With the rapid integration of renewable energy sources into power grids, distributed generation systems, particularly those utilizing solar inverters, have become increasingly prevalent. However, the proliferation of nonlinear loads in distribution networks has led to severe harmonic pollution, compromising power quality. Traditional harmonic mitigation devices, such as passive and active filters, entail significant investment and maintenance costs. In contrast, solar inverters, which often operate below their full capacity due to the intermittent nature of solar power, present an economical opportunity for providing ancillary services like harmonic compensation. Yet, a major practical challenge arises from the absence of grid-side current transformers in many installations, due to physical constraints or the limitations of conventional current sensors in handling harmonic frequencies. This paper proposes a novel harmonic compensation method that leverages solar inverters without requiring grid-side current transformers. By injecting specific harmonic currents to estimate grid impedance and subsequently deriving grid-side harmonic currents from voltage measurements, this approach enables effective harmonic suppression. The method is validated through simulation studies, demonstrating its feasibility in real-world applications.
The core idea of this method revolves around using the solar inverter as a multifunctional device that not only feeds solar power into the grid but also compensates for harmonic currents. In typical setups, solar inverters lack direct access to grid-side or load-side current measurements, making traditional harmonic detection techniques impractical. Our solution circumvents this by estimating the grid impedance through controlled harmonic injection, thereby eliminating the need for additional current sensors. This not only reduces hardware costs but also enhances the utilization of solar inverter capacity. The following sections detail the system topology, harmonic current estimation design, control strategy, and simulation results, all from the perspective of our research and implementation.
System Topology and Model
The proposed system for harmonic compensation using a solar inverter without a grid-side current transformer is illustrated below. In this configuration, the solar inverter is connected to the grid through an LCL filter, while nonlinear loads are attached at the point of common coupling (PCC). The grid is modeled as an ideal voltage source in series with an impedance, representing the Thevenin equivalent of the distribution network. The solar inverter serves dual purposes: it injects active power from photovoltaic panels and generates compensatory harmonic currents to cancel out those produced by nonlinear loads. Key to this approach is the estimation of grid impedance, which is achieved by deliberately injecting non-characteristic harmonic currents into the grid and analyzing the resulting voltage distortions.
The system operates in two phases: first, during an initial calibration period, the solar inverter injects a low-magnitude, non-characteristic frequency current (e.g., 75 Hz) to estimate the grid impedance. Second, in the compensation phase, the estimated impedance is used to compute grid-side harmonic currents from measured PCC voltages, and these currents are then used as references for the inverter’s current control loop. This closed-loop control enables the solar inverter to suppress harmonics while maintaining its primary function of power generation. The entire process is implemented digitally, relying on real-time signal processing techniques such as discrete Fourier transform (DFT) for harmonic extraction.
Design of Harmonic Current Estimation Method
The harmonic current estimation comprises two main steps: grid impedance estimation and grid-side harmonic current calculation. Both steps are critical for ensuring accurate compensation without direct current measurements.
Impedance Estimation Principle
To estimate grid impedance, the solar inverter injects a harmonic current at a selected frequency, typically a non-characteristic interharmonic like 75 Hz. This frequency is chosen because it is less likely to be present in the grid background, minimizing interference. The injection is performed by superimposing a sinusoidal component at the desired frequency onto the inverter’s current reference. The resulting voltage at the PCC is sampled, and the harmonic components of both the injected current and the PCC voltage are extracted using a sliding-window iterative DFT algorithm. This algorithm allows for real-time computation of magnitude and phase with minimal latency, essential for dynamic grid conditions.
