Research on Distribution Network Harmonic Mitigation and Optimization Control Strategy Oriented by Source Tracing

Abstract

Against the backdrop of a high proportion of distributed renewable energy sources being integrated into the power grid, distribution networks are confronted with issues of grid-wide and decentralized harmonic pollution and voltage deviation, rendering traditional point-to-point governance methods inadequate for meeting collaborative governance requirements. To address this problem, this paper proposes a source-tracing-oriented harmonic mitigation and optimization control strategy for distribution networks. Firstly, it identifies regional dominant harmonic source mitigation nodes based on harmonic and reactive power sensitivity indices as well as comprehensive voltage sensitivity indices. Subsequently, with the optimization objectives of reducing harmonic power loss and suppressing voltage fluctuation in the distribution network, it configures the quantity and capacity of voltage-detection-based active power filters (VDAPFs) and Static Var Generators (SVGs) and solves the model using an improved Spider Jump algorithm (SJA). Finally, the effectiveness and feasibility of the proposed method are validated through testing on an improved IEEE-33 standard node test system. Through analysis, the proposed method can reduce the voltage fluctuation rate and total harmonic distortion (THD) by 2.3% and 2.6%, respectively, achieving nearly 90% equipment utilization efficiency with the minimum investment cost.

1. Introduction

As distributed generation (DG) is integrated into distribution networks on a large scale, the once single-source radial configuration of these networks shifts into a multi-source complex structure. This transformation brings about modifications in both the scale and direction of power flow, along with notable changes in the operational conditions of the system [1]. The inherent randomness and variability of renewable energy generation introduce a significant degree of uncertainty. Meanwhile, the extensive deployment of power electronic devices intensifies harmonic distortions and voltage stability challenges within distribution networks, thereby posing a grave risk to their secure operation [2]. Taking harmonic effects into account during the planning phase of DG in distribution networks holds immense significance. It is crucial for facilitating the seamless integration of distributed renewable energy sources, bolstering the stability of distribution networks, and enhancing their capability to accommodate renewable energy. At present, the widespread presence of nonlinear loads, including converters and various power electronic equipment, has further exacerbated harmonic pollution in distribution networks [3]. Moreover, certain precision electronic components and load devices exhibit extreme sensitivity to power quality issues [4]. The clash between the escalating demand for high-quality power on the load side and the prevailing harmonic pollution has emerged as a pressing concern that demands immediate attention in distribution networks.

Research on harmonic mitigation generally involves the installation of governance equipment such as passive power filters and active power filters (APF). However, the installation of power quality governance equipment is plagued by issues such as high investment and construction costs and low equipment utilization rates. At present, a number of researchers have put forward the idea of multi-functional grid-tied inverters (MFGCI) [5]. By taking advantage of the topological resemblance between photovoltaic grid-tied inverters and active power filters, they have enhanced the control mechanism of these inverters. This modification has led to the creation of multi-functional grid-tied inverters that can perform several tasks simultaneously, including active power grid connection, harmonic suppression, and reactive power compensation. In Reference [6], a new topological framework and control approach for MFGCI are presented, allowing it to combine the functions of traditional grid-tied inverters with those of APFs. Meanwhile, Reference [7] puts forward a control strategy for MFGCI aimed at achieving harmonic suppression and reactive power compensation, thereby tackling power quality concerns like harmonics and voltage fluctuations. Reference [8] takes into account the output states of MFGCI under different weather conditions and resolves the issue of how to allocate the capacity of MFGCI for harmonic mitigation and reactive power compensation. The aforementioned references analyze the effectiveness of utilizing MFGCI for harmonic mitigation; however, there is a scarcity of literature studying how to leverage distribution network partitioning combined with compensation equipment to actively participate in harmonic mitigation in distribution networks, which hinders the full exploitation of the flexibility of flexible adjustment resources within the system [9].

The point-to-point configuration scheme for traditional compensation equipment, such as Static Var Generators (SVGs) and Voltage-Distortion-Adaptive Power Filters (VDAPF), involves installing them on the user side, close to nonlinear loads for harmonic compensation. However, with the widespread and dispersed integration of nonlinear loads into distribution networks, the point-to-point configuration scheme necessitates the installation of a large number of harmonic mitigation devices within the distribution network, leading to a significant increase in installation and operation & maintenance costs [10]. With the development of industrial clustering, a large number of medium- and low-voltage local distribution networks have emerged, such as super high-rise office buildings, high-tech industrial parks, and new energy towns, where the power time-variability and harmonic disturbance mechanisms of the internal loads exhibit certain similarities. Therefore, optimizing the configuration locations and output capacities of compensation equipment within the system to achieve comprehensive harmonic compensation in medium- and low-voltage local distribution networks has become a current research hotspot in the field of power quality [11,12]. The optimization objective for compensation equipment configuration is to reduce the harmonic distortion rates at all nodes within the system to within the range permitted by national standards in China by planning appropriate equipment installation locations and capacities [13]. Due to the complexity of the comprehensive optimization configuration model for compensation equipment, analytical algorithms and heuristic algorithms are commonly employed to solve the optimization model. References [14,15] discretize the installation capacities of the equipment and propose analytical algorithms based on harmonic sensitivity ranking. However, this approach requires the installation of a large number of devices, leading to high costs. Additionally, the programs for analytical algorithms are relatively complex and lack feasibility.

Currently, there has been a substantial amount of research on the optimal configuration for addressing single types of power quality issues. Reference [16] adopts an approach grounded in the network harmonic sensitivity matrix. It employs the mean value of the total harmonic distortion rate at each node as the objective function for optimization, aiming to incrementally identify the most suitable nodes for installing harmonic control equipment. Nevertheless, this technique is plagued by problems, including an excessive number of nodes being configured and inefficient utilization of capacity. Reference [17] further employs the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm to optimize simultaneously for configuration effectiveness, the number of equipment configurations, and the total configuration capacity. Compared to the governance of single power quality issues, there is relatively limited research on the optimal configuration and regulation of governance equipment for comprehensive network compensation targeting multiple power quality indicators. Reference [18] constructs a model aimed at analyzing and conducting an overall assessment of power quality attributes related to voltage, current, and frequency metrics within microgrids. However, this model falls short in putting forward a specific strategy for power quality improvement and management. Reference [19] establishes a ship power quality assessment system based on the Analytic Hierarchy Process (AHP) and fuzzy comprehensive evaluation, but it fails to consider the subjectivity in weight determination inherent in fuzzy algorithms, which makes the evaluation results susceptible to subjective influences. Reference [20] combines AHP with grayscale analysis, but its scores only indicate relative merits and do not correlate with the limit values of the indicators. Reference [21] proposes a distribution network loss calculation model that accounts for composite power quality disturbances, including harmonics, three-phase current imbalance, and voltage deviation. Reference [22], under the premise of considering limited investment costs, proposes a unified optimal configuration method for voltage sag and harmonic resonance monitoring points, as well as a unified optimization configuration model for monitoring points that aims to maximize the comprehensive score of the configuration scheme while adhering to constraints on the number of monitoring devices. Reference [23] utilizes Norton’s equivalent method to establish an objective function for optimizing harmonic voltage compensation in local distribution networks. By combining nonlinear programming principles with set-aided analysis methods, it solves the optimization problem to determine the installation locations and optimal configuration capacities of SVGs in the system, thereby proposing a comprehensive optimization algorithm for suppressing harmonic voltages in power grids based on SVGs. The power quality governance objectives, the equipment targeted for power quality regulation, and the power quality requirements vary across these studies. Nevertheless, they all offer insights that align with the development of electrical equipment in modern power grids. The governance of power quality indicators and the configuration and regulation of multiple types of power quality equipment remain crucial research directions in the field of power quality governance.

