CN115034293A

CN115034293A - Power distribution network dynamic reconstruction method based on improved double-scale spectral clustering algorithm

Info

Publication number: CN115034293A
Application number: CN202210570755.XA
Authority: CN
Inventors: 粟世玮; 张谦
Original assignee: China Three Gorges University CTGU
Current assignee: China Three Gorges University CTGU
Priority date: 2022-05-24
Filing date: 2022-05-24
Publication date: 2022-09-09

Abstract

The dynamic reconstruction method of the power distribution network based on the improved double-scale spectral clustering algorithm is used for predicting node loads and distributed power source power of the power distribution network in a future time period to obtain power predicted values of all time points, forming an equivalent daily load curve and determining parameters of the power distribution system and DG parameters; performing cluster analysis on the running states of the power distribution network in the time section, arranging the clustering results according to the time sequence to determine the number of segments and the starting and stopping moments of each segment, and performing primary and secondary time interval division; constructing a dynamic reconstruction mathematical model of the power distribution network with the lowest daily loss cost as a target function; and solving the dynamic reconstruction mathematical model of the power distribution network by adopting Monte Carlo simulation random power flow based on Latin hypercube sampling and an improved wolf optimization algorithm. The invention can obtain a segmentation scheme according with the equivalent load dynamic change rule, effectively reduce the network loss and the times of switching actions, and improve the economical efficiency and the reliability of the operation of a power distribution system.

Description

Power distribution network dynamic reconstruction method based on improved double-scale spectral clustering algorithm

Technical Field

The invention relates to the technical field of dynamic reconfiguration of a power distribution network, in particular to a dynamic reconfiguration method of the power distribution network based on an improved double-scale spectral clustering algorithm.

Background

The reconstruction of the power distribution network is a common measure for optimizing the operation of the power distribution network, and a better network operation topology is sought by changing the switch combination state in the system, so that the aims of reducing the network loss, lightening the voltage imbalance, balancing the load, eliminating the overload and the like are fulfilled. The power distribution network reconstruction is generally divided into static reconstruction and dynamic reconstruction, the static reconstruction only optimizes data and constraint conditions of a network section at a certain time, and the pure pursuit of an optimal grid structure meeting a specific target at a certain time has no practical significance. The method aims at the fact that a large number of clean energy sources such as photovoltaic energy, wind power energy and the like are connected into a power distribution network, the load state and Distributed Generation (DG) output force dynamically change along with time, dynamic reconfiguration is conducted on network topology for a period of time according to the operation working condition of the system, and the obtained more flexible network operation topology has higher practical value.

Considering the safety influence on the power distribution network caused by the switch service life limitation and frequent actions, the network loss and the switch on-off times are balanced by quantifying the switch action loss through time interval division. At present, two solving schemes exist for dynamic reconstruction of a power distribution network: the first scheme is that static reconstruction is directly carried out in each unit time interval, reconstruction time interval combination is carried out by comparing the similarity of the grid structure or setting running state thresholds such as dynamic loss reduction parameters, voltage and the like, the process is relatively complicated, the consumed time is long, and certain artificial subjectivity exists in the preset number of sections or the threshold. The second scheme is that the load curve change of one day is simulated, then the curve is divided into time intervals, the time intervals are divided based on the information entropy equivalent daily load curve or the load curve monotonicity, only the influence of the whole load change of the system is considered, and the influence of the change of each node on the flow distribution of the system is not considered; and determining a reconstruction time period by adopting improved fuzzy optimal clustering, wherein clustering only considers the difference of load curve amplitudes and ignores the difference of curve forms, the accuracy of a clustering result is influenced, and time period aggregation of the clustering result without considering the time sequence characteristics of loads can cause excessive reconstruction segments.

Disclosure of Invention

In order to solve the technical problems, the invention provides a power distribution network dynamic reconstruction method based on an improved dual-scale spectral clustering algorithm, which can obtain a segmentation scheme according with the equivalent load dynamic change rule, effectively reduce the network loss and the switching action times, improve the economical efficiency and the reliability of the operation of a power distribution system, and has higher practical value.

The technical scheme adopted by the invention is as follows:

the dynamic reconstruction method of the power distribution network based on the improved double-scale spectral clustering algorithm comprises the following steps:

step 1: predicting node loads and distributed power source power of a power distribution network in a future time period to obtain power predicted values of all time points, forming an equivalent daily load curve, and determining parameters of a power distribution system and DG parameters;

step 2: classifying equivalent load power: according to the result of the dual-scale spectral clustering, the running state of the power distribution network in the time section is subjected to clustering analysis, the class of the load in each time period is determined, the clustering results are arranged according to the time sequence to determine the number of segments and the starting and stopping time of each segment, and preliminary time period division is completed;

and step 3: on the basis of the primary time interval division in the step 2, performing secondary time interval division by using a self-adaptive time interval aggregation algorithm until the switching action times are met, and taking the secondary time interval division result as a final time interval division result;

and 4, step 4: uncertainty of output of a distributed fan and a photovoltaic power generation system is fully considered, and a probabilistic model is adopted to describe the uncertainty; constructing a power distribution network dynamic reconstruction mathematical model taking the lowest daily loss cost as an objective function, wherein the constraint conditions of the mathematical optimization model comprise power flow equation constraint, node voltage constraint, branch power flow constraint and network topology constraint;

and 5: and (4) solving the dynamic reconstruction mathematical model of the power distribution network in the step (4) by adopting Monte Carlo simulation random power flow based on Latin hypercube sampling and an improved wolf optimization algorithm to obtain an optimal grid structure and a corresponding objective function value.

In the step 1, according to mathematical models of wind power generation, photovoltaic power generation and conventional loads, a Monte Carlo simulation method is adopted to obtain daily prediction curves of the wind power generation, the photovoltaic power generation and the conventional loads, the wind/light power generation is regarded as negative loads, and the daily prediction curves of the wind turbine generation, the photovoltaic power generation and the conventional loads are superposed to synthesize an equivalent daily load curve; and extracting the power value of the equivalent daily load curve at each time point to form a data matrix, wherein the row of the data matrix represents the time number, and the column represents the node number.

In step 1, it is assumed that the reconstruction research period of the system has N time points, and the states of all loads at the t-th time point can be represented as X _t ＝[x _t1 ,x _t2 ,…,x _tn ]Wherein: n is the number of nodes, x _ti Denotes the complex power of node i at time t, where t is the number of times.

The load status of the nodes of the network over time can be represented by X as follows:

in the formula: x is the number of ₁₁ 、x ₁₂ 、…x _1n Respectively representing the complex power of nodes 1 and 2 … n at time 1; x is the number of ₂₁ 、x ₂₂ 、…x _2n Respectively representing the complex power of nodes 1 and 2 … n at time 2; x is the number of _N1 、x _N2 、…X _Nn Respectively represents the complex power of the nodes 1 and 2 … N at the time point N; x ₁ X ₂ … X _N The load states at all times, time 1 and time 2 …, time N, respectively, where T is the transpose of the matrix vector.

