Improved Performance of Hybrid PV and Wind Generating System Connected to the Grid Using Finite-Set Model Predictive Control

This article proposes coordinated model predictive control (MPC) techniques for a DC-coupled hybrid microgrid system with solar photovoltaic and wind generated system. To achieve optimum power generation in the microgrid, the finite-control-set MPC (FCS-MPC) controls both PV-wind generated power using a DC-DC converter and a controlled rectifier. The mathematical formulation of the proposed hybrid microgrid system is described, and maximum power point tracking is employed to guarantee that the grid receives the maximum power. Furthermore, the 3- $\Phi $ bidirectional two-level inverter is connected between the DC-bus and AC grid which is controlled by the grid side FCS-MPC controller. The FCS-MPC is used in all system control parts, eliminating the use of four proportional controllers (PI) and giving a better dynamic response. Additionally, the outcomes are evaluated in comparison to current techniques. The proposed power management technique is also based on the relationship between the overall demand and the produced power provided by both WDG and PV sources. Due to the unpredictability of the sources, several scenarios, including (i) Fixed radiation and fixed wind speed, (ii) Wind speed variation and constant radiation, and (iii) Changing solar radiation and steady wind speed, are considered to validate the performance of the proposed scheme. The findings are then discussed.


PSO
Particle swarm optimization. RERs Renewable energy resources. STC Standard test conditions. TSR Tip-speed ratio. VOC Voltage-oriented control. VSI Voltage source inverter. WGS Wind generating system. WT Wind turbines. SPV Solar photovoltaic.

