The proliferation of grid-connected photovoltaic (PV) generation has transformed modern power systems. As the penetration level of solar energy increases, the dynamic interaction between PV power plants and the grid becomes critically important, particularly during grid disturbances. The solar inverter, serving as the sole grid interface for the PV array, governs this interaction. Its behavior during grid voltage sags, defined as its Low-Voltage Ride-Through (LVRT) capability, is therefore a fundamental aspect of grid stability. Mastering the LVRT characteristics of the solar inverter is paramount for accurately analyzing the impact of large-scale PV integration on power system dynamics, including transient stability and voltage recovery.
However, analyzing the LVRT characteristics of a commercial solar inverter presents a classic “grey-box” challenge. While the power circuit topologies (e.g., two-level, three-level, T-type) and overarching control structures (e.g., vector control in the synchronous reference frame) are generally known and documented, the precise implementation of control strategies, logic switching conditions, and all internal controller parameters are almost always proprietary information held closely by manufacturers. This lack of transparency means we cannot rely solely on white-box, first-principles modeling. Conversely, a purely black-box, input-output characterization lacks the structural understanding necessary for developing generalized models or extrapolating behavior to untested conditions. Therefore, a structured, systems-level approach is required to deconstruct the solar inverter into identifiable subsystems, analyze their influence on the overall LVRT response, and develop methodologies to extract the key governing parameters from standardized tests.
This work adopts such an approach. First, based on a review of common topologies and control objectives, the internal functional blocks of a typical grid-connected solar inverter are consolidated into three primary sequential stages: the DC-Link Voltage Transformation Stage, the AC Current Command Generation Stage, and the AC Current Tracking Stage. This decomposition, applicable to both central and string solar inverter architectures, provides a framework for targeted analysis.
The DC-Link Voltage Transformation Stage is responsible for managing the power flow from the PV source to the DC-link capacitor. In a two-stage solar inverter, this typically involves a DC-DC converter (e.g., a Boost converter) performing Maximum Power Point Tracking (MPPT). During an LVRT event, the MPPT is usually suspended, and this stage switches to a protective control mode to prevent excessive DC-link overvoltage. A common control law in this mode is:
$$ d = d_0 – K_{Udc} (U_{dc} – U_{dc}^{max}) $$
where \(d\) is the duty cycle, \(d_0\) is the pre-fault duty cycle, \(K_{Udc}\) is a proportional control gain, \(U_{dc}\) is the measured DC-link voltage, and \(U_{dc}^{max}\) is the allowed maximum voltage. The objective is to limit the DC-link voltage rise caused by the power imbalance when the AC-side power output drops suddenly due to the voltage sag.
The AC Current Command Generation Stage is the core logic unit that defines the solar inverter‘s grid support functions. During normal operation, it generates current references (\(i_{d,ref}\), \(i_{q,ref}\)) for active and reactive power control or voltage support. Upon detection of a voltage dip below a threshold (e.g., 0.9 p.u.), it immediately switches to an LVRT current reference algorithm mandated by grid codes like GB/T 19964-2012. A typical form of this algorithm is:
$$ i_{q,ref} = \min( K_{q,LV} \cdot (U_{LV} – U_{term}), I_{q}^{max} ) $$
$$ i_{d,ref} = I_{d,LVRT} $$
where \(K_{q,LV}\) is the reactive current support coefficient, \(U_{LV}\) is the LVRT entry threshold voltage (e.g., 0.9 p.u.), \(U_{term}\) is the terminal voltage, \(I_{q}^{max}\) is the maximum allowable current, and \(I_{d,LVRT}\) is a limited active current reference. After fault clearance, the active current reference often ramps up with a defined slope \(K_{id,ref}\) to prevent inrush currents.
The AC Current Tracking Stage encompasses the inner current control loops (typically PI regulators in the dq-frame), the PWM modulator, and the power semiconductor bridge. Its function is to force the actual output currents (\(i_d\), \(i_q\)) to rapidly and accurately follow the references (\(i_{d,ref}\), \(i_{q,ref}\)) provided by the previous stage. This stage is designed for high bandwidth and fast response, typically achieving reference tracking within a few milliseconds.
