CN107017632B - A Power System Active Disconnection Section Search Method and Islanding Adjustment Strategy - Google Patents

Abstract

The present invention proposes a kind of electric system Active Splitting section searching method and isolated island adjustable strategies.First, electric system Active Splitting section searching method improves the spectral clustering to grow up in machine learning field, the spectral clustering containing constraint is proposed, in terms of and the coherent constraints of generating set, to convert generalized eigenvalue Solve problems for off-the-line section search problem.To overcome in the spectral clustering containing constraint using, search efficiency low disadvantage sensitive to initial center point existing for tradition k-medoids algorithm, proposing to improve k-medoids algorithm and combining it with constraint spectral clustering, to seek optimal solution column section.Then, for each isolated island for being unsatisfactory for security constraint, its generating set power output is optimized and revised, some loads can also be cut down, when necessary to maintain the safe operation of each isolated island.Finally, illustrating feasibility and validity of the invention by taking 118 node of IEEE as an example.

Description

A Power System Active Disconnection Section Search Method and Islanding Adjustment Strategy

technical field

The invention relates to the field of power system restoration, in particular to the strategy of actively disconnecting section search and islanding adjustment of the power system.

Background technique

As an emergency control method, decoupling is the last line of defense for the safe and stable operation of the power system. Its function is to isolate the asynchronous cluster, block the propagation of faults, and avoid large-scale power outages. The traditional out-of-step separation method uses offline analysis to determine the separation section and install the separation device, which has been widely used in the actual power system. However, with the continuous expansion of the system scale and the formation of cross-regional interconnection grids, it is difficult for out-of-step splitting to adapt to the current complex and changeable system conditions. If we can start from the overall situation of the power system, use the wide-area measurement system (WAMS) and high-speed communication system that have been widely used in recent years to monitor the system status in real time, and make coordinated decisions based on fault information before the system collapses, and actively Decomposing a large system into several independent small systems can effectively prevent cascading failures. This disassembly method based on real-time information online decision-making is called active disassembly. In the active solution, how to determine the optimal solution section is the core problem. For this problem, experts and scholars at home and abroad have proposed some methods, which can be generally divided into three categories, namely, methods based on slow coherence theory, artificial intelligence and graph theory. method.

Contents of the invention

In order to determine the optimal solution section, the present invention proposes an active solution section search method for a power system based on the graph partition criterion—Normal cut criterion (Ncut), which converts the NP-hard graph partition problem into an eigenvalue solving problem, And by solving the generalized eigenvalue problem and clustering and dividing part of the eigenvectors, the solution section of the system that satisfies the coherence constraints is finally obtained.

After the power system is disassembled, in order to ensure the safe and stable operation of each island, it is necessary to optimize and adjust the island nodes. Therefore, the present invention also proposes an island adjustment strategy based on the above method.

In order to solve the problems of the technologies described above, the technical solution of the present invention is as follows:

A power system active disassembly section search method is an active disassembly section search method based on constrained spectral clustering. It introduces unit coherence constraints into the spectral clustering algorithm, uses constraints to supervise the clustering process and limits feasible Solution space, so as to obtain the solution section that satisfies the constraints;

Let the undirected edge weight graph G=(V, E) represent the power system of n nodes, where V is the point set of graph G, E is the edge set of graph G, and the weight value of each edge e _ij in graph G is given is w _ij , define weighted adjacency matrix W, degree matrix D and graph size V _g (G), where the matrix elements of weighted adjacency matrix W and degree matrix D are:

The graph scale V _g (G) is:

Let P _ij be the power flow from node i to node j on line ij, then the matrix elements of the weighted adjacency matrix W of the system are:

In the constructed spectral clustering algorithm with constraints, unit coherence constraints can be described by two types of constraints, namely MustLink, referred to as ML and Cannot Link, referred to as CL; the representation of ML constraints between two nodes needs to ensure that the two The nodes are in the same partition, and the corresponding CL constraints represent that the two nodes must be in different partitions when the graph is divided; in order to reflect the two types of constraints of ML and CL in the spectral clustering algorithm, an n×n constraint matrix is defined Q, its matrix elements are shown in formula (5):

In the formula: i and j represent any two nodes in the power system;

Define the clustering index vector u∈{-1, 1} ⁿ , assuming that the graph is divided to form two independent subgraphs, graph J and graph M respectively, if node i belongs to graph J then u _i =1, if node i belongs to graph M then u _i =-1; from this we can get:

