[Retracted] Optimization of Grid-Connected Photovoltaic Power Generation Technology Based on Nonlinear Back-Stepping Controller

Xuan, Feng; Han, Mengyang; Kumar, Avinash; Vishwakarma, Satyendra; Kannan, Nithiyananthan; Jain, Rituraj

doi:https://doi.org/10.1155/2022/2713874

Mathematical Problems in Engineering

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Research Article | Open Access

Volume 2022 | Article ID 2713874 | https://doi.org/10.1155/2022/2713874

[Retracted] Optimization of Grid-Connected Photovoltaic Power Generation Technology Based on Nonlinear Back-Stepping Controller

Feng Xuan,¹Mengyang Han,¹Avinash Kumar,²Satyendra Vishwakarma,³Nithiyananthan Kannan,⁴and Rituraj Jain⁵

Academic Editor: Vijay Kumar

Received15 Jan 2022

Revised25 Feb 2022

Accepted01 Mar 2022

Published30 Apr 2022

Abstract

To address the issue of energy scarcity and to use solar photovoltaic energy as a renewable source, a three-phase grid-connected photovoltaic inverter system with uncertain system model parameters is investigated, which converts DC power into AC power, feeds it into the grid, and maintains the grid-connected part’s quality. An enhanced back-stepping approach is proposed to explore the control strategy of three-phase solar grid-connected inverter, which includes adaptive control, dissipative theory, sliding mode control, and rapid terminal sliding mode control, respectively. It is verified that the system is subjected to external interference F = 5 during 0.5 s–0.8 s. As per the simulation results, the improved adaptive terminal sliding mode control method can suppress the interference to a certain extent and has strong robustness to the external interference. When compared with the adaptive sliding mode control approach, the anti-interference ability is better, and the system stability is improved. Then, to improve the above approach, a high speed terminal sliding mode control method is proposed, which can swiftly converge in finite time and the estimated value of uncertain parameters is closer to the actual value, thereby boosting the system’s robustness.