The equivalent circuit for impedance estimation can be represented as follows: the grid is modeled as a voltage source $U_s$ in series with an impedance $Z_{ih} = r_g + j\omega l_g$, where $r_g$ is the resistive part and $l_g$ is the inductive part. The solar inverter is treated as a controlled current source injecting $I_{g-ih}$, and the nonlinear load is approximated as a constant harmonic current source $i_h$. By neglecting the load impedance due to its high magnitude relative to grid impedance, the relationship between the injected current and the PCC voltage harmonic component $U_{g-ih}$ is given by Ohm’s law. The impedance is calculated using the real and imaginary parts of the extracted harmonics:
Let $u_{reg\_ih}$ and $u_{meg\_ih}$ be the real and imaginary parts of $U_{g-ih}$, and $i_{reg\_ih}$ and $i_{meg\_ih}$ be the real and imaginary parts of $I_{g-ih}$. Then:
$$ r_g = \frac{u_{reg\_ih} \times i_{reg\_ih} + u_{meg\_ih} \times i_{meg\_ih}}{i_{reg\_ih}^2 + i_{meg\_ih}^2} $$
$$ \omega l_g = \frac{u_{meg\_ih} \times i_{reg\_ih} – u_{reg\_ih} \times i_{meg\_ih}}{i_{reg\_ih}^2 + i_{meg\_ih}^2} $$
To improve accuracy, multiple injections at different phases are performed, and the results are averaged to mitigate errors from grid disturbances. This impedance estimation module is integrated into the solar inverter’s control system, enabling periodic updates to adapt to changing grid conditions.
Grid-Side Harmonic Current Estimation Principle
Once the grid impedance is estimated, the grid-side harmonic currents can be derived from the PCC voltage harmonics. For each harmonic frequency of interest (e.g., 3rd, 5th, 7th up to 25th), the PCC voltage is continuously sampled, and its harmonic components are extracted using the same DFT method. The estimated harmonic current for a specific frequency is then computed based on the estimated impedance values. For a harmonic voltage component with real part $u_{re}$ and imaginary part $u_{me}$ at angular frequency $\omega_h = k\omega_0$ (where $k$ is the harmonic order and $\omega_0$ is the fundamental frequency), the corresponding harmonic current components are:
$$ i_{re} = \frac{u_{re} \times r_g + u_{me} \times \omega_h l_g}{r_g^2 + (\omega_h l_g)^2} $$
$$ i_{me} = \frac{u_{me} \times r_g – u_{re} \times \omega_h l_g}{r_g^2 + (\omega_h l_g)^2} $$
The instantaneous harmonic current waveform for each order is reconstructed by combining these components with sine and cosine basis signals. The total estimated grid-side harmonic current $I_{sh}$ is the sum of all targeted harmonics:
$$ I_{sh} = \sum_{k=3}^{n} I_{an}(k) $$
where $I_{an}(k)$ is the estimated current for the $k$-th harmonic. This estimated current serves as the reference for the solar inverter’s compensation control, effectively replacing the need for direct measurement from a grid-side current transformer.
Harmonic Compensation Control Strategy
The control strategy for the solar inverter integrates both power generation and harmonic compensation. A repetitive control scheme is employed due to its high accuracy in tracking periodic signals like harmonics. The block diagram of the control system includes a current loop where the estimated grid-side harmonic current $i_{gsh}$ is added to the inverter’s output harmonic current $i_{out_h}$ to form the compensation reference $i_{ref}$. This reference is compared with the actual inverter output current $i_{out}$, and the error is processed through a repetitive controller to generate the modulation signal.
The repetitive controller, as implemented in our solar inverter system, consists of a delay line for period matching, a compensator for stability, and feedback gains for dynamic response. The transfer function can be expressed as:
$$ G_{rc}(z) = \frac{K_s z^{-N}}{1 – K_f z^{-N}} + K_r $$
where $K_s$ is the repetitive gain, $K_f$ is the forget factor (close to 1), $K_r$ is the direct feedback gain, and $N$ is the number of samples per fundamental period. This structure ensures zero steady-state error for harmonic frequencies while maintaining robustness against grid variations. The output of the repetitive controller is combined with the grid voltage feedforward to produce the pulse-width modulation (PWM) signals for the inverter switches, enabling simultaneous injection of active power and harmonic currents.
