Solar power generation is a vital clean energy source, characterized by its cleanliness, renewability, and pollution-free advantages, and has been widely promoted and applied globally. However, the operational characteristics of photovoltaic power generation systems pose numerous challenges to the grid, with harmonic issues being particularly prominent. Existing methods, such as adding specific harmonic components to PWM three-phase modulation reference voltage waveforms, can mitigate stator current distortion and reduce torque pulsation, thereby enhancing system flexibility. Nevertheless, due to the nonlinearity of the solar inverter and the controlled motor, discrepancies between the given voltage and actual values prevent complete elimination of rotor position observer errors. Although observer accuracy has significantly improved, under extreme operating conditions like sudden load torque changes or step changes in given speed, speed signals are prone to failure, affecting system stability and accuracy. Some approaches involve constructing composite harmonic voltage models and employing algorithms like Adaptive Linear Neuron (ADALINE) to extract harmonic components from motor currents and compute compensation voltages, effectively suppressing harmonics. However, the training process of ADALINE algorithms can be influenced by variations in motor parameters, leading to unstable harmonic suppression effects. To ensure the operational quality of solar inverters, this paper introduces an improved Backpropagation (BP) neural network, using a distributed photovoltaic grid-connected system as a case study, to design a harmonic suppression method for solar inverters.
The proliferation of solar inverters in modern energy systems underscores the importance of addressing harmonic distortions. Solar inverters convert direct current from photovoltaic panels into alternating current for grid integration, but this process often introduces harmonics that degrade power quality. Harmonics can cause voltage distortions, increased losses, and interference with other devices, necessitating robust suppression techniques. Traditional methods, including passive filters and fixed control strategies, have limitations in adaptability and efficiency, especially under dynamic operating conditions. The improved BP neural network offers a data-driven approach to dynamically identify and suppress harmonics, enhancing the performance of solar inverters in distributed generation systems.
Signal Modeling of Distributed Photovoltaic Grid-Connected Solar Inverters
To better understand the dynamic characteristics and output signals of solar inverters, this study extracts and models the output signals of distributed photovoltaic grid-connected solar inverters. During the operation of a solar inverter, Pulse Width Modulation (PWM) techniques are employed to control output voltage and current. The calculation process is represented by Equation (1):
$$ u(t) = \sum_{k=1}^{\infty} d(k) \cdot R(t – kT) $$
where \( u(t) \) is the output voltage signal of the solar inverter, \( k \) represents different frequency components, \( d(k) \) denotes the amplitude of each frequency component, \( R \) is the rectangular pulse function, \( t \) is the specific time instant in the time-varying output voltage signal of the solar inverter, indicating the time parameter at different moments, and \( T \) is the PWM period.
For in-depth analysis of the output voltage signal of the solar inverter and to identify harmonic components, Fourier series are applied to the sampled output voltage signal. The Fourier series calculation for periodic signals is given by Equation (2):
$$ U(t) = a_0 + \sum_{n=1}^{\infty} \left[ a_n \cos(n w_0 t) + b_n \sin(n w_0 t) \right] $$
where \( U(t) \) is the time-varying function of the output voltage of the solar inverter, \( a_0 \) is the DC component, \( n \) represents the \( n \)-th harmonic, \( w_0 \) is the fundamental angular frequency, and \( b_n \) is the cosine coefficient of the \( n \)-th harmonic.
To improve the power factor of the solar inverter, power factor correction is necessary. Using the corrected power factor, the output signal model of the solar inverter is established as shown in Equation (3):
$$ E = \frac{P \cdot U(t)}{S} = \frac{V \cdot I \cdot \cos \phi \cdot U(t)}{V \cdot I} = \cos \phi \cdot U(t) $$
where \( E \) is the signal model of the solar inverter, \( P \) 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.
Through these steps, the signal modeling for distributed photovoltaic grid-connected solar inverters is completed. This model provides a foundation for harmonic analysis and suppression, enabling precise control over the output of solar inverters in various operating conditions.
| Item | Parameter |
|---|---|
| Inverter Model | XINVERT-30KTL |
| Output Capacity | Single-phase/30 kVA |
| Output Voltage (V) | 220 ± 6.6 |
| Output Frequency (Hz) | 50 ± 0.05 |
| Waveform Distortion Rate (%) | < 5 |
| Power Factor | 0.8 |
| Overload Capacity | 150% overload, 10 s |
| Conversion Efficiency (%) | 98.6 |
| MPPT Efficiency (%) | 99.9 |
Harmonic Identification in Solar Inverter Loads Using Improved BP Neural Network
After completing the signal modeling for distributed photovoltaic grid-connected solar inverters, an improved BP neural network is introduced to identify harmonics in solar inverter loads. In this process, signal transformation is required to extract and analyze harmonic components from the output of solar inverters. Based on the time-domain signal output from the solar inverter, the transformation is computed using Equation (4):
$$ X(f) = \int_{-\infty}^{\infty} E \cdot x(t) \cdot e^{-j2\pi ft} dt $$
where \( X(f) \) is the amplitude of harmonics at different frequencies, \( x(t) \) is the time-domain signal output from the solar inverter, and \( e \) is the transformation coefficient, often related to the exponential function in Fourier transforms.
