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Scientific Reports volume 14, Article number: 18078 (2024 ) Cite this article distribution transformer
An Author Correction to this article was published on 19 September 2024
This article has been updated
Simulation and implementation of a single DC-link-based three-phase inverter are investigated in this article. The primary focus is on designing a single DC-link three-phase inverter for high power applications. Unlike conventional inverters that require 600 V to generate 400 V (RMS) at the output, the proposed system achieves this with only 330 V, facilitated by a 12-terminal 1:1 transformer. The system employs Proportional Integral (PI) and Neural Network (NN) controllers to optimize performance. Various Carrier-Based Pulse Width Modulation (CB-PWM) techniques, including Phase Disposition (PD), Phase Opposition Disposition (POD), and Alternative Phase Opposition Disposition (APOD), are implemented and evaluated based on Total Harmonics Distortion (THD) concerning the Modulation Index (MI) of the inverter. The proposed inverter achieves a THD reduction to 4.8%, demonstrating superior performance compared to recent studies. The system’s performance is validated through extensive MATLAB/Simulink simulations and practical implementation using XILINX FPGA software, confirming the efficacy of the proposed design.
In recent years, the importance of Renewable Energy Sources (RES) has surged, with Photovoltaic (PV) systems playing a pivotal role in the power sector due to their clean, silent operation, cost-effectiveness, and continuous availability during daylight hours1. To efficiently convert PV energy into electrical energy, it is crucial to design inverters that meet IEEE 519 power quality standards. There are two primary power conversion stages: direct conversion, which lacks an intermediate stage and requires inverters designed with twice the nominal power handling capacity, and indirect conversion, which includes a DC-DC power conversion stage responsible for Maximum Power Point Tracking (MPPT) and current injection into the grid2. Indirect conversion stages offer higher efficiency and lower operating power, making them suitable for RES applications.
DC-DC converters, essential in indirect conversion, are categorized as isolated or non-isolated. Isolated converters, utilizing high-voltage transformers, achieve high boosting capability but suffer from eddy current losses and reduced efficiency due to transformer leakage inductance. Non-isolated converters, while enhancing voltage levels from low input DC voltage, face limitations such as switching losses and diode reverse recovery issues3. Despite these drawbacks, conventional DC-DC converters remain preferred for grid-connected two-stage systems due to their simple control characteristics.
High-voltage gain DC-DC converters have been developed to overcome these challenges, providing high DC output voltage from input DC voltage and interfacing effectively between input sources and load combinations. Conventional three-phase two-level inverters, typically used in grid-connected applications, generate up to 31% Total Harmonic Distortion (THD)4. To address the limitations of these inverters, various Multilevel Inverter (MLI) topologies have been proposed, which improve efficiency and reduce THD5.
MLIs are classified based on input voltage magnitudes into symmetrical (equal voltage rating) and asymmetrical (unequal voltage rating) types. Recent studies have explored single DC-link three-phase inverters, which require lower DC link voltages, reducing system complexity and cost6. For instance7, introduced a single DC-link MLI topology that significantly improves voltage utilization and reduces THD. Similarly8, proposed an advanced MC-PWM technique for high power applications, achieving better control and reduced harmonic distortion.
PWM techniques for MLIs are categorized into fundamental switching modulation, high-frequency switching modulation, and variable frequency switching modulation. Among these, high-frequency switching modulations such as Phase Disposition (PD), Phase Opposition Disposition (POD), and Alternative Phase Opposition Disposition (APOD) are particularly suitable for high power applications9. Recent advancements in PWM techniques, including Multi-Carrier PWM (MC-PWM) methods, have been explored to control inverters and enhance performance. MC-PWM techniques involve selecting (N-1) carriers with high frequency and equal magnitude, where “N” indicates the inverter levels. This article investigates a single DC-link based three-phase inverter using MC-PWM techniques, aiming to improve voltage utilization and reduce THD. The proposed inverter system is examined through MATLAB/Simulink simulations and verified with an experimental setup.
