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Article

A Network Partition-Based Optimal Reactive Power Allocation and Sizing Method in Active Distribution Network

by
Deshu Gan
1,*,
Huabao Ling
1,
Zhijian Mao
1,
Ran Gu
2,
Kangxin Zhou
2 and
Keman Lin
2
1
Guangdong Power Grid Co., Ltd., Zhuhai Power Supply Bureau, Zhuhai 519000, China
2
College of Energy and Electrical Engineering, Hohai University, Nanjing 211100, China
*
Author to whom correspondence should be addressed.
Processes 2025, 13(8), 2524; https://doi.org/10.3390/pr13082524
Submission received: 17 June 2025 / Revised: 28 July 2025 / Accepted: 6 August 2025 / Published: 11 August 2025

Abstract

To address the node voltage fluctuation and over-limit caused by the high penetration of distributed photovoltaic (PV) generation connected to distribution networks, this paper proposes a network partition-based optimal reactive power allocation and sizing method in the active distribution network (ADN). A network index incorporating network partition and critical node identification is introduced to obtain the optimal location for the reactive power compensation. A singular value entropy-based adaptive spectral clustering algorithm is applied to obtain the initial zones and obtain the critical nodes of each zone on the basis of the proposed network indexes. This method avoids the unreasonable scheme and enhances the efficiency and clarity of partitioning. The improved decimal coding method is proposed to improve the efficiency of the proposed method. A case study on the IEEE 33-node distribution system is carried out to verify the feasibility and effectiveness of the proposed method. The results show that compared with the conventional methods, the proposed method can effectively reduce voltage variations and control the voltage within the safe limit.

