1. Introduction
Dynamic power transactions, varying electricity pricing, and the intermittent nature of renewable energy output in relation to load demand are some of the issues grid-connected PV systems face [
1]. The PV system and the grid must be seamlessly integrated to harvest generated power efficiently. The PV system and the electricity grid’s utility must meet technical requirements to guarantee safety and dependability. Grid-connected solar sources usually use DC–AC inverters to supply P and/or Q to the line. Appropriate power control strategies are required for inverters to manage the amount of P and Q injection to meet the local load profile. Several power electronics-based techniques, such as the widely used vector-type control, have been developed to regulate P and Q injection. Furthermore, PV arrays can produce the required amount of Q with proper inverter controls to provide voltage support [
2,
3].
In [
2], the authors examined hybrid renewable hydrogen systems intended for stand-alone use. They achieved this by modeling hybrid PV-H2 systems through simulations. This strategy combined PV technology, which turns sunshine into electricity, with renewable energy-powered hydrogen (H2) manufacturing devices. The study assessed the effectiveness, viability, and possible advantages of combining these technologies to produce self-sufficient and sustainable energy solutions using simulations. Fuel cells use electrochemical reactions to make electricity, whereas PV panels use sunshine to generate power. Moreover, Yunez-Cano et al. investigated a PV/H2 system, including measurements of the H2 unit’s dimensions and assessments of the power production of the solar array [
4]. Most research has concentrated on using PV energy as a stand-alone or grid-connected system with storage options. However, little research has been conducted on integrating PV interconnections with hydrogen fuel systems. It faces multiple challenges, including fluctuating electricity prices, power transaction momentum, and the disparity between renewable energy production and load demand [
4].
The PID controller’s performance and the hybrid renewable energy system’s overall stability and efficiency were improved by [
5]. It used the ASCA technique to dynamically modify the PID controller’s gains to maximize its adaptability to changing circumstances and variations in load. This enhanced the system’s capacity to sustain precise and steady control under various operational conditions. The study intended to increase disturbance rejection, minimize transient responses, and improve reference signal tracking by optimizing the PID controller using AS-CA-based methods, ultimately improving system performance.
In [
6], a novel method for controlling voltage in distribution networks was presented, which tackles the difficulties caused by random PV power generation. The project aimed to improve voltage stability, reduce infrastructure costs, and facilitate the effective integration of renewable energy sources into distribution networks by employing a hierarchical control technique and accounting for PV production unpredictability.
Presenting a novel converter-less control technique for a hybrid renewable energy system that combines fuel cells, solar PV, wind, and battery energy storage was the aim of [
7]. The goal of [
8] was to do away with traditional power electronic converters, which would simplify the architecture and improve the system’s overall performance, stability, and efficiency. Offering a novel strategy for enhancing the performance of hybrid energy systems advanced the fields of control techniques and renewable energy systems.
Three-phase PV grid-connected inverters working in unbalanced grid situations were the subject of a comparative examination of current control techniques in [
9]. For grid-connected PV systems, the research offered useful insights into controlling current imbalances and preserving system stability by assessing the effectiveness of various control mechanisms.
The plan reduced harmonics, improved performance in low-voltage situations, and synchronized the grid without needing a phase-locked loop (PLL) in unusual grid scenarios [
10]. Instead of depending on traditional PLL approaches, it used cutting-edge techniques to accomplish grid synchronization, guarantee continuous operation during voltage decreases, and increase power quality. By offering a creative control approach that improved the efficiency and stability of grid-connected solar systems, it advanced the fields of power electronics and renewable energy systems [
10].
The creation of a control plan for PV-STATCOM, a hybrid PV and synchronous condenser system had the efficient control of reactive power and grid voltage as the primary goals. The method used a cutting-edge idea known as the Synchronverter, which combines a synchronous machine with a power electronic converter to improve grid stability and power quality. This creative approach advanced grid support technology and power electronics applications for integrating renewable energy [
11].
In our study, we extensively analyzed the performance of both the SMC and traditional PI control systems in the context of MPPT for PV systems. Our evaluation encompassed various operational scenarios, including dynamic changes in solar radiation and load conditions.
