In modern distribution networks, the widespread distribution of harmonic pollution sources leads to widespread deterioration of power quality across the entire network. This makes the collaborative mitigation of harmonics by multiple converters a research hotspot. However, existing methods face challenges such as difficulty in accurately sensing harmonic phasors, high computational complexity, stringent real-time control requirements, and challenges related to control stability and current limits, making it difficult to achieve ideal mitigation effects in practice. To address these issues, we propose a comprehensive harmonic mitigation method for distribution networks based on the local control of solar inverters. The proposed control combines two local harmonic control methods for converters: local harmonic current compensation control and harmonic virtual conductance control. The control objective is to minimize the global voltage harmonic distortion rate. The method encompasses three steps: configuration of mitigation schemes, centralized solving of control commands, and real-time correction of harmonic current commands. This approach maximizes the utilization of the remaining capacity of solar inverters for harmonic mitigation. Compared to existing methods, the proposed control achieves better mitigation effects and can comprehensively improve the power quality of the distribution network when grid operating conditions change.
1. Introduction and Overview of Converter Harmonic Mitigation Methods
The extensive integration of distributed generators and power electronic devices has led to a wide distribution of power quality pollution sources. This results in local power quality issues being a product of multi-source harmonics, which cannot be resolved by simply relying on traditional local compensation of harmonic sources. Consequently, methods for comprehensive power quality management across the entire substation area using multiple converters have increasingly attracted scholarly attention. Existing harmonic mitigation schemes mostly rely on high-precision monitoring devices to collect real-time harmonic voltage and current phasors from each node. Then, control algorithms are employed to enable each participating converter to adjust its output current based on global information, working collaboratively to achieve optimal mitigation effects.
However, these existing schemes heavily rely on real-time acquisition of harmonic voltage and current phases. The phase error of the fundamental voltage is amplified by a factor of h in the h-th harmonic. Furthermore, the time synchronization system is often subject to various interferences, with errors potentially reaching 2.3 ms. Additionally, determining the harmonic current command for each converter requires global optimization calculations within a short period. These factors make it difficult for methods that rely on real-time adjustment of the output harmonics of multiple converters to achieve their theoretical performance. To alleviate the burden of global communication and optimization, some studies employ methods like zonal management, online impedance estimation, and collaborative distributed optimization to enhance the feasibility of control strategies. However, when multiple converters are involved simultaneously, and when the remaining capacity of the converters changes, online impedance estimation becomes challenging. Moreover, existing methods often contain linearization assumptions and are difficult to avoid the interference of phase errors. A strategy combining centralized optimization with local control is an effective solution to the problems of inaccurate time synchronization of multi-node harmonic data and the lack of real-time processing capability of centralized/distributed controllers.
For centralized optimization combined with local control using harmonic virtual conductance, although from the perspective of harmonic power flow, a larger harmonic conductance implies a more significant harmonic mitigation effect, extracting harmonic voltages becomes inaccurate when the node harmonic voltage is low. Moreover, when multiple converters adopt large harmonic conductance, they may face stability issues. Furthermore, unlike dedicated power quality equipment such as active power filters (APFs), using distributed generators like solar inverters for harmonic mitigation means that the real-time output of a solar inverter affects its mitigation capacity. Load fluctuations also make it difficult for the virtual conductance obtained from centralized optimization to adapt in real-time, leading to problems such as current exceeding limits, excessively low node harmonic voltages, or underutilization of remaining capacity during real-time control. These issues are rarely mentioned in other studies.
To address the limitations of existing controls, we propose a comprehensive harmonic mitigation strategy for distribution networks based on the local control of solar inverters. This strategy combines centralized optimization with two local harmonic control methods. First, a mitigation scheme is configured based on historical operating data of the distribution network through simulation. At the centralized optimization level, the results of harmonic state estimation obtained every 3 minutes are used to solve for the control commands of each solar inverter and transmit them to the participating solar inverters. At the real-time control level, the solar inverters performing local harmonic control generate their output harmonic current commands based on the received control commands and the actual operating conditions. The advantages compared to existing schemes are:
1) It only requires the existing 3-minute-interval harmonic state estimation results and transmits control commands through one-way communication. Solar inverters achieve comprehensive mitigation based on local harmonic control from two aspects: local cancellation of harmonic current and improvement of grid harmonic admittance distribution. This effectively avoids communication delays, computational bottlenecks, and the challenges of coordinating multiple converters.
