CN112507601A - Power system partition standby configuration method based on spectral clustering - Google Patents

Power system partition standby configuration method based on spectral clustering Download PDF

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CN112507601A
CN112507601A CN202011084466.6A CN202011084466A CN112507601A CN 112507601 A CN112507601 A CN 112507601A CN 202011084466 A CN202011084466 A CN 202011084466A CN 112507601 A CN112507601 A CN 112507601A
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standby
generator set
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CN112507601B (en
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倪秋龙
李祥
朱炳铨
唐剑
徐立中
董航
黄佳斌
苏宜靖
黄启航
陈鸿鑫
郭超
丁一
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Zhejiang University ZJU
State Grid Zhejiang Electric Power Co Ltd
Hangzhou Power Supply Co of State Grid Zhejiang Electric Power Co Ltd
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State Grid Zhejiang Electric Power Co Ltd
Hangzhou Power Supply Co of State Grid Zhejiang Electric Power Co Ltd
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Abstract

The invention discloses a power system partition standby configuration method based on spectral clustering. Selecting a plurality of lines which are easy to block according to the operation of the power system, and calculating a power transfer distribution factor matrix of the lines; calculating a node similarity matrix according to the power transfer distribution factor matrix; calculating an adjacency matrix and a degree matrix; calculating and standardizing a Laplace matrix, solving eigenvalues and eigenvectors, and extracting and constructing an eigenvector matrix; carrying out row-by-row normalization to obtain a new characteristic matrix, and clustering rows to obtain a standby partition result; and establishing a partition standby combined optimization scheduling model, solving to obtain a scheduling arrangement result, and controlling each node to work according to the scheduling arrangement result to realize partition standby configuration. The method of the invention considers the influence of active change of each node on the line tide in the operation process of the system, improves the utilization rate of the reserved standby, and realizes the effective operation of the system under the condition of ensuring the safety of the system.

Description

Power system partition standby configuration method based on spectral clustering
Technical Field
The invention belongs to a power system configuration control method in the field of power system reserve capacity allocation and scheduling, and particularly relates to a power system partition reserve configuration method based on spectral clustering.
Background
In order to ensure real-time balance of power supply of a power system and deal with uncertain factors such as load fluctuation, generator set faults and the like, the system needs to be configured with sufficient spare capacity. In the current dispatching mode in China, due to the constraint of transmission capacity of a transmission line, standby resources can not be effectively transmitted to a power shortage area, more standby capacity needs to be configured to deal with the fluctuation of renewable energy power generation along with the increase of the permeability of renewable energy, and the standby transmission blockage of the line is aggravated, so that the reliable operation of a system is influenced. The method is characterized in that partitions are set for standby, lines which are prone to being blocked are placed on the boundaries of the partitions, standby requirements in the partitions are provided by generator sets in the regions as far as possible, and the problem that standby cannot be used due to insufficient transmission capacity of the lines is solved. The traditional power system partitioning method is mainly based on the geographical position or the experience of a dispatcher, is lack of flexibility, and is difficult to deal with the output resistor plugs of the system in different running states.
Disclosure of Invention
Aiming at the technical problem that the backup is unavailable due to insufficient transmission capacity of a line in the existing scheduling mode, the invention provides a partition backup configuration method of a power system based on spectral clustering, which considers the influence of active change of each node on the line tide in the operation process of the system, slows down the transmission blocking degree of the line which is easy to block by the system, increases the utilization rate of the reserved backup of the power system, and realizes effective operation and low-consumption operation of the system under the condition of ensuring the safety.
As shown in fig. 1, the technical solution of the present invention is as follows:
step 1: selecting a plurality of lines which are easy to block according to the operation condition of the power system and the load distribution condition of the nodes, and calculating a power transfer distribution factor matrix H' of the lines which are easy to block;
the node is a connection point of a branch in the network; when the power system network model is established, a part of electrical equipment is collected to serve as power system nodes, all the power system nodes are connected through power transmission lines, and power generating sets are arranged in the power system nodes.
