As a researcher in power electronics and grid integration, I have extensively studied the challenges faced by solar inverters during grid disturbances. The increasing penetration of large-capacity photovoltaic (PV) systems into the grid has highlighted critical issues related to voltage stability. Specifically, grid voltage swells—often caused by single-phase ground faults, sudden load disconnections, switching of reactive power compensation devices, or grid recovery after faults—can lead to voltage rises that exceed normal limits. When grid voltage abruptly increases, it can cause reverse power flow from the grid side, pushing solar inverters out of their linear operating region and into over-modulation. This reduces control margin and triggers over-voltage and over-current protections, resulting in inverter disconnection. Such disconnections adversely impact grid stability and reliability. Therefore, grid codes mandate that grid-connected equipment, including solar inverters, must withstand voltage swells for a specified duration while maintaining normal operation—a capability known as High Voltage Ride-Through (HVRT). This article analyzes the HVRT requirement for a grid voltage swell of 1.3 per unit (pu) lasting 1 second and proposes a strategy to suppress over-modulation by elevating the DC-link voltage, ensuring reliable performance of solar inverters during such events.
The core issue during HVRT is over-modulation, which occurs when the grid voltage swell forces the inverter’s modulation index beyond its linear range. To address this, we must first detect over-modulation and implement control measures to prevent inverter tripping. HVRT involves both hardware and software aspects: hardware must be designed to withstand elevated voltages (e.g., contactors and control power supplies rated for 1.3 pu for at least 1 second), while software algorithms monitor grid voltage and DC-link voltage in real-time to identify over-modulation conditions. Upon detection, HVRT control is activated to regulate output current and elevate DC voltage, thereby mitigating over-modulation. Once grid voltage normalizes, the system resumes standard grid-tied operation. This analysis focuses on the over-modulation phenomenon in two-level Space Vector Pulse Width Modulation (SVPWM) inverters, examining the relationship between voltage swell magnitude, DC voltage, and modulation index. We propose a concrete method to suppress over-modulation during HVRT, supported by theoretical derivations and experimental validation.
Analysis of Over-Modulation During HVRT
Over-modulation in solar inverters arises when the grid voltage swell increases the required output voltage beyond the inverter’s linear modulation capability. In SVPWM control for two-level inverters, the voltage space vector diagram is divided into six sectors, with the vertices of six non-zero vectors forming a hexagon. The inner circle of this hexagon represents the linear modulation region, while the area between the inner and outer circles corresponds to over-modulation regions. Let us define key parameters: the DC-link voltage is \(V_{DC}\), the peak of the output phase voltage fundamental component is \(u_{om}\), and the modulation index is \(m\). The output phase voltage \(u_{AN}\) can be expressed using Fourier analysis:
$$ u_{AN} = \frac{2V_{DC}}{\pi} \left[ \sin(\omega t) – \frac{1}{5}\sin(5\omega t) – \frac{1}{7}\sin(7\omega t) + \frac{1}{11}\sin(11\omega t) + \frac{1}{13}\sin(13\omega t) – \cdots \right] $$
where \(\omega\) is the angular frequency. The fundamental peak voltage is:
$$ u_{om} = \frac{2V_{DC}}{\pi} m $$
In the linear modulation region, the maximum fundamental peak occurs when the voltage vector lies on the inner circle, giving:
$$ u_{om,max} = \frac{V_{DC}}{\sqrt{3}} $$
Thus, the maximum modulation index in linear region is:
$$ m_{max} = \frac{\pi}{2\sqrt{3}} \approx 0.91 $$
When \(m \leq 0.91\), the solar inverter operates in linear modulation without distortion. For \(m > 0.91\), the system enters over-modulation regions: Over-modulation Region I (\(0.91 < m \leq 0.95\)) and Over-modulation Region II (\(0.95 < m \leq 1\)). In these regions, control algorithms must be adjusted to maintain output within the hexagon boundaries.
To relate over-modulation to grid voltage swells, consider a voltage swell factor \(\sigma > 1\), where the grid voltage peak becomes \(\sigma u_{om}\). Neglecting filter inductor voltage drops and assuming constant \(V_{DC}\) during the swell, the modulation index during the swell is:
$$ m(\sigma) = \frac{\pi \sigma u_{om}}{2 V_{DC}} $$
For a nominal system with \(V_{DC} = 460 \, \text{V}\) and \(u_{om} = 220.2 \, \text{V}\) (corresponding to 311 V peak line-to-line voltage), we can plot \(m(\sigma)\). The critical point occurs when \(m = 0.91\), corresponding to \(\sigma \approx 1.17\). Therefore, for voltage swells with \(\sigma > 1.17\), over-modulation is inevitable. This underscores the need for HVRT strategies in solar inverters to handle common grid faults where swells can reach 1.3 pu.