2) The proposed control, while maintaining the maximum power output of the solar inverter, allocates harmonic mitigation commands based on the remaining capacity of different solar inverters, achieving coordinated optimization of new energy consumption and distribution network power quality.
3) It considers the dynamic characteristics of harmonic virtual conductance control and designs stability constraints to avoid system instability risks.
4) By incorporating a real-time mitigation current adjustment strategy based on the actual operating conditions of the solar inverter, it ensures maximum utilization of remaining capacity while guaranteeing safe operation of the equipment when the grid fluctuates.
2. Proposed Harmonic Collaborative Mitigation Method
2.1 Configuration of Solar Inverter Harmonic Mitigation Scheme
Before initiating harmonic mitigation, it is necessary to design local harmonic control schemes for different solar inverters and equip them with high-precision voltage and current sensors to meet the mitigation requirements. Specifically, based on the harmonic mitigation effect, each solar inverter is retrofitted using one of two methods: harmonic current local compensation control or harmonic virtual conductance control (using one method at a time is practically necessary). Compared to the approach in existing literature where all participating converters use harmonic virtual conductance control, combining the two local control schemes not only leverages their respective advantages but also helps avoid system stability issues. To determine the configuration scheme for different solar inverters in the distribution network, it is necessary to use historical operating data of the distribution network for comprehensive mitigation simulation calculations and select the scheme with the best average effect. Given the constant changes in power system operating states, clustering the operating states to extract representative typical scenarios is done to reduce computational complexity. The objective function for K-means clustering is to minimize the within-cluster sum of squares distance. The Calinski-Harabasz index is used to select the optimal number of clusters (K).
For modeling harmonic sources in the distribution network, the Norton equivalent circuit is used, as shown in Table 1.
| Parameter | Symbol | Description |
|---|---|---|
| Harmonic Impedance | $z_{i, h}$ | Node i impedance for harmonic h |
| Harmonic Current Source | $\dot{i}_{i, h}$ | Node i current source for harmonic h |
| Node Voltage | $\dot{u}_{i, h}$ | Node i voltage for harmonic h |
| Load Current | $\dot{i}_{Li, h}$ | Node i load current for harmonic h |
The parameters of the Norton circuit can be calculated using the fluctuation method.
2.2 Minute-Level Timescale: Centralized Optimization of Solar Inverter Control Commands
The PQMS collects harmonic voltage and current phasors. Using the non-synchronized data averaged over 3 minutes, harmonic state estimation is performed to obtain the magnitudes and angles of the harmonic voltages and currents. Based on the results of this 3-minute harmonic state estimation, the centralized controller performs an optimization to solve for the control commands, specifically the current compensation coefficient $k_{i, h}$ or the harmonic conductance $g_{i, h}$, for each solar inverter. These commands are then transmitted via one-way communication to the respective solar inverters.
The optimization objective is to minimize the weighted sum of the total harmonic distortion (THD) of node voltages, as shown in Equation (1).
$$ F_{THD} = \min \sum_{i=1}^{n} c_i f_{THD, i} \tag{1} $$
Here, $c_i$ is the weight coefficient for node i, and $f_{THD, i}$ is the voltage total harmonic distortion at node i. The THD for node i can be expressed by Equation (2), where $u_{i,1}$ is the fundamental voltage magnitude.
$$ f_{THD, i} = \frac{\sqrt{\sum_{h=5,7,\ldots}^{6k\pm1} u_{i, h}^2}}{u_{i, 1}} \tag{2} $$
The constraints for this optimization problem include:
a) Harmonic Power Flow Constraints: These are the Kirchhoff’s laws governing the harmonic domain, expressed as the node voltage equation. For the h-th harmonic, the power flow equation is given in Equation (3), where $\mathbf{I}_h$ is the nodal injected current vector, $\mathbf{U}_h$ is the nodal voltage vector, and $\mathbf{Y}_h$ is the nodal admittance matrix. The specific form considering the two control methods is shown in Equation (4).
