CN116109134A - Risk assessment method for voltage transgression based on analytical probabilistic power flow - Google Patents

Abstract

The invention discloses a voltage out-of-limit risk assessment method based on analytic probability power flow, which comprises the following steps: acquiring historical data of an injection power predicted value and a predicted error; modeling the conditional probability distribution of the node injection power prediction error, and quantifying the uncertainty of the injection power of each node of the power distribution network; obtaining a probability density function of the node voltage amplitude; judging whether the node belongs to a voltage higher-limit risk node or not; outputting probability density curves of voltage amplitude values of all nodes at all times, and evaluating voltage out-of-limit risks; according to the invention, a probability power flow calculation method of an active power distribution network is researched, an active power distribution network voltage second-order approximate probability evaluation method based on an analytic probability power flow method is provided, and an expression method of the traditional power distribution network power flow distribution is optimized into a probability form; in order to describe uncertainty of node voltage distribution of an active power distribution network, a voltage probability assessment method capable of reflecting uncertainty of node voltage and injection power is provided.

Description

Voltage over-limit risk assessment method based on analytical probabilistic power flow

Technical Field

The present invention relates to the technical field of distribution network operation and evaluation methods, and in particular to a voltage over-limit risk evaluation method based on analytical probabilistic power flow.

Background Art

Due to the large-scale access of new elements such as distributed power sources with high penetration rates and electric vehicles to the distribution network, the uncertainty of the power flow distribution in the distribution network is increasing. The traditional power flow calculation method of the distribution network based on forward and backward iteration cannot meet the requirements of the above uncertainty.

Therefore, on the basis of using the Gaussian mixture model to describe the uncertainty elements of the node voltage and injected power of the active distribution network, in order to further reflect the probabilistic characteristics of the power flow distribution within the distribution network, it is necessary to propose a probabilistic power flow calculation method that can reflect the uncertainty of the node voltage and injected power, and optimize the expression method of the traditional distribution network power flow distribution into a probabilistic form.

Summary of the invention

The purpose of this section is to summarize some aspects of embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the specification abstract and the invention title of this application to avoid blurring the purpose of this section, the specification abstract and the invention title, and such simplifications or omissions cannot be used to limit the scope of the present invention.

In view of the above-mentioned problems, the present invention is proposed.

Therefore, the technical problems solved by the present invention are: optimizing the expression method of traditional distribution network flow distribution into a probabilistic form; the traditional distribution network flow calculation method based on forward and backward iteration cannot meet the above uncertainty requirements, and how to characterize the uncertainty of active distribution network flow distribution.

In order to solve the above technical problems, the present invention provides the following technical solutions: a voltage over-limit risk assessment method based on analytical probabilistic power flow, comprising:

Obtain historical data of injection power prediction value and prediction error;

The conditional probability distribution of the node injection power prediction error is modeled to quantify the uncertainty of the injection power at each node in the distribution network;

The node voltage is processed to obtain a probability density function of the node voltage amplitude;

Analyze the voltage over-limit risk of each node and determine whether the node is a high-risk node for voltage over-limit;

The probability density curve of the voltage amplitude at each node at each moment is output, and the voltage over-limit risk is evaluated.

The voltage over-limit risk assessment method based on analytical probability power flow of the present invention is characterized in that: the conditional probability distribution modeling of the node injection power prediction error includes:

Using random vector _X1 to represent the actual value of the injected power and random vector _X2 to represent the predicted value of the injected power of W nodes, the random vector of the prediction error can be expressed as:

_Xe = _X1 - _X2 ;

The injection power prediction value X ₂ , injection power prediction error X _e , and time T can be further expressed as

Wherein, X _1n represents the actual value of the injected power of node n; X _en represents the predicted value of the injected power of node n; and T _n represents the nth moment.

The voltage over-limit risk assessment method based on analytical probability power flow of the present invention is characterized in that the conditional probability distribution modeling of the node injection power prediction error also includes:

Let Y = [X ₂ T] ^T , and use GMM to represent the joint probability density function of the prediction error, prediction value and time multidimensional random vector [X _e ^T T ^T ] ^T

Among them, x, y are individuals of random variables X, Y; M is the number of Gaussian components in GMM; _wm , _μm and _σm are the weight, mean and variance of the m-th Gaussian component; N() represents Gaussian distribution.

