In modern power systems, the integration of photovoltaic (PV) generation has introduced challenges due to its intermittent nature. Large-scale PV plants can significantly impact power flow distribution, and their fluctuations may threaten system frequency and voltage stability. As a key component, solar inverters must possess reliable voltage ride-through capabilities to ensure grid security. This research focuses on developing a method to identify control parameters for solar inverters under fault conditions, leveraging symmetrical and asymmetrical fault sets. By analyzing the electromechanical simulation model structure of solar inverters, critical parameters are defined and tested comprehensively. The proposed approach uses least squares identification to derive model parameters, validated through time-domain simulations, ensuring accuracy for grid integration studies.
The importance of solar inverters in maintaining grid stability cannot be overstated. Solar inverters convert DC power from PV arrays to AC power, and their dynamic response during voltage sags or swells is crucial. Voltage ride-through characteristics, including low-voltage ride-through (LVRT) and high-voltage ride-through (HVRT), are essential for solar inverters to remain connected during disturbances. This study addresses the need for precise parameter identification to enhance simulation models, supporting safe and stable power system operation.
Solar inverters are modeled in electromechanical simulation programs like PSD-BPA, which include multiple modules: PV generation models, steady-state control modules, fault ride-through modules, and protection systems. The fault ride-through module, in particular, handles active and reactive power control during voltage anomalies. Understanding these models is vital for parameter identification, as inaccuracies can lead to unreliable stability assessments. This paper details the structure of these models and the methodology for parameter extraction.
The PV generation model forms the foundation of solar inverter simulations. It is based on the I-V characteristics of PV cells, adjusted for real-world conditions. The output of a PV array depends on temperature and irradiance, and the model equations account for these factors. For instance, the short-circuit current, open-circuit voltage, and maximum power point parameters are scaled using series and parallel connections of solar cells. The key equations are as follows:
First, parameters are normalized under standard conditions (temperature T_ref = 15°C, irradiance S_ref = 1000 W/m²):
$$ T’ = T – T_{\text{ref}} $$
$$ S’ = \frac{S}{S_{\text{ref}}} – 1 $$
$$ I’_{\text{sc}} = I_{\text{sc}} \cdot \frac{S}{S_{\text{ref}}} (1 + a T’) $$
$$ U’_{\text{oc}} = U_{\text{oc}} \cdot (1 – c T’) \ln(e + b S’) $$
$$ I’_{\text{m}} = I_{\text{sc}} \cdot \frac{S}{S_{\text{ref}}} (1 + a T’) $$
$$ U’_{\text{m}} = U_{\text{m}} \cdot (1 – c T’) \ln(e + b S’) $$
Here, I_sc, U_oc, I_m, and U_m represent short-circuit current, open-circuit voltage, current at maximum power, and voltage at maximum power, respectively. Constants a, b, and c are typically set to 0.0015 °C⁻¹, 0.5, and 0.0018 °C⁻¹. The PV cell current is then calculated as:
$$ I_L = I_{\text{sc}} \left[1 – C_1 \left( \exp\left( \frac{V}{C_2 U_{\text{oc}}} \right) – 1 \right) \right] $$
$$ C_1 = \left(1 – \frac{I_m}{I_{\text{sc}}} \right) \exp\left( -\frac{U_m}{C_2 U_{\text{oc}}} \right) $$
$$ C_2 = \left( \frac{U_m}{U_{\text{oc}}} – 1 \right) \left[ \ln \left(1 – \frac{I_m}{I_{\text{sc}}} \right) \right]^{-1} $$
For a PV array, these parameters are scaled based on the number of series (N_se) and parallel (N_sh) connections:
$$ I_{\text{scc-AR}} = N_{\text{sh}} \cdot I_{\text{scc}} $$
$$ I_{\text{mm-AR}} = N_{\text{sh}} \cdot I_{\text{mm}} $$
$$ U_{\text{occ-AR}} = N_{\text{se}} \cdot U_{\text{occ}} $$
$$ U_{\text{mm-AR}} = N_{\text{se}} \cdot U_{\text{mm}} $$
This model ensures that the solar inverter simulation accurately represents the PV array’s behavior under varying environmental conditions. Solar inverters must then manage this power output during grid faults, which is where voltage ride-through capabilities come into play.
Voltage ride-through characteristics for solar inverters are defined by standards such as NB/T 32004-2018. During LVRT, solar inverters must maintain connection and provide active and reactive power support when voltage drops below a threshold (e.g., 0.9 p.u.). Similarly, for HVRT, solar inverters handle overvoltage conditions (e.g., above 1.1 p.u.). The dynamic response involves three phases: the fault period (A and D segments), post-fault hold period (B and E segments), and recovery period (C and F segments). The active and reactive power profiles during these events are critical for grid stability.
