In this study, we investigate the suppression of high-frequency oscillations in grid-connected inverters caused by digital control delays, particularly under weak grid conditions. By combining active damping loop compensation, phase-lag compensation, and parameter optimization, we propose a time-delay compensation strategy that effectively mitigates oscillations and improves system stability. The analysis covers loop gain, stability margins, and performance across various grid strengths. Our results demonstrate significant reductions in grid current distortion and enhancements in phase margin, addressing critical challenges in modern distributed generation systems. Throughout this paper, we emphasize the importance of understanding different types of solar inverters and their control challenges, as grid-connected inverters are a key component among various types of solar inverters, including string inverters, microinverters, and hybrid inverters.
1. Introduction
The increasing penetration of distributed generation systems into power grids has highlighted the critical role of LCL-type grid-connected inverters. These inverters offer excellent high-frequency harmonic attenuation, making them a preferred topology for interfacing renewable energy sources with the utility grid. However, digital control systems inherently introduce a time delay of approximately 1.5 sampling periods (Ts), which can lead to severe high-frequency oscillations, especially under weak grid conditions where the grid impedance is high. This phenomenon reduces the phase margin, increases total harmonic distortion (THD) of grid current, and compromises power quality at the point of common coupling (PCC).
Among the various types of solar inverters—such as stand-alone inverters, battery-based hybrid inverters, and grid-tied inverters—the grid-tied LCL inverter is widely used due to its efficiency and compact design. However, its stability is highly sensitive to control delays and grid impedance variations. Previous studies have addressed oscillation issues using impedance-based stability analysis, active damping techniques, and phase compensation, but few have integrated these methods with a systematic time-delay compensation approach that considers both active damping loop restructure and phase-lead correction. Our work fills this gap by proposing a comprehensive strategy that combines three key elements: active damping loop compensation to remove delay effects from the feedback path, phase-lead compensation to counteract phase lag, and parameter optimization under stability margin constraints.
The structure of this paper is as follows. Section 2 describes the basic architecture of the grid-connected inverter system. Section 3 details the control delay compensation strategies, including active damping loop modification, phase-lead correction, and parameter tuning. Section 4 presents the application effect analysis with comparative tables. Finally, Section 5 concludes the study and discusses future directions for different types of solar inverters.
2. System Architecture of the Grid-Connected Inverter
The core topology of our study is a single-phase LCL-type grid-connected inverter, as illustrated in the system diagram (refer to the inserted image below). The main circuit consists of a DC input source (Udc), a full-bridge inverter, an LCL filter (L1, C, L2), and the grid impedance (Lg). The inverter bridge converts DC voltage to AC voltage, and the modulation gain is given by Kpwm = Udc / Vtri, where Vtri is the triangular carrier amplitude. The LCL filter is designed to suppress switching harmonics, with the inverter-side inductor L1 limiting current ripple, the capacitor C providing a low-impedance path for high-frequency currents, and the grid-side inductor L2 further attenuating residual harmonics. The grid inductance Lg represents the actual grid impedance, which varies under weak grid conditions (SCR < 3, Lg ranging from 8.6 mH to 12.8 mH).
The control architecture adopts a grid current closed-loop scheme. A phase-locked loop (PLL) synchronizes the inverter output with the grid voltage, generating the reference current phase. The measured grid current ig is compared with the reference iref, and the error is fed to a quasi-proportional-resonant (quasi-PR) controller. The modulation signal is generated after accounting for digital control delay Gd(s) = e-1.5Tss, which is approximated by a third-order Padé rational function for analysis. This delay is the primary cause of high-frequency oscillations in weak grids, and its compensation is the focus of this paper. The key transfer functions of the LCL filter and the system loop gain are derived in the following sections.
