Accurate control parameters of solar inverters are fundamental for analyzing the fault characteristics of photovoltaic power sources. During fault conditions, the current loop control parameters of solar inverters play a decisive role in their dynamic behavior, and precise fault characteristic analysis is essential for relay protection. However, due to technical confidentiality, manufacturers do not disclose exact parameters, necessitating the identification of these control parameters. This paper addresses the challenge of low sensitivity in integral coefficients and poor identification performance when multiple parameters are identified simultaneously by proposing a novel method that leverages fault and recovery characteristics. By analyzing the system’s current responses during fault occurrence and recovery, the proportional and integral coefficients are separated based on their underlying mechanisms. This separation allows for independent identification using data from distinct control stages, effectively resolving low-sensitivity issues and enhancing identification accuracy. A semi-physical simulation model was developed on the Real-Time Digital Simulator (RTDS) platform, and the method’s effectiveness was validated through simulation data.
The increasing integration of solar inverters into power grids has made their fault current contributions significant. However, the lack of公开 control parameters complicates accurate fault analysis. Most grid-connected solar inverters employ grid-following control strategies, with direct current loop control during low-voltage ride-through (LVRT) periods. Identifying the current loop parameters directly reflects the fault current magnitude of such photovoltaic sources. The core difficulty in parameter identification lies in the underdetermined system model, where the number of equations is fewer than the unknown parameters, leading to non-convergence. Existing approaches can be categorized into rank-augmentation and order-reduction methods.
Rank-augmentation methods increase the number of equations by injecting additional signals, such as time-domain perturbations or frequency-domain excitations, but they often require specialized equipment or models, limiting practical applicability. Order-reduction methods simplify the model or separate parameters to reduce the number of unknowns. For instance, black-box models like Hammerstein-Wiener or NARX reduce parameter counts but may lack accuracy under large disturbances. Other techniques leverage operational condition differences or temporal sequences to separate parameters, yet they often fail to address sensitivity disparities, resulting in inaccurate identification of low-sensitivity parameters like the integral coefficient.
To overcome these limitations, we propose a method that analytically separates the proportional coefficient (Kp) and integral coefficient (Ki) by exploiting the distinct current responses during fault and recovery stages. During faults, the current response is influenced by both parameters, but during the recovery phase, after exponential components decay, the response depends solely on Ki. This separation prevents high-sensitivity parameters from affecting low-sensitivity ones, improving overall accuracy. The method involves data acquisition, coordinate transformation, slope fitting for recovery characteristics, and stepwise parameter optimization using genetic particle swarm algorithms.
The photovoltaic grid-connected system is modeled with a typical structure, as illustrated below, featuring a voltage-source converter with LCL filter and dual-loop control. The system uses decoupling control to compensate for coupling effects and voltage disturbances. Under grid standards, during voltage dips between 20% and 90% of nominal, solar inverters must provide dynamic reactive support for LVRT. Post-fault, active power recovery follows a ramp characteristic with a minimum rate of 30% rated power per second. The control strategy switches to current reference-based operation during faults, with d-axis and q-axis current references set accordingly.
The mathematical model in the dq-frame is derived from Park transformation, ignoring capacitor effects for fundamental frequency analysis. The circuit equations are:
$$ \frac{di_d}{dt} = -\frac{R}{L}i_d + \omega i_q + \frac{1}{L}(u_d – e_d) $$
$$ \frac{di_q}{dt} = -\omega i_d – \frac{R}{L}i_q + \frac{1}{L}(u_q – e_q) $$
where R and L are the equivalent resistance and inductance from the inverter to the point of common coupling (PCC), and ω is the grid angular frequency. The current loop control equations with PI controllers are:
$$ u_d = K_p(i_{dref} – i_d) + K_i \int (i_{dref} – i_d)dt – \omega L i_q + e_d $$
$$ u_q = K_p(i_{qref} – i_q) + K_i \int (i_{qref} – i_q)dt + \omega L i_d + e_q $$
Here, Kp and Ki are the proportional and integral coefficients, respectively. During faults, the references are modified: the d-axis current reference is capped to avoid overcurrent, and the q-axis reference provides reactive support based on voltage dip severity.