1. Introduction

In recent years, distributed photovoltaic (PV) generation has experienced rapid development. By the end of December 2023, China’s cumulative installed capacity of distributed PV had reached 254.438 GW, significantly increasing the complexity of distribution network planning and operation. Consequently, conventional distribution networks are gradually evolving into ADN. The ADN is a distribution system that actively controls and manages local distributed energy resources through a flexible network topology to regulate power flow [1]. The uncertainty of distributed PV output makes the operation state of ADN change rapidly [2,3], resulting in the random fluctuations of node voltage. Some lines have a reversal power flow during periods with high PV output, which leads to increased network loss, voltage overstep, and other problems. This bi-directional power flow threatens the safe and stable operation of ADN. Considering that the sizing and location of the reactive power compensator cannot be arbitrarily modified once deployed, it is crucial to determine their optimal allocation and sizing in advance. By considering network partitioning and the randomness of PV output, the proposed approach aims to enhance ADN stability and operational efficiency. Given these complexities, it is imperative to identify critical nodes within the network whose characteristics have a strong impact on system stability. Understanding node criticality under uncertain PV conditions provides a targeted approach for mitigating voltage issues and optimizing compensation strategies.
In conventional distribution networks, load fluctuation is an important uncertainty factor affecting reactive power optimization [4]. However, the fluctuation of distributed PV generation and load is the primary source of uncertainty, which causes the voltage fluctuation and additional system loss in ADN. To address this issue, Ref. [5] proposed a comprehensive method of reactive power optimization based on the probability of typical scenarios of wind power output, and adopted an adaptive weighted genetic algorithm to obtain the optimal scheme. Ref. [6] proposes a reactive power optimization method that simultaneously considers the random fluctuations of wind power, distributed PV generation, and load variations, with network loss minimization as the optimization objective.
Since the reactive power compensation of ADN is implemented in a limited area for efficiency, the partitioned-based schemes are usually adopted. Ref. [7] proposed a grid reactive voltage partitioning method that considers the wind power stability and accuracy in a comprehensive manner, enhancing the stability of the power grid voltage. Current studies mostly achieve reactive power optimization by initiating optimal scheduling of adjustable resources such as PV inverters and reactive power compensators, while research on optimizing the location and sizing of reactive power compensators based on the network partitioning to achieve this goal remains relatively limited.
For the critical node identification, research is mainly conducted based on complex network theory [8,9,10,11]. Ref. [8] proposed the node evaluation index clusters and branch evaluation index clusters, establishing a comprehensive criticality index for identifying critical nodes. Based on entropy theory, Ref. [9] combines singular value entropy and power flow distribution entropy to formulate a comprehensive evaluation index for critical node identification. Nevertheless, these methods do not consider the impact range and node correlation of critical nodes. In terms of network partitioning, the clustering algorithm is widely used [12,13,14]. Ref. [12], an agglomerative hierarchical clustering algorithm was applied for partitioning the reactive power source control space. Ref. [13] divides the distribution network into multiple zones based on electrical distance and regional voltage regulation capability as partitioning performance indexes. Ref. [15] proposed a critical node identification algorithm considering electrical topology and power flow distribution, and introduced the PageRank algorithm to get the node importance. Ref. [16] proposed a two-level offline partitioning method for ADN with high PV penetration. However, these studies did not combine network partition with reactive power allocation and sizing to get the optimal reactive power compensation.
This paper proposes a network partition-based method for optimal reactive power allocation and sizing. The method aims to ensure voltage stability in ADN with high PV penetration. This method is targeted to obtain the optimal allocation and sizing of reactive power compensation to ensure the voltage stability of the ADN considering PV uncertainty. The improved partition and critical nodes identification index is introduced, including the regional coupling index and the critical node index, considering the influence of PV output. An initial partition and critical nodes identification selection method based on adaptive spectral clustering and singular value entropy is adopted to improve the efficiency and controllability of the critical node identification. The efficiency is also enhanced by the improved decimal coding method.
The major contributions are given as follows:
(1)
A network partition and critical node identification method based on the improved partition and critical nodes identification index, and an adaptive spectral clustering and singular value entropy-based network partition method of ADN are proposed. This method enables more accurate and efficient identification of partitions and critical nodes at the same time, providing a more effective foundation for reactive power compensation.
(2)
An optimal allocation and sizing of reactive power compensation approach that employs an immune genetic algorithm is presented to determine the location and sizing of SVG in order to minimize the total system loss and voltage fluctuation. It enhances optimization efficiency and system voltage stability by minimizing total power loss and voltage deviations under multiple PV scenarios.
The rest of this article is organized as follows. Section 2 introduces the network partition and critical node identification method, and Section Section 3 optimizes the capacity configuration in the photovoltaic scenario. This is followed by the case study in Section Section 4. Finally, Section Section 5 concludes this article.

2. Network Partition and Critical Node Identification

2.1. Active Distribution Network

High penetration of distributed PV systems makes ADN a complex network. The operational state of the ADN constantly changes with the fluctuation of PV output and load. These variations alter the network power flow, making the original reactive power compensator configuration less optimal. The deviation of the variables of the critical node leads to similar changes in the surrounding nodes. Based on the above operation principle, the partition of the ADN is conducted by putting the nodes with strong connections into one partition and the nodes with weak connections into different partitions. Identifying the critical node on the basis of network partition for reactive power compensation achieves the voltage regulation capability with minimum compensated reactive power capacity. The schematic figure of the proposed partition and critical node identification in the IEEE-9 nodes system is shown in Figure 1.

2.2. Index of Network Partitioning and Critical Node Identification

The selected critical node not only enables the effective control of the node voltages in the partition, but also has the least influence on the nodes outside the partition. Taking the partition and the critical nodes obtained in the following text as the initial scheme, the index of critical node identification and the index of regional coupling are calculated as the synthesis index of the partition. Critical node identification index considers the node observability and controllability index, while the regional coupling index considers the intra-regional coupling index and the inter-regional coupling index. The judgment index is set for the critical node and partition, and the optimal critical node and partition are obtained by using the improved immune genetic algorithm.

