Large-scale distributed photovoltaic cluster partition method based on SLM algorithm

The traditional distribution network with centralized control faces the problems of communication delay, large amount of calculation and too many control devices. This research offers a distributed power cluster division technique based on Smart Local Moving (SLM) to overcome the problem of challenging regulation of distributed power supply in modern distribution networks. First of all, on the basis of the modularity division standard, introduce the comprehensive cluster division index of intra-group reactive power and active matching degree index, so as to ensure the strength of the cluster structure on the basis of making it have a certain degree of voltage regulation capability. Secondly, the cluster division scheme of distributed power supply is formed based on SLM algorithm. Lastly, the feasibility and efficacy of the suggested method are validated using IEEE33 cluster partitioning.


Introduction
In recent years, renewable energy generation has been applied more and more in new energy.On June 20, 2021, the National Energy Administration issued a notice on the pilot program of ' county-wide photovoltaic ', vigorously developing distributed photovoltaic and further promoting the reform of China 's energy system [1] .The distributed generation cluster division technology is a new solution, which can reduce the power fluctuation and uncertainty of the distributed generation cluster under the premise of ensuring the power density of the distributed generation cluster [2] .
Nowadays, the concept of cluster control has been more and more recognized by many researchers.Zhenbo Wei [3] adopts the complex network method based on community to divide the voltage control area, and uses the modularity degree as the evaluation index to evaluate the regional quality.However, this method has the problem of high time complexity.In the previous study, Ming Ding [4] et used genetic algorithm to dynamically adaptively partition the distributed power supply according to the cluster according to the change of the topology of the power grid.However, due to the poor convergence of the intelligent optimization algorithm, the system adjustment time is long.Mingyi Pan et [5] used the hierarchical clustering algorithm to divide the system operation management cluster by taking the distance between nodes as the measurement standard.This algorithm is simple in principle and high in efficiency, but it does not have enough global search ability and is easy to fall into local extremum.
In order to build a cluster division model based on the comprehensive performance index system, which fully takes into account the structural strength of the cluster to make the cluster size more balanced, the indexes of reactive power and active power cooperation within the cluster are first introduced on the basis of the modularity division standard.Secondly, the distributed photovoltaic power cluster is divided based on the SLM algorithm, so that each cluster can automatically generate the optimal partition with high modularity value in a short time.Finally, the accuracy and efficiency of the proposed method on cluster partitioning is verified by an example.

Cluster division index
The cluster division of large-scale distributed power supply is an important basic work of cluster regulation.A single node with high reactive voltage sensitivity, strong electrical coupling, and near electrical distance can be separated into the same cluster using an appropriate cluster division technique.

Modularity index
Cluster structures in complex networks are typically made up of network nodes with comparable characteristics or functions, which are basically regional couplings of chemical, physical, or psychological relationships among nodes in the network [6] .Newman et.Proposed the concept of modularity function to quantify the structural strength in within intricate [7] .The following definition for modularity has been used: Where ij A is the boundary value in the electrical matrix connecting i and j ; m is the total of the weights of all the power network's edges; i k is the sum of all edge weights of the connecting node i ; j k is the sum of all edge weights of the connecting node j ; i c and j c are the community numbers of nodes i and j , if nodes i and j belong to the same association, ( , ) Modularity degree values range from 0 to 1.

Intra-group reactive power and active power coordination index
At present, the control architecture of power that is widely distributed grid-connected hierarchical group control strategy can be divided into inter-group coordination optimization layer and intra-group autonomy layer [8] .In order to achieve local consumption of distributed PV power, the active transfer between clusters should be reduced.Therefore, the matching index needs to take into account the degree matching of active and reactive power within the cluster, and the larger the active and reactive power matching index indicates the higher degree of power balance within the cluster.Among them, the reactive power coordination index is the following: Where i Q is the reactive power coordination index of cluster i ; s Q is the value of reactive power supply to the nodes within the cluster; n Q is the reactive power value demanded by the nodes within the cluster; n is amount of clusters; The average reactive power balance Q  of n clusters of the divided regional distribution network is defined as the reactive power coordination index within the cluster.
The active power coordination index is used to describe the coordination relationship between active power demand and supply within the cluster.The calculation formula is: Where i P is the intra-group active power coordination index of cluster i ; s P is the active power supply value of the cluster's internal nodes; n P is the demand value of the internal nodes of the cluster's active nodes; The average active power balance degree P  of n clusters in the divided regional distribution network is defined as the active power coordination degree index in the group.