Step 2: calculating a node similarity matrix S according to the power transfer distribution factor matrix H';
in specific implementation, the node similarity matrix S may be used to assign weights to lines between nodes in the power system, where if the nodes are wirelessly connected, the weights are zero, and if the nodes are wirelessly connected, the weights are corresponding similarities, so as to construct the non-oriented weighting graph G.
And step 3: calculating an adjacent matrix W and a degree matrix D by the node similarity matrix S;
and 4, step 4: the Laplace matrix L is calculated by subtracting the adjacency matrix W from the utilization matrix D, and the Laplace matrix is normalized by D-1/2LD-1/2Processing, then solving eigenvalues and eigenvectors of the normalized Laplacian matrix, extracting eigenvectors corresponding to the minimum m eigenvalues and forming an eigenvector matrix f;
and 5: normalizing the feature vector matrix F row by row to obtain a new feature matrix F, wherein the new feature matrix F is an n multiplied by m matrix, each row in the new feature matrix F is clustered by a k-means method by using a row unit to obtain Q types of results which are used as standby partition results, and all nodes in each type are classified into a standby partition;
step 6: and establishing a partition and standby combined optimization scheduling model by using the standby partition results, solving to obtain a scheduling arrangement result, and adjusting the running state, the planned output and the standby allocation of the generator set at each moment according to the scheduling arrangement result.
In the step 1, the method specifically comprises the following steps:
firstly, calculating a power transmission distribution factor of a line easy to block, wherein the calculation formula is as follows:
Figure BDA0002719876300000021
in the formula, PTDFk-iRepresenting the power transmission profile, X, of node i to the susceptible line kciFor node admittance matrix B under direct current power flow0Row c, column i, element X of the inverse matrixdiFor node admittance matrix B under direct current power flow0Of the d-th row and i-th column element, x of the inverse matrixkThe reactance value of the easy-to-block line k;
constructing a power transfer distribution factor matrix (PTDF) matrix H' of the easy-to-block line as follows:
Figure BDA0002719876300000022
hk,i＝PTDFk-i
wherein h isk,iRepresenting the ith row and the ith column of elements in a power transfer distribution factor matrix H', namely the power transmission distribution factor of a node i to a line k easy to block; n is the total number of nodes of the power system. One column represents a node and one row represents a line that is susceptible to blocking.
In step 2, the invention converts the power system energy into an undirected weighted graph G, which is described by a node set V and a line set E. Node set V ═ V1,v2,...,vnThe node is expressed as a set formed by all nodes in the power grid, wherein n is the number of all the nodes, and a line set E is { E ═ E }1,e2,...,enlRepresents the set of all lines in the system, and nl is the total number of lines in the power system.
In the step 2, the similarity s between the nodesijObtaining the following result according to the calculation processing of a power transfer distribution factor matrix H' of the line easy to block:
Figure BDA0002719876300000031
σi＝d(Hi,Hz)
wherein σiScale parameter, d (H), representing node ii,Hz) Is composed ofThe smallest z-th distance value in all distances between the node i and each other node, wherein in the invention, z is 7; hiRepresenting a column vector where a node i in a power transfer distribution factor matrix H' is corresponding to, namely a column vector of an ith column;
Figure BDA0002719876300000036
denotes the two norm, sijRepresenting the similarity between node i and node j; exp () represents an exponential function; from similarity sijAnd the element is used as the element of the ith row and the jth column in the node similarity matrix S, so that the node similarity matrix S is obtained.
In the step 3, the adjacency matrix W is obtained by processing as follows: when there is a line connection between node i and node j (node v)iAnd node vjThere is an edge connection), the element W of the jth row and jth column of the adjacent matrix WijIs taken as wij＝sij，sijRepresenting the similarity between node i and node j; when the wireless link between node i and node j is connected, the element W of the jth row and jth column of the adjacency matrix Wij＝0：
Figure BDA0002719876300000032
Wherein E represents a set formed by all lines of the power system;
the line is weighted with a weight value of wij. Forming a contiguous matrix W, W being a symmetric matrix of n × n:
Figure BDA0002719876300000033
processing the computation degree matrix D according to the adjacency matrix W as follows:
Figure BDA0002719876300000034
wherein, wijRepresents the ith row of the adjacency matrix WElement of j column, diThe ith element on the opposite corner of the degree matrix D is represented, and the off-diagonal elements of the degree matrix D are all 0.
