A power distribution network voltage out-of-limit risk assessment method considering variable correlation

Abstract

A power distribution network voltage out-of-limit risk assessment method considering variable correlation, comprising the following steps: based on historical samples of load power, the probability model of the load is characterized by a kernel density estimation method considering boundary effect; based on historical samples of DG output and corresponding external environmental factors, the conditional probability model of the DG is characterized by a kernel density estimation method considering boundary effect; based on Rosenblatt inverse transformation and the conditional probability model of the DG, the independence transformation of the DG output variable is realized, the probability characteristics of the node voltage are calculated by the semi-invariant method based on the probability model of the load and the probability model of each DG after transformation; the out-of-limit probability is determined according to the probability characteristics of the node voltage, the out-of-limit severity of each node voltage is determined based on the utility function, and the quantitative characterization of the node voltage out-of-limit risk is realized. The present application can accurately reflect the probability characteristics of the node voltage amplitude and realize accurate assessment of the voltage out-of-limit risk.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power systems; in particular, it relates to a power distribution network voltage out-of-limit risk assessment method, and more particularly to a power distribution network voltage out-of-limit risk assessment method considering variable correlation. BACKGROUND

[0002] On the side of the power distribution network, with the large number of DGs being connected, the unidirectional power flow in the power distribution network gradually evolves into a multidirectional power flow, and the traditional passive power distribution network gradually evolves into a new active power distribution network. Due to the fact that the DG output is largely affected by natural environmental factors such as light intensity, cloud conditions, temperature, geographical location, and atmospheric circulation, the output is unstable and has strong randomness and volatility, and the fluctuating load also brings uncertainty factors to the power distribution network. A large number of uncertain factors will have a significant impact on the stable operation of the power distribution network system, leading to an increased risk of node voltage out-of-limit, and bringing new challenges to the coordinated control of node voltage. Therefore, it is necessary to quantitatively evaluate the voltage out-of-limit risk of the DG-containing power distribution network to provide information for the coordinated control of node voltage. Since the wind and light energy characteristics are relatively consistent in the same region or surrounding areas, the DG unit output also usually has the same trend. The correlation between DG output variables makes it impossible to directly use the semi-invariant method probabilistic load flow (PLFCM) for calculation, and therefore, the correlation of DG output variables must be considered when voltage is evaluated by PLFCM. In addition, risk is a comprehensive measure of the probability of an event occurring and the severity of the consequences of the event, and both effects should be considered when performing risk assessment. The traditional risk assessment usually only considers the probability of the voltage out-of-limit risk event occurring, without considering whether the consequences are serious. SUMMARY

[0003] The present application is proposed to overcome the deficiencies of the prior art, and provides a power distribution network voltage out-of-limit risk assessment method considering variable correlation, which comprehensively considers the voltage out-of-limit probability and severity, and quantitatively analyzes the voltage out-of-limit risk of the power distribution network containing distributed power sources from the node and system levels.

[0004] The object of the present application can be achieved by the following technical solutions:

[0005] A power distribution network voltage out-of-limit risk assessment method considering variable correlation, comprising the following steps:

[0006] S1: Based on the historical samples of load power, the probability model of the load is depicted by a kernel density estimation method considering the boundary effect;

[0007] S2: Based on the historical samples of DG output and corresponding external environmental factors, the conditional probability model of DG is depicted by the kernel density estimation method considering boundary effect;

[0008] S3: Based on the Rosenblatt inverse transformation and the conditional probability model of DG, the independence transformation of DG output variable is realized, and the probability model of each DG after transformation is calculated by the kernel density estimation method considering boundary effect. The probability characteristics of node voltage are calculated by the semi-invariant method based on the probability model of load and the probability model of each DG after transformation;

[0009] S4: The over-limit probability is determined according to the probability characteristics of node voltage, and the over-limit severity of each node voltage is determined based on the utility function, so as to realize the quantitative depiction of node voltage over-limit risk.