In the formula: u ^T Qu represents the degree to which the constraints are satisfied. When Q _ij = 1 and u _i and u _j have the same sign, its value is larger; when Q _ij = 1 and u _i and u _j have different signs or Q _ij =-1 and when u _i and u _j have the same sign, its value is smaller; it can be seen that the larger u ^T Qu is, the more likely the clustering result satisfies the given constraints;

In order to meet different constraint strengths, u and Q are relaxed in the range of real numbers, that is, u and Q can take any real value; after such relaxation, if units i and j are coherent units, they belong to ML constraints, given Q _ij >0, the larger the value, the stronger the coherence constraint between the two units; if the units i and j are non-coherent units, which belong to the CL constraint, Q _ij <0 can be given, and the smaller the value, the stronger the coherence constraints between the two units. The stronger the separation constraints between units; thus, the unit coherence and separation constraints can be introduced into the spectral clustering process;

Define the normalized Laplacian matrix L _N and the normalized constraint matrix Q _N as shown in formula (7) and formula (8);

L _N = D ^-1/2 LD ^1/2 (7)

Q _N =D ^-1/2 QD ^1/2 (8)

Define the vector v=D ^1/2 u and the constraint lower limit constant β, then the graph partition problem with constraints can be expressed by the optimization problem described by formula (9):

In the formula: the objective function v ^T L _N v is the Ncut value of the graph division; v ^T Q _N v>β defines the lower limit of the degree of satisfaction of the given constraints; v ^T v=V _g (G) ensures that v is a normalized vector; v≠ D ^1/2 1 excludes trivial solutions, that is, avoids meaningless graph segmentation schemes;

Solve the generalized eigenvalue problem of formula (10), that is, obtain the solution of the optimization problem described by formula (9), wherein the value range of the constraint lower limit constant β is given by formula (11);

λ _min (Q _N )×V _g (G)<β<λ _k (Q _N )×V _g (G) (11)

In the formula: λ _min (Q _N ) and λ _k (Q _N ) are the smallest eigenvalue and the kth smallest eigenvalue of the matrix Q _N respectively; k is the number of partitions after the system is sorted;

The power system active disconnection section search method includes the following steps:

1) Determining the number k of split partitions according to the unit co-modulation information;

2) Calculate the weighted adjacency matrix W, unnormalized Laplacian matrix L, and normalized Laplacian matrix L _N of the power system respectively according to the power system topology and power flow state;

3) Construct the constraint matrix Q according to the unit coherence information, and calculate the normalized constraint matrix Q _N ;

4) Determine the constraint lower limit constant β;

5) Solving formula Described generalized eigenvalue problems;

6) Eliminate the eigenvectors corresponding to non-positive eigenvalues, and normalize the remaining eigenvectors:

7) Let the eigenvectors (v ₁ , v ₂ , ..., v _k ) corresponding to the first k smallest eigenvalues form a matrix V∈R ^n×k ;

8) Each row of V is regarded as a vector in the k-dimensional space, and the clustering algorithm is used for clustering and division. The category of each row in the obtained clustering result is the partition to which each node in the power system belongs. Thus, The system split section can be determined.

Preferably, step 8) adopts the improved k-medoids clustering algorithm to carry out clustering division, and its specific process is: arbitrarily select some objects as the initial center point, and all non-center point objects are carried out according to the principle of the minimum distance from the center point After the first division, the initial center point is adjusted within the cluster, and the point in each cluster with the smallest distance from other points in the same cluster is selected as the fine-tuned center point; after the initial center point is determined, each time the center point is replaced, use Gradually expanding search, that is, the search range of the new center point is limited to the set candidate set, and the candidate set gradually expands as the number of iterations increases, that is, the mth center point replacement iteration is currently being performed, and the candidate set is set to be away from the original center All non-central point objects in the nearest m clusters, the new central point is searched within the scope of the candidate set; when the m+1th central point is replaced, the candidate set is the non-central point objects in the m+1 nearest clusters. The center point object, and so on; in this way, as the number of iterations increases gradually, the candidate set of new center points gradually expands until it expands to the whole world or completes clustering.

The islanding adjustment strategy based on the active decoupling section search method of the power system is an island node adjustment strategy combining the proximity principle and power flow tracking. After decoupling, in order to ensure the safe and stable operation of each island, it is necessary to optimize and adjust the island nodes;

The details are as follows: after obtaining the optimal disassembly section, firstly calculate the node adjustment domain of degree 1 to n of the faulty node and the utilization coefficient of nodes in the adjustment domain to the disassembly section; then, starting from the faulty node, according to the degree of the adjustment domain from small to small In the same adjustment domain, the power generation node with a higher utilization factor for the transmission section will be adjusted first. If there is still unbalanced power after the adjustment of the generator, the node load will be reduced in the same way until the island is reached. until the safe operation requirements are met.