1. Introduction

Consequently, renewable energies are considered preferable than fossil fuels since they rely on plentiful and free natural resources. Solar power is a renewable range of energy. Solar power generation equipment is widely available and moderately priced, making it one of the most popular renewable energy sources due to its high efficiency [1, 2]. With the advancement and popularization of solar power generation technology, research into photovoltaic grid-connected power production technology has emerged as a hot research area at the moment. The solar grid-connected inverter connects the entire huge power grid to renewable energy generation, and it is the most crucial core component of the entire photovoltaic power generation system. The grid-connected inverter transforms DC electricity to AC power, feeds it into the grid, and preserves the grid-connected part’s quality [3]. Solar photovoltaic (PV) energy is a potentially useful and environmentally beneficial source of energy that has received much research due to its widespread availability, cheap maintenance costs, and lack of greenhouse gas emissions. In actuality, the gases emitted by typical fuel combustion have serious effects on living organs, human health, and the ozone layer. Research and practice show that solar energy directly radiates the Earth with abundant energy, widely distributed, reproducible, and nonpolluting and is an internationally recognized ideal alternative energy source [4, 5]. Every second, the sun emits approximately 5 million watts of energy to the Earth. Solar energy is utilised to generate photovoltaic power, and solar cells convert light energy into electrical energy. With technological advancement, solar power generating has become one of the most reliable power generation systems [6]. For two different grid-connected PV inverters, a particle swarm optimization-based DC-link voltage control technique is shown. The artificial intelligence-based controller is tested using a two-stage grid-connected Photovoltaic Generator (PVG). PVG, a boost converter, a DC-link, an inverter, an LCL filter, and the external grid are all part of the system [7, 8]. While comparing with other energy generating technologies, photovoltaic power generating devices have great advantages, have unlimited resources and distribution characteristics, do not need to transport, no resource depletion problem, do not need to burn, not gas emission pollution, no rotating components caused by wear and tear, long service life, do not need relevant personnel maintenance and management, and so on [9]. Domestic photovoltaic industry development lags considerably; in 2007, the installed capacity of battery production data is very small, and the sustainable development gap is large, despite the implementation of a number of policy, fiscal, and tax aspects. According to statistics, China's power generation in 2007 had a total installed capacity of 2.07 GW, which is a very small part of the world's 30.2 GW. By 2016, it had reached 334.54 GW, accounting for almost half of the global total. The National Energy Administration clearly points out that in 2020, the target of installed capacity is 100 GW, and the target of installed photovoltaic power generation is 1000 GW by 2050 [10]. As energy consumption grows, solar photovoltaic power generation has become an important part of renewable energy development. Our country's geographical area is a big advantage, which is about a quarter of the desert, making good use of one percent of the area can satisfy our country's power consumption of a year, many countries compared to China’s regional conditions, unusually rich solar energy resources. Compared with the annual radiation amount in general area, the average radiation amount in western China is about 1.75 times, so solar power generation has great advantages in the development of China [11]. The ability of a photovoltaic grid-connected power generation system to use equipment, techniques, or procedures to reduce the influence of natural and man-made noise on radio communications needs some serious attention. Peak power, high efficiency, control power sent into the grid, and low overall harmonic distortion of grid currents are all required for the conversion connection, according to the decision. Significant progress has been made in optimizing techniques for accomplishing the triple objectives throughout the preceding decade. The traditional PID controller is widely used in industry and literature due to its robustness, low cost, and ease of installation. Traditional control approaches (PI regulator or state regulator) produce good results in linearization. These techniques, however, become insufficient and unreliable for nonlinear systems or systems with changeable features, especially when the system’s performance objectives are strict [12, 13]. Chen et al. investigated the voltage-current double-loop control of a single-phase voltage-type PWM inverter. The PI regulator is used in the outer voltage loop to detect the supplied value, and the PI regulator is also used in the inner current loop to track the given current. This method controls the inverter with fast dynamic response and good robustness [14]. Liu et al. proposed a three-phase VPWM inverter based on voltage-current double-loop control to improve the dependence of the beat-free control on the inverter parameters and the output delay and poor dynamic response of repeated control. This method can be tracked quickly in the case of sudden load change [15]. Paul Raj and Meenakshi Sundaram proposed that PI control tracking sinusoidal current signal produces steady-state error, and its anti-interference ability is relatively poor. Therefore, the resonance of PR controller is used to increase the gain of the controlled signal at a specific frequency to eliminate the phase error, and a good grid-connected waveform quality is obtained [16]. In addition, PV output current varies with quickly changing weather variables like [R] as sun irradiation and temperature. However, there is a potential mismatch here between Highest Power Point (MPP) of the PV module and the load characteristics; a Maximum Power Point Tracking (MPPT) technique is required [17, 18]. However, there are challenges with grid-connected solar power generation systems, such as power quality, stability, and power mismatch, that academics are continuously researching in order to find better solutions. Solar power plants confront a dynamic sunlight availability issue, which influences the quantity of power available to the PVG. The output voltage and current of the PVG vary on Sundays because of changes in irradiance and temperature, as illustrated in the PVG’s IV-Characteristic. Even during the fluctuating behavior of Sundays, suitable control methods, usually known as Maximum Power Point Tracking (MPPT) algorithms, are used to maintain maximum and consistent output power [19, 20].

SMC (sliding mode control) is a nonlinear control scheme in control systems that adjusts a nonlinear system’s dynamics by applying a discrete control signal (or, more precisely, a collection modulation index) that allows the current to “slide” along a cross section of both the system’s normal behavior. Fast terminal sliding mode control is a common control approach that has already been actively investigated and applied for over 60 years due to its simplicity and robustness. The mode employs an interrupted control to generate a zone of attraction around a well before switching mechanism. The central planning law is not a function that changes with time. Instead, it can switch from one systematic strategy to some other depending on where it is in the state space. This paper uses an improved method of adaptive controlling to design the controller. k-class functions were introduced into the virtual functions of each step to design an improved nonlinear three-phase photovoltaic grid-connected inverter controller, which maintained the stability of DC voltage and grid-connected unit power factor while making the system state convergence faster and the oscillation amplitude smaller [21].

Solar photovoltaic power generation has become an essential aspect of renewable energy development as energy demand grows. This proposed model will help to use the energy efficiently with minimum losses. Moreover, the entire process is ecofriendly as it makes use of sun energy. The novelty of the work lies in the fact that it will help to increase the power factor of the inverter and to keep the power output maximum and stable.