[0010] Further, the S1 specifically comprises:

[0011] S11: The historical data of node load is expressed in the form of matrix P L :

[0012]

[0013] In the formula, is the local load power monitoring value of node k at time i, N L is the number of load nodes, and T is the total time;

[0014] S12: According to P L , the power data set of node k at time t in different natural days is extracted

[0015]

[0016] In the formula, T d is the number of monitoring sampling points in a day;

[0017] S13: Based on the kernel density estimation method considering boundary effect, the power data set is used to estimate the probability density function of load:

[0018]

[0019] In the formula, K B (·) represents the boundary kernel function; N represents the number of samples; h represents the bandwidth; x represents the kernel density estimation point; X i represents the i th sample data in the data set . represents the estimated probability density function.

[0020] In which, the boundary kernel function K B(·) is a linear combination of the selected kernel functions K(x) and xK(x):

[0021]

[0022] where K(x) represents the adopted kernel function; a i (i = 0, 1, 2) are integral parameters.

[0023] Further, the S2 specifically comprises:

[0024] S21: normalize the historical data of DG output according to the respective maximum capacity, and limit the data in the bounded interval [0, 1];

[0025] S22: based on the kernel density method considering boundary effect, jointly depict the single DG output probability density function at time t according to the normalized data and the historical data of the corresponding external environmental factors:

[0026]

[0027] where P i is the historical sample of DG output; X i is the historical sample of the corresponding condition variable; h1 and h2 are bandwidth parameters; and is the kernel function, p t is the estimated point, x t is the value of the condition variable at time t.

[0028] S31: consider the boundary characteristics of DG output and the corresponding external environmental factors, and depict the joint probability density function of DG output at time t;

[0029] S32: calculate the conditional cumulative distribution function according to the joint probability density function;

[0030] S33: realize the independent transformation of DG output variable based on the Rosenblatt inverse transformation according to the conditional cumulative distribution function;

[0031] S34: based on the load probability model and the transformed DG conditional probability model, calculate the semi-invariant of each order of the input variable, and calculate the semi-invariant of each order of the output variable through the probability flow calculation; the input variable includes load and DG output, and the output variable includes node voltage;

[0032] S35: based on the Cornish-Fisher series, fit the semi-invariant of the output variable into a probability distribution to obtain the probability distribution characteristics of the node voltage.

[0033] Further, the S3 specifically comprises:

[0034] DG output joint probability density function at time t:

[0035]

[0036] where N represents the number of samples; respectively represent the bandwidth parameters of the d DGs; respectively represent the bandwidth parameters of the corresponding conditional variables; P Dij represents the i-th output sample of the j-th DG; X ik represents the i-th sample of the k-th conditional variable; K Bj (·) and represents the kernel function, represents the estimated point; x 1t is the value of the first conditional variable at time t; x dt is the value of the d-th conditional variable at time t; is the j-th estimated point; is the bandwidth parameter of the j-th DG; x kt is the value of the k-th conditional variable at time t; is the bandwidth parameter of the k-th conditional variable.

[0037] Step S32 is specifically:

[0038]

[0039]

[0040] where f(x1, x2,..., xi-1) represents the joint probability density function of the first i-1 DGs; f(x1, x2,..., xi) represents the joint probability density function of the first i DGs; f(x1, x2,..., xi, xi+1,..., xd) represents the conditional probability density function. i-1 i i|1,2,...,i-1

[0041] Step S33 is specifically:

[0042] S331: generate m samples of standard normal distribution functions U1, U2,..., U n ;

[0043] S332: obtain m samples of one DG output x1;

[0044] x1=F1 -1 [Φ(u1)]

[0045] where u1 represents a sample of random variable U1; Φ(·) represents the cumulative distribution function of the normal distribution; represents the inverse function of F1(·);

[0046] ​​​S333: Propagate to n DGs, has,

[0047]

[0048] where u n represents the sample of the random variable U n , x1,..., x n-1 represents the sample of the first n-1 DGs; F -1n|1,2,...,n-1 (·) represents the inverse function of F n|1,2,...,n-1 (·).

