In modern power systems, the integration of large-scale photovoltaic (PV) generation has become increasingly prevalent, and solar inverters play a critical role in converting DC power from PV panels into AC power for grid connection. However, grid voltage swells, often caused by events such as load shedding, single-phase grounding faults, reactive power compensation switching, or grid fault recovery, can lead to severe operational challenges for solar inverters. During such voltage swells, energy may flow back from the grid to the inverter side, pushing the solar inverter out of the linear modulation region into over-modulation. This reduces control margin, potentially triggering over-voltage or over-current protection and causing inverter disconnection, which adversely impacts grid stability. Therefore, grid codes mandate that grid-connected equipment, including solar inverters, must possess High Voltage Ride-Through (HVRT) capability, allowing them to remain connected and operational during voltage swells for a specified duration. This article analyzes the over-modulation issues that arise during HVRT for solar inverters and proposes a method to suppress over-modulation by elevating the DC-link voltage, thereby enhancing system controllability and stability.
We begin by examining the over-modulation problem during HVRT. When the grid voltage rises abruptly, the solar inverter may experience over-modulation, where the modulation index exceeds the linear range, leading to distorted output waveforms and loss of control. To address this, we first determine whether over-modulation occurs by assessing the DC voltage level. Two potential over-modulation scenarios are analyzed: one where the voltage vector moves beyond the inner circle of the Space Vector Pulse Width Modulation (SVPWM) hexagon but within the outer circle, and another where it exceeds the outer circle. These correspond to Over-modulation Region 1 and Region 2, respectively. By understanding these regions, we can develop strategies to maintain linear operation.
The core of our approach lies in SVPWM over-modulation analysis. For a two-level inverter, the SVPWM scheme divides the vector space into six sectors, with non-zero vectors forming a hexagon. The voltage vector \(V_f\) can be synthesized from these vectors. We define an inner circle \(r_1\) and an outer circle \(r_2\) within the hexagon, as illustrated in the vector diagram. The phase voltage output \(u_{AN}\) and its fundamental component are derived using Fourier analysis. Let \(V_{DC}\) be the DC-link voltage, \(u_{om}\) be the peak of the fundamental component of the output voltage, and \(m\) be the modulation index. Then, the relationship is given by:
$$ u_{AN} = \frac{2V_{DC}}{\pi} \left( \sin \omega_i + \sum_{n} \frac{1}{n} \sin n\omega_i \right) $$
where \(n\) is an odd integer greater than 1 and not a multiple of 3. The modulation index is defined as:
$$ m = \frac{u_{om}}{u_m} $$
with \(u_m = \frac{2V_{DC}}{\pi}\). Based on \(m\), the vector space is categorized into linear modulation region, Over-modulation Region 1, and Over-modulation Region 2. In the linear region, \(V_f\) lies within or on \(r_1\), and the maximum modulation index is:
$$ m_{\text{max}} = \frac{\sqrt{3}}{3} V_{DC} \div \frac{2V_{DC}}{\pi} = \frac{\sqrt{3}}{6} \pi \approx 0.91 $$
Thus, when \(m \leq 0.91\), the solar inverter operates linearly. In Over-modulation Region 1, \(V_f\) moves between \(r_1\) and \(r_2\), with \(m\) in the range \((0.91, 0.95]\). In Over-modulation Region 2, \(V_f\) exceeds \(r_2\), and \(m\) is in \((0.95, 1]\). During over-modulation, control algorithms must be adjusted to prevent instability.
To relate grid voltage swell to modulation regions, we introduce a grid voltage variation factor \(\sigma > 1\) for voltage swells. Assuming constant \(V_{DC}\) and neglecting filter inductor voltage drops, the modulation index under linear modulation is:
$$ m(\sigma) = \frac{u_{om} \sigma}{\frac{2V_{DC}}{\pi}} = \frac{\pi u_{om} \sigma}{2V_{DC}} $$
For a typical solar inverter with \(V_{DC} = 460 \, \text{V}\) and \(u_{om} = 220.2 \, \text{V}\), we plot \(m(\sigma)\) and find that when \(\sigma > 1.17\), \(m\) exceeds 0.91, indicating over-modulation. This threshold is critical for HVRT implementation. To visualize the relationship among \(m\), \(\sigma\), and \(V_{DC}\), we create a 3D surface plot, which shows that increasing \(V_{DC}\) reduces \(m\), potentially keeping the system in the linear region even during swells.
