With the rapid advancement of distributed generation technologies, renewable energy sources have been extensively developed and efficiently utilized. The utility interactive inverter serves as a critical interface for energy conversion between distributed power sources and the grid, and its operational state directly impacts the stable operation and power quality of grid-connected systems. However, as large-scale distributed power sources are integrated into the grid, the actual grid structure has quietly transformed into a weak grid characterized by non-ideal factors. In weak grid environments, the dynamic interaction between the utility interactive inverter and the grid, exacerbated by significant and unstable grid impedance variations, poses severe challenges to the robustness of the inverter. LCL-type utility interactive inverters exhibit superior high-frequency harmonic suppression capabilities compared to conventional L-type inverters, attracting considerable attention from researchers worldwide. Nevertheless, the resonant characteristics inherent to LCL filters can adversely affect system stability, particularly in weak grids where wide-ranging grid impedance variations further aggravate this issue, compromising the robust stability and grid current quality of the inverter. Therefore, current research focuses on effectively suppressing LCL filter resonance without adding extra sensors. To enhance the robustness of LCL-type utility interactive inverters in weak grids, numerous studies have been conducted, primarily concentrating on改进 grid current control strategies, optimizing filter design, and incorporating advanced control algorithms. While these approaches have successfully mitigated LCL filter resonance and improved system robustness, achieving optimal control in complex and variable weak grid environments remains challenging. This paper aims to investigate robustness enhancement techniques for LCL-type utility interactive inverters in weak grids, proposing an effective and practical control strategy to provide theoretical and technical support for the reliable operation of distributed generation grid-connected systems.
To accurately simulate and analyze the impact of grid impedance uncertainty in weak grids on the operational stability of LCL-type utility interactive inverters, we first establish a precise mathematical model. The topology of the LCL-type utility interactive inverter is illustrated below. Based on Kirchhoff’s voltage and current laws, we develop a mathematical model in the α-β coordinate system to deeply understand its dynamic behavior. The first-order differential equation for the inverter-side voltage can be expressed as:
$$ L_1 \frac{dI_{\alpha}}{dt} = U_{pv\alpha} – U_{pc\alpha} – R_1 I_{\alpha} $$
$$ L_1 \frac{dI_{\beta}}{dt} = U_{pv\beta} – U_{pc\beta} – R_1 I_{\beta} $$
where \( I_{\alpha} \) and \( I_{\beta} \) are the α-axis and β-axis components of the inverter-side current, respectively; \( U_{pv\alpha} \) and \( U_{pv\beta} \) are the α-axis and β-axis components of the inverter output voltage; \( U_{pc\alpha} \) and \( U_{pc\beta} \) are the α-axis and β-axis components of the voltage at the point of common coupling (PCC); \( L_1 \) is the inverter-side inductance; and \( R_1 \) is the equivalent resistance of the inverter-side inductor.
The relationship between the grid-side voltage and the inverter-side voltage and capacitor branch voltage is given by:
$$ L_2 \frac{d(I_g)_{\alpha}}{dt} = U_{pc\alpha} – U_{g\alpha} – R_2 (I_g)_{\alpha} – Z_g (I_g)_{\alpha} $$
$$ L_2 \frac{d(I_g)_{\beta}}{dt} = U_{pc\beta} – U_{g\beta} – R_2 (I_g)_{\beta} – Z_g (I_g)_{\beta} $$
where \( (I_g)_{\alpha} \) and \( (I_g)_{\beta} \) are the α-axis and β-axis components of the grid-side current; \( U_{g\alpha} \) and \( U_{g\beta} \) are the α-axis and β-axis components of the grid voltage; \( L_2 \) is the grid-side inductance; \( R_2 \) is the equivalent resistance of the grid-side inductor; and \( Z_g \) is the grid impedance.
Additionally, we establish the filter capacitor current model, which reveals the relationship between the inverter-side current and the grid-side current in the LCL-type utility interactive inverter. This relationship is expressed as:
$$ I_{c\alpha} = I_{\alpha} – (I_g)_{\alpha} $$
$$ I_{c\beta} = I_{\beta} – (I_g)_{\beta} $$
where \( I_{c\alpha} \) and \( I_{c\beta} \) are the α-axis and β-axis components of the filter capacitor current, and \( C \) is the filter capacitance value.