Analyzing the fault transient, assuming an instantaneous voltage drop at time t0, the current response exhibits a step response characteristic. Combining the differential equations, the d-axis current can be expressed as:
$$ i_d(t) = C_1 e^{r_1(t-t_0)} + C_2 e^{r_2(t-t_0)} + i_{dref}(t_0^+), \quad t > t_0 $$
where r1 and r2 are roots of the characteristic equation, and C1, C2 are constants derived from initial conditions. Both Kp and Ki influence this response, making simultaneous identification challenging due to sensitivity differences.
During the recovery phase, starting at time t1, the d-axis current reference follows a ramp characteristic:
$$ i_{dref}(t) = k_d (t – t_1) + i_{dref0} $$
where kd is the ramp slope. The current response during recovery is:
$$ i_d(t) = C_3 e^{r_1(t-t_1)} + C_4 e^{r_2(t-t_1)} + k_d (t – t_1) + i_{dref0} + A, \quad t > t_1 $$
After the exponential terms decay, the steady-state error A depends solely on Ki, kd, and R:
$$ A = -\frac{k_d R}{K_i} $$
This allows Ki to be identified independently once kd is determined. The recovery slope kd is fitted from post-fault data using least squares, and data compensation accounts for low-pass filter effects in practical systems.
The stepwise identification procedure is as follows: First, three-phase voltage and current data during fault and recovery are acquired. Phase information is extracted for dq-transformation. Second, the recovery slope kd is identified by fitting filtered data segments until convergence. Third, Ki is optimized using the steady-state error from the recovery phase, with genetic particle swarm algorithms enhancing robustness. Finally, Kp is identified by substituting Ki into the fault-stage equations. Adaptive weight coefficients in the optimization balance global and local search capabilities.
Experimental validation on an RTDS-based hardware-in-the-loop setup confirmed the method’s efficacy. The system parameters included a 10kV grid, LCL filter, and solar inverter controllers with known Kp = 0.285 and Ki = 6.0. Symmetrical faults with varying impedances caused voltage dips to 20%, 30%, and 40% of nominal. The recovery slope kd ranged from 0.6 to 1.0 per unit. Results demonstrated high accuracy, with average errors below 4% for both parameters under noise-free conditions. For instance, with a 20% voltage dip and kd = 0.6, Ki was identified as 6.118 (2.26% error) and Kp as 0.280 (1.75% error).
| Parameter | True Value | Identified Value | Error (%) |
|---|---|---|---|
| Kp | 0.285 | 0.280 | 1.75 |
| Ki | 6.0 | 6.118 | 2.26 |
| kd | 0.6 | 0.598 | 0.33 |
Stability tests over 20 iterations for different voltage dips showed consistent performance, with error variances below 1%. Noise robustness was evaluated by adding Gaussian white noise at signal-to-noise ratios (SNR) of 40 dB, 30 dB, and 20 dB. The method tolerated up to 30 dB SNR, with errors rising to 12.51% for Ki and 15.27% for Kp at 20 dB, indicating practicality for real-world applications.
Comparisons with traditional simultaneous identification methods—using particle swarm, genetic particle swarm, and differential evolution algorithms—revealed that our stepwise approach significantly outperforms in accuracy. For example, simultaneous identification yielded Ki errors over 39%, whereas stepwise identification reduced errors to below 2.57%. This underscores the advantage of parameter separation based on physical insights.
In conclusion, the proposed method effectively identifies current loop control parameters of solar inverters by leveraging fault and recovery characteristics. It separates Kp and Ki through analytical modeling, eliminating cross-sensitivity issues. Experimental results validate its precision and robustness, with errors under 4% in ideal conditions and tolerance to moderate noise. Future work will extend to asymmetric faults and other control strategies. This approach enhances the reliability of protection systems in grids with high solar inverter penetration, ensuring accurate fault analysis and stable operation.
The methodology is independent of the optimization algorithm used, making it versatile. It embodies the physical principle that Type-1 systems exhibit steady-state errors to ramp inputs, which is exploited for parameter decoupling. By focusing on solar inverters, this research contributes to the broader goal of integrating renewable energy sources securely into power networks. The use of advanced identification techniques for solar inverters underscores their critical role in modern energy systems, and the stepwise process ensures that low-sensitivity parameters are accurately captured without interference from high-sensitivity counterparts.