Preferably, firstly define the associated nodes of the split-section line as faulty nodes, and call the point set that is connected to the faulty node through a line and remove the non-identical island nodes as the 1-degree node adjustment domain; The point set connected by a line and except the non-identical island nodes is a 2-degree node adjustment domain, and so on; the larger the degree of the node adjustment domain, the farther the node in the domain is from the faulty node; if the point set V _j is the point set V _i If it is directly connected by a line, then the V _j search process is recorded as f _s (V _i )=V _j , then the n-degree node adjustment domain of the faulty node can be calculated by the following formula:

V _e ⁿ =f _s (V _e ^n-1 )-V _t (12)

In the formula: V _e is the faulty node, V _e ⁿ is the n-degree node adjustment domain of the faulty node, V _t is the point set that is in a different island from V _e ; formula (12) is a recursive formula, and the breadth search algorithm can be used BFS recursively calculates the 1, 2, ..., n-degree node adjustment domain of the faulty node V _e ;

After that, the relative distance between each node and the fault node can be determined;

For the nodes in the same adjustment domain, the power flow tracking method is used to calculate the utilization coefficient of the transmission section, so as to determine the order of adjustment; the power flow tracking method is based on the basic assumption of proportional sharing, and can determine the distribution of the output power of each generator in the system , and each load obtains power from different generator sets and transmission channels; specifically, on the basis of sequential power flow tracing and reverse sequence power flow tracing, the utilization coefficients of generators and loads on transmission lines are defined, as shown in equation (13) and Formula (14) shows:

In the formula: (a _g ) _v,ij and (a _d ) _k,ij are the utilization coefficients of generator Ge and load Load on line ij respectively, P _i is the power flowing into node i, A _u and A _d are power flow The reverse order distribution matrix and sequential distribution matrix of tracing; the utilization coefficient of generators or loads on split sections is the sum of the utilization coefficients of the lines contained in the section; the above line utilization coefficients defined based on the power flow tracing method represent the generator and load The degree of utilization of the line, and when the line fails, the generator or load power with a large utilization factor should be adjusted first.

Description of drawings

Fig. 1 is a flow chart of the active split section search method and island optimization and adjustment strategy of the present invention.

Fig. 2 is a flow chart of the improved k-medoids algorithm adopted in the present invention.

FIG. 3 is a schematic diagram of an implementation process of an island optimization adjustment strategy according to the present invention.

FIG. 4 is a schematic diagram of IEEE 118 node system partition results.

Detailed ways

The drawings are for illustrative purposes only and should not be construed as limitations on this patent; in order to better illustrate this embodiment, some parts in the drawings will be omitted, enlarged or reduced, and do not represent the size of the actual product;

For those skilled in the art, it is understandable that some well-known structures and descriptions thereof may be omitted in the drawings. The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

The present invention is a search method for splitting sections based on constrained spectral clustering, and develops an optimal adjustment strategy for isolated islands after splitting. The implementation process is shown in Figure 1-3.

The active section search of the system can be regarded as a graph partition problem, which can be solved by using the basic theory of graph partition and spectral clustering algorithm. The essence of graph partitioning is to disconnect some edges in the graph according to a given partition criterion, thereby dividing the graph into several independent subgraphs, and the sum of the weights of these disconnected edges is the cut value. Common graph partition criteria include minimum cut criterion (Mincut), normal cut criterion (Ncut), and ratio cut criterion (Rcut). In order to avoid isolated nodes during graph division, this patent adopts the Ncut graph division criterion, and the graph division problem can be described as the minimum value problem of Ncut. The minimum value problem of the Ncut graph division criterion is an NP-complete problem, and the calculation time increases exponentially with the complexity of the problem. The spectral clustering algorithm can transform the NP-hard graph partition problem into an eigenvalue solving problem, so that some effective algorithms for solving eigenvalues can be used to solve the graph partition problem, which greatly speeds up the solution efficiency.