The complete LVRT transient can be understood through the interaction of these stages. When a symmetrical voltage sag occurs:
- The AC Current Command Generation Stage detects the low voltage and switches its output references according to the LVRT algorithm, drastically reducing \(i_{d,ref}\) and increasing \(i_{q,ref}\).
- The AC Current Tracking Stage responds quickly, forcing the actual AC-side currents to the new references. Consequently, the AC-side active power \(P_{ac} \approx 1.5 \cdot u_d \cdot i_{d,ref}\) drops sharply.
- This creates a power imbalance: the PV array still injects power \(P_{pv}\) into the DC-link, but the power leaving via the inverter \(P_{ac}\) is now much smaller. The excess power charges the DC-link capacitor, causing \(U_{dc}\) to rise: $$ C \cdot U_{dc} \frac{dU_{dc}}{dt} = P_{pv} – P_{ac} $$.
- The rising \(U_{dc}\) triggers the DC-Link Voltage Transformation Stage’s protective control. By adjusting the duty cycle \(d\), it increases the PV array voltage \(U_{pv}\), moving the operating point away from the maximum power point on the P-V curve, thereby actively reducing \(P_{pv}\) to eventually re-establish power balance at a lower level.
This coupling illustrates that while all stages participate, their influence on the observable AC-side electrical characteristics (currents, powers) varies significantly.
To quantitatively assess the sensitivity of the overall LVRT response to each stage, time-domain electromagnetic transient (EMT) simulations of detailed solar inverter models are instrumental. By varying parameters or even the fundamental structure of one stage while keeping others constant, and comparing the resulting AC-side outputs, the dominant stage can be identified. The following analysis summarizes findings from such simulation studies.
Influence of the DC-Link Voltage Transformation Stage: This stage primarily affects the DC-side dynamics (\(U_{dc}\), \(U_{pv}\)). Its parameters, such as the voltage limit \(U_{dc}^{max}\) and the proportional gain \(K_{Udc}\), have a strong impact on the magnitude and shape of the DC-link overvoltage transient. However, its influence on the steady-state AC-side active and reactive power output during the fault is relatively minor, due to the decoupling effect of the DC-link capacitor and the primary control exerted by the current references. It can, however, influence overshoots during control mode transitions. The table below summarizes simulation results for a string solar inverter under different parameter sets for this stage during a voltage sag to 0.5 p.u.
| Parameter Set | \(U_{dc}^{max}\) (p.u.) | \(K_{Udc}\) | Max \(U_{dc}\) (p.u.) | Impact on AC Power P, Q |
|---|---|---|---|---|
| Set A | 1.05 | 0.001 | 1.08 | Negligible change in steady-state |
| Set B | 1.00 | 0.001 | 1.05 | Negligible change in steady-state |
| Set C | 0.95 | 0.002 | 1.03 | Negligible change in steady-state |
Influence of the AC Current Command Generation Stage: This stage is unequivocally the dominant factor for the AC-side LVRT characteristics. Its parameters directly and decisively determine the magnitude of reactive current support, the level of active current retention, and the recovery rate post-fault. Changes in its parameters (\(K_{q,LV}\), \(I_{d,LVRT}\), \(K_{id,ref}\)) lead to direct and substantial changes in the measured AC currents and powers. Furthermore, because active power output couples back to the DC-side, this stage also indirectly but significantly influences DC-link voltage dynamics. Simulation results clearly demonstrate this dominant effect.
