Robust Speed Controller for PMSG Wind System Based on Harris Hawks Optimization via Wind Speed Estimation: A Real Case Study

Modern wind power systems have recently tended to focus on achieving fast-tracking wind speeds (WSs), high maximum power point tracking (MPPT) efficacy without mechanical sensors, and high performance under uncertain WS together with an effective control system. Therefore, a sensorless MPPT method is introduced, which calculates the actual WS to save system installation costs and boost performance levels. The implemented MPPT method is based on the approximating of the 3-order polynomial to the aerodynamics torque power coefficient. In this study, three-speed control strategies (SCSs) for a grid-connected permanent magnet synchronous wind generator (PMSWG) are examined and assessed. Harris Hawks’ algorithm (HHA)-based PI controller (HHA-PIC) is used in place of (the conventional proportional-integral controller (CPIC), and adaptive fuzzy logic controller (AFLC)) as a speed controller to overcome their drawbacks. To track the generator speed to the desired speed, the HHA-PIC is used. All the CPIC, AFLC, and HHA-PIC have been carefully thought out and constructed to satisfy the speed control loop’s responsive performance. Additionally, a comparison of SCSs amongst the categories under investigation is done. The effect of HHA on the functionality of SCS is verified using MATLAB/SIMULINK. To ensure the efficacy and supremacy of the HHA-PIC over the CPIC and AFLC, a wide variety of WSs (step change, ramp, and real fluctuations) are applied. The HHA-PIC boosts system efficiency over AFLC and CPIC by 0.81% and 8.48%, respectively. Finally, it can be said that HHA is a crucial remedy for the problems with CPIC and is superior to AFLC.