Several recent studies have focused on improving the efficiency and performance of single DC-link inverters and PWM techniques. For instance10, explored a novel single DC-link MLI topology, demonstrating significant improvements in voltage utilization and THD reduction. Reference11 presented an MC-PWM technique tailored for high power applications, achieving better control and reduced harmonic distortion. Another study by12 introduced a hybrid PWM method, combining features of different PWM techniques to enhance inverter performance. Furthermore13, analyzed the impact of various PWM schemes on the harmonic profile of MLIs, providing valuable insights for optimizing inverter design. Reference14 discussed the use of artificial intelligence in improving the control strategies for MLIs, showcasing the potential of integrating AI with power electronics. Lastly15, investigated the thermal performance of single DC-link inverters, highlighting the importance of thermal management in improving overall system efficiency.
For instance, a study by Mahesh et al. (2020) introduced an advanced PD-PWM method that demonstrated a significant reduction in THD for high power applications14. This method involved the use of multiple carriers with slight phase shifts to achieve better harmonic performance. Another recent work by Lee and Kim (2021) explored the application of neural network-based controllers in conjunction with CB-PWM techniques to dynamically adjust the modulation index, thereby optimizing the inverter’s performance under varying load conditions15.
Moreover, the integration of Proportional Integral (PI) controllers with neural networks (NN) has been investigated to provide adaptive control in MLIs. The hybrid PI-NN controller can adapt to changing load conditions and improve the inverter’s response time and stability16. This approach not only enhances the efficiency but also ensures robust performance in real-time applications.
A novel single DC-link multilevel inverter topology was proposed by Zhang et al. (2021), which utilized a combination of CB-PWM techniques and AI-based controllers. This topology achieved higher voltage utilization and lower THD compared to conventional inverters, making it highly suitable for high power PV applications17. Additionally, the study highlighted the importance of thermal management in such inverter systems to maintain performance and reliability over extended periods.
Furthermore, the use of Field Programmable Gate Arrays (FPGAs) for the implementation of CB-PWM techniques has gained traction. FPGAs offer high-speed processing capabilities, enabling real-time generation of switching pulses with minimal delay. This was demonstrated in a study by Singh et al. (2022), where the FPGA-based control system significantly improved the dynamic response of the inverter and reduced computational overhead18.
These advancements underscore the potential of single DC-link based three-phase MLIs with optimized CB-PWM techniques for enhancing the efficiency and performance of PV systems. The combination of advanced control strategies, innovative inverter topologies, and high-speed processing technologies paves the way for more reliable and efficient renewable energy solutions.
A study by Zhang et al.19 demonstrated a novel multilevel inverter with a THD of 5.3% using a hybrid PWM technique. Our proposed inverter, utilizing multi-carrier PWM techniques, achieves a lower THD of 4.8%, highlighting its superior harmonic performance.
Kumar and Singh20 investigated a transformer-less multilevel inverter, reporting a THD of 6.1%. In contrast, our inverter design, incorporating a 12-terminal transformer, achieves a THD reduction to 4.8%, proving its efficacy in enhancing power quality.
Recent advancements in multilevel inverter (MLI) technology have led to the development of innovative topologies that significantly enhance performance and efficiency. Notable among these is the “13-level switched-capacitor multilevel inverter with a single DC source,” which simplifies the design by reducing the number of required DC sources while achieving higher output levels21. Another key development is the “Dual boost five-level switched-capacitor inverter with a common ground,” which addresses common grounding issues, ensuring safer and more reliable operation in grid-connected systems. Furthermore, the “Seventeen-level switched capacitor inverters with the capability of high voltage gain and low inrush current” demonstrate the potential for substantial voltage amplification while minimizing inrush currents, thereby enhancing the lifespan of power electronic components22. Lastly, the “Single-stage five-level common ground transformerless inverter with an extendable structure for centralized photovoltaics” presents a scalable solution for photovoltaic applications, offering high efficiency and simplified integration into existing infrastructure23.
This inverter topology is required only 330 V dc bus voltage to generate the rated 400 V ac supply which is very less when compared to the other topologies.
This inverter uses only 15 switches to build a three-phase system and only one dc link. So, ultimately cost and inverter size is greatly reduced.
The 12 terminal transformers provide galvanic isolation between the input and output systems. This increases the reliability of the system.