[0049] Step S34 is specifically:

[0050] obtaining the origin moments of each order corresponding to each input variable, and obtaining the semi-invariant of each order of the input variable injection power variation ΔW according to the relationship between the origin moments and the semi-invariant;

[0051] obtaining the semi-invariant of each order of the output variable ΔX according to the semi-invariant of each order of the injection power variation ΔW:

[0052]

[0053] wherein, is the kth semi-invariant of the input variable DG output injection power variation; is the kth semi-invariant of the input variable load injection power variation.

[0054] The origin moment of the input variable load is calculated by the density function obtained by the kernel density estimation based on the consideration of the boundary effect through the load historical data:

[0055]

[0056] wherein, α v represents the vth origin moment;

[0057] The origin moment of the input variable DG output needs to be first generated to be independent of the sample subject to the standard normal distribution, and then the sample of the DG output variable is obtained by using the Rosenblatt inverse transformation. Finally, the sample obtained by the inverse transformation is calculated based on the density function obtained by the kernel density estimation considering the boundary effect.

[0058] Step S35 is specifically:

[0059] Assuming that α is the quantile of the random variable X, x(α) can be represented as:

[0060]

[0061] wherein, ζ(α) = Φ -1 (α), gv representing the v-th order normalized semi-invariant, according to x(α) = F -1 The cumulative distribution function F(x) of the output random variable X can be obtained, so as to obtain the node voltage out-of-limit probability.

[0062] Further, the step S4 is specifically:

[0063] S41: calculating the node voltage out-of-limit probability:

[0064]

[0065] In the formula, r(V i ) is the voltage out-of-limit probability of the node i, F(V i ) is the voltage cumulative distribution function of the node i, and are the upper and lower limit values of the voltage of the node i;

[0066] S42: calculating the node voltage out-of-limit severity:

[0067]

[0068] In the formula, k is a risk factor, and the greater the value, the more sensitive to the risk; θ(V i ) is a voltage offset index, defined as:

[0069]

[0070] S43: calculating the node out-of-limit risk comprehensive evaluation index:

[0071] Considering the voltage out-of-limit probability and the out-of-limit severity, the voltage out-of-limit comprehensive risk index R i of the node i and the comprehensive risk index R s of the system level can be defined as:

[0072]

[0073]

[0074] In the formula, n is the number of system nodes; f(V i ) is the voltage probability density function of the node i, which can be obtained by numerical differentiation from F(V i ).

[0075] Compared with the prior art, the present application has the following beneficial effects:

[0076] 1. The probability density calculation method based on boundary kernel density adopted by the application considers the influence of boundary effect, and the obtained load probability model and DG conditional probability model considering external environmental factors are more in line with the actual situation, thereby providing a basis for accurate assessment of voltage out-of-limit risk based on semi-invariant method probability power flow.

[0077] 2. The power distribution network voltage out-of-limit risk assessment method considering variable correlation provided by the application fully considers the correlation between DG outputs, and realizes accurate assessment of voltage out-of-limit risk of a new type of power distribution network with large-scale DG access.

[0078] 3. The comprehensive risk assessment system provided by the application comprehensively considers voltage out-of-limit probability and severity, and quantitatively analyzes voltage out-of-limit risk of a power distribution network with distributed power supply from the node and system level. DETAILED DESCRIPTION

[0079] Figure 1 is a flowchart of the application;

[0080] Figure 2 is the result of two estimation methods and the actual probability density function;

[0081] Figure 3 is an example topology graph;

[0082] Figure 4 is the probability density function and the cumulative distribution function of node 26;

[0083] Figure 5 is the probability density function and the cumulative distribution function of node 33. DETAILED DESCRIPTION

[0084] The application will be described in detail below in combination with the drawings and specific embodiments. The embodiments are implemented on the premise of the technical solution of the application, and detailed implementation modes and specific operation processes are given, but the protection scope of the application is not limited to the following embodiments.

[0085] The embodiment provides a power distribution network voltage out-of-limit risk assessment method considering variable correlation, and a flowchart thereof is as shown in Figure 1 The method comprises the following steps:

[0086] Step S1, based on historical samples of load power, the probability model of the load is described through a kernel density estimation method considering boundary effect.

[0087] Suppose that in the power distribution network, the number of load nodes is N L , then the load data of the power distribution network at time i is .

