In modern renewable energy systems, photovoltaic (PV) power generation has become a cornerstone due to its sustainability and scalability. However, the integration of PV systems into the main grid poses significant challenges, primarily because PV units output direct current (DC) power, while the grid operates on alternating current (AC). The key device enabling this integration is the on-grid inverter, which converts DC to AC and synchronizes with the grid. Among various types, three-phase on-grid inverters are widely adopted for their efficiency and stability in high-power applications. Nevertheless, the inherent uncertainty in PV output—driven by factors like solar irradiance and temperature fluctuations—introduces voltage instability in the inverter, complicating control efforts. This instability can lead to power quality degradation, equipment damage, and reduced grid reliability. Therefore, developing robust voltage stability control methods is paramount. In this article, I propose a novel voltage stability control method for three-phase on-grid inverters based on an adaptive prediction algorithm. This method leverages historical voltage data and system parameters to predict future inverter outputs and compute control parameters, thereby maintaining voltage within acceptable grid limits. By addressing the nonlinearities and disturbances in PV systems, the approach enhances the performance and reliability of on-grid inverters, contributing to stable grid operation.
To understand the need for voltage stability control, it is essential to analyze the sources of voltage deviation in three-phase on-grid inverters. Voltage deviation refers to the difference between the inverter’s output voltage and the desired grid voltage. Several factors contribute to this deviation, each impacting the overall system performance. The primary causes include input voltage fluctuations from PV panels due to varying environmental conditions, grid voltage swings caused by load changes and network disturbances, errors in inverter control strategies, dynamic load variations, aging of inverter components, and external electromagnetic interference. These factors collectively induce voltage imbalances and harmonics, which can adversely affect the grid. For instance, voltage deviations may lead to increased harmonic distortion, reduced inverter efficiency, and potential tripping of protection devices. In severe cases, they can destabilize the entire power system, highlighting the criticality of precise voltage control. The on-grid inverter, as the interface between PV systems and the grid, must mitigate these deviations to ensure seamless energy transfer. Thus, a comprehensive analysis of voltage deviation is the foundation for designing effective control strategies.
The internal dynamics of a three-phase on-grid inverter are governed by the relationship between voltage and current in its circuit components. A typical inverter consists of DC input from PV panels, a three-phase bridge converter, filter inductors and capacitors, and an AC output connected to the grid. The mathematical model describing the voltage-current relationship is crucial for control design. For each phase (i = 1, 2, 3), the dynamics can be expressed as:
$$ L_i \frac{di_i}{dt} = U_i – U_{ai} – R_i \cdot i_i – C_i $$
where \( L_i \) represents the filter inductance, \( i_i \) is the phase current, \( U_i \) is the DC input voltage from the PV side, \( U_{ai} \) is the AC output voltage, \( R_i \) denotes the line impedance, and \( C_i \) is the filter capacitance. This equation assumes that the three phases are independent and decoupled, allowing for separate control of each phase. The output voltage \( U_{ai} \) is influenced by both the input and the grid voltage \( U_s \). In practice, the on-grid inverter must regulate \( U_{ai} \) to match \( U_s \) in magnitude and phase, ensuring proper synchronization. The complexity arises from the time-varying nature of these parameters, especially under fluctuating PV generation. Therefore, a dynamic model that accounts for real-time changes is necessary for accurate control. The adaptive prediction algorithm builds upon this model to forecast voltage behavior and adjust control actions accordingly.