2. Grid-Connected Photovoltaic Inverter

PV energy systems are becoming more popular as a potential replacement for traditional fossil fuel electricity. Design and operation of power converters, as well as how to achieve high efficiency for a variety of power combinations, are key components of energy PV systems [22, 23]. As per the relation between photovoltaic power generation and power system, it can be categorized into off-grid and grid-connected system modes. The off-grid system is not connected to the power grid, which is equivalent to a mobile charging power supply providing electric energy to remote mountainous areas, whereas the photovoltaic grid-connected system is connected to the power system as a link to provide electric energy to the entire system [24]. The solar grid-connected power generating system, which is typically consisting of photovoltaic arrays, inverters, and power grid, has taken the lead in the world. Photovoltaic array link as shown in Figure 1, photovoltaic cells in series, through the inverter will generate electricity to the filter link to filter, improve the waveform quality, improve through certain eventually to the power grid, the entire process, through the majority of the power point detecting control, enables the pv array to maintain in the most powerful state, and inverter control may help to generate the current output of the inverter to satisfy the grid needs.

As per the power level and different distribution of photovoltaic array, the photovoltaic grid-connected architecture can be divided into six forms, such as centralized, multibranch, dc, and fast mode. In terms of the power level, the centralized structure occupies a dominant position, and the master-slave structure or multibranch structure will also be adopted [25]. If it is small power, the development of building integration and the increase of home users, ac block mode, and DC block mode will be widely used; multibranch structure, string type will also be applied in them.

Peak power, high efficiency, control power fed into the grid, and low overall harmonic distortion of grid currents are all required for the conversion connection. As a result, the control strategy adopted determines the performance of grid-connected inverters [26, 27]. There are many kinds of grid-connected inverters. According to the series division of inverter power conversion, it can be categorized into two types: single-stage inverter and multistage inverter. According to the inverter, the phase can be divided into single-phase inverter and three-phase inverter; the small distributed photovoltaic power generation system is generally suitable for the occasion of single-phase inverter; three-phase grid-connected photovoltaic inverters are frequently used in large-scale photovoltaic power generation systems. According to the varying input and output modes of the inverter, it can be categorized as voltage source inverter and current source inverter. According to whether there is an isolation transformer that can be divided into isolated type and nonisolated type, in the isolated type, the inverter according to the different working frequency is divided into high frequency isolation type and power frequency isolation type and then in the nonisolated type is divided into single-stage type and multilevel type two topology structures. The inverter circuit of photovoltaic grid-connected inverter is mainly divided into half-bridge, push pull, and full bridge inverter.

2.1. Improved the Adaptive Back-Stepping Method Combined with Dissipative Theory to Design a Controller for Three-Phase Grid-Connected Photovoltaic Inverter

In the 1970s, the scholar Willems proposed the concept of dissipation, which is to establish the relationship between the storage function and the supply rate to abstract and express the form of heat dissipated by systems such as heat [28]. In nonlinear robust control theory, concepts such as dissipative system, supply rate as well as storage function of the dissipative system are used and defined in a nonlinear system as follows:where x is the state quantity, u is the input quantity, and y is the output vector.

If there is a nonnegative function such that V(0) = 0, then the following equation is true:

System (1) is a dissipative system with supplying rate of S(u, y), and the function V(x) is said to be of this dissipative system.

2.2. Storage Function

The nonnegative storage function V(x) is regarded as the energy function, and s(u, y) is the supply of energy to the system per unit time; then, the right end of Equation (2) can be recognized as the energy supply obtained by the system in time period and the left end as the energy storage increment in the period. In the same period, the energy increment stored by the system is not more than the energy supplied by the system, and the system has energy loss during the period. Systems with such properties are called dissipative systems.

In the system described in Equation (1), x(0) = 0 is an asymptotically stable dissipative system, which is a positive number given in advance, and the supply rate is as follows:

According to definition (1) and properties of function , the following equation holds:

Equation (4) indicates that the gain of nonlinear system is not more than or equal to A given positive value .

In view of the unknown model parameters of the photovoltaic grid-connected inverter and the existence of certain external interference to the system, the dissipative theory is combined with the back-stepping method and self-adaptation. In the design process, every step meets the requirements of dissipative property. Then, Lyapunov function is designed step by step, and the control law is derived by simulation. The response curves of system variables with and without disturbance are obtained, respectively, which is better than the traditional Lyapunov method. In considering the change of the lead to changes in the parameters of the electronic device, as well as the system problem of uncertain disturbance, in the use of the adaptive back-stepping method into the design of robust controller, it is assumed that we construct a storage function V (x) for the supply rate of the dissipative system problem, for the design improvements and join K function controller. Finally, through MATLAB/Simulink software simulation test, we verify whether the idea is feasible.