The relationship between modulation index \(m\), swell factor \(\sigma\), and DC voltage \(V_{DC}\) is further illustrated by a three-dimensional surface derived from:
$$ m(\sigma, V_{DC}) = \frac{\pi \sigma u_{om}}{2 V_{DC}} $$
This surface shows that for higher \(V_{DC}\), \(m\) decreases, keeping the system in linear modulation even for larger \(\sigma\). Below is a table summarizing the modulation index thresholds for different swell factors at fixed DC voltage:
| Swell Factor (\(\sigma\)) | Modulation Index (\(m\)) at \(V_{DC} = 460 \, \text{V}\) | Operating Region |
|---|---|---|
| 1.0 | 0.75 | Linear |
| 1.1 | 0.83 | Linear |
| 1.17 | 0.91 | Linear/Over-modulation Boundary |
| 1.2 | 0.93 | Over-modulation I |
| 1.3 | 1.01 | Over-modulation II |
This table confirms that solar inverters face over-modulation during typical HVRT scenarios, necessitating active control measures.
HVRT Strategy: DC Voltage Elevation for Over-Modulation Suppression
To enable HVRT in solar inverters, we propose a control strategy that elevates the DC-link voltage during grid voltage swells, thereby reducing the modulation index and suppressing over-modulation. The approach is based on real-time monitoring of grid voltage and DC voltage. Define \(V_1\) as the normal DC voltage during grid-tied operation, \(V_\alpha\) as the DC voltage required to maintain linear modulation during a swell of factor \(\sigma\), and \(V_o\) as the open-circuit DC voltage of the PV array. The DC voltage elevation function \(\Delta V_f\) is given by:
$$ \Delta V_f =
\begin{cases}
0 & \text{if } V_\alpha \leq V_1 \\
V_\alpha – V_1 + \Delta V_2 & \text{if } V_1 < V_\alpha \leq V_o \\
V_o – V_1 + \Delta V_2 & \text{if } V_\alpha > V_o
\end{cases} $$
where \(\Delta V_2\) is a fixed compensation margin to account for dynamic variations. Here, \(V_\alpha\) is calculated from the swell condition to keep \(m \leq 0.91\):
$$ V_\alpha = \frac{\pi \sigma u_{om}}{2 m_{max}} = \frac{\pi \sigma u_{om}}{2 \times 0.91} $$
If \(V_\alpha \leq V_1\), no over-modulation occurs, and the solar inverter operates normally. If \(V_1 < V_\alpha \leq V_o\), over-modulation is imminent, and DC voltage is elevated by \(\Delta V_f\). If \(V_\alpha > V_o\), the PV array cannot provide sufficient voltage, and the system relies on \(\Delta V_2\) for minimal ride-through capability.
The control flowchart for implementing HVRT in solar inverters is as follows:
- Continuously monitor grid voltage amplitude and detect swells exceeding a threshold (e.g., \(\sigma > 1.1\)).
- Calculate \(V_\alpha\) based on the measured swell factor \(\sigma\).
- Compute \(\Delta V_f\) using the above piecewise function.
- If \(\Delta V_f > 0\), adjust the voltage reference in the DC-link controller to elevate DC voltage by \(\Delta V_f\).
- Regulate output current to maintain grid synchronization and power quality.
- Once grid voltage returns to normal, ramp down DC voltage to \(V_1\) and resume standard operation.
This strategy ensures that solar inverters remain in linear modulation during HVRT events, enhancing control margin and stability.
To validate the effectiveness of DC voltage elevation, consider a numerical example. Assume a solar inverter with \(V_1 = 460 \, \text{V}\), \(u_{om} = 220.2 \, \text{V}\), and \(V_o = 600 \, \text{V}\). For a swell of \(\sigma = 1.3\), we compute \(V_\alpha\):
$$ V_\alpha = \frac{\pi \times 1.3 \times 220.2}{2 \times 0.91} \approx 518 \, \text{V} $$
Since \(V_1 < V_\alpha < V_o\), we have \(\Delta V_f = 518 – 460 + \Delta V_2\). With \(\Delta V_2 = 10 \, \text{V}\) as a safety margin, \(\Delta V_f = 68 \, \text{V}\). Thus, elevating DC voltage to \(528 \, \text{V}\) reduces the modulation index to:
$$ m = \frac{\pi \times 1.3 \times 220.2}{2 \times 528} \approx 0.89 $$
which is within the linear region. This demonstrates how DC voltage elevation suppresses over-modulation in solar inverters.