In the step 2, the preliminary time interval division of the operation state of the power distribution network in the scheduling interval comprises the following steps:

s2.1: and (3) constructing a similarity matrix by adopting a Gaussian kernel function:

the similarity measurement between the loads is crucial to the clustering effect, and in order to make up for the deficiency that the similarity between the loads is measured by Euclidean distance in the traditional clustering technology, the similarity measurement based on distance and form is comprehensively considered, the Euclidean distance reflects the numerical distance of the power of each load point at different moments, the cosine distance represents the relative difference of the load sequences at different moments in the direction, and the definition is shown as the following formula:

in the formula：d _e,tt' The Euclidean distance of the load sequence between the time t and the time t'; x is the number of _ti 、x _t'i Respectively the power of a node i between the time t and the time t', and n is the total number of the nodes;

in the formula: d is a radical of _c,tt' The cosine distance of the load sequence between times t and t';

the invention adopts a double-scale similarity matrix to calculate the load comprehensive distance combining the Euclidean distance and the cosine distance, and can consider the similarity degree of the load distance and the form change. The Euclidean distance and the cosine distance are defined to calculate similarity matrixes under two different measures under the same data set, the two matrixes are normalized by an extreme value normalization method to obtain a corresponding matrix A, B, and the double-scale matrix is defined as follows:

P＝αA+δB；

in the formula: p is a double-scale similarity matrix, alpha and delta are respectively the weight of Euclidean distance and cosine distance, and the two similarity measurement modes are considered to be effective, wherein alpha and delta are respectively 0.5.

And (3) constructing a similarity matrix required by spectral clustering by using the Gaussian kernel function, wherein the Gaussian kernel function of the similarity matrix is defined as follows:

in the formula: h is a similarity matrix; p _t,t' Is an element of the dual-scale similarity matrix P; γ is a width function of the kernel function.

S2.2: the spectral clustering algorithm is established on the basis of spectrogram theory in graph theory, essentially converts the clustering problem into the optimal partitioning problem of the graph, is a point-to-cluster algorithm, can cluster in sample space with any shape, and converges to the global optimal solution. The feature value of the similarity matrix is calculated to be the optimal classification number b of the spectral clustering, and the feature vectors corresponding to the first b feature values are solved;

performing clustering analysis by using the eigenvalue and the eigenvector of the similarity matrix, calculating the eigenvalue of the similarity matrix, namely the optimal classification number b of the spectral clustering, and solving the eigenvectors corresponding to the previous b eigenvalues, wherein the method specifically comprises the following steps:

calculating the comprehensive distance of a load sequence between time t and time t' to form a double-scale similarity matrix P;

two, a diagonal matrix D is defined, wherein

D _tt Is a diagonal element of the diagonal matrix, H _tt' Is a similarity matrix element, T is the time number, and T is the total time number; constructing a Laplace matrix L ═ D ^-1/2 HD ^-1/2 ；

Calculating eigenvectors v corresponding to the b maximum eigenvalues of the Laplace matrix L ₁ 、v ₂ …v _b Forming a matrix V ═ V ₁ ,v ₂ ,…v _b ]Where b is the maximum possible number of clusters.

S2.3: and performing k-means clustering on the feature matrix formed by the selected feature vectors, and outputting corresponding clustering centers to obtain the category of the load in each unit time interval.

In the formula:

is the corresponding cluster center, a is the time period to which it belongs, k _a Number of periods included in a period, V _k The elements of the matrix are constructed for the feature vectors.

S2.4: considering the time sequence characteristics of the loads, recording the cluster numbers of the loads at all times, arranging according to the time sequence, and collecting adjacent time periods belonging to the same cluster into a segment to form an initial segment number C ₁ And finishing the preliminary time interval division, which comprises the following specific steps:

recording cluster numbers corresponding to load states of each hour in a day, and arranging the cluster numbers according to a time sequence;

secondly, observing cluster numbers corresponding to the unit time interval 1, collecting the unit time interval 2 and the unit time interval 1, forming a reconstruction time interval I if the unit time interval 2 and the unit time interval 1 belong to the same type, and dividing the unit time interval 2 into a reconstruction time interval II if the unit time interval 2 and the unit time interval 1 belong to different clusters;

if the unit time interval 2 is left in the reconstruction time interval I, judging whether the clusters of the unit time interval 3 and the time interval in the reconstruction time interval I are the same or not, and repeating the step 2. And if the unit time interval 2 is divided into the reconstruction time interval II, judging whether the clusters of the unit time interval 2 and the unit time interval 3 are the same, if so, dividing the unit time interval 3 into the reconstruction time interval II, otherwise, dividing into the reconstruction time interval III. And the rest is done, and the preliminary reconstruction time interval division of all unit time intervals is finished.

In the step 3, secondary time interval division is performed on the basis of the step 2, specifically:

on the basis of the preliminary time interval division, the whole time zone is divided into C ₁ Segments, and adjacent time segments belong to different clusters, and maximum reconstruction times C are compared _max And C ₁ If C is the magnitude of ₁ >C _max And performing time interval aggregation on the division results. The method specifically comprises the following steps:

s3.1: calculating the load L of the time interval t according to the equivalent daily load curve _t Maximum load L of relative daily load curve _max T 1,2 … N; n is the total time number before time interval division is not carried out;

the expression is as follows:

definition of degree of load deflection by statistical theory

Standard deviation of (2), the standard deviation can reflect load curvatureThe fluctuation condition of the line, the smaller the load fluctuation in the adjacent time interval, the higher the adaptability of the same net rack, is defined as follows:

in the formula: s. the _L T is the standard deviation of the degree of load deflection in the combined time period and is the number of times.

S3.2: calculating the standard deviation of the load offset of each time interval after the initial segmentation, merging the y time interval after the initial segmentation with the y-1 time interval and the y +1 time interval without setting a threshold value every time the time intervals with the minimum standard deviation are merged, and calculating the standard deviation S of the load offset of the new time interval after merging _L,y-1&y And S _L,y&y+1 The following three merging ways are provided for comparing the two types:

(ii) if S _L，y-1&y <S _L,y&y+1 Then the y period is merged with the y-1 period, i.e., forward merged;

② if S _L，y-1&y >S _L,y&y+1 Merging the y time period with the y +1 time period, namely merging backwards;

(iii) if S _L，y-1&y ＝S _L,y&y+1 The y period is combined with either the y-1 period or the y +1 period.

And if the time interval is not merged, and the final time interval division scheme is obtained.

In the step 4, random characteristics of wind and light output are considered, and a probabilistic model is adopted for description; the method comprises the following steps of establishing a dynamic reconstruction mathematical optimization model based on opportunity constraint by taking the time-day loss cost lower than the confidence level constraint as an objective function:

firstly, a distributed fan output randomness model:

the invention adopts a variable-speed constant-frequency wind power generation model, utilizes Monte Carlo simulation and two-parameter Weibull distribution to simulate the output of a fan, and the relationship between the output power and the wind speed is as follows:

in the formula: p _w,t Active power, P, emitted by the fan at time t _r Rated power for the generator; v. of _t Is the wind speed at time t, v _ci For cutting into the wind speed, v _r Rated wind speed, v _co For cutting out the wind speed, where A ═ P _r /(v _r -v _ci )，B＝-Av _ci 。

The expected value of the output power of the fan can be obtained by the following formula:

in the formula: e (P) _DG,t ) Is the desired value of the output power of the fan, f (v) _t ) The wind speed probability density function is a wind speed probability density function, the fan is a constant power factor model, and the wind driven generator can be simplified into a PQ node.