2.2.1. Index of Critical Node Identification

The features of the critical node are mainly reflected in two aspects: Firstly, the voltage of the critical node represents the voltage level of the whole control area to a certain extent (observability); Secondly, when the voltage of the whole area is deviated from the normal operating state, the recovery of the voltage of the critical node contributes to the recovery of the surrounding nodes (controllability). The observability index is defined to describe the connection between the critical node voltage and the average voltage magnitude of the partition. The controllability index is defined to describe the change of the voltage at the critical node with the PV output changes. The critical node is selected based on the comprehensive index, which combines both the observability index and the controllability index.
The observability index of the critical node is defined as follows:
N o b = k S k α m k 2 + β m k 2 l k
where Sk is the set of load nodes in region k; lk is the number of load nodes in the region. αmk and βmk are the reactive and active voltage sensitivity of the critical node to any other node.
The controllability index of the critical node is defined as follows:
N c o = V m Q p v + V m P p v l p v
where Vm is the voltage of the critical node; Ppv and Qpv are the active power and reactive power of PV nodes in the region, respectively. lpv is the number of PV nodes.
The comprehensive index of critical node selection is defined as follows:
N = max ρ 1 N o b + ρ 2 N c o
where ρ1 and ρ2 are the respective weights of observability and controllability. Considering the high importance of observability and controllability, this paper sets ρ1 + ρ2 = 1.

2.2.2. Index of Regional Coupling

Regional division of ADN needs to meet two main requirements: (1) strong coupling within the region; (2) weak coupling between regions. In order to measure the degree of coupling between any two nodes in the same zone, the intra-regional coupling index and inter-regional coupling index are defined.
The intra-regional coupling index is defined as follows:
C i n = 1 l k l k 1 j = 1 l k i = 1 , i j l k d i j max d i j
where lk is the number of nodes in region k; dij is the electrical distance between nodes i and j. The smaller the index is, the closer the electrical coupling of the nodes in the region will be.
The inter-regional coupling index is defined as follows:
C o u t = 1 p k i P k d i j min i P k ( d i j )
where pk is the number of critical nodes in region k; Pk is a set of critical nodes in region k. The smaller the index is, the weaker the influence of voltage control in other regions on the local region will be.

2.2.3. The Synthesis Model of Partition

According to the above indexes, the objective function of partition is listed:
min F ( x ) = N max N k + C i n k C i n min + C o u t k C o u t min Satisfy   constraint Conditions λ Dissatisfy   constraint   conditions
where λ is the penalty term when the constraint condition is violated; N max , C   i n   min , C   o u t   min are the maximum and minimum values of the corresponding objective function for all individuals in the current iteration step.
The corresponding constraints are as follows:
(1)
Restriction on the number of nodes in a partition: A single node cannot be an area by itself, and the number of nodes in a single area cannot exceed 2/3 of the total number of nodes.
(2)
Connectivity constraint: Nodes in one partition must be connected. Nodes without connections cannot be divided into the same partition.
This paper uses an improved immune genetic algorithm to solve the key node selection and partitioning problems of ADN.