For active power control during voltage ride-through, the solar inverter’s strategy is segmented. In the A segment (during fault), the reference active current or power is adjusted based on voltage measurements. The equations are:
$$ I_{P_{\text{ref}}} = K_V \cdot V_t + K_I \cdot I_{P0} + I_{P_{\text{SET}}}, \quad \text{IP\_FLG} = 1 $$
$$ P_{\text{ref}} = K_p \cdot P_0 + P_{\text{SET}}, \quad \text{IP\_FLG} = 2 $$
Here, I_P0 is the initial active current, V_t is the terminal voltage, and P_0 is the initial active power. In the B segment (post-fault hold), the reference active current is set to a percentage of the initial value:
$$ I_{P_{\text{ref}}} = \min( K_I \cdot I_{P0} + I_{P_{\text{SET}}}, I_{P0} ), \quad \text{IP\_FLG2} = 0 $$
The C segment (recovery) involves gradual restoration, such as linear ramping. For reactive power control, similar segments apply. In the D segment (during fault), the reference reactive current is computed as:
$$ I_{Q_{\text{ref}}} = K_V \cdot (V_{\text{SET}} – V_t) + K_I \cdot I_{Q0} + I_{Q_{\text{SET}}}, \quad \text{IQ\_FLG1} = 3 $$
$$ Q_{\text{ref}} = K_Q \cdot Q_0 + Q_{\text{SET}}, \quad \text{IQ\_FLG1} = 2 $$
Where I_Q0 is the initial reactive current and Q_0 is the initial reactive power. The E and F segments handle post-fault hold and recovery, respectively. These models form the basis for parameter identification in solar inverters.
To identify the parameters for solar inverters, extensive testing under symmetrical and asymmetrical faults is conducted. A fault set is designed with voltage disturbances ranging from 20% to 130% of nominal, in 1% steps. This includes three-phase short-circuit faults (symmetrical) and two-phase faults (asymmetrical). Data from manufacturer-provided electromagnetic models are collected and normalized. The test results are summarized in tables below, showing voltage, active power, reactive power, active current, and reactive current for different operating conditions.
For symmetrical faults at high power, the data are as follows:
| Operating Condition | Positive-Sequence Voltage (p.u.) | Active Power (p.u.) | Reactive Power (p.u.) | Active Current (p.u.) | Reactive Current (p.u.) |
|---|---|---|---|---|---|
| 1 | 0.071558 | 0.071558 | 0.071558 | 0.071558 | 0.071558 |
| 2 | 0.265627 | 0.000444 | 0.001983 | 0.282205 | 0.007464 |
| 3 | 0.401587 | 0.000194 | 0.004581 | 0.350683 | 0.011406 |
| 4 | 0.627894 | 0.000194 | 0.007342 | 0.337772 | 0.011693 |
| 5 | 0.903425 | 0.000212 | 0.983387 | 0.121117 | 1.088509 |
| 6 | 1.188283 | 0.000346 | 0.985720 | -0.04728 | 0.829533 |
| 7 | 1.277839 | 0.000587 | 0.984271 | -0.22615 | 0.434138 |
For symmetrical faults at low power, the data are:
| Operating Condition | Positive-Sequence Voltage (p.u.) | Active Power (p.u.) | Reactive Power (p.u.) | Active Current (p.u.) | Reactive Current (p.u.) |
|---|---|---|---|---|---|
| 1 | 0.07186 | 0.00228 | 0.00860 | 0.08217 | 0.11971 |
| 2 | 0.26569 | 0.00025 | 0.00246 | 0.28462 | 0.00925 |
| 3 | 0.40156 | 0.00020 | 0.00503 | 0.35071 | 0.01253 |
| 4 | 0.62789 | 0.00019 | 0.00727 | 0.33778 | 0.01159 |
| 5 | 0.90057 | 0.00018 | 0.19842 | 0.12424 | 0.22033 |
| 6 | 1.18705 | 0.00035 | 0.19791 | -0.0396 | 0.16673 |
| 7 | 1.27664 | 0.00047 | 0.19844 | -0.2223 | 0.15544 |
For asymmetrical faults at high power, the data are:
| Operating Condition | Positive-Sequence Voltage (p.u.) | Active Power (p.u.) | Reactive Power (p.u.) | Active Current (p.u.) | Reactive Current (p.u.) |
|---|---|---|---|---|---|
| 1 | 0.362809 | 0.329424 | -0.04926 | 0.190974 | -0.13576 |
| 2 | 0.495584 | 0.263375 | -0.02925 | 0.262892 | -0.05902 |
| 3 | 0.594578 | 0.21388 | -0.01557 | 0.316415 | -0.02619 |
| 4 | 0.748527 | 0.131575 | 0.000197 | 0.268383 | 0.000264 |
| 5 | 0.936243 | 0.033642 | 0.985321 | 0.120586 | 1.052420 |
| 6 | 1.130007 | 0.065557 | 0.982656 | 0.062156 | 0.869602 |