The voltage over-limit risk assessment method based on analytical probabilistic power flow described in the present invention is characterized in that: the uncertainty of the injected power of each node in the distribution network is quantified, including: under the condition of a given time series distribution of the actual value of the injected power, it can be seen from the conditional probability invariance of the GMM that the conditional probability of the prediction error still obeys the GMM; the conditional probability distribution of the injection power prediction error of W nodes can be obtained, and the uncertainty of the injected power of each node in the distribution network can be accurately quantified.

The voltage over-limit risk assessment method based on analytical probabilistic power flow of the present invention is characterized in that: the node voltage processing includes:

Performing second-order approximation on the node voltage, we can obtain the characteristic function of the voltage amplitude:

a、b均为二次型函数系数，t则表示当前的相对时刻。in,

a and b are both quadratic function coefficients, and t represents the current relative time.

The voltage over-limit risk assessment method based on analytical probability power flow of the present invention is characterized in that the probability density function of the prediction error of each node is expressed as:

The probability distribution of node voltage prediction error f _ΔV (Δv) obeys the weighted form of m Gauss components with mean Aμ _m and variance Aσ _m A ^T , and the weight of each component is still ω _m , which is the same as the probability distribution of node injection power;

Where A is the coefficient matrix; T is the transpose; w _m , μ _m and σ _m are the weight, mean and variance of the m-th Gaussian component, and the superscript represents the node position.

The voltage over-limit risk assessment method based on analytical probability power flow of the present invention is characterized in that: the determination of whether a node is a voltage over-limit high risk node is expressed as:

Where: p(Z) is the probability of event Z occurring; if E ^* represents the nominal voltage of the distribution network line, then [E ^* _-ΔElow , E ^* + _ΔEover ] is the allowable range of voltage deviation; α is the allowable threshold of voltage over-limit probability, which is taken as 0.5 in this paper.

The voltage over-limit risk assessment method based on analytical probability power flow of the present invention is characterized in that the probability density curve of the output node voltage amplitude includes:

If the time t is greater than or equal to 96 and the node i is greater than or equal to the total number of nodes, then the curve is output;

If the condition that time t is greater than or equal to 96 and node i is greater than or equal to the total number of nodes is not satisfied, the conditional probability distribution of the node injection power prediction error is recalculated.

A computer device comprises: a memory and a processor; the memory stores a computer program, wherein the processor implements the steps of any one of the methods of the present invention when executing the computer program.

A computer-readable storage medium stores a computer program, wherein the computer program, when executed by a processor, implements the steps of any one of the methods of the present invention.

The beneficial effects of the present invention are as follows: the present invention studies the probabilistic power flow calculation method of the active distribution network, and proposes a voltage over-limit risk assessment method based on the analytical probabilistic power flow; establishes a data-driven full probability model of distribution network uncertainty factors; and further obtains the node injection power prediction error, laying the foundation for analyzing the node voltage over-limit risk considering the prediction error; proposes an active distribution network voltage second-order approximate probability assessment method based on the analytical probabilistic power flow method, and optimizes the expression method of the traditional distribution network power flow distribution into a probabilistic form; in order to characterize the uncertainty of the node voltage distribution of the active distribution network, a voltage probability assessment method that can reflect the uncertainty of the node voltage and the injected power is proposed.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

FIG1 is an overall flow chart of a voltage over-limit risk assessment method based on analytical probabilistic power flow provided by a first embodiment of the present invention;

FIG2 is a diagram of an IEEE 33-node distribution network containing distributed power sources in a voltage over-limit risk assessment method based on analytical probabilistic power flow provided by a second embodiment of the present invention;

3 is a time series probability distribution diagram of the prediction error of the injected power of the node 14 in the voltage over-limit risk assessment method based on the analytical probability power flow provided by the second embodiment of the present invention;

4 is a time series probability distribution diagram of the prediction error of the injected power of node 8 in the voltage over-limit risk assessment method based on analytical probability power flow provided by the second embodiment of the present invention;

5 is a voltage over-limit risk analysis diagram of an active distribution network node according to a voltage over-limit risk assessment method based on analytical probabilistic power flow provided by a second embodiment of the present invention;

FIG. 6 is a diagram showing the internal structure of a computer device in two embodiments of the present invention.

DETAILED DESCRIPTION

In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.

The present invention is described in detail with reference to schematic diagrams. When describing the embodiments of the present invention, for the sake of convenience, the cross-sectional diagrams showing the device structure will not be partially enlarged according to the general scale, and the schematic diagrams are only examples, which should not limit the scope of protection of the present invention. In addition, in actual production, the three-dimensional dimensions of length, width and depth should be included.

