1. Introduction
Recently, the availability of existing central electric energy generation has not been sufficient to meet the high and growing demand for this energy. This energy generation is considered a major and widely interesting research subject, represents a great challenge, and is one of the most important reasons for world countries’ economic development. Many countries and some private sectors invest huge amounts of money to cater to the high and growing demand locally, using mostly conventional generators such as coal, diesel turbine, or gas turbine. The use of these sources is becoming limited due to their high prices, and inefficient and untidy operation [
1]. It is also known that this serious production contributes to increasing carbon dioxide emissions and global warming, as well as pollution of the Earth. It represents a depletion of natural resource stocks, which primarily constitutes a threat to future generation capabilities [
2]. These obstacles made several governments of countries exploit all kinds of distributed energy resources based on renewable energy technologies or green energy technologies, due to their natural renewal. As they are environmentally friendly as well, they are clean and do not contribute to global warming.
Among the different renewable energy technologies (fuel cells, wind energy, hydropower, photovoltaic (PV), or solar energy, etc.), PV-system-based distributed energy resources are considered as one of the available resources in unlimited quantities in most world regions, and the most promising technology due to highreliability in operating, efficiency, and high potential capability [
3,
4,
5]. The use of the PV system in generating electric power helps isolated villages and regions to supply energy continuously while relying on storing surplus energy for use in critical times. Also, the use of the PV system leads to a reduction in the cost of importing energy for non-oil-producing countries, as well as reducing the cost of energy production, which makes the consumption bill somewhat low, and this is a good thing. In addition, it is free of pollutants, which have recently drawn much attention and have encouraged researchers to develop better techniques to produce a good PV system [
6,
7]. The highest generation level from the available renewable sources is shown by PV. In 2018, it was 36%, while all other sources were just 26% [
5]. In the electrical power world, one of the major issues in connecting PV systems to the grid is resolving the power quality problems caused by the rapid increase in non-linear loads connected to the electrical grids, such as harmonic currents or voltages, reactive power, power factor, and growing demand of active power [
8]. A typical grid-connected PV system is composed of a PV, a DC–DC power converter, DC-link energy storage, a three-level multifunctional voltage source inverter (MVSI)-based shunt active power filter (SAPF), a grid filter, and the control circuit. The use of SAPF in the electric power generation system helps greatly to improve the quality of power and current, which makes the periodic maintenance of the equipment less while also reducing the cost. Moreover, SAPF is an inverter, which can be two or three levels. The higher the SAPF level, the higher the quality of the current, which helps protect the devices and significantly reduces the bill for changing spare parts.
The PV systems with MVSI are connected to the grid at the point of common coupling (PCC). Many control techniques, along with some flexible devices, are used to control voltage, current, and, consequently, the power injected from the PV system to the grid at this PCC. Hence, this PCC is effective in remedying and eliminating most power quality problems. In any PV grid-connected systems, the DC–DC boost converter with maximum power point tracking (MPPT) is used to modify the voltage to the desired value and to extract the maximum power obtained from the PV array through the adjustment of a duty cycle [
9]. These modified voltages, at the maximum power value, transformed to the MVSI may be used as SAPFs for the control of the exchange of both the active and reactive powers between the PV system and grids [
10]. The PV system and MVSI are used together to maximize energy production from the PV system and serve as active power filters devoted to enhancing power quality at the same time. The control of the MPPT in the PV system and the MVSI-based SAPF can be combined in one control circuit.
