As the global transition to renewable energy accelerates, solar power systems have become integral to modern electrical grids. Among the critical components, solar inverters play a pivotal role in converting DC power from photovoltaic (PV) panels into AC power suitable for grid integration. Understanding the behavior of these inverters under fault conditions is essential for ensuring grid stability and protection. However, due to technical confidentiality, manufacturers often do not disclose precise control parameters, such as those in the current loop, which dictate fault responses. This paper addresses the challenge of identifying these parameters by leveraging fault and recovery characteristics, with a focus on various types of solar inverters, including grid-following and grid-forming variants. The proposed method separates proportional and integral coefficients through analytical modeling, enhancing identification accuracy without relying on invasive signal injection. Through real-time simulations and experimental data, we validate the effectiveness of this approach, contributing to improved fault analysis and protection schemes in solar-rich power systems.
The proliferation of solar energy has led to diverse types of solar inverters, each with unique control strategies and fault responses. Common types of solar inverters include string inverters, central inverters, and microinverters, which are often categorized based on their grid interaction as grid-following or grid-forming inverters. Grid-following inverters, the focus of this study, synchronize with the grid voltage and are prevalent in large-scale PV plants. Their control parameters, particularly in the current loop, significantly influence fault current contributions, making accurate parameter identification crucial for relay protection settings. For instance, during low-voltage ride-through (LVRT) events, these inverters must inject reactive current to support grid voltage, and their dynamic response is governed by proportional-integral (PI) controllers. The inability to access exact parameters from manufacturers necessitates robust identification methods, which are explored here through fault transient and recovery phase analysis.
To model the behavior of grid-connected PV inverters, consider a typical system with a voltage source converter (VSC) employing dq-axis control. The system equations in the dq reference frame are derived from Park transformations, accounting for the dynamics of the LCL filter and grid interface. The current loop control can be expressed as:
$$ u_d = k_p (i_{dref} – i_d) + k_i \int (i_{dref} – i_d) dt – \omega L i_q + e_d $$
$$ u_q = k_p (i_{qref} – i_q) + k_i \int (i_{qref} – i_q) dt + \omega L i_d + e_q $$
where \( k_p \) and \( k_i \) are the proportional and integral coefficients of the PI controller, \( i_{dref} \) and \( i_{qref} \) are the d-axis and q-axis current references, \( i_d \) and \( i_q \) are the actual currents, \( \omega \) is the grid angular frequency, \( L \) is the filter inductance, and \( e_d \) and \( e_q \) are the grid voltages. During faults, the voltage outer loop is disabled, and current references are adjusted per grid codes, such as providing reactive current support when voltage drops below 90% of nominal. The fault response involves a transient current that depends on both \( k_p \) and \( k_i \), but their simultaneous identification is challenging due to parameter sensitivity differences. Specifically, \( k_i \) often exhibits lower sensitivity, leading to poor accuracy when identified alongside \( k_p \).
The proposed method exploits the distinct characteristics of fault occurrence and recovery phases. During a fault, the current response to a step change in reference can be modeled as a second-order system. For a fault at time \( t_0 \), the d-axis current response is:
$$ i_d(t) = C_1 e^{r_1 (t – t_0)} + C_2 e^{r_2 (t – t_0)} + i_{dref}(t_0^+) \quad \text{for} \quad t > t_0 $$
where \( C_1 \) and \( C_2 \) are constants derived from initial conditions, and \( r_1 \) and \( r_2 \) are roots of the characteristic equation involving \( k_p \), \( k_i \), resistance \( R \), and inductance \( L \). This equation shows that both parameters influence the transient, making separation difficult. However, during the recovery phase—initiated after fault clearance—the current reference ramps up with a slope \( k_d \) to meet power restoration requirements, as per standards like IEEE 1547. The recovery current response, after exponential terms decay, simplifies to:
$$ i_d(t) – i_{dref}(t) = -\frac{k_d R}{k_i} \quad \text{for} \quad t > t_1 $$
where \( t_1 \) is the recovery start time. This expression depends solely on \( k_i \), allowing its independent identification. Once \( k_i \) is determined, \( k_p \) can be identified from the fault transient data. This separation mitigates the impact of sensitivity disparities, enhancing overall accuracy.