The core of the proposed method is the adaptive prediction algorithm, which estimates the future output voltage of the on-grid inverter based on historical data and system parameters. This algorithm is designed to handle the nonlinear and stochastic nature of PV systems, making it suitable for real-time voltage control. The process begins with collecting historical voltage data in time-series format. Let \( U_{ai}^j \) represent the output voltage of phase i at time j, where j ranges from 1 to t, the total sampling period. The dataset for each phase can be denoted as:
$$ U_{a1} = \{ U_{a1}^1, U_{a1}^2, \dots, U_{a1}^t \} $$
$$ U_{a2} = \{ U_{a2}^1, U_{a2}^2, \dots, U_{a2}^t \} $$
$$ U_{a3} = \{ U_{a3}^1, U_{a3}^2, \dots, U_{a3}^t \} $$
Using this data, an adaptive prediction model is constructed to forecast the voltage at the next time step (t+1). The model incorporates weighting coefficients that adjust dynamically to minimize prediction error. The general form of the prediction equation is:
$$ U_{ai}^{t+1} = \frac{\sum_{i=1}^{3} \sum_{j=1}^{t} \omega_{ai}^j U_{ai}^j}{\alpha_o} \pm \epsilon_{ai} $$
Here, \( U_{ai}^{t+1} \) is the predicted voltage for phase i at time t+1, \( \omega_{ai}^j \) are adaptive coefficients assigned to each historical data point, \( \alpha_o \) is a normalization factor bounded between 0 and 1, and \( \epsilon_{ai} \) is an adjustment term that accounts for model uncertainties. The adaptive coefficients are updated iteratively during training to refine the prediction accuracy. This model effectively captures the temporal dependencies in inverter voltage, enabling proactive control of the on-grid inverter.
To ensure the prediction model’s reliability, it undergoes a training process where its outputs are compared against known actual voltage values. The prediction error is computed as:
$$ \Delta U_{ai}^{t+1} = U_{ai}^{t+1} – \hat{U}_{ai}^{t+1} $$
where \( \hat{U}_{ai}^{t+1} \) is the actual measured voltage. The training continues until the error falls below a predefined threshold \( \zeta \), which is set based on the desired voltage control precision. During each iteration, the adaptive coefficients \( \omega_{ai}^j \) are adjusted using optimization techniques, such as gradient descent, to minimize \( \Delta U_{ai}^{t+1} \). Once trained, the model provides accurate voltage forecasts, which are essential for stabilizing the on-grid inverter. The iterative nature of this algorithm allows it to adapt to changing conditions, such as sudden shifts in PV output or grid disturbances, ensuring robust performance over time. This adaptability is a key advantage over traditional fixed-parameter control methods.
With the predicted voltage \( \hat{U}_{ai}^{t+1} \) from the trained model, the next step is to compute control parameters that will adjust the inverter’s operation to maintain voltage stability. The control parameter \( Q_t \) is derived to minimize the deviation between the predicted voltage and the grid voltage \( U_s \). It is calculated as:
$$ Q_t = \frac{|\hat{U}_{ai}^{t+1} – U_s|}{\lambda^*} $$
where \( \lambda^* \) is a unit control parameter that scales the deviation into an actionable control signal. This parameter \( Q_t \) represents the required adjustment to bring the inverter’s output voltage closer to the grid reference. In practice, \( Q_t \) is transmitted to the inverter’s control device, such as a pulse-width modulation (PWM) controller, which modulates the switching signals to regulate the output. By continuously updating \( Q_t \) based on real-time predictions, the on-grid inverter can dynamically compensate for voltage deviations, ensuring stable operation even under varying PV generation. This closed-loop control mechanism enhances the resilience of the PV system and supports grid integration. The effectiveness of this approach hinges on the accuracy of the adaptive prediction algorithm, which underscores the importance of robust modeling and training.
To validate the proposed method, an experimental platform was established, simulating a three-phase on-grid inverter connected to a PV system and the main grid. The platform includes a DC source emulating PV output, a three-phase inverter module, filter components, and a grid connection via a voltage regulator. Nonlinear loads were incorporated to mimic real-world grid disturbances. Key parameters of the setup are summarized in the table below, which provides a concise overview of the system configuration.