I. INTRODUCTION
The control of coupled power electronics converters has attracted a lot of attention in this decade. For example, with the use of solar photovoltaic, (PV) and wind generating system, (WGS) to produce renewable energy, power electronics converters are coupled in these supposed microgrids, such as [1], [2,], [3]. In the transportation section, another area of use for connected power electronics converters, such as those in [4], [5], [6], and [7], is the electrification of drive trains in conjunction with a battery as a form of energy storage. The mechanisms for charging, testing, or simulating batteries are often built on an effective AC-DC power electronics converter that provides power to one or more power electronics converters (such as DC/DC power converters), such as those found in [8] and [9]. Due to the large and quickly changing load power demands, controlling these power electronics converters is a complex operation. As a result, power converters that have sampling times of a few microseconds or less require extremely dynamic and reliable control methods. System limits must also be regularly considered in control to effectively operate and avoid damaging the power converters. The power converters of the coupled systems are commonly controlled by PI controller-based cascaded control structures. They cannot utilize knowledge regarding anticipated future states or preferred input behavior. They do not take system limits into account systematically. MPC concepts, which are the emphasis of control concepts for power electronics converters control, can consider these factors [10], [11], [12], [13], [14]. They often do not consider other connected power converters because they are made to control just one power converter. As a result, the control of (extensive) interconnected systems is typically dependent on local decentralized control schemes, with no information being exchanged between the power converters, as seen in [1], [15], [16], [17], [18], and [19]. Without changing the overall control strategy, decentralized MPC techniques can be simply scaled up by adding more power converters and establishing quick data exchange amongst the power converters. As opposed to that, every modification to the load power or a power converter's setpoint causes an unidentified disruption in the neighboring power converters.
Furthermore, power converters often exhibit the CPL trend at their entry points. It poses a significant load behavior challenge for the components they supply and can significantly impair the stability of the complete coupled power converters system [20], [21]. To optimize the overall dynamics of the power converters and for financial reasons, it is preferred in order to minimize the size of these energy storage components. To overcome these problems, a mode-adaptive MPC approach in microgrids without data transfer is described in [17]. Compared to fixed control methods, this adaptive control scheme improves stability.
The system's overall control performance can be enhanced by either a centralized control technique or information sharing between the distributed controllers. A centralized FCS-MPC is proposed in [22] for a connected back-to-back power converter. According to the comparison, a centralized approach works better than a PI-based DMPC. In this study, there is one step of -the prediction horizon. The authors in [23] provide an expansion to two prediction horizons. The authors in [24] present a centralized MPC for AC/DC power converters that operate in parallel. These centralized MPC techniques have relatively small prediction horizons, which means that known future behavior (such as setpoints) cannot be fully utilized. For (big) interconnected systems, centralized techniques typically fall short of real-time requirements in a few microseconds. Finally, when there are more connected systems, the computing effort rises dramatically.
Some of these problems can be avoided by using coordinated MPCs integrated into EMS. Here, simply a data link is provided to enable the coordinated MPC techniques, while several MPC techniques locally regulate power converters, such as [25], [26], [27], and [28], to share the projected future trends. This kind of MPC approach is primarily used in power plant systems and microgrid applications [29], [30], [31]. These systems typically have substantially lower dynamics and employ sample rates in the region of one second compared to connected power converters. For AC/DC-link systems, the authors in [32] compare a coordinated MPC, a centralized MPC, and a PID control based on PSO. The comparison demonstrates that the coordinated MPC has significant advantages over the centralized MPC in practical implementation and outperforms PID-based techniques for controlling interconnected systems. This application used a fifty-step prediction horizon and a ten-millisecond sample period. An FCS-MPC with a prediction horizon of two steps is the foundation of the coordinated MPC technique for a back-to-back converter introduced in [33]. The active front end (AFE) rectifier and inverter MPCs communicate the anticipated condition and potential switching combinations. One may attain a sampling time of one hundred microseconds.
Rule-based and optimization-based control techniques are the two categories under which EMS systems are typically categorized [29], [30], [31], [32], [33]. Direct or fuzzy rules are used in rule-based techniques to allocate the required amount of electricity among the various energy sources. The hybrid system's power characteristics or optimization methods can be used to derive the rules in these methods [32]. These EMS systems are reliable, do not rely on actual performance, and can effectively distribute power across diverse energy sources by utilizing a straightforward strategy. These methods are appropriate for real-time control applications [29], [30], [31], [32], [33]. Reference values are obtained in optimization-based techniques in accordance with the improvement of a momentary cost function. These approaches require significant computing effort and are complex, which influence the EMS systems' response [33].
The authors of [34] have proposed a distributed EMS based on a hybrid system's rule-based approach. The energy storage devices' power capability, remaining capacity, and demand power are all factors that the suggested EMS in this study considers. In [21], a rule-based EMS is set up to guarantee the proposed system's reliable performance in a variety of AC microgrid operating modes. The solution performs better and is simpler than the conventional cascade control method.
A thorough analysis of HES is provided in [35], which includes an overview of the many configurations and classifications of HES and information on optimization, storage, and size. The numerous configurations and combinations of HES, the kinds of converters utilized, as well as certain control mechanisms, a crucial component of HES, HES size, and HES' energy management under various scenarios, the various types of energy systems and their parts are all covered.
Based on the coordinated MPC approach, this study presents an EMS system for a DC-coupled hybrid grid-connected PV/WGS microgrid. The recommended DC-coupled hybrid MG configuration and controller scheme is shown in Fig. 1. The recommended configuration has two power sources: solar PV and WGS. The proposed control approach is divided into two parts: controllers at the device and system levels. A coordinated MPC control strategy with the solar PV control unit, WGS control block, and DC/AC power converter control block is described for device-level controllers. A centralized control unit (EMS) for communication between multiple device-level control blocks and optimized power distribution among various power sources are also included in the system-level control. In line with the working limits of individual sources, the EMS produces the proper set values for controlling the current and the power of DC-DC and DC-AC converters, respectively. Additionally, a WGS rectifier control is employed to extract the maximum power. It is also important to note that all controllers are developed using an MPC technique.
Consequently, the following are the primary contributions of this study: • A complete model is developed to determine the solar output and the MPPT characteristics.
• Three power converters are developed: (i) a DC/AC bi-directional grid-connected inverter, (ii) a DC-DC converter for solar PV, and (iii) a controlled rectifier for the WGS generating system.
• To control the AC/DC converter, the MPDPC technique aims to achieve a faster dynamic response and reduce ripple. The adopted strategy is further validated through simulation data with conventional methods.  • A coordinated MPC technique is implemented for the regulation of power and current of AC-DC and DC-DC converters, respectively.
• An EMS method is applied to create the appropriate set points per each power source's operational objectives.

