In the context of weak power grids, characterized by high equivalent impedance and low short-circuit capacity, the operational stability of string solar inverters faces significant challenges. The interaction between the solar inverter’s output impedance and the grid impedance can trigger resonance, leading to voltage and current instability at the point of common coupling. Traditional control methods for solar inverters, which often rely on voltage and current vectors as input conditions, are highly susceptible to these impedance characteristics. This sensitivity can degrade the quality of power injected by the solar inverter and, in severe cases, cause the entire system to become unstable. To address these issues, I present a robust control method for enhancing the stability of string solar inverters in weak grid environments, grounded in a comprehensive impedance analysis.
My approach begins by modeling the electrical interconnection of the solar inverter. In a typical string configuration, multiple photovoltaic strings are connected in series before being fed into a single solar inverter. This connection introduces line resistance, which, from an impedance perspective, constitutes the real part of the overall system impedance. An increase in line resistance directly elevates the equivalent impedance, thereby reducing the stability margin at the solar inverter’s port. To counteract this, I derive and optimize the closed-loop transfer function of the solar inverter. The initial port impedance characteristic of the solar inverter can be expressed as:
$$ Z_i(s) = \frac{U_c(s)}{I_r(s) T_c(s) – I_c(s)} $$
Here, \( Z_i(s) \) represents the solar inverter’s port impedance, \( T_c(s) \) is the closed-loop transfer function, \( U_c(s) \) and \( I_c(s) \) are the response voltage and current to an excitation signal, and \( I_r(s) \) is the reference signal. By analyzing the response parameters at the port’s input and output, I eliminate the intermediate variable to derive an optimized transfer function:
$$ T’_c(s) = \frac{I_{c1}(s)U_{c2}(s) – I_{c2}(s)U_{c1}(s)}{I_{r2}(s)U_{c2}(s) – I_{r2}(s)U_{c1}(s)} $$
Using this optimized function \( T’_c(s) \), I can then compute an enhanced port stability impedance for the solar inverter:
$$ Z’_i(s) = T’_c(s) \times \frac{|U_{c1}(s)||I_{r2}(s)| – |U_{c2}(s)||I_{r1}(s)|}{|I_{c2}(s)||I_{r1}(s)| – |I_{c1}(s)||I_{r2}(s)|} $$
This enhanced impedance \( Z’_i(s) \) is critical for actively suppressing the operational resonance of the solar inverter. By shaping the inverter’s output impedance to better match the grid, the risk of instability is significantly reduced.
| Parameter | Value |
|---|---|
| Maximum Input Voltage | 1,100 V |
| Rated Input Voltage | 585 V |
| Full Load MPPT Voltage Range | 550 – 850 V |
| Maximum Number of Strings per MPPT | 2 |
| Maximum Input Current per Terminal | 30 A |
| Minimum Input Voltage / Start Voltage | 200 V / 250 V |
| MPPT Voltage Range | 200 – 1,000 V |
| Number of MPPTs | 9 |
| Maximum Input Current | 234 A |
| Maximum DC Short-Circuit Current | 360 A |
To further suppress resonance, I construct an equivalent model of the solar inverter where it is represented as an ideal current source in parallel with an equivalent admittance. The stability condition for the solar inverter is determined by the current gain \( K_i \), defined as the ratio of the inverter’s equivalent admittance \( Y_1 \) to the grid admittance \( Y_g \):
$$ K_i = \frac{Y_1}{Y_g} $$
Perfect stability is achieved when \( K_i = 1 \), indicating a match between the inverter and grid admittances. Conversely, when \( K_i \neq 1 \), resonance can occur. I quantify the total resonant behavior of the system:
$$ I_0 = \sum_{i=1}^{n} Z_i(s) i_g $$
$$ I_g = \frac{Z_i(s)I_0 – u_g Y_0}{1 + sL_g Y_0} $$
$$ Y_0 = \sum_{i=1}^{n} Z_i(s) Y_i $$
To actively suppress this resonance, I apply a filtering action based on the resonant frequencies, yielding suppressed parameters:
$$ I’_0 = \sum_{i=1}^{n} Z_i(s) I_0 f_0 $$
$$ I’_g = \frac{Z_i(s)I_g – u_g Y_0 f_g}{I_g} $$
$$ Y’_0 = \sum_{i=1}^{n} Z_i(s) Y_0 f_y $$
When the conditions \( I’_0 < I_0 \), \( I’_g < I_g \), and \( Y’_0 < Y_0 \) are satisfied, the operational resonance of the solar inverter is effectively contained. The following results from an experimental setup demonstrate this suppression.
The final step in my methodology involves compensating for residual resonance using reactive power decoupling vectors. These vectors are derived from the residual resonance components of the solar inverter, providing reactive power support to further enhance stability.
To validate the effectiveness of my proposed method, I conducted a series of experiments using an SG100CX string solar inverter prototype. The photovoltaic inverter was set to a reference output power, and a power step-change was introduced to observe the dynamic response. A single-phase three-unit solar inverter platform was built, featuring an AD7606 sampling module, current and voltage sensors, a DC power supply, and various loads.
In the first experiment, I focused on resonance suppression. The oscilloscope waveforms clearly showed that my method effectively identified and eliminated the abnormal peak resonances that would otherwise destabilize the solar inverter. The post-suppression waveform was smooth and stable, in stark contrast to the distorted pre-suppression waveform.
The second experiment validated reactive power compensation. The solar inverter was started with a specific inductive load, and an additional load was paralleled after 0.8 seconds. My enhanced control method successfully balanced the active power within 2.0 seconds and regulated the reactive power to zero, demonstrating its ability to prevent unwanted power oscillations that could lead to instability.
| Control Method | Voltage Range | Current Range | Stability Assessment |
|---|---|---|---|
| Improved LADRC-PI Dual Closed-Loop Control | -40 V to +60 V | -40 A to +20 A | Unstable, severe fluctuations |
| Improved Particle Swarm Algorithm Control | -40 V to +50 V | -40 A to +40 A | Unstable, current very high |
| Proposed Impedance Analysis Method | -80 V to +80 V | -20 A to +20 A | Stable, smooth waveform |
In the third experiment, I performed a comparative analysis of the grid-connected voltage and current vectors against two other prevalent solar inverter control strategies: a method based on an improved Linear Active Disturbance Rejection Control-Proportional-Integral (LADRC-PI) dual closed-loop and a method based on an improved Particle Swarm Algorithm (PSO). The results are summarized in the table above. The LADRC-PI method resulted in voltage fluctuating between -40V and +60V and current between -40A and +20A, indicative of instability. The PSO-based method showed voltage between -40V and +50V and a very large current swing between -40A and +40A. In contrast, my impedance analysis-based control method yielded a stable voltage waveform fluctuating between -80V and +80V and a stable current waveform between -20A and +20A, with no observable spike resonance or significant distortion.
In conclusion, my proposed method provides a sophisticated and effective solution for enhancing the stability of string solar inverters in challenging weak grid environments. By directly addressing the root cause of instability through proactive impedance shaping and resonance suppression, the method ensures a robust and high-quality power output from the solar inverter. The experimental validation confirms that the solar inverter maintains stable operation, making it a reliable choice for long-term deployment in weak grid conditions. The integration of impedance analysis, port stability enhancement, and reactive decoupling compensation offers a comprehensive strategy that significantly outperforms traditional control approaches, ensuring the solar inverter operates at its full potential without succumbing to grid-induced instabilities.