I. INTRODUCTION
In the domains of international politics, economics, science, and technology, there is now widespread agreement that greenhouse gas (GG) emissions must be controlled and the effects of global warming must be mitigated. The overuse and use of fossil fuels (FFs) by humans is the primary The associate editor coordinating the review of this manuscript and approving it for publication was Ton Duc Do . cause of the buildup of GGs, particularly CO 2 , in the atmosphere. The overall global use of FFs and CO 2 emissions in 2019 were 583.9 exajoules and 34169.0 million tonnes, respectively, per the BP Statistical Review of World's energy 2020 [1], [2]. Roughly 5.0% of the world's energy is produced by renewable generators, hydroelectricity and nuclear power being the exceptions. Approximately 1% each year, or 340 million tonnes per year, more CO 2 is still being released into the atmosphere [3], [4]. Energy from renewable sources VOLUME 11, 2023 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ (EFRSs), particularly wind energy (WE), have been used to address these issues as environmental dangers were more widely known and there was a goal to limit the use of fossil fuels [5], [6], [7]. It is constantly expanding to meet the rising demand for power in the world due to its clean and environmental dangers [8]. As a result, it is anticipated to supply 20% of the world's energy demand by 2030 [9], [10]. Fixed speed (FS) and variable speed (VS) are the two basic principles used in worldwide WE marketing. The FS generators are straightforward and cost-effective, but they require a gearbox and have a limited speed range. Globally expanded VS eliminates the need for a gearbox and enables maximum power harvest regardless of wind speed (WS) [11], [12]. The VS uses a variety of machine types, including permanent magnet synchronous wind generators (PMSWGs), doubly fed induction wind generators, and squirrel cage induction wind generators [13], [14]. The PMSWG has numerous advantages compared to the other sorts described, including excellent performance and power density as well as great reliability and efficiency. Additionally, removing the gearboxes and DC excitation increases the WE unit efficiency by 10% [11], [13]. Lately, 3-phase PMSWGs have been used in a variety of industries to improve fault tolerance while reducing phase current and torque pulsation ratio [15]. The main shortcomings of these technologies continue to be their expensive power converters and intricate control mechanisms [16].
To assure utilizing all accessible energy at fluctuating WSs, maximum power point tracking (MPPT) methods were researched [17], [18], [19]. Precise WS measurement is necessary in an MPPT setup in order to properly control the mechanical speed and achieve the desired value. A variety of anemometers having precision and quality of (5-10) % are placed at various locations near the turbine region in order to measure the WS. A perfect measurement of the effective WS is necessary for the turbine to be controlled effectively; however, the anemometer is unable to provide this information. Additionally, the anemometer has a high upfront and ongoing cost, which lowers total system durability [20], [21], [22]. WS estimation (WSE) methods are being used instead of sensors because they reduce system complexity, increase efficiency, and deliver precise WS measurements. In [17] and [23], various WSE approaches were discussed. The polynomial-based estimating (PBE) technique is one of them and is straightforward and precise [17], [24]. Thus, it is taken into account here just to calculate the WS.
Due to the necessity of energy these days, a lot of time and effort has been put into the MPPT research area for WE systems. The majority of these studies used traditional algorithms like P&O and modified P&O, while other studies used metaheuristic optimization techniques to optimize either the PIC or the artificial neural network-based controller. A study that compared two methods (P&O and HCS), for a hybrid PV/WE technology was presented in [25]. To power, the WE-producing system, a brushless power split system was introduced, and a comparison with a single MPPT was made [26]. The use of a new MPPT technique based on adaptive active fault tolerant control solved some issues that came with the operation of WE generation [27]. A fractional control mechanism for adjusting the WE system's pitch angle to maximize the power it produces was presented in [28] and compared with the traditional PI sort. Installing fuzzy logic control (FLC) for MPPT increased the system harvest power and system efficiency [29]. As an approach to maximize the power produced by the WE system, a neural network (NN) with a radial basis function was presented [30]. Additionally, a modified particle swarm optimizer (PSO) was employed to implement the learning process while the gradient descent technique was used to train the NN.
An MPPT technique with changeable step sizes by perturbing the ω r of the WE system was established in [31]. A selfadaptive P&O strategy for MPPT integrated with the WE system was described in [32], to increase its output power (P). A contrast with FLC, variable P&O, and fixed step P&O was made in this study to increase the P, adaptive P&O, and hybrid P&O control approaches for MPPT fitted with WE systems were given in [33]. Control of the MPPT fitted with the WE system by choosing a slide mode extremum was done in [34]. The settings of the built-in controller were optimized using an upgraded invasive weed method. In [35], two MPPT techniques: λ and optimum torque control (OTC) were installed in WE arrangement and assessed. For the purpose of replicating MPPT for WE systems, [36] demonstrated a hybrid technique integrating HCS and power signal feedback control, and the PIC was optimized using PSO. Reference [37] used NN with reinforcement learning to act out MPPT for the WE system. For the MPPT-WE system, a dsPIC30F4011 was established in [38]. In order to simulate MPPT implemented in the WE system in Saudi Arabia, [39] proposed a method built on a grasshopper optimizer (GOA). In comparison to other optimizers, the GOA managed the boost converter duty cycle to increase P.
Various controllers can be divided into several sorts, like linear, nonlinear, or predictive. It is possible for controllers to adjust the required regulated variables and enhance the whole dynamic system. Though economical and easy to build, linear controllers have several drawbacks, including poor dynamic response, poor efficacy, and high sensitivity to outside disruptions [40], [41]. The continuous model predictive controller (MPC) and the finite control set MPC are two forms of MPCs that are effective at predicting and enhancing system behavior, however, MPC is quite complex and requires a lot of computations [42], [43]. To create the converter switching signals in continuous mode, a modulator is required, however in the alternate mode, this is not necessary [44]. To obtain the MP of the WE system, MPC-based MPPT was proposed in [45]. An MPPT for a WE system utilizing a PIC that had its tracking speed increased employing an ant colony optimizer was built in [46]. The use of metaheuristic algorithms is still limited and requires more attention, despite the large number of applied methods used to simulate MPPT with WE systems.
Additionally, hill-climbing search algorithms may not be successful in extracting the MPP and have some restrictions on tracking speed and efficiency. The most modern optimization techniques, including, swarming methods, and the Elliptic Curve, have been successfully used to regulate various controlled variables including torque and current in a variety of engineering challenges. In both the machine and grid side, pitch control loops, optimized controllers were employed instead of the conventional proportional-integral controller (CPIC) [47], [48].
An effective metaheuristic strategy harris hawk's algorithm (HHA) is employed to close the gap left by the usage of the earlier techniques. In this work, the optimal power output of a PMSWG is investigated for a variety of WS profiles (step change, ramp changes, and real fluctuations). Without employing any sensors, the effective WS is estimated via the WSE technique. Additionally, it lowers the cost of system installation, gets rid of WE system complexity, raises reliability, and boosts efficiency. Numerous disadvantages of employing a CPIC as a speed controller directly impact the WE system's dynamic response. The CPIC of the speed control loop (SCL) is fine-tuned using the HHA to reduce these limitations. The adaptive fuzzy logic controller (AFLC) is designed and implemented as a speed controller to highlight the merits of the proposed system. To monitor the machine speed to the reference amplitude, the HHA-PIC is used. The CPIC, AFLC, and the HHA-PIC are all well thought out and developed to guarantee the SCL's obedient behavior. The transfer function (TF) notion is used in the formulation of the PIC gains. Additionally, an illustration scheme is used to demonstrate the HHA design. Additionally, a comparison of SCLs amongst the categories under research is conducted.
The following is how this paper is formed: The WE system mathematical model and control are presented in Section II. Section III provides a description of the WSE algorithm. Section IV provides clarification on the SCLs and HHA. Simulation results are presented in Section V. In the final section (VI), the work's result is reported. Fig. 1 shows the researched system and its control system. An exterior SCL and two inner current control loops make up the wind-side converter (WSC). SCL is in charge to control the generator\mechanical\rotor speed (ω r ), and the current control loops are applied for maximizing the generated power. The back-to-back power electronic converter connects the PMSWG to the electric grid (EG), and the gridside converter injects output power (P) into the EG.

