling, and the computational efficiency is improved by an order of magnitude compared to Monte Carlo simulation.

[0175] S5', Statistical Moment Spectrum Decomposition and Distribution Reconstruction: Substitute the semi-invariants of the node voltages and line power flows obtained in S4' into the normal measure disturbance series expansion formula. This embodiment uses the voltage of node 7 as an example for illustration; its cumulative distribution function's α quantile can be calculated by the following formula:

[0176]

[0177] in, for, For standard normal quantiles, , for, The probability density functions of the voltages at nodes 7, 11, and 13 are reconstructed using the expansion of the third-order and fourth-order semi-invariants, respectively.

[0178] S6', Probability-Severity Two-Layer Coupled Risk Assessment: Based on the probability distribution of reconstructed state variables, a two-layer coupled risk assessment is performed to obtain system operation risk indicators.

[0179] At the object risk layer, the voltage over-limit risk is calculated for each load node (PQ node). .

[0180] At the system risk level, a comprehensive weighting system is established to calculate system voltage risk. .

[0181] S7', Multi-scenario Risk Assessment and Strategy Generation:

[0182] like Figure 7 The figures show the permeability at different rates. PQ The calculation results of the node voltage over-limit risk index intuitively show the trend of risk change with the increase of penetration rate. This embodiment, based on actual grid operation, sets up four distributed photovoltaic penetration rate scenarios with penetration rates of 154.97%, 176.43%, 195.02%, and 234.98%, corresponding to different photovoltaic access nodes and capacity configurations. Figure 7 Figure (a) shows the distribution of system voltage exceedance risk under different penetration rate scenarios, illustrating the voltage exceedance risk values ​​of each load node (PQ node) under four typical photovoltaic penetration rates. As can be seen from the figure, as the penetration rate increases from 154.97% to 234.98%, the voltage risk of each node increases non-linearly, especially at the end nodes (such as node 14) and nodes near the photovoltaic access point, where the system voltage operation risk increases from 0.1078% to 1.1050%, expanding by 10.25 times. This vividly reveals the cumulative impact of high-penetration photovoltaic access on voltage safety.

[0183] and Figure 7 Figure (b) shows the trend of voltage exceedance risk at critical nodes as a function of penetration rate, focusing on three critical load nodes (nodes 7, 4, and 11) and illustrating the changing trend of their voltage exceedance risk with increasing photovoltaic penetration rate. The results show that as penetration rate increases, the voltage risk at each critical node continues to grow, and the growth rate varies at different penetration rate stages: after penetration rate exceeds 200%, the risk growth slope at node 11 increases significantly, indicating that this node is more sensitive to high-penetration photovoltaic grid connection. This figure further reveals the differentiated response characteristics of nodes at different locations within the system to changes in photovoltaic penetration rate, helping to identify the weakest nodes in voltage security.

[0184] The computational efficiency and accuracy of the high-penetration distributed photovoltaic system operation safety analysis method provided in Example 1 are quantitatively evaluated using the following indicators:

[0185] (1) The probability distribution fitting adopts the mean absolute error index. Quantitative assessment:

[0186]

[0187] in, These are empirical probability density values. To fit the probability density values, This represents the number of sampling points.

[0188] (2) The mean absolute percentage error index of the mean and variance is used in the probabilistic power flow calculation. , Quantitative assessment:

[0189]

[0190]

[0191] in, The total number of nodes to be evaluated. For the first The mean of the probability distribution of the state variables. The first Monte Carlo simulation (MCS) calculated for the The mean of the probability distribution of the state variables. For the first The variance of the probability distribution of the state variables. The first Monte Carlo simulation (MCS) calculated for the The variance of the probability distribution of the state variables.

[0192] Based on the above-mentioned quantitative evaluation indicators, the results calculated by the risk assessment Monte Carlo simulation (MCS) in this embodiment have an error of no more than 2.56% compared with the traditional Monte Carlo simulation results, while the calculation time is reduced by more than 90% compared with Monte Carlo simulation.

[0193] like Figure 7As shown, comparing the risk assessment results of the four scenarios reveals that as the penetration rate increases from 154.97% to 234.98%, the system voltage operation risk increases from 0.1078% to 1.1050%, a 10.25-fold increase. The key weak links are end node 14 and the lines connecting to the main grid (lines 1-2 and 2-3). Based on this, the system automatically generates a risk mitigation strategy suggestion: configuring a Static Var Generator (SVG) with a capacity of 20% of the photovoltaic capacity at node 14 can reduce the voltage risk in scenario 4 from 1.1050% to 0.9750%.