The computer simulation results are validated through an FPGA-based experimental setup.
To overcome the limitations of conventional topologies, a novel three-phase inverter design using a 12-terminal transformer and a single DC source is presented in this article. This design aims to enhance voltage utilization and reduce system complexity. Figure 1 illustrates the circuit diagram of the proposed transformer-based three-phase five-level inverter with a single DC-link system. The auxiliary switch (ASa5) comprises four diodes arranged in a bridge configuration, with switches Ha1 and Ha2 forming one leg, and switches Ha3 and Ha4 forming the other leg. Among these five switches, Ha1, Ha2, and ASa5 operate at high frequency (carrier frequency), while the remaining two switches, Ha3 and Ha4, function at a low frequency of 50 Hz.
Circuit diagram of the proposed system.
The operation of the proposed inverter can be better understood by examining the inverter currents and voltages at various modulation index (MI) values, as depicted in Fig. 2. This figure demonstrates how the inverter generates different voltage levels based on the applied MI, showcasing the flexibility and efficiency of the design.
Output voltages and currents of the inverter with different modulation index (MI) values.
The proposed three-phase inverter is capable of generating five distinct voltage levels. The operating modes of the inverter are summarized with current flow diagrams to provide a clear understanding of the switching sequences and the resulting voltage levels. Figure 3 presents the active and inactive switching states along with their corresponding voltage levels, highlighting the inverter’s ability to produce multiple voltage levels with a single DC-link system.
To evaluate the performance of the inverter, different MI values are applied, resulting in three distinct test cases: (i) MI > 1, (ii) MI < 0.5, and (iii) 0.5 < MI < 1. These test cases help to analyze the inverter’s behavior under various operating conditions. It is observed that when the MI range is more than 0.7, the inverter successfully generates a five-level output voltage. Conversely, when the MI is 0.5, the inverter produces only a three-level output voltage. This occurs because the reference signal is unable to meet the specific carrier signal required for generating higher voltage levels.
The auxiliary switch configuration with ASa5 and its integration into the inverter circuit plays a crucial role in achieving these multiple voltage levels. The high-frequency operation of switches Ha1, Ha2, and ASa5 ensures efficient voltage modulation, while the low-frequency operation of switches Ha3 and Ha4 minimizes switching losses, contributing to the overall efficiency of the inverter.
The proposed inverter design offers several advantages over conventional topologies. By utilizing a single DC-link and a transformer-based approach, the system reduces the need for multiple DC sources, thereby lowering costs and simplifying the overall design. Additionally, the ability to generate multiple voltage levels enhances the inverter’s performance in terms of voltage utilization and harmonic distortion reduction, making it a viable solution for high power applications.
In conclusion, the proposed single DC-link based three-phase five-level inverter demonstrates significant improvements in voltage utilization and system efficiency. The detailed analysis of its operating modes, switching states, and performance under various MI values confirms its potential for practical implementation in renewable energy systems and other high power applications.
Significance of controllers and PWM techniques t in both converter and inverterhe:
Controllers and PWM techniques in DC-DC converters are crucial for maximizing energy extraction from solar panels through MPPT algorithms, ensuring stable output voltages, and optimizing efficiency by minimizing switching losses.
In inverters, PWM techniques like SPWM and CB-PWM reduce harmonic distortion in output waveforms, meeting power quality standards. Controllers synchronize with grids, manage power flow, and enhance stability. Advanced strategies like NN controllers improve dynamic response and efficiency under varying loads.
Among the different PWM techniques, the sine PWM technique has been applied to the inverter. In this approach, to generate the switching pulses, three Carrier-Based PWM (PD, POD, and APOD) techniques are simulated and verified using MATLAB/Simulink Simulation. In MC PWM, m-1 carriers are compared with the reference sine wave to produce a switching pulse. Here, four triangles are considered and all carriers have an equal magnitude and frequency. Figure 4 represents the switching logic of the multicarrier modulation
where “m” is the number of the carrier wave, Am is the amplitude of a sine wave, and AC is the amplitude of a carrier wave. The intersection point of both the reference wave and carrier wave desired the switching pulses to the inverter. From Fig. 5 it is observed that there are six transition regions and defined as:
Switching logic of multicarrier modulation techniques.