II. MATHEMATICAL MODELLING OF THE PROPOSED SYSTEM
In this work, the suggested hybrid renewable energy system (HRES) consists of three main components: PV array, WGS, and beside grid, as demonstrated in Fig. 1. Each component in the hybrid microgrid energy system (HMGES) has its control unit with specific functions during different conditions. The following subsections discuss the mathematical representation of each component as well as the technical and financial specifications.

A. MATHEMATICAL REPRESENTATION OF THE PV PANEL
PV array is one of the principal sources of renewable energy in the developed HMGES. The proposed study employs a monocrystalline silicon flat plat SunPower-305-SPR SPV model with a typical rating of 305 Watt and 13% efficiency. Table 1 demonstrates the technical specs of individual modules of the employed SPV according to the manufacturing data [36]. The module output power and efficiency are determined according to two main factors: the working temperature and solar radiation. Accordingly, the PV output power, efficiency, and the actual PV cell temperature can be expressed by [37] and [38] where, T PV is the actual temperature, T air is the ambient temperature, T PV ,STC is the temperature of the PV cell at STC, and T NOCT is the nominal operating temperature. Meanwhile, G T is the PV array's average hourly solar radiation at the recommended working temperature, G .T .,STC represents the solar radiation (SR) at STC (1 kW/m 2 ). In addition, η SPV represents the efficiency measured at STC, P PVn represents nominal power, and γ SR is the intensity coefficient for the solar cell efficiency. The effect of these two factors on the generated power is shown in Fig. 2-a and b.

B. MATHEMATICAL REPRESENTATION OF WIND GENERATING SYSTEM
WT is coupled to PMSG in the WDG system. A controlled rectifier changes AC into DC power, which is used to control the generated power. The technical details of the WT under investigation are provided in Table 2 [39]. The amount of WT-generated power is determined according to different parameters, as expressed in (4). Concurrently, one can determine the generated WT power as a function of the turbine coefficients and wind speed, as mentioned in Eq. (5) [40].

C. MATHEMATICAL MODEL OF THE GRID AND ITS SPECIFICATIONS
Generally, the interconnecting converter is employed to exchange power between AC and DC MG systems. The prime power converter (PPC) was modelled generically. According to [41], the PPC rating should be greater than the power generated from combined AC and DC sides, as described by where N conv is the converter size in kW, η AC/DC represents the efficiency of the AC to DC converter, and η DC/AC represents the efficiency of the DC to AC converter.

III. PROPOSED CONTROL STRATEGIES FOR SYSTEM COMPONENTS
In this section, the details control methods for all systems and converters will be discussed.