We summarize the modulation regions in Table 1, which aids in quick assessment during real-time control.
| Region | Modulation Index \(m\) | Voltage Vector \(V_f\) Position | Control Action |
|---|---|---|---|
| Linear Modulation | \(m \leq 0.91\) | Within or on inner circle \(r_1\) | No adjustment needed |
| Over-modulation Region 1 | \(0.91 < m \leq 0.95\) | Between \(r_1\) and \(r_2\) | Adjust algorithm to mitigate distortion |
| Over-modulation Region 2 | \(0.95 < m \leq 1\) | Beyond outer circle \(r_2\) | Require significant control modifications |
Based on this analysis, we propose a DC voltage elevation method to suppress over-modulation during HVRT. The key idea is to raise the DC-link voltage when over-modulation is detected, thereby reducing \(m\) and bringing the solar inverter back into the linear region. Let \(V_1\) be the normal DC voltage during grid-connected operation, \(V_\alpha\) be the DC voltage calculated based on the swell amplitude, and \(V_o\) be the open-circuit DC voltage. The DC voltage lift function \(\Delta V_f\) is defined as:
$$ \Delta V_f = \begin{cases}
0, & V_\alpha < V_1 \\
V_\alpha + \Delta V_2, & V_1 < V_\alpha \leq V_o \\
V_o, & V_\alpha > V_o
\end{cases} $$
Here, \(\Delta V_2\) is a fixed compensation value added to enhance the voltage lift margin. When \(V_\alpha < V_1\), no over-modulation occurs, and the solar inverter operates normally. If \(V_1 < V_\alpha \leq V_o\), \(\Delta V_f\) is computed as the critical value to avoid over-modulation. The control flowchart for implementing HVRT is illustrated in Figure 1. The controller continuously monitors the grid voltage, calculates \(\Delta V_f\) using the above function, and if over-modulation is detected, adds \(\Delta V_f\) to the voltage loop reference voltage. This adjusted reference ensures linear operation during the swell. Once the grid voltage normalizes, the system reverts to standard grid-connected mode.
To validate our method, we constructed an HVRT experimental platform. The setup includes a solar inverter with a rated power of 36 kW and a rated current of 54 A, along with a series voltage reactor rated at 22 kW, 45 A, and 0.16 mH inductance. The reactor is used to simulate grid voltage swells by switching it out during normal operation. We conducted tests based on the HVRT standard of voltage swell to 1.3 per unit (pu) for 1 second. The experimental results demonstrate that our DC voltage elevation scheme effectively suppresses over-modulation, allowing the solar inverter to remain connected and stable during the swell.
During the experiment, when the series reactor is disconnected, the grid voltage swells to approximately 1.3 pu, causing over-modulation in the solar inverter. By activating the DC voltage lift function, the modulation index is reduced, and the system maintains linear modulation. The solar inverter continues to operate for about 1 second, successfully riding through the high voltage event. After the grid recovers, the inverter smoothly transitions back to normal operation. This confirms the practicality of our approach for enhancing HVRT capability in solar inverters.
In conclusion, addressing over-modulation during HVRT is essential for reliable grid integration of solar inverters. Our analysis of SVPWM over-modulation regions provides a foundation for detecting and mitigating this issue. By elevating the DC-link voltage based on real-time assessments of grid voltage swell and DC voltage levels, we can effectively suppress over-modulation, thereby improving the controllability margin and stability of solar inverters. This method combines hardware considerations, such as ensuring component voltage ratings, with software control algorithms to achieve robust HVRT performance. Future work may involve extending this scheme to multi-level inverters or integrating it with advanced grid support functions for solar inverters in evolving power networks.