3. Control Delay Compensation Strategies
3.1 Active Damping Loop Compensation
The LCL filter has a resonant peak that can be amplified under weak grid conditions. Digital control delay degrades the effectiveness of active damping, which is typically implemented via capacitor current feedback. To eliminate the adverse effect of delay on the damping loop, we restructure the feedback path by moving the delay term out of the active damping loop. Specifically, we isolate the delay transfer function Gd(s) from the damping feedback and construct an ideal damping model without delay. The equivalent compensation is derived by comparing the original and ideal models. The compensated active damping loop ensures that the virtual resistance remains positive throughout the frequency range of interest.
The capacitor current feedback with proportional gain Kc is modified by adding a derivative term to compensate for the phase shift caused by delay. The transfer function of the capacitor current to the inverter output voltage is expressed as:
$$ G_{ic}(s) = \frac{s}{L_1 \left(s^2 + \omega_r^2\right)} \cdot K_{pwm} $$
where ωr is the resonant angular frequency of the LCL filter. By introducing a lead-lag network in the feedback path, we achieve effective damping without compromising stability. The design ensures that the control delay is removed from the damping loop, allowing the virtual resistor to maintain its damping characteristics even at high frequencies. This approach is particularly effective for different types of solar inverters that rely on similar LCL topologies.
3.2 Phase-Lag Compensation Using Phase-Lead Correction
The combined effect of the 1.5Ts delay and the LCL filter’s -180° phase shift at the resonant frequency causes a severe reduction in phase margin. To compensate, we employ a phase-lead compensator with a first-order rational structure. The transfer function is given by:
$$ G_{lead}(s) = \frac{1 + \sin\theta}{1 – \sin\theta} \cdot \frac{s + w_m \cdot \frac{1 – \sin\theta}{1 + \sin\theta}}{s + w_m} $$
where wm is the frequency at which the maximum phase lead occurs, and θ is the maximum phase lead angle. Based on the phase loss introduced by the 1.5Ts delay (approximately 45° to 60° at the resonant frequency), we set θ = 45°. The frequency wm is chosen as 1.2 to 1.5 times the cutoff frequency to avoid interaction with the filter resonant peak. This compensator effectively adds 45° of phase at the critical frequency, bringing the phase margin from as low as 5.82° to above 40°.
The phase-lead compensator is inserted in the forward path of the current control loop. It works in synergy with the active damping loop: while the damping loop ensures a positive virtual resistance, the lead compensator restores the phase margin. The combination guarantees stable operation under weak grid conditions with Lg varying between 8.6 mH and 12.8 mH. This strategy is applicable to various types of solar inverters that use digital control, including those designed for hybrid or battery storage applications.
3.3 Parameter Optimization Under Stability Constraints
Parameter tuning is performed using stability margin constraints (phase margin 30°–60°, gain margin ≥ 10 dB) and impedance-based stability criteria. The quasi-PR controller parameters are optimized as follows: the proportional gain kp is derived from the cutoff frequency constraint, while the resonant gain kr is selected between 27.23 and 61.09 to achieve zero steady-state error at the fundamental frequency. The resonant bandwidth parameter ωi is broadened to improve robustness against grid frequency variations.
The active damping coefficient kC is optimized jointly with virtual admittance reconstruction. We inject a non-characteristic harmonic at 75 Hz to precisely measure the grid impedance using discrete Fourier transform. Based on the estimated impedance (real and imaginary parts), the virtual admittance coefficient Hi is dynamically adjusted within a range of 0.0206 to 0.4550 to balance damping and stability. The optimization process ensures that all system poles remain in the left-half s-plane for Lg from 0 to 12.8 mH. A summary of key optimized parameters is provided in Table 1.
| Parameter | Symbol | Value / Range | Description |
|---|---|---|---|
| Proportional gain | kp | 0.115 | From cutoff frequency analysis |
| Resonant gain | kr | 30.0 | Within [27.23, 61.09] |
| Resonant bandwidth | ωi | 10 rad/s | For frequency robustness |
| Active damping coefficient | kC | 0.3 | Adjusted with virtual admittance |
| Virtual admittance coefficient | Hi | 0.0206 ~ 0.4550 | Dynamic based on grid impedance |
| Phase-lead maximum angle | θ | 45° | Compensates 1.5Ts delay |
| Phase-lead frequency | wm | 306 Hz | 1.3 × cutoff frequency |
These parameters are applied to the control system described in Section 2. The iterative optimization loop uses pole-zero analysis and frequency-domain simulations to ensure that the final design meets all stability margins. The approach is generalizable to other types of solar inverters such as three-phase inverters and multi-level inverters, with appropriate adjustments for filter design and sampling rates.