At the same time, in the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "upper, lower, inner and outer" are based on the directions or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore cannot be understood as limiting the present invention. In addition, the terms "first, second or third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

In the present invention, unless otherwise clearly specified and limited, the terms "install, connect, connect" should be understood in a broad sense, for example: it can be a fixed connection, a detachable connection or an integral connection; it can also be a mechanical connection, an electrical connection or a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

Example 1

1 , which is an embodiment of the present invention, provides a voltage over-limit risk assessment method based on analytical probabilistic power flow, including:

S1: Obtain historical data of injection power prediction value and prediction error.

It should be noted that the historical data of the injection power prediction value and the prediction error are input at intervals of 15 minutes.

It should be noted that for reactive power flow, taking node voltage as an example, there is a strong nonlinear relationship between the input and output variables, and the DC power flow equation cannot be directly used to replace it. If the traditional linearization method is used to solve the probability density of the node voltage of the distribution network, the accuracy is low. Therefore, this paper uses a second-order polynomial to approximate the node voltage, and uses the prediction error probability density function of the node injection power to obtain the probability distribution of the node voltage within the distribution network.

S2: Modeling the conditional probability distribution of node injection power prediction error;

Furthermore, the probability characterization method of power prediction error includes:

Taking the random variable X representing the load power of a certain node or the output prediction error of distributed generation as an example, the probability distribution is characterized by the superposition form of several Gaussian distributions.

in

Where: M is the number of Gaussian components of the GMM model; ω _m is the weight of the mth Gaussian component; N _m () is the mth one-dimensional normal distribution; μ _m and σ _m are the mean and covariance of the mth Gaussian component, respectively.

服从GMM，则其边缘概率分布和条件概率分布也服从GMM。It can be proved that GMM has marginal probability invariance and conditional probability invariance, that is: if the random variable

If it obeys GMM, then its marginal probability distribution and conditional probability distribution also obey GMM.

为随机变量X在事件

发生条件下的条件概率。Where: f _X (x) is the marginal probability density of the random variable X;

For the random variable X in the event

The conditional probability of occurrence.

On the other hand, the power error full probability model includes:

Assuming that the injected power of W nodes in the distribution network is random, the random vector _X1 represents the actual value of the injected power, and the random vector _X2 represents the predicted value of the injected power of W nodes. Then the random vector of the prediction error can be expressed as _Xe = _X1 - _X2

The injection power prediction value X ₂ , injection power prediction error X _e , and time T can be further expressed as

Wherein, X _1n represents the actual value of the injected power of node n; X _en represents the predicted value of the injected power of node n; and T _n represents the nth moment.

Let Y = [X ₂ T] ^T , and use GMM to represent the joint probability density function of the prediction error, prediction value and time multidimensional random vector [X _e ^T T ^T ] ^T

in

In the formula, x, y are individuals of random variables X, Y; M is the number of Gaussian components in GMM; _wm , _μm and _σm are the weight, mean and variance of the m-th Gaussian component; N() represents Gaussian distribution.

The historical data are fitted using the EM algorithm to solve the parameters w _m , μ _m and σ _m in the formula.

Given the time series distribution of the actual value of the injected power, the conditional probability of the prediction error still obeys the GMM according to the conditional probability invariance of the GMM, that is,

in

Where Ω _m is the weight of the m-th Gaussian component in the conditional probability density

Based on this, the conditional probability distribution of the injection power prediction error of W nodes can be obtained, and the uncertainty of the injection power of each node in the distribution network can be accurately quantified.

S3: Process the node voltage to obtain a probability density function of the node voltage amplitude.

In a distribution network with N+1 nodes, the number of balancing nodes is 1, the number of PV nodes is n, and the remaining nodes are PQ nodes. The power flow calculation equation can be written as

Where, _Pi and _Qi represent the active injection power and reactive injection power of node i, respectively; _Ui represents the voltage amplitude of node i; N represents the number of nodes; _Gij and _Bij represent the conductance and susceptance between node i and node j, respectively; _θi represents the node voltage phase angle;

The above formula can be further condensed into

[PQ] ^T = g(U,θ)

Take the partial derivative of the injected power of node i on both sides of the equation, and we get

为紧缩形式的雅克比矩阵；

为电压幅值和相角对节点i的注入功率Pi的一阶灵敏度。Where: κ is a column vector whose i-th element is 1 and the rest of the elements are 0;

is the Jacobian matrix in compact form;

is the first-order sensitivity of the voltage amplitude and phase angle to the injected power Pi at node i.

