CN117833374A - Distributed flexible resource cluster division method and system based on random walk algorithm - Google Patents
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Abstract
The invention discloses a distributed flexible resource cluster division method and system based on a random walk algorithm, and belongs to the field of distributed power grid-connected operation regulation and control. The method comprises the following steps: s1, establishing a comprehensive index of distributed flexible resource cluster division, and acquiring a comprehensive evaluation index value; s2, constructing a comprehensive evaluation index network of the distributed flexible resources based on the comprehensive evaluation index value; s3, calculating a transition probability matrix of the node based on the comprehensive evaluation index network; s4, executing a node random walk process according to the transition probability matrix, and calculating a similarity matrix; s5, merging clusters, and repeating the process after updating the similarity matrix until the required number of clusters is reached; s6, outputting a final cluster division result. The invention can fully exert the adjustable capacity of the distributed flexible resources while realizing the efficient consumption of the large-scale distributed resources.
Description
Technical Field
The invention belongs to the field of distributed power grid-connected operation regulation and control research, and particularly relates to a distributed flexible resource cluster division method based on a random walk algorithm.
Background
After the distributed power supply is accessed into the power distribution network in a large scale, the power supply flexibility of the power distribution network and the utilization rate of renewable energy sources are increased, but a series of challenges are brought to the power distribution network, including voltage fluctuation, power quality problems, complexity increase of protection and control strategies, and interference to the traditional power distribution network operation and scheduling modes can be generated. These challenges require finer management and regulation of the distribution network to ensure safe, stable and reliable operation of the grid. In order to minimize the negative impact of the distributed power sources on the distribution network and to bring its potential value into play, it is necessary to make full use of the distributed flexible resources in the distribution network for adaptive regulation. This may enable real-time control by encouraging consumers to adjust their power usage patterns according to grid demand using demand response strategies, deploying energy storage systems to mitigate voltage and frequency fluctuations, allowing distributed resources to enter the auxiliary service market for real-time control, etc. However, large-scale flexible resources are scattered in the power distribution network, and flexible aggregation is needed to realize scale effects so as to effectively participate in the regulation and control of the power distribution network.
Because distributed flexible resources (such as distributed power generation, energy storage equipment, controllable load and the like) have the characteristics of numerous quantity, small scale and distributed positions, the aggregation of the distributed flexible resources is favorable for optimizing the scheduling of the resources and better serving a power system, and therefore, targeted research on the aggregation of the distributed flexible resources at home and abroad is developed, but most of the research is focused on the scheduling control of a distributed flexible resource aggregation unit, and the existing cluster division research is mainly performed according to the distance between nodes. The dividing method only depends on the distance between the nodes, and cannot account for the power balance condition of the nodes, so that the independent balance of the active power and the reactive power of each divided cluster cannot be realized.
The existing patent 'a distributed generation cluster division method (202310145805.4) based on an improved K-means algorithm' and 'a distribution network cluster division method (202211099003.6) based on a comprehensive cluster division index' also consider the power balance condition of a system, but the adopted method has the problems of complex calculation and low efficiency.
Disclosure of Invention
The present invention aims to solve at least one of the technical problems existing in the prior art.
The technical scheme of the invention is as follows: a distributed flexible resource cluster dividing method based on a random walk algorithm comprises the following steps:
s1, establishing a comprehensive index of distributed flexible resource cluster division, and acquiring a comprehensive evaluation index value;
s2, constructing a comprehensive evaluation index network of the distributed flexible resources based on the comprehensive evaluation index value;
s3, calculating a transition probability matrix of the node based on the comprehensive evaluation index network;
s4, executing a node random walk process according to the transition probability matrix, and calculating a similarity matrix;
s5, merging clusters, and repeating a node random walk process after updating the similarity matrix until the required number of clusters is reached;
s6, outputting a final cluster division result.
In step S1, the comprehensive index includes an electrical distance index, an active power index and a reactive power index of different distributed flexible resources.
The electrical distance index is as follows:
wherein d ij Is an index value of the electrical distance between the node i and the node j, Z total R is the total impedance k X is the line resistance between node i and node j k Is the line reactance value between node i and node j.
The active power index is as follows:
ΔP i ＝P supply,i -P load,i
wherein DeltaP i Is the active balance index of the node i, P supply,i Is the active power supplied by node i, P load,i Is the load active power of node i.