In practical applications, various types of solar inverters exhibit different control behaviors during faults. For example, string inverters in distributed PV systems may have faster response times due to their modular design, whereas central inverters in utility-scale plants might prioritize stability over agility. The proposed identification method is applicable across these types of solar inverters, as it relies on generic current loop dynamics. To illustrate, consider the parameter identification process using experimental data from a real-time digital simulator (RTDS). The setup includes a grid-connected PV system with a symmetrical fault applied, and data is collected for voltage dips to 20%, 30%, and 40% of nominal voltage. The recovery slope \( k_d \) is first identified by fitting a ramp function to the post-fault current data, followed by \( k_i \) estimation from the steady-state error, and finally \( k_p \) from the fault transient.
The effectiveness of this method is validated through multiple tests with different noise levels. For instance, under a 20% voltage dip and a recovery slope of 0.6 pu/s, the identified parameters show errors below 3% for \( k_i \) and 2% for \( k_p \) in noise-free conditions. With additive Gaussian noise at 30 dB signal-to-noise ratio (SNR), errors remain acceptable, demonstrating robustness. The table below summarizes identification results for various scenarios, highlighting the consistency across different types of solar inverters and operating conditions.
| Voltage Dip (%) | Recovery Slope \( k_d \) (pu/s) | True \( k_p \) | Identified \( k_p \) | Error \( k_p \) (%) | True \( k_i \) | Identified \( k_i \) | Error \( k_i \) (%) |
|---|---|---|---|---|---|---|---|
| 20 | 0.6 | 0.285 | 0.280 | 1.75 | 6.0 | 6.118 | 1.97 |
| 20 | 0.8 | 0.285 | 0.283 | 0.70 | 6.0 | 6.135 | 2.26 |
| 20 | 1.0 | 0.285 | 0.282 | 1.05 | 6.0 | 6.154 | 2.57 |
| 30 | 0.7 | 0.285 | 0.281 | 1.40 | 6.0 | 6.142 | 2.37 |
| 40 | 0.9 | 0.285 | 0.279 | 2.11 | 6.0 | 6.168 | 2.80 |
Furthermore, the method is compared with traditional simultaneous identification approaches, such as particle swarm optimization (PSO) and differential evolution, which often struggle with low-sensitivity parameters. In contrast, the proposed stepwise identification reduces errors significantly, as shown in the following table. This underscores the importance of leveraging fault recovery characteristics for accurate parameter estimation in various types of solar inverters.
| Identification Method | Algorithm | True \( k_p \) | Identified \( k_p \) | Error \( k_p \) (%) | True \( k_i \) | Identified \( k_i \) | Error \( k_i \) (%) |
|---|---|---|---|---|---|---|---|
| Simultaneous | PSO | 0.285 | 0.277 | 2.80 | 6.0 | 9.06 | 51.03 |
| Simultaneous | Differential Evolution | 0.285 | 0.276 | 3.15 | 6.0 | 8.62 | 43.67 |
| Stepwise (Proposed) | Genetic PSO | 0.285 | 0.280 | 1.75 | 6.0 | 6.118 | 1.97 |
The robustness of the method is also tested under noisy conditions. For example, with 30 dB SNR, the average identification errors for \( k_p \) and \( k_i \) are below 4%, making it suitable for real-world applications where measurement noise is prevalent. The core principle—decoupling parameters based on physical insights—ensures that the method is transferable across different optimization algorithms and types of solar inverters, including those with advanced features like active power filtering or battery integration.
In conclusion, this paper presents a novel parameter identification technique for solar inverters that capitalizes on fault and recovery dynamics. By analytically separating proportional and integral coefficients, the method overcomes limitations of traditional approaches, achieving high accuracy and noise immunity. Future work could extend this to asymmetric faults and other types of solar inverters, such as hybrid systems with energy storage, further enhancing grid resilience. As solar penetration grows, such advancements will be vital for reliable power system operation and protection.