Suppose the graph G=(V, E) is an undirected edge weight graph, where V is the point set of the graph, and E is the edge set of the graph. Given the weight of each edge e _ij in graph G as w _ij , define its weighted adjacency matrix W, degree matrix D and graph size V _g (G) as follows:

Although the traditional spectral clustering algorithm can be used to obtain the minimum canonical cut of the graph, it cannot guarantee the coherence constraints of the generator set that the active splitting problem needs to satisfy. To this end, it is necessary to consider the characteristics of the active splitting problem and improve the spectral clustering algorithm to take into account the coherence constraints of the generator set. Here, the unit coherence constraint is introduced into the spectral clustering algorithm, and the constraint conditions are used to supervise the clustering process and limit the feasible solution space, so as to obtain the solution section that satisfies the constraint conditions. Let the undirected edge weight graph G=(V, E) represent the power system of n nodes, P _ij is the power flow from node i to node j on the line ij, then the weighted adjacency matrix W of the system is:

In the constructed spectral clustering algorithm with constraints, unit coherence constraints can be described by two types of constraints, namely Must Link (abbreviated as ML) and Cannot Link (abbreviated as CL). The ML constraint between two nodes indicates that the two nodes must be in the same partition when the graph is divided, and the corresponding CL constraint indicates that the two nodes must be in different partitions when the graph is divided. In order to reflect the two types of constraints of ML and CL in the spectral clustering algorithm, an n×n constraint matrix Q is defined, and its matrix elements are shown in formula (5):

In the formula: i and j represent any two nodes in the system.

Define the clustering index vector u∈{-1, 1} ⁿ , assuming that the graph is divided to form two independent subgraphs, graph J and graph M respectively, if node i belongs to graph J then u _i =1, if node i belongs to graph M then u _i =-1. Therefore:

In the formula: u ^T Qu represents the degree to which the constraints are satisfied: when Q _ij = 1 and u _i and u _j have the same sign, its value is larger; when Q _ij = 1 and u _i and u _j have different signs or Q _ij =-1 and u _i and u _j have the same sign, its value is smaller. It can be seen that the larger u ^T Qu is, the more likely the clustering result satisfies the given constraints.

In order to satisfy different constraint strengths, the relaxation process is performed on u and Q in the range of real numbers, that is, u and Q can take any real value. After such relaxation processing, if units i and j are coherent units, which belong to ML constraints, Q _ij >0 can be set, and the larger the value, the stronger the coherence constraints between the two units; if units i and j are non- The coherent units belong to CL constraints, then Q _ij <0 can be given, and the smaller the value, the stronger the separation constraints between the two units. Thus, the unit coherence and separation constraints can be introduced into the spectral clustering process.

Define the normalized Laplacian matrix L _N and the normalized constraint matrix Q _N as shown in formula (7) and formula (8), where L _N and the above L _rw are two different forms of the normalized Laplacian matrix.

L _N = D ^-1/2 LD ^1/2 (7)

Q _N =D ^-1/2 QD ^1/2 (8)

Define the vector v=D ^1/2 u and the constraint lower limit constant β, then the graph partition problem with constraints can be expressed by the optimization problem described in formula (9):

In the formula: the objective function v ^T L _N v is the Ncut value of graph division; v ^T Q _N v>β defines the lower limit of the degree of satisfaction of the given constraints; v ^T v=V _g (G) ensures that v is a normalized vector; v≠ D ^1/2 1 rules out trivial solutions, i.e. avoids meaningless graph partitioning schemes. According to the Karush-Kuhn-Tucker theorem, and through relevant mathematical derivations, it can be obtained that by solving the generalized eigenvalue problem of formula (10), the solution of the optimization problem described by formula (9) can be obtained, where the value of the lower limit constant β is constrained The range is given by equation (11).

λ _min (Q _N )×V _g (G)<β<λ _k (Q _N )×V _g (G) (11)

In the formula: λ _min (Q _N ) and λ _k (Q _N ) are the smallest eigenvalue and the kth smallest eigenvalue of the matrix Q _N respectively; k is the number of partitions after the system is sorted. The larger β is, the greater the probability that the obtained solution satisfies the given constraints.

To sum up, the process of spectral clustering algorithm considering constraints is as follows:

1) Determining the number k of split partitions according to the unit co-modulation information;

2) Calculate the system adjacency matrix W, unnormalized Laplacian matrix L, and normalized Laplacian matrix L _N according to the system topology and power flow state;

3) Construct the constraint matrix Q according to the unit coherence information, and calculate the normalized constraint matrix Q _N ;

4) Determine the constraint lower limit constant β according to formula (11);

5) solving the generalized eigenvalue problem described by formula (10);

6) Eliminate the eigenvectors corresponding to non-positive eigenvalues, and normalize the remaining eigenvectors:

7) Let the eigenvectors (v ₁ , v ₂ , ..., v _k ) corresponding to the first k smallest eigenvalues form a matrix V∈R ^n×k ;

8) Treat each row of V as a vector in k-dimensional space, use k-means or k-medoids and other clustering algorithms for clustering and division, and the category of each row in the obtained clustering result is each node in the system The partition to which it belongs, from which the system disassembly section can be determined.

