As renewable energy integration accelerates, the utility interactive inverter serves as a critical interface between distributed generation sources and the power grid. Its primary function is to convert DC power from sources like photovoltaics into AC power that meets grid standards. To ensure high-quality power injection, filters are essential for attenuating switching harmonics. Among various filter topologies, the LCL filter is widely adopted due to its superior harmonic attenuation capabilities and reduced size compared to simple L filters. However, the LCL filter introduces a third-order resonant peak, which can destabilize the system, especially under weak grid conditions where grid impedance varies widely. Weak grids, characterized by significant grid impedance and background harmonics, pose severe challenges to the stability and performance of utility interactive inverters. Traditional control strategies, such as grid voltage proportional feedforward, are commonly employed to mitigate grid voltage disturbances and improve current quality. Yet, this approach can introduce positive feedback loops coupled with grid impedance, reducing system phase margin and leading to resonance or instability when grid impedance changes. In this article, I propose an impedance reshaping and resonance suppression strategy that combines an improved grid voltage feedforward method with lead compensation. This strategy aims to enhance the robustness of utility interactive inverters in weak grids while maintaining excellent current quality. I will begin by modeling the LCL-type utility interactive inverter system, analyze the impact of traditional feedforward control, detail the proposed strategy with parameter design, and validate its effectiveness through simulations.
The proliferation of utility interactive inverters is central to the modern power grid’s evolution toward sustainability. These inverters must not only convert power efficiently but also ensure stable operation under varying grid conditions. The LCL filter, while effective, introduces a resonance frequency that can interact with grid impedance, causing oscillations. In weak grids, where grid impedance is non-negligible and often inductive, this interaction becomes more pronounced. Background harmonics from nonlinear loads further exacerbate power quality issues. Consequently, advanced control strategies are required to dampen resonances and maintain stability. Existing methods include active damping via capacitor current feedback, passive damping with resistors, and hybrid approaches. However, many of these techniques struggle with robustness against wide grid impedance variations. Grid voltage feedforward is popular for harmonic rejection, but it can degrade stability margins. My research focuses on addressing this trade-off by reshaping the inverter’s output impedance through innovative feedforward and compensation techniques, ensuring that utility interactive inverters remain stable and reliable even in challenging weak grid environments.
To understand the stability issues, I first establish a model for the LCL-type utility interactive inverter. The main circuit topology includes a DC voltage source Udc, inverter bridge, LCL filter with inverter-side inductance L1, grid-side inductance L2, and filter capacitance Cf, and the grid with impedance Zg = sLg (assuming the resistive part is negligible for worst-case analysis). The control system typically employs a current controller, such as a quasi-proportional resonant (QPR) controller, for precise grid current tracking. The block diagram of the control system can be transformed into an equivalent impedance model. The grid current ig(s) can be expressed as:
$$ i_g(s) = i(s) – \frac{U_g(s)}{Z_{out}(s)} \cdot \frac{1}{1 + \frac{Z_g(s)}{Z_{out}(s)}} $$
where i(s) is the equivalent current source and Zout(s) is the output impedance of the utility interactive inverter. The expressions are:
$$ i(s) = i_{ref} \cdot \frac{G_{QPR}(s) G_{x1}(s) G_{x2}(s)}{1 + G_{QPR}(s) G_{x1}(s) G_{x2}(s) H_1} $$
$$ Z_{out}(s) = \frac{1 + G_{QPR}(s) G_{x1}(s) G_{x2}(s) H_1}{G_{x2}(s)} $$
with Gx1(s) and Gx2(s) defined as:
$$ G_{x1}(s) = \frac{K_{pwm}}{s^2 C_f L_1 + s K_C K_{pwm} C_f + 1} $$
$$ G_{x2}(s) = \frac{s^2 L_1 C_f + s K_C K_{pwm} C_f + 1}{s^3 C_f L_1 L_2 + s^2 K_C K_{pwm} C_f L_2 + s (L_1 + L_2)} $$
Here, Kpwm is the inverter gain, KC is the capacitor current feedback coefficient, H1 is the grid current feedback coefficient, and GQPR(s) is the QPR controller transfer function:
$$ G_{QPR}(s) = K_p + \frac{2K_r \omega_c s}{s^2 + 2\omega_c s + \omega_0^2} $$
where Kp and Kr are proportional and resonant coefficients, ω0 is the fundamental angular frequency (314 rad/s), and ωc is the bandwidth (3.14 rad/s). Stability criteria based on impedance analysis require that the phase margin at the intersection frequency of Zout(s) and Zg(s) be positive. Specifically, for inductive grid impedance, ∠Zg(jωs) = 90°, so stability demands ∠Zout(jωs) > -90°.