2.3. Mathematical Model of the System considering Uncertain Parameters and Uncertain Disturbances

Various model uncertain parameters were evaluated and are shown in Figures 2–4. Moreover, these parameters are compared with the adaptive control system. Considering that the equivalent resistance of the filter inductor will change so that the resistance value cannot be determined, an unknown parameter is added to the model, and considering that the system will be affected by external interference during operation, an uncertain disturbance vector is added to the system model, where , and finally Equations (5)–(7) can be obtained:

The improved adaptive back-stepping method was applied to design the controller in combination with the dissipative theory. In the design process, k-class functions were added to the virtual control quantity of each step, the control rate was calculated through the distributed design, and the derivative of the system energy storage function was satisfied with the dissipative inequality. In this paper, the design of the uncertain disturbance W has the same disturbance attenuation coefficient . The details are as follows.

Step 1. Define . For the first stage of system (5), is regarded as a virtual control quantity, and the stabilization function Equations (8) and (9) are adopted:In the formula, is the designed k-class function, and is both the designed normal number .Define the Lyapunov function (10) of the first subsystem of system (5):The derivative of is obtained as follows:Energy supply rate function (10) is as follows:To make the unit power factor of the system grid-connected, is simulated according to the designed controller, and the simulation results are as follows.
In Figure 2, the system state variables in the design of the improved adaptive control method combined with the theory of dissipative under the control of the fast response and stable in the short period of time in balance, to achieve the control objectives of the design, show the envisioned adaptive inverse control train of thought on the basis of footwork, joining the K function. This control method is feasible and effective.
In Figures 3 and 4, in the traditional adaptive control method, the dissipation theory combined with the adaptive control method and the improved adaptive dissipation of this section design three methods, respectively, to the state variables comparing the simulation results. This method is the fastest, the oscillation amplitude is tiny, and only the early controller gain is larger, and it may be combined to increase the dissipation adaptive response speed. Therefore, K functions can be added for free adjustment. The initial error value in Figure 3 is relatively small, so larger parameter is selected to improve the transient performance of the system. It is obvious that, compared with the other two methods, the control method in this chapter does tend to stable the equilibrium state quickly. As shown in Figure 4, the initial error value is relatively large, so a small parameter is selected to limit the gain of the controller to a certain extent. The control approach proposed in this paper, as shown in Figure 1, is actually relatively good. Figure 3, also shows that the disturbance disappears after 1.5 seconds; at the time of 1 second system disturbance, three control methods improve the dissipation adaptive control method. The dissipation of disturbance resistance is strong. The adaptive control method of traditional adaptive method by perturbation amplitude is large, and the improvement of dissipative adaptive control method at the time of 1.5 seconds brings quickly stable state. It is verified that the method can restrain the uncertain interference, and the system performance is good.

3. Experimental Analyses

To validate the efficiency of the grid-connected existing feedback-based droop control scheme and the enhanced grid-connected current active damper control method based just on tracking point of difference proposed in this work, a simulation of the an LCL inverter has been built throughout MATLAB/Simulink, and the two control techniques were compared. The effectiveness of the droop control scheme based on energy current input is validated as is the effectiveness of the enhanced control scheme based on traceability differentiator. Among these are the LCL converter system components, monitoring differentiation characteristics, and the difference approach for getting the second-order derivatives signal of the grid-connected current dependent on the grid-connected current feedback control scheme. The simulation in this work uses A-phase as the goal to assist viewing and because of three-phase symmetry. The grid voltage and grid-connected current of A-phase are given in Figure 5, where the purpose of the grid voltage is to give a reference to the phase of grid-connected current. After the simulating parameters are given, the simulation verification is carried out from three aspects: steady-state simulation, dynamic simulation, and antinoise capability.

The voltage and current waveforms of nonactive damping control, active damping control strategy based on grid-connected current feedback, and grid-connected current feedback active damping control strategy based on tracking differentiator can be obtained after the system has been stabilized, as shown in Figure 5.