The reactive power index is as follows:
ΔQ i ＝Q supply,i -Q load,i
wherein DeltaQ i Is reactive balance index of node i, Q supply,i Is the reactive power supplied by node i, Q load,i Is the load reactive power of node i.
The comprehensive evaluation index value is as follows:
w ij ＝α×d ij +β×|ΔP i -ΔP j |+γ|ΔQ i -ΔQ j |
wherein w is ij To comprehensively evaluate the index value, ΔP j Is an active balance index of node j, deltaQ j Is reactive balance index of node j, and alpha, beta and gamma are the weights of the indexes.
In step S2, using nodes to represent distributed flexible resources, and using the comprehensive evaluation index value as the weight of the edge to construct a weighted undirected graph X, specifically:
X＝[w ij ] i＝1...n,j＝1...n
where n is the total number of nodes.
In step S3, a transition probability matrix T of each node in the weighted undirected graph is calculated, and matrix elements T of the transition probability matrix T ij Expressed as:
wherein w is ik An index value is evaluated for the combination between node i and node k.
In step S4, for each pair of nodes i and j, performing a random walk of step r;
after executing the random walk process of the cluster dividing nodes in the step r, calculating a similarity matrix S of the cluster, and setting M ij The number of times from node i to node j in the r-step random walk is defined as the similarity matrix S:
wherein S is ij Is the similarity value between nodes i and j after r steps of random walk.
In step S5, each node is an independent cluster, calculates the distance between clusters, finds the cluster pair with the smallest distance, and updates the similarity matrix and the number of clusters.
The distance between clusters is calculated based on a similarity matrix S, which distance is defined as the inverse of the similarity between the two clusters, expressed as:
wherein c i And c j Representing two different clusters.
The updating of the similarity matrix is realized through iteration, specifically:
(1) defining a threshold co, representing the minimum threshold value of the similarity matrix variation;
(2) in each iteration, calculating the variation of all nodes of the similarity matrix;
(3) if the variation of all nodes in the similarity matrix is smaller than the threshold co, indicating that the similarity matrix has converged to a stable state, and terminating iteration;
(4) if the variation of the similarity matrix is greater than the threshold co, it is indicated that the similarity matrix has not converged to a steady state, and a next iteration is required.
A distributed flexible resource cluster dividing system based on a random walk algorithm comprises:
the index module is used for establishing comprehensive indexes of distributed flexible resource cluster division and acquiring comprehensive evaluation index values;
the construction module is used for constructing a comprehensive evaluation index network of the distributed flexible resources based on the comprehensive evaluation index value;
the node module is used for calculating a transition probability matrix of the node based on the comprehensive evaluation index network;
the similarity matrix module is used for executing a node random walk process according to the transition probability matrix and calculating a similarity matrix;
the cluster module is used for merging clusters, and repeating the process after updating the similarity matrix until the required number of clusters is reached;
and the output module is used for outputting the final cluster division result.
In operation, the comprehensive index of distributed flexible resource cluster division is established, the comprehensive evaluation index value is obtained, and quantitative evaluation of the electrical distance and power balance among all distributed power supply nodes is realized;
constructing a comprehensive evaluation index network of the distributed flexible resources, and combining the evaluation index values of all nodes to form comprehensive performance evaluation of the whole power distribution network;
and merging clusters by using an Agglomerate method, so as to realize distributed power cluster division based on network performance indexes.
The invention realizes the cluster division of large-scale distributed flexible resources based on the random walk algorithm, and can fully exert the adjustable capacity of the distributed flexible resources while realizing the efficient consumption of the large-scale distributed resources.
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FIG. 1 is a flow chart of the present invention;
fig. 2 is a network topology of an IEEE14 node in an embodiment.
Detailed Description
The present application is further described below with reference to the accompanying drawings. The following examples are only for more clearly illustrating the technical solutions of the present invention and are not intended to limit the scope of protection of the present application.
The invention discloses a distributed flexible resource cluster dividing method based on a random walk algorithm, which is shown in figures 1-2 and comprises the following steps:
s1, establishing comprehensive indexes of distributed flexible resource cluster division, acquiring comprehensive evaluation index values, and quantitatively evaluating the electrical distance and power balance among distributed power supply nodes;
and calculating cluster division indexes of different distributed flexible resources according to the electric distance, active balance and reactive balance of the distributed units.