Traditional grid voltage proportional feedforward adds a path with transfer function Gf(s) = 1/Kpwm to cancel grid voltage disturbances. However, due to grid impedance, the point of common coupling voltage Upcc includes a term sLgig, creating a positive feedback loop. The modified output impedance becomes:
$$ Z’_{out}(s) = \frac{1 + G_{QPR}(s) G_{x1}(s) G_{x2}(s) H_1}{G_{x2}(s)[1 – G_f(s) G_{x1}(s)]} $$
This feedforward reduces the magnitude of output impedance at low frequencies, improving harmonic rejection, but it severely degrades the phase characteristics. As shown in Bode plots, the phase of Z’out(s) can dip below -90° in low-frequency regions, shrinking the stability region. When grid impedance increases, the intersection point shifts into this unstable zone, causing resonance. This underscores the vulnerability of utility interactive inverters under weak grid conditions with conventional feedforward.
To address this, I propose an improved strategy that reshapes the output impedance. The first part involves modifying the grid voltage feedforward by inserting a second-order generalized integrator (SOGI) in series. SOGI is a bandpass filter that selectively passes fundamental frequency components with zero phase shift, attenuating higher frequencies. Its transfer function is:
$$ G_Y(s) = \frac{n \omega_0 s}{s^2 + n \omega_0 s + \omega_0^2} $$
where n is a coefficient determining bandwidth; I choose n = 0.8 as a trade-off between dynamic response and harmonic attenuation. The SOGI-based feedforward reduces the positive feedback effect by decoupling the feedforward from grid impedance at higher frequencies. The output impedance with this improvement is:
$$ Z”_{out}(s) = \frac{1 + G_{QPR}(s) G_{x1}(s) G_{x2}(s) H_1}{G_{x2}(s)[1 – G_f(s) G_Y(s) G_{x1}(s)]} $$
This enhances phase margin but may still be insufficient for large grid impedance variations. Therefore, I introduce a lead compensation block in the current forward path. The lead compensator transfer function is:
$$ G_n(s) = m \frac{1 + a b s}{1 + b s} $$
where a, b, and m are constants designed to provide phase boost at the target frequency. The maximum phase lead θmax occurs at frequency ωmax = 1/(b\sqrt{a}) and is given by:
$$ \theta_{\text{max}} = \arcsin\left(\frac{a-1}{a+1}\right) $$
To ensure unity gain at ωmax, m is set as:
$$ m = \sqrt{\frac{1 + b^2 \omega_{\text{max}}^2}{1 + a^2 b^4 \omega_{\text{max}}^4 + (1+a^2) b^2 \omega_{\text{max}}^2}} $$
The overall output impedance with both improvements becomes:
$$ Z”’_{out}(s) = \frac{1 + G_{QPR}(s) G_n(s) G_{x1}(s) G_{x2}(s) H_1}{G_{x2}(s)[1 – G_f(s) G_Y(s) G_{x1}(s)]} $$
This reshaped impedance exhibits higher phase margins at intersection points with grid impedance, ensuring stability. The design process involves online grid impedance measurement using signal injection techniques. For instance, injecting a harmonic at frequency fV and analyzing the phase and magnitude of Upcc and ig yields grid inductance Lgest:
$$ L_{gest} = \frac{|X_{gest}(f_V)| \sin(\angle X_{gest}(f_V))}{2\pi f_V}, \quad \text{where } X_{gest}(f_V) = \frac{U_{pcc}(f_V)}{i_g(f_V)} \text{ and } \angle X_{gest}(f_V) = \angle U_{pcc}(f_V) – \angle i_g(f_V) $$
Based on measured impedance, parameters a, b, and m are tuned. For example, with Lg = 10 mH, the intersection frequency is around 150 Hz (ωmax ≈ 942 rad/s). To achieve a phase margin over 30°, I set θmax = 30°, giving a = 3. Then, b = 6.12 × 10-4 and m = 0.58 are calculated. This systematic design ensures robustness for utility interactive inverters across a wide grid impedance range.