[0088]

[0089] wherein, is the local load power monitoring value of node k at time i. Assuming that there are T time points of load power history data, the load history data of the node is represented as matrix P L :

[0090]

[0091] wherein, is the local load power monitoring value of node k at time i, N L is the number of load nodes, and T is the total number of time points;

[0092] S12: According to P L extract the power data set of node k at time t in different natural days

[0093] The power data of each column of formula (2) can be decomposed into two parts, i.e., the basic data with a day as a period and the random fluctuation data, according to the life rule. Therefore, when performing PLFCM, according to P L extract the power data set of node k at time t in different natural days

[0094]

[0095] wherein, T d is the number of monitoring sampling points in a day;

[0096] S13: Based on the boundary effect considering kernel density estimation method, the power data set P t L,k estimates the probability density function of the load:

[0097] A significant feature of the load is that it is bounded, and the consumed power is always greater than zero. Therefore, the influence of the boundary effect needs to be considered when performing kernel density estimation (KDE). The present application adopts a boundary kernel to correct the boundary effect, as shown below,

[0098]

[0099] When x≥h, the new kernel function K B (x) is K(x), and when 0≤x<h (i.e., at the boundary), it adjusts the original kernel function.

[0100] Combined with the kernel density estimation KDE calculation formula shown in formula (3) (4) and the Epanechnikov kernel function, the calculation formula of the boundary kernel density estimation (BKDE) can be obtained,

[0101]

[0102] where K B denotes the boundary kernel function; N denotes the number of samples; h denotes the bandwidth; x denotes the kernel density estimation point; X i denotes the i-th sample data in the data set denotes the estimated probability density function.

[0103]

[0104] where I(·) is the indicator function, which is equal to 1 when z satisfies the condition, and 0 otherwise.

[0105] Taking an exponential distribution with a parameter of 1 as an example, which is a typical distribution with zero as the left boundary, 1000 random numbers are generated from the exponential distribution, and then the probability density function estimated by the kernel density estimation KDE and the probability density function estimated by the kernel density estimation considering boundary effects BKDE are used to estimate the probability density function. Figure 2 The results of the two estimation methods and the true probability density function pdf are shown.

[0106] Observation Figure 2 It can be found that, compared with the true probability density function, the probability density function KDE calculated by the kernel density estimation has a significant decrease at the interval boundary, while the probability density function BKDE calculated by the kernel density estimation considering boundary effects is more consistent with the true situation, and the deviation problem near the boundary is well improved.

[0107] Step S2, based on the historical samples of DG output and corresponding external environmental factors, the conditional probability model of DG is described by boundary kernel density.

[0108] S21: The historical data of DG output is normalized according to the respective maximum capacity, and the data is limited in the bounded interval [0, 1];

[0109] For DG, the output power is limited between zero and the maximum capacity, and after normalization according to the maximum capacity, the double boundary is [0, 1];

[0110] S22: Based on the kernel density method considering boundary effects, the normalized data and the historical data of corresponding external environmental factors are used to jointly describe the probability density function of single DG output at time t:

[0111] ​In addition to the bounded feature, another remarkable feature of DG output is its close relation to external factors. As photovoltaic, for example, can result in significant difference of power data at different time of day due to the difference of light intensity. Therefore, the probability density function (pdf) of DG output at time t can be characterized by its conditional pdf and the conditional variable prediction at time t.

[0112] The probability density function (pdf) of DG output at time t can be expressed as,

[0113]

[0114] where p t is the DG output at time t; x t is the conditional variable prediction at time t; f P is the conditional pdf of DG output; f X is the pdf of conditional variable; and f P,X is the multivariate pdf.

[0115] With BKDE, the conditional pdf of DG output can be expressed as:

[0116]

[0117] where P i is the DG output historical sample; X i is the corresponding conditional variable historical sample; h1 and h2 are bandwidth parameters; K B1 (·) and K B2 (·) are kernel functions; p t is the estimation point; x t is the value of conditional variable at time t.

[0118] Different DG types correspond to different conditional variables. In this paper, the conditional variable of photovoltaic is total light intensity, and the conditional variable of wind power is wind speed.