$$ \mathbf{I}_h = \mathbf{Y}_h \mathbf{U}_h \tag{3} $$
$$ \begin{bmatrix} \vdots \\ (1-k_{j,h})\dot{i}_{j,h} \\ \vdots \end{bmatrix} = \begin{bmatrix} y_{11,h}+g_{1,h} & \cdots & y_{1n,h} \\ \vdots & \ddots & \vdots \\ y_{n1,h} & \cdots & y_{nn,h} \end{bmatrix} \begin{bmatrix} \dot{u}_{1,h} \\ \vdots \\ \dot{u}_{n,h} \end{bmatrix} \tag{4} $$
b) Solar Inverter Harmonic Compensation Capacity Constraints: The RMS value of the current output by the solar inverter must not exceed its maximum limit, as shown in Equation (5). For a solar inverter using virtual conductance control, the injected harmonic current magnitude is given by Equation (6). For a solar inverter using current compensation control, it is given by Equation (7).
$$ i_{PVi, h}^2 + i_{id}^2 + i_{iq}^2 \le i_{ilim}^2 \tag{5} $$
$$ i_{PVi, h} = \sqrt{\sum_{h=5,7,\ldots}^{6k\pm1} (g_{i, h} u_{i, h})^2} \tag{6} $$
$$ i_{PVi, h} = \sqrt{\sum_{h=5,7,\ldots}^{6k\pm1} (k_{i, h} i_{i, h})^2} \tag{7} $$
c) Virtual Conductance Control Stability Constraints: To ensure system stability and accuracy of measurement, a minimum allowable voltage $u_{low}$ is set for the harmonic voltage after mitigation. The constraint in Equation (8) prevents the virtual conductance from becoming excessively large.
$$ (u_{i, h} – u_{low}) g_{i, h} \ge 0 \tag{8} $$
This optimization problem is a non-convex quadratic program and can be solved using a solver like Gurobi by transforming it into a mixed-integer programming problem.
2.3 Real-Time Control: Adjusting Mitigation Current Command Based on Solar Inverter Operating Conditions
Based on the received $g_{i, h}$ or $k_{i, h}$ from the centralized solver, each participating solar inverter generates an initial harmonic mitigation current reference $\dot{i}_{PV, h}[0]$. It then modifies this reference based on its actual operating conditions and local real-time measurements to produce the final reference $\dot{i}_{PVi, h}$. The algorithm for real-time adjustment is described in Table 2.
| Control Type | Condition | Action |
|---|---|---|
| Virtual Conductance Control $ (i_{PVi, h} = m_h g_{i, h} u_{i, h})$ | All harmonics $\ge u_{low}$ | $m_h = i_{ilim} / \text{RMS of all } i_{PVi, h}[0] \text{ and no overcurrent}$ |
| Some harmonics $< u_{low}$ | Adjust $m_h$ for low harmonics via integral control until $u_{i,h} \ge u_{low}$ or $g_{i,h}=0$. Assign remaining capacity to other harmonics. | |
| All harmonics $< u_{low}$ | Adjust all $m_h$ equally until no overcurrent, or scale down equally if overcurrent occurs. | |
| Current Compensation Control $ (i_{PVi, h} = k_{i, h} i_{i, h})$ | RMS of harmonic currents exceeds limit | Scale down all $k_{i, h}$ proportionally to meet the limit. |
| RMS of harmonic currents is within the limit | Scale up all $k_{i, h}$ proportionally until the limit is reached or $k_{i, h}=1$ for any harmonic. |
Finally, the resulting $\dot{i}_{PVi, h}$ is added to the fundamental active and reactive current references. The total current reference is tracked by a multi-PR controller, enabling the solar inverter to simultaneously perform its primary power generation function and provide harmonic mitigation.