The degree matrix D is an n × n diagonal matrix, as follows:
Figure BDA0002719876300000035
in the step 5, the feature vector matrix f is normalized line by line according to the following formula:
Figure BDA0002719876300000041
wherein f isijElements representing the ith row and jth column in a feature vector matrix f, fij *Elements, f, representing the ith row and jth column in the normalized eigenvector matrix fioRepresenting the elements of the ith row and the ith column in the feature vector matrix f.
In step 6, the optimization goal of the partitioned standby combined optimization scheduling model is that the sum of the power generation cost and the standby cost in all time periods scheduled in the day before is the minimum, and the optimization goal is specifically as follows:
Figure BDA0002719876300000042
in the formula, t is a time period number; NT is a time period set in a scheduling cycle; i represents a node number of the power system; n is a node number set of the power system; NGiThe method comprises the steps of collecting generator sets in a node i of the power system; GCgThe power generation cost function of the generator set is a quadratic function; pg,tIs the active output level of the generator set g at time t; RU (RU)g,tAnd PRUg,tRespectively representing the amount of the standby generator set g in the positive operation at the time t and the margin coefficient; RDg,tAnd PRDg,tRespectively representing the quantity of the negative operation standby of the generator set g at the time t and a margin coefficient; NLGgIs a fixed operating coefficient of the generator set g; SUgAnd SDgThe starting margin coefficient and the shutdown margin coefficient of the generator set g are obtained; x is the number ofg,t、yg,t、zg,tThe variable is 0-1 and respectively represents the running state, the starting state and the shutdown state of the generator set g at the time t;
meanwhile, the following node energy balance constraint, node voltage constraint, generator set output constraint, generator set climbing constraint, generator set positive running standby constraint, generator set negative running standby constraint, generator set climbing constraint, partition standby capacity constraint, line tide constraint, generator set minimum running and stopping time constraint and integer variable constraint are established, and the following steps are shown:
1) node energy balance constraint:
Figure BDA0002719876300000043
in the formula, NWiThe method comprises the steps of collecting wind generating sets in a node i of the power system; pw,tThe output of the wind generating set w at the moment t; NLiLoad set in the node i of the power system; pd,tIs the active load at time t; b isijRepresenting the admittance of a transmission line between node i and node j; thetai,tThe phase of the voltage at node i at time t; j is a node in the node set which is connected with the node i;
2) and (3) output restraint of the generator set:
Figure BDA0002719876300000044
in the formula (I), the compound is shown in the specification,
Figure BDA0002719876300000051
and
Figure BDA0002719876300000052
respectively representing the active output upper and lower limits of the generator set;
3) the generator set is in operation for standby restraint:
Figure BDA0002719876300000053
Figure BDA0002719876300000054
wherein T10 represents 10 minutes;
Figure BDA0002719876300000055
the maximum climbing rate of the generator set g;
4) and (3) carrying out negative operation standby restraint on the generator set:
Figure BDA0002719876300000056
Figure BDA0002719876300000057
in the formula (I), the compound is shown in the specification,
Figure BDA0002719876300000058
the maximum downward climbing speed of the generator set g;
5) and (3) generator set climbing restraint:
Figure BDA0002719876300000059
Figure BDA00027198763000000510
in the formula, T represents the time length between adjacent scheduling moments;
6) partition spare capacity constraint:
Figure BDA00027198763000000511
Figure BDA00027198763000000512
wherein, PTDFaIndicating the a-th standby partition in the power system standby partition result;
Figure BDA00027198763000000513
respectively setting positive and negative standby requirements of the a-th standby partition in the standby partition result at the moment t of the power system;
7) and (3) line power flow constraint:
Figure BDA00027198763000000514
in the formula (I), the compound is shown in the specification,
Figure BDA00027198763000000515
expressed as the maximum transmission capacity of the transmission line between node i and node j;
8) minimum run and downtime constraints for the generator set:
Figure BDA00027198763000000516
Figure BDA00027198763000000517
wherein, DTgRepresenting a minimum shutdown duration for the generator set; λ denotes the time interval, UTgRepresenting a minimum operating duration of the generator set;
9) integer variable constraints
yg,t-zg,t＝xg,t-1-xg,t
yg,t+zg,t＝1
xg,t,yg,t,zg,t∈{0,1}
Finally, proceed withSolving to obtain the running state x of the generator set g at the time tg,tActive power output level P of generator set g in running state at time tg,tAnd the negative running standby quantity RD of the generator set g at the time tg,tAnd the positive running standby quantity RU of the generator set g at the time tg,tAnd performing partition standby configuration adjustment on the dispatching arrangement result to adjust the running state, planned output and standby allocation of the generator set at the corresponding moment.