| 7 | 1.189206 | 0.094632 | 0.977359 | -0.03972 | 0.821858 |
For asymmetrical faults at low power, the data are:
| Operating Condition | Positive-Sequence Voltage (p.u.) | Active Power (p.u.) | Reactive Power (p.u.) | Active Current (p.u.) | Reactive Current (p.u.) |
|---|---|---|---|---|---|
| 1 | 0.363182 | 0.329394 | -0.05124 | 0.189591 | -0.14108 |
| 2 | 0.495588 | 0.263373 | -0.02883 | 0.262819 | -0.05817 |
| 3 | 0.594577 | 0.213882 | -0.01532 | 0.316432 | -0.02576 |
| 4 | 0.748543 | 0.131576 | 0.000161 | 0.268381 | 0.000215 |
| 5 | 0.933531 | 0.033595 | 0.197353 | 0.123777 | 0.211405 |
| 6 | 1.125731 | 0.065810 | 0.196583 | 0.069561 | 0.174627 |
| 7 | 1.186799 | 0.097784 | 0.190591 | -0.03753 | 0.160593 |
These datasets provide a comprehensive view of solar inverter behavior under various fault conditions. The next step involves parameter identification using the least squares method to fit the PSD-BPA model parameters. For symmetrical faults, the active power control parameters are identified as follows:
| Parameter Name | LVRT Value | HVRT Value |
|---|---|---|
| FLG1 | 2 | 1 |
| K_p or K_V | 0.000 | 1 |
| K_I | 0.090 | 0.000 |
| P_SET or I_PSET (A) | -27.1 | 0 |
| FLG2 | 1 | 0 |
| K_I (FLG2) | 0.400 | — |
| I_PSET (A) (FLG2) | 0 | — |
| TIM2 | 0.000 | — |
| FLG3 | 1 | 0 |
| Slope or Time Constant | 12.000 | — |
From this, the active power control strategy for symmetrical faults is derived as:
$$ I_{P_{\text{ref}}} = \begin{cases}
0.09 I_{P0} + 0.104, & 0.1 < V_t < 0.9 \\
P_0, & 0.9 < V_t < 1.2
\end{cases} $$
For asymmetrical faults, the parameters are similar, with the strategy being:
$$ I_{P_{\text{ref}}} = \begin{cases}
0.09 I_{P0} + 0.518, & 0.1 < V_t < 0.93 \\
P_0, & 0.93 < V_t < 1.2
\end{cases} $$
For reactive power control under symmetrical faults, the parameters are:
| Parameter Name | LVRT Value | HVRT Value |
|---|---|---|
| FLG1 | 3 | 3 |
| K_V | 1.501 | 1.610 |
| K_I | 0.000 | 0.000 |
| I_QSET (A) | 382.1 | 286.9 |
| V_SET | 0.900 | 1.100 |
| FLG2 | 0 | 0 |
| FLG3 | 0 | 0 |
The reactive power control strategy for symmetrical faults is:
$$ I_{Q_{\text{ref}}} = \begin{cases}
-1.501 (0.9 – V_t) + 0.124, & 0.1 < V_t < 0.9 \\
-1.610 (1.1 – V_t) + 0.020, & 0.9 < V_t < 1.3
\end{cases} $$
For asymmetrical faults, the reactive parameters are:
| Parameter Name | LVRT Value | HVRT Value |
|---|---|---|
| FLG1 | 3 | 3 |
| K_V | 1.239 | 1.554 |
| K_I | 0.000 | 0.000 |
| I_QSET (A) | 457.7 | 269.3 |
| V_SET | 0.900 | 1.100 |
| FLG2 | 0 | 0 |
| FLG3 | 0 | 0 |
With the strategy:
$$ I_{Q_{\text{ref}}} = \begin{cases}
-1.239 (0.9 – V_t) + 0.173, & 0.1 < V_t < 0.93 \\
-1.554 (1.1 – V_t) + 0.075, & 0.93 < V_t < 1.3
\end{cases} $$
Validation of these identified parameters is performed using PSD-BPA software for time-domain simulations. The results show minimal error between measured and simulated values, adhering to standards such as GB/T 32892-2016. This confirms the reliability of the parameter identification method for solar inverters. The comprehensive testing and least squares fitting ensure that the models accurately represent solar inverter behavior across a wide voltage range (0.1 p.u. to 1.4 p.u.), enhancing their applicability in grid studies.
In conclusion, this study presents a robust methodology for testing and identifying voltage ride-through parameters in solar inverters. By employing symmetrical and asymmetrical fault sets, the control strategies of solar inverters are thoroughly characterized. The use of least squares identification in PSD-BPA models yields high-precision parameters, validated through simulations. This approach ensures that solar inverters can be accurately modeled for grid integration, contributing to improved power system stability and reliability. Future work could extend this method to other inverter-based resources, further advancing renewable energy integration.