Building on this, the error backpropagation algorithm in the improved BP neural network is employed to establish an error function for the solar inverter signal based on the difference between the neural network’s actual output value and the target output value. The error function calculation is given by Equation (5):
$$ K = \sum_{k=1}^{m} \left[ \frac{1}{2} (t(k) – y(k))^2 + X(k) \right] $$
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 when processing the \( k \)-th sample data, and \( X(k) \) is the error value in the frequency domain.
During error backpropagation, it is necessary to compute the gradient of the error with respect to the weights and adjust the weights accordingly. Key steps in gradient calculation involve computing the error signal for the output layer and the error signal for the hidden layer, as shown in Equations (6) and (7):
$$ \delta_1 = -(K – y) \cdot f'(\chi) $$
where \( \delta_1 \) is the error signal of the output layer, \( y \) is the actual output value of the neural network, and \( f'(\chi) \) is the derivative of the gradient of the error signal with respect to the weights.
$$ \delta_2 = -\left( \sum \delta_0 \cdot W \right) \cdot f’ $$
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.
Using the obtained error signals, harmonics in the solar inverter load are identified. The harmonic calculation is given by Equation (8):
$$ M = \frac{\delta_1 \cdot \delta_2}{N’} $$
where \( M \) is the harmonic signal of the solar inverter load, and \( N’ \) is the total number of samples.
The above methods complete the identification of harmonics in solar inverter loads based on the improved BP neural network. This approach allows for adaptive learning from operational data, making it suitable for real-time applications in solar inverters where conditions vary frequently.
| 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 |
Hybrid Harmonic Suppression in Solar Inverters
After identifying harmonics, to suppress hybrid harmonics in the output of solar inverters, a filter is integrated into the solar inverter circuit. Taking a passive filter as an example, its design is typically based on the principle that the resonant frequency of the inductor and capacitor matches the frequency of the harmonics that need to be suppressed. The resonant frequency is designed according to the harmonic frequency to be suppressed, as calculated in Equation (9):
$$ Q_0 = \frac{1}{2\pi \sqrt{LC}} $$
where \( Q_0 \) is the resonant frequency of the filter, \( L \) is the inductance value, and \( C \) is the capacitance value. By adjusting the values of \( L \) and \( C \), the resonant frequency of the filter can be matched to the harmonic frequency that needs suppression, achieving the goal of harmonic suppression.
In addition to passive filters, the improved BP neural network can be utilized to dynamically adjust the control strategy of the solar inverter to suppress hybrid harmonics. Assuming the neural network output is the control parameter adjustment amount \( \Delta p \), such as the adjustment amount of PWM duty cycle, the new control parameter of the solar inverter is calculated using Equation (10):
$$ p = p’ + \Delta p $$
where \( p \) is the updated control parameter of the solar inverter, \( p’ \) is the original control parameter of the solar inverter, and \( \Delta p \) is the control parameter adjustment amount. The neural network inputs harmonic information from the output of the solar inverter, learns, and outputs the adjustment amount for control parameters, enabling dynamic suppression of output harmonics from the solar inverter.
These steps complete the hybrid harmonic suppression in solar inverters. The combination of passive filtering and neural network-based control allows for comprehensive harmonic management, addressing both steady-state and transient harmonics in solar inverters.
Experimental Comparison
In this experiment, a commercial-residential project is selected as the research pilot for distributed photovoltaic grid-connected systems, focusing on solar inverters. This project is the first demonstration project in the pilot area to practice building-integrated photovoltaic solar power generation roof technology. In 2008, the area deployed 288 high-efficiency battery modules. The modules are installed on the roofs of four 25-story high-rise buildings, each configured with a 12.6 kW installation capacity, occupying an installation area of 92 m², meaning 72 modules are used per building. The project selects monocrystalline 175 W modules and adopts a full feed-in tariff generation mode, with a daily average power generation of about 200 kWh, all of which is transmitted to the grid.
According to statistics, the annual power generation of this project is 62,000 kWh, with high environmental benefits and strong energy-saving and emission-reduction capabilities. The specifications, models, and technical parameters of the solar inverters in the grid connection are analyzed, as shown in Table 1. A photovoltaic power station experienced insufficient harmonic suppression capability in its solar inverters, leading to grid harmonic content exceeding standards. The solar inverters used in this station are of a certain brand’s 50 kVA model, with a harmonic suppression capability that does not meet national standards. The Total Harmonic Current Distortion (THDi) indicator is 7.2%, significantly exceeding the national limit of 5%.