The spectral clustering is a clustering method derived from graph theory, and the purpose of clustering is achieved by clustering the eigenvectors of the data Laplacian matrix and solving the optimal segmentation set of the graph.
The invention has the beneficial effects that:
1) the partition standby configuration method adopted by the technical scheme is less influenced by the distribution characteristics of the power data, can be converged to a global optimal solution, and is stable in partition standby configuration result.
2) The invention can construct reasonable standby partitions, takes the influence of standby resource calling on the line trend into consideration, slows down the transmission blocking degree of the lines which are easy to block by the power system, improves the utilization rate of reserved standby, and realizes the effective operation and low-cost operation of the power system under the condition of ensuring the safety of the power system.
Drawings
FIG. 1 is a flow chart of the technical solution of the present invention;
FIG. 2 is a diagram of a 30-node system topology according to an embodiment of the present invention;
FIG. 3 is a graph of predicted load versus actual load for a system according to an embodiment;
FIG. 4 is a graph of predicted output curve and actual output curve of the wind turbine generator set according to the embodiment;
fig. 5 is a partition result diagram of the embodiment with the period t 1;
FIG. 6 is a graph showing the results of the forward and backward load shedding for the divisional regions according to the embodiment;
FIG. 7 is a pre-and post-partition backup utilization curve for an embodiment.
Detailed Description
The method of the present invention will be further described with reference to the following examples and the accompanying drawings.
The embodiment of the invention and the implementation process thereof are as follows:
step 1: and selecting a plurality of easily-blocked lines according to the predicted load distribution and the predicted wind power output of the system nodes, and calculating a power transfer distribution factor matrix H' of the easily-blocked lines.
Step 2: and calculating a node similarity matrix S by H', weighting the system line, and constructing an undirected weighted graph G ═ V, E }.
The power system abstraction is converted into an undirected weighted graph G, which can be described by a vertex set V and an edge set E. Set of vertices V ═ V1,v2,...,vnThe node is expressed as a set formed by all bus nodes in the power grid, wherein n is the number of all nodes, and an edge set E is { E ═ E }1,e2,...,enlAnd represents the set of all lines in the system, and nl is the total number of lines in the system.
For two points V in the set of vertices ViAnd vjSimilarity between nodes sijPTDF metric by its vulnerable blocking line:
Figure BDA0002719876300000071
wherein the scale parameter σi＝d(Hi,Hz)，d(Hi,Hz) The z-th distance value, which is the smallest of all distances between the node i and each of the other nodes, in the present invention, z takes 7. HiAnd the column vector corresponding to the node i in the power transfer distribution factor matrix H', namely the column vector of the ith column, is represented.
And step 3: an adjacency matrix W and a degree matrix D are calculated from the matrix S.