Transition regions of MC-PWM techniques.
Region 1: \(0 < t < \theta_{1}\) , Region 2: \(\theta_{1} < t < \theta_{2}\) .
Region 3: \(\theta_{2} < t < \Pi\) , Region 4: \(\Pi < t < \theta_{3}\) .
Region 5: \(\theta_{3} < t < \theta_{4}\) , Region 6: \(\theta_{4} < t < 2\Pi\) .
For a generation of switching logic, 2 kHz frequency has been considered as carrier frequency and 50 Hz as the reference frequency. Therefore, frequency modulation is defined as
The PI controller has two parameters: Proportional and Integral.
Taking Laplace Transformation on both sides
where TI = Integral time constant.
The transfer function (T.F) is
where KP specifies the proportional, KI specifies the integral. Figure 6 represents the PI with unity feedback.
By using PI controller, we could achieve accurate desired value, fast response, and with less error in steady-state. But at the same time, it is complex mathematical modeling and also difficult to design. To overcome these limitations of the conventional PI controller, the neural network (NN) controller is investigated in this article.
For the proper inverter operation, dc-link voltage is to be maintained constantly and the selection of the suitable controller is a very important task. The switching circuit is a highly non-linear nature; modeling of a conventional controller is very difficult to obtain mathematical modeling15,19. Hence, in this proposed approach NN controller is applied to evaluate the inverter performance. Hence, the design of an adaptive controller is indispensable24,25,26. In this article, the NN controller is applied for the proposed system to increase the performance in the non-linear nature. In this controller, a Back Propagation (BP) network is considered to be an efficient technique for training multi-layer NN27,28. The BP offers a computationally effective technique, for varying the weights in a feed-forward network. Figure 7 shows the structure of the NN controller.
The architecture of the neural network.
This controller mostly discusses 3-layers: input, output, and hidden layers. In this, the individual layer has several sample elements and the input elements are taken from the system output and compared (adjusted) with utilizing some weights to get the desired output.
where h(x) is a transfer function, usually a nonlinear function such as the “tan-sigmoid,” x = (x1,…,xM) is the input vector of the NN with M elements, wi are the multiplicative weights for each input “b” a bias or correction factor. Finding wi and biases is the objective of the NN training process. The objective of this network is to train the net to attain a balance between the ability to react properly to the patterns that are used for training and the capability to deliver better responses to the input that is similar. In this, NN ten hidden layers are taken, so the input and the hidden layers are connected by weights like W11, W12,…….., W110. Similarly, the weights of hidden and output layers are considered W11, W21, ………W101. In this controller, first, the input activation values are taken and then sigmoidal activation considers all hidden layers. Later, consider the hidden layers activation values then find the sigmoidal activation function of the output layer. This is considered as one sample training, in this controller, a total of 4001 samples are considered. In every training step, the weights are changed according to the error16. Finally, all the weights are adjusted and get less error on the output side. For proper inverter operation, maintaining a constant DC-link voltage is crucial, and selecting a suitable controller is essential due to the non-linear nature of the switching circuit. Traditional controllers are challenging to model mathematically, so this study employs a Neural Network (NN) controller to enhance performance. The NN controller uses a Back Propagation (BP) network to efficiently train multi-layer networks, adjusting weights and biases to minimize errors and optimize modulation strategies. Various Carrier-Based PWM (CB-PWM) techniques, including Phase Disposition (PD), Phase Opposition Disposition (POD), and Alternative Phase Opposition Disposition (APOD), are applied to control the inverter. These techniques reduce harmonic distortion, with the NN controller demonstrating superior performance in minimizing Total Harmonic Distortion (THD) compared to conventional PI controllers. The effectiveness of the proposed system is validated through MATLAB/Simulink simulations and an FPGA-based hardware setup, showing significant improvements in power quality.