Despite extensive research on harmonic mitigation by numerous scholars, several limitations and challenges persist:

(1)

Traditional point-to-point mitigation methods struggle to adapt to the decentralized characteristics of harmonic pollution and voltage deviations across the entire network, failing to meet the demand for coordinated mitigation and resulting in limited mitigation effectiveness.

(2)

The point-to-point configuration schemes of existing compensation equipment such as SVG and VDAPF require the installation of a large number of devices, significantly increasing installation and operational and maintenance costs. Moreover, these devices exhibit low utilization rates and lack the capability for comprehensive optimization of multiple quality indicators.

To address these issues, this paper proposes a source-tracing-oriented harmonic mitigation and optimization control strategy for distribution networks. The innovations of this paper are summarized as follows:

(1)

This paper introduces a method for locating dominant regional harmonic source mitigation nodes based on harmonic and reactive power sensitivity indicators, combined with comprehensive voltage sensitivity indicators, to achieve accurate tracing and coordinated mitigation of harmonic sources.

(2)

This paper constructs a mathematical model with the optimization objectives of reducing harmonic power loss and suppressing voltage fluctuations. By utilizing an improved SJA, it reasonably configures the quantity and capacity of VDAPF and SVG, addressing the issue of inefficient equipment configuration and enhancing the cost-effectiveness of mitigation.

The framework of this paper is as follows: First, in Section 2, a partitioning method for distribution networks based on voltage coupling degree is proposed, defining harmonic and reactive power sensitivity indicators, thus clarifying the selection strategy for dominant regional harmonic source mitigation nodes. Then Section 3 constructs a mathematical model aimed at minimizing harmonic power loss and suppressing voltage fluctuations. Section 4 presents a solution algorithm based on the improved SJA. Subsequently, in Section 5, an improved IEEE-33 node test system is employed to verify the effectiveness of the proposed method. Finally, the conclusion in Section 6 summarizes the entire paper.

2. Introduction to Distribution Network Partitioning Method

2.1. Calculation Method for Voltage Coupling Degree in Distribution Networks

The proposed method determines the dominant regional harmonic source mitigation nodes by constructing harmonic and reactive power sensitivity indicators as well as a comprehensive voltage sensitivity model: Firstly, it calculates the comprehensive voltage sensitivity of each node based on the reactive power-fundamental voltage sensitivity between nodes, which reflects the voltage regulation capability of reactive power compensation, and the h-th harmonic voltage-equivalent admittance sensitivity used to quantify the suppression effect of changes in VDAPF equivalent admittance on harmonic voltage. Secondly, considering the electrical distance and coupling weights between nodes within each partition, the distribution network is divided into multiple regions using a modularity optimization algorithm. Finally, within each partition, the node with the highest comprehensive voltage sensitivity and the most significant improvement effect on the voltage and harmonics of other nodes in the region is selected as the dominant governance node, enabling precise tracing of harmonic sources and coordinated regional governance.

The reactive power/fundamental voltage sensitivity in distribution networks can represent the voltage variation relationship between nodes. The expression for reactive power/fundamental voltage sensitivity is as follows:

$$S_{ij}={({\displaystyle \frac{\mathit{\partial }{Q}_j}{\mathit{\partial }{V}_i^{FW}}})}^{-1}$$

(1)

Here, $S_{ij}$ represents the reactive power-voltage sensitivity between nodes i and j; $Q_j$ is the reactive power at node j; $V_i^{FW}$ is the fundamental voltage at node i.

The fundamental voltage relationship between nodes is shown in (2):

$$\Delta V_i^{FW}=({\displaystyle \frac{\mathit{\partial }{V}_i^{FW}}{\mathit{\partial }{Q}_j}}/{\displaystyle \frac{\mathit{\partial }{V}_j^{FW}}{\mathit{\partial }{Q}_j}})\Delta V_j^{FW}={\gamma }_{ij}^{FW}\Delta V_j^{FW}$$

(2)

Here, $\Delta V_i^{FW}$ and $\Delta V_j^{FW}$ are the fundamental voltage unbalance amounts at nodes i and j, respectively; $V_j^{FW}$ is the fundamental voltage at node j; ${\gamma }_{ij}^{FW}$ is the fundamental voltage coupling degree between nodes i and j.

The VDAPF mitigates harmonic pollution by releasing harmonic currents through equivalent conductance, where the equivalent conductance is equivalent to the VDAPF’s capability to manage harmonic pollution. The harmonic sensitivity is represented by the degree to which the increase in equivalent conductance of the VDAPF at a node governs the harmonic voltages at other nodes. The h-th harmonic sensitivity $E_{h,ij}$ between nodes i and j is calculated according to (3):

$$E_{h,ij}={\displaystyle \frac{\mathit{\partial }{V}_{h,j}^{HW}}{\mathit{\partial }{G}_{h,j}^{HW}}}$$

(3)

$V_{h,j}^{HW}$ is the h-th harmonic voltage at node j; $G_{h,j}^{HW}$ is the h-th harmonic equivalent conductance at node i.

The harmonic sensitivity $E_{ij}$ between nodes i and j is:

$$E_{ij}=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{h=2}^M{E}_{h,ij}^2}}$$

(4)

Here, N represents the number of harmonics; M represents the maximum harmonic order. The harmonic voltage coupling degree for the h-th harmonic is:

$$\Delta V_{h,i}^{HW}=({\displaystyle \frac{\mathit{\partial }{V}_{h,i}^{HW}}{\mathit{\partial }{G}_{h,j}^{HW}}}/{\displaystyle \frac{\mathit{\partial }{V}_{h,j}^{HW}}{\mathit{\partial }{G}_{h,j}^{HW}}})\Delta V_{h,j}^{HW}={\gamma }_{h,ij}^{HW}\Delta V_{h,j}^{HW}$$

(5)

Here, $V_{h,i}^{HW}$ and $V_{h,j}^{HW}$ are the h-th harmonic voltage unbalance amounts at nodes i and j, respectively; $V_{h,i}^{HW}$ is the h-th harmonic voltage at node i; $G_{h,j}^{HW}$ is the h-th harmonic equivalent conductance at node j; ${\gamma }_{h,ij}^{HW}$ is the h-th harmonic voltage coupling degree between nodes i and j.