[0194] Furthermore, to objectively evaluate the superiority of the method provided in Embodiment 1, this embodiment was compared with a large-scale Monte Carlo simulation (MCS, 15,000 samplings) on the same test system. Table 2 below shows the efficiency comparison of the two methods in calculating the node voltage probability distribution, and Table 3 below shows the accuracy comparison of the risk assessment results of this embodiment under different scenarios. From Tables 2 and 3... Figure 7 As can be seen, the method of the present invention significantly reduces the computation time to 2.43 seconds compared to the 31.03 seconds of the MCS result, improving performance by 92.2%, while maintaining a high level of computational accuracy: the mean error of voltage amplitude is 0.0169%, the variance error is 1.4104%, and the maximum error of the risk assessment result is only 2.56%. This fully demonstrates that this embodiment has significant advantages in computational accuracy, efficiency, and practicality when dealing with the risk assessment problem of high-penetration distributed photovoltaic systems, providing an advanced and reliable technical solution for the safe operation and risk prevention of power systems.

[0195] Table 2 Comparison of probability distribution calculation efficiency between this embodiment and MCS

[0196]

[0197] Table 3 Comparison of computational accuracy between this embodiment and MCS in different scenarios

[0198]

[0199] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing the operational safety of a high-penetration distributed photovoltaic system, characterized in that, include: Historical power output data of distributed photovoltaic (PV) power generation in different regions is collected and normalized. Based on this data, a joint probability distribution model is performed, from which samples are extracted as original random variables. Specifically, the joint probability distribution modeling involves: employing a two-stage adaptive clustering initialization strategy to optimize the historical PV power output data in two stages; then, using an SA-GMM model to model the joint probability distribution characteristics of PV power output, and outputting a probability density function. The two-stage adaptive clustering initialization strategy includes: In the first stage, the historical photovoltaic data was divided into coarse-grained segments based on the improved BWP-AP clustering. In the second stage, starting with the AP clustering results, K-means++ iteration is performed to recalculate the optimal center. The recalculated optimal data is modeled using the SA-GMM joint probability distribution. Based on the adaptive order-probability weighted moment-polynomial response surface fitting method, the original random variables are mapped to standard normal variables, and the standard normal variables are expressed in the form of a variable-order polynomial; wherein, the adaptive order-probability weighted moment-polynomial response surface fitting method specifically refers to: Calculate the probability weighted moments of each order for the samples; adaptively select the optimal polynomial order within a preset order range based on the principle of minimizing fitting error; linearly transform the probability weighted moment vector into a polynomial coefficient vector based on the fixed transformation matrix corresponding to the optimal polynomial order; where, for any polynomial order m, there exists a unique... 3D fixed transformation matrix This makes the polynomial coefficient vector With probability weighted moment vector Satisfies a linear relationship: , It is an m+1 dimensional probability weighted moment vector; The Nataf transformation is performed based on the variable-order polynomial form to convert the correlated photovoltaic output random variable set into an independent standard normal random variable set; probabilistic power flow calculation is performed on the standard normal random variable set to obtain the probability distribution of node voltage and line power flow state variables; risk assessment is performed based on the probability distribution to obtain system operation risk indicators; The variable-order polynomial is represented using the following logic: in, For the original random variable, Let be the coefficients of the polynomial of order k with the i-th variable. Let be the i-th variable and be a standard normal variable of order k, where m is the order of the polynomial.

2. The method for analyzing the operational safety of a high-penetration distributed photovoltaic system according to claim 1, characterized in that, The method further includes: For various pre-defined distributed photovoltaic penetration scenarios, risk assessment results and risk mitigation strategies are output.

3. The method for analyzing the operational safety of a high-penetration distributed photovoltaic system according to claim 1, characterized in that, The first stage of the two-stage adaptive clustering initialization strategy is specifically as follows: First, construct the sample similarity matrix. M is the total number of samples, and then the preference parameters are defined. Feasible range , This indicates the prior tendency to select this cluster center. These are the lower and upper limits of the preference parameter, respectively. Then, in the parameter... Within the search space, the following adaptive optimization process is performed: in, For optimal parameter values, Preference parameters For each candidate parameter value, AP clustering is performed based on the corresponding BWP value. By iteratively updating the responsibility matrix R and availability matrix A, the number of clusters K and the set of cluster centers are obtained. Introduce inter-class / intra-class partitioning index As a clustering quality evaluation standard, the inter-cluster / intra-cluster partitioning index is represented by the following logic: in, These represent the average distances between and within classes, respectively; based on preset preference parameters. search space Within the framework, the optimal parameter values ​​are adaptively determined with the goal of maximizing BWP. The output corresponds to Number of candidate clusters and set of candidate cluster centers ,in For the first Cluster centers.

4. The method for analyzing the operational safety of a high-penetration distributed photovoltaic system according to claim 1, characterized in that, The step of adaptively selecting the optimal polynomial order within a preset order range based on the principle of minimizing fitting error specifically involves: The maximum order M is preset. The fitting error of polynomial response surfaces of orders 1 to M to the empirical distribution is calculated sequentially. The order that minimizes the fitting error is selected as the optimal order.