After the above steps, the unit coherence constraint represented by Q can be properly considered in the clustering process, and by solving the generalized eigenvalue problem and clustering and dividing part of the eigenvectors, the system solution that satisfies the coherence constraint can finally be obtained section.

When solving the last step of the spectral clustering algorithm with constraints, it is necessary to cluster the row vectors of the matrix V. Commonly used clustering algorithms include k-means algorithm, k-medoids algorithm, etc. Aiming at the disadvantages of the traditional k-medoids algorithm being sensitive to the initial center point and low search efficiency, the present invention improves it to improve the clustering quality of the algorithm and shorten the calculation time. Specifically, the improved k-medoids algorithm randomly selects several objects as the initial center point, and first divides all non-center point objects according to the principle of the minimum distance from the center point, and then adjusts the initial center point within the cluster. Select the point in each cluster with the smallest distance from other points in the same cluster as the center point after fine-tuning. After the initial center point is determined, the global search is no longer used every time the center point is replaced, but the gradual expansion search is used, that is, the search range of the new center point is limited to the set candidate set, and the candidate set grows with the increase of the number of iterations. Gradually expand. If the i-th center point replacement iteration is currently being performed, the candidate set can be set to all non-center point objects in the i clusters (including this cluster) closest to the original center point, and the new center point is searched within the range of the candidate set ; When the center point is replaced for the i+1th time, the candidate set is the non-center point object in the i+1 nearest cluster, and so on. In this way, as the number of iterations increases gradually, the candidate set of new center points gradually expands until it expands to the whole world or completes clustering.

After the power system is disconnected, in order to ensure the safe and stable operation of each island, it is necessary to optimize and adjust the island nodes. For a large-scale power system, decoupling can be regarded as multiple faults occurring at the decoupling section of each island, and the impact of the fault usually affects a certain range rather than the entire system. Therefore, in an emergency, it is generally carried out according to the principle of proximity or the principle of importance Island node adjustment, that is, prioritizing the adjustment of nodes close to the fault or greatly affected by the fault. Based on these two principles, an island node adjustment strategy combining the proximity principle and power flow tracking is proposed here.

Define the associated nodes of the decomposed section lines as faulty nodes, call the point set that is connected to the faulty node through a line and remove the non-identical island nodes as the 1-degree node adjustment domain; call the nodes in the 1-degree node adjustment domain through a line and The point set that removes non-identical island nodes adjusts the domain for nodes of degree 2, and so on. The greater the degree of the node adjustment domain, the farther the nodes in the domain are from the faulty nodes. If the point set V _j is directly connected to the point set V _i through a line, then the search process of V _j is recorded as f _s (V _i )=V _j . In this way, the n-degree node adjustment domain of the faulty node can be calculated by the following formula:

V _e ⁿ =f _s (V _e ^n-1 )-V _t (12)

In the formula: V _e is the faulty node; V _e ⁿ is the n-degree node adjustment domain of the faulty node; V _t is a point set that is in a different island from V _e . Equation (12) is a recursive formula, and Breadth First Search (BFS) can be used to recursively calculate the 1, 2, ..., n-degree node adjustment domains of the faulty node _Ve . After that, the relative distance between each node and the faulty node can be determined.

For nodes in the same adjustment domain, the power flow tracking method can be used to calculate their utilization coefficients for transmission sections, so as to determine the order of adjustment. Based on the basic assumption of proportional sharing, the power flow tracing method can determine the distribution of the output power of each generator in the system, as well as the source and transmission channel of each load from different generator sets. On the basis of sequential power flow tracking and reverse sequence power flow tracking, the present invention defines the utilization coefficients of generators and loads for transmission lines, as shown in formula (13) and formula (14) respectively:

In the formula: (a _g ) _v,ij and (a _d ) _{k, ij} are the utilization coefficients of generator v and load k on line ij respectively; P _i is the power flowing into node i; A _u and A _d are the power flow Tracked reverse order assignment matrix and sequential assignment matrix. The utilization factor of the generator or load on the split section is the sum of the utilization factors of the lines contained in the section. The above-mentioned line utilization coefficient defined based on the power flow tracing method characterizes the degree of utilization of the line by generators and loads. When the line is faulty, measures such as power generation rescheduling can be adopted in order to avoid the power flow of some branches exceeding the limit caused by power flow transfer. The greater the utilization coefficient of the generator on the line, the greater the impact of its output adjustment on the branch power flow, and the more significant the adjustment effect. Therefore, when the line fails, the generator or load power with a large utilization factor should be adjusted first.