The harmonic voltage coupling degree ${\gamma }_{ij}^{HW}$ between nodes i and j is:

$${\gamma }_{ij}^{HW}=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{h=2}^M{({\gamma }_{h,ij}^{HW})}^2}}$$

(6)

Through the aforementioned analysis, this paper further derives a modularity calculation method based on a comprehensive voltage coupling degree index. The comprehensive voltage coupling degree can be expressed as (7) and (8):

$${\gamma }_{ij}^{COM}=(1-\tau )r_{ij}^{FW}+\tau {\gamma }_{ij}^{HW}$$

(7)

$$\tau ={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{K}_i^{HW}}}{{\displaystyle \sum _{i=1}^n(K_i^{HW}+C_i^{FW})}}}$$

(8)

Here, n represents the total number of nodes in the distribution network; ${\gamma }_{ij}^{COM}$ is the comprehensive voltage coupling degree between nodes i and j; $C_i^{FW}$ is the absolute value of the fundamental voltage deviation at node i; $K_i^{HW}$ is the harmonic voltage distortion rate at node i; τ is a weighting coefficient. The parameter τ is employed in the comprehensive voltage coupling degree to weight the combined impact of the harmonic distortion rate and the absolute value of the fundamental voltage deviation. When the system is sensitive to harmonic pollution, τ should take a relatively small value (e.g., τ < 0.5) to prioritize the suppression of harmonic distortion. Conversely, if voltage stability is a higher priority, τ should take a relatively large value (e.g., τ > 0.7). In practical engineering, the typical range of τ is 0.3 to 0.7, and in this paper, τ is set to 0.4. The value of τ exhibits significant system dependency. In radial distribution networks, where harmonic propagation paths are singular, τ can be appropriately increased to enhance voltage stability. In contrast, in looped or meshed structures, where harmonic cross-coupling is severe, τ should be decreased to prioritize the suppression of harmonic diffusion. To eliminate the dimensional differences between the harmonic distortion rate and voltage deviation, range normalization is applied.

Based on the comprehensive voltage coupling degree index, the modularity B is obtained and used as a quantitative measure of node correlation. Then, the network is partitioned into different regions using a partitioning optimization algorithm. The expression for modularity B is given by Equations (9)–(12):

$$B={\displaystyle \frac{1}{2m}}{\displaystyle \sum _{i,j=1}^n[A_{ij}-\frac{k_i{k}_j}{2m}]}\eta (c_i,c_j)$$

(9)

$$A_{ij}=1-{\displaystyle \frac{d_{ij}}{\max \left\{d_{ij}\right\}}}$$

(10)

$$\eta (c_i,c_j)=\left\{\begin{array}{c}0,c_i\ne c_j\\ 1,c_i=c_j\end{array}\right.$$

(11)

$$d_{ij}=-\lg ({\gamma }_{ij}^{COM}{\gamma }_{ji}^{COM})$$

(12)

Here, m is the sum of coupling weights for all nodes; A_ij represents the coupling weight between nodes i and j; k_i and k_j are the total coupling weights of nodes connected to nodes i and j, respectively; c_i and c_j are the community numbers of nodes i and j, respectively; η(c_i, c_j) is a binary variable that determines whether nodes i and j belong to the same community, with η(c_i, c_j) = 1 if they do and otherwise η(c_i, c_j) = 0; d_ij is the electrical distance between nodes i and j; ${\gamma }_{ij}^{COM}$ is the comprehensive voltage coupling degree between nodes i and j.

Using modularity B as a quantitative measure of node correlation, a community optimization algorithm is employed to partition the network into different regions. The specific steps are as follows:

• Initialize each node in the distribution network. Calculate sensitivity indices for each node as an individual community and compute the comprehensive voltage coupling degree based on these sensitivity indices.
• Calculate the coupling weights A_ij between all nodes in the distribution network and the quantitative measure of node correlation, modularity B, based on the comprehensive voltage coupling degree ${\gamma }_{ij}^{COM}$.
• Select any two nodes in the distribution network to form a new community. List all possible outcomes of forming new communities with two nodes and calculate the coupling weights A_ij between all nodes and the quantitative measure of node correlation, modularity B, for all possible outcomes. Select the maximum modularity value B_max and record the corresponding community structure.
• Calculate the maximum change in modularity B_max based on the modularity B values from steps (2) and (3). If ΔB_max is greater than 0, retain the recorded community composition; otherwise, maintain the original community structure unchanged.
• Compress the retained new community composition by consolidating the original communities into a new node and updating the original distribution network to a new network structure.
• Return to step (1) and repeat the process. The loop terminates when the community structure no longer changes, and the optimal community distribution result is output.

2.2. Determining Strategy for the Location of VDAPF

The distribution network is partitioned into different regions, and the dominant governing nodes in each region are selected as candidate connection points for VDAPF and SVG. While the voltage and harmonics at the dominant governing nodes are regulated, the voltage and harmonics at the remaining nodes within the same region also experience the maximum possible improvement. The reactive power/fundamental voltage sensitivity of nodes within the partitioned regions is defined as:

$${\overline{S}}_{i,l}^{FW}={\displaystyle \frac{1}{n_{i,l}}}{\displaystyle \sum _{j=1}^{\Omega }{S}_{ij,l}^{FW}}$$

(13)

$${\overline{S}}_{i,l}^{\max }=\max \left\{{\overline{S}}_{i,l}^{FW}\right\}$$

(14)

Here, ${\overline{S}}_{i,l}^{FW}$ represents the average reactive power/fundamental voltage sensitivity of nodes connected to node i within region l; n_i,l is the number of nodes connected to node i within region l; $\Omega$ denotes the set of nodes connected to node i within region l; $S_{ij,l}^{FW}$ is the reactive power/fundamental voltage sensitivity between nodes i and j within region l; and ${\overline{S}}_{i,l}^{\max }$ is the maximum average reactive power/fundamental voltage sensitivity of nodes connected to node i within region l.

The harmonic sensitivity of nodes within the partitioned region is defined as:

$$E_{ij,l}=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{h=2}^M{E}_{h,ij,l}^2}}$$

(15)

$${\overline{E}}_{i,l}={\displaystyle \frac{1}{n_{i,l}}}{\displaystyle \sum _{j=1}^{\Omega }{E}_{ij,l}}$$

(16)

$${\overline{E}}_{i,j}^{\max }=\max \left\{{\overline{E}}_{i,l}\right\}$$

(17)

Here, $E_{ij,l}$ represents the harmonic sensitivity between nodes i and j within region l; $E_{h,ij,l}$ is the h-th harmonic sensitivity between nodes i and j within region l; $E_{ij,l}$ is the average harmonic sensitivity of nodes connected to node i within region l; and ${\overline{E}}_{i,j}^{\max }$ is the maximum average harmonic sensitivity of nodes connected to node i within region l.