To transform the time-domain equations into the frequency domain, we introduce the complex variable \( s \) and perform Laplace transforms. The open-loop transfer function from the inverter-side voltage to the grid-side current in the frequency domain can be represented as:
$$ G_{open}(s) = \frac{I_g(s)}{U_{pv}(s)} = \frac{1}{s^3 L_1 L_2 C + s^2 (L_1 R_2 C + L_2 R_1 C) + s (L_1 + L_2 + R_1 R_2 C) + (R_1 + R_2)} $$
This mathematical model provides a foundational understanding of the dynamic behavior of the LCL-type utility interactive inverter in weak grid environments, facilitating subsequent optimization and control design.
To enhance the filtering performance and dynamic response capability of the LCL filter, we optimize its parameters through rational design, aiming to balance filtering performance and system stability, ensuring that the LCL-type utility interactive inverter maintains good output characteristics in weak grid environments. The key parameter optimization constraints are summarized in the following table:
| Parameter | Constraint Equation | Description |
|---|---|---|
| Total Inductance \( L_1 + L_2 \) | $$ L_1 + L_2 \leq \frac{E_p}{I_p \cdot k} $$ | Limits inductance to prevent degraded dynamic response; \( E_p \) is voltage peak, \( I_p \) is inductor current peak, \( k \) is safety factor. |
| Filter Capacitance \( C \) | $$ C \leq \frac{P_r}{\omega_b V_t^2} $$ | Constraints capacitance to avoid excessive reactive power; \( P_r \) is rated power, \( \omega_b \) is grid fundamental angular frequency, \( V_t \) is rated voltage. |
| Resonant Frequency \( f_r \) | $$ f_r = \frac{1}{2\pi \sqrt{(L_1 + L_2 + L_g)C}} $$ | Defines resonance frequency influenced by grid impedance \( L_g \). |
| Stability Margin Constraint | $$ \arctan\left(\frac{\omega_c L_{eq}}{R_{eq}}\right) \geq \theta_{min} $$ | Ensures sufficient phase margin; \( \omega_c \) is cutoff frequency, \( L_{eq} \) and \( R_{eq} \) are equivalent inductance and resistance, \( \theta_{min} \) is minimum phase margin. |
These optimizations improve the robustness of the LCL-type utility interactive inverter in weak grids, ensuring good filtering and dynamic response under various operating conditions. However, real-time grid impedance variations remain a challenge. To address this, we implement a grid impedance adaptive control strategy.
The strategy begins with real-time detection of grid impedance variations using the small-signal injection method. By injecting a small harmonic signal \( I_{inj}(t) \) at the output of the utility interactive inverter and analyzing the voltage \( V_{pcc}(t) \) and current \( I_{pcc}(t) \) at the PCC via fast Fourier transform, the grid impedance \( Z_g(s) \) magnitude and phase can be accurately calculated:
$$ Z_g(s) = \frac{V_{pcc}(s)}{I_{pcc}(s) + I_{inj}(s)} $$
where \( V_{pcc}(s) \), \( I_{pcc}(s) \), and \( I_{inj}(s) \) are the Laplace transforms of \( V_{pcc}(t) \), \( I_{pcc}(t) \), and \( I_{inj}(t) \), respectively. This detection provides timely and accurate grid impedance information for adaptive control.
Upon obtaining grid impedance data, we design an adaptive controller based on an adaptive filtering algorithm to dynamically adjust the control parameters of the LCL-type utility interactive inverter. This controller flexibly modifies key parameters such as current reference, voltage reference, or control gains in response to grid impedance changes, ensuring stable output and system robustness under various grid conditions. For example, the adjustment of the current reference \( I_{ref}(s) \) can be expressed as:
$$ I_{ref}(s) = I_b(s) + K_1 \cdot |Z_g(s)| + K_2 \cdot \angle Z_g(s) + K_3 \cdot \frac{d|Z_g(s)|}{dt} $$
where \( I_b(s) \) is the base current reference, \( |Z_g(s)| \) is the magnitude of grid impedance, \( \angle Z_g(s) \) is the phase angle, and \( K_1 \), \( K_2 \), \( K_3 \) are gain coefficients of the adaptive controller.