A. MPPT OF PV ARRAY
The PV-generated power and efficiency decrease during high temperatures, although the high levels of PV radiation increase these two factors. The solar output voltage at the peak power point (V mpp ) must be maintained even when the temperature and radiation change. MPPT methods could be used to accomplish this, as investigated in many articles. The MPPT techniques are separated into two main categories; the direct techniques include incremental conductance (IC), perturbation and observation (P&O), as well as sophisticated methods like ANN and fuzzy logic-based schemes [42], while the indirect techniques, like the short-circuit and open-circuit methods [43], [44]. Due to the requirement for a prior understanding of the PV's operating characteristics, it is difficult to accurately monitor the MPP using indirect techniques at any cell temperature or solar radiation [45]. Conversely, in the direct methods, the voltage levels of both PV and DC-bus are controlled through by moderating the signal used as a DC-DC converter's reference. The main features of utilizing P&O or IC methods are their compatibility with digital controllers and industrial inverters, no prior knowledge is  needed about the PV, and their reduced cost [46]. The main limitation in -of the P&O method is the voltage oscillation during transient changes in weather conditions. In contrast, the IC method improves tracking speed and accuracy problems [42]. The main advantages of using intelligent techniques over direct ones are their improved tracking speed and precision, nonetheless their complexity and expensive application costs. [47]. In this context, the IC method can be combined with a direct control method to enhance the system characteristics [48].
Hence, in this paper, the IC technique is combined with the MPC to perform the MPPT operation for the PV system. Firstly, the IC is used to generate the optimum current from the PV, I ref _PV achieved by the MPP.  updated using the incremental value E, which is a trade-off between the power oscillation and the speed of tracking the MPP. Then, this optimum current is fed to the MPC to control the ON/OFF states of the DC-DC converter. To use the MPC, the discrete model for the DC-DC converter state, i L , is needed to be defined to predict the next step. As mentioned, there are two possible switching states, 1 or 0. Based on the switching states and Euler discretization rule for the dynamic model of the DC-DC boost converter, the predicted value of the inductor current, i L (k+1), which equals the PV output current, is calculated by where k and (k + 1) are the current and next instant, respectively. S is the switching state 1 or 0. V pv , T s , V DC are the PV output voltage, the sampling time, and the DC-bus voltage. The value of this predicted current i L (k+1) changes based on the switching state. Hence, to generate the MPPT, the switching state is calculated, which is chosen to minimize the error between the predicted input DC-DC boost converter current and the reference derived from the IC method. This cost function is given by where I is the penalty function which is used to prevent the PV array from damage and is determined by The schematic diagram is demonstrated in Fig. 4 displays the MPPT control of the PV array. The PI control is employed to improve the tracking accuracy by damping the ripple oscillation and enhancing the computation accuracy.

B. MPPT FROM THE WGS
There are three categories: WT fixed speed, variable speed with pitch control, and full-controlled variable speed [49]. DFIG and PMSG have been widely used in WDG systems due to their ability to realize maximum power and wide speed control operation [50]. The MPPT methods reported in the literature for variable speed WTs are classified into PSF, P&O, and wind speed measurement (WSM). In the PSF technique, the MPP is tracked by shaft speed control, and the controller must be provided with the maximum power curve. [51]. The P&O technique has excellent reliability but ineffective efficiency. In the P&O technique, No prior knowledge of the maximum WT power at different wind speeds or generator data is required [52]. The WSM technique involves two feedback signals: the wind and the turbine speeds for calculating the TSR. So this technique is known as the TSR as well [53]. In the above MPPT techniques, the WT is pushed to stop operating when the output power exceeds the rated power during working above the recommended wind speed. For this purpose, the pitch angle control (PAC) is applied for the variable speed turbine to keep the WT generating the rated output power and reduce the overloading [49], [54]. The blade PAC can be accomplished using different controllers such as (PI, PID, sliding mode control, fuzzy logic control (FLC), FLC-PI, and FLC-PID) [55]. One of the main limitations of implementing conventional controllers is the need to accurately determine the controller gains to ensure robust operation [54], [55].
In this work, the PMSG is adopted, where the dynamic model is constructed using MATLAB/Simulink software in the dq-synchronous frame. Meanwhile, the following formulations are used to represent the wind power coefficient of the WT [56], [57]: where C a = 0.51760, C b = 116.0, C c = 5.0, C d = 0.40, C f = 21.0 and C g = 0.00680. λ is the TSR, R represents the blade radius, and V ωd the wind speed. The relation between C p and λ at various blade pitch angles, β is presented in Fig. 5.
The observation is that at a specific value of β, the maximum point of C p−opt exists at only one value of λ opt . In this paper, the TSR is adopted to extract the MPP from the WGS, where two control methods can be used. The first one employs two cascaded PI controllers, while the second uses FCS-MPC to generate the control signals for the controlled rectifier. More details about each method are given in the following sub-sections.