A photovoltaic output model:

because the illumination intensity of the photovoltaic meets the Beta distribution, the power output probability density function of the photovoltaic generator is assumed as follows:

in the formula: gamma is a Gamma function, P _s For outputting power, P, from the solar panel _smax For the maximum value of the output power of the solar panel, alpha and Beta respectively represent the shape parameters of Beta distribution

In the formula: u and δ are the standard deviation and variance, respectively, of the illumination intensity over a period of time.

The desired value of the photovoltaic output power can be derived:

in the formula: f (P) _s ) As a function of the power output probability density of the photovoltaic generator, E (P) _s ) The photovoltaic output power desired value.

The photovoltaic power generation system can ensure that the power factor is constant through a capacitor, and can be regarded as a PQ node in the power flow calculation.

The objective function probability constraint is shown as follows:

minF；

Pr(f(X,ξ)≤F)≥β；

in the formula: f is the optimal target value which can be realized when a certain confidence level is met, X is a control variable, xi is a state variable, Pr (·) is the probability of event qualification, and beta is the confidence level. c. C _Ploss Is the electricity price of time period t, P _loss.t Is the network loss of a time interval t, and the delta t is 1 h; omega _b Is a branch set, M represents a time interval after time interval division, M is the total number of divided segments, c _act Cost of single switching action, s _l,m-1 、s _l,m The state of the switch on the branch l at the time interval m-1 and the time interval m is respectively 0 when the switch is opened and 1 when the switch is closed; f (X, xi) is the value of the comprehensive operation cost of the system in the state xi.

The constraints are as follows:

the method comprises the following steps of:

in the formula: p _i ⁱⁿ And

respectively injecting active power and reactive power to the node i; v. of _i Is the voltage amplitude at node i; g _ij 、B _ij 、θ _ij Conductance between nodes i and j, respectivelySusceptance and voltage phase angle values, i, j ═ 1,2, …, n, where n is the total number of nodes.

And secondly, node voltage constraint:

Pr(V _i,min ≤V _i ≤V _i,max )≥β _V ；

in the formula: v _i Is the voltage amplitude of node i; v _i,min And V _i,max Respectively an upper limit and a lower limit of the node voltage; beta is a _V For voltage constraint confidence level, Pr (V) _i,min ≤V _i ≤V _i,max ) Is the probability of passing the node voltage.

And thirdly, branch power flow constraint power constraint:

Pr(|τ _ij P _l |≤P _l,max )≥β _I

in the formula: tau. _ij Is the state of branch ij, P _l Is the transmission power of line l; p is _l,max Is the upper limit of transmission power of line l; beta is a _I Confidence level of line transmission power, Pr (| τ) _ij P _l |≤P _l,max ) The probability that the branch transmission power is qualified.

Fourthly, radial network structure constraint:

in the formula: n \ F is a set formed by other nodes of the system except the root node; n is a radical of hydrogen _n 、N _f Number of all nodes and root nodes, λ, respectively _ij,t The on-off state of the switch (i, j) in the period of t is closed to be 1, otherwise, the on-off state is 0; t is a certain moment, and T is the total number of moments; (i, j) ∈ Ω _b To belong to a branch set omega _b One branch of (1).

Fifthly DG output restriction:

Pr(0≤P _DG,i ≤P _DG,i,max )≥β _DG

in the formula: p _DG,i To the DG output, P, at node i _DG,i,max Is the DG upper limit of the output, beta, at node i _DG Is DG output confidence level, Pr (0 ≦ P) _DG,i ≤P _DG,i,max ) And (4) the probability that the DG output at the node i is qualified.

Sixthly, restricting the switch operation times:

in the formula: lambda [ alpha ] _ij,t 、λ _ij,t-1 On-off states of switches (i, j) for time period t and time period t-1, respectively, N _s Is the upper limit of the operation times of the total switch action.

The step 5 comprises the following steps:

s5.1: setting system parameters: reading network parameters and parameters of a fan and photovoltaic equipment, and setting algorithm related parameters including maximum iteration number K _max ，

S5.2: latin hypercube sampling: sampling random variables such as wind speed, solar radiation intensity and load (active and reactive components) to form a sampling matrix S _LSH ；

S5.3: initializing a population:

for a radiation type network under the reconstruction of a power distribution network, the requirement that the number of basic loops is equal to that of interconnection switches is met, the positions of disconnection switches are changed, the disconnection switches are required to be respectively subordinate to each basic loop, and a loop formed by taking the interconnection switches as a starting point and along the counterclockwise direction is defined as the basic loop. In order to obtain a set of initial feasible solutions, the invention adopts a search mode of a loop group to obtain, and the specific process is as follows:

for a distribution network with M rings, the ith ring contains l branches _i Then the possible tree structure of this network is

And (4) seed preparation. Firstly, closing the disconnected switch in one loop, maintaining the switch states of other loops unchanged, opening the next switch along the loop direction on the premise of ensuring radialization, storing the obtained feasible solution into a feasible solution set, and repeating the operations on all the switches of all the loops in sequence until the switching schemes and the initial states of all the loops are reachedThe starting switching scheme is consistent.

The feasible solutions obtained in the above manner are aggregated into an initial population.

S5.4: calculating a fitness value: and calculating random power flow for the corresponding network topology scheme corresponding to each wolf individual to obtain a system network loss value, a node voltage and a branch power flow out-of-limit probability, punishing the scheme violating the chance constraint to obtain a corresponding objective function value, and further calculating the fitness value of each individual.

S5.5: the positions of three individuals with the minimum fitness value are selected as alpha, beta and delta, and the rank classification of the wolf group can know that alpha is the leader in the wolf group, beta is the second rank, is next to the existence of alpha and is next to delta wolf. Because wolf colony follows command hunting of alpha, beta and delta, individuals are independent of one another, information communication among individuals is lacked, the algorithm has low convergence speed, low convergence precision and the like, a competition cooperation mechanism is introduced, and except for the individuals of alpha, beta and delta, the competition mechanism is carried out according to the following formula:

in the formula:

are respectively an individual wolf after cooperation mechanism

And individual wolf

The location of the location;

s5, 6: calculating the distances between other wolf individuals and alpha, beta and delta, wherein the specific expression is as follows:

in the formula: d _α 、D _β 、D _δ The distances between the ith generation of ith individuals and alpha, beta and delta respectively,

and

the positions of alpha, beta and delta at the k generation,

is the location of the ith individual in the kth generation. C2. rand, [0,1 ]]A random number in between.

In order to improve the convergence speed and the optimization precision, the Cauchy mutation operator is updated for the positions of other wolfs, the capability of the algorithm to get rid of local optimum is effectively improved, and the premature phenomenon is avoided.

The variation formula is:

x _g (k)＝x _g (k)+η×C(0,1)；

in the formula: x is the number of _g And (t) is a K-generation global optimal solution, eta is a variation weight, C (0,1) is standard Cauchy random distribution in the first iteration, and lambda is an adjusting parameter. K. K is _max Respectively the current iteration number and the maximum iteration number.