Assigning weight to opposite sides, the weight value is wij. For wijWhen v isiAnd vjWhen there is an edge connection (wireless path between nodes i, j), wij＝sij>0, when v isiAnd vjWhen there is no edge connection, wij＝0。
Figure BDA0002719876300000072
Forming a contiguous matrix W, W being a symmetric matrix of n,
Figure BDA0002719876300000073
for any vertex V in vertex set ViThe degree expression of the vertex is:
Figure BDA0002719876300000074
i.e. equal to the weight w of all edges connected to the vertexijThe sum, representing the relationship with all other vertices. The degree matrix D is an n × n diagonal matrix, as follows:
Figure BDA0002719876300000075
and 4, step 4: calculating a corresponding Laplace matrix L and normalizing the Laplace matrix D-1/2LD-1/2. And solving the normalized Laplace matrix eigenvalue and eigenvector, and extracting the eigenvector matrix f corresponding to the minimum m eigenvalues.
And 5: and normalizing the feature vector matrix F line by line to construct a new feature matrix F. And clustering the rows in the new characteristic matrix F by a k-means method to obtain Q-type results.
The method for the row-by-row normalized calculation of the feature vector matrix f comprises the following steps:
Figure BDA0002719876300000081
step 6: and establishing a partition standby combined optimization scheduling model based on the standby partition results, and solving to obtain a scheduling arrangement result.
The optimization goal of the partitioned standby combined optimization scheduling model is that the sum of the power generation cost and the standby cost in all time periods scheduled in the day before is the minimum, and the optimization goal is specifically as follows:
Figure BDA0002719876300000082
in the formula, t is a time period number; NT is a time period set in a scheduling cycle; i represents a node number of the power system; n is a node number set of the power system; NGiThe method comprises the steps of collecting generator sets in a node i of the power system; GCgThe power generation cost function of the generator set is a quadratic function; pg,tIs the active output level of the generator set g at time t; RU (RU)g,tAnd PRUg,tRespectively representing the positive running standby quantity and the marginal coefficient of the generator set g at the time t; RDg,tAnd PRDg,tRespectively the negative running standby quantity and the marginal coefficient of the generator set g at the time t; NLGgIs a fixed operating coefficient of the generator set g; SUgAnd SDgThe starting margin coefficient and the shutdown margin coefficient of the generator set g are obtained; x is the number ofg,t，yg,t，zg,tAnd variables of 0-1 represent the running state, the starting state and the shutdown state of the generator set g at the time t respectively.
The constraint conditions required to be met by the model comprise node energy balance constraint, node voltage constraint, generator set output constraint, generator set climbing constraint, generator set positive operation standby constraint, generator set negative operation standby constraint, generator set climbing constraint, partition standby capacity constraint, line tide constraint, generator set minimum operation and downtime constraint and integer variable constraint. The mathematical expression of its constraints is as follows:
1) node energy balance constraint:
Figure BDA0002719876300000083
in the formula, NWiThe method comprises the steps of collecting wind generating sets in a node i of the power system; pw,tThe output of the wind generating set w at the moment t; NLiLoad set in the node i of the power system; pd,tWhen isThe active load of the moment t; b isijRepresenting the admittance of a transmission line between node i and node j; thetai,tThe phase of the voltage at node i at time t; j e i is the set of all nodes associated with node i.
2) And (3) output restraint of the generator set:
Figure BDA0002719876300000091
in the formula (I), the compound is shown in the specification,
Figure BDA0002719876300000092
and
Figure BDA0002719876300000093
respectively representing the upper limit and the lower limit of the active output of the generator set.
3) The generator set is in operation for standby restraint:
Figure BDA0002719876300000094
Figure BDA0002719876300000095
wherein T10 represents 10 minutes;
Figure BDA0002719876300000096
the maximum descent rate of the generator set g.
4) And (3) carrying out negative operation standby restraint on the generator set:
Figure BDA0002719876300000097
Figure BDA0002719876300000098
in the formula (I), the compound is shown in the specification,
Figure BDA0002719876300000099
the maximum descent rate of the generator set g.
