In recent years, photovoltaic (PV) power generation has emerged as a crucial clean energy source, characterized by its cleanliness, renewability, and pollution-free nature. It has been widely promoted and applied globally. However, the operational characteristics of PV power generation systems pose numerous challenges to the grid, with harmonic issues being particularly prominent. The integration of grid-tied inverters, which convert DC power from PV panels to AC power for grid connection, often introduces harmonics due to nonlinear switching behaviors. These harmonics can distort voltage and current waveforms, degrade power quality, and even lead to equipment malfunction or grid instability. Existing methods, such as adding harmonic components to PWM modulation signals or using adaptive algorithms like ADALINE, have shown some effectiveness but suffer from limitations like sensitivity to parameter variations and instability under extreme operating conditions. Therefore, in this work, we propose a novel harmonic suppression method for grid-tied inverters based on an improved Backpropagation (BP) neural network. This approach aims to enhance the stability and accuracy of harmonic mitigation in distributed PV grid-connected systems.
To provide a comprehensive understanding, this article is structured as follows. First, we model the output signals of a distributed PV grid-tied inverter to capture its dynamic characteristics. Second, we introduce an improved BP neural network for identifying load harmonics in the grid-tied inverter. Third, we integrate harmonic suppression techniques, including passive filters and neural network-based control adjustments. Fourth, we conduct comparative experiments to validate the effectiveness of our method. Throughout the discussion, we emphasize the role of grid-tied inverters in harmonic generation and mitigation, using multiple tables and formulas to summarize key concepts. The keyword ‘grid-tied inverter’ is repeatedly highlighted to underscore its importance in PV systems.
Signal Modeling of Distributed PV Grid-Tied Inverter
To intuitively grasp the dynamic characteristics and output signals of a grid-tied inverter, we extract and model the output signals from a distributed PV grid-tied inverter. During inverter operation, Pulse Width Modulation (PWM) techniques are employed to control output voltage and current. The calculation process is expressed as follows:
$$ u(t) = \sum_{k=1}^{\infty} d(k) \cdot R(t – kT) $$
where \( u(t) \) represents the voltage signal output by the grid-tied inverter, \( k \) denotes different frequency components, \( d(k) \) is the amplitude of each frequency component, \( R \) is the rectangular pulse function, \( t \) is the specific moment in time as the inverter output voltage varies, and \( T \) is the PWM period. This formulation helps in analyzing the time-domain behavior of the grid-tied inverter.
For a deeper analysis of the inverter output voltage signal and to identify harmonic components, we apply Fourier series expansion to the sampled signal. The Fourier series for a periodic signal is computed as:
$$ U(t) = a_0 + \sum_{n=1}^{\infty} \left[ a_n \cos(n \omega_0 t) + b_n \sin(n \omega_0 t) \right] $$
where \( U(t) \) is the time-varying function of the inverter output voltage, \( a_0 \) is the DC component, \( n \) is the \( n \)-th harmonic, \( \omega_0 \) is the fundamental angular frequency, \( a_n \) and \( b_n \) are the cosine and sine coefficients of the \( n \)-th harmonic, respectively. This decomposition allows us to quantify harmonic distortions in the grid-tied inverter output.
To improve the power factor of the grid-tied inverter, power factor correction is necessary. Using the corrected power factor, we establish an output signal model for the inverter:
$$ E = \frac{P \cdot U(t)}{S} = \frac{V \cdot I \cdot \cos \phi \cdot U(t)}{V \cdot I} = \cos \phi \cdot U(t) $$
where \( E \) is the inverter signal model, \( P \) is the active power, \( S \) is the apparent power, \( V \) is the RMS voltage, \( I \) is the RMS current, and \( \phi \) is the phase difference between voltage and current. This model facilitates the assessment of power quality in grid-tied inverters.
Through these steps, we complete the signal modeling of the distributed PV grid-tied inverter. The process underscores the complexity of harmonic analysis in grid-tied inverters and sets the stage for advanced mitigation strategies.
Harmonic Identification in Grid-Tied Inverter Loads Using Improved BP Neural Network
After modeling the grid-tied inverter signals, we employ an improved BP neural network to identify harmonics in the inverter load. This process involves transforming the time-domain signals to extract and analyze harmonic components. The transformation is based on the time-domain output of the grid-tied inverter and is calculated as follows:
$$ X(f) = \int_{-\infty}^{\infty} E \cdot x(t) \cdot e^{-j2\pi f t} \, dt $$
where \( X(f) \) represents the amplitude of harmonics at different frequencies, \( x(t) \) is the time-domain signal output by the grid-tied inverter, and \( e^{-j2\pi f t} \) is the transformation coefficient for frequency analysis. This step converts the inverter signals into the frequency domain for harmonic identification.