[0119] Step S3, based on the Rosenblatt inverse transform and the conditional probability model of DG, realize the independent transformation of DG output variable, and calculate the probability model of each DG after transformation through the kernel density estimation method considering the boundary effect. Based on the probability model of load and the probability model of each DG after transformation, the voltage out-of-limit probability is calculated by the semi-invariant method.

[0120] S31: considering the boundary feature of DG output and the corresponding external environmental factors, the joint probability density function of DG output at time t is characterized.

[0121] The DGs with close geographical position have similar output due to the characteristics of wind and solar energy, which presents spatial correlation. Therefore, in order to lay a foundation for the subsequent Rosenblatt inverse transform and PLFCM calculation, the accurate joint probability density function of DG output needs to be described first.

[0122] Considering the boundary characteristics of DG output and external condition factors, the joint probability density function of DG output at time t can be expressed as follows,

[0123]

[0124] In the formula, N represents the number of samples; respectively represent the bandwidth parameters of d DGs; respectively represent the bandwidth parameters of corresponding condition variables; P Dij represents the i th output sample of the j th DG; X ik represents the i th sample of the k th condition variable; K Bj (·) and represents the kernel function, represents the estimated point; x 1t is the value of the first condition variable at time t; x dt is the value of the d th condition variable at time t; is the j th estimated point; is the bandwidth parameter of the j th DG; x kt is the value of the k th condition variable at time t; is the bandwidth parameter of the k th condition variable.

[0125] S32: Calculate the conditional cumulative distribution function according to the joint probability density function;

[0126] Rosenblatt transform can directly convert a set of correlated non-normal variables X = (X1, X2,..., X n ) T into independent standard normal variables U = (U1, U2,..., U n ) T According to the principle of equal probability edge transformation, we have:

[0127]

[0128] Taking the inverse of the above formula, we can get the independent standard normal variable U, that is:

[0129]

[0130] The above equation is called the Rosenblatt transform. It is unaffected by the type of distribution or whether the correlation is linear, and is an accurate transformation method. The conditional cumulative distribution function can be obtained from the previously derived joint probability density function.

[0131]

[0132]

[0133] S33: Based on the conditional cumulative distribution function and the inverse Rosenblatt transform, the output variables of the DG are made independent; the basic steps are as follows:

[0134] S331: Generate m functions U1, U2, ..., U that follow a standard normal distribution. n The sample.

[0135] S332: Find m samples of one of the DG outputs x1.

[0136]

[0137] In the formula, u1 represents a sample of random variable U1; Φ(·) represents the cumulative distribution function of the normal distribution; The inverse function of F1(·);

[0138] S333: Extended to n DG locations

[0139]

[0140] In the formula, u n Represents random variable U n The samples, x1, ..., x n-1 F represents the sample of the first n-1 DG outputs obtained; -1n|1,2,...,n-1 (·) represents F n|1,2,...,n-1 The inverse function of (·).

[0141] Figure 3 The example topology diagram of this invention is shown, with a wind farm connected at 26 nodes and photovoltaic power plants connected at 33 and 15 nodes respectively. Tables 1 and 2 show the Pearson linear correlation coefficient, Kendall correlation coefficient, and Spearman correlation coefficient between each pair of WT, PV1, and PV2 before and after the Rosenblatt inverse transform.

[0142] Table 1. Correlation coefficients before transformation

[0143] Pearson Kendall Spearman WT / PV1 -0.2913 -0.2144 -0.2922 WT / PV2 -0.2882 -0.2126 -0.2896 PV1 / PV2 0.9926 0.9511 0.9937

[0144] Table 2. Correlation coefficients after transformation

[0145] Pearson Kendall Spearman WT / PV1 -0.0873 -0.1193 -0.0800 WT / PV2 -0.0925 -0.0625 -0.0929 PV1 / PV2 0.1256 0.0795 0.1004

[0146] The results show that the absolute values of the correlation coefficients of the DG output after transformation are basically reduced to below 0.1, and the correlation is greatly reduced, which can be regarded as independent of each other. The PLFCM can be calculated according to the transformed DG output.