A. WIND TURBINE (WT) MODEL
The produced mechanical power (P m ), tip speed ratio (λ), power coefficient (C p ), and mechanical torque (T m ) for the turbine model can be formulated as follows [49], [50], [51]: where ρ, β, A, and v w are the air density, pitch angle, blades area, and WS, respectively. Fig. 2 depicts the four operational zones of the WE system broken down into these regions. The turbine is restricted from operating in areas 0 and 3 to protect it from any mechanical dangers. The MPPT runs in region 1 just under-rated WS to maximize the power generated at various WSs. In all other cases, the pitch control is used to ensure that the turbine is operated safely over the allowed WS until the cutout amplitude. As shown in Fig. 3, the ω r is adjusted to track the MPP at any WS to function with the ideal values of, λ, C p , and β.

B. PMSWG MODEL
The PMSWG's model is fully defined in [50], [52], and [53] and its stator voltages (V ds and V qs ) are presented via Park's transformation: whereλ d = L ds dI d dt ,λ q = L qs dI q dt , and the subscript ''s'' denotes stator.
The symbols R s , I ds , I qs , ω e , and L ds , L qs are the resistance, currents, electrical angular speed, and inductances, respectively.
The flux components are written as: ψ ds = L ds I ds + ψ pm (7) ψ qs = L qs I qs (8) where ψ pm is the permanent magnet (PM) flux linkage fundamental value. The electromagnetic torque (T e ) can really be defined in the following way: n p ψ ds I ds − ψ qs I qs = 3 2 n p ψ pm I qs + I ds I qs L ds − L qs (9) For the surface-mounted PMs sort, (L ds -L qs ). I ds is set\forced to zero to remove losses. So, T e will be written as: The system's mechanical Eq. is written as in (11): where f and J are the friction coefficient, and moment of inertia, respectively.

C. CONTROL OF WSC
Since SPL is a component of the WSC system, its control function is covered in this article. As seen in Fig. 1, the WSC's job is to maximize the power that the WS captures. To achieve optimum operation during the WS fluctuation, the MPPT is used. As seen in Figs. 2 and 3, its function is to achieve Cp = 0.48 and λ = 8.1 in zone 1 with β = 0. The WSC also uses two control loops to implement field-oriented control. The MPPT method is used to adjust ω r at its desired value before applying the SPL. To reduce ω r error, a variety of controller sorts, including traditional or improved PI controllers, are used as speed controllers. The inner one is in charge of producing the switching pulses and controlling the machine currently. The space vector modulation controls the machine current with its reference to enhance the produced T e , which is linked to I qs and forces I ds to 0. Fig. 4 depicts the SCL concept in detail [12], [54], [55].
ν W is calculated as a function of (P m , ω r ) via the next 3-order polynomial Eq. (14), implementing a numerical analysis solution, and a single root is feasible from the three roots.
The wind system constants are presented in Table 1 [56].
For calculating P m as a function of (ω r , I qs ), Eq. (15) is expressed as follows:

IV. INVESTIGATED CONTROLLERS FOR SPEED LOOP A. PI CONTROLLER
The SCL controls the ω r at its ideal value, which is created by the WSE method, to harvest the greatest power for all WS changes. Therefore, a precise CPIC design by a thorough TF of the entire system is crucial. Using a 2-mass model, the TF has been calculated from the drive train's (DT) dynamics as a function of (ω r , T e ). Through a spring and damper, the high-speed mass of the PMSWG is connected to the low-speed mass of the turbine. The linearization model is used to describe the 2-mass DT (16)(17)(18)(19) [47], [56], [57],.
where the symbols (H g , H t ), T sh , ω t , θ r , (K s , f ) are the inertia constant of (generator and turbine), shaft torsional torque, turbine speed, shaft twist angle, shaft stiffness, and damping coefficients, respectively. Both of P m and wind-power (P wind ) can be written as: Implementation of linearization concept around ω r and from Eq. (5) T m is expressed as: The SCL schematic block diagram is presented in Fig. 5.
α ω S+α ω is the inner current CL, α ω is the converter's CL bandwidth. The controller gains (K p(ω) , K i(ω) ) are designed as The dynamics of the converter's CL are ignored when (ω ≪ α ω ). Therefore, the speed CL-TF is written as in (23).
where ω n , and ζ are the CL bandwidth, and the damming ratio of the PIC, respectively. Also, ω 2 2H g , and K = 1.5n p ψ pm T base . The attained controller gains for precise operation based on this analysis are (K p = 5, and K i = 100).