It can be seen from Figure 5 that the THD of grid-connected current without active damping control is 4.52%. Although it meets the standard that the grid-connected current THD is less than or equal to 5%, its THD is still relatively large compared with the standard of grid-connected current. After the grid-connected current feedback control is added, the THD of grid-connected current is 3.52%. Compared with the control without active damping, its THD decreases by 1%, and the enhancement degree is 22.1%. The improved control strategy with tracking differentiator has a THD of 2.36% of grid-connected current. Compared with the control without active damping, its THD decreases by 2.16% and the degree of improvement is 44.7%. Compared with the grid-connected current feedback active damping control strategy, its THD is reduced by 1.16% and the degree of improvement is 32.9%. As a result, while both active damping control techniques can minimize grid-connected current oscillation, the enhanced active damping control strategy produces better grid-connected current quality than the active damping control strategy based on grid-connected current feedback.

4. Results

This research introduces the control problem of three-phase grid-connected photovoltaic inverter system with uncertain system model parameters studied. First, a system model of the synchronous rotating dq coordinate system is obtained using coordinate transformation, which takes into account the nonlinear system and the uncertainty of system parameters; the method of adaptive back-stepping control strategy was used to design the controller, and an adaptive control strategy based on sliding mode control method is introduced. And the hyperbolic tangent function is used to exchange the sign function in the sliding mode control method to improve common chattering, and simulation results show that the system in 0.5 s to 0.8 s with interference F = 5, improved adaptive terminal sliding mode control approach that suppress the interference ofa, strong robustness to external disturbance. Compared with the ordinary adaptation control method, the improved adaptation controlling method is more superior.

4.1. Analysis

When connected to the grid, however, solar power generation systems confront challenges such as power quality, stability, and power mismatch, which are being actively explored by researchers in order to provide a better solution. The issue of dynamic sunlight availability impacts solar-powered power plants, causing the power available to the PVG to fluctuate. The PVG’s output voltage and current vary on Sundays because of changes in irradiance and temperature, as seen in the PVG’s IV-Characteristic. Proper control methods, often known as Maximum Power Point Tracking (MPPT) algorithms, are used to ensure maximum and constant output power even throughout Sunday’s erratic behavior. It integrates adaptive control, dissipative theory, sliding mode control, and quick terminal sliding mode control to examine the control strategy of a three-phase solar grid-connected inverter. The updated control technique with the tracking differentiator has a THD of 2.36 percent of the grid-connected current. When compared with the control without active damping, THD is reduced by 2.16 percent, with a degree of improvement of 44.7 percent. When compared with the grid-connected current feedback active damping control strategy, THD is reduced by 1.16 percent, with a degree of improvement of 32.9 percent. As a result, from the aspect of grid-connected current quality, both active damping control techniques can reduce grid-connected current oscillation. When a three-phase solar grid-connected inverter is subjected to external interference F = 5 for 0.5s–0.8s, the simulated results show that it can suppress the interference to some extent and has good robustness to external interference and external disturbance.

5. Conclusion

Since the fossil fuel-based energy resources are degrading, it is a matter of urgency to rely on plentiful natural or renewable resources. Solar energy is among them. The paper describes a particle swarm optimization-based DC-link voltage control technique for three-stage grid-connected PV inverters. The Performance Evaluation Group (PVG) is used to analyze the quality of AI-based controllers. To assure the efficiency of the grid-connected existing feedback-based droop control scheme and the enhanced grid-connected current active dampers control method based just on tracking point of difference proposed in this work, a simulation of the an LCL inverter has been built throughout MATLAB/Simulink and the two control techniques were compared. The effectiveness of the droop control scheme based on energy current input is validated, as is the effectiveness of the enhanced control scheme based on traceability differentiator. It combines adaptive control, dissipative theory, sliding mode control, and fast terminal sliding mode control, respectively, to study the control strategy of three-phase photovoltaic grid-connected inverter. The simulation findings demonstrate that the system in 0.5 s to 0.8 s of interference F = 5, and according to the simulation results, the enhanced adaptive terminal sliding mode control technique suppresses interference and has high robustness to external disturbance. The suggested technique has been found to be stable and to produce better outcomes than alternative strategies. Uncertainties in DC-link voltage and grid parametric sensitivity system analyses have been saved for further investigation.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Disclosure

The preprint of this manuscript is at [29].

Conflicts of Interest

The authors declare that there are no conflicts of interest.

Acknowledgments

The authors are thankful to training Plan of young backbone teachers in Henan Colleges and Universities; and Research and Practice Project of Henan Vocational Education Teaching Reform.

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Copyright © 2022 Feng Xuan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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