Simulation Results and Analysis
To validate the proposed method, a simulation model was developed using MATLAB/Simulink, based on the parameters listed in Table 1. The solar inverter system was tested under scenarios with nonlinear loads generating significant harmonics. The impedance estimation module was activated initially, followed by the harmonic compensation phase.
| Parameter | Value | Description |
|---|---|---|
| Grid voltage ($u_s$) | 220 V | RMS phase voltage |
| Grid resistance ($r_g$) | 0.25 Ω | Estimated resistive part |
| Grid inductance ($l_g$) | 0.5 mH | Estimated inductive part |
| Repetitive gain ($K_s$) | 1.35 | Controller parameter |
| Forget factor ($K_f$) | 0.9 | Controller parameter |
| Direct feedback gain ($K_r$) | 1.8 | Controller parameter |
| Injection frequency | 75 Hz | For impedance estimation |
| Harmonic orders compensated | 3,5,7,9,11,13,15,17,19,23,25 | Targeted harmonics |
The impedance estimation results, as shown in Figure 8 (though not referenced by number), indicated stable values after the injection period. The estimated resistance $r_g$ converged to approximately 0.251 Ω with minimal oscillation, while the inductance $l_g$ settled around 0.501 mH. These values closely matched the actual grid parameters, demonstrating the accuracy of our estimation technique within the solar inverter framework.
During harmonic compensation, the solar inverter successfully reduced the grid-side current distortion. Before compensation, the total harmonic distortion (THD) of the grid current was measured at 61.41%, dominated by lower-order harmonics. After activating the compensation at 0.15 seconds in the simulation, the THD dropped to 6.67%, as evidenced by FFT analysis. The waveform of the grid current became nearly sinusoidal, confirming the effectiveness of the method. The estimated harmonic currents tracked the actual harmonics closely, even during transients, ensuring reliable compensation performance.
A key observation from the simulation is that the solar inverter maintained its primary function of power delivery throughout the process. The dual-control approach allowed seamless switching between impedance estimation and compensation modes without disrupting the active power flow. This highlights the practicality of using solar inverters for ancillary services in real-world grids.
Discussion and Implications
The proposed method offers a cost-effective solution for harmonic mitigation in distribution networks with high penetration of solar inverters. By eliminating the need for grid-side current transformers, it reduces installation complexity and hardware costs, making it especially suitable for retrofitting existing solar systems. The reliance on impedance estimation also makes the system adaptive to grid changes, such as variations in network topology or load conditions.
However, challenges remain in improving the precision of impedance estimation and harmonic current calculation. Factors like background noise, grid voltage fluctuations, and the presence of other distributed generators can affect accuracy. Future work could explore advanced signal processing techniques, such as adaptive filtering or machine learning algorithms, to enhance robustness. Additionally, extending the method to three-phase solar inverter systems would broaden its applicability in industrial settings.
From an engineering perspective, this approach maximizes the utilization of solar inverter capacity, contributing to grid stability and power quality. As solar power continues to expand globally, integrating such multifunctional capabilities into inverters will become increasingly important for smart grid development.
Conclusion
In this paper, we have presented a harmonic compensation method that leverages solar inverters without requiring grid-side current transformers. Through impedance estimation via harmonic injection and subsequent derivation of grid-side harmonic currents, the solar inverter can effectively suppress harmonics while performing its primary role of power generation. Simulation results confirm the feasibility and performance of the method, showing significant reduction in current distortion. This work provides a novel solution for enhancing power quality in distributed generation systems, paving the way for more efficient and economical use of solar inverter resources. Further research will focus on optimizing estimation algorithms and validating the approach in practical installations with varying grid conditions.
The integration of harmonic compensation into solar inverters represents a step toward multifunctional grid-supportive devices, aligning with the goals of modern power systems for sustainability and reliability. As technology advances, we anticipate wider adoption of such techniques, driven by the growing need for clean energy and high-quality power supply.