MPPT technique is a very important phase to improve the performance of the PV system by maximizing the energy harvested from the PV system during climate changes. Due to these changes and the non-linearity of the PV characteristic, efficient research and robust control techniques were conducted for MPPT techniques. These MPPT techniques include the perturbation and observation method (P and O) [
11], inductance increment (INC) [
12], open-circuit voltage [
13], short-circuit current [
14], and proportional-integral (PI) controller [
15]. However, these techniques are ineffective when weather conditions change rapidly, as oscillations appear around the optimum point in the steady-state region. To deal with this problem, there are several techniques, such as non-linear control-type techniques such as sliding mode control (SMC) [
16], backstepping control [
17], synergetic control [
18], and super-twisting algorithm (STA) [
19]. These techniques have properties to control, mainly, the non-linear systems, and they are also distinguished by their precision, great robustness, and stability vis-à-vis the internal parameters system and the load uncertainties, but they seem difficult to use because they require a large amount of data regarding radiative change and temperature. Non-linear strategies, despite their high ability to improve system performance, reduce power ripples, and improve current quality, have many drawbacks, including complexity, as they are characterized by complexity, and difficulty in application to complex systems, as is the case in the backstepping control strategy.
Intelligent control systems such as fuzzy logic control (FLC) [
20], neural network (NN) [
21], and the hybrid of the two as an adaptive neuro-fuzzy inference system (ANFIS) [
22] were presented to improve the MPPT techniques. The ANFIS algorithm can convert linguistics into numerical values through membership functions and best alternatives, but this process is time-consuming, and require sophisticated hardware and complicated programming. On the other hand, the advantage of smart strategies is that they are characterized by high accuracy, ease of use, ease of implementation, and high durability, as there are no mathematical rules that limit their spread. Smart strategies rely heavily on user experience.
Reducing the total harmonic distortion (THD) is one of the important issues of injecting energy into the grid from solar panels. The SAPF, which is implemented using two-level inverters, is well-recognized for its efficiency in eliminating harmonics and compensating reactive power [
23]. This technique is primarily used to compensate for medium power range non-linear loads because of the limitations of semiconductor devices. However, high switching frequencies of the two-level inverter can result in problems when dealing with increased non-linear load power. Inverters’ static switches have high switch currents, and to reduce switched currents at a given power, multiple switches of the inverter may be necessary, leading to an increase in switch voltage [
24,
25]. To overcome this drawback, one possible solution is to interface the PV system to the utility grid via a multilevel inverter, since it offers many advantages such as lower harmonics rate, better electromagnetic compatibility, and lower switching losses [
26,
27]. The neutral-point-clamped (NPC) inverter topology is extensively used in medium- and high-power applications for compensating reactive power and eliminating harmonics in electrical networks, as described in reference [
28,
29]. These inverters offer numerous advantages such as reduced harmonics in the output voltages, decreased source current harmonics, lower switching losses, reduced voltage stress on power semiconductors, and the ability to overcome issues associated with SAPF based on two-level inverters. The performance of SAPF based on three-level NPC inverters is determined by the selected strategies for generating reference harmonic currents with good tracking quality; dynamic, robust, and stable injected currents; DC bus voltage regulation; and the precise generation of gate-switching pulses. The impact of switching frequency and gate-switching pulses on the performance of three-level NPC inverters has been explored by several researchers [
30,
31].
On the flip side, how well the SAPF performs is heavily reliant on its control strategies. To effectively regulate power flow in a power system, voltage-oriented control (VOC) is commonly employed, as it employs an internal current control loop that yields a strong dynamic response [
32]. However, recent publications proposed other control strategies, such as predictive control [
33] and direct power control (DPC) [
34], as an alternative to the VOC technique.
Over the past few years, the DPC technique has gained wider usage due to its fast dynamic performance and simple control implementation when compared to other methods [
34]. Also, the DPC strategy is one of the linear strategies that have spread recently in the field of renewable energies, as it depends on estimating capacities and can be easily applied to complex systems. DPC eliminates the need for internal current control loops and a pulse-width modulation (PWM) technique modulator block by using a switching table based on instantaneous errors between commanded and estimated values of active/reactive powers and voltage position vectors to select inverter switching states. The accurate and quick estimation of active and reactive line powers is crucial for successful DPC implementation. The DPC strategy depends on the use of two hysteresis comparators to control the active and reactive power, where the use of these traditional controllers creates several problems and defects, which limits their spread in the field of controlling electrical machines. DPC is based on direct torque control (DTC), which was originally proposed in 1986 by Takahashi and Nogushi for controlling an induction motor [
35]. In 1995, Mannienen introduced basic principles of DTC control applied to the line inverter, which may have a similar structure to the induction motor, but with connections to the grid and a line filter [
36]. In 1998, Noguchi proposed DPC for a PWM inverter without power source voltage sensors, and the same idea was developed by Malinowski in 2001 based on virtual flux estimation for a three-phase PWM rectifier system [
37].