In summary, after using the method proposed by the present invention to obtain the optimal disassembly section, first calculate the 1-n degree node adjustment domain of the faulty node and the utilization coefficient of the nodes in the adjustment domain to the disassembly section; then, start from the faulty node , according to the degree of the adjustment domain, the generator nodes are adjusted from small to large, and in the same adjustment domain, the power generation nodes with a larger utilization coefficient of the transmission section are preferentially adjusted. After the generator is adjusted, if there is still unbalanced power, the node load will be reduced in the same way until the island meets the safe operation requirements. In order to ensure the principle of proximity, the adjustment domain should not be too large, and generally consider the adjustment domain of 3 degrees or less.

1) Active section search

The effectiveness of the present invention is illustrated by taking the IEEE 118 node standard test system as an example. The program is implemented based on MATLABR2014a software, the main frequency of the CPU of the experimental PC is 2.2GHz, and the memory is 4G. The IEEE 118 node system is shown in Figure 4, and the grouping results of coherent units after the system suffers a large disturbance are shown in Table 1. The method proposed by the present invention is used to search for the decomposed section of the system, and the obtained system partition (isolated island) results are shown in Figure 4. The system decoupling section is {15-33, 19-34, 23-24, 30-38, 77-82, 80-96, 80-99, 97-96, 98-100}, and the active power flow between isolated islands is 130.9 MW, see Table 2 for the power imbalance in the island.

Table 1 Grouping results of IEEE 118-node system coherence clusters

Table 1 Coherent groups of generators in the IEEE 118-bus system

Table 2 IEEE 118-node system island power balance

Table 2 Power imbalances in isolated islands of the IEEE 118-bussystem

From the results of the above calculation example, it can be seen that after the system is actively separated by the method of the present invention, the coherent units are all in the same partition and the non-coherent units are in different partitions, and the active power impact flow and island power imbalance are small. Therefore, the method of the present invention can effectively meet the coherent constraints of the unit, and while ensuring that the active power impact flow is small, it also takes into account the power balance requirements of the island, which is conducive to the stable operation of the island and the recovery of the system after decoupling. The calculation time of the calculation example is 73ms, which can meet the requirements of online active section search.

2) Island optimization adjustment

Taking island 3 in Figure 4 as an example, the island optimization adjustment process based on node adjustment domain and line utilization coefficient is described. Considering the small scale of Island 3, here we consider the node adjustment domains of degree 2 and below. Table 3 lists the fault nodes (that is, the associated nodes of the split-section line), the nodes included in the 1-degree node adjustment domain and the 2-degree node adjustment domain, and the utilization coefficient of each node on the transmission section.

Table 3 Node adjustment domain and split section utilization coefficient

Table 3 Node adjustment domains and utilization coefficients of interfaces among various islands

After the system is disassembled, the outputs of the generators 100, 103 and 89 are adjusted in sequence from the faulty node according to the degree of the adjustment domain from small to large. After the output of the generator is adjusted, if the island 3 still does not meet the safety constraints, the load is adjusted in sequence according to the adjustment domain and the utilization coefficient. The adjustment sequence is 96, 99, 82, 100, 95, 83/92/94/101 /103/104/106, 84/88/89/91/93/102/105/107/110, until island 3 satisfies the security constraints. Wherein, i/j means that node i and node j can be adjusted at the same time. The operation mode adjustment process of island 1 and island 2 is similar to that of island 3, and will not be repeated here.

Apparently, the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limiting the implementation of the present invention. For those of ordinary skill in the art, on the basis of the above description, other changes or changes in different forms can also be made. It is not necessary and impossible to exhaustively enumerate all implementation modes here. All modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the claims of the present invention.

