1. Introduction
Global energy production has been steadily increasing to meet the electricity needs of society and industry, with most of the energy produced from fossil fuels [
1]. However, fossil fuel resources are limited and expected to run out eventually, necessitating alternative energy resources to contribute significantly to global energy production and, ultimately, replace fossil fuels. In addition, these fuels have a detrimental effect on the environment because they contribute to pollution. To mitigate this adverse effect, we can employ renewable energy sources, including biofuel, solar, hydropower, biomass, wind, tidal, and geothermal, etc. [
2,
3]. Some renewable energy sources can be integrated into the existing energy systems. Such integrated energy systems can boost energy efficiency and decrease operational expenses, and they are more environmentally friendly [
4,
5].
Photovoltaic (PV) panels are being widely used to capture solar energy. Although they still have limited efficiency, they have several advantages, such as no additional fuel consumption, perfect silence, minimal maintenance costs, ease of installation, etc. [
6,
7]. PV plants are broadly classified into stand-alone and grid-connected [
8]. Stand-alone plants provide electricity to isolated consumers far from the power grid or have low electricity demand [
9,
10,
11]. Grid-connected systems are tied to the electricity grid and feed it whenever they generate more than the local demand, although they may cause some problems to the grid, like harmonic distortion and phase unbalance [
12,
13,
14].
As incident solar energy varies a great deal due to the motion of the sun and climatic conditions, maximum power point tracking (MPPT) control schemes are essentially used to extract the maximum amount of available energy from an installed capacity. As an illustration, by implementing MPPT on a single BP SX 150S PV module, a maximum power of 144
is achieved with an efficiency of 96%. A facility with 72,000 sun power PV modules could generate around 10.368
. However, the same facility could only generate just 7.56
without MPPT with an efficiency of approximately 70% [
15]. With MPPT, the solar energy conversion systems boast even up to 98% power extraction/conversion efficiency. In small domestic systems, an improvement in this figure will not mean much; however, in large PV farms, even a fractional improvement will significantly change the generated output.
MPPT works using the perturb-and-observe (P&O) technique [
16,
17,
18]; it is a simple technique with a low computational burden, making it straightforward to implement. The incremental conductance (IncCond) technique also has almost similar advantages [
19,
20]. However, both methods are less effective when there are rapid changes in irradiation and oscillations in the steady state [
21]. Therefore, several other sophisticated control methods have been used to improve the performance of MPPT.
The fuzzy logic control is used as an alternative to improve the MPPT performance. This method can be optimized with a combination of particle swarm optimization (PSO) and genetic algorithms (GA), resulting in a much-improved performance compared to P&O and IncCond methods in tracking the PV reference voltage with higher speed and precision [
22]. However, fuzzy logic combined with metaheuristic schemes takes multiple iterations to attain the low desired error, necessitating a fast processor to acquire a solution in the shortest time.
The adaptive neuro-fuzzy inference system (ANFIS) with PSO can also track the PV reference voltage more accurately than P&O and IncCond [
23,
24]. A hybrid ANFIS technique collects fuzzy data with learned rules to properly adjust membership values before the error is reduced to the minimum possible values. The learned system becomes a hybrid MPPT controller when membership settings are changed. Nevertheless, this technique requires a strategy to enhance efficiency by circumventing the procedural complexities of ANFIS-based hybridization approaches.
The artificial neural network (ANN) algorithm can also accurately track the MPP with slight overshoots. The optimal application of the ANN algorithm depends on the number of neurons in the hidden layer, the selection of the activation function, and neural network training; its precision can be improved by increasing the number of neurons and hidden layers [
25]. However, in the event of an adverse change, it will take a long time again to achieve the optimal PV reference voltage tracking.
Robust integral backstepping control is also used for MPPT with PV reference voltage obtained through neuro-fuzzy techniques. The simulation results have shown faster and more accurate tracking compared to P&O and PID with parametric uncertainties under climatic changes. However, there are still oscillations in the extracted power from the PV [
26].
A two-loop control is developed to keep track of the MPP more effectively; the first loop determines the maximum power voltage reference of the solar array based on the current PV voltage, temperature, irradiance, etc., and then the second loop regulates the output to the reference voltage using the sliding mode control (SMC) [
27,
28]. This technique is reported to have improved the power converter efficiency by close to 99%. The overall performance is not optimal because there is still chattering around the steady state.
The terminal sliding mode control (TSMC) can track the reference with finite time convergence and has a superior output response compared to PI control. Nevertheless, the comparison with the PI controller is insufficient; it should also be compared to some advanced approaches, particularly those based on SMC [
29].