(1) Electrical distance index for different distributed flexible resources
In a power distribution network, the electrical distance between a distributed flexible node i and a node j is calculated by taking into account the impedance summation of all lines between the two nodes. First, a path from node i to node j is identified. In radial distribution networks, this path is unique. Second, since each line or cable has its specific resistance R and reactance X. These values may be obtained from manufacturer data, standard manuals, or in-field measurements. For each line or cable on the path from node i to node j, the impedances z=r+jx thereof are added up to give a total impedance Z total . The formula is:
where n is the number of lines or cables on the path from node i to node j. Finally, calculating an electrical distance index value from node i to node j by the following formula:
wherein d is ij Is an index value of the electrical distance between the node i and the node j, R k X is the line resistance between node i and node j k Is the line reactance value between node i and node j.
(2) Active power index and reactive power index
The active balance index and the reactive balance index are intended to evaluate the power balance status of nodes in the distribution network. These metrics mainly take into account the differences between the power supply and the load on the nodes. Active balance index delta P of node i i Power supply P defined as node i supply,i With load power P load,i Difference between:
ΔP i ＝P supply,i -P load,i (3)
wherein P is supply,i Is the active power supplied by node i from a distributed power generation source such as photovoltaic or wind power. P (P) load,i Is the load active power of node i.
Likewise, the reactive balance index Δq of node i i Reactive power Q of the power supply defined as node i supply,i Reactive power Q with load load,i Difference between:
ΔQ i ＝Q supply,i -Q load,i (4)
wherein Q is supply,i Is the reactive power supplied by node i from reactive compensation resources in the distribution network. Q (Q) load,i Is the load reactive power of node i.
Weighting the three indexes to obtain a comprehensive evaluation index value, namely
w ij ＝α×d ij +β×|ΔP i -ΔP j |+γ×|ΔQ i -ΔQ j | (5)
Wherein alpha, beta and gamma are the weight of each index, and delta P j Is an active balance index of node j, deltaQ j Is a reactive balance index of the node j and can be set according to actual requirements.
The cluster division algorithm of the distributed flexible resource in the invention comprises the following steps: if two nodes belong to the same community, the path of the random walk is likely to be "stuck" within the community, i.e. divided into the same cluster. The algorithm can provide different degrees of cluster division without knowing the cluster division quantity information in advance, and is suitable for a large-scale network.
The cluster division step of the distributed flexible resource by using the random walk algorithm comprises the following steps:
s2: and constructing a comprehensive evaluation index network of the distributed flexible resources, and combining the evaluation index values of all nodes to form comprehensive performance evaluation of the whole power distribution network (comprising the following steps S3 and S4).
Using nodes to represent distributed flexible resources, using the above calculated comprehensive assessment index value w ij As the weight of the edge, a weighted undirected graph X (i.e. a comprehensive evaluation index network) is constructed, specifically:
X＝[w ij ] i＝1...n,j＝1...n (6)
where n is the total number of nodes.
S3: and calculating a transition probability matrix T of each node in the weighted undirected graph, and representing random walk probability among the nodes. Matrix element T of transition probability matrix T ij Represented as
Wherein w is ik An index value is evaluated for the combination between node i and node k.
S4: a node random walk process in cluster division is performed.
For each pair of nodes i and j, a random walk of r steps is performed. Each step is based on the corresponding probability T in the transition probability matrix T ij The next node is selected. Where r determines the range of cluster division and when the value of r is small, random walk is mainly performed in the local area. Therefore, the range of the divided clusters is smaller, and the number of the clusters is more. But too small a value of r may cause the algorithm to misclassify nodes that actually have the same attribute into different clusters. When the r value is increased, the random walk algorithm can realize a larger range of cluster division results.
After executing the random walk process of the cluster dividing nodes in the step r, calculating a similarity matrix S of the cluster, and setting M ij The number of times from node i to node j in the r-step random walk can be defined as the similarity matrix S
Wherein S is ij Is the similarity value between nodes i and j after r steps of random walk.
S5: clusters were pooled using the Agglomerate method. First, each node is its own cluster. Then, the two clusters with the highest similarity are found and combined, and the process (namely the node random walk process) is repeated after the similarity matrix is updated until the required number of clusters is reached, so that the distributed power supply cluster division based on the network performance index is realized.
The Agglomerate method is a bottom-up hierarchical clustering method whose basic idea is to start with treating each node as an independent cluster and then gradually merge the closest clusters until a certain stop condition or a predetermined number of clusters is reached. The following is the basic steps of the Agglimerate method:
(1) Initially, each node is a separate cluster. Thus, if there are N nodes, there are N clusters initially.