[0147] S34: Based on the load probability model and the transformed DG conditional probability model, the semi-invariants of each order of the input variables are calculated, and the semi-invariants of each order of the output variables are calculated through the probability power flow calculation; the input variables include the load and the DG output, and the output variables include the node voltage;

[0148] The original point distance corresponding to each input variable of each order is obtained, and the semi-invariants of the injection power variation ΔW of the input variables are obtained according to the relationship between the original point matrix and the semi-invariant;

[0149] The semi-invariant can be calculated according to the original point matrix of no more than its order, and the present application only takes the first eight orders.

[0150] For the original point matrix of the input variable load, the semi-invariants of each order of the original point matrix can be calculated through the density function obtained based on the BKDE from the historical data:

[0151]

[0152] In the formula, α v represents the v-order original point matrix.

[0153] For the original point matrix of the input variable DG output with correlation, the samples of the DG output variable are first generated by using the Rosenblatt inverse transformation to obtain the samples of the DG output variable, and then the density function is calculated based on the kernel density estimation considering the boundary effect.

[0154] According to the semi-invariants of each order of the injection power variation ΔW, the semi-invariants of each order of the output variable ΔX are obtained:

[0155]

[0156] In the formula, is the k-order semi-invariant of the input variable DG output injection power variation; is the k-order semi-invariant of the input variable load injection power variation.

[0157] S35: Based on the Cornish-Fisher series, the semi-invariants of the output variables are fitted into a probability distribution, and the probability distribution characteristics of the node voltage are obtained:

[0158] The series expansion can fit the semi-invariant of the output variable into a probability distribution, and the cumulative probability distribution function of the output variable is calculated by the Cornish-Fisher series.

[0159]

[0160] wherein ζ(alpha) = Φ -1 (alpha), g v represents the normalized semi-invariant of order v. According to x(alpha) = F -1 (alpha), the cumulative distribution function F(x) of the output random variable X can be obtained, so as to obtain the node voltage out-of-limit probability.

[0161] It is assumed that according to the numerical weather forecast (NWP), the wind speed prediction value of the wind farm at 11 o'clock on a certain day is 10 m / s, the light intensity at photovoltaic power station 1 is 850 W / m 2 , and the light intensity at photovoltaic power station 2 is 900 W / m 2 . Figures 4-5 The voltage probability distribution and cumulative distribution diagrams of node 26 and node 33 are shown, and 5000 times of Monte Carlo simulation (MCS) is set as a comparison. It can be found that the calculation results of the PLFCM method based on the BKDE and the Rosenblatt inverse transform of the present application are basically consistent with the results obtained by the MCS method. Figure 4 、 5

[0162] Step S4, determine the severity of node voltage out-of-limit based on the utility preference index type function, and combine the voltage out-of-limit probability to realize the quantitative characterization of node voltage out-of-limit risk.

[0163] S41: calculate the voltage out-of-limit probability of the distribution network node:

[0164] The voltage out-of-limit probability refers to the probability of the node deviating from the voltage allowed range, including the voltage upper limit and lower limit, which can be obtained by PLFCM:

[0165]

[0166] wherein r(V i ) is the voltage out-of-limit probability of node i, F(V i ) is the voltage cumulative distribution function of node i, and are the voltage upper and lower limit values of node i.

[0167] S42: calculate the severity of node voltage out-of-limit:​

[0168] The voltage excursion severity reflects the severity of the system and the device when the voltage deviates from the allowable value. In reality, many electrical devices will produce more serious consequences as the voltage deviation becomes more serious, such as production equipment working voltage just deviates from the allowable value, which will lead to product quality decline, and with the deepening of the voltage excursion degree, even affect the safety of the device itself, cause serious consequences such as device damage. Therefore, the severity evaluation function should be more sensitive to reflect the consequences of serious deviation. The present application adopts the utility preference index function to define the severity function of the node voltage excursion.