This study’s key contribution and validity lie in improving the performance of PV systems connected to a grid. It was made possible by a suggested strategy that increases system efficiency and robustness by utilizing SMC and adaptive approaches. PI control and SMC, two control schemes for MPPT in PV systems, are compared in this paper. Both control systems’ performance were assessed under various operational scenarios, including load and solar radiation variations. According to this investigation, under rapidly changing weather and solar radiation conditions, the SMC system performed better than the PI control system regarding voltage stability, current tracking, and output capability. Adaptive methods were used to increase the system’s resilience and efficiency, enabling it to change in response to environmental conditions. As a result, the system achieved high performance and stability even amidst load fluctuations and solar radiation variability, highlighting the clear superiority of the SMC system compared to the PI control system.
This strategy employs innovative techniques to improve power quality, such as reducing voltage fluctuations and minimizing harmonic distortions. It contributes to the stability and reliability of the electrical grid.
This technique guarantees continued functioning during voltage drops, which can harm system performance for various reasons. By keeping the solar system operating smoothly even in the event of voltage decreases, this technique upholds the dependability of the power supply.
Summarizing the research introduction,
Table 1 presents a comparative analysis of the approaches that have been applied in various studies on renewable and non-renewable energy systems. It is possible to gain a better knowledge of the evolution and trends in this field over time by contrasting the characteristics of the current study with those of earlier studies. It is also useful for determining gaps in the state of the field and assessing the efficacy of various control strategies.
This study aims to examine and contrast the use of two control strategies, PI and SMC, in a grid-connected PV system that operates in different solar radiation scenarios. This study looks into how the system reacts to variations in solar radiation, which greatly impact the PV array’s power output. Various performance metrics, such as tracking accuracy, steady-state error, and resilience to disturbances, are employed to evaluate and contrast the effectiveness of the two control strategies. The findings of this study provide valuable insights into the feasibility and efficiency of employing these control strategies within grid-connected PV systems, especially when faced with changing solar radiation levels.
2. System Description
Figure 1 shows the schematic of a three-phase grid-connected PV generating system. It is composed of two main parts: the control part, which integrates MPPT, PI, and SMC into an inverter controller for the three-phase PV grid-connected system; and the power part, which includes a PV array source, DC link capacitor, converter, inverter, RL filter, transformer, and grid connection.
This study’s controller uses a variable step-size approach to increase system responsiveness. The P-V curve is compared with a freshly created curve to find the ideal step size, locating the operational point either close to the MPPT region or on a distant P-V characteristic. If the operating point is distant from the MPPT, the controller applies a high voltage reference equivalent to the step voltage.
2.1. Proposed Control of the Three-Phase Grid-Connected System
The PV power generation system’s efficient use of generated power is one of its main benefits when connected to a grid [
17,
18,
19,
20]. The crucial phase of the mathematical modeling for PV cells, which is a basic component of the analysis and design of PV control systems, is shown in
Figure 2. The equation shows the temperature and PV current relationship, affecting the PV array’s energy output.
where I is the PV current of the PV module,
is the saturation current of the diode, I
Ph is the generated current from the PV system, R
S is the resistance of series in Ω, R
Sh is the resistance of parallel in Ω, K is the constant of Boltzmann, q is the charge of the electron, and T is the temperature [ºK].
The inverter is essential for connecting PV systems to a grid by converting DC power to AC. As shown in
Figure 3, the controller system used in this study uses a four-step procedure. It first subjects the system to Park’s transformations. The controller system then goes through four stages, as shown in
Figure 3. To ensure operation at the unity power factor, the reference currents (Iqref and Idref) are first compared with the actual currents (Iq and Id). It then compares the VSI output voltage signal with the reference voltage signal to generate the PWM signals, modifying the inverter’s switching sequence to control the output voltage and current [
4,
21,
22,
23,
24,
25,
26,
27]. Grid-connected PV systems can operate efficiently in various solar radiation scenarios thanks to this all-inclusive control system. To further detect the grid frequency and produce the angle (θ) needed to synchronize the inverter with the grid, a phase-locked loop (PLL) is employed. By employing Park’s transformations, this angle makes it easier to convert the reference currents from stationary to revolving reference frame values, which are then compared with the actual currents. To guarantee that the inverter sends power to the main grid at the proper voltage, frequency, and power factor, the current regulators’ error signals are used as the inputs.