Claims (4)

1. a kind of electric system Active Splitting section searching method, which is characterized in that be a kind of active based on constraint spectral clustering Splitting fracture surface searching method is that unit coherent constraints are introduced into spectral clustering, utilizes constraint condition supervision clustering process And solution space is limited, to obtain the off-the-line section for meeting constraint condition；

If nonoriented edge weight graph G=(V, E) characterizes the electric system of n node, wherein V is the point set for scheming G, and E is the side collection for scheming G, is given Surely scheme each edge e in G_ijWeight be w_ij, define weighted adjacent matrix W, degree matrix D and figure scale V_g(G), wherein weighted adjacent Matrix W, the matrix element for spending matrix D are as follows:

Figure scale V_g(G) are as follows:

Enable P_ijFor the trend for flowing to node j on route i-j from node i, then the matrix element of the weighted adjacent matrix W of system are as follows:

In the spectral clustering containing constraint constructed, two class constraint specifications, i.e. Must Link, letter is can be used in unit coherent constraints Claim ML and Cannot Link, abbreviation CL；ML constraint between two nodes, which is characterized in when figure divides, need to guarantee that the two nodes are in In same subregion, and corresponding CL constraint is then characterized in when figure divides need to guarantee that the two nodes are in different subregions；To compose The constraint of ML and CL these two types is embodied in clustering algorithm, defines the constraint matrix Q of n × n, shown in matrix element such as formula (5):

In formula: i and j indicates any two node in electric system；

It defines clustering target vector u ∈ { -1,1 }ⁿ, it is assumed that figure forms two independent subgraphs after dividing, respectively figure J and figure M, if section Point i belongs to figure J then u_i=1, the u if node i belongs to figure M_i=-1；It can thus be concluded that:

In formula: u^TThe degree that Qu characterization constraint condition is satisfied, works as Q_ij=1 and u_iAnd u_jWhen jack per line, it is worth larger；Work as Q_ij=1 and u_iAnd u_jContrary sign or Q_ij=-1 and u_iAnd u_jWhen jack per line, value is smaller；It follows that u^TQu is bigger, and cluster result meets to concludeing a contract or treaty A possibility that beam condition, is bigger；

To meet different constraint strengths, relaxation processes are carried out within the scope of real number to u and Q, i.e. u and Q can use any real number value； After such relaxation processes, if unit i and j are people having the same aspiration and interest unit, belong to ML constraint, give Q_ij> 0, value is bigger to indicate the two Coherent constraints between unit are stronger；If unit i and j are non-coherent unit, belong to CL constraint, Q can be given_ij< 0, it is worth smaller Indicate that the separation constraint between the two units is stronger；Unit can be introduced spectral clustering mistake with reconciliation separation constraint as a result, Cheng Zhong；

Definition standard Laplacian matrix L_NWith standardization constraint matrix Q_NRespectively as shown in formula (7) and formula (8)；

L_N=D^-1/2LD^1/2 (7)

Q_N=D^-1/2QD^1/2 (8)

Definition vector v=D^1/2U and constraint lower limit constant beta, then the Graph partition problem containing constraint can use formula (9) described optimization Problem indicates:

In formula: objective function v^TL_NV is the Ncut value that figure divides；v^TQ_NV > β defines specifying constraint satisfaction degree lower limit；v^Tv =V_g(G) ensure that v is normalization vector；v≠D^1/21 eliminates trivial solution, that is, avoids meaningless figure splitting scheme；

The generalized eigenvalue problem of solution formula (10) is to get the solution for arriving optimization problem described in formula (9), wherein constraint lower limit is normal The value range of number β is given by formula (11)；

λ_min(Q_N)×V_g(G) < β < λ_k(Q_N)×V_g(G) (11)

In formula: λ_min(Q_N) and λ_k(Q_N) it is respectively matrix Q_NMinimal eigenvalue and k-th of minimal eigenvalue；K is after system sectionalizing Subregion number；

Electric system Active Splitting section searching method the following steps are included:

1) off-the-line subregion number k is determined according to unit people having the same aspiration and interest information；

2) it according to electric system topological structure and flow state, calculates separately the weighted adjacent matrix W of electric system, standardize Laplacian matrix L, the Laplacian matrix L of standardization_N；

3) according to unit people having the same aspiration and interest information structuring constraint matrix Q, and standardization constraint matrix Q is calculated_N；

4) constraint lower limit constant beta is determined；

5) formula is solvedThe generalized eigenvalue problem of description；

6) the corresponding feature vector of non-positive characteristic value is rejected, and remaining feature vector is subjected to standardization processing:

7) feature vector (v corresponding to k minimal eigenvalue before enabling₁, v₂..., v_k) constitute matrix V ∈ R^n×k；

8) regard every a line of V as a vector in k dimension space, clustering, obtained cluster are carried out using clustering algorithm As a result every a line generic is exactly subregion belonging to each node in electric system in, thus can determine that system sectionalizing is disconnected Face.