Then the calculation formula for the voltage first-order sensitivity is:

The partial derivatives of the injected powers Pi and Pj at nodes i and j are obtained by taking the partial derivatives of the equal sign of the power flow calculation equation.

为电压幅值和相角对节点i和j的注入功率Pi和Pj的二阶灵敏度；

为紧缩形式的海森矩阵。Where:

is the second-order sensitivity of the voltage amplitude and phase angle to the injected powers Pi and Pj at nodes i and j;

is the Hessian matrix in compact form.

The first-order sensitivity and second-order sensitivity of voltage amplitude and phase angle to node injection power are

Therefore, the second-order approximation of the voltage at the PQ node of the distribution network to the injected power is:

为节点i电压初始值；P_Θ为N-n个PQ节点的注入功率实际值；

为N-n个PQ节点的注入功率基准值。Where: Ui is the voltage amplitude of node i;

is the initial value of the voltage at node i; P _Θ is the actual value of the injected power at Nn PQ nodes;

is the injection power reference value of Nn PQ nodes.

According to tests, the second-order voltage approximation can not only greatly alleviate the computational burden caused by the high-order approximation, but also ensure the accuracy of the analytical probabilistic power flow calculation.

Since the spatiotemporal distribution of the power injected into the distribution network nodes has strong uncertainty, it can be characterized by a Gaussian mixture model. Considering the correlation between the injected powers of the nodes, the probability distribution of the injected power deviation X of N-n nodes is recorded as

X～GMM(x；μ,σ)

Where: GMM(x; μ, σ) is the Gaussian mixture probability distribution, where μ and σ are the mean vector and covariance matrix respectively; X is the injection power deviation of Nn nodes, that is,

Arrangement available

Where X~GMM(x;μ,σ)

Where: T is the transpose, Y is the voltage amplitude set of the PQ node, that is, Y = {U _i |i∈Θ}; Y0 is the initial value set of the voltage amplitude of the PQ node, that is,

From the above formula, we can see that the random variable Y is a quadratic function of X, and its distribution function can be expressed as

Since Ψ is usually a non-diagonal matrix, the probability expression of Y contains cross multipliers such as XiXj, and X is a random variable represented by a multi-dimensional Gaussian distribution, in which the variables are highly correlated and it is difficult to perform direct integration operations. Therefore, according to the eigenvalue theorem that "a non-diagonal matrix can be transformed into a diagonal matrix through its eigenvector matrix", and using the Choles decomposition, the correlated multi-dimensional Gaussian distribution random variables are transformed into independent multi-dimensional Gaussian distribution random variables through linear transformation. Based on this, it can be equivalent to the following quadratic form:

Where X ^* ~ GMM (x ^* ; 0, 1)

Where a, b and c are the coefficients of quadratic functions; X* is the linear transformation of X.

Then through the formula

Each term in the above formula of any dimensional Gaussian distribution obeys the ^χ2 distribution, and its characteristic function is

Where:

On the basis of accurately characterizing the prediction error of the power injection of the distribution network nodes, in order to further calculate the node voltage prediction error of W nodes ΔV = [ΔV ₁ ΔV ₂ L ΔV _W ] ^T , we write

Where: Ei is the predicted value of the voltage at node i; _ΔPi and _ΔQi are the probability distributions of the injected active power and reactive power prediction errors at node i, respectively; _ΔVi represents the voltage prediction error at node i; _Pi and _Qi represent the injected active power and injected reactive power at node i.

In short:

ΔV＝ _SPΔP + _SQΔQ

Among them, _SP and _SQ represent active sensitivity and reactive sensitivity.

Since distributed power inverters have certain reactive power regulation capabilities, the randomness of reactive power injected into nodes is much smaller than active power. Therefore, this paper mainly analyzes the impact of active power injection into nodes on the voltage distribution of each node in the distribution network, and accordingly simplifies Δv to

The conditional probability of the prediction error of the active power injected by the obtained node can be further used to obtain the probability density function of the prediction error of each node:

in

It can be seen from this that the probability distribution of the node voltage prediction error f _ΔV (Δv) obeys the weighted form of m Gauss components with mean Aμ _m and variance Aσ _m A ^T , and the weight of each component is still ω _m , which is the same as the probability distribution of the node injection power.