The SMC optimization with backstepping super-twisting sliding mode control (BSTSMC) can maximize power extraction with superior performance tracking accuracy, finite-time convergence, and fast dynamic response compared to P&O, PID, and conventional sliding mode control (CSMC) with parametric uncertainties [
30]. However, the chattering problem still exists.
SMC is a variable structure control with two major benefits: ease of tailoring the system’s dynamic behavior by selecting a specific switching function and insensitivity of the closed-loop performance to a class of uncertainties [
31]. SMC comprises three steps: creating a sliding surface in state space, developing a switching control law to reach the sliding surface, and building an equivalent control to ensure that the system state trajectories remain on the sliding surface [
32].
The sliding surface significantly affects the SMC’s performance [
33]; generally, the sliding surface in a CSMC is simply a positive constant multiplied by the tracking error. However, the sliding surface can be modified using several control techniques like P, PI, PID, and many more. The objective of modifying the sliding surface is to improve the tracking error performance of the controller.
Integral sliding mode control (ISMC) modifies the sliding surface to eliminate the reaching phase, which can improve the transient response. However, the effectiveness of tracking performance in the transient response of ISMC is inferior to GSMC [
34,
35]. Then, to reduce the chattering, it was suggested that the switching element be smoothed with a low-pass filter. It was known through simulations that ISMC can track the reference with superior performance in chattering attenuation. In the other article [
36], the ISMC approach with a proportional-integral (PI) sliding surface can preserve the transient performance besides eliminating steady-state errors. Nevertheless, some chattering is still there due to the switching control.
SMC combined with PID sliding surface has shown improved tracking performance. The error tracking the performance of this SMC improvement outperforms the super twisting sliding mode control (ST-SMC) and nonsingular terminal sliding mode control (NT-SMC) when a disturbance signal is present. However, there are no clear guidelines to calculate the PID gains
, and
[
37]. The sliding surface PID is also applied to eliminate the chattering problem by replacing the switching function with a hyperbolic function; however, the performance is not very convincing [
38].
Quasi-sliding mode control (QSMC) can also reduce the chattering defining a boundary layer; the determination process of the boundary layer, however, is not clearly known [
39].
This paper proposes the application of GSMC to optimize the MPPT. GSMC is an enhancement to SMC that aims to improve the control system performance by reducing errors, accelerating convergence to steady state, and allowing robustness against uncertainties and disturbances. The proposed strategy is outlined as follows.
The GSMC ensures system stability throughout the control process. As improvements in the control law, the following are also proposed.
The proposed controller aims to eliminate the reaching phase and accelerate the PV reference voltage tracking response, hence improving the power extraction efficiency.
The main contributions of this paper are as follows:
Design of a two-loop MPPT control using GSMC with adaptive gain scheduling exhibiting smaller rise and settling times, no chattering, and low steady-state error.
Performance analysis of the proposed controller under varying temperature and irradiance and with parametric uncertainties and load variations; extracted power and energy computations to highlight the expected gains over the other MPPT and control schemes.
Stability analysis of the overall system to prove Lyapunov stability.
The remaining sections are organized as follows:
Section 2 presents the modeling of the PV module and boost converter,
Section 3 describes the proposed global sliding mode MPPT controller,
Section 4 explains the simulation results, and the conclusions are shown in
Section 5.
4. Simulation Results
Extensive MATLAB™/Simulink™ simulations are conducted to evaluate the performance of the proposed GSMC-MPPT control system. A single Kyocera™ KC200GH-2P PV module panel rated for 200
with the parameters given in
Table 1 is considered. The boost converter and controller parameters are given in
Table 2.
As the scalability of any such control scheme depends on the scalability of the front-end, i.e., the switching devices in the DC–DC converter, it is expected that the proposed control scheme should not have any problems with the scaling up or down. To verify this argument, a system will be developed as a future work and tested practically.
The proposed controller was simulated under climatic changes with parametric uncertainties and load variations on a computing machine with an Intel® CoreTM i7-1195G7 @ 2.90 (8 CPUs), 2.9 , 16 GB RAM, 11th generation. With this machine, a 0.9 simulation took 1.28 with a 4 × 10−5 sampling time. This demonstrates that the proposed controller is not computationally expensive. In practical applications, high-end microcontrollers, FPGAs with a frequency of 250 and the Raspberry™ Pi™ with a frequency of 1.5 can be utilized.
The current study does not evaluate the effect of dust, sand, or moss covering the PV arrays; it also does not discuss partial shading on PV modules because this article focuses on improving the controller’s performance in extracting maximum power from a PV capacity. To evaluate the robustness of the proposed controller, this paper discusses the impact of parametric uncertainties and load variations under different temperatures and irradiances.