2. electric system Active Splitting section searching method according to claim 1, which is characterized in that step 8), which uses, to be changed Clustering, detailed process are carried out into k-medoids clustering algorithm are as follows: arbitrarily choose several objects as initial center point, And carry out all non-central point objects after dividing for the first time with the smallest principle by with a distance from central point, to initial center point in cluster It is inside adjusted, chooses in each cluster and with other point distances of cluster and the smallest point as the central point after fine tuning；It is initial determining After central point, when replacing central point every time, searched for using gradual-enlargement type, i.e., new center searching range is only limitted to the candidate of setting Collection, Candidate Set are gradually expanded with the increase of the number of iterations, i.e., the current positive m subcenter point that carries out replaces iteration, Candidate Set All non-central point objects being set as in the m cluster nearest from former central point, new central point are searched within the scope of Candidate Set Rope；In the replacement of m+1 subcenter point, Candidate Set is then the non-central point object in m+1 nearest clusters, and so on；In this way, As the number of iterations gradually increases, the Candidate Set of new central point is also gradually expanded, until being expanded to global or completing to cluster.

3. based on the isolated island adjustable strategies of the described in any item electric system Active Splitting section searching methods of claim 1-2, It is characterized in that, being a kind of isolated island node adjustable strategies that nearby principle is combined with power flow tracing, using poly- based on constraint spectrum After the Active Splitting section searching method of class carries out off-the-line to electric system, for guarantee each isolated island can safe and stable operation, need Adjustment is optimized to isolated island node；

Specifically: after obtaining optimal off-the-line section, first in 1 to the n degree node regulatory domain and regulatory domain of calculating malfunctioning node Usage factor of the node to off-the-line section；Then, it since malfunctioning node, is sent out by regulatory domain degree size by small and the earth adjustment Motor node, then preferential adjustment is to the biggish power generation node of transmission cross-section usage factor under identical regulatory domain, to generator If there are still imbalance powers after adjustment, node load is cut down by same procedure, until isolated island reaches safe operation and wants Until asking.

4. isolated island adjustable strategies according to claim 3, which is characterized in that define off-the-line section route associated nodes be Malfunctioning node, the point set for being connected and removing non-equal isolated island node by a route with malfunctioning node is referred to as 1 degree of node adjustment Domain；The point set for being connected and removing non-equal isolated island node by a route with the node in 1 degree of node regulatory domain is referred to as 2 degree of sections Point regulatory domain, and so on；The degree of node regulatory domain is bigger, and domain interior nodes are relatively remoter from malfunctioning node；If point set V_jIt is Point set V_iIt is connected directly by a route, then V_jSearch process is denoted as f_s(V_i)=V_j, then the n degree node adjustment of malfunctioning node Domain can be calculated with following formula:

V_e ⁿ=f_s(V_e ^n-1)-V_t (12)

In formula: V_eFor malfunctioning node,For the n degree node regulatory domain of malfunctioning node, V_tFor with V_eIt is in the point set of different isolated islands； Formula (12) is a recurrence formula, and breadth first search method BFS recurrence can be used and find out malfunctioning node V_e1,2 ..., n degree node Regulatory domain；

Later, the relative distance of each node and malfunctioning node can be specified；

For the node in same regulatory domain, its usage factor to transmission cross-section is calculated using power flow tracing method, so that it is determined that Successive adjustment sequence；The basic assumption that power flow tracing method is shared based on ratio, can determine that the output power of each generator is being Distribution and each load in system obtain source and the transfer passage of power from different generating sets；Specifically in sequence tide On the basis of stream tracking and backward power flow tracing, generator and load are defined to the usage factor of transmission line of electricity, respectively such as formula (13) and shown in formula (14):

In formula: (a_g)_{Ge ,ij}(a_d)_{Load ,ij}The respectively usage factor of generator Ge and load Load to route i-j, P_iFor stream The power of ingress i, A_uAnd A_dThe respectively backward allocation matrix and order-assigned matrix of power flow tracing；Generator or load pair The usage factor of off-the-line section is the sum of the usage factor to route contained by section；The above-mentioned line defined based on power flow tracing method Road usage factor characterizes generator and load to the producing level of route, and usage factor should be preferentially adjusted when line fault Big generator or load power.