| Parameter Changed | Effect on LVRT AC-Side Response |
|---|---|
| Increase \(K_{q,LV}\) | Higher reactive current \(I_q\) injection during sag, stronger grid voltage support. |
| Increase \(I_{d,LVRT}\) | Higher retained active power \(P\) during sag, shorter power recovery time after fault. |
| Increase \(K_{id,ref}\) | Faster active power ramp-up after fault clearance, shorter recovery time. |
Influence of the AC Current Tracking Stage: The influence of this stage is generally the weakest among the three for LVRT analysis, provided it is properly designed and stable. Its main role is to faithfully execute the commands from the previous stage. Variations in the power circuit topology (e.g., two-level vs. three-level NPC) or minor tuning of the current controller PI gains have minimal impact on the fundamental shape and magnitude of the AC current and power waveforms during the LVRT sequence. The primary differences may manifest as slight variations in high-frequency switching harmonics, minor oscillations in the DC-link midpoint voltage for three-level topologies, or small differences in overshoot during transitions. For large-scale power system stability studies where fundamental frequency behavior is of interest, this stage can often be simplified or even idealized as a perfect controlled current source with a small time delay.
This sensitivity analysis leads to a crucial conclusion: for the purpose of analyzing and modeling the solar inverter‘s interaction with the grid during LVRT events—focusing on its fundamental frequency current and power output—the AC Current Command Generation Stage is the key governing subsystem. Therefore, the problem of characterizing an unknown commercial solar inverter largely reduces to the problem of identifying the structure and parameters of its internal LVRT current reference algorithms.
Based on this premise, a generalized, practical parameter testing method is proposed. The goal is to empirically determine the LVRT current command formulas without prior knowledge of the manufacturer’s code. The test setup follows standard guidelines, comprising a programmable DC source (simulating the PV array), the unit under test (solar inverter), and a grid disturbance generator capable of creating precise voltage sags at the Point of Common Coupling (PCC).
Testing and Identification Procedure:
- Pre-Fault Operating Points: Conduct multiple tests, varying the pre-fault operating condition of the solar inverter. This should include combinations of high/medium/low active power levels (e.g., 1.0, 0.5, 0.2 p.u.) and different reactive power setpoints (zero, inductive, capacitive).
- Fault Scenarios: For each operating point, apply symmetrical three-phase voltage sags to different depth ranges (e.g., 0-0.2, 0.3-0.5, 0.6-0.8 p.u.). The duration should comply with relevant grid codes.
- Data Acquisition & Steady-State Extraction: Record high-sampled voltage and current waveforms. For each test, calculate the pre-fault steady-state values (\(P_0\), \(Q_0\), \(I_{d0}\), \(I_{q0}\), \(U_0\)) and the steady-state values during the fault plateau (\(P_{LV}\), \(Q_{LV}\), \(I_{d,LV}\), \(I_{q,LV}\), \(U_{term}\)). Also, measure the ramp rate of active current recovery after fault clearance.
- Repeatability: Key tests should be repeated to ensure consistency of results.
- Parameter Identification for Current Commands: This is the core step. The measured steady-state fault currents (\(I_{d,LV}\), \(I_{q,LV}\)) are assumed equal to the internal references (\(i_{d,ref}\), \(i_{q,ref}\)). A generic form for the reactive current command is hypothesized:
$$ I_{q,LV} = \min( K_{q,LV} (U_{LV} – U_{term}) + K_{flag} I_{q0} + I_{q0,LV},\ I_{max} ) $$
The parameters \(K_{q,LV}\) (reactive support factor), \(U_{LV}\) (entry threshold, often 0.9), \(K_{flag}\) (dependency on pre-fault Q), \(I_{q0,LV}\) (offset), and \(I_{max}\) (current limit) are to be identified.- \(I_{max}\) is found as the maximum observed current magnitude across all tests.
- \(K_{flag}\) is determined by checking if tests from the same voltage depth but different pre-fault \(I_{q0}\) yield the same \(I_{q,LV}\). If yes, \(K_{flag}=0\); else, \(K_{flag}=1\).
- For data points not limited by \(I_{max}\), the equation becomes linear: \(I_{q,LV} = K_{q,LV} (U_{LV} – U_{term}) + K_{flag} I_{q0} + I_{q0,LV}\). Using multiple test data points (\(U_{term,i}\), \(I_{q0,i}\), \(I_{q,LV,i}\)), a linear least-squares regression solves for \(K_{q,LV}\) and \(I_{q0,LV}\).