The effectiveness of the proposed impedance reshaping strategy is verified through simulations in MATLAB/Simulink. The system parameters are summarized in Table 1.
| Parameter | Value |
|---|---|
| DC voltage Udc | 400 V |
| Grid voltage Ug | 220 V (RMS) |
| Fundamental frequency f0 | 50 Hz |
| Inverter-side inductance L1 | 0.6 mH |
| Grid-side inductance L2 | 0.15 mH |
| Filter capacitance Cf | 10 μF |
| Proportional coefficient Kp | 0.3 |
| Resonant coefficient Kr | 75 |
| Controller bandwidth ωc | 3.14 rad/s |
| Fundamental angular frequency ω0 | 314 rad/s |
| Reference current iref | 30 A |
| Current feedback coefficient H1 | 0.15 |
Simulation results compare traditional feedforward and the proposed strategy under various grid impedances. With zero grid impedance, both methods yield stable grid current with low distortion, confirming that the utility interactive inverter operates reliably in stiff grids. However, as grid inductance increases to 3 mH and 10 mH, traditional feedforward leads to severe resonance in grid current, evidenced by oscillations and high harmonic content. In contrast, the proposed impedance reshaping strategy maintains smooth sinusoidal current waveforms with minimal distortion, demonstrating effective resonance suppression. The phase margins calculated from Bode plots are significantly improved: for Lg = 1 mH, 3 mH, 5 mH, and 10 mH, the margins are 51.0°, 57.3°, 55.7°, and 38.0°, respectively, all above the 30° threshold for stability. This highlights the robustness of the strategy for utility interactive inverters in weak grids.
Dynamic performance is also tested by stepping the reference current from 30 A to 15 A. The grid current tracks the reference within half a cycle without overshoot or instability, proving the strategy’s fast response and suitability for real-time applications. These simulations validate that the combined use of SOGI-based feedforward and lead compensation effectively reshapes the output impedance, enhancing stability without compromising harmonic rejection. The utility interactive inverter thus achieves high performance under diverse weak grid scenarios.
In conclusion, this article addresses the stability challenges of LCL-type utility interactive inverters in weak grids. Traditional grid voltage proportional feedforward, while beneficial for harmonic suppression, can induce positive feedback that reduces phase margin and leads to resonance as grid impedance varies. To mitigate this, I propose an impedance reshaping strategy that integrates an improved feedforward path with a second-order generalized integrator and a lead compensation block. The SOGI attenuates high-frequency coupling between feedforward and grid impedance, while the lead compensator boosts phase margin at critical frequencies. This approach ensures that the output impedance of the utility interactive inverter maintains sufficient phase margin over a wide range of grid impedances, preventing resonance. Parameter design guidelines are provided based on online impedance measurement. Simulations confirm that the strategy enhances stability, improves current quality, and offers robust dynamic response. Future work could explore adaptive tuning of compensation parameters for varying grid conditions and hardware implementation. Overall, this research contributes to the reliable integration of renewable energy by advancing control methods for utility interactive inverters in modern power grids.
The implications of this work extend to practical applications where grid conditions are unpredictable. Utility interactive inverters equipped with this impedance reshaping strategy can operate stably in rural or remote areas with weak grid infrastructure, facilitating the deployment of solar and wind power. Additionally, the strategy’s compatibility with existing control frameworks minimizes implementation complexity. By ensuring stability, it reduces the risk of grid disturbances and enhances overall power system reliability. As renewable penetration grows, such advanced control techniques will be crucial for maintaining grid integrity and supporting the energy transition.
In summary, the proposed method represents a significant step forward in the design of robust utility interactive inverters. It balances harmonic rejection and stability through intelligent impedance reshaping, offering a comprehensive solution for weak grid challenges. Continued innovation in this field will further optimize performance and enable seamless integration of distributed generation, paving the way for a sustainable energy future.