2.3. Improved Immune Genetic Algorithm

Initial Scheme Acquisition

When solving the objective function of partition, it is important to get an appropriate initial network partition and a critical node identification scheme. An appropriate scheme avoids unreasonable zoning to improve the efficiency of optimization. This paper uses the improved adaptive spectral clustering and singular value entropy method based on Ref. [17] to get the initial scheme.
Based on the graph theory, the spectral clustering algorithm is applied to the ADN in the sample space with an arbitrary shape, and converges the problem to a global optimal solution. The electrical distance is introduced to the similarity matrix. The autoencoder is used to extract the features of the nodes in ADN, including the voltage amplitude and phase angle, active power, and reactive power. The similarity matrix is obtained by taking the Fréchet distance between the features of different nodes. The improved adaptive spectral clustering algorithm is used for partitioning based on the similarity matrix obtained from the Fréchet distance to avoid the unreasonable situation where nodes that are far apart are clustered into one partition.
Singular value entropy is a quantitative index derived from the singular values of a matrix, commonly used to measure the complexity or disorder of system states. Based on the entropy theory, this paper introduces the singular value entropy to describe the influence of different disturbances on the voltage magnitude of each node. The critical node is identified, which gets the largest value of singular value entropy in each partition.
The singular value entropy of the Jacobian matrix J is defined as follows:
H Σ = i = 1 m μ i ln μ i
where μ i is the result of the normalization of singular values. When μ 1 = μ 2 = μ m , HΣ takes the maximum lnm. At this time, the changes in the load of each node in the network cause consistent changes in voltage amplitude and phase angle, so the impact of the load change of each node on the ADN is balanced.
The sensitivity of HΣ to the active power of node i is defined as follows:
H Σ i = H Σ P i
where Pi is the reactive power of node i. A larger value of HΣi means that the change in the active power of the nodes causes a larger variation in HΣ, resulting in a larger variation in the elements of Σ. The load change of the node leads to large fluctuations of node voltage amplitude and phase angle. By calculating the singular value entropy HΣi of all the nodes in each partition and sorting them in order, the node with the largest HΣi is selected as the critical node of this partition.
Conventional optimization algorithms need to be updated and iterated by solving the fitness value, while the network partitions and critical nodes need to undergo complex transformations before the fitness value can be calculated [18]. The immune genetic algorithm is an evolutionary optimization technique inspired by the principles of the biological immune system. The immune genetic algorithm directly utilizes the chromosomes to represent network partitions and critical nodes, and is more suitable for problems related to network partitions. In this paper, the immune genetic algorithm is adopted to solve the proposed problem of network partition and critical node identification in the AND [19].
The conventional practice is to directly allocate the chromosomal gene segments to each node using the binary coding method. However, when the scale of the ADN increases, each time a node is added, the solution space will grow exponentially. Therefore, the efficiency of the algorithm decreases significantly, making it difficult to find an optimal solution within a limited time.
In order to avoid the disadvantages of binary coding, this paper adopts an improved decimal coding method in the process of solving the genetic algorithm. The first nine digits of the code represent the partition and are arranged in the order of nodes. Nodes with the same number are classified into the same partition. The rest of the code represents the critical code. Taking a 9-node power system as an example, its partition and critical nodes can be encoded into the following chromosomes:
g = ( g 1 g 2 g 9 g 18 ) = 123123223 9 digit 000100101 9 digit
where 1 indicates that the node is a critical node, and 0 indicates that the node is not a critical node.
The procedure of network partitioning and critical nodes identification of the ADN is shown in Figure 2.
By adopting this encoding method, the increase in the number of partitions does not affect the length of the chromosome. This improved decimal coding method is applicable for a network with a large number of nodes, which adopts a relatively short chromosome to represent the partitioning scheme. The theoretical solution space size of this method is much smaller than the binary coding method. The improved decimal coding method increases the effective feasible solution density and reduces the computation complexity. Meanwhile, this encoding method does not affect the length of chromosomes when the number of partitions increases, thereby reducing the computation complexity as well.

3. Optimal Configuration of Reactive Power Compensation

3.1. Clustering and Typical Scenario Extraction

This paper introduces the multi-dimensional scaling analysis to cluster scenarios and extract typical scenarios of distributed PV in ADN. The principle of multi-dimensional scaling analysis is to use the similarity between pairs of samples to build a suitable low-dimensional space, and ensure the similarity of samples in low-dimensional and high-dimensional spaces as much as possible [20]. Firstly, Fréchet distance is used to measure the similarity between the time series data, and the similarity matrix is obtained. Then, samples in the original space are mapped to the low-dimensional space, and the distance between samples in the two spaces is ensured as much as possible during the mapping process. Finally, the pressure function is used to measure the quality of dimensionality reduction.
The Gaussian mixed model (GMM) is used to generate typical PV output scenarios [21]. GMM is the suitable clustering number using the Bayesian Information Criterion (BIC) to determine [22]. The BIC value corresponding to the lowest K value is the GMM of the optimal clustering number. The generated typical PV output scenario will be applied in the following ADN optimal allocation and sizing of reactive power compensation.