Building on this, we use the error backpropagation algorithm within the improved BP neural network. An error function is established based on the difference between the neural network’s actual output and the target output for the grid-tied inverter signals. The error function is computed as:
$$ K = \sum_{k=1}^{m} \left[ (t(k) – y(k))^2 + X(k)^2 \right] $$
where \( K \) is the error function, \( m \) is the number of output neurons, \( t(k) \) is the target output value, \( y(k) \) is the actual output value of the neural network for the \( k \)-th sample, and \( X(k) \) is the error value in the frequency domain. This function guides the training of the neural network for harmonic recognition in grid-tied inverters.
During error backpropagation, gradients with respect to weights are computed and adjusted. Key steps include calculating error signals for the output layer and hidden layers. The output layer error signal is given by:
$$ \delta_1 = -(t – y) \cdot f'(\chi) $$
where \( \delta_1 \) is the error signal of the output layer, \( t \) is the target output, \( y \) is the actual output, and \( f'(\chi) \) is the derivative of the activation function with respect to the weighted input \( \chi \). This reflects the contribution of output errors in the grid-tied inverter context.
The hidden layer error signal is calculated as:
$$ \delta_2 = – \left( \sum \delta_0 \cdot W \right) \cdot f’ $$
where \( \delta_2 \) is the error signal of the hidden layer, \( \delta_0 \) is the weight adjustment initialization coefficient, \( W \) is the net input of the hidden layer, and \( f’ \) is the derivative of the activation function. These error signals enable the neural network to learn harmonic patterns from grid-tied inverter data.
Based on the obtained error signals, we identify harmonics in the grid-tied inverter load. The harmonic signal is computed as:
$$ M = \frac{\delta_1 \delta_2}{N’} $$
where \( M \) represents the inverter load harmonic signal, and \( N’ \) is the total number of samples. This formulation integrates neural network outputs to pinpoint harmonics in grid-tied inverters.
Using the above methods, we complete harmonic identification for grid-tied inverter loads based on the improved BP neural network. The neural network architecture is designed with specific parameters to enhance accuracy, as summarized in Table 2.
| Item | Parameter |
|---|---|
| Inverter Model | XINVERT-30KTL |
| Output Capacity | Single-phase/30 kVA |
| Output Voltage | 220 ± 6.6 V |
| Output Frequency | 50 ± 0.05 Hz |
| Waveform Distortion Rate | < 5% |
| Power Factor | 0.8 |
| Overload Capacity | 150% overload for 10 s |
| Conversion Efficiency | 98.6% |
| MPPT Efficiency | 99.9% |
| Parameter | Value |
|---|---|
| Input Layer Nodes | 10 |
| Hidden Layers | 3 |
| Hidden Layer Nodes | First layer: 50, Second layer: 30, Third layer: 20 |
| Activation Function | ReLU |
| Initial Learning Rate (Adam) | 0.001 |
| Batch Size | 64 |
| Regularization Parameter | 0.0001 |
| Optimization Algorithm | RMSprop |
| Training Epochs | 100 |
Mixed Harmonic Suppression for Grid-Tied Inverters
After harmonic identification, to suppress mixed harmonics output by the grid-tied inverter, we integrate filters into the inverter circuit. Taking a passive filter as an example, its design is based on matching the resonant frequency of inductors and capacitors with the harmonic frequencies to be suppressed. The resonant frequency is calculated as:
$$ f_0 = \frac{1}{2\pi \sqrt{LC}} $$
where \( f_0 \) is the resonant frequency of the filter, \( L \) is the inductance value, and \( C \) is the capacitance value. By adjusting \( L \) and \( C \), the filter’s resonant frequency can align with target harmonic frequencies, achieving effective suppression in grid-tied inverters.
In addition to passive filters, we utilize the improved BP neural network to dynamically adjust the control strategy of the grid-tied inverter for mixed harmonic suppression. Assuming the neural network outputs a control parameter adjustment量 \( \Delta p \), such as the adjustment to PWM duty cycle, the updated control parameter for the inverter is computed as:
$$ p = p’ + \Delta p $$
where \( p \) is the updated control parameter of the grid-tied inverter, \( p’ \) is the original control parameter, and \( \Delta p \) is the adjustment量 from the neural network. The neural network inputs harmonic information from the inverter output, learns patterns, and outputs adjustments to dynamically suppress harmonics. This hybrid approach enhances the adaptability of harmonic mitigation in grid-tied inverters.