In this incident, excessive harmonic content not only caused grid voltage waveform distortion but also triggered protection device misoperations, resulting in a partial power outage. Statistics show that the affected area experienced a power outage for 5 hours, causing inconvenience to businesses and residents, with economic losses amounting to 80,000 yuan. This underscores the critical need for effective harmonic suppression in solar inverters to ensure grid stability and reliability.
Experimental Setup
The XINVERT-30KTL grid-connected solar inverter is selected as the test object, ensuring it has basic grid-connected functions and harmonic generation characteristics. A device capable of real-time monitoring and recording the harmonic characteristics of the output voltage of the solar inverter, such as a harmonic analyzer, is prepared. A data acquisition system is constructed to real-time collect waveform data of the output voltage of the solar inverter. This system includes components such as sensors, data acquisition cards, and data storage devices. Based on the characteristics of the solar inverter and experimental requirements, an improved BP neural network model is designed and built, with technical parameters detailed in Table 2.
On this basis, an experimental platform simulating a photovoltaic grid-connected environment is set up, including photovoltaic panels, solar inverters, and grid simulation devices. This ensures that the experimental environment can realistically reflect the harmonic generation situation of the solar inverter during actual operation. The data acquisition system is started to real-time collect the output voltage waveform data of the solar inverter during grid-connected operation, ensuring the accuracy and completeness of data collection. The collected waveform data is imported into the improved BP neural network model for preprocessing and analysis.
Harmonic components in the waveform are extracted, and the THDi value before harmonic suppression is calculated. The generated harmonic suppression strategy is applied to the solar inverter, and changes in the output voltage waveform of the solar inverter are monitored in real-time. The harmonic analyzer is used to measure and record the THDi value after harmonic suppression. To meet the comparison needs of experimental results, the method proposed in this paper is compared with the suppression method based on a sliding mode observer from literature and the suppression method based on composite harmonic voltage ADALINE from another literature, for harmonic suppression in distributed photovoltaic grid-connected solar inverters.
Experimental Results
The harmonic suppression effect on the output voltage of the solar inverter is a key indicator for evaluating the performance of distributed photovoltaic grid-connected solar inverters. It is an important link in ensuring grid power quality and the safe and stable operation of equipment. Based on the analyzed harmonic components and THDi values, corresponding harmonic suppression strategies are generated and applied to the solar inverter. The harmonic suppression effects of the three methods are compared, and the application effect of the improved BP neural network is intuitively evaluated.
Based on the above, three methods are used to suppress a large number of harmonics in the output voltage of the solar inverter. The suppression effects are shown in the figures below. After using the methods from the literature, the output voltage waveform diagrams of the solar inverter clearly show that the voltage still carries a large number of harmonics, meaning the smoothness of the voltage waveform diagram is very low. After using the method proposed in this paper to suppress harmonics in the solar inverter, the smoothness of the voltage waveform diagram of the solar inverter is high.
These experimental results demonstrate that among the three methods, only the use of the method designed in this paper can effectively suppress harmonics in solar inverters, improving the efficiency of solar inverters in photovoltaic grid connections. The improved BP neural network adapts to varying operational conditions of solar inverters, providing superior harmonic suppression compared to traditional methods. This is crucial for enhancing the reliability of solar power systems and reducing maintenance costs associated with harmonic-related issues in solar inverters.
Conclusion
In the process of solar power generation, the influence of natural factors such as light intensity and ambient temperature causes solar inverters to generate a large number of harmonics during operation. Harmonics not only affect the normal operation of the grid and the normal operation of other equipment but also lead to a decrease in grid power quality and even trigger grid accidents. Existing harmonic suppression methods, such as using harmonic filters and passive filters, can reduce harmonic generation to a certain extent, but their effects are limited, and they have issues such as high costs and complex maintenance. Therefore, finding a more efficient and intelligent harmonic suppression method is very important. Applying BP neural networks to harmonic suppression in photovoltaic grid-connected solar inverters allows for real-time monitoring and analysis of parameters such as output current and voltage of the solar inverter, enabling intelligent identification and suppression of harmonics. Improving and optimizing the BP neural network can further enhance the accuracy and efficiency of harmonic suppression. This paper studies solar inverter signal modeling, load harmonic identification, and hybrid harmonic suppression, effectively suppressing harmonics in solar power generation systems, improving grid power quality, and ensuring the safe and stable operation of the grid. The integration of advanced neural networks with traditional filtering techniques represents a significant step forward in the management of solar inverters, paving the way for more resilient and efficient renewable energy systems.
The future of solar inverters lies in smart, adaptive control systems that can preemptively address harmonic issues. As solar penetration increases, the role of solar inverters in grid stability becomes more critical. Continued research into machine learning applications for solar inverters will likely yield even more robust solutions, further solidifying the position of solar energy as a cornerstone of clean power generation. The improved BP neural network method outlined here offers a scalable framework for enhancing the performance of solar inverters across diverse installations, from small-scale residential to large-scale utility projects.