4.1. Response under Standard Operation Conditions
These simulations are conducted at 25 °C, the irradiation level of 1000
and a load resistance of 40 Ω. Using Equation (21), the reference voltage
is obtained as 26.3
, which exactly corresponds to the rated voltage in the PV panel’s specifications.
Figure 6 shows the
tracking performance of the CSMC-, QSMC-, and GSMC-based MPPT controllers, and
Table 3 gives the comparative performance parameters. It is evident that the proposed GSMC-based controller shows a superior performance by achieving the least rise time, settling time, and overshoot among all three controllers.
Figure 7 shows the error analyses of the three controllers under standard conditions. These errors include the integral square error (ISE), integral time square error (ITSE), integral time absolute error (ITAE), and the integral absolute (IAE). It is again evident that the GSMC-based controller’s performance is superior to the other controllers.
4.2. Response under Varying Temperature
This set of simulations is performed under varying temperature conditions, as shown in
Figure 8; the irradiance and the load resistance are the same and constant as before.
With the temperature variations, the
also varies.
Figure 9 illustrates the comparison of
tracking responses. While the CSMC-based MPPT controller can track the reference, it produces chattering, whereas the QSMC and GSMC-based MPPT controllers can achieve it without chattering. Furthermore, the proposed GSMC-based controller again has the most superior performance among the three controllers, as evident from
Table 4.
Figure 10 illustrates the controllers’ responsiveness to the extracted power; the figure depicts identical responses to those of
Figure 9. Moreover,
Figure 11 demonstrates the error responses.
These simulations indicate that the proposed controller with adaptive gain scheduling and a modified equivalent is not only faster in transient response but also consistent in performance despite the set point changes owing to varying temperatures. The proposed controller successfully follows the set point in minimum time because the reaching phase is eliminated, and the states are placed directly on the sliding surface. The error is reduced owing to adaptive gain scheduling, which reduces errors by automatically adjusting the switching control’s gain according to Equation (35). The response is expected to be even better for slowly varying parameters, as is the real scenario.
4.3. Response under Varying Temperature and Irradiance
The third set of simulations compares the response of the proposed controller with those of the QSMC- and CSMC-based controllers under varying temperature and irradiance conditions, shown in
Figure 12. These scenarios are designed to have both in-phase and out-of-phase changes in temperature and irradiance. This test compares the controller performance in terms of the tracking performance (tracking error) and the stability (transient performance): rise time, settling time, and overshoot and undershoot. In the simulation, the load resistance is set to 40 Ω.
A comparison of the peak power under varying temperatures and irradiances is also shown in
Figure 13. Furthermore,
Figure 14 depicts the
tracking response. The performance comparison of the three controllers is given in
Table 5.
Figure 15 shows the power response, which again shows the better performance of the proposed controller.
Responses of equivalent control, switching control and sliding surface under varying temperature and irradiance conditions are shown in
Figure 16,
Figure 17 and
Figure 18, respectively, for the three controllers.
Figure 16 depicts switching control with a chattering amplitude of around 180. To reduce chattering, as illustrated in
Figure 17 and
Figure 18, the switching control is constrained by a saturation function with a boundary layer of the sliding surface.
Figure 19 displays the error comparison between the three controllers at varying temperature and irradiance conditions. As seen from the figure, the CSMC controller has larger errors than QSMC and GSMC controllers in IAE, ISE, ITAE, and ITSE. The error is not optimally reduced in CSMC because the controller does not have enough robustness against these changes. By contrast, the proposed controller can reduce errors effectively by adjusting the robustness via gain scheduling.
4.4. Response to Parametric Uncertainties and Load Changes under Varying Temperature and Irradiance
The fourth set of simulations compares the performance of the three controllers under varying temperatures and irradiances with parametric uncertainties and load variations. Inductor uncertainty is introduced according to the following schedule (nominal 22 ):
Sub-interval 1 (0–0.3 ): 15 .
Sub-interval 2 (0.3–0.45 ): 55 .
Sub-interval 3 (0.45–0.9 ): 15 .
Moreover, the load varies according to the following schedule:
Sub-interval 1 (0–0.65 ): 40 Ω.
Sub-interval 2 (0.65–0.75): 50 Ω.
Sub-interval 3 (0.75–0.9 ): 40 Ω.
The performance of three controllers for rise time, settling time, overshoot, and steady-state error is given in
Table 6. It is evident that the proposed controller has outperformed the other two in all aspects.
Figure 20 depicts the
tracking response of the controllers, and
Figure 21 shows the extracted power.