3. Simulation and Experimental Verification
3.1 Distribution Network Simulation Results
We built an IEEE 13-node distribution network in MATLAB/Simulink. The network includes three solar inverters, linear and non-linear loads. The non-linear loads are three-phase uncontrolled rectifiers injecting significant 5th, 7th, 11th, 13th, 17th, and 19th harmonics. Based on typical scenarios, the mitigation scheme was configured as follows: the solar inverter at node 14 uses virtual conductance control, while those at nodes 3 and 12 use harmonic current compensation control.
Table 3 shows the initial THD levels and the results after applying different mitigation methods. The optimization objective was to minimize the sum of THDs for all nodes. The results in Table 3 demonstrate that our proposed method reduces the average node THD to 3.863%, which is lower than 4.059% achieved by the existing method and 4.766% by point-to-point mitigation. All nodes meet the standard of THD < 5% after adopting our method.
| Mitigation Method | Before Mitigation | Point-to-Point | Existing Method | Proposed Method |
|---|---|---|---|---|
| Average Node THD (%) | 6.945 | 4.766 | 4.059 | 3.863 |
| Nodes with THD > 5% | Several | Several | Few | None |
The effectiveness of the real-time current adjustment capability of the proposed method was also validated. When the grid conditions changed, such as a reduction in the available capacity of a solar inverter, the control algorithm successfully limited the harmonic currents to prevent overcurrent while maximizing the utilization of the remaining capacity for mitigation.
3.2 Physical Experiment Results
A physical experiment was conducted on a laboratory-scale microgrid. The system consisted of an ideal voltage source, two solar inverters, two harmonic sources (uncontrolled rectifier loads), and network impedances. Solar inverter 1 was configured to use virtual conductance control, while Solar inverter 2 used harmonic current compensation control, as determined by the centralized optimization. The experimental results are summarized in Table 4.
| Node | Condition | THD (%) Before | THD (%) with Existing Method | THD (%) with Proposed Method |
|---|---|---|---|---|
| Node 1 | Initial | 3.991 | 1.804 | 1.556 |
| Node 2 | Initial | 4.007 | 1.517 | 1.163 |
| Node 3 | Initial | 4.507 | 2.121 | 1.994 |
| Average | 4.168 | 1.814 | 1.571 | |
| Node 3 | After 10% Load Increase | – | 2.460 | 2.313 |
The results in Table 4 clearly show that our proposed method outperforms the existing method in reducing the THD at all three nodes. The average THD after mitigation using our method is 1.571%, compared to 1.814% for the existing method. When the load at node 3 was increased by 10%, the solar inverters successfully adjusted their output to prevent overcurrent while maintaining a superior mitigation effect (2.313% THD) compared to the existing method (2.460% THD). The output currents of the solar inverters were observed to contain the required harmonic components superimposed on the fundamental current, confirming the effective implementation of the local control strategy.
4. Conclusion
This paper presents a comprehensive harmonic mitigation strategy for distribution networks based on the local control of solar inverters. The strategy combines a 3-minute centralized optimization with real-time local control. The centralized optimization determines the optimal harmonic current compensation coefficients or harmonic virtual conductance values for each solar inverter, respecting power flow, capacity, and stability constraints. The local controller in each solar inverter** then uses these parameters to generate its output current, while also implementing a real-time adjustment algorithm to prevent overcurrent and maximize the utilization of the **solar inverter‘s remaining capacity for mitigation under fluctuating grid conditions.
Both simulation and physical experimental results validate the effectiveness of the proposed method. Compared to existing comprehensive mitigation methods that only use virtual conductance, our method, which combines both local harmonic current compensation and virtual conductance control, achieves a better reduction in the overall voltage THD across the distribution network. The real-time adjustment algorithm ensures robust performance under changing operating conditions, such as variations in solar power output and load levels. The use of a 3-minute optimization cycle and one-way communication reduces the reliance on high-bandwidth, real-time communication and complex synchronous phasor measurements, making the proposed scheme practically feasible for existing distribution networks with solar inverters.