5) And (3) generator set climbing restraint:
Figure BDA00027198763000000910
Figure BDA00027198763000000911
6) partition spare capacity constraint:
Figure BDA00027198763000000912
Figure BDA00027198763000000913
wherein, PTDFaIndicating the a-th standby partition in the power system standby partition result;
Figure BDA00027198763000000914
the positive and negative standby requirements of the a-th standby partition in the standby partition result at the moment t of the power system are respectively.
7) And (3) line power flow constraint:
Figure BDA00027198763000000915
in the formula (I), the compound is shown in the specification,
Figure BDA00027198763000000916
expressed as the maximum transmission capacity of the transmission line between node i and node j.
8) Minimum run and downtime constraints for the generator set:
Figure BDA00027198763000000917
Figure BDA00027198763000000918
wherein, DTgRepresenting a minimum shutdown duration for the generator set; UT (unified device)gRepresenting a minimum operating duration of the genset.
9) Integer variable constraints
yg,t-zg,t＝xg,t-1-xg,t
yg,t+zg,t＝1
xg,t,yg,t,zg,t∈{0,1}
Examples
The invention is adopted to carry out partition standby configuration scheduling on the 30-node system, and the topological structure of the 30-node system is shown in figure 2. The system scheduling cycle is set to be one day, namely 24h, the regional reserve capacity is set to be 10% of predicted load in a region and 15% of predicted wind generating set output, and the 30-node system generating set parameters are shown in table 1:
TABLE 1 Generator set parameters
Figure BDA0002719876300000101
The system predicted load data and the actual load data are shown in fig. 3, and the fan predicted output data and the actual fan output data are shown in fig. 4.
And calculating to obtain an easy-to-block line by utilizing the predicted load and the predicted fan output of each time period, calculating a PTDF matrix about the easy-to-block line, dividing nodes by utilizing a spectral clustering algorithm, and establishing a standby partition of the corresponding time period. the system spare partition for period t1 is shown in fig. 5.
And establishing a partition standby combined optimization scheduling model based on the standby partitions, and solving by using CPLEX to obtain a power-on/off plan, an output level and an operation standby arrangement of the generator set.
Because the load and the wind power predicted output have certain errors, real-time scheduling needs to be carried out based on the actual load and the actual wind power output of the system at each time interval on the basis of the planned output and the standby output of the day-ahead scheduling. Compared with the method of the invention, the action of improving the standby utilization rate (the standby utilization rate is the actually called standby capacity/the configured total standby capacity) is realized by configuring the upper limit of the output of the generator set as the positive running standby capacity of the generator set at the moment before the day and configuring the lower limit as the negative running standby capacity at the moment, and performing real-time scheduling solution, wherein the load shedding amount before and after the partition is shown in fig. 6, and the standby utilization rate curve before and after the partition is shown in fig. 7.
As can be seen from fig. 6 and 7, the method of the present invention can avoid a large amount of load shedding and improve the utilization rate of the reserved spare. When the backup allocation is arranged, compared with the traditional backup allocation method, the method also needs to consider the influence of the backup resource calling on the line trend, slow down the transmission blocking degree of the line which is easy to block by the system and ensure the reliable operation of the power system.

Claims (6)

1. A power system partition standby configuration method based on spectral clustering is characterized by comprising the following steps:
step 1: selecting a plurality of lines which are easy to block according to the operation condition of the power system and the load distribution condition of the nodes, and calculating a power transfer distribution factor matrix H' of the lines which are easy to block;
step 2: calculating a node similarity matrix S according to the power transfer distribution factor matrix H';
and step 3: calculating an adjacent matrix W and a degree matrix D by the node similarity matrix S;
and 4, step 4: the Laplace matrix L is calculated by subtracting the adjacency matrix W from the utilization matrix D, and the Laplace matrix is normalized by D-1/2LD-1/2Processing, then solving eigenvalues and eigenvectors of the normalized Laplacian matrix, extracting eigenvectors corresponding to the minimum m eigenvalues and forming an eigenvector matrix f;
and 5: normalizing the feature vector matrix F row by row to obtain a new feature matrix F, clustering rows in the new feature matrix F by using a k-means method according to row units in the new feature matrix F to obtain Q-class results as standby partition results, and classifying all nodes in each class into a standby partition;
step 6: and establishing a partition and standby combined optimization scheduling model by using the standby partition results, solving to obtain a scheduling arrangement result, and adjusting the running state, the planned output and the standby allocation of the generator set at each moment according to the scheduling arrangement result.