Comprehensive performance index
In summary, the comprehensive performance index F for evaluating the advantages and disadvantages of large-scale distributed photovoltaic power cluster division is proposed by weighted combination of modularity index, intra-group active and reactive power coordination index and cluster scale index:  are the weight coefficients of each index respectively, and ++= .According to different cluster division objectives, different weight coefficients are selected to obtain the corresponding cluster division results.

Cluster partition method based on SLM algorithm
Since the distribution network itself has similar characteristics to the community structure after access to large-scale distributed photovoltaics [9] , the community division algorithm can be used for cluster division.The feature of the SLM algorithm is to traverse all communities in the current community structure.For each community, a subnet is constructed, and then a local mobility heuristic algorithm is used to identify the communities in the subnet.
Figure 1 depicts the SLM algorithm's flowchart:  The SLM algorithm can re-divide the nodes that have been divided into the same cluster, thus solving the problem of cluster merging and single node moving between clusters.

Example analysis
4.1 Supply of Photovoltaic power to a 10 kV distribution system In this paper, the photovoltaic power supply is connected to the IEEE33 node 10 kV distribution system.The distribution system has a total of 33 nodes, including a total of 20 photovoltaic power supply nodes.The distribution network structure for the photovoltaic power supply is depicted in Figure 2 [10] .

Cluster division results
This example clusters two scenarios.In scene 1, the light intensity at noon on a sunny day in summer is strong, larger photovoltaic power output and smaller loads.Scenario 2 chooses the case of low light intensity on a cloudy day in summer.In this paper, the photovoltaic power supplies are operated in gridconnected mode, and all the photovoltaic power supply control methods are the same.The load parameters of each node and the capacity of the photovoltaic power supply displays in Figure 3 to Figure 5.In addition, this study compares the cluster division technique under the common algorithm of modified K-means in order to confirm the logic of the cluster division method in this research [11] .The photovoltaic power nodes in the 2 scenarios are clustered under the same distribution network and the same metrics respectively, and Table 1 displays the outcomes.It can be seen from the cluster division results that there is no single node as a cluster in both scenarios, indicating that this algorithm is more suitable for cluster division of large-scale photovoltaic power supply.The strategy proposed in this paper allows already divided clusters to be divided again, solves the problems of cluster merging and single node moving between clusters, and is more reasonable in terms of division results

Conclusion
The main findings regarding the SLM algorithm based scaled distributed photovoltaic cluster segmentation strategy proposed in this paper are as follows.
1) In contrast to relying only on modularity for cluster segmentation, this paper proposes a comprehensive performance index that takes into account electrical distance, power ratio between active and reactive power within the cluster.Via the mutual cooperation between nodes within the cluster, the power flow between the clusters is reduced, and the power is balanced locally to the greatest extent, thereby improving the cluster division results.
2) It can be seen from the example that the SLM algorithm is used to divide the cluster of large-scale photovoltaic power supply, which makes the system modularity of the cluster division result higher, and can quickly and accurately carry out photovoltaic power supply cluster division in response to largescale photovoltaic power supply access situation.

Figure 3 .
Figure 3. Active power of every node in different scenarios.

Figure 4 .
Figure 4. Reactive power of every node in different scenarios.

Figure 5 .
Figure 5. capacity of each distribution network node's photovoltaic system.

Table 1 .
Cluster partitioning results in different scenarios