In this starting, the activation values are taken
The output voltage \({V}_{out}(t)\) in PD is given by
The output voltage \({V}_{out}(t)\) in POD is given by
A computer-based simulation has been carried out to validate the system. The proposed system was controlled by both the PI and NN controller and duly verified using MATLAB/Simulink. The DC-link voltage of the inverter is almost half the rate of a conventional three-phase inverter. The DC-link voltage rating is only 330 V and it is very less as compared to the conventional inverter and it is shown in Fig. 8.
DC link voltage (a) PI controller (b) NN controller.
The simulation results of the three-phase inverter are shown in Figs. 9, 10. Figure 9a,b depicted the five-level output voltage of the inverter with a rating of 335 V peak value. Figure 10a,b depicted the three-phase load voltages and currents. From all depictions, it is clear that the NN controller gives a significantly better performance as compared to the PI controller in terms of settling times.
Inverter output voltages (a) PI controller (b) NN controller.
Three-phase inverter output voltage and current (a) with PI controller (b) with NN controller.
Tables 1, 2, 3 gives the analysis of the power quality of the proposed inverter with a PI controller and NN controller. The proposed system is examined for various modulation index ranges from 0.4 to 1. The THD performance is analyzed with respect to the modulation index and also made a comparative analysis. From the comparative analysis, it is clear that both controllers are performed well and produced the THD level less than the IEEE standard 519 recommended practices26,29.
Figure 11 represents the voltage and current THD of the inverter by using the PI controller and the inverter switches are controlled by CB-PWM techniques at MI of 1. Figure 11a,b represent the voltage and current percentage THDs values of inverter using PD-PWM technique are 15.74 and 2.38% respectively. Figure 11c,d represents the voltage and current percentage THDs values of inverter using POD-PWM technique are 19.85% and 2.44% respectively. Figure 11e,f represent the voltage and current percentage THDs values of inverter using APOD-PWM technique are 23.41 and 2.49% respectively.
Voltage and current THDs of the inverter by using PI controller (MI = 1).
Figure 12 represents the voltage and current THD of the inverter by using the NN controller and the inverter switches are controlled by CB-PWM techniques at MI of 1. Figure 12a,b represents the voltage and current percentage THDs values of inverter using PD-PWM technique are 14.70 and 2.09% respectively. Figure 12c,d represents the voltage and current percentage THDs values of inverter using POD-PWM technique are 18.80 and 2.13% respectively. Figure 12e,f represent the voltage and current percentage THDs values of inverter using APOD-PWM technique are 19.85 and 2.16% respectively.
Voltage and current THDs of the inverter by using NN controller (MI = 1).
Table. 4 represents the THD analysis of the three-phase five-level inverter controlled by using PI and NN controllers with different CB-PWM techniques. By using the PI controller, the proposed inverter produced more THD percentage than the NN controller. In the NN controller, the APOD and POD techniques have more THD percentage of voltage and current of 22.34 and 2.16%, 18.80 and 2.13% respectively, whereas the PD-PWM technique has less %THD of voltage and current of 14.70 and 2.09%. Therefore PD-PWM technique is offering significantly good performance than other PWM techniques. Figure 13 indicates the voltage and current THD analysis of the proposed system controlled by using PI and NN controllers with different CB-PWM techniques. The Summary of the THD spectrum of both PI and NN controllers is tabulated in Table 4. The performances of the inverter have been analyzed by using both PI and NN controllers in terms of THD. From Table 4, it is seen that the proposed inverter performs well. Among the three CB-PWM techniques, a PD-PWM offers significantly improved performance as compared to the others.
Voltage and Current THD analysis of the inverter.
To validation of the simulation results, an FPGA-based experimental setup has been developed. The SPARTAN-6 XC6SLX9 controller has been used to generate the CB-PWM signal to the three-phase inverter. In this XILINX ModelSim software is used in VHDL coding of FPGA simulation. A three-phase inverter is constructed by using IGBTs. For the control of the front side high-voltage gain converter, both PI and NN controllers have been applied. In this control scheme, 5 kHz carrier frequency is compared with the 50 Hz for reference frequency used. Figure 14 represents the switching pulses of the high-voltage gain converter by using PI and NN controllers. Figure 15 represents the inverter output currents by using PI and NN controllers. It is observed that the experimental load inverter current with the NN controller has significantly improved performance than the PI controller in terms of ripple content.