The proposed tables generally exhibit superior performance compared to the classical table in reference [
38], but many of them, as indicated in reference [
39], rely on assumptions that simplify the dependence solely on the grid voltage angle. This is noted in references [
39,
40]. To achieve a switching table that is both accurate and efficient across a wide range of power levels, information on line inductance is necessary, as mentioned in reference [
38]. Malinowski [
37] introduced an alternative control strategy called the DPC technique with space vector modulation (SVM), which combines the advantages of VOC and DPC and employs an SVM block instead of a switching table, resulting in a fixed switching frequency [
41]. However, the conventional DPC–SVM technique uses a PI controller to determine the control angle and amplitude on reference voltage (
Vref), and an overshoot in power can occur if the gain values of the PI controller are not correctly adjusted [
41,
42]. To prevent these issues, alternative solutions have been proposed.
Various techniques have been suggested to address the shortcomings of the DPC approach, including the implementation of smart techniques such as neural networks [
43], fuzzy logic [
44], genetic algorithms [
45], and particle swarm optimization [
46]. Even though these techniques have been successful in reducing problems such as energy ripples, they have not entirely removed them, and the overall quality issue still exists. Non-linear strategies such as the SMC technique [
47], backstepping control [
48], synergetic control [
49], third-order SMC [
50], and STA technique [
51] have also been employed to enhance DPC performance, resulting in reduced power ripples and significantly improved current quality. However, these non-linear strategies add complexity and can result in undesirable phenomena such as chattering, which can negatively impact the system or hardware being studied. Therefore, it is important to identify a more efficient strategy that is simple and easy to implement and can serve as an optimal solution for controlling the three-phase SAPF. The aforementioned strategies used to control power generation systems to raise the quality of current and energy have their pros and cons, where the problem of some strategies lies in the complexity and difficulty of application. In addition, the connection of control strategies to the mathematical form of the system under study makes the response of the system in case of parameter change unsatisfactory. Therefore, a new strategy is given and used in this work that does not use the system parameters, which makes it provide excellent results in the case of changing the system parameters.
In this presented work, a simplified super-twisting algorithm (SSTA) control for grid-connected PV power systems and feeding non-linear load at the same time to a three-level multifunctional voltage source inverter to mitigate the power quality problems is used. This study presents a novel, SSTA control for grid-connected solar systems that consider feeding a non-linear load. In addition, a three-level multipurpose voltage source inverter is also introduced concurrently to mitigate power quality issues.
The primary goal of the proposed system is to face the power quality problems and alleviate their effects on the utility grid, with more emphasis on compensating for non-linear load harmonics and reactive power compensating. Furthermore, the use of a three-level NPC inverter in both compensating function and injecting active power into the grid is another way to enhance the power quality in the proposed power generation system. What is interesting in the proposed system is the optimal utilization of the PV energy sources through dual functioning by feeding energy to the utility grid and supporting the MSVI during harmonics disturbances compensation periods. The Matlab/Simulink platform is used to model the whole structure. The simulation results are provided, together with analysis and comparisons to the conventional PI, allowing evaluation of the proposed control measures.
The outline and contributions of this paper are presented as follows:
The SSTA controller is designed to optimize the performance of the PV system;
The design of the SSTA controller involves regulating the MVSI using the DPC–SVM technique, to reduce the THD value of the grid current;
Enhance the power quality and robustness;
The SSTA minimizes the tracking error and active powers ripples;
Reduce the overshoot, and enhance the dynamic response of PV and DC bus voltages;
Increase the durability of the filtration system;
SSTA strategy guarantees the global stabilization of the PV–SAPAF despite the variation.