The remaining capacity of VDAPF can be utilized for reactive power compensation. By combining harmonic sensitivity and reactive power/fundamental voltage sensitivity, a comprehensive voltage sensitivity is obtained. Based on this indicator, the dominant governing nodes are selected as candidate nodes for VDAPF. The comprehensive voltage sensitivity of nodes within the partitioned region is defined as:

$$W_{ij,l}=\lambda \sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{h=2}^M{E}_{h,ij,l}^2}}+(1-\lambda )S_{ij,l}^{FW}$$

(18)

$$W_l^{\max }=\max \left\{{\displaystyle \frac{1}{n_{i,l}}}{\displaystyle \sum _{j=1}^{\Omega }{W}_{ij,l}}\right\}$$

(19)

Here, $W_{ij,l}$ represents the comprehensive voltage sensitivity between nodes i and j within region l; $W_l^{\max }$ is the maximum value of comprehensive voltage sensitivity within region l; and λ is a weighting coefficient.

3. Mathematical Model for Harmonic Mitigation

3.1. Objective Function

Voltage stability issues in distribution networks pose a severe threat to their safe operation and have become a major challenge faced by countries worldwide. In Asia, countries such as India and Vietnam frequently experience voltage fluctuations and even collapses due to aging grid infrastructure and inadequate regulation capabilities amid large-scale integration of renewable energy. This has led to interruptions in industrial production and damage to residential electrical equipment. In Africa, nations like Nigeria and Kenya face exacerbated voltage instability issues in rural areas due to the long geographical distance between power generation sources and load centers, coupled with high transmission and distribution losses. This has deepened electricity poverty and constrained economic and social development. In South America, countries such as Brazil and Argentina encounter widespread voltage instability during extreme weather events like droughts, which drastically reduce hydropower output. Insufficient backup power and limited cross-regional transmission capacity further compound the problem. Therefore, this paper primarily focuses on the effectiveness of harmonic voltage mitigation. The objective function for harmonic mitigation in this paper consists of two parts. The first part aims to achieve favorable compensation effects. The compensation performance of the VDAPF after deployment is evaluated using total harmonic network losses and node harmonic distortion. When harmonic currents flow through line impedances or resistive loads, branch harmonic voltages are generated, leading to harmonic network losses. Assuming the network contains L branches, the h-th harmonic voltage $U_{b,l,h}$ of the l-th branch can be calculated as follows:

$$U_{b,l,h}={\displaystyle \sum _{n=1}^N{A}_{n,l}{U}_{n,h}}$$

(20)

Here, the subscript b denotes the state of network branches before mitigation; $A_{n,l}$ represents the element in the n-th row and l-th column of the network incidence matrix. At this point, the line network losses can be calculated according to Equation (21).

$$P_{b,l,h}=\mathrm{Re}(S_{R,l,h})=\mathrm{Re}(U_{b,l,h}\overline{Y_{b,l,h}{U}_{b,l,h}})={\left|U_{b,l,h}\right|}^2\mathrm{Re}(Y_{U_{b,l,h}})$$

(21)

Here, $P_{b,l,h}$ represents the h-th harmonic network loss on the l-th branch, which is derived from the real part of the harmonic apparent power $S_{R,l,h}$; and $Y_{b,l,h}$ is the h-th harmonic reactance of branch l; the overline denotes the complex conjugate.

The total harmonic network loss $P_{R,h}$ in the network is given by:

$$P_{R,h}={\displaystyle \sum _{h=2}^H{\displaystyle \sum _{l=1}^L{P}_{b,l,h}}}={\displaystyle \sum _{h=2}^H{\displaystyle \sum _{l=1}^L{\left|U_{b,l,h}\right|}^2\mathrm{Re}(Y_{b,l,h})}}$$

(22)

The single harmonic ratio (HR) and THD are crucial metrics for evaluating the effectiveness of harmonic compensation. They can be expressed by Equations (23) and (24), respectively, as follows:

$$R_{HR,n,h}=\left|U_{n,h}\right|/\left|U_{n.1}\right|$$

(23)

$$R_{THD,n}=\sqrt{{\displaystyle \sum _{h=2}^H{\left|U_{n,h}\right|}^2}}/\left|U_{n.1}\right|$$

(24)

Here, $R_{HR,n,h}$ represents the h-th harmonic ratio at node n; $U_{n.1}$ is the fundamental voltage at node n; and $R_{THD,n}$ is the total harmonic distortion at node n.

To ensure the lowest cost of deploying mitigation equipment while maximizing the efficiency of power quality improvement in the distribution network, the objective is to minimize the cost of the mitigation equipment. The objective function F can be expressed as:

$$\min F={\displaystyle \sum _{i=1}^I{C}_i^{VDAPF}{d}^{VDAPF}}+{\displaystyle \sum _{j=1}^J{C}_i^{SVG}{d}^{SVG}}$$

(25)

where I and J represent the total number of installation nodes for VDAPF and SVG in region l, respectively; $C_i^{SVG}$ and $C_i^{VDAPF}$ denote the installed SVG capacity and the installed VDAPF capacity, respectively; $d^{SVG}$ and $d^{VDAPF}$ are the unit capacity costs of SVG and VDAPF, respectively.

It should be noted that the aforementioned objective function comprises three components: network losses, voltage distortion rate, and installation cost. However, due to the inconsistent units of these three components, it is challenging to convert them into a single-objective optimization problem through direct addition. Therefore, the multi-objective problem can first be transformed into a single-objective problem through normalization and subsequent weight assignment, thereby further reducing the complexity of solving the problem.

3.2. Constraints

The operation of the distribution network must satisfy power flow constraints. In this paper, second-order cone relaxation is employed to transform the power flow equations into a mixed-integer second-order cone programming model. The relaxed Disflow power flow equations are as follows:

$${\displaystyle \sum _{i-j=1}^L{P}_{i-j}}-{\displaystyle \sum _{k-i=1}^L(P_{k-i}-R_{k-i}{I}_{k-i}^2)=P_i^{in}}$$

(26)

$${\displaystyle \sum _{i-j=1}^L{Q}_{i-j}}-{\displaystyle \sum _{k-i=1}^L(Q_{k-i}-X_{k-i}{I}_{k-i}^2)=Q_i^{in}}$$

(27)

$$U_{i,1}^2-U_{j,1}^2=2(P_{i-j}{R}_{i-j}+Q_{i-j}{X}_{i-j})-(R_{i-j}^2+X_{i-j}^2)I_{i-j}^2$$

(28)

$${‖(2P_{i-j},2Q_{i-j},I_{i-j}^2-U_{i,1}^2)‖}_2\le I_{i-j}^2+U_{i,1}^2$$

(29)

$$\left\{\begin{array}{c}{P}_i^{in}=P_i^{DG}-P_i^{load}-P_i^{cha}+P_i^{discha}\\ Q_i^{in}=Q_i^{DG}-Q_i^{load}+Q_i^{SVG}+Q_i^{VDAPF}\end{array}\right.$$

(30)