(2) Calculating the distance between clusters: calculating a distance between clusters based on the calculated similarity matrix S, the distance being defined as the inverse of the similarity between the two clusters, expressed as:
wherein c i And c j Representing two different clusters. And then find the cluster pair with the smallest distance, combine them, and update the cluster number and similarity matrix.
In the random walk algorithm, the update of the similarity matrix is realized through iteration, and each iteration can change the similarity matrix. Whether the algorithm has converged to a steady state can be determined by comparing the change of the similarity matrix between two adjacent iterations. Specifically, the judgment can be made by the following method:
(1) defining a threshold co, representing the minimum threshold value of the similarity matrix variation;
(2) in each iteration, the variation of all nodes of the similarity matrix, namely the absolute value of the difference, is calculated.
(3) If the variation of all nodes in the similarity matrix is smaller than the threshold co, which means that the similarity matrix has converged to a steady state, the algorithm can terminate the iteration.
(4) If the variation of the similarity matrix is greater than the threshold co, it is indicated that the similarity matrix has not converged to a steady state, and a next iteration is required.
S6: and outputting a final cluster division result, wherein the final cluster division result comprises a cluster number to which each distributed flexible resource belongs.
A distributed flexible resource cluster dividing system based on a random walk algorithm comprises:
the index module is used for establishing comprehensive indexes of distributed flexible resource cluster division and acquiring comprehensive evaluation index values;
the construction module is used for constructing a comprehensive evaluation index network of the distributed flexible resources based on the comprehensive evaluation index value;
the node module is used for calculating a transition probability matrix of the node based on the comprehensive evaluation index network;
the similarity matrix module is used for executing a node random walk process according to the transition probability matrix and calculating a similarity matrix;
the cluster module is used for merging clusters, and repeating the process after updating the similarity matrix until the required number of clusters is reached;
and the output module is used for outputting the final cluster division result.
The core idea of the random walk algorithm in the invention is as follows: if two nodes belong to the same community, the path of the random walk is likely to be "stuck" within the community, i.e. divided into the same cluster. The algorithm can provide different degrees of cluster division without knowing the cluster division quantity information in advance, and is suitable for a large-scale network.
Specific example analyses were as follows:
in order to verify the feasibility and effectiveness of the cluster division algorithm, an IEEE-14 node system is selected, the cluster division algorithm is divided by a random walk algorithm, and the result is analyzed and described. The network topology is as in fig. 2.
Under the condition that the distributed power source permeability of the selected system is the largest, nodes 1, 2, 3, 6, 7 and 8 are traditional power source nodes, do not participate in cluster division, and only comprise load nodes in a list. And then calculating the electrical distance between the nodes according to a formula, and carrying out per unit processing, wherein the calculation result is shown in table 1.
TABLE 1IEEE14 node Electrical distance
The obtained cluster division result is compared with the conventional clustering method result based on the above data, as shown in table 2.
Table 2 cluster partition results
As the analysis result shows, since the nodes 4 and 5 are far from other nodes in electrical distance, it is reasonable to divide them into two clusters respectively under the algorithm of the present invention. Meanwhile, the active and reactive power characteristics among clusters are not considered in the conventional clustering algorithm, and the number of the clusters divided is more. The cluster division algorithm provided by the invention can reasonably determine the number of clusters according to the power balance characteristics of different nodes, and the obtained distributed flexible resource clusters are more representative.
The foregoing is only a preferred embodiment of the invention, it being noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the invention.
Claims (13)
1. The distributed flexible resource cluster dividing method based on the random walk algorithm is characterized by comprising the following steps of:
s1, establishing a comprehensive index of distributed flexible resource cluster division, and acquiring a comprehensive evaluation index value;
s2, constructing a comprehensive evaluation index network of the distributed flexible resources based on the comprehensive evaluation index value;
s3, calculating a transition probability matrix of the node based on the comprehensive evaluation index network;
s4, executing a node random walk process according to the transition probability matrix, and calculating a similarity matrix;
s5, merging clusters, and repeating a node random walk process after updating the similarity matrix until the required number of clusters is reached;
s6, outputting a final cluster division result.
2. The method for partitioning a distributed flexible resource cluster based on a random walk algorithm of claim 1,
in step S1, the comprehensive index includes an electrical distance index, an active power index and a reactive power index of different distributed flexible resources.