The PWM approach manages the switches and the inverter’s output voltage and current by producing switching signals at a set frequency and adjusting the duty cycle. To guarantee effective power transfer to the grid, the VSI is operated at unity power factor. The controller ensures power quality and system stability, which regulates the VSI’s output voltage and current to maintain a consistent voltage and frequency at the point of common coupling (PCC) with the grid [
27].
To obtain the currents flowing from the VSI to the grid, a synchronous d-q axes transformation is used, which is expressed by the following equations [
27]:
where
,
are the active and reactive power outputs from the VSI to the grid;
are the currents flowing from the VSI to the grid in the d-q axis;
are the phase voltages in the d-q axis;
is the desired angular velocity command;
are the phase voltages a, b, and c from the VSI to the grid in the d-q axis;
is a symmetrically configured three-phase resistor; and
is the inductor impedance.
2.2. PI Control
Utilizing a PI controller, the dynamic total error signals are addressed. The controller’s objective is to reduce the dynamic total error signal to zero as the system comes closer to the intended operation state. The PI controller controls the output voltage, which operates based on the error between the reference and output signals. An output proportionate to the instantaneous error is produced by the proportional control component, and an output proportional to the integral of the error is produced by the integral control component. The block diagram of the PI controller is shown in
Figure 4. A standard PI controller’s transfer function can be written as follows [
26,
27,
28,
29,
30,
31]:
where
,
is the PI controller gains for proportional and integral control gain and
(S) is the function of the variable s.
2.3. Adaptive Surface SMC
SMC is a technique used in systems with variable structures. This method, characterized by its discontinuous nature, attains control by employing certain control inputs to move the operational point of the system along a manifold or sliding surface. Choosing an appropriate sliding surface is part of the controller’s design process. SMC is an adaptive control method that amplifies the controller’s proportional gain, improving system accuracy and reactivity [
24,
25,
26].
SMC is shown graphically in
Figure 5 utilizing a phase plane depiction. The error (e(t)) and its derivative
are included in this representation. It is observed that, independent of the initial conditions, the trajectory of the system converges to the surface in a finite amount of time (the reaching mode), and then moves along the surface in the direction of the desired destination (the sliding mode) [
31,
32,
33,
34,
35]. Making a custom sliding surface is the first step of the SMC design process. The system’s dynamics are confined to this sliding surface to follow the equations of the surface, guaranteeing stability and alignment with the intended parameters.
Creating a feedback control law that allows the system’s trajectory to approach the sliding surface is essential to achieving the sliding surface in time. The sliding mode refers to how the system moves on the sliding surface. Notably, the tracking error, e(t), and its derivatives influence the sliding surface, denoted as S(t) [
34,
35].
where n denotes the system order and λ is a positive scalar that shapes S(t). The designer selects λ and plays a crucial role in determining the system’s performance on the sliding surface [
34,
35]. Specifically, for a second-order process (when n = 2), the first-time derivative of the sliding surface, as indicated by Equation (7), is expressed as follows:
The standard approach for deriving the corresponding SMC legislation is Filippov’s construction. The primary goal of control is to guarantee that the controlled variable reaches the reference value. This means that in a steady state, the tracking error e(t) and its derivatives have to approach zero. The following procedural actions are taken to accomplish this goal:
Formulating a control law that ensures the controlled variable converges towards its reference value while complying with Equation (9) comes after the sliding surface has been chosen. This control law can be derived by changing the selected sliding surface in the system’s dynamic equations. The SMC law, denoted as (t), typically achieves rapid motion to bring the system state onto the sliding surface followed by slower motion.
The SMC law comprises two additive components: a continuous segment,
(t), and a discontinuous segment,
(t).
When examining the tracking error, denoted as e(t), which represents the difference between the reference signal r(t) and the system output y(t), a sliding surface in the error space can be defined using the coefficients obtained for the control law. This control law is recognized as the predictive PID control law. The sliding surface can be articulated as follows:
where
,
are the design parameters.