Experimental Validation and Platform
We constructed an HVRT test platform to verify the proposed strategy for solar inverters. The platform comprises a 36 kW solar inverter with a nominal current of 54 A, interfaced with a grid simulator and a DC source emulating PV arrays. A series inductor (0.16 mH, 45 A) is used to simulate grid impedance. Voltage swells are induced by disconnecting this inductor during operation, causing a sudden rise to 1.3 pu. The inverter’s control system implements the DC voltage elevation algorithm in real-time using a digital signal processor.
The experimental results show that during a grid voltage swell to 1.3 pu, the solar inverter initially experiences over-modulation, but the HVRT control quickly elevates DC voltage, as illustrated in the waveform capture. The DC voltage rises from 460 V to approximately 530 V within 20 ms, maintaining the modulation index below 0.91. The inverter continues to operate normally for over 1 second, with stable output current and grid synchronization. After the swell subsides, DC voltage returns to nominal, and the system resumes standard grid-tied operation. These results confirm that the proposed strategy effectively suppresses over-modulation, enabling solar inverters to comply with HVRT requirements.
Below is a table summarizing key performance metrics from the HVRT test:
| Parameter | Normal Operation | During HVRT (Swell to 1.3 pu) |
|---|---|---|
| Grid Voltage (pu) | 1.0 | 1.3 |
| DC-Link Voltage (V) | 460 | 530 |
| Modulation Index (\(m\)) | 0.75 | 0.89 |
| Output Current THD (%) | < 3 | < 5 |
| Ride-Through Duration | N/A | 1.0 s |
The slight increase in Total Harmonic Distortion (THD) during HVRT is within acceptable limits for solar inverters, as per grid standards.
Discussion and Implications for Solar Inverters
The proposed HVRT strategy has significant implications for the design and operation of solar inverters in modern power grids. By actively elevating DC voltage, solar inverters can maintain linear modulation during voltage swells, avoiding disconnection and supporting grid stability. This approach complements hardware enhancements, such as using components rated for higher voltages. Moreover, the strategy is scalable to larger solar inverters and can be integrated with advanced grid-support functions like reactive power injection during faults.
From a control perspective, the key challenge is the rapid detection of voltage swells and precise calculation of \(\Delta V_f\). We recommend using phase-locked loops (PLLs) with fast response times and adaptive algorithms that account for PV array characteristics. For solar inverters with battery energy storage, the DC voltage elevation can be supplemented by battery power, enhancing ride-through capability. The following equation generalizes the DC voltage requirement for solar inverters during swells:
$$ V_{DC,req} = \frac{\pi \sigma u_{om}}{2 m_{max}} + \Delta V_{margin} $$
where \(\Delta V_{margin}\) includes losses and dynamic overshoot.
Furthermore, the interaction between multiple solar inverters during grid swells must be considered. Coordinated control could prevent overvoltage in the DC link and ensure uniform power sharing. Simulation studies using tools like MATLAB/Simulink can optimize parameters for various grid scenarios. Below is a formula for the maximum swell factor tolerable without DC voltage elevation, given a solar inverter’s DC voltage limit \(V_{DC,max}\):
$$ \sigma_{max} = \frac{2 m_{max} V_{DC,max}}{\pi u_{om}} $$
For \(V_{DC,max} = 600 \, \text{V}\) and \(u_{om} = 220.2 \, \text{V}\), \(\sigma_{max} \approx 1.58\), indicating that solar inverters with higher DC voltage ratings inherently have better HVRT performance.
Conclusion
In this article, I have analyzed the over-modulation problem in solar inverters during grid voltage swells and proposed a High Voltage Ride-Through strategy based on DC voltage elevation. The SVPWM modulation index is critically linked to swell magnitude and DC voltage; for swells above 1.17 pu, over-modulation occurs, risking inverter tripping. By elevating DC voltage, the modulation index is reduced, keeping solar inverters in the linear operating region. The control algorithm dynamically computes the required voltage boost based on real-time measurements. Experimental validation on a 36 kW solar inverter platform confirms that the strategy successfully suppresses over-modulation during a 1.3 pu, 1-second swell, enabling compliant HVRT performance. This approach enhances the grid integration of solar inverters, contributing to power system resilience. Future work will focus on optimizing the strategy for multi-inverter systems and integrating it with other grid-support functions for solar energy applications.