Thus, the combination of the work is as follows. In
Section 2, PV–SAPF system models are presented. In
Section 3, the proposed non-linear control-based SSTA technique is discussed. In
Section 4, application for PV system and SAPF designed controllers is examined.
Section 5 presents and discusses the numerical results of the research carried out. In
Section 6, the conclusions are presented.
7. Simplified STA Controller
Under steady-state conditions, with an adequate control law, the sliding mode control forces the state of the system to meet the above conditions, i.e.,
,
[
60]. Usually, SMC law needs the measurement of the time derivative of the sliding function and provides a discontinuous form, which is sometimes inconvenient because of the chattering phenomenon [
61]. The STA control represents an alternative to overcome this constraint. In fact, it provides a continuous output and needs only the measurement of the sliding functions [
62]. On the other hand, the STA technique is a non-linear strategy that is characterized by simplicity and ease of implementation compared to several strategies such as backstepping control. Compared to the SMC technique, the STA technique delivers better results in terms of power ripples and improved current quality. Also, it significantly reduces the phenomenon of chattering. In addition, it can be easily applied in the case of complex systems, which makes it among the best solutions in the field of control. The classical STA control law is given by the following formula:
where
is the error or sliding surface, and
and
are positive values.
The bloc diagram of this non-linear controller is represented in
Figure 9. In
Figure 10, an equivalent structure is represented for the STA technique; it behaves similar to a PI controller but with non-linear gains (because of sign (
)). These gains can be deduced as follows:
where
and
are the fixed proportional and integral gains, respectively (entries in vectors
and
). One can easily see that the obtained equivalent controllers have a similar form to a conventional PI controller, however, with non-linear gains
and
. These gains are adaptive with respect to σ, and the new proportional gain
is smaller than the fixed one,
when
, and greater than when
. As a result, during the transient state (especially in the case of load change), the tracking error (which is, in fact,
S) is large (
, and, therefore, the gain
becomes lower than the fixed gain
to improve the stability of the system. The same behavior of the adaptive integral action can be noted. In fact, during transient states, a smaller gain is imposed (
), to reduce sensitivity to transient disturbance. When the system reaches the sliding surface, the sliding function is zero (or almost zero); in this case, the proportional and integral actions impose gains
, or
s
, or
, offering, therefore, better steady-state performances than a fixed PI controller.
Despite the simplicity and ease of implementation, many drawbacks limit the spread of the STA strategy in the field of control, such as the difficulty of adjusting the dynamic response, its impact on changing system parameters, and the problem of chattering.
The study aims to enhance the dynamic response and simplify the STA algorithm. The SSTA technique is proposed as a new approach to the traditional STA algorithm in [
63], which is represented by Equation (17). The stability of the proposed SSTA controller is evaluated using the Lyapunov theory [
63]. However, the SSTA technique is a modification or change in the traditional strategy, where simplicity and ease of implementation are the biggest advantages of this controller. According to reference [
63], the SSTA technique has higher robustness and performance compared to conventional control. The proposed SSTA algorithm is found to be simpler than the conventional STA technique.
where
K is the positive gain (
K ≠ 0).
By using the parameter (k), the response of the system can be easily adjusted, as the genetic algorithm can be used to determine the value of K, and, thus, obtain an ideal dynamic response.
The operational concept of the suggested SSTA controller is depicted in
Figure 11. This figure demonstrates that the proposed SSTA controller can be easily and cost-effectively implemented in any system without the need for a mathematical representation of the system.
9. SVM Technique
SVM technique is among the techniques that are used for inverter control, whereby a series of pulses are generated necessary to operate the inverter relays. Compared to PWM technique, it is better and more robust, providing very satisfactory results for THD value. The disadvantage of this strategy is that it is complicated compared to the PWM technique, especially in the case of a multi-level inverter.