| Parameter Name | Parameter Value |
|---|---|
| Inverter-side inductance (mH) | 4.3 |
| Grid-side inductance (mH) | 1.1 |
| Resonant coefficient | 200 |
| Proportional coefficient | 40 |
| Grid frequency (Hz) | 50 |
| Filter capacitance (μF) | 3.3 |
| DC-side voltage (V) | 150 |
| Integral coefficient | 314.16 |
| Resonant angular frequency (rad/s) | 314 |
| Resonant frequency bandwidth | 3.14 |
These parameters were carefully selected to reflect typical on-grid inverter applications, ensuring the experiments are representative of real scenarios. The adaptive prediction algorithm was implemented in a digital signal processor (DSP) controller, which processed voltage data and computed control parameters in real time. Performance was evaluated by measuring voltage prediction errors and the inverter’s ability to maintain output within grid tolerance limits. The results demonstrated significant improvements over conventional methods, such as those based on second-order linear active disturbance rejection or internal model principles. For instance, the proposed method achieved a minimum voltage prediction error of 1%, substantially lower than comparative approaches. This accuracy directly translated to better voltage regulation, with the inverter output consistently staying within ±5% of the grid voltage, as per standard grid codes. The on-grid inverter thus exhibited enhanced stability and reliability, validating the efficacy of the adaptive prediction algorithm.
The experimental analysis further involved comparing the proposed method with two existing techniques: a voltage-controlled on-grid inverter method using instantaneous power reduction (Method A) and a second-order linear active disturbance rejection-based method for wind power on-grid inverters (Method B). Voltage prediction errors were recorded over multiple trials, and the results are encapsulated in the following formula, which summarizes the average error reduction:
$$ \text{Error Reduction} = \frac{\text{Error}_{\text{Method A}} – \text{Error}_{\text{Proposed}}}{\text{Error}_{\text{Method A}}} \times 100\% $$
For the proposed method, the error reduction exceeded 50% in most cases, highlighting its superior predictive capability. Additionally, the inverter’s output voltage under control was monitored, showing that the adaptive prediction algorithm effectively suppressed deviations caused by sudden changes in PV input or grid voltage dips. The control parameter \( Q_t \) was adjusted smoothly, preventing abrupt switching actions that could stress the on-grid inverter components. This dynamic responsiveness is crucial for prolonging the lifespan of the inverter and maintaining power quality. The table below provides a snapshot of voltage control performance across different operating conditions, emphasizing the method’s robustness.
| Operating Condition | Voltage Deviation (Proposed Method) | Voltage Deviation (Method A) | Voltage Deviation (Method B) |
|---|---|---|---|
| Steady PV output | 0.5% | 2.1% | 3.0% |
| Rapid irradiance change | 1.2% | 4.5% | 5.8% |
| Grid voltage sag | 1.0% | 3.8% | 4.2% |
| Nonlinear load switching | 1.5% | 5.0% | 6.1% |
As evident, the proposed method consistently maintains voltage deviation within acceptable limits, outperforming the alternatives. This performance is attributed to the adaptive nature of the prediction algorithm, which continuously learns from system behavior and updates its model. The on-grid inverter, therefore, operates more efficiently, reducing energy losses and enhancing overall system stability. Furthermore, the method’s computational efficiency allows for implementation on low-cost hardware, making it scalable for large-scale PV installations. The integration of such advanced control strategies is pivotal for the future of smart grids, where distributed energy resources like PV systems play a dominant role.
In conclusion, the voltage stability control method for three-phase on-grid inverters using an adaptive prediction algorithm offers a significant advancement in PV grid integration. By analyzing voltage deviation sources, modeling inverter dynamics, and leveraging predictive control, the method ensures precise voltage regulation under uncertain PV generation. The adaptive prediction algorithm excels in forecasting future voltages with minimal error, enabling proactive adjustments that keep the inverter output aligned with grid requirements. Experimental results confirm its effectiveness, demonstrating reduced prediction errors and stable voltage profiles compared to existing methods. This approach not only improves the performance of on-grid inverters but also contributes to grid reliability and power quality. As the adoption of renewable energy grows, such intelligent control systems will be essential for managing the complexities of modern power networks. Future work may explore integrating this method with other grid-support functions, such as frequency regulation and harmonic mitigation, to further enhance the versatility of on-grid inverters. Overall, the proposed method represents a robust solution for voltage stability in three-phase on-grid inverters, paving the way for more resilient and efficient PV systems.