S4: In order to analyze the risk of voltage exceeding the limit at each node, it is necessary to obtain the marginal probability density function of the voltage prediction error of all nodes of a single line f _ΔV (Δv)

服从均值为

协方差矩阵为

的m个Gauss分量的叠加。其概率分布可表达为It can be seen that the probability density function of the voltage prediction error of node i is

The mean is

The covariance matrix is

The superposition of m Gauss components. Its probability distribution can be expressed as

Among them, Φ() represents Gaussian distribution, the same as N() above.

Node i that meets the conditions can be considered as a node with high risk of voltage exceeding the limit.

Where: p(Z) is the probability of event Z occurring; if E ^* represents the nominal voltage of the distribution network line, then [E ^* _-ΔElow , E ^* + _ΔEover ] is the allowable range of voltage deviation; α is the allowable threshold of voltage over-limit probability, which is taken as 0.5 in this paper.

It should be noted that if the time t is greater than or equal to 96 and the node i is greater than or equal to the total number of nodes, the curve is output; if the time t is greater than or equal to 96 and the node i is greater than or equal to the total number of nodes, the conditional probability distribution of the node injection power prediction error is recalculated.

This embodiment also provides a computing device, including a memory and a processor; the memory is used to store computer executable instructions, and the processor is used to execute computer executable instructions to implement a motor rotor position compensation method based on a neural network in a stealth environment as proposed in the above embodiment.

This embodiment also provides a storage medium on which a computer program is stored. When the program is executed by a processor, the motor rotor position compensation method based on a neural network as proposed in the above embodiment is implemented.

The storage medium proposed in this embodiment and the method for realizing the compensation of the motor rotor position based on a neural network in a stealth environment proposed in the above embodiment belong to the same inventive concept. The technical details not fully described in this embodiment can be referred to the above embodiment, and this embodiment has the same beneficial effects as the above embodiment.

A person of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory, magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive memory, magnetic memory, ferroelectric memory, phase change memory, graphene memory, etc. Volatile memory may include random access memory or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory or dynamic random access memory, etc. The database involved in the embodiments provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic unit, a data processing logic unit based on quantum computing, etc., but is not limited thereto.

Example 2

2-6 , which is an embodiment of the present invention, provides a voltage over-limit risk assessment method based on analytical probabilistic power flow. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments.

In order to verify the proposed full probability model of uncertainty factors of active distribution network, the IEEE 33-node distribution system standard example shown in Figure 2 is adopted. Distributed power sources represented by photovoltaic units and wind turbines are installed at nodes 7, 14, 15, 19, and 31. Their maximum active output and inverter reactive capacity are shown in Table 1; random loads are connected at nodes 8, 17, 18, 24, and 30. The load types and numbers are shown in Table 2, and their sequential power demands have strong uncertainty; the remaining nodes are connected to industrial loads with very weak uncertainty, and their power demands are shown in Table 3.

Table 1 Installation location and capacity of distributed generation in IEEE 33-node distribution network

Table 2 Random load types and numbers of IEEE 33-node distribution network

Table 3 Active/reactive power of industrial loads in IEEE 33-node distribution network

On this basis, the prediction error of node injection power is considered. For distributed power sources, the maximum active output shown in Table 1 is used as the rated value, and the node injection power is converted to the per-unit value; for random loads, the load demand benchmark value shown in Table 2 is used as the rated value, and the load power demand is converted to the per-unit value.

Node injection power error analysis:

Since the injection power prediction values of distributed power nodes and random load nodes have certain errors, the Gaussian mixture model is used to characterize the time series probability distribution of the injection power prediction error of each node. As shown in Figures 3 and 4, node 14 is used as a representative to analyze the time series probability distribution of the injection power prediction error of distributed power, and node 8 is used as a representative to analyze the time series probability distribution of the random load power demand prediction error. Taking the photovoltaic unit as an example to analyze the active output of distributed power sources, at 8:00, the prediction error is small when the prediction value is 0.3p.u. and 0.6p.u.; at 14:00, the prediction error is small when the prediction value is 0.9p.u.; at 20:00, the prediction error is small when the prediction value is 0.3p.u.; at 2:00, the prediction error is small when the prediction value is 0.3p.u.; the prediction error is small when the prediction value is 0.3p.u.. Take node 8 as a representative to analyze the time series probability distribution of the random load power demand prediction error. Taking the electric vehicle charging station as an example to analyze the random load power demand, at 8:00, the prediction value is 0.3p.u., the prediction error is small; at 14:00, the prediction value is 0.3p.u., the prediction error is small; at 20:00, the prediction value is 0.3p.u., the prediction error is small; at 2:00, the prediction value is 0.3p.u., the prediction error is small.