S5.7: if the maximum iteration number is reached, turning to the step S5.9, otherwise, turning to the step S5.8;

s5.8: re-ordering the grey wolves, determining the positions of the grey wolves, and turning to the step S5.4;

s5.9: and (5) repeating the step S5.3 to the step S5.8 on the time-segment division result until all reconstruction time segments are met, outputting an optimal grid structure and a corresponding objective function value, and ending the algorithm.

The invention discloses a power distribution network dynamic reconstruction method based on an improved double-scale spectral clustering algorithm, which has the following technical effects:

1) according to the method, the load is subjected to preliminary time interval division through a dual-scale spectral clustering algorithm, the similarity of the distance and the form of the load sequence at each moment can be considered, the time interval is reasonably divided by utilizing self-adaptive time interval aggregation, the number of segments and a threshold value are not required to be preset, dynamic reconstruction is converted into a plurality of static reconstruction problems, and the purpose of balancing network loss and switching times is achieved.

2) The method fully considers the randomness and the time sequence of wind and light output, and establishes a power distribution network dynamic reconstruction model of Monte Carlo simulation power flow based on opportunity constraint and Latin hypercube sampling, so that network reconstruction has more practical significance; the improved grey wolf algorithm can be used for rapidly converging and avoiding premature and falling into local optimum, the optimum grid structure can be found under the condition of few iteration times, and the economical efficiency and the reliability of the operation of the power distribution network are effectively improved.

3) The invention provides a dynamic reconstruction strategy based on improved double-scale spectral clustering. The strategy is that firstly, a dual-scale similarity measurement spectrum clustering algorithm based on form and amplitude is adopted to cluster the loads, and a self-adaptive clustering algorithm reflecting the fluctuation characteristics of the equivalent daily load curve is further utilized to reasonably divide time segments; establishing a dynamic reconstruction model with the lowest daily loss cost as a target, wherein the constraint conditions to be met mainly comprise power balance constraint, node voltage constraint, DG output constraint, branch capacity constraint and open-loop operation constraint of the power distribution network, the node voltage, the branch power flow constraint and the DG output constraint are described by opportunity constraint, and the random power flow of the Monte Carlo simulation method based on Latin hypercube sampling is adopted for inspection to reconstruct the active power distribution network in time segments; the improved grey wolf algorithm is used for solving the dynamic reconstruction model of the power distribution network, so that a time interval division scheme which accords with the curve change trend can be obtained, the network loss can be obviously reduced, and the switching action times can be obviously reduced.

Drawings

FIG. 1 is a sectional flow chart of the equivalent daily load curve of the method of the present invention.

FIG. 2 is a flow chart of a dynamic reconstruction model for solving the power distribution network by using the improved Hui wolf algorithm.

FIG. 3 is a diagram of a test system architecture.

Fig. 4 is a graph of the result of time division of the equivalent daily load curve.

Fig. 5 is a comparison diagram of the network loss change of the system at each time before and after reconstruction.

FIG. 6 is a graph comparing the change of node voltage states before and after reconstruction.

FIG. 7 is a flow chart of an initial feasible solution set.

Detailed Description

According to the dynamic reconstruction method of the power distribution network based on the improved double-scale spectral clustering algorithm, as uncontrollable distributed power sources represented by photovoltaic and fans are widely connected to the power distribution network, the time-varying property and uncertainty of the output of the distributed power sources become factors which need to be considered in the reconstruction process of the power distribution network; in the dynamic reconstruction process, balancing network loss and switching action times, comprehensively considering dynamic changes of distributed power supplies and load predicted values, determining a time interval division scheme by using double-scale spectral clustering and a self-adaptive time interval aggregation algorithm, and converting dynamic reconstruction of the power distribution network into a plurality of static reconstruction problems; in order to reduce the influence of uncertain factors on the reconstruction of the power distribution network, the probability constraint is adopted to process the uncertainty problem of wind-solar output, so that the economic performance of the scheme can be optimized and the safety can be met; in addition, the power distribution network reconstruction is considered to be a nondeterministic polynomial problem of multi-constraint, non-linearity and combination optimization, an improved wolf algorithm is provided to solve the dynamic reconstruction problem, the optimization precision and the convergence speed are higher, the safe and economic operation of the power distribution network is ensured, and the method comprises the following steps:

step 1, predicting node loads and distributed power source power of a power distribution network in a future time period to obtain power predicted values of all time points, forming an equivalent daily load curve, and determining power distribution system parameters and DG parameters;

the invention utilizes an improved IEEE33 node system to carry out simulation verification, the reference voltage of the test system is 12.66kV, the reference power is 10MW, fans with the rated power of 400kW are respectively connected to the

system nodes

7 and 21, the cut-in wind speed, the rated wind speed and the cut-out wind speed are 4, 14 and 24m/s, and the total area is 5000 m/s and is respectively connected to the

nodes

16 and 25 ² The load and DG output are assumed to be constant per hour. Assuming that the single switch operation does not exceed 3 times, the total switch operation times does not exceed 15 times, the single switch operation is 7 yuan, the electricity purchase price is 0.7 yuan/kWh, in the gray wolf algorithm, the algorithm population scale is set to be 50, the maximum iteration time is 100, and the confidence level of an objective function, branch power and node voltage in opportunity constraint planning is 0.9.

According to the mathematical models of wind power generation, photovoltaic power generation and conventional loads, a Monte Carlo simulation method is adopted to obtain daily prediction curves of the wind power generation, the photovoltaic power generation and the conventional loads, wind/light power generation is regarded as negative loads, and the daily prediction curves of the wind turbine power generation, the photovoltaic power generation and the conventional loads are superposed to synthesize an equivalent daily load curve. And extracting the power value of the equivalent daily load curve at each time point to form a data matrix, wherein the row of the matrix represents the time number, and the column represents the node number. Assuming that the reconstruction study period of the system has N time points, the state of all loads at the t-th time point can be represented as X _t ＝[x _t1 ,x _t2 ,…,x _tn ]Where n is the number of nodes, x _ki Representing the complex power of node i at time t, the load status of the nodes over the entire period of the network can be represented by X, as follows.

Step 2: classifying equivalent load power:

according to the result of the dual-scale spectral clustering, the running state of the power distribution network in the time section is subjected to clustering analysis, the class of the load in each time period is determined, the clustering results are arranged according to the time sequence to determine the number of segments and the starting and stopping time of each segment, and the primary segmentation is completed;

s2.1, constructing a similarity matrix by adopting a Gaussian kernel function:

in the formula: in the formula: d _e,tt' 、d _c,tt' Euclidean and cosine distances, x, of the load sequences at times t and t', respectively _ti 、x _t'i The power of the node i at the time t and t' respectively, and n is the total number of the nodes.

The invention adopts a double-scale similarity matrix to calculate the load comprehensive distance combining the Euclidean distance and the cosine distance, and can consider the similarity degree of the load distance and the form change. The Euclidean distance and the cosine distance are defined to calculate similarity matrixes under two different metrics under the same data set, the two matrixes are normalized by an extremum normalization method to obtain a corresponding matrix A, B, and the dual-scale matrix is defined as follows:

P＝αA+δB

And constructing a similarity matrix required by spectral clustering by using a Gaussian kernel function, wherein the Gaussian kernel function of the similarity matrix is defined as follows:

in the formula: h is a similarity matrix; p is _t,t' Is an element of the dual-scale similarity matrix P; γ is a width function of the kernel function.