[0169]

[0170] In the formula, k is a risk factor, the greater the value, the more sensitive to risk; θ(V i ) is a voltage excursion index, defined as:

[0171]

[0172] S43: Calculate the node excursion risk comprehensive evaluation index:

[0173] Considering the voltage excursion probability and the excursion severity, the voltage excursion comprehensive risk index R i of the node i and the comprehensive risk index R s of the system level can be defined as:

[0174]

[0175]

[0176] In the formula, n is the number of system nodes; f(V i ) is the voltage probability density function of node i, which can be obtained by numerical differentiation from F(V i ).

[0177] According to the previously calculated node voltage excursion probability combined with the corresponding severity, the corresponding risk index can be calculated. Table 3 shows the voltage excursion probability and risk index of each node.

[0178] Table 3 Voltage excursion probability and risk index of nodes

[0179]

[0180]

[0181] The preferred embodiments of the present application have been described above in detail. It should be understood that modifications and variations to the present application can be affected by those skilled in the art without departing from the scope of the application. Accordingly, it is intended that all of the subject matter of the above description and the claims be interpreted to encompass all such modifications and changes.

Claims

1. A method for assessing the risk of voltage exceeding limits in distribution networks that takes into account the correlation of variables, characterized in that, Includes the following steps: S1: Based on historical samples of load power, a probabilistic model of the load is characterized by a kernel density estimation method that considers boundary effects; S2: Based on historical samples of DG output and corresponding external environmental factors, the conditional probability model of DG is characterized by the kernel density estimation method that considers boundary effects. S3: Based on the Rosenblatt inverse transform and the conditional probability model of DG, the output variables of DG are transformed independently. The probability model of each DG after transformation is calculated by the kernel density estimation method considering the boundary effect. Based on the probability model of the load and the probability model of each DG after transformation, the probability characteristics of the node voltage are calculated by the semi-invariant method of probabilistic power flow. S4: Determine the over-limit probability based on the probabilistic characteristics of node voltage, and determine the severity of over-limit for each node voltage based on the utility function, thereby achieving a quantitative characterization of the risk of over-limit for node voltage. Step S2 is as follows: S21: Normalize the historical power output data of DG according to their respective maximum capacity, and restrict the data to a bounded interval [0,1]. S22: Based on the kernel density estimation method considering boundary effects, the probability density function of a single DG output at time t is jointly characterized by normalized data and historical data of corresponding external environmental factors. ； In the formula, P i This is a historical example of DG's efforts; X i These are historical samples corresponding to the condition variables; h1 and h2 are bandwidth parameters; (·)and (·) is the boundary kernel function, p t The point where x is the estimated output of DG at time t. t It is the value of the condition variable at time t; Step S3 is as follows: S31: Considering the boundary characteristics of DG output and the corresponding external environmental factors, characterize the joint probability density function of DG output at time t; S32: Calculate the conditional cumulative distribution function based on the joint probability density function; S33: Based on the conditional cumulative distribution function and the Rosenblatt inverse transform, realize the independent transformation of the DG output variable; S34: Based on the load probability model and the transformed DG conditional probability model, calculate the semi-invariants of each order of the input variables, and calculate the semi-invariants of each order of the output variables through the probabilistic power flow. Input variables include load and DG output, and output variables include node voltage; S35: Based on the Cornish-Fisher series, the semi-invariants of the output variables are fitted to a probability distribution to obtain the probability distribution characteristics of the node voltage. The joint probability density function of the DG output at time t in step S31 is: ； In the formula, N represents the number of samples; ,..., These represent the bandwidth parameters of the 1st to dth DGs, respectively. ..., These represent the bandwidth parameters of the corresponding condition variables; X represents the i-th output sample of the j-th DG; ik This represents the i-th sample of the k-th condition variable; and Represents the boundary kernel function. Points representing the estimated output of DG from the 1st to the dth; x 1t It is the value of the first condition variable at time t; x dt It is the value of the d-th condition variable at time t; It is the point where the output of the j-th DG is estimated; It is the bandwidth parameter of the j-th DG; x kt It is the value of the k-th condition variable at time t; It is the bandwidth parameter of the k-th condition variable.