Figure 22,
Figure 23 and
Figure 24 depict the switching control, equivalent control, and sliding surfaces of the three controllers, respectively. In
Figure 22, the switching control exhibits a high chattering characteristic with an amplitude of approximately 140. This chattering will deteriorate the system’s performance and reduce its life due to overheating. Switching control with a QSMC-based controller can reduce the chattering, although not as much as the proposed GSMC-based controller can do. As illustrated in
Figure 24, the chattering phenomenon can be significantly decreased using the proposed controller, using Equations (36) and (37), which implement adaptive gain scheduling and the saturation function with a boundary layer. The adaptive gain scheduling scheme adjusts the gain on switching control based on the error between the output and reference. The gain increases as the error increases, and vice versa. This strategy aims to improve the robustness of the controller. Furthermore, the boundary layer can prevent chattering by using switching control outside the boundary layer and linear feedback control inside the boundary layer.
Figure 25 compares the proposed controller’s errors with those of the QSMC- and CSMC-based ones for extracting the maximum power from solar PV.
4.5. Extracted Power and Energy
Figure 26 shows the irradiance and temperature variations in Jeddah City on 6 July 2000 [
47]. This particular scenario is selected as there are many sharp variations, especially in irradiance. On a clear, sunny day, these variations will be very smooth and will not evidently demonstrate the actions of the conversion system.
Figure 27 shows the power extracted on a single day (6 July 2000) in Jeddah City from a PV system with a single Kyocera™ KC200GH-2P module using the three controllers.
Table 7 gives the comparison of average extracted power from the plots of
Figure 27, daily energy output, and system’s conversion efficiency from the three controllers. It is evident that the proposed GSMC-based MPPT controller has the highest efficiency, followed by the QSMC-based and CSMC-based controllers. Although there seems to be just a slight gain of the proposed controller over the other two, this can translate to significant gains on a large scale.
Using data in
Table 7 as an example, by implementing the proposed controller with uncertainties under climatic changes for a large-scale solar farm using 72,000 PV modules on the same day, it would have generated an output of around 82.45
(PV output: 82.468
) with an efficiency of 99.98%. The two MPPT schemes using CSMC-based and QSMC-based controllers would have delivered 80.728
and 81.766
with an efficiency of 97.89% and 99.15%, respectively. On the same day, both P&O-based and IncCond-based MPPT schemes would have been able to deliver just 79.697
and 79.714
with an efficiency of 96.64% and 96.66%, respectively [
48]. Nevertheless, the same facility without MPPT would only generate approximately 57.728
with an efficiency of around 70%.
5. Conclusions
In this paper, a GSMC-MPPT controller with adaptive gain scheduling is proposed to track the MPP of a PV system. The proposed controller’s performance is compared with CSMC- and QSMC-based MPPT controllers under varying temperatures and irradiances and with load variations and parametric uncertainties. Without parametric uncertainties, the proposed MPPT control scheme outperformed other controllers in simulations, reaching the set point with a rise time of 0.03 as opposed to 0.11 and 0.22 for QSMC and CSMC, respectively. With parametric changes, the proposed controller showed an overshoot of 1.2 around a steady state value of 21.9 , as compared to 1.51 and 1.45 for QSMC and CSMC, respectively. Furthermore, the proposed controller and the QSMC-based controller both have a steady-state error of 0.3 , whereas the CSMC-based controller has a larger error.
The proposed MPPT controller performs much better than the other two controllers because the controller eliminates the reaching phase and places the system states directly onto the sliding surface; with adaptive gain scheduling, it can automatically adjust the gain of the switching control based on the IAE calculations to minimize errors and adjust the robustness. Based on the results and calculations of ISE, ITSE, ISE, and IAE, the proposed controller response exhibits a faster rise time, low tracking error, and no chattering due to the switching control. The energy calculations have further supported the conclusions as there will be significant gains with the proposed GSMC-based MPPT controller for large solar farms.
As is the case with any control scheme—especially linearized ones—when dealing with nonlinear systems, both the transient and steady-state performances are not global. Although the adaptive gain scheduling control will certainly expand the horizon, it can never encompass all possible scenarios. Moreover, selection of a proper sliding profile is critical as it will affect the controllable horizon. Nevertheless, the proposed scheme is expected to enjoy all the benefits of GSMC and be further enhanced due to the adaptive gain scheduling. On the other hand, this paper does not take into account the effects of dust, sand, moss covering, and partial shading, etc., as the focus is on improving the controller performance in extracting maximum power from a given PV capacity.
As a future work, the scheme will be implemented on an experimental setup. The system will involve extensive sensing of all the crucial parameters to obtain the real states of the system. Although the proposed scheme is not computationally expensive, it will be tested with different computational hardware, like microcontroller, DSP, FPGA, etc., to see the effects on the system performance.