S2.2: the spectral clustering algorithm generally utilizes the characteristic values and the characteristic vectors of the similarity matrix to carry out clustering analysis, the characteristic value of the similarity matrix is calculated to be the optimal classification number b of the spectral clustering, and the characteristic vectors corresponding to the former b characteristic values are solved;

s2.3: and performing k-means clustering on the feature matrix formed by the selected feature vectors to obtain the category of the load in each unit time interval.

S2.4: considering the time sequence characteristics of the loads, recording the cluster numbers of the loads at all times, arranging according to the time sequence, and collecting adjacent time periods belonging to the same cluster into a segment to form an initial segment number C ₁ And finishing the preliminary segmentation.

And step 3: on the basis of primary time interval division, performing secondary time interval division by using a self-adaptive time interval aggregation algorithm until the switching action times are met, and taking a secondary time interval division result as a final time interval division result;

on the basis of the preliminary time interval division, the whole time zone is divided into C ₁ Segments, and adjacent time segments belong to different clusters, and maximum reconstruction times C are compared _max And C ₁ If C is the magnitude of ₁ >C _max And carrying out time interval aggregation on the division results, wherein the time interval aggregation comprises the following specific steps:

s3.1: calculating the load L in the time period t (t is 1,2 … N) according to the equivalent daily load curve _t Maximum load L of relative daily load curve _max The expression of the percentage (c) is as follows:

computer systemMethod for defining load deflection degree by using theory of design

The standard deviation can reflect the fluctuation condition of the load curve, and the smaller the load fluctuation in the adjacent time period is, the higher the adaptability of the same net rack is. The definition is as follows:

s3.2, calculating the standard deviation of the load deviation degree of each time interval after the initial segmentation, merging the time intervals with the minimum standard deviation each time without setting a threshold value, merging the time intervals y after the initial segmentation with the time interval y-1 and the time interval y +1 respectively, and solving the standard deviation S of the load deviation degree of the new time interval after merging _L,y-1&y And S _L,y&y+1 The following three merging ways are provided for comparing the two types:

if S _L，y-1&y <S _L,y&y+1 Then the y period is merged with the y-1 period, i.e., forward merged;

if S _L，y-1&y >S _L,y&y+1 Merging the y time period with the y +1 time period, namely merging backwards;

(S if) _L，y-1&y ＝S _L,y&y+1 The y period is combined with either the y-1 period or the y +1 period. And if so, the time intervals are not combined until the constraint of the times of the switching actions is met, and a final time interval division scheme is obtained.

The time interval division flow chart of the dual-scale spectral clustering algorithm combined with the adaptive time interval aggregation is shown in fig. 1.

And 4, step 4: uncertainty of output of a distributed fan and a photovoltaic power generation system is fully considered, and a probabilistic model is adopted to describe the uncertainty; and constructing a mathematical optimization model taking the lowest daily loss cost as an objective function, wherein the constraint conditions comprise a power flow equation constraint, a node voltage constraint, a branch power flow constraint and a network topology constraint.

Firstly, a distributed fan output randomness model:

in the formula: p _r For rated power of the generator, v _ci For cutting into the wind speed, v _r At rated wind speed, v _co For cutting out wind speed, where A ═ P _r /(v _r -v _ci )，B＝-Av _ci 。

in the formula: e (P) _DG,t ) Is the desired value of the output power of the fan, f (v) _t ) The wind speed probability density function is adopted, the fan is a constant power factor model, and the wind driven generator can be simplified into a PQ node.

A photovoltaic output model:

in the formula: gamma is a Gamma function, P _s For the output power, P, of the solar panel _smax The maximum value of the output power of the solar panel is shown, alpha and Beta are Beta distribution shape parameters, and u and delta are standard deviation and variance of the illumination intensity in a certain period.

The desired value of the photovoltaic output power can be derived:

in the formula: e (P) _s ) The photovoltaic output power desired value. The photovoltaic power generation system can ensure that the power factor is constant through a capacitor, and can be considered as a PQ node in power flow calculation.

The objective function probability constraint is shown as follows:

minF

Pr(f(X,ξ)≤F)≥β

in the formula: f is the optimal target value which can be realized when a certain confidence level is met, X is a control variable, xi is a state variable, Pr (·) is the probability of event qualification, and beta is the confidence level. c. C _Ploss Is the electricity price of time period t, P _loss.t Is the network loss of a time interval t, and the delta t is 1 h; omega _b Is a branch set, M is the total number of divided segments, c _act Cost of single switching action, s _j,m And in the time period m, the state of the switch on the branch l is 0 when the switch is switched off and 1 when the switch is switched on.

The constraints are as follows:

the method comprises the following steps of:

in the formula: p _i ⁱⁿ And

respectively injecting active power and reactive power to the node i; v. of _i Is the voltage magnitude at node i; g _ij 、B _ij 、θ _ij Respectively, conductance, susceptance, and voltage angle values between nodes i and j, i, j being 1,2, …, n, where n is the total number of nodes.

And secondly, node voltage constraint:

Pr(V _i,min ≤V _i ≤V _i,max )≥β _V

in the formula: v _i,min And V _i,max Respectively an upper limit and a lower limit of the node voltage; beta is a _V A voltage constraint confidence level.

Flow constraint power constraint of branch

Pr(|τ _ij P _l |≤P _l,max )≥β _I

In the formula: p is _l Is the transmission power of line l; p _l,max Is the upper limit of transmission power of line l; beta is a _I Confidence level of line transmission power.

Fourth, radial network structure constraint:

in the formula: n \ F is a set formed by other nodes of the system except the root node, N _n And N _f For all nodes and root node numbers, λ _ij,t For a period t the on-off state of the switch (i, j), the closure is 1, otherwise 0.

Fifthly DG output restriction:

Pr(0≤P _DG,i ≤P _DG,i,max )≥β _DG

in the formula: p _DG,i,max Is the DG upper limit of the output, beta, at node i _DG The DG output confidence level.

Sixthly, restricting the switch operation times:

in the formula: n is a radical of hydrogen _s Is the upper limit of the operation times of the total switch action.

And 5: and solving the dynamic reconstruction mathematical model of the power distribution network by adopting a Monte Carlo simulation random power flow based on Latin hypercube sampling and an improved wolf optimization algorithm method to obtain an optimal grid structure and a corresponding objective function value. The flow chart of the improved wolf pack for solving the dynamic reconfiguration problem of the power distribution network is shown in figure 2.

S5.1, setting system parameters:

reading network parameters and parameters of a fan and photovoltaic equipment, and setting algorithm related parameters including maximum iteration number K _max ，

S5.2, sampling by Latin hypercube, sampling random variables such as wind speed, solar radiation intensity and load (active and reactive components) to form a sampling matrix S _LSH ；

S5.3, initializing a population:

and obtaining an initial feasible solution set by adopting a loop group searching mode. When solving, the states of other loop switches need to be maintained unchanged, and whether the conditions of the radiation type network can be met when each switch of a certain loop is respectively disconnected is gradually judged, so that a feasible solution of the loop can be obtained. This operation is repeated for all basic loops until the final on-off state of each loop is the same as the initial rack configuration. The feasible solutions obtained in the above manner are aggregated into an initial population.