The reference voltage is modulated using the SVM technique. The following four steps can resume this one: localization of the sector, location of the region in the sector, calculation of the switching times, and, finally, finding the switching states. A TLI is characterized by 27 switching states or vectors represented by the hexagon in
Figure 20, which is divided into six equal sectors, each of which is also divided into four regions. Among the 27 possible states, 24 are active states, and 3 are zero states that lie at the center of the hexagon [
64,
65]. The voltage vectors form four groups are, namely, the large vectors group, the medium vectors group, the small vectors group, and the zero vectors group, as shown in
Table 2.
In the
reference frames, this vector has a magnitude and angle given as:
The reference voltage vector scans all six sectors at the fundamental frequency of the desired output voltage. Then, it is required to continuously detect the sector in which the voltage vector is progressing as follows:
If then is located in sector A;
If then is located in sector B;
If then is located in sector C;
If then is located in sector D;
If then is located in sector E;
If then is located in sector F.
Inside the located sector, one must define the region of the voltage vector. From the space vector diagram in
Figure 19, the reference voltage vector can be seen as the sum of two components
and
, such as:
Now, the regions are located as follows:
If then is located in region 1;
If then is located in region 2;
If then is located in region 3;
If then is located in region 4.
Inside the region, the reference control vector
is now expressed during a sample period by the nearest vectors. The simplest illustrative example is the case of region 2 in sector A, as illustrated in
Figure 21 in which one can write.
Splitting this into real and imaginary parts gives:
is the modulation index. Using the same procedure, the dwelling time in other regions in sector A can be obtained, as shown in
Table 3.
10. Results
In this part, the results of the proposed SSTA strategy in this paper are compared with the results of the traditional PI strategy under different working conditions. The system parameters are represented in
Table 4. In addition, the parameters of the SSTA technique are as follows:
, and
.
The obtained results are represented in
Figure 22,
Figure 23,
Figure 24,
Figure 25,
Figure 26,
Figure 27,
Figure 28,
Figure 29,
Figure 30,
Figure 31,
Figure 32,
Figure 33,
Figure 34,
Figure 35 and
Figure 36.
Figure 22,
Figure 23 and
Figure 24 represent the references (profile) used in this work for PV irradiation, temperature, and load power, respectively.
Figure 25 represents the power flow at different modes based on SSTA control. Results indicate that the capabilities
Pg,
Pl, and
Ppv perfectly track changes in reference values. In addition, larger ripples are observed in the time domain [0, 0.1 s] for power
Pg before filtering. The distribution of power flow within the proposed system, from the sources of generation to the consumption of load, is categorized into six distinct cases:
Case 1: It can be noticed that from t = 0 to 0.3 s when there is no irradiance, the grid supplies nearly 15 kW. The majority of this power is utilized by the non-linear load of 14.4 kW, and the remaining amount is utilized to balance the active filter losses to maintain the DC bus voltage constant. This can be expressed as , where ppv is equal to zero.
Case 2: During the time interval from t = 3 to 0.6 s, it is evident that the PV is generating almost 10 kW of power, and the grid is providing 4.2 kW while corresponding to the new irradiation profile, and temperature. The non-linear load of 14.4 kW is the main consumer of this power, and the rest of the power is used to balance the losses of the active filter so that the DC bus voltage remains constant. The equation expresses this relationship, with .
Case 3: Between t = 0.6 s and t = 0.9 s, there is an increase in load power by 18 kW while the PV power decreases by 7.6 kW. During this phase, the non-linear load is supplied by two power sources: PV and grid 11.3 kW, with the total power being the sum of the two sources , where .
Case 4: Between the time intervals of 0.9 s and 1.2 s, the power generated by the PV system 15 kW matches the power demand of the load of 14.8 kW. During this period, the utility grid does not generate any power, PL = PPV, and .
Case 5: During the time from 1.2 s to 1.5 s, the power generated by the PV system is 15 kW, which exceeds the power demand of 7.6 kW. As a result, 7.4 kW of surplus power is sent to the grid, and .