1) MPPT-BASED TWO PI CONTROLLERS
As mentioned before, the controlled rectifier is used instead of the switch-mode rectifier; hence the controller algorithm is different. Using the PMSG's dynamic model as a foundation, the dq-axis currents are used for control, where both can achieve a separate objective. The q-axis reference current value is used to extract the maximum power, whereas the d-axis is used to reduce the losses. The reference q-axis reference current, i * qs is obtained based on the optimum wind power, P opt , and it can be given out by [58] i The optimum wind power, P opt , can be calculated from: The optimum power is extracted for the investigated WT parameters at a tip-speed ratio of 8.1, which corresponds 0.48 wind power coefficient [59]. On the other hand, the reference point of the d-axis current is adjusted to zero, i * ds = 0, to reduce the power losses [60]. After determining the dq-axis reference values, both dq-axis current references (i * ds , i * qs ) are compared with their measured values. Subsequently, two PI controllers are utilized to ensure the actual values track their references fine. Furthermore, the compensation is used to get a complete decoupling. Finally, the controlled rectifier pulses are obtained based on the compensated output from the two PI controls and then converted to abc references. Fig. 6 shows the MPPT control from the WGS-based two PI controllers.

2) MPPT BASED FCS-MPC
The FCS-MPC is employed instead of the PI control for faster transient and better dynamic responses to extract the MPPT. Using the FCS-MPC for the controlled rectifier has many advantages over the PI controller, such as removing two PI controllers, and hence four tuning gains can be avoided. Besides removing the pulse width modulation techniques. Moreover, selecting the best switching vector gives a minimum cost function value.
The FCS-MPC can be elaborated into three essential steps to optimizing its efficiency. The first step is to measure the desired states. Then the prediction condition comes next, and finally, the control variable is optimized using the desired cost function. The best switching voltage vector is selected based on the cost function minimization. The mathematical details of the FCS-MPC are as follows: • Measuring the rotating speed, and stator currents VOLUME 10, 2022 I q (k) and I d (k) represent the dq-axis actual currents, represents the permanent magnet flux linkage, and ω e represents the electrical rotating speed. • Design of the proposed cost function, g as given by wehere W is the current limitation to protect the machine from overcurrent, the wrong switching vector can be directly avoided. This current limitation can be determined by The observation is that the cost function does not require the weighting factor. Meanwhile, the reference values for the dq-axis current are inserted directly into the cost function. The flowchart of the applied FCS-MPC for the controlled rectifier is demonstrated in Fig.7. Moreover, the overall Machine side rectifier controller based on the FCS-MPC for maximum power extraction is illustrated in Fig. 8.

C. GRID SIDE CONVERTER CONTROL
It is critical to match the generated voltage and frequency to the grid requirements. Thus, equipping the three-phase VSI with a specific controller is mandatory. This controller contains three parts phase-locked loop control, DC-bus voltage controller, and grid current controller. Details of each controller will be discussed in the following subsection.

1) PHASE-LOCKED LOOP
The main target of the PLL is to extract the grid voltage angle for proper alignment of the d-axis with the voltage vector in the VOC [15]. Based on the VOC principles, the q-axis grid voltage is adjusted to zero (v qg = 0). The PLL function is to keep the d-axis of the grid voltage with respect to the voltage vector, and hence the q-axis voltage is formulated by where, ωt o represents the angle of the voltage vector and ωt the angle of the d-axis. Both angles are measured with respect to α-axis. The diagram of the PLL technique is illustrated in Fig. 9.