If the initial error at time t = 0 is e(0) = 0, the tracking objective can be conceptualized as maintaining the error on the sliding surface S(t) = 0 for all t ≥ 0. Once the system trajectory reaches the sliding surface S(t) = 0, it persists on it while sliding toward the origin, = 0 and = 0.
An SMC law’s primary goal is to direct the error e(t) in the direction of the sliding surface, and then follow it as it moves in the direction of the origin. Because of this, the sliding surface’s stability is critical, which means that:
The control goal is to ascertain a control input u(t) in such a manner that the closed-loop system adeptly traces the intended trajectory, implying that the tracking error e(t) should converge to zero. The SMC process can be delineated into two distinct phases:
Sliding Phase (S(t) = 0): During this phase, the system operates in a manner where the sliding surface S(t) remains at zero and its derivative
also remains zero.
Reaching Phase (S(t) ≠ 0): In this phase, the system deviates from the sliding surface S(t), and S(t) becomes nonzero.
These two phases, which are each independently derived, correlate to two different sorts of control laws:
Sliding Control: This control law is used when the system is nearing S(t) = 0 or in the sliding phase. Maintaining the system on the sliding surface is its main goal.
Hitting Control: This control law is triggered when the system is in the reaching phase, or when S(t) is not equal to zero. Its purpose is to direct the system towards the sliding surface once again.
These two control laws collaborate to ensure that the system reaches the sliding surface and remains on it to achieve the desired tracking performance. The derivative of the sliding surface defined by Equation (11) can be expressed as
An essential requirement for the output trajectory to stay on the sliding surface S(t) is that
.
If the control gains K
p, K
I, and K
D are accurately chosen with proper consideration of the prediction horizon, control horizon, and weights, and ensuring that the characteristic polynomial is strictly Hurwitzian—indicating that the roots of the polynomial are strictly located in the open left half of the complex plane—this suggests that:
The discrepancy, e(t) = r(t) − y(t), can be expressed concerning the physical parameters of the plant, with r(t) representing the command signal and y(t) signifying the measured output signal. The discontinuous segment of SMC, identified as U_d(t), commonly incorporates a nonlinear element encompassing the control law’s switching element. This controller aspect is recognized for its discontinuity precisely at the sliding surface. It is frequently structured based on a relay-like function, allowing for swift transitions between control structures with a theoretically infinite switching speed.
The successive stages involved in fine-tuning the SMC system, as outlined by Equation (7) through (15), are illustrated visually in the flow chart presented in
Figure 6. This diagram provides an organized synopsis of the tuning procedure, detailing each stage and their interrelationships to attain efficient control.
4. Conclusions
In conclusion, the research described in this work focused on comparing and implementing PI control and SMC schemes, two different control methods. Improving a PV system’s performance was the main goal. The results demonstrate the greater effectiveness of the SMC system over the PI control system in a number of critical areas, such as precision, efficiency, and stability. In particular, the PV system’s maximum power point was tracked with remarkable accuracy by the SMC system, even in difficult conditions with rapid and unpredictable variations in solar radiation brought on by weather patterns. This performance stands in sharp contrast to that of the PI control system, which showed reduced precision and stability and increased oscillations in the active current. The SMC system also showed excellent grid voltage and current stability.
Additionally, it improved the modulation index relationship, which is a key component for controlling power electronic systems’ control dynamics. Compared to the PI control, the SMC showed improved efficiency and stability for both voltage and power output. The power output improvements ranged from 5% to 10%, while voltage variations were reduced by almost 75%. Additionally, compared to PI management, SMC minimized grid current fluctuations by around 30% and reduced grid power output changes by about 20%, to ensure a more consistent grid performance. This study provides compelling evidence that the SMC system is a viable option for optimizing PV system performance and achieving increased energy production efficiency. Through the efficient resolution of issues concerning accuracy, stability, and power output optimization, the SMC technique has great potential to further the development of renewable energy systems. The proposed SMC has proven to be highly efficient during random radiation and, therefore, the proposed system can work effectively in a partial shading scenario.