2. The power system partition standby configuration method based on spectral clustering according to claim 1, characterized in that: in the step 1, the method specifically comprises the following steps:
firstly, calculating a power transmission distribution factor of a line easy to block, wherein the calculation formula is as follows:
Figure FDA0002719876290000011
in the formula, PTDFk-iRepresenting the power transmission profile, X, of node i to the susceptible line kciFor node admittance matrix B under direct current power flow0Row c, column i, element X of the inverse matrixdiFor node admittance matrix B under direct current power flow0Of the d-th row and i-th column element, x of the inverse matrixkThe reactance value of the easy-to-block line k;
constructing a power transfer distribution factor matrix (PTDF) matrix H' of the easy-to-block line as follows:
Figure FDA0002719876290000012
hk,i＝PTDFk-i
wherein h isk,iRepresenting the ith row and the ith column of elements in a power transfer distribution factor matrix H', namely the power transmission distribution factor of a node i to a line k easy to block; n is the total number of nodes of the power system.
3. The power system partition standby configuration method based on spectral clustering according to claim 1, characterized in that: in the step 2, the similarity s between the nodesijObtaining the following result according to the calculation processing of a power transfer distribution factor matrix H' of the line easy to block:
Figure FDA0002719876290000021
σi＝d(Hi,Hz)
wherein σiScale parameter, d (H), representing node ii,Hz) The z-th distance value which is the smallest of all distances between the node i and each of the other nodes; hiRepresenting a column vector where a node i in a power transfer distribution factor matrix H' is corresponding to, namely a column vector of an ith column;
Figure FDA0002719876290000025
denotes the two norm, sijRepresenting the similarity between node i and node j; exp () represents an exponential function; from similarity sijAnd the element is used as the element of the ith row and the jth column in the node similarity matrix S, so that the node similarity matrix S is obtained.
4. The power system partition standby configuration method based on spectral clustering according to claim 1, characterized in that: in the step 3, the adjacency matrix W is obtained by processing as follows: when there is a line connection between node i and node j, the element W of the jth row and jth column of the adjacency matrix WijIs taken as wij＝sij，sijRepresenting the similarity between node i and node j; when the wireless link between node i and node j is connected, the element W of the jth row and jth column of the adjacency matrix Wij＝0：
Figure FDA0002719876290000022
Wherein E represents a set formed by all lines of the power system;
processing the computation degree matrix D according to the adjacency matrix W as follows:
Figure FDA0002719876290000023
wherein, wijElements representing the ith row and the jth column of the adjacency matrix W, diThe ith element on the opposite corner of the degree matrix D is represented, and the off-diagonal elements of the degree matrix D are all 0.
5. The power system partition standby configuration method based on spectral clustering according to claim 1, characterized in that: in the step 5, the feature vector matrix f is normalized line by line according to the following formula:
Figure FDA0002719876290000024
wherein f isijElements representing the ith row and jth column in a feature vector matrix f, fij *Elements, f, representing the ith row and jth column in the normalized eigenvector matrix fioRepresenting the elements of the ith row and the ith column in the feature vector matrix f.