S5.4, calculating a fitness value:

and calculating random power flow for the corresponding network topology scheme corresponding to each individual wolf, obtaining a system network loss value, node voltage and branch power flow out-of-limit probability, punishing the scheme violating the chance constraint, obtaining a corresponding objective function value, and further calculating the fitness value of each individual.

And S5.5, selecting the positions of three individuals with the minimum fitness values as alpha, beta and delta, and knowing that alpha is a leader in the wolf group, beta is a second grade, is second only to the existence of alpha and is then delta wolf according to the classification of the wolf group. Because wolf groups obey command hunting of alpha, beta and delta, individuals are independent of each other, information exchange among individuals is lacked, so that the convergence speed of the algorithm is low, the convergence precision is low, and the like, a competition and cooperation mechanism is introduced, wherein the individuals except the alpha, beta and delta carry out the competition and cooperation mechanism according to the following formula:

in the formula:

are respectively an individual wolf after cooperation mechanism

And individual wolf

Where it is located.

S5.6, calculating the distances between other wolf individuals and alpha, beta and delta, and updating the Cauchy mutation operator for the positions of other wolfs in order to improve the convergence speed and the optimization precision, thereby effectively improving the ability of the algorithm to get rid of local optimization and avoiding the occurrence of premature phenomenon.

The variation formula is:

x _g (k)＝x _g (k)+η×C(0,1)

in the formula: x is a radical of a fluorine atom _g And (t) is a k-generation global optimal solution, eta is a variation weight, C (0,1) is standard Cauchy random distribution in the first iteration, and lambda is an adjusting parameter.

S5.7: if the maximum iteration times are reached, the step S5.9 is carried out, otherwise, the step S5.8 is carried out;

Example (b):

method for dynamically reconstructing power distribution network for verifying improved dual-scale spectral clustering algorithmThe effectiveness is verified by simulation by utilizing an improved IEEE33 node system, the reference voltage of the test system is 12.66kV, the reference power is 10MW, fans with the rated power of 400kW are respectively connected to the

nodes

7 and 21 of the system, the cut-in wind speed, the rated wind speed and the cut-out wind speed are 4, 14 and 24m/s, and the total area is 5000 m/s and is respectively connected to the

nodes

16 and 25 ² The load and DG output are assumed to be constant per hour. Assuming that a single switch is operated for no more than 3 times, the total switch operation time is no more than 15 times, the single switch operation is 7 yuan, the electricity purchase price is 0.7 yuan/kWh, in the gray wolf algorithm of the invention, the algorithm population scale is set to be 50, the maximum iteration time is 100, the confidence level of an objective function, branch power and node voltage in opportunity constraint planning is 0.9, and the structure diagram of the test system is shown in fig. 3.

In order to verify the reasonability and superiority of the active power distribution network dynamic reconstruction method based on the time-interval division of the improved dual-scale spectral clustering algorithm, the method described in the step 2 and the step 3 is utilized to carry out time-interval division on the equivalent daily load curve synthesized by the multi-type power, the equivalent daily load curve is finally divided into 4 sections, and the specific division result and the average load of each section after the division are shown in a figure 4. The invention sets three schemes for comparison, and a table 1 shows comparison results aiming at different reconstruction schemes, wherein the scheme 1 is used for performing static reconstruction on each unit time interval before division; the scheme 2 adopts an improved time interval division scheme of recursive ordered clustering to reconstruct; scheme 3 adopts the time interval division scheme based on the combination of the dual-scale spectral clustering and the adaptive aggregation algorithm to carry out dynamic reconstruction on the power distribution network.

Table 1 comparison of results for different reconstruction schemes

As can be seen from table 1, although the segmented static reconfiguration can maintain the optimal network topology structure at each unit time interval, the overall network loss value is the lowest, but the switching action times are the most, and the switching action time constraint is not satisfied; and the second scheme and the third scheme balance the relation between the network loss and the switching action times by dividing the whole time period, thereby reducing the switching action times and reducing the network loss cost to a lower level. The time segmentation number of the scheme 2 is 5 segments, the reconstruction times are 4, the time segmentation number of the scheme 3 is 4 segments, and the reconstruction times are 3, so that the scheme 3 is more obvious in reduction of the reconstruction times, daily loss cost and switching operation times than the scheme 2, the reconstruction times of the scheme 3 are less than those of the scheme 2, the total switching operation times are reduced by 6 times, and the daily loss cost is reduced by 97.02 yuan, which shows the reasonability and effectiveness of the time period division method based on the combination of the information entropy and the self-adaptive time period aggregation.

Fig. 5 and 6 show the changes of the network loss and the system node voltage level at each moment before and after the system reconfiguration. As can be seen from fig. 5, when the time period I (0:00-7:00) is reconstructed, the reduction of the network loss is not obvious due to the light load; from the early peak of the day, the system load is obviously increased, so in the reconstruction period II (7: 00-15:00), the system network loss is greatly reduced, and the economic improvement is very obvious; during the reconstruction period III (15:00-24:00), the load is greatly reduced at night, the output fluctuation of the fan is large, and the reconstruction considering the opportunity constraint can still effectively reduce the network loss under the condition of safe operation of the system.

Fig. 6 shows that the voltage level of each node is integrally increased after dynamic reconfiguration by using the voltage distribution of each node before and after reconfiguration at a certain time, the lowest voltage 0.8016p.u is increased to 0.92p.u. from 0.8016p.u. before reconfiguration, and the stability of the voltage can be greatly improved by reconfiguration, so that the voltage fluctuation of the system is reduced.

Claims

1. The dynamic reconstruction method of the power distribution network based on the improved double-scale spectral clustering algorithm is characterized by comprising the following steps of:

step 2: performing cluster analysis on the running states of the power distribution network in the time section, and arranging the clustering results according to the time sequence to determine the number of segments and the starting and stopping moments of each segment so as to finish preliminary time interval division;

and step 3: on the basis of the primary time interval division in the step 2, performing secondary time interval division by using a self-adaptive time interval aggregation algorithm until the switching action times are met;

and 4, step 4: constructing a dynamic reconstruction mathematical model of the power distribution network with the lowest daily loss cost as a target function;

and 5: and (4) solving the dynamic reconstruction mathematical model of the power distribution network in the step (4) by adopting Monte Carlo simulation random power flow based on Latin hypercube sampling and an improved wolf optimization algorithm.

2. The power distribution network dynamic reconstruction method based on the improved dual-scale spectral clustering algorithm according to claim 1, characterized in that: in the step 1, according to mathematical models of wind power generation, photovoltaic power generation and conventional loads, a Monte Carlo simulation method is adopted to obtain daily prediction curves of the wind power generation, the photovoltaic power generation and the conventional loads, the wind/light power generation is regarded as negative loads, and the daily prediction curves of the wind turbine generation, the photovoltaic power generation and the conventional loads are superposed to synthesize an equivalent daily load curve; and extracting the power value of the equivalent daily load curve at each time point to form a data matrix, wherein the row of the data matrix represents the time number, and the column represents the node number.