3. The method for partitioning a distributed flexible resource cluster based on a random walk algorithm according to claim 2, wherein the electrical distance index is:
wherein d ij Is an index value of the electrical distance between the node i and the node j, Z total R is the total impedance k X is the line resistance between node i and node j k Is the line reactance value between node i and node j.
4. The method for partitioning a distributed flexible resource cluster based on a random walk algorithm as claimed in claim 3, wherein said active power index is:
ΔP i ＝P supply,i -P load,i
wherein DeltaP i Is the active balance index of the node i, P supply,i Is the active power supplied by node i, P load,i Is the load active power of node i.
5. The method for partitioning a distributed flexible resource cluster based on a random walk algorithm as claimed in claim 4, wherein the reactive power index is:
ΔQ i ＝Q supply,i -Q load,i
wherein DeltaQ i Is reactive balance index of node i, Q supply,i Is the reactive power supplied by node i, Q load,i Is the load reactive power of node i.
6. The method for partitioning a distributed flexible resource cluster based on a random walk algorithm according to claim 5, wherein the comprehensive evaluation index value is:
w ij ＝α×d ij +β×|ΔP i -ΔP j |+γ×|ΔQ i -ΔQ j |
wherein w is ij To comprehensively evaluate the index value, ΔP j Is an active balance index of node j, deltaQ j Is reactive balance index of node j, and alpha, beta and gamma are the weights of the indexes.
7. The method for partitioning a distributed flexible resource cluster based on a random walk algorithm of claim 6,
in step S2, using nodes to represent distributed flexible resources, and using the comprehensive evaluation index value as the weight of the edge to construct a weighted undirected graph X, specifically:
X＝[w ij ] i＝1...n,j＝1...n
where n is the total number of nodes.
8. The method for partitioning a distributed flexible resource cluster based on a random walk algorithm of claim 7,
in step S3, a transition probability matrix T of each node in the weighted undirected graph is calculated, and matrix elements T of the transition probability matrix T ij Expressed as:
wherein w is ik An index value is evaluated for the combination between node i and node k.
9. The method for partitioning a distributed flexible resource cluster based on a random walk algorithm of claim 8,
in step S4, for each pair of nodes i and j, performing a random walk of step r;
after executing the random walk process of the cluster dividing nodes in the step r, calculating a similarity matrix S of the cluster, and setting M ij The number of times from node i to node j in the r-step random walk is defined as the similarity matrix S:
wherein S is ij Is the similarity value between nodes i and j after r steps of random walk.
10. The method for partitioning a distributed flexible resource cluster based on a random walk algorithm of claim 1,
in step S5, each node is an independent cluster, calculates the distance between clusters, finds the cluster pair with the smallest distance, and updates the similarity matrix and the number of clusters.
11. The method for partitioning a distributed flexible resource cluster based on a random walk algorithm of claim 10,
the distance between clusters is calculated based on a similarity matrix S, which distance is defined as the inverse of the similarity between the two clusters, expressed as:
wherein c i And c j Representing two different clusters.
12. The method for partitioning a distributed flexible resource cluster based on a random walk algorithm of claim 10,
the updating of the similarity matrix is realized through iteration, specifically:
(1) defining a threshold co, representing the minimum threshold value of the similarity matrix variation;
(2) in each iteration, calculating the variation of all nodes of the similarity matrix;
(3) if the variation of all nodes in the similarity matrix is smaller than the threshold co, indicating that the similarity matrix has converged to a stable state, and terminating iteration;
(4) if the variation of the similarity matrix is greater than the threshold co, it is indicated that the similarity matrix has not converged to a steady state, and a next iteration is required.
13. The distributed flexible resource cluster dividing system based on the random walk algorithm is characterized by comprising the following components:
the index module is used for establishing comprehensive indexes of distributed flexible resource cluster division and acquiring comprehensive evaluation index values;
the construction module is used for constructing a comprehensive evaluation index network of the distributed flexible resources based on the comprehensive evaluation index value;
the node module is used for calculating a transition probability matrix of the node based on the comprehensive evaluation index network;
the similarity matrix module is used for executing a node random walk process according to the transition probability matrix and calculating a similarity matrix;
the cluster module is used for merging clusters, and repeating the process after updating the similarity matrix until the required number of clusters is reached;
and the output module is used for outputting the final cluster division result.
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