6. The power system partition standby configuration method based on spectral clustering according to claim 1, characterized in that: in step 6, the optimization goal of the partitioned standby combined optimization scheduling model is that the sum of the power generation cost and the standby cost in all time periods scheduled in the day before is the minimum, and the optimization goal is specifically as follows:
Figure FDA0002719876290000031
in the formula, t is a time period number; NT is a time period set in a scheduling cycle; i represents the power trainNumbering nodes of the system; n is a node number set of the power system; NGiThe method comprises the steps of collecting generator sets in a node i of the power system; GCgThe power generation cost function of the generator set is a quadratic function; pg,tIs the active output level of the generator set g at time t; RU (RU)g,tAnd PRUg,tRespectively representing the amount of the standby generator set g in the positive operation at the time t and the margin coefficient; RDg,tAnd PRDg,tRespectively representing the quantity of the negative operation standby of the generator set g at the time t and a margin coefficient; NLGgIs a fixed operating coefficient of the generator set g; SUgAnd SDgThe starting margin coefficient and the shutdown margin coefficient of the generator set g are obtained; x is the number ofg,t、yg,t、zg,tThe variable is 0-1 and respectively represents the running state, the starting state and the shutdown state of the generator set g at the time t;
meanwhile, the following node energy balance constraint, node voltage constraint, generator set output constraint, generator set climbing constraint, generator set positive running standby constraint, generator set negative running standby constraint, generator set climbing constraint, partition standby capacity constraint, line tide constraint, generator set minimum running and stopping time constraint and integer variable constraint are established, and the following steps are shown:
1) node energy balance constraint:
Figure FDA0002719876290000032
in the formula, NWiThe method comprises the steps of collecting wind generating sets in a node i of the power system; pw,tThe output of the wind generating set w at the moment t; NLiLoad set in the node i of the power system; pd,tIs the active load at time t; b isijRepresenting the admittance of a transmission line between node i and node j; thetai,tThe phase of the voltage at node i at time t; j is a node in the node set which is connected with the node i;
2) and (3) output restraint of the generator set:
Figure FDA0002719876290000033
in the formula (I), the compound is shown in the specification,
Figure FDA0002719876290000034
and
Figure FDA0002719876290000035
respectively representing the active output upper and lower limits of the generator set;
3) the generator set is in operation for standby restraint:
Figure FDA0002719876290000036
Figure FDA0002719876290000037
wherein T10 represents 10 minutes;
Figure FDA0002719876290000041
the maximum climbing rate of the generator set g;
4) and (3) carrying out negative operation standby restraint on the generator set:
Figure FDA0002719876290000042
Figure FDA0002719876290000043
in the formula (I), the compound is shown in the specification,
Figure FDA0002719876290000044
the maximum downward climbing speed of the generator set g;
5) and (3) generator set climbing restraint:
Figure FDA0002719876290000045
Figure FDA0002719876290000046
in the formula, T represents the time length between adjacent scheduling moments;
6) partition spare capacity constraint:
Figure FDA0002719876290000047
Figure FDA0002719876290000048
wherein, PTDFaIndicating the a-th standby partition in the power system standby partition result;
Figure FDA0002719876290000049
respectively setting positive and negative standby requirements of the a-th standby partition in the standby partition result at the moment t of the power system;
7) and (3) line power flow constraint:
Figure FDA00027198762900000410
in the formula (I), the compound is shown in the specification,
Figure FDA00027198762900000411
expressed as the maximum transmission capacity of the transmission line between node i and node j;
8) minimum run and downtime constraints for the generator set:
Figure FDA00027198762900000412
Figure FDA00027198762900000413
wherein, DTgRepresenting a minimum shutdown duration for the generator set; λ denotes the time interval, UTgRepresenting a minimum operating duration of the generator set;
9) integer variable constraints
yg,t-zg,t＝xg,t-1-xg,t
yg,t+zg,t＝1
xg,t,yg,t,zg,t∈{0,1}
Finally, solving is carried out to obtain the running state x of the generator set g at the time tg,tActive power output level P of generator set g in running state at time tg,tAnd the negative running standby quantity RD of the generator set g at the time tg,tAnd the positive running standby quantity RU of the generator set g at the time tg,tAnd performing partition standby configuration adjustment on the dispatching arrangement result to adjust the running state, planned output and standby allocation of the generator set at the corresponding moment.
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