Case 6: Between 1.5 s and 1.8 s, there is a rise in the load power by 14.4 kW, while the PV power decreases by 8.7 kW. This mode bears resemblance to Case 2, and , with .
Figure 26 represents the PV output current, voltage, and power response for both the proposed and classical strategies. With this figure, the voltage, current, and power follow the references well with ripples in the case of using a PI controller compared to an SSTA controller. Moreover, the proposed strategy provides a better response time to voltage, current, and power than the PI controller.
Figure 26 represents the PV output current, voltage, and power with their references for both the proposed and classical strategy before and after connecting at the grid at 0.3 s. Before connecting PV to the grid, the output current and power are equal to zero. The comparison of these behaviors shows that the PV output current and power perfectly track their references with zero ripple and steady-state error in the case of the SSTA technique. It can be observed that the PV output current, voltage, and power overshoot at all points of the varying irradiation are greatly reduced with very small response time to voltage, current, and power in the case of the SSTA technique compared to the PI controller.
Figure 27 depicts the response of the used controllers’ DC bus voltage. The voltage tracks its reference value of (800 V) both before and after connecting the PV to the grid at t = 0.3 s. The performance indicators provided in
Table 5 reveal that the SSTA outperforms the PI in terms of response time. The DC link voltage stability is significantly impacted by changing irradiation levels and non-linear loads. The SSTA strategy demonstrates less overshoot and fewer ripples. Furthermore, the error in steady-state is minimal when using the SSTA strategy, compared to the PI controller. Grid active power is represented in
Figure 28. This capacity follows the reference satisfactorily for both the traditional and the proposed strategy with an advantage to the proposed strategy in terms of ripples compared to the traditional strategy. The imaginary power on the grid side is illustrated in
Figure 29. It can be observed that both control methods keep the imaginary power at zero, which verifies the earlier conclusion regarding the power factor. However, the SSTA technique demonstrates less fluctuation around zero compared to the traditional strategy, indicating that it may be a more effective means of regulating the power factor.
Figure 30 and
Figure 31 represent the three-phase grid currents in the case of the traditional and proposed strategies, respectively. Through these forms, the current takes the form of a sinusoid, and its value is related to the values of the references used with the presence of ripples in the two controls, where these ripples are greater in the case of the traditional strategy.
Figure 32 and
Figure 33 represent the first phase of the grid current and voltage for the strategies used in this paper. The voltage and current take a sinusoidal form and their values are closely related to the system, as ripples are observed at the voltage and current levels.
Figure 34 represents the value of THD of grid currents before and after filtering, where the value of THD of current is 23.30% and the amplitude of the fundamental signal (50 Hz) is 29.58 amperes.
Figure 35 and
Figure 36 represent the FFT analysis of grid current phase after filtering in the case of using the SSTA control and PI control, respectively. Through these two forms, the SSTA strategy provides better values of THD of grid current phase in different cases, with a larger fundamental (50 Hz) amplitude value compared to the traditional strategy, which indicates the robustness of the proposed strategy in improving the quality of the current.
The comparative results between the proposed SSTA control and the PI control are presented in
Table 5,
Table 6 and
Table 7. From these tables, the proposed control provides superior values compared to the control based on the PI controller in terms of overshoot, THD value of source current, voltage ripples, setting time, undershoot, etc. Therefore, it can be said that the proposed control is the best in the field of control. Moreover, it is noted that the reduction percentage of the THD value of current is less in the case of after filtering G (W/m
2) = 0 (see
Table 7). However, the percentage reduction is greater in the case of after filtering G (W/m
2) = 1000. Therefore, it can be said that the higher the value of G (W/m
2), the greater the percentage of reduction in the value of THD of current.
In
Table 8, the work performed is compared with some works published in the same field in terms of the value of THD of current. Through this table, the proposed control presents a value of THD of current that is very satisfactory compared to several controls that have been published in scientific works. Accordingly, it can be said that SSTA control can be relied upon as one of the best solutions in the field of control, especially in the field of renewable energies. In addition, these obtained results prove the results obtained in the work [
63].