To ensure system stability and dynamic response, we incorporate stability analysis into the adaptive control design. The system transfer function \( H(s) \) is mathematically represented as:
$$ H(s) = \frac{Q(s)}{U(s)} = \frac{G_c(s) \cdot G_{open}(s)}{1 + G_c(s) \cdot G_{open}(s) \cdot Z_L(s)} $$
where \( G_c(s) \) is the controller transfer function, \( Z_L(s) \) is the load impedance transfer function, and \( Q(s) \) and \( U(s) \) are the Laplace transforms of system output and input, respectively. By ensuring that the characteristic equation roots of \( H(s) \) lie in the left-half plane of the complex plane, system stability and dynamic response are guaranteed. This adaptive control strategy enables stable operation and good output characteristics for LCL-type utility interactive inverters in weak grids through real-time impedance detection, dynamic parameter adjustment, and optimized feedforward functions.
To validate the proposed robustness enhancement techniques, we construct an experimental platform for testing the LCL-type utility interactive inverter in weak grid conditions. The platform includes a high-precision oscilloscope for real-time monitoring of grid current, voltage waveforms, and inverter output signal quality, along with configurable power modules that simulate various grid impedance and harmonic conditions to assess inverter performance in complex grid environments. Key components such as the main control circuit, drive circuit, and auxiliary power supply are integrated to ensure comprehensive testing. The detailed equipment list for the experimental platform is provided in the table below:
| Equipment | Specification | Purpose |
|---|---|---|
| Oscilloscope | High-precision, multi-channel | Monitor waveforms and signal quality |
| Power Module | Configurable with variable impedance | Simulate weak grid conditions |
| LCL-Type Utility Interactive Inverter | Custom-built with optimized parameters | Test robustness enhancement techniques |
| Main Control Circuit | Microprocessor-based | Implement control strategies |
| Drive Circuit | Insulated gate bipolar transistor drivers | Convert control signals to drive signals |
| Auxiliary Power Supply | DC power source | Provide system power |
With the experimental platform set up, we conduct tests to evaluate the robustness of the LCL-type utility interactive inverter under different grid impedance conditions, such as \( Z_g = 8 \text{ mH} \), \( Z_g = 14 \text{ mH} \), and \( Z_g = 22 \text{ mH} \), after applying the proposed robustness enhancement techniques. The experimental results demonstrate that as capacitance values increase, the oscillation period of the utility interactive inverter circuit gradually lengthens, but the voltage peak does not change significantly, indicating high robustness and adaptability to capacitance variations in weak grid environments. Even with substantial changes in capacitance, the inverter maintains stable output voltage and current, ensuring grid stability. This is attributed to the optimized LCL filter structure and the effective application of robustness enhancement techniques, which involve precise parameter design and advanced control strategies. The utility interactive inverter successfully adapts to the complexity of weak grid environments, guaranteeing stable power transmission. The experimental waveforms, though not shown in detail here, confirm that the proposed techniques significantly improve the stability, adaptability, and robust performance of the LCL-type utility interactive inverter in complex grid conditions.
In conclusion, this paper comprehensively analyzes the resonant characteristics of LCL filters and the non-ideal factors of grid impedance in weak grid environments, proposing an innovative control strategy for robustness enhancement. The strategy significantly improves the robust stability and grid current quality of the utility interactive inverter. Without adding extra sensors, it achieves adaptive regulation to grid impedance changes through optimized control algorithms, enhancing system dynamic response and stability. The mathematical modeling, parameter optimization, and adaptive control design provide a solid foundation for reliable operation of LCL-type utility interactive inverters in weak grids. Future work will focus on deepening research in this field, refining existing control strategies, incorporating the latest technological advancements, and exploring new control methods to further contribute to the stability and power quality of distributed generation grid-connected systems. The utility interactive inverter remains a pivotal component in modern power systems, and its robustness in weak grids is essential for sustainable energy integration.