It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims (10)

1. The voltage out-of-limit risk assessment method based on the analytic probability power flow is characterized by comprising the following steps of:

acquiring historical data of an injection power predicted value and a predicted error;

modeling the conditional probability distribution of the node injection power prediction error, and quantifying the uncertainty of the injection power of each node of the power distribution network;

processing the node voltage to obtain a probability density function of the node voltage amplitude;

analyzing the out-of-limit risk of the voltage of each node, and judging whether the node belongs to a voltage out-of-limit high risk node or not;

and outputting probability density curves of voltage amplitude values of all nodes at all times, and evaluating the voltage out-of-limit risk.

2. The analytical probabilistic power flow-based voltage threshold risk assessment method according to claim 1, wherein: the modeling of the conditional probability distribution of the node injection power prediction error comprises the following steps:

using random vectors X ₁ Representing the actual value of the injection power, a random vector X ₂ The random vector of prediction errors can be expressed as:

X _e ＝X ₁ -X ₂ ；

injection power predictive value X ₂ Prediction error of injection power X _e Time T may be further expressed as

wherein ,X_1n Representing the actual value of the injection power of node n; x is X _en Representing an injection power prediction value for node n; t (T) _n Indicating the nth time.

3. The analytical probabilistic power flow-based voltage threshold risk assessment method according to claim 1 or 2, characterized in that: the modeling of the conditional probability distribution of the node injection power prediction error further comprises:

note y= [ X ] ₂ T] ^T Characterization of prediction error, prediction value and time multidimensional random vector [ X ] by GMM _e ^T T ^T ] ^T Is a joint probability density function of (2)

Wherein X, Y are individuals of random variables X, Y; m is the number of Gaussian components in the GMM; w (w) _m ，μ _m and σ_m The weight, the mean and the variance of the m-th dimension Gaussian component; n () represents a gaussian distribution.

4. The analytical probabilistic power flow-based voltage threshold risk assessment method according to claim 3, wherein: the uncertainty of the injection power of each node of the quantified distribution network comprises the following steps: under the condition of given injection power actual value time sequence distribution, the conditional probability of the prediction error still obeys the GMM by the invariance of the conditional probability of the GMM; the conditional probability distribution of the prediction errors of the injection power of the W nodes can be obtained, and the uncertainty of the injection power of each node of the power distribution network can be accurately quantified.

5. The analytical probabilistic power flow-based voltage threshold risk assessment method of claim 4, wherein: the node voltage processing includes:

performing second-order approximation processing on the node voltage to obtain a characteristic function of the voltage amplitude value:

wherein ,

a. b are quadratic function coefficients, and t represents the current relative moment.

6. The analytical probabilistic power flow-based voltage threshold risk assessment method of claim 5, wherein: the probability density function of the prediction error of each node is expressed as:

probability distribution f of node voltage prediction error _ΔV (Deltav) obeys m averages A [ mu ] _m Variance A sigma _m A ^T Gauss component weighted versions of (2) and each component still has a weight of ω _m The probability distribution of the injection power of the node is the same as that of the node;

wherein A is a coefficient matrix; t is the transpose; w (w) _m ，μ _m and σ_m For the weight, mean and variance of the m-th dimension gaussian component,the superscript represents the node location.

7. The method for evaluating voltage threshold risk based on analytical probabilistic power flow according to any one of claims 1 or 6, wherein: whether the judging node belongs to a voltage higher-limit risk node is expressed as follows:

wherein: p (Z) is the probability of event Z occurrence; if E ^* Representing the nominal voltage of the distribution network line, [ E ] ^* -ΔE _low ，E ^* +ΔE _over ]Is the voltage offset allowable range; alpha is the voltage threshold allowed by the probability of out of limit, taken here as 0.5.

8. The analytical probabilistic power flow-based voltage threshold risk assessment method of claim 7, wherein: a probability density curve of output node voltage magnitude, comprising:

if the time t is more than or equal to 96 and the node i is more than or equal to the total node number, outputting a curve;

if the time t is not more than 96 and the node i is more than or equal to the total node number, the conditional probability distribution of the node injection power prediction error is recalculated.

9. A computer device, comprising: a memory and a processor; the memory stores a computer program characterized in that: the processor, when executing the computer program, implements the steps of the method of any one of claims 1 to 8.

10. A computer-readable storage medium having stored thereon a computer program, characterized by: the computer program implementing the steps of the method of any one of claims 1 to 8 when executed by a processor.

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