3.2. Optimal Sizing of the Reactive Power Compensation

After the critical nodes and partitions are obtained, the optimal allocation and sizing of reactive power compensation needs to be determined, considering the operation scenarios of distributed PV. In this paper, the critical nodes are selected to be the optimal location of reactive power compensation. The voltage control scheme of the ADN determines the reactive power allocation and capacity of the ADN with the knowledge of load and PV output [23,24], and adjusts the control variables to improve the power quality and reduce the operating cost. The capacity of each reactive power compensator is obtained by the Particle Swarm Optimization (PSO) algorithm. The objective function is to minimize the voltage deviation and active power loss with the least capacity of the reactive power compensation in each partition:
min λ c k = 1 K |   Q p , k c | + λ v i = 1 N Δ V i + λ p i = 1 N P l o s s , i
where K is the number of partitions, | Q p , k c | is the absolute value of the capacity of the reactive power compensation, N is the number of nodes, Δ V i is the voltage deviation of each node, Ploss is the network active power losses, λ c , λ v , λ p are the weighting factors corresponding to the reactive power compensation, voltage deviation, and power loss, respectively.
The constraints are as follows:
(1)
Power flow constraint
Power flow equations represent the relationship between network voltage and power.
P i V i j = 1 N V j G i j cos ( δ i δ j ) + B i j sin ( δ i δ j ) = 0 Q i V i j = 1 N V j G i j sin ( δ i δ j ) + B i j cos ( δ i δ j ) = 0
where i = 1, …, N. N is the number of buses; Pi and Qi are the active and reactive power of bus i, respectively; Gij and Bij are the transfer conductance and susceptance between bus i and bus j, respectively.
(2)
Voltage constraint
Voltage limits guarantee the voltage of all the system nodes within the acceptable limits.
V i min V i V i max , i = 1 , , N
where Vi is the voltage of bus i.
(3)
Transformer constraints
The following two inequality constraints represent the limits of transformer tap adjustment in order to prevent excessive adjustment of the transformer tap.
n c min n c ( k ) n c max
Δ n c min | n c ( k ) n c ( k 1 ) | Δ n c max
where nc is the tap position of the transformer.
(4)
Reactive power compensator constraints
Each reactive power compensator has a limit on its output, which is related to its capacity.
Q C , i min Q C , i Q C , i max , i = 1 , , N c
where Qc,i is the reactive power of the compensator and Nc is the number of reactive power compensators.
(5)
Constraint of the zonal reactive power balance
The reactive power in each zone is provided by the reactive power compensator deployed at the critical nodes in the same zone, so the reactive power balance index in the area is defined as follows:
R b = k = 1 K Q p , k max + i = 1 l k Q l , i 2 k = 1 K Q p , k max + k = 1 K i = 1 l k Q l , i
where K is the number of partitions; Q p , k max is the feasible reactive power upper limit of the reactive power compensator of the critical nodes in partition k; Ql,i is the reactive load in partition k; lk indicates the number of load nodes in area K. The smaller the reactive power balance index is, the better the reactive power balance achieves.
(6)
Reactive power balance chance constraint
Considering that node load fluctuations in ADN are random and frequent, a chance constraint is introduced to ensure that the capacity of reactive power compensation equipment can meet the demands in the majority of scenarios. The chance constraint is defined as follows:
j = 1 N s c e n e P Q k max Q k , j β
where Nscenario is the number of scenarios; P( ) is the event probability, obtained by GMM clustering method; Qk,j is the sum of reactive power of the jth scenario in partition k; Q p , k max is the maximum reactive power output of the controller node where reactive power compensation is deployed in area k; β is the confidence level that satisfies the reactive power balance constraint, and the greater the β is, the lower the tolerance for the reactive power balance in the unsatisfied partition.
To sum up, the optimization algorithm obtains the optimal sizing of the reactive power compensator installed at the critical node identified in Section 2. The optimal configuration considers various scenarios of PV extracted by GMM that meet the requirements of unchanged critical nodes and network partitions in different scenarios. Meanwhile, it meets the reactive power balance conditions in each partition and achieves stable and reliable operation of the grid under the minimum device capacity. This optimal allocation and sizing of the reactive power compensation strategy ensures voltage stability and economic efficiency across various PV operational scenarios, significantly reducing the overall reactive power equipment capacity within the partition. The proposed method maintains regional voltages within safe operational ranges, thereby enhancing the overall efficiency and reliability of the Active Distribution Network.