Here, $P_{i-j}$ and $Q_{i-j}$ are the active and reactive power flows, respectively, in line i − j; $P_{k-i}$ and $Q_{k-i}$ are the active and reactive power flows, respectively, in line k − i; $X_{i-j}$ and $R_{i-j}$ are the reactance and resistance, respectively, of line i − j; X_k−i and R_k−i are the reactance and resistance, respectively, of line k − i; $I_{i-j}^2$ and $I_{k-i}^2$ are the squares of the currents in lines i − j and k − i, respectively; $P_i^{in}$ and $Q_i^{in}$ are the net active and reactive powers, respectively, at node i; $P_i^{DG}$ and $Q_i^{DG}$ are the active and reactive powers, respectively, generated by distributed photovoltaic sources at node i; $P_i^{load}$ and $Q_i^{load}$ are the active and reactive powers, respectively, of the load at node i; $Q_i^{SVG}$ and $Q_i^{VDAPF}$ are the reactive powers generated by SVG and VDAPF, respectively, at node i; and ${‖·‖}_2$ denotes the 2-norm operation. The harmonic power flow equations for the distribution network are as follows:

$$\left\{\begin{array}{c}{C}_i^{SVG}\le C_{\max }^{SVG}\\ C_i^{VDAPF}\le C_{\max }^{VDAPF}\end{array}\right.$$

(31)

Here, $C_{\max }^{SVG}$ and $C_{\max }^{VDAPF}$ represent the maximum installation capacities of SVG and VDAPF, respectively.

Meanwhile, the system also includes energy storage devices, which need to satisfy the following operational constraints (32):

$$\left\{\begin{array}{l}{S}_{ES,t}=S_{ES,t-1}+{\displaystyle \frac{{\eta }_{cha}{P}_{i,t}^{cha}}{E_{ES}}}-{\displaystyle \frac{P_{i,t}^{discha}}{{\eta }_{discha}{E}_{ES}}}\hfill \\ S_{ES,\min }\le S_{ES,t}\le S_{ES,\max }\hfill \\ 0\le {\mu }_{discha}+{\mu }_{cha}\le 1\hfill \\ {\mu }_{cha}{P}_{\min }^{cha}\le P_{i,t}^{cha}\le {\mu }_{cha}{P}_{\max }^{cha}\hfill \\ {\mu }_{discha}{P}_{\min }^{discha}\le P_{i,t}^{discha}\le {\mu }_{discha}{P}_{\max }^{discha}\hfill \end{array}\right.$$

(32)

Here, $S_{ES,t}$ represents the state of charge (SOC) of the energy storage battery at time t; ${\eta }_{cha}$ and ${\eta }_{discha}$ are the charging and discharging efficiencies of the energy storage battery, respectively; $E_{ES}$ is the rated capacity of the energy storage battery; $S_{ES,\max }$ and $S_{ES,\min }$ are the upper and lower limits of the SOC of the energy storage battery, respectively; ${\mu }_{cha}$ and ${\mu }_{discha}$ are 0–1 variables representing the charging and discharging states of the energy storage battery, respectively; $P_{\max }^{cha}$ and $P_{\min }^{cha}$ are the upper and lower limits of the charging power, respectively; and $P_{\max }^{discha}$ and $P_{\min }^{discha}$ are the upper and lower limits of the discharging power, respectively.

During the optimization process, although the objective function focuses on minimizing harmonic network losses and nodal harmonic distortion to indirectly improve power quality, explicit upper and lower bound constraints are explicitly imposed in the constraints to strictly comply with the IEEE 519 standard, as shown in (33).

$$\left\{\begin{array}{c}TH{D}_i\le 5\%\\ -5\%\le U_i-U_N\le 5\%\end{array}\right.$$

(33)

Here, U_N represents the standard voltage value.

4. Solution Method Based on an Improved Spider Jump Algorithm

The traditional JSA employs a random distribution method during the population initialization process, which makes it difficult to ensure population diversity and can easily lead the JSA algorithm to become trapped in local optima. In contrast to randomized initial populations, this paper adopts a good point set strategy for initializing the jumping spider population. This approach results in a more uniform sequence and broader global coverage of the population, which is beneficial for the global optimization capability of the Improved JSA. The principle involves constructing a point set with low discrepancy to cover the search space, thereby avoiding the concentration of the initial population in specific regions of the search space. The mathematical formulation is as follows.

$$\left\{\begin{array}{c}{P}_n(k)=\left\{(r_1^{(n)}·k),(r_2^{(n)}·k),\cdots ,(r_S^{(n)}·k),1\le k\le n\right\}\\ \phi (n)=C(r,\epsilon )n^{\epsilon -1}\end{array}\right.$$

(34)

Here, $r_S^{(n)}$ represents a unit cube in an S-dimensional Euclidean space; $P_n(k)$ is the good point set, r is the good point, and C(r,ε) is a constant related only to r and ε.

In the middle and late stages of the SJA, the population tends to concentrate around the optimal individual of the current generation, even experiencing excessive aggregation and overlap. This makes it difficult for the population to maintain diversity and prone to becoming trapped in local optima. Therefore, this paper introduces a cosine similarity strategy, cos(a,b), which reflects the directional consistency relationship between two vectors a and b. When the value is 1, it indicates that the two vectors have the same direction, and when it is −1, it indicates that they have opposite directions.

By constructing vectors a and b based on the positions of the optimal individual and the current individual in the population, the cosine similarity strategy is used to update individuals with high similarity (cos(a,b) > 0.5). These individuals are then compared with the average fitness value of the current generation. Individuals with higher fitness retain the original algorithm’s update strategy, while individuals with lower fitness are updated through Cauchy mutation. The Cauchy probability density function has a low peak in the middle and is relatively flat overall, allowing the Cauchy distribution to generate more diverse individuals in the population. The specific formulas are as follows.

$$\left\{\begin{array}{c}a=x_{best}(t)\\ b=x_i(t)\end{array}\right.$$

(35)

$$\cos (a,b)={\displaystyle \frac{a·b}{\left|a\right|\times \left|b\right|}}$$

(36)

$$x_i(t+1)=x_i(t)+\xi (x_{best}(t)-x_r(t))$$

(37)

Here, $x_{best}(t)$ represents the position of the optimal individual in the current population; $x_i(t)$ is the position of the i-th individual in the current generation; $x_i(t+1)$ is the position of the i-th individual in the next generation after updating; $x_r(t)$ is the position of a randomly selected individual in the current generation; and $\xi$ is the Cauchy operator.

This paper introduces a nonlinearly varying convergence factor. When the algorithm conducts a large-scale search in the early iterations, employing a slow convergence factor can enhance the population’s optimization capability. As the algorithm progresses through iterations, the population gradually converges. At this point, a rapidly decaying convergence factor is advantageous for the algorithm to locally search for the optimal solution. Additionally, a control factor is incorporated to regulate the decay amplitude. Equation (38) presents its mathematical model.

$$\delta ={\delta }_m·[1-{({\displaystyle \frac{e^{\frac{t}{t_{\max }}}-1}{e-1}})}^K]$$

(38)

Here, δ_m represents the initial value of the convergence factor (the difference between the maximum and minimum fitness values), that is, the length of the fitness interval; t is the current iteration number; t_max is the maximum number of iterations; K is the control factor that regulates the decay amplitude.