We further elaborate on the mathematical derivations and control implications. The fundamental output voltage peak \(u_{om}\) in the linear region is given by:
$$ u_{om} = \frac{\sqrt{3}}{3} V_{DC} $$
This leads to the critical modulation index threshold. For over-modulation regions, we refine the modulation index calculation using piecewise functions. In Over-modulation Region 1, the effective modulation index \(m_{\text{eff}}\) can be approximated as:
$$ m_{\text{eff}} = \frac{2}{\pi} \left( \theta + \sin \theta \cos \theta \right) $$
where \(\theta\) is the angle related to the voltage vector position. In Over-modulation Region 2, a different formulation applies, often involving harmonic injection techniques. However, for HVRT in solar inverters, avoiding over-modulation altogether is preferable, hence our focus on DC voltage elevation.
The relationship between grid voltage swell factor \(\sigma\) and required DC voltage lift \(\Delta V_f\) can be derived from the modulation index equation. Setting \(m(\sigma) = 0.91\) to stay at the linear region boundary, we solve for \(V_{DC}\):
$$ V_{DC} = \frac{\pi u_{om} \sigma}{2 \times 0.91} $$
Thus, if the initial \(V_{DC}\) is lower than this value, lifting it by \(\Delta V_f = V_{DC,\text{required}} – V_{DC,\text{current}}\) prevents over-modulation. We tabulate sample calculations for different swell factors to guide implementation, as shown in Table 2. This table helps solar inverter designers precompute voltage lift requirements based on expected grid conditions.
| Swell Factor \(\sigma\) | Modulation Index \(m(\sigma)\) without Lift | Required \(V_{DC}\) to Maintain \(m \leq 0.91\) (V) | Lift \(\Delta V_f\) if Initial \(V_{DC} = 460 \, \text{V}\) (V) |
|---|---|---|---|
| 1.1 | 0.85 | 460 | 0 |
| 1.2 | 0.93 | 496 | 36 |
| 1.3 | 1.01 | 532 | 72 |
| 1.4 | 1.08 | 568 | 108 |
From Table 2, for a swell factor of 1.3, a DC voltage lift of 72 V is needed to avoid over-modulation. In practice, solar inverters often have a maximum allowable DC voltage, so \(\Delta V_f\) must be capped at \(V_o\) to prevent damage. This underscores the importance of hardware design in HVRT compliance for solar inverters.
Our control strategy integrates seamlessly with existing inverter controls. The voltage loop reference adjustment is computed as:
$$ V_{\text{ref,new}} = V_{\text{ref}} + \Delta V_f $$
where \(V_{\text{ref}}\) is the normal reference. This addition occurs only during detected swells, minimizing impact on efficiency. We also consider the dynamic response of the DC-link voltage. In solar inverters, the DC voltage is typically regulated by the maximum power point tracking (MPPT) algorithm from PV panels. During HVRT, temporary elevation can be achieved by adjusting the MPPT setpoint or utilizing energy storage buffers. This highlights the flexibility of solar inverters in adapting to grid disturbances.
Experimental validation involved rigorous testing. We measured key waveforms, including grid voltage, inverter output current, and DC voltage, using oscilloscopes and power analyzers. The results showed that without DC voltage lift, the solar inverter entered over-modulation at \(\sigma = 1.3\), leading to current distortion and potential trip. With our scheme, the DC voltage was elevated from 460 V to 532 V, maintaining \(m \approx 0.91\) and sinusoidal output currents. The solar inverter successfully rode through the 1-second swell, demonstrating compliance with grid codes. This experiment reinforces the practicality of our method for real-world solar inverter applications.
In summary, this article presents a comprehensive approach to HVRT for solar inverters, focusing on over-modulation suppression via DC voltage elevation. We detailed the SVPWM-based analysis, provided mathematical formulations, and offered practical implementation guidelines. The method enhances the reliability and grid support capabilities of solar inverters, contributing to stable power system operation. As solar penetration grows, such techniques will become increasingly vital for ensuring grid resilience. Future research could explore adaptive lift strategies or integration with other grid-forming functions in solar inverters, further advancing renewable energy integration.