2) DC-BUS VOLTAGE CONTROL
The DC-bus voltage is constantly maintained by regulating the grid d-axis current. This is illustrated based on the inputoutput power balance and considering the system is lossless Based on the principle of the VOC where v qg = 0 and v dg = v ph1 Eq. (19) can be modified to (20) This equation can be rewritten after taking linearization around the equilibrium point to dv dc dt (21) wherev dg andî dg are the perturbation in the d-axis voltage and current, respectively. By neglecting the steady-state and higher-order terms, results it can be written by It is evident that the magnitude of the DC-bus voltage varies according to the value of the d-axis output current. Thus, it uses a PI control technique to regulate the DC-bus voltage.

3) GRID CURRENT CONTROL (GCC)
After generating the reference d-axis current from the DC-bus voltage control loop and selecting the reference value of the q-axis current to achieve unity or leading or lagging power factor. The grid current control can be designed. In this work, the GCC can be designed based on two methods, the first one depends on the application of two PI controls, and the second is based on the FCS-MPC. More analyses about each method are in the following.

a: GCC BASED ON PI CONTROLLERS
The dq-axis output voltages from the inverter can be expressed by [63] v (24) where ω f represents the grid angular frequency, R f , L f are the filter resistance and inductance. These two equations can be rewritten by The effects of filter values can be replaced by PI controllers as in the following relations.
From the above equations, it could be observed that the dq-axis output currents are regulated by adjusting the dq-axis voltages of the inverter (v di , v qi ). As mentioned before, the DC-bus voltage control loop achieves the reference value of the d-axis current. Meanwhile, the q-axis reference current is kept to zero to obtain a unity power factor. Voltage compensation removes the coupling between the d-and q-axis. The block control diagram, including the pulses generation, is illustrated in Fig. 10.

b: GCC BASED ON FCS-MPC
The FCS-MPC is used to overcome the slow dynamic response, more time for tuning gains, and the complex process of generating the pulses to the VSI when PI controllers are used. The FCS-MPC is easier, simpler, and has faster VOLUME 10, 2022 dynamic responses. Based on the stationary reference frame, the αβ-axis current can be predicted as follows Then the cost function can be implemented as follows The schematic of the grid side inverter based on the FCS-MPC is shown in Fig. 11.

IV. PROPOSED ENERGY MANAGEMENT STRATEGIES
Due to the fluctuating nature of RERs, the optimal output power can be higher or lower than the required load demand. Accordingly, the proposed energy management strategy (PEMS) is employed to improve the HRES system performance under various conditions. The schematic diagram shown in Fig. 12 demonstrates the hybrid system components incorporated with their individual controller. The main objectives of the PEMS are:   • Extracting the optimal power from each generating unit by utilizing MPPT techniques to the WDG and the PV array.
• Organizing the total produced power across all generating units.   • Maintaining the DC-link voltage to a constant magnitude during different sudden disturbances.
• Injecting the extracted power into the grid achieves the unity power factor and synchronizes the voltage magnitude and frequency with the grid requirements.

V. TECHNICAL EVALUATION USING THE PROPOSED HMGES BASED ON MODEL PREDICTIVE CONTROL
This section presents the optimized system's technical evaluation developed using MATLAB/Simulink. The optimal HMGES parts were formulated in MATLAB/Simulink with the ratings listed in Table 1 and 2. The technical analysis   has three basic objectives: achieving effective management between key system components; ensuring uninterrupted, continuous, consistent voltage and frequency feeding of the VOLUME 10, 2022  FIGURE 19. Optimum generated power from PV and WG systems at case 1.

FIGURE 20.
Optimum and actual wind power coefficient during case 1.

FIGURE 21.
Reference and actual Q-axis current generated from the WGS during case 1.