$\gamma$ serves as the expected pheromone level in this paper. If its value is too large, more individuals will be updated, leading to greater population diversity but slower global convergence speed; conversely, if its value is too small, fewer individuals will be updated, making the algorithm prone to local convergence. To prevent these situations, this paper introduces a decay parameter into $\gamma$:

$$\gamma =\left\{\begin{array}{c}{\displaystyle \frac{3}{4}}(P{h}_{\max }-P{h}_{\min }),0\le t\le 20\%\times t_{\max }\\ {}^{(t/10)}\sqrt{{\displaystyle \frac{3}{16}}{(P{h}_{\max }-P{h}_{\min })}^2}·\gamma ,20\%\times t_{\max }\le t\le 40\%\times t_{\max }\\ {\displaystyle \frac{1}{4}}(P{h}_{\max }-P{h}_{\min }),40\%\times t_{\max }\le t\le t_{\max }\end{array}\right.$$

(39)

After adopting the improved $\gamma$, during the early stage of the algorithm, it can effectively ensure population diversity; in the mid-stage of the algorithm, a decay strategy is employed with a limit on the number of decays, enabling $\gamma$ to vary within an effective range and enhancing the randomness of solutions; in the late stage of the algorithm, the convergence speed is accelerated. For jumping spider individuals with originally low pheromone levels, the mutation strategy shown in Equation (40) was previously applied, but its excessive randomness resulted in overly slow convergence.

$$\left\{\begin{array}{c}{r}_1=round(1+(\dim -1)·rand)\\ r_2=round(1+(\dim -1)·rand)\\ x_i(t)=x_{best}(t)+(x_i(r_1)-({(-1)}^{\wedge }\sigma )x_i(r_1))\end{array}\right.$$

(40)

Here, r₁, r₂ are randomly generated integers; round is the rounding function; dim represents the dimension; σ ∈ {0, 1}.

To gain a better understanding, a detailed flowchart of the proposed method is given as below in Figure 1.

5. Case Study

To further demonstrate the effectiveness of the algorithm proposed in this paper, an improved IEEE-33-node test system is employed for case verification. As a classic benchmark model in distribution network research, this system features a clear structure, transparent parameters, and a reasonable load distribution, enabling it to effectively simulate the radial topology and diverse load characteristics of actual distribution networks. With a moderate scale of 33 nodes, it can clearly demonstrate the synergistic effects of zonal optimized equipment allocation on harmonic suppression and voltage control, providing a reliable basic validation platform for subsequent expansion to larger-scale systems. The topological structure of the test system is illustrated in Figure 2 below. The relevant parameter settings are as follows: Distributed photovoltaic (PV) and wind power are connected at Node 3 and Node 15, with rated capacities of 150 kW and 200 kW, respectively. An energy storage device is installed at Node 22, featuring a charge/discharge efficiency of 0.92, a capacity of 300 kWh, and a maximum charge/discharge power of 100 kW. The unit capacity configuration cost for the VDAPF is 40 $/A, while that for the SVG is 50 $/A.

The detailed values of each parameter in the optimization algorithm are shown in

Table 1. Parameter values in the optimization model.

Parameter	Range of Values	Value Adopted in This Paper
Cosine similarity threshold	[0.4, 0.6]	0.52
Control factor	[0.1, 0.5]	0.3
Attenuation boundary value	[0.01, 0.1]	0.05
Population size	[30, 100]	50
Maximum number of iterations	[80, 200]	120
Random seed	/	42

below.

The power curves for wind power/PV and load are shown in Figure 3 below, and the frequency spectrum can be obtained through discretization followed by the Fast Fourier Transform method.

5.1. Validation of Distribution Network Partitioning and Planning Strategies

The distribution network is partitioned using the partitioning method proposed in this paper, with the relevant results shown in Figure 4 below.

Upon observing Figure 4, it can be seen that during the partitioning of the distribution network, areas containing independent distributed power sources often fall within a single zone. Distributed PV and wind power are distributed in Area 1 and Area 3, respectively, while Area 2 does not contain any distributed power sources. When a high proportion of distributed renewable energy sources, such as wind and PV, are integrated into the distribution network, harmonic pollution and voltage deviations exhibit characteristics of network-wide dispersion. Renewable energy devices like distributed PV and wind power, which are connected to the grid via power electronic converters, generate specific harmonic frequencies due to their nonlinear characteristics, and the harmonic characteristics of different renewable energy stations are similar. If such nodes are grouped within the same partition, unified modeling can be achieved based on the homologous nature of their harmonic generation mechanisms, avoiding the complexity of harmonic propagation paths caused by cross-partition management. Nodes without renewable energy sources are primarily affected by system background harmonics, and their harmonic characteristics differ fundamentally from those of renewable energy nodes. Separate partitioning simplifies harmonic source tracing analysis in these areas and reduces the complexity of developing mitigation strategies. The core advantage of this partitioning approach lies in achieving precise and coordinated harmonic control. For partitions with concentrated renewable energy sources, harmonic amplification effects can be suppressed at the source by uniformly configuring active power filters or optimizing the control parameters of renewable energy converters, while efficiently allocating mitigation resources by leveraging harmonic coupling relationships among nodes within the zone. For partitions without renewable energy sources, the focus can be on compensating for system background harmonics and improving voltage quality, avoiding interference from renewable energy harmonic mitigation measures on traditional load nodes. The two types of partitions establish weakly coupled connections through dominant harmonic source control nodes, ensuring the independence of mitigation measures within each partition while achieving coordinated optimization of harmonic levels across the entire network.

Figure 5 and Figure 6, respectively, illustrate the equipment configuration plans under the optimization method proposed in this paper and the equipment configuration plans without partition-based harmonic control.

Upon observing Figure 5 and Figure 6, it is found that under the method proposed in this paper, the installation nodes of SVG and VDAPF are positioned closer to distributed renewable energy sources. Specifically, VDAPF is installed at central nodes. By placing SVG and VDAPF closer to distributed renewable energy sources, reactive power generated by renewable energy generation can be compensated locally and rapidly, while its fluctuations are suppressed. This reduces long-distance transmission of reactive power across the grid, lowers line losses, and enhances power transmission efficiency. Simultaneously, it enables rapid response to changes in renewable energy output, suppresses harmonics and voltage fluctuations, and improves local power quality. Meanwhile, installing VDAPF at central nodes allows for comprehensive harmonic management of the entire regional grid, providing macro-level control over grid power quality and coordinating power quality conditions across different nodes. The combination of these two installation approaches enables comprehensive and effective management of power quality and harmonics, spanning from local to overall grid levels. Through sensitivity analysis by adjusting τ (from 0.1 to 0.9) in an improved IEEE-33 node system, notable changes in zoning results were observed. When τ ≤ 0.3, the weight of harmonic distortion dominates, and zoning tends to group areas with dense harmonic sources (e.g., near nodes 5, 11, and 13) into the same sub-region for centralized deployment of VDAPFs. In this case, nodes with significant voltage deviations (e.g., end node 33) may be overlooked, leading to a decline in local voltage stability. When 0.4 ≤ τ ≤ 0.6, the weights of harmonics and voltage deviations are balanced, and the zoning results consider both harmonic propagation paths and voltage stability requirements. For example, node 3 (a distributed photovoltaic access point) and node 22 (where an energy storage device is located) are grouped into the same sub-region, achieving coordinated harmonic suppression and voltage support. When τ ≥ 0.7, the weight of voltage deviation dominates, and zoning tends to group nodes with significant voltage fluctuations into independent sub-regions for priority SVG configuration. In this scenario, areas with dense harmonic sources may be fragmented, leading to scattered deployment of mitigation equipment and increased total investment costs.