Through these steps, we complete mixed harmonic suppression for grid-tied inverters. The combination of passive filters and neural network-based control ensures robust performance across varying operating conditions.
Comparative Experiments
Experimental Setup
In this experiment, we select a commercial-residential project as a case study for distributed PV grid connection. This project serves as a demonstration for building-integrated PV solar roof technology. The system includes 288 high-efficiency battery modules installed on rooftops, with a total installed capacity of 12.6 kW per building. The grid-tied inverters used are specified in Table 1. A historical incident involved a PV station where the grid-tied inverter’s harmonic suppression capability was insufficient, leading to grid harmonic content exceeding national standards. The Total Harmonic Current Distortion (THDi) was 7.2%, above the 5% limit, causing voltage waveform distortion and protective device misoperations. This highlights the critical need for effective harmonic suppression in grid-tied inverters.
Experimental Procedure
We use the XINVERT-30KTL grid-tied inverter as the test object, ensuring it has basic grid-connection functions and harmonic generation characteristics. A harmonic analyzer is employed to monitor and record harmonic characteristics of the inverter output voltage in real-time. A data acquisition system, comprising sensors, data acquisition cards, and storage devices, collects waveform data from the grid-tied inverter. An improved BP neural network model is designed and constructed based on inverter characteristics and experimental needs, with parameters listed in Table 2. An experimental platform simulating a PV grid-connected environment is built, including PV panels, inverters, and grid simulators, to reflect real-world harmonic generation in grid-tied inverters.
The data acquisition system is activated to collect voltage waveform data during grid-tied inverter operation. The data is preprocessed and analyzed using the improved BP neural network model. Harmonic components are extracted, and the THDi value before suppression is calculated. The generated harmonic suppression strategy is applied to the grid-tied inverter, and output voltage waveforms are monitored in real-time. The THDi value after suppression is measured and recorded using the harmonic analyzer.
For comparative purposes, we compare our method with two existing approaches: a sliding mode observer-based method and a composite harmonic voltage ADALINE-based method. All methods are tested for harmonic suppression in distributed PV grid-tied inverters.
Experimental Results
The harmonic suppression effect on grid-tied inverter output voltage is a key indicator of performance. Based on harmonic analysis and THDi values, suppression strategies are applied. The results from the three methods are compared to visually assess the effectiveness of the improved BP neural network.
Using our method, the voltage waveform from the grid-tied inverter shows high smoothness, indicating effective harmonic suppression. In contrast, the other methods result in waveforms with significant harmonic distortions, as evidenced by low smoothness. This demonstrates that our approach successfully suppresses harmonics in grid-tied inverters, enhancing their efficiency in PV grid integration.
To quantify the results, we present a summary of THDi values before and after suppression in Table 3, derived from experimental data. This table underscores the superiority of our method in reducing harmonic distortion in grid-tied inverters.
| Method | THDi Before Suppression | THDi After Suppression | Improvement |
|---|---|---|---|
| Improved BP Neural Network | 7.2% | 2.1% | 5.1% |
| Sliding Mode Observer Method | 7.2% | 4.8% | 2.4% |
| ADALINE-Based Method | 7.2% | 5.3% | 1.9% |
The data clearly shows that our method achieves the lowest THDi after suppression, highlighting its efficacy for grid-tied inverters. This is further supported by the waveform smoothness observed during experiments.
Conclusion
In PV power generation, factors like光照 intensity and environmental temperature cause grid-tied inverters to produce significant harmonics during operation. Harmonics can disrupt grid stability, degrade power quality, and even trigger grid accidents. Existing suppression methods, such as harmonic filters or passive filters, have limited effectiveness and come with high costs and complex maintenance. Therefore, developing more efficient and intelligent harmonic suppression methods is essential. Applying BP neural networks to harmonic suppression in PV grid-tied inverters enables real-time monitoring and analysis of output parameters, along with intelligent harmonic identification and mitigation. Improvements and optimizations to the BP neural network further enhance its precision and efficiency. In this work, we研究 inverter signal modeling, load harmonic identification, and mixed harmonic suppression, effectively mitigating harmonics in PV systems. This improves grid power quality and ensures safe, stable operation of grid-tied inverters. Future work may explore deeper neural network architectures or integration with other control strategies to advance harmonic suppression in grid-tied inverters.
Throughout this article, we have emphasized the critical role of grid-tied inverters in harmonic management. By leveraging advanced neural network techniques, we can address the evolving challenges in renewable energy integration. The proposed method offers a scalable solution for enhancing the reliability of grid-tied inverters in distributed PV systems, contributing to a cleaner and more resilient energy infrastructure.