FIGURE 22.
Reference and actual D-axis current generated from the WGS during case 1.
loads; and maintaining the voltage at the dc-bus under various conditions. It should be noted that until the generated   voltage reaches its steady-state value, which is discovered after 5 seconds, the WDG is regarded as starting at no load. In other words, the loads are first supplied by the SPV array and the batteries (if necessary). The four seasons of the year were examined using technical analysis in the following ways: The technical evaluation is implemented using the MATLAB/Simulink environment. The capacities listed in Tables A1 and A2 were used to construct the HMGES components in MATLAB/Simulink. The technical analysis has three objectives: (i) achieving effective management between system components, (ii) ensuring maximum power from renewable sources, and (iii) all generated power is supplied to the grid by maintaining unity power factor and constant voltage at the DC-bus irrespective of loading condition. It should   be noted that the WGS supplies the generated power after 2 seconds until the generated voltage reaches its steady-state value, where it starts at no load. In other words, the grid is first connected by the SPV array. Technical evaluation is analyzed under four different cases as follows:

A. CASE 1 COMPARATIVE ANALYSIS OF THE OUTCOMES BETWEEN MPC AND CONTEMPORARY PI BASED SVM
In this case, the performance comparison for the overall system using the MPC and the PI controller-based SVM is presented. Due to the use of the SVM in the grid side converter and the machine side converter, the presented results    focus on the output from these two controllers. To achieve this comparison, a constant wind speed of 6 m/s and constant radiation of 1000 kWh/m 2 is adopted. The tuning gains used for all PI controllers used in GSC, MSC, and IC are presented in Tables 3, 4, and 5 respectively. Figure 13 shows the optimum and actual wind power coefficient while Fig. 14       compared to SVM as depicted in Figs. 15 and 16 respectively. This reduction in the current variation reduces the developed torque and hence increases the generator lifetime. In addition, the use of MPC leads to lower current distortion in the injected current to the grid as illustrated by the αβ-axis currents shown in Figs. 17 and 18.

B. CASE 2: FIXED RADIATION AND FIXED WIND SPEED
The MPC is used to assess the potential of the proposed HRESs using a rated value of solar radiation of 1000 kWh/m 2 and a fixed value of wind speed of 8 m/s, which is normal in most places. Because the system is connected to the grid and not an isolated load, there are no restrictions on the amount  of generated power that can be sent to the grid, and so the entire generated power will be sent to the grid. The PV injects power from the starting as it is static generation. Meanwhile, the wind generating system injects power to the grid after 2 s till the generator reaches to steady state and overcomes the inertia. Figure 19 shows the amount of generated power from both the PV system and WGS. After 2 seconds, the actual wind power coefficient closely follows the optimal one, as seen in Fig. 20. As shown in Fig. 21, the value of the Q-axis current generated by the WGS closely reflects the reference value responsible for producing the maximum power from the wind.
Meanwhile, the reference value for the d-axis current is zero to reduce the loss. The actual value tracks this reference value very well, as confirmed from Fig. 22. Figure 23 shows the DC-link voltage regulated to be constant through the grid side converter aided with the PI controller. Further, the MPC is used to regulate the injected current to the grid where the  actual values of the αβ-axis current track their references value very well, as seen in Figs. 24 and 25. Finally, the phase-A voltage and current are shown in Fig. 26-a and b, respectively. It is observed that the control succeeded in achieving the unity power factor.

C. CASE 3: WIND SPEED VARIATION AND CONSTANT RADIATION
The effect of wind speed fluctuation and constant radiation on the control and overall HRES is investigated in this scenario. The radiation level is set to 500 W/m 2 , and the wind speed profile is depicted in Fig. 27. Figures 28 and 29 show the average output PV voltage and current, confirming that VOLUME 10, 2022 the MPC extracts the MPP from the PV panels successfully. Meanwhile, the MPP from the wind generating system is proven by Fig. 30, which shows the MPC's ability to extract MPP at various wind speeds. The optimal quantity of the generated power from both PV and WGS is shown in Fig. 31. The reference and the actual DC-link voltage values is shown in Fig. 32. It is noticed that the actual value tracks the reference value but with a disturbance at wind speed changes. Figure 33-a