5. The method for analyzing the operational safety of a high-penetration distributed photovoltaic system according to claim 1, characterized in that, For the polynomial coefficient vector There is a recursive relationship between transformation matrices of different orders, with lower-order matrices being submatrices of higher-order matrices; the polynomial coefficient vector can be obtained directly through a single matrix multiplication. in, Let be a vector consisting of all polynomial coefficients corresponding to the i-th variable. It is a vector The m-th element in the polynomial is the coefficient of the i-th variable and the polynomial of order m.

6. The method for analyzing the operational safety of a high-penetration distributed photovoltaic system according to claim 1, characterized in that, Probabilistic power flow calculations are performed on the aforementioned set of standard normal random variables to obtain the probability distributions of node voltage and line power flow state variables, including the following: Based on the linearized power flow equations and the semi-invariant method, probabilistic power flow calculations are performed on the standard normal random variable set to obtain the semi-invariants of each order of node voltage and line power flow state variables. The probability distributions of node voltage and line power flow state variables are obtained based on the statistical moment spectrum decomposition distribution reconstruction method.

7. The method for analyzing the operational safety of a high-penetration distributed photovoltaic system according to claim 1, characterized in that, The risk assessment performed based on the probability distribution yields system operational risk indicators including the following: Taking node voltage state variables and line power flow state variables as evaluation objects, calculate the independent risk index for each evaluation object, including node voltage overload risk value and line power flow overload risk value, and solve it by integrating the corresponding probability density function and the preset overload severity function. The system comprehensive risk index is obtained by weighting and summing the node voltage over-limit risk value and the line power flow overload risk value based on multi-dimensional weights.

8. The method for analyzing the operational safety of a high-penetration distributed photovoltaic system according to claim 7, characterized in that, The severity function for exceeding the limit adopts an exponential utility function form, derived from the severity function for exceeding the limit at node voltages. and the function of severity of line power flow overload Composition, using the following logic to represent the severity function of node voltage. : in, This indicates an exponential operation. For the actual observed or instantaneous value of the node voltage, when It is undervoltage. This is a safe zone. This is an overvoltage. These are the severity sensitivity coefficients for undervoltage and overvoltage, respectively, used to determine the rate at which severity increases with the depth of exceedance. ; The severity function of line power flow can be represented using the following logic. : in, These are the actual observed or instantaneous values ​​of the power flow along the line. This represents the thermal stability limit of the circuit. The sensitivity coefficient for current overload.

9. A high-penetration distributed photovoltaic system operation safety analysis system, characterized in that, include: The probability distribution modeling module is used to collect historical photovoltaic (PV) output data from different regions and perform normalization processing; based on the data, it performs joint probability distribution modeling, extracting samples as original random variables; specifically, the joint probability distribution modeling involves: using a two-stage adaptive clustering initialization strategy to optimize the historical PV output data in two stages, and then using the SA-GMM model to model the joint probability distribution characteristics of PV output, outputting a probability density function. The two-stage adaptive clustering initialization strategy includes: In the first stage, the historical photovoltaic data was divided into coarse-grained segments based on the improved BWP-AP clustering. In the second stage, starting with the AP clustering results, K-means++ iteration is performed to recalculate the optimal center. The recalculated optimal data is modeled using the SA-GMM joint probability distribution. The polynomial response surface fitting module, based on the adaptive order-probability weighted moment-polynomial response surface fitting method, maps the original random variables to standard normal variables and expresses the standard normal variables in a variable-order polynomial form; wherein, the adaptive order-probability weighted moment-polynomial response surface fitting method specifically includes: Calculate the probability weighted moments of each order for the samples; adaptively select the optimal polynomial order within a preset order range based on the principle of minimizing fitting error; linearly transform the probability weighted moment vector into a polynomial coefficient vector based on the fixed transformation matrix corresponding to the optimal polynomial order; where, for any polynomial order m, there exists a unique... 3D fixed transformation matrix This makes the polynomial coefficient vector With probability weighted moment vector Satisfies a linear relationship: , It is an m+1 dimensional probability weighted moment vector; The probabilistic power flow calculation module performs Nataf transformation based on a variable-order polynomial form to convert a set of correlated photovoltaic output random variables into a set of mutually independent standard normal random variables; it then performs probabilistic power flow calculation on the set of standard normal random variables to obtain the probability distribution of node voltage and line power flow state variables. The risk assessment module performs risk assessment based on the probability distribution to obtain system operation risk indicators; The variable-order polynomial is represented using the following logic: in, For the original random variable, Let be the coefficients of the polynomial of order k with the i-th variable. Let be the i-th variable and be a standard normal variable of order k, where m is the order of the polynomial.

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