Switching pulses of PI and NN controllers.
Inverter output currents of PI and NN controllers.
Figure 16a,b represent the experimental waveforms of the five-level output voltage of the inverter (220Vrms). Figure 16 notices that the NN controller-based systems produce a good performance as compared to the PI controller-based system. Figure 17 represents the total hardware setup for the three-phase five-level inverter system.
Each phase inverter output voltages (a) NN controller (b) PI controller.
Hardware setup for three-phase five-level inverter.
Table 5 indicates the THD comparison between proposed and existing inverter systems. From Table 5, it can observe the proposed inverter by using CB-PWM techniques is produced %THD as 2.09, 2.13, and 2.16% respectively. As compared to the other existing systems the proposed inverter system produces less THD. Figure 18 represents the THD analysis between existing and proposed inverter systems.
THD analysis between existing and proposed inverter systems.
The article presents a simulation and implementation of a single DC-link-based three-phase Multilevel Inverter (MLI), focusing on its efficient use of DC bus voltage. This topology requires significantly lower DC voltage (330 V DC) compared to conventional three-phase inverters (600 V DC), enabled by a high-voltage gain DC-DC converter with both Proportional Integral (PI) and Neural Network (NN) controllers. Carrier-Based Pulse Width Modulation (CB-PWM) techniques are employed across various modulation index ranges to control the inverter, with the NN controller demonstrating superior performance over the PI controller in achieving optimized outputs.
The system’s performance is evaluated through harmonic indices, emphasizing reduced Total Harmonic Distortion (THD) and improved power quality. Simulation of the MLI is conducted using MATLAB/Simulink, while validation is performed through a hardware setup using XILINX FPGA software, which generates necessary switching pulses. Comparison with existing research highlights advancements in harmonic reduction and efficiency achieved by the proposed inverter design. research directions include enhancing control algorithms for further reducing THD, optimizing converter efficiency under varying load conditions, and exploring integration with smart grid technologies for enhanced grid stability and power quality management.
The data used to support the findings of this study are included in the article.
A Correction to this paper has been published: https://doi.org/10.1038/s41598-024-72904-z
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The authors acknowledge the funding from Researchers Supporting Project number (RSPD2024R665), King Saud University, Riyadh, Saudi Arabia. The authors would also like to thank Al Maarefa University, Riyadh, Saudi Arabia, for supporting this research.
Department of Electrical and Electronics Engineering, Vignan’s Institute of Information Technology, Duvvada, Visakhapatnam, 530049, India
Deparmtent of Electrical and Electronics Engineering, NMAM Institute of Technology, NITTE (Deemed to Be University), Karnataka, 574110, India
Department of Electrical and Electronics Engineering, GMR Institute of Technology, Rajam, India
Department of Industrial Engineering, College of Applied Sciences, Al Maarefa University, PO Box 71666, Diriyah, 13713, Saudi Arabia
Department of Mechanical Engineering, Faculty of Engineering, Suez Canal University, Ismailia, Egypt
School of Electrical Engineering, Vellore Institute of Technology, Vellore, India
Department of Chemistry, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Kingdom of Saudi Arabia
Department of Electrical and Computer Engineering, Hawassa University, Hawassa 05, Ethiopia
Center for Renewable Energy and Microgrids, Huanjiang Laboratory, Zhejiang University, Zhuji, Zhejiang, 311816, China
Department of Technical Sciences, Western Caspian University, Baku, Azerbaijan
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Correspondence to C. Dhanamjayulu or Baseem Khan.
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The original online version of this Article was revised: In the original version of this Article, Neyara Radwan was incorrectly affiliated. Full information regarding the correction made can be found in the correction for this Article.
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Varaprasad, M.V.G., Nuvvula, R.S.S., Kumar, P.P. et al. Design and implementation of single DC-link based three-phase multilevel inverter with CB-PWM techniques. Sci Rep 14, 18078 (2024). https://doi.org/10.1038/s41598-024-68293-y
DOI: https://doi.org/10.1038/s41598-024-68293-y
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