2. The method for assessing the risk of voltage exceedance in distribution networks considering variable correlation as described in claim 1, characterized in that, Step S1 is as follows: S11: Represent the historical data of node load as a matrix P L : ； In the formula, Let be the local load power monitoring value of node k at time i, where i = 1, 2, ..., T; k = 1, 2, ..., N. L N L Where T is the number of load nodes and T is the total number of time intervals; S12: According to P L Extract the power dataset P of node k at time t within different natural days. t L,k : ； In the formula, T d The number of monitoring sampling points within a day; S13: Based on a kernel density estimation method considering boundary effects, using the power dataset P t L,k Estimated probability density function of the load: ； In the formula, K B (·) represents the boundary kernel function; N represents the number of samples; h represents the bandwidth; x represents the kernel density estimation point; X i Represents dataset P t L,k The i-th sample data in; This represents the probability density function of the estimate.

3. The method for assessing the risk of voltage exceedance in distribution networks considering variable correlation as described in claim 2, characterized in that, Kernel function K for kernel density considering boundary effects B (x) is a linear combination of K(x) and xK(x). ； In the formula, K(x) represents the kernel function used; a i (x)(i=0,1,2) is the integration parameter.

4. The method for assessing the risk of voltage exceedance in distribution networks considering variable correlation as described in claim 1, characterized in that, Step S32 is as follows: ； In the formula, f(x1,x2,...,x) i-1 f(x1, x2, ..., x) represents the joint probability density function of the first i-1 DGs; i f represents the joint probability density function of the first i DGs; i|1,2,...,i-1 F represents the conditional probability density function; i|1,2,...,i-1 This represents the conditional cumulative distribution function.

5. The method for assessing the risk of voltage exceeding limits in distribution networks considering variable correlation as described in claim 4, characterized in that, Step S33 is as follows: S331: Generate m functions U1, U2, ..., U that follow a standard normal distribution. n ; S332: Obtain m samples of one of the DG outputs x1; x1=F1 -1 [Φ(u1)]; In the formula, u1 represents a sample of random variable U1; Φ(·) represents the cumulative distribution function of the normal distribution; The inverse function of F1(·); S333: Extended to n DG locations ； In the formula, u n Represents random variable U n The samples, x1, ..., x n-1 This represents the samples of the first n-1 DG outputs that have been obtained. (·) represents F n|1,2,...,n-1 The inverse function of (·).

6. The method for assessing the risk of voltage exceedance in distribution networks considering variable correlation as described in claim 5, characterized in that, Step S34 is as follows: Obtain the raw moments of each input variable, and calculate the semi-invariants of each order of the injected power change ΔW of the input variable based on the relationship between the raw moments and semi-invariants. Based on the semi-invariants of the injected power change ΔW, the semi-invariants of the output variable ΔX are obtained: ； In the formula, Inject a k-order semi-invariant of the power change into the input variable DG output; The input variable load is injected with a k-th order semi-invariant of power change.

7. The method for assessing the risk of voltage exceedance in distribution networks considering variable correlation as described in claim 6, characterized in that, Step S35 is as follows: Let α be the quantile of the random variable X, then x(α) can be expressed as: ； In the formula, ζ(α)=Φ -1 (α), g v Representing a normalized semi-invariant of order v, according to x(α)=F -1 (α) can be used to obtain the cumulative distribution function F(x) of the output random variable X, and thus the cumulative distribution function of the node voltage can be obtained.

8. The method for assessing the risk of voltage exceedance in distribution networks considering variable correlation as described in claim 7, characterized in that, Step S4 is as follows: S41: Calculate the probability of voltage exceeding the limit at distribution network nodes: ； In the formula, r(V i F(V) represents the voltage limit exceedance probability of node i. i ) is the cumulative voltage distribution function at node i. and These are the upper and lower allowable voltage limits for node i; S42: Calculating the severity of node voltage exceedance based on utility function: ； In the formula, k is the risk factor; the larger the value, the more sensitive it is to risk; θ(V i () is the voltage offset index, defined as: ； S43: Calculate the comprehensive assessment index of node over-limit risk, including the comprehensive over-limit risk index R of node i. i And system-level comprehensive risk indicator R s : Taking into account both the probability and severity of voltage over-limit, R i and R s Defined as: ； In the formula, n is the number of system nodes; f(V i Let be the voltage probability density function of node i.

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