4. Case Study

In this section, the proposed algorithm is verified on an IEEE-33 bus distribution system with a total load of 3715 + j2300 kVA. Eight PV units are installed in the system as shown in Table 1. The Static Var Generator (SVG), which is a power electronic device to provide reactive power compensation of a wide range, is implemented as the reactive power compensator in this paper. The system topology is shown in Figure 3.

4.1. Network Partition and Critical Node Identification

The test case is partitioned by the proposed spectral clustering method described in Section Section 3. The partition scheme A is obtained by the proposed improved immune genetic algorithm. This scheme has no situation where isolated nodes or disconnected nodes are divided into one area. The fitness value and the partitioning result of Scheme A are shown in Table 2.
Table 2 summarizes the partitioning results for Schemes A, B, and C. Scheme A is obtained by the proposed method. Scheme B considers only the regional coupling indexes, and Scheme C is derived from the initial clustering results. According to Figure 4, scheme A achieves the lowest intra-regional as well as the inter-regional coupling indexes among all three schemes. The partition result of Scheme A indicates the strongest internal connectivity and weakest external interactions among all three methods. Both schemes B and C primarily emphasize strong internal coupling within each region but overlook the weak coupling between different regions. As a result, these schemes lead to voltage fluctuation in one region, having a bigger impact on the voltage of adjacent regions. Overall, the comparison demonstrates that Scheme A offers a more balanced partition of the network, which ensures a more effective voltage control performance and minimizes the unwanted interactions between different zones.
The proposed method not only obtains the optimal partition but also the optimal critical nodes. The critical nodes of the above four schemes are shown in Figure 5. Nodes with the same color background in the figure are in the same partition, and the red nodes are the critical nodes in the partition. As can be seen from the figure, the critical node of the proposed method is mainly located near the PV nodes and the end of the network, which conforms to the principle of reactive power compensation local balance, verifying the superiority of the proposed critical node selection and partition. The singular value entropy of each critical node of the three schemes is shown in Table 3. Singular value entropy describes the uniformity of the singular value distribution. The smaller the singular value entropy is, the more obvious the critical nodes are. The singular value entropy of Scheme A is generally lower than that of Scheme B and Scheme C, which shows that the contributions of critical nodes to the system are more concentrated, and the identification results are more accurate. The optimal partitioning and critical node scheme are shown in Table 4.