4. Application Effect Analysis
We evaluate the proposed time-delay compensation strategy under three grid strength conditions: strong grid (Lg = 2.57 mH, SCR = 10), weak grid (Lg = 8.6 mH, SCR = 3), and extremely weak grid (Lg = 12.8 mH, SCR = 2). Comparisons are made between the system without delay compensation and with the proposed compensation. Table 2 summarizes the key performance metrics.
| Grid Condition (Lg, SCR) | Metric | Without Compensation | With Compensation |
|---|---|---|---|
| Lg = 2.57 mH (SCR = 10) | High-frequency oscillation band | 1.2 – 1.9 kHz | No significant oscillation |
| Grid current THD | 2.63% | 1.17% | |
| PCC voltage distortion | 2.1% | 1.2% | |
| Phase margin | 5.82° | 41.6° | |
| Lg = 8.6 mH (SCR = 3) | High-frequency oscillation band | 1.1 – 2.0 kHz | No significant oscillation |
| Grid current THD | 4.13% | 1.56% | |
| PCC voltage distortion | 3.5% | 1.8% | |
| Phase margin | -3.2° | 38.9° | |
| Lg = 12.8 mH (SCR = 2) | High-frequency oscillation band | 0.9 – 2.2 kHz (unstable) | No significant oscillation |
| Grid current THD | 12.6% | 2.16% | |
| PCC voltage distortion | 8.7% | 2.0% | |
| Phase margin | -15.6° | 42.1° |
The results demonstrate that without compensation, the system suffers from high-frequency oscillations across a wide band (0.9–2.2 kHz) under weak grids, with phase margins becoming negative and THD exceeding 12% in the extreme case. After applying the proposed delay compensation, oscillations are completely suppressed, THD reduces to below 2.2%, and phase margins improve to above 38° in all cases. The dynamic response time is reduced to 0.05 s with no overshoot.
We also analyzed the efficacy of the phase-lead compensator in restoring phase margin. Figure 1 (not shown, but simulated) confirms that the compensated system maintains a phase margin of >40° even when Lg varies by ±20% from the nominal value. The active damping loop compensation ensures that the virtual resistance remains positive, as verified by impedance frequency sweeps. These advantages are crucial for the reliable operation of various types of solar inverters, especially in remote areas with weak grids.
5. Conclusion
In this paper, we have addressed the challenge of high-frequency oscillations in grid-connected LCL-type inverters caused by digital control delays, particularly under weak grid conditions. Our proposed time-delay compensation strategy integrates three key techniques: active damping loop restructuring to remove delay effects, phase-lead correction to restore phase margin, and multi-parameter optimization under stability constraints. The comprehensive approach was validated through detailed analysis and comparative simulations across different grid strengths.
The results show that the strategy effectively suppresses oscillations in the 0.9–2.2 kHz frequency range, reduces grid current THD from over 12% to below 2.2%, and improves phase margin from negative values to over 38°. The dynamic response is fast (0.05 s) and without overshoot, while power losses are minimized through active damping. The methodology is applicable to a wide range of types of solar inverters, including single-phase and three-phase topologies, as well as hybrid inverters that incorporate battery storage. Future work will extend this approach to multi-parallel inverters and to scenarios with more complex grid conditions, such as harmonics and imbalances.
The successful implementation of this delay compensation strategy contributes to the stable and efficient integration of renewable energy systems into the grid. By addressing the fundamental issue of digital control delays, we provide a robust solution that enhances the reliability of all types of solar inverters in modern power systems.