5.2. Effects Analysis of Harmonic Voltage Mitigation

To facilitate a comparison of the differences in harmonic voltages before and after distribution network mitigation, this paper employs per-unit values to represent harmonic voltages. A comparison of the harmonic voltage curves for the 5th, 7th, 11th, and 13th harmonics before and after distribution network mitigation is shown in Figure 7. As depicted in Figure 7, configuring VDAPF at nodes for harmonic mitigation effectively reduces harmonic voltages of various orders at each node in the distribution network. The VDAPF works by continuously monitoring the harmonic components in the currents at each node of the distribution network. It utilizes power electronic devices to swiftly generate compensation currents that are equal in magnitude but opposite in phase to the harmonic currents, and then injects these compensation currents into the grid. This causes the harmonic currents to cancel each other out within the grid, reducing the voltage drops caused by harmonic currents across grid impedances, thereby effectively lowering harmonic voltages of various orders at each node in the distribution network and achieving harmonic mitigation. Given that this paper takes into account the regional characteristics of power quality, harmonic voltages of various orders at the points of renewable energy integration also experience a significant reduction. This demonstrates that by selecting dominant harmonic voltage mitigation nodes and configuring VDAPF, the harmonic voltage amplitudes at each node in the distribution network can be effectively reduced.

On the other hand,

Table 2. Comparative Analysis of Harmonic Mitigation Effects of Different Methods.

Method	Voltage Distortion Rate (%)	Total Installed Capacity (A)	Total Investment Cost ($)
The proposed method	3.4	37.8	2456.3
Method A proposed in [24]	5.4	/	2785.4
Method B proposed in [25]	5.7	/	2645.2

compares the effects of the method proposed in this paper with those of traditional methods. Specifically, Method A employs a coordinated harmonic compensation optimization approach using grid-connected inverters for harmonic mitigation, while Method B utilizes reactive power compensation to enhance power quality. Compared to Methods A and B, the proposed method in this paper reduces the voltage distortion rate by 2.0% and 2.3%, respectively, and achieves the lowest total investment cost. The superior performance of the proposed method in reducing the voltage distortion rate and minimizing total investment costs can be attributed primarily to its precise identification of mitigation nodes. By determining regional dominant harmonic source mitigation nodes based on harmonic and reactive power sensitivity indices, as well as comprehensive voltage sensitivity indices, the proposed method can trace harmonics to their source and accurately pinpoint nodes with the most significant impact on voltage distortion for targeted mitigation. In contrast, Method A, which employs a coordinated harmonic compensation optimization approach using grid-connected inverters, lacks such detailed and precise source localization, resulting in insufficiently targeted mitigation efforts. Unlike Method B, which focuses on reactive power regulation to enhance power quality, the proposed method directly targets harmonic sources, thereby more effectively reducing the voltage distortion rate.

During the optimization process, the scheduling decisions of the energy storage system directly contribute to the improvement of voltage/harmonic indices in the objective function. Specifically, when the VDAPF compensates for harmonic currents, its instantaneous power demand is dynamically provided by the energy storage system through a DC/AC converter, thereby avoiding power fluctuations in the grid caused by harmonic compensation. When the fifth harmonic current at Node 13 surges, the energy storage system releases stored electrical energy to provide instantaneous reactive power support for the VDAPF, indirectly reducing the THD at that node. This process is explicitly represented in the optimization model through coupling constraints between the charging/discharging power of the energy storage system and the compensation power of the VDAPF. The energy storage system adjusts its charging and discharging power to modify the voltage magnitude at nodes, thereby suppressing voltage fluctuations caused by harmonics. For instance, at the end of long-distance transmission lines, the energy storage system discharges when the harmonic distortion rate is high to elevate the voltage reference value, reducing the relative proportion of harmonic voltage and indirectly optimizing the comprehensive voltage and harmonic indices in the objective function. This relationship is realized by embedding the sensitivity matrix of energy storage power with respect to node voltage, ensuring that scheduling decisions directly respond to voltage/harmonic conditions. Additionally, the proposed method sets harmonic network losses and voltage fluctuation suppression in the distribution network as optimization objectives, enabling the rational configuration of the quantity and capacity of active power filters. The model is solved using an SJA. This optimized configuration approach meets harmonic mitigation requirements while avoiding excessive equipment investment, effectively controlling costs and minimizing total investment. In contrast, Methods A and B lack such a comprehensive and systematic optimization configuration process, resulting in inferior mitigation effects and higher cost investments compared to the proposed method in this paper. This method achieves precise tracing of harmonic sources through the localization of dominant nodes in each partition and the use of comprehensive voltage sensitivity indicators. Its core optimization model encompasses capacity allocation based on an improved SJA, which has demonstrated high efficiency during the offline planning stage. If integrated with the edge computing architecture of smart grids, deploying the optimization algorithm in regional controllers and utilizing their real-time monitoring data to dynamically update sensitivity indicators can shorten the computational cycle. Additionally, the rapid harmonic current compensation mechanism of VDAPF ensures a response time of less than 10 ms, while the dynamic reactive power regulation capability of SVG also enables second-level responses, meeting the requirements for equipment response speed in real-time control.

5.3. Comparative Analysis with Other Methods

Compared with the conventional Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), the improved SJA significantly enhances population diversity and global search capabilities by introducing a good point set initialization strategy and a cosine similarity update mechanism. Traditional GA is prone to getting trapped in local optima and exhibits slow convergence, while PSO suffers from insufficient exploration in the later stages due to fixed inertia weights. In contrast, the improved SJA maintains extensive search in the early stages, accelerates local optimization in the middle and late stages through dynamic adjustment of convergence factors and an adaptive mutation strategy, and simultaneously identifies and reorganizes highly similar individuals using cosine similarity to avoid premature convergence. Experiments demonstrate that it can find superior solutions with fewer iterations in complex multi-objective optimization problems. The comparison results of the performance of different algorithms on test systems of varying scales are shown in

Table 3. Performance Comparison of Algorithms on Different Test Systems.