- Active Current Command Identification: The active current command often has different possible structures. Common forms include:
- Priority on reactive current, active limited by total current: \(I_{d,LV} = \min( P_0/U_{term},\ \sqrt{I_{max}^2 – I_{q,LV}^2} )\)
- Priority on reactive current, simple subtraction: \(I_{d,LV} = \min( P_0/U_{term},\ I_{max} – |I_{q,LV}| )\)
- Independent active current reference: \(I_{d,LV} = K_1 I_{d0} + K_2 U_{term} + I_{d0,LV}\)
The identification process involves testing each hypothesized form. For each form, calculate the estimated active current \(I_{d,est,i}\) for every test \(i\) using the already-identified \(I_{q,LV}\) and measured values. Then compute the Residual Sum of Squares (RSS) between the estimates and the measured \(I_{d,LV,i}\):
$$ RSS = \sum_{i=1}^{n} (I_{d,est,i} – I_{d,LV,i})^2 $$
The form that yields the smallest RSS is selected as the correct structure, and its parameters (\(I_{max}\), \(K_1\), \(K_2\), etc.) are identified accordingly, often via least-squares fitting for linear forms or direct observation for limits. - Model Validation: The final step is to implement the identified command formulas into a simulation model (e.g., an average model in EMT software) of the solar inverter. The model is then subjected to the same voltage sag tests, and its simulated outputs (currents, powers) are quantitatively compared against the actual test measurements. Standard metrics like mean deviation and maximum deviation in pre-fault, fault, and post-fault intervals are used to validate the accuracy of the identified parameters.
This methodology’s effectiveness and universality have been validated through laboratory testing on both string and central solar inverter units from different manufacturers. For a 36 kW string solar inverter, testing revealed an LVRT algorithm where the reactive current was governed by \(i_{q,ref} = \min(2 \times (0.9 – U_{term}),\ 1.08)\) and the active current was fixed at \(i_{d,ref} = 0.16\) p.u. For a 500 kW central solar inverter, the identified algorithm was \(i_{q,ref} = \min(1.53 \times (0.9 – U_{term}),\ 1.05)\) and \(i_{d,ref} = \min( P_0/U_{term},\ 1.05 – |i_{q,ref}| )\). In both cases, simulation models using only these identified command formulas—while employing generic, non-manufacturer-specific parameters for the DC-link control and current tracking stages—achieved excellent agreement with experimental results. The table below shows sample validation metrics for the central inverter during a deep sag test, demonstrating the model’s accuracy.
| Validation Interval | Metric | Voltage (p.u.) | Current (p.u.) | Active P (p.u.) | Reactive Q (p.u.) |
|---|---|---|---|---|---|
| Fault (Steady-State) | Mean Dev. (F1) | 0.0018 | 0.0334 | 0.0069 | 0.0043 |
| Fault (Steady-State) | Max Dev. (F3) | 0.0019 | 0.0748 | 0.0069 | 0.0101 |
| Post-Fault Recovery | Mean Dev. (F1) | 0.0148 | 0.0152 | 0.0039 | 0.0095 |
| Overall Weighted (FG) | Weighted Dev. | 0.0164 | 0.0270 | 0.0085 | 0.0056 |
In conclusion, the low-voltage ride-through behavior of a grid-connected solar inverter, while complex, can be systematically analyzed by deconstructing the system into three functional stages. Among these, the AC Current Command Generation Stage is identified as the dominant subsystem governing the essential grid-support characteristics during faults. When internal control strategies are unknown, a practical and generalizable parameter testing method focused on identifying this stage’s algorithms proves highly effective. By applying controlled voltage sags and analyzing the steady-state current response, the key parameters of the reactive and active current reference formulas can be accurately extracted. This approach, validated on both string and centralized solar inverter technologies, provides a powerful “grey-box” solution for obtaining accurate models necessary for power system planning, stability analysis, and integration studies of high-penetration photovoltaic generation. Future work may investigate the extended application of this methodology under weak grid conditions, where the impedance of the network significantly interacts with the solar inverter control, potentially altering the dominance hierarchy of the internal stages.