4.2. Reactive Power Compensation Configuration

The PV data used in the reactive power optimization simulation is the actual PV output data from somewhere in the southeast of China in 2020, with a data interval of 5 min. The SVGs are installed on the critical node of each partition obtained in Section 4.1. According to the optimal configuration model of the reactive power compensator proposed in this paper, the confidence level β of the reactive power balance constraint is set to 0.9. The PSO algorithm is adopted to solve the scheme mentioned above. The SVG configuration is obtained in Table 5.
Scenario without reactive power compensation is set for comparison based on the interval dynamic state estimation. Both cases are simulated according to the different PV scenarios. The voltage operates within the intervals caused by the PV and load fluctuation. The node voltage amplitude of the ADN under uncertainty resulting from low PV output (1 a.m.) and the results of high PV output (13 p.m.) are shown in Figure 6. The blue curves represent the predicted voltage with no SVG compensation, while the red curves represent the controlled voltage with SVG compensation. The shaded regions describe the interval ranges formed by the upper and lower bounds of node voltage across the system. The SVG reactive power output is shown in Table 6. As shown in Figure 6, in the case of low PV output, the voltages of 23 nodes in AND exceed the operation limits, which is below 0.97 p.u. Equipped with SVG obtained by the proposed method, the violation of the voltage operation threshold is eliminated in all the scenarios considering PV and load fluctuations. The voltage of nodes located at the end of the lines rises from 0.92 p.u. to 0.98 p.u. The average amplitude of the voltage rises from 0.95 p.u. to 0.98 p.u. by implementing reactive power compensation. The voltage level has increased by 4.48% compared to the case without SVG. Meanwhile, in the case of high PV output, the voltages of 19 nodes in AND exceed the operation limits, which is above 1.03 p.u. Equipped with SVG obtained by the proposed method, the voltage of nodes located at the end of the lines drops from 1.12 p.u. to 1.02 p.u. The average amplitude of the voltage drops from 1.04 p.u. to 1.00 p.u. by implementing reactive power compensation. The voltage level has increased by 3.33% compared to the case without SVG. Overall, the controlled voltage has significantly improved compared to the predicted voltage. The controlled voltage is within the safety limit, which effectively solved the voltage variations and over-limit under different conditions of overvoltage and undervoltage.
These results verify that the proposed scheme is effective in controlling voltage within limits in both overvoltage and undervoltage conditions, enhancing the operational reliability and robustness of the ADN.

5. Conclusions

This paper proposes a network partition-based optimal allocation and sizing of reactive power compensation in ADN. The problem is solved by introducing the observability index, controllability index, and regional coupling index to obtain the optimal partition and identify the critical nodes. Then, the reactive power allocation for ADN was optimized, and the optimal reactive power compensator capacity meeting the constraint conditions was solved to control the voltage within the safe range.
The simulation results show that the proposed method achieves the smallest regional coupling index, which indicates its feasibility compared to the other schemes. It also demonstrates its effectiveness in eliminating the violation of node voltage constraints and improving the voltage level, considering the PV and load fluctuations.
There are still some limitations in this study. This paper only considers distributed PV as a distributed energy source and SVG as a reactive power compensator, and does not study coordination between multiple distributed energy sources and reactive power compensators. However, in real power grids, there are various distributed energy sources, which make the power grid more complex than what is described in this paper. A more efficient reactive power optimization scheme will be proposed, considering more distributed energy sources in future work. The future work includes the verification of the method in the larger-scale systems, such as IEEE 69 and 90 node systems.

Author Contributions

Conceptualization, D.G., H.L. and Z.M.; methodology, D.G.; software, D.G. and R.G.; validation, R.G.; formal analysis, D.G.; investigation, H.L. and Z.M.; resources, H.L. and Z.M.; data curation, R.G.; writing—original draft preparation, D.G.; writing—review and editing, R.G., K.Z. and K.L.; visualization, R.G. and K.L.; supervision, H.L.; project administration, D.G. and K.L.; funding acquisition, D.G. and K.L. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported in part by the Technology project “Research on Balance Control and Scheduling System Based on Distributed New Energy” (GDKJXM20230753(030400KC23070012)).

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

Author Deshu Gan, Huabao Ling, Zhijian Mao was employed by the company Guangdong Power Grid Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Abbreviations

The following abbreviations are used in this manuscript:
PVPhotovoltaic
ADNActive distribution network
GMMGaussian mixed model
PSOParticle Swarm Optimization
BICBayesian information criterion
SVGStatic Var Generator