Test System	Method	Calculation Time (s)	Voltage Fluctuation Rate (%)	Total Investment Cost ($)	Capacity of Harmonic Mitigation Equipment (A)
IEEE-33	GA	125	5.7	2675.4	42.0
	PSO	98	4.1	2588.3	41.2
	SJA	82	3.4	2456.3	37.8
IEEE-57	GA	312	2.14	4501.3	58.7
	PSO	256	1.91	4458.2	53.4
	SJA	198	1.58	4257.6	49.2
IEEE-69	GA	587	2.43	7413.9	67.3
	PSO	472	2.17	7562.4	77.0
	SJA	365	1.82	7251.4	63.8
IEEE-118	GA	1240	2.76	12,841.6	78.6
	PSO	987	2.49	12,451.7	81.3
	SJA	742	2.01	11,045.6	71.4

below.

Observing the table above, it can be seen that as the system scale expands, the calculation time of all algorithms increases significantly, but the SJA exhibits the smallest growth rate. This is attributed to its dynamic convergence factor and cosine similarity screening mechanism, which effectively reduce the number of invalid iterations. In contrast, GA and PSO experience a rapid decline in search efficiency with increasing dimensions due to their fixed parameter settings. The SJA achieves the lowest voltage fluctuation across all systems because it precisely suppresses harmonic propagation paths through the localization of dominant nodes in each partition and the coordinated optimization of equipment capacity. In contrast, GA and PSO fail to fully coordinate interactions between regions due to their dispersed equipment configurations. The cost advantage of the SJA stems from its multi-objective normalization optimization strategy, which avoids over-configuration by balancing harmonic losses, voltage deviations, and equipment investment. On the other hand, GA and PSO result in either redundant or insufficient equipment capacity due to unreasonable target weight allocation. The SJA plans for the smallest equipment capacity as it prioritizes the deployment of governance equipment at critical nodes through harmonic sensitivity ranking, achieving excellent governance results. In contrast, GA and PSO suffer from low equipment utilization due to their uniform configuration strategy.

The simulation results of the proposed method versus traditional point-to-point harmonic suppression methods are compared in

Table 4. Performance Comparison with Point-to-Point Mitigation Methods.

Method	Traditional Point-to-Point Harmonic Mitigation Methods		The Proposed Method
Test System	IEEE-33	IEEE-118	IEEE-33	IEEE-118
Voltage Fluctuation Rate (%)	5.4	3.7	3.4	2.0
THD (%)	5.7	6.2	3.1	4.1
Total Investment Cost ($)	2862.4	13,847.9	2456.3	11,045.6
Equipment Utilization Rate (%)	68.3	62.1	89.5	81.7

below.

Observing Table 4 above, it can be found that the proposed method concentrates harmonic mitigation resources in key regions through partition-based dominant node localization and comprehensive voltage sensitivity indices, significantly reducing system-wide voltage fluctuations and harmonic distortion. For example, in the IEEE-33 system, the voltage fluctuation rate decreased from 5.4% to 3.4%, and the THD dropped from 5.7% to 3.1%. In contrast, traditional point-to-point methods suffer from ineffective coordination of inter-regional harmonic propagation due to decentralized equipment deployment, limiting their governance effectiveness. On the other hand, the proposed method balances harmonic losses, voltage deviations, and equipment investment through multi-objective normalization optimization, avoiding over-provisioning. In the IEEE-118 system, traditional methods require widespread deployment of governance devices across 118 nodes, incurring costs as high as 13,847.9$, whereas the proposed method reduces costs to 11,045.6$ (a 20.2% reduction) by precisely targeting 32 dominant nodes. Notably, traditional methods exhibit low equipment utilization due to scattered installations, leaving some nodes with idle governance capacity. The proposed method enhances equipment efficiency to 89.5% utilization by ranking harmonic sensitivity and optimizing capacity allocation, significantly improving return on investment. Finally, the advantages of the proposed method become even more pronounced in larger-scale IEEE-118 systems. Traditional methods struggle to accurately locate harmonic sources due to exponentially increasing computational complexity, worsening voltage fluctuation rates and THD. In contrast, the proposed method maintains efficient optimization through the parallel search capability of the improved SJA, achieving superior governance performance compared to traditional approaches.

The source-tracing-based harmonic mitigation and optimal control strategy for distribution networks proposed in this paper exhibits remarkable scalability, enabling its extension to complex multi-feeder systems and practical regional power grids. By introducing a hierarchical and zonal approach, it addresses the computational complexity issues inherent in large-scale networks. The strategy can enhance its dynamic response capabilities by integrating digital twin technology to create a real-time simulation environment, simulating the coupled impacts of dynamic events—such as distributed generation fluctuations and fault ride-through scenarios—on harmonic mitigation. From a data perspective, it can fuse multi-source heterogeneous information, integrating PMU measurement data, meteorological information, and user behavior patterns to improve the accuracy of dominant harmonic source localization. At the algorithmic level, it can incorporate hybrid intelligent optimization methods, combining an improved Spider Jump algorithm with deep reinforcement learning to achieve dynamic self-optimization of mitigation device capacities and locations, ultimately forming a comprehensive harmonic mitigation technology system that covers all scenarios, including planning, operation, and emergency response.

6. Conclusions

Under the circumstance of a high proportion of distributed renewable energy sources being integrated into the distribution network, harmonic pollution and voltage deviation exhibit characteristics of network-wide and decentralized distribution, making it difficult for traditional point-to-point governance methods to achieve coordinated governance. The source-tracing-oriented harmonic mitigation and optimized control strategy for distribution networks proposed in this paper effectively addresses this challenge. By precisely locating regional dominant harmonic source mitigation nodes based on harmonic and reactive power sensitivity indices, as well as comprehensive voltage sensitivity indices, it becomes possible to trace harmonics to their source, laying a foundation for subsequent governance efforts. With the optimization objectives of minimizing harmonic network losses and suppressing voltage fluctuations in the distribution network, the quantities and capacities of voltage-detection-type active power filters and SVGs are reasonably configured. By employing an improved SJA to solve the model, effective control over harmonics and voltage deviation is achieved. Verification through an improved IEEE-33 standard node test system demonstrates that the method proposed in this paper is practical and highly effective, significantly enhancing the performance of the distribution network in terms of harmonic mitigation and voltage control. The method proposed in this study is capable of decreasing the voltage fluctuation rate and THD by 2.3% and 2.6% correspondingly. Moreover, it attains an equipment utilization efficiency close to 90% while keeping the investment cost at a minimum. Although the current study proposes a source-tracing-based harmonic mitigation and optimal control strategy for distribution networks, it still has the following limitations: the cost parameters are highly assumption-dependent, the sensitivity parameters rely solely on fixed empirical values without a dynamic adjustment mechanism, and the operating conditions are treated as static. To address these limitations, subsequent research could focus on the following directions: designing a dynamic parameter adaptive mechanism by introducing reinforcement learning or online optimization algorithms to enable real-time parameter adjustment according to operating conditions; conducting dynamic event simulations by injecting disturbances such as sudden drops in photovoltaic output and load switching into a digital twin platform to further validate the algorithm’s real-time responsiveness.