3. The power distribution network dynamic reconstruction method based on the improved dual-scale spectral clustering algorithm according to claim 2 is characterized in that: in step 1, it is assumed that the reconstruction study period of the system has N time points, and the states of all loads at the t-th time point can be represented as X _t ＝[x _t1 ,x _t2 ,…,x _tn ]Wherein: n is the number of nodes, x _ti Representing the complex power of a node i at the time t, wherein t is the time number; the load status of the nodes over the entire time period of the network can be represented by X as follows:

in the formula: x is a radical of a fluorine atom ₁₁ 、x ₁₂ 、…x _1n Respectively representing the complex power of nodes 1 and 2 … n at time 1; x is the number of ₂₁ 、x ₂₂ 、…x _2n Respectively representing the complex power of nodes 1 and 2 … n at time 2; x is the number of _N1 、x _N2 、…X _Nn Respectively represent the complex power of nodes 1 and 2 … N at the time point N; x ₁ X ₂ … X _N The load states at all times, time 1 and time 2 …, time N, respectively, where T is the transpose of the matrix vector.

4. The method for dynamically reconstructing the power distribution network based on the improved dual-scale spectral clustering algorithm according to claim 1 is characterized in that: in the step 2, the preliminary time interval division of the operation state of the distribution network in the scheduling interval comprises the following steps:

s2.1: considering similarity measurement based on distance and morphology, euclidean distance reflects the numerical distance of the power of each load point at different moments, and cosine distance represents the relative difference of the load sequence in direction at different moments, which is defined as the following formula:

in the formula: d _e,tt' The Euclidean distance of the load sequence between the time t and the time t'; x is the number of _ti 、x _t'i Respectively the power of a node i between the time t and the time t', and n is the total number of the nodes;

in the formula: d _c,tt' The cosine distance of the load sequence between times t and t';

the Euclidean distance and the cosine distance are defined to calculate similarity matrixes under two different metrics under the same data set, the two matrixes are normalized by an extremum normalization method to obtain a corresponding matrix A, B, and the dual-scale matrix is defined as follows:

P＝αA+δB；

in the formula: p is a double-scale similarity matrix, alpha and delta are respectively the weight of Euclidean distance and cosine distance, and two similarity measurement modes are considered to be effective;

in the formula: h is a similarity matrix; p _t,t' Is an element of the dual-scale similarity matrix P; gamma is the width function of the kernel function;

s2.2: performing clustering analysis by using the eigenvalue and the eigenvector of the similarity matrix, calculating the eigenvalue of the similarity matrix, namely the optimal classification number b of the spectral clustering, and solving the eigenvectors corresponding to the previous b eigenvalues, wherein the method specifically comprises the following steps:

a diagonal matrix D is defined, wherein

D _tt Is a diagonal element of a diagonal matrix, H _tt' Is a similarity matrix element, T is the time number, and T is the total time number; constructing a Laplace matrix L ═ D ^-1/2 HD ^-1/2 ；

Calculating eigenvectors v corresponding to the b maximum eigenvalues of the Laplace matrix L ₁ 、v ₂ …v _b Forming a matrix V ═ V ₁ ,v ₂ ,…v _b ]Wherein b is the maximum possible cluster number;

s2.3: performing k-means clustering on a feature matrix formed by the selected feature vectors, and outputting corresponding clustering centers to obtain the category of the load in each unit time interval;

in the formula:

is the corresponding cluster center, a is the time period to which it belongs, k _a Number of periods included in a period, V _k Forming elements of a matrix for the eigenvectors;

s2.4: considering the time sequence characteristics of the loads, recording the cluster numbers of the loads at all times, arranging according to the time sequence, and collecting adjacent time periods belonging to the same cluster into a segment to form an initial segment number C ₁ And finishing the preliminary time interval division.

5. The power distribution network dynamic reconstruction method based on the improved dual-scale spectral clustering algorithm according to claim 4, characterized in that: in the step 3, secondary time interval division is performed on the basis of the step 2, and the method specifically comprises the following steps:

on the basis of the preliminary time interval division, the whole time zone is divided into C ₁ Segments, and adjacent time segments belong to different clusters, and maximum reconstruction times C are compared _max And C ₁ If C is the magnitude of ₁ >C _max Performing time interval aggregation on the division results; the method specifically comprises the following steps:

s3.1: calculating the load L of the time interval t according to the equivalent daily load curve _t Maximum load L of relative daily load curve _max T 1,2 … N; n is the total time before time interval division is not carried out;

the expression is as follows:

definition of degree of load deflection by statistical theory

The standard deviation of (2) can reflect the fluctuation condition of the load curve, and the smaller the load fluctuation in adjacent time intervals is, the higher the adaptability of the same grid frame is, the definition is as follows:

in the formula: s _L The standard deviation of the load deviation degree in the combined time period, and t is the time number;

(iii) if S _L，y-1&y ＝S _L,y&y+1 The y time period is combined with any time period of the y-1 time period or the y +1 time period;

and if so, the time intervals are not combined until the constraint of the times of the switching actions is met, and a final time interval division scheme is obtained.

6. The power distribution network dynamic reconstruction method based on the improved dual-scale spectral clustering algorithm according to claim 4, characterized in that:

firstly, a distributed fan output randomness model:

a variable-speed constant-frequency wind power generation model is adopted, the output of a fan is simulated by utilizing Monte Carlo simulation and two-parameter Weibull distribution, and the relationship between the output power and the wind speed is as follows:

in the formula: p _w,t Active power, P, emitted by the fan at time t _r Rated power for the generator; v. of _t Is the wind speed at time t, v _ci For the cut-in wind speed, v _r Rated wind speed, v _co For cutting out wind speed, where A ═ P _r /(v _r -v _ci )，B＝-Av _ci ；

in the formula: e (P) _DG,t ) Is the desired value of the output power of the fan, f (v) _t ) Is a wind speed probability density function;

a photovoltaic output model:

setting a power output probability density function of the photovoltaic generator as follows:

in the formula: gamma function, P _s For outputting power, P, from the solar panel _smax For the maximum value of the output power of the solar panel, alpha and Beta respectively represent the shape parameters of Beta distribution

In the formula: u and delta are respectively the standard deviation and variance of the illumination intensity in a certain period of time;

the desired value of the photovoltaic output power can be derived:

in the formula: f (P) _s ) As a function of the power output probability density of the photovoltaic generator, E (P) _s ) The photovoltaic output power expected value is obtained; the objective function probability constraint is shown as follows:

min F；

Pr(f(X,ξ)≤F)≥β；

in the formula: f is an optimal target value which can be realized when a certain confidence level is met, X is a control variable, xi is a state variable, Pr (·) is the probability of event qualification, and beta is the confidence level; c. C _Ploss Is the electricity price of time period t, P _loss.t Is the network loss of a time interval t, and the delta t is 1 h; omega _b Is a branch set, M represents a time interval after time interval division, M is the total number of divided segments, c _act Cost of single switching action, s _l,m-1 、s _l,m The state of the switch on the branch l at the time interval m-1 and the time interval m is respectively 0 when the switch is opened and 1 when the switch is closed; f (X, xi) is the value of the comprehensive operation cost of the system in a state xi;

the constraints are as follows:

the method comprises the following steps of:

in the formula: p _i ⁱⁿ And

respectively inject into the node iPower and reactive power; v. of _i Is the voltage amplitude at node i; g _ij 、B _ij 、θ _ij Conductance, susceptance, and voltage angle values between nodes i and j, respectively, i, j being 1,2, …, n, where n is the total number of nodes;

the node voltage is restrained:

Pr(V _i,min ≤V _i ≤V _i,max )≥β _V ；

in the formula: v _i Is the voltage amplitude of node i; v _i,min And V _i,max Respectively an upper limit and a lower limit of the node voltage; beta is a _V For voltage constraint confidence level, Pr (V) _i,min ≤V _i ≤V _i,max ) The probability of node voltage qualification;

thirdly, power constraint is restrained by branch power flow:

Pr(|τ _ij P _l |≤P _l,max )≥β _I

in the formula: tau. _ij Is the state of branch ij, P _l Is the transmission power of line l; p _l,max The transmission power upper limit of the line l; beta is a _I Confidence level of line transmission power, Pr (| τ) _ij P _l |≤P _l,max ) Probability of qualified transmission power for a branch;

fourthly, radial network structure constraint:

in the formula: n \ F is a set formed by other nodes of the system except the root node; n is a radical of _n 、N _f Number of all nodes and root nodes, λ, respectively _ij,t The on-off state of the switch (i, j) in the period of t is closed to be 1, otherwise, the on-off state is 0; t is a certain moment, and T is the total moment; (i, j) ∈ Ω _b To belong to a branch set omega _b A certain branch of;

fifthly, DG output constraint:

Pr(0≤P _DG,i ≤P _DG,i,max )≥β _DG

in the formula: p is _DG,i Is a nodeDG force, P at i _DG,i,max Is the DG upper limit of the output, beta, at node i _DG Is DG output confidence level, Pr (0 ≦ P) _DG,i ≤P _DG,i,max ) The probability that DG output at the node i is qualified is given;

sixthly, restricting the switch operation times:

in the formula: lambda _ij,t 、λ _ij,t-1 On-off states of switches (i, j) for time period t and time period t-1, respectively, N _s Is the upper limit of the operation times of the total switch action.

7. The power distribution network dynamic reconstruction method based on the improved dual-scale spectral clustering algorithm according to claim 4, characterized in that: the step 5 comprises the following steps:

s5.1: reading network parameters and parameters of a fan and photovoltaic equipment, and setting algorithm related parameters including maximum iteration number K _max ，

S5.2: sampling random variables such as wind speed, solar radiation intensity and load to form a sampling matrix S _LSH ；

S5.3: defining a loop formed along the anticlockwise direction by taking the interconnection switch as a starting point as a basic loop; in order to obtain a set of initial feasible solutions, the method adopts a search mode of a loop group to obtain the initial feasible solutions, and the specific process is as follows:

Seed growing; firstly, closing the disconnected switch in one loop, maintaining the switch states of other loops unchanged, opening the next switch along the loop direction on the premise of ensuring radialization, storing the obtained feasible solution into a feasible solution set, and repeating the operations on all the switches of all the loops in sequence until the switches of all the loops are in a same orderThe switching scheme is consistent with the initial switching scheme;

the feasible solution set obtained by the method is used as an initial population;

s5.4: calculating a random power flow for a corresponding network topology scheme corresponding to each individual wolf, obtaining a system network loss value, a node voltage and a branch power flow out-of-limit probability, punishing a scheme violating opportunity constraint, obtaining a corresponding objective function value, and further calculating a fitness value of each individual;

s5.5: selecting the positions of three individuals with the minimum fitness values as alpha, beta and delta, and knowing according to the ranking of the wolf group, wherein alpha is a leader in the wolf group, beta is a second ranking, is only second to the existence of alpha, and is next to the delta wolf; because wolf groups obey command hunting of alpha, beta and delta, individuals are independent of each other, information exchange among individuals is lacked, so that the convergence speed of the algorithm is low, the convergence precision is low, and the like, a competition and cooperation mechanism is introduced, wherein the individuals except the alpha, beta and delta carry out the competition and cooperation mechanism according to the following formula:

in the formula:

are the individual wolfs after the cooperation mechanism respectively

And individual wolf

The location of the location;

s5.6: calculating the distances between other wolf individuals and alpha, beta and delta, wherein the specific expression is as follows:

and

the positions of alpha, beta and delta at the k generation,

is the location of the ith individual in the kth generation; c2. rand, [0,1 ]]A random number in between;

the variation formula is as follows:

x _g (k)＝x _g (k)+η×C(0,1)；

in the formula: x is the number of _g (t) is a K-generation global optimal solution, eta is a variation weight, C (0,1) is standard Cauchy random distribution during first iteration, and lambda is an adjustment parameter; K. k _max Respectively the current iteration times and the maximum iteration times;

s5.9: and (5) repeating the steps from S5.3 to S5.8 on the time interval division result until all the reconstruction time intervals are met, outputting the optimal grid structure and the corresponding objective function value, and ending the algorithm.

8. The method for dividing the time section of the power distribution network based on the adaptive aggregation algorithm is characterized by comprising the following steps of:

step a: performing cluster analysis on the running states of the power distribution network in the time section, and arranging the clustering results according to the time sequence to determine the number of segments and the starting and stopping moments of each segment so as to finish preliminary time interval division;

step b: and b, on the basis of the primary time interval division in the step a, performing secondary time interval division by using a self-adaptive time interval aggregation algorithm until the switching action times are met, wherein the secondary time interval division result is used as a final time interval division result.

9. The dynamic reconstruction mathematical optimization model based on opportunity constraint is characterized by comprising the following steps:

firstly, a distributed fan output randomness model:

in the formula: p _w,t Active power, P, emitted by the fan at time t _r Rated power for the generator; v. of _t Is the wind speed at time t, v _ci For cutting into the wind speed, v _r At rated wind speed, v _co For cutting out wind speed, where A ═ P _r /(v _r -v _ci )，B＝-Av _ci ；

a photovoltaic output model:

the power output probability density function of the photovoltaic generator is set as follows:

in the formula: gamma function, P _s For outputting power, P, from the solar panel _smax Alpha and Beta respectively represent the shape parameters of Beta distribution for the maximum value of the output power of the solar panel;

the desired value of the photovoltaic output power can be derived:

in the formula: f (P) _s ) As a function of the power output probability density of the photovoltaic generator, E (P) _s ) The photovoltaic output power expected value is obtained;

the objective function probability constraint is shown as follows:

min F；

Pr(f(X,ξ)≤F)≥β；

in the formula: f is an optimal target value which can be realized when a certain confidence level is met, X is a control variable, xi is a state variable, Pr (·) is the probability of event qualification, and beta is the confidence level; c. C _Ploss Is the electricity price of time period t, P _loss.t Is the network loss of a time interval t, and the delta t is 1 h; omega _b For branch set, M represents time interval after time interval division, M is total number of divided segments, c _act Cost of single switching action, s _l,m-1 、s _l,m The state of the switch on the branch l at the time interval m-1 and the time interval m is respectively 0 when the switch is opened and 1 when the switch is closed; f (X, xi) is the value of the comprehensive operation cost of the system in the state xi.