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Figure 1. The schematic figure of the proposed partition and critical node identification method in the IEEE-9 node systems.
Figure 1. The schematic figure of the proposed partition and critical node identification method in the IEEE-9 node systems.
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Figure 2. Flowchart of the proposed partitioning scheme.
Figure 2. Flowchart of the proposed partitioning scheme.
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Figure 3. Topology of the IEEE-33 bus distribution system.
Figure 3. Topology of the IEEE-33 bus distribution system.
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Figure 4. Comparison of partition indexes.
Figure 4. Comparison of partition indexes.
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Figure 5. Partition and critical nodes in three cases.
Figure 5. Partition and critical nodes in three cases.
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Figure 6. Predicted voltage interval and voltage interval after control.
Figure 6. Predicted voltage interval and voltage interval after control.
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Table 1. Capacity and location of PV units.
Table 1. Capacity and location of PV units.
PV Location (Nodes)PV Capacity (MW)
16, 18, 281.0
19, 331.2
14, 251.5
221.8
Table 2. Partition scheme.
Table 2. Partition scheme.
SchemeFitness ValuePartition Scheme
A603.787(23, 24, 25), (10, 11, 12, 13, 14, 15, 16, 17, 18), (26, 27, 28, 29, 30, 31, 32, 33), (1, 2, 3, 4, 5, 6, 7, 8, 9), (19, 20, 21, 22)
B\(1, 2, 19, 20, 21, 22), (3, 4, 5, 23, 24, 25), (6, 7, 8, 9, 10, 11, 26, 27), (12, 13, 14, 15, 16, 17, 18),
(28, 29, 30, 31, 32, 33)
C\(1, 2, 3, 4, 5, 6, 7, 8, 19), (9, 10, 11, 12, 13, 14, 15, 16, 17, 18), (20, 21, 22), (23, 24, 25),
(26, 27, 28, 29, 30), (31, 32, 33)
Table 3. Singular value entropy of critical nodes.
Table 3. Singular value entropy of critical nodes.
Scheme AScheme BScheme C
Critical NodeSingular Value EntropyCritical NodeSingular Value EntropyCritical NodeSingular Value Entropy
60.42420.42460.424
150.41830.419120.419
200.41490.417220.419
240.419130.419230.412
300.410290.411300.410
\\\\320.411
Table 4. Optimal partitioning scheme.
Table 4. Optimal partitioning scheme.
PartitionCritical NodeBuses in the PartitionLoads (kVA)
161,2,3,4,5,6,7,8,9890 + j450
21510,11,12,13,14,15,16,17,18615 + j290
32019,20,21,22360 + j160
42423,24,25930 + j450
53026,27,28,29,30,31,32,33920 + j950
Table 5. SVG configuration.
Table 5. SVG configuration.
NodeSVG Capacity (MVar)
61.70
151.70
200.50
241.00
301.60
Table 6. Average reactive power output of SVG.
Table 6. Average reactive power output of SVG.
Node1 a.m. (MVar)13 p.m. (MVar)
6−0.855051.69072
15−0.801641.69971
20−0.119400.31579
24−0.41520−0.71154
30−1.565920.97247
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Gan, D.; Ling, H.; Mao, Z.; Gu, R.; Zhou, K.; Lin, K. A Network Partition-Based Optimal Reactive Power Allocation and Sizing Method in Active Distribution Network. Processes 2025, 13, 2524. https://doi.org/10.3390/pr13082524

AMA Style

Gan D, Ling H, Mao Z, Gu R, Zhou K, Lin K. A Network Partition-Based Optimal Reactive Power Allocation and Sizing Method in Active Distribution Network. Processes. 2025; 13(8):2524. https://doi.org/10.3390/pr13082524

Chicago/Turabian Style

Gan, Deshu, Huabao Ling, Zhijian Mao, Ran Gu, Kangxin Zhou, and Keman Lin. 2025. "A Network Partition-Based Optimal Reactive Power Allocation and Sizing Method in Active Distribution Network" Processes 13, no. 8: 2524. https://doi.org/10.3390/pr13082524

APA Style

Gan, D., Ling, H., Mao, Z., Gu, R., Zhou, K., & Lin, K. (2025). A Network Partition-Based Optimal Reactive Power Allocation and Sizing Method in Active Distribution Network. Processes, 13(8), 2524. https://doi.org/10.3390/pr13082524

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