D. CASE 4: SOLAR RADIATION VARIATION AND CONSTANT WIND SPEED
This scenario is offered to check the variability of solar radiation and fixed wind speed for further testing of the MPC and the overall system. The wind speed is kept constant at 6m/s while the solar radiation, shown in Fig. 36, increases from 400 to 600 W/m 2 . Figure 37 demonstrates the optimal generated wind and PV power where the wind-generated power remains constant at the optimum value and the PV output power changes in response to the PV radiation. The DC-bus voltage is regulated at the reference value as shown in Fig. 38. This demonstrates the MPC controller's capacity to control MPP in WGS and PV systems in which the actual values of the DQ-axis current generated from the wind follow the reference one as reported in Figs. 39-a and b.
Meanwhile, the MPC for the grid side converter is working well, as proven from responses αβ-axis of the grid currents, and also Phase-A grid voltage and current as shown in Figs. 40 and 41, respectively. It is observed that the injected current increases with the increase of solar radiation.
The main findings of the results can be summarized as follows.
• MPC is comparable to traditional control methods, and it generally outperforms them in terms of flexibility and performance.
• The main driver for tackling real-world issues in the field of power electronics is the flexibility of the proposed MPC technology.
• Under a variety of model uncertainties, voltage prediction and the steady-state performance of the proposed control method are enhanced.
• The reference current can be correctly and quickly tracked using the suggested MPC approach, which also exhibits good steady state and dynamic performance. The suggested MPC has the highest steady-state performance.
• In the majority of instances of model mismatches, the performance degradation of the suggested control system is minimal and acceptable given the current measurement error.
• The suggested control method is adaptable to various cost functions; as a result, it is superior in terms of real hardware implementation.
• It has been established through analysis of the grid current THD that the proposed method is more resistant to grid variation than the PI control strategy.
• The high-order harmonics of the output current can be realised by the suggested MPC algorithm, which is advantageous for the filter design.
• When compared to the traditional PI control scheme, the suggested FCS-MPC control method operates well, has good tracking capability, rejects disturbances, and responds more quickly.
• This method's application requires fewer computational resources.
• The MPC algorithm that is being given has reduced sensitivity to the filter settings.
• The suggested solution directly incorporates MPC results, which are simple to include in DSP controller.
The suggested control strategy has a simpler structure than standard approaches that employ classical controllers, making it easier to implement and tune.

VI. CONCLUSION
This research shows that the finite-control-set MPC linked with a hybrid PV/WT-powered microgrid improves the performance of the grid-connected systems. Maximum power extraction is accomplished for both PVs by implementing the IC algorithm-based MPC for the PV system. In addition, the FCS-MPC is used to extract the MPP from the wind generating system. The DC-bus voltage is regulated along with the FCS-MPC to achieve the unity power factor through the three-phase grid-connected inverter. The proposed system was simulated in the following four scenarios: Case I: a comparative analysis of the outcomes between MPC and contemporary PI based SVM. Case II: during both fixed wind speed and radiation, the optimal power produced by the hybrid system under 1000kWh/m 2 of irradiation for 8kW and 8m/s of wind speed to create 12kW is shown. The suggested machine controller ensures the optimal wind power output based on simulation findings by keeping the power coefficient at the reference value and regulating the DC-bus voltage. In Case III: variable wind speed and fixed irradiance, the WT's dynamic performance is examined by maintaining constant irradiance. At a rate of 4 s, the wind speed is reduced from 9 m/s to 7 m/s, but a low irradiance of 500 W/m 2 is maintained for PV panels. The simulation validated the anticipated case II's dynamic response. Situation IV: variable irradiance and fixed wind speed is another dynamic case in which the IC-based MPC was developed and followed the maximum power. In each case mentioned earlier, the threephase inverter references and phase currents indicate that the suggested system is more precise than the current PI. The voltage of the DC-bus was controlled to be almost equal to the reference voltages.