B. ADAPTIVE FLC MPPT CONTROL
Due to its simplicity, ability to tackle system nonlinearity, and lack of information regarding mathematical modeling, FLC approaches are now more frequently used in a variety of applications [58]. Weird tracking behavior is caused by the nonlinearity of WE systems and climatic conditions. As a result, adaptive FLC-based MPPT techniques can be used to track the MPP in the PMSG WE system with less    down into. These stages contain steps for fuzzing, evaluating rules, and defuzzification. Fig. 6 illustrates the reaction of the adaptive FLC adjustable parameters to system modifications, including output scaling factor, fuzzy rule, and membership function [29], [59]. Application of adaptive FLC can enable the PMSG to run at MPP as well as high dynamic performance under high variable wind speed. As a result, when providing a new control scheme superior to this recent scheme, is considered a robust, efficient, and effective approach.

C. HHA-PIC MPPT CONTROL
The HHA is a metaheuristic approach that mimics the HH's successful chase technique's cooperative behavior. Like other techniques, it contains the phases of exploration and exploitation. The HHA is broken down into two exploration phases and four exploitation steps in the formulas below. The following processes are employed by HHs to kill their rabbits and are mimicked and modeled by the HHA model. It was chosen for this research due when put to the test on 6 constrained design engineering tasks and 29 unconstrained benchmark problems, it outperformed the other 11 techniques [60]. The HH's behavior towards prey is represented by the following equations, and the concept of the HHA is properly described in [60], [61], and [62]. A flowchart for the SCL's application of the proposed HHA is given in Fig. 7.
Exploration phase: The transition from exploration to exploitation: Exploitation phase: a) Soft besiege, C ≥ 1 2 and |E| ≥ 1 where c) soft besiege with progressive rapid dives, C < 1 2 and |E| ≥ 1 d) hard besiege with progressive rapid dives, C < 1 2 and |E| < 1 The problem formulation for the SCL is built on the objective function to minimize integral time absolute error (ITAE) given in (34) as a starting point. Table 2 shows the selected PI gains for the examined choices.

V. SIMULATED RESULTS AND DISCUSSIONS
The simulation results are run under three different WS profiles (step change, ramp, and real variations) and examined to show the efficacy of the HHA-PIC. To demonstrate the usefulness of the suggested approach, the performance of the two researched controllers is compared under all simulated situations. Additionally, the WE system efficiency is calculated over the course of the entire scenario to pinpoint the proposed controller's perfection in performing at optimal λ, C P values under variable WSs. Table 3 lists the simulated PMSWG parameters. Moreover, the impact of the moment of inertia on the dynamic performance is given in the Appendix.

A. CASE 1: STEP CHANGE OF WS
The outcome of various turbine parameters is depicted in Fig. 8. Fig. 8 (a) depicts the studied WS profile to investigate the impacts of stepping up and down on the turbine characteristics. The settling time via CPIC, AFLC, and HHA-PIC is 0.124 s, 0.0941, and 0.0086, respectively. Fig. 8(b) and (c) show λ and C P which guarantees operation at desired values (8.1 and 0.48, respectively). The CPIC reaches the optimal values λ and C P slowly, taking 0.174 s, compared to the AFLC, taking 0.0094 s, and HHA-PIC's taking 0.0076 s. The generated P m is displayed with all controllers and exhibits an improvement for the proposed method over the alternate in Fig. 8 (e). Figuring out how to set the ω r to the desired value is shown in Fig. 8(d), which demonstrates how well the HHA-PIC tracks its reference than the other simulated types. Fig. 8 demonstrates how the suggested WE system can compute the P m using the current sensor and ω r sensor with little fluctuations. Additionally, compared to the CPIC, and AFLC, the HHA-PIC achieves maximum power with much less inaccuracy. Findings highlight the efficiency of the WSE method and the superiority of HHA-PIC over CPIC, and AFLC particularly at the beginning and changing conditions.

B. CASE 2: RAMP OF WS
In this case, the WS varies up and down with smooth ramp rates with a mean speed of 6 m/s, as seen in Fig. 9 (a), with VOLUME 11, 2023 and optimal values, respectively. The capability of the WSC to track the ω r with its reference value displayed in Fig. 9(d).    Fig. 9 shows that the AFLC is better than CPI in terms of less overshoot, fewer oscillations, and fast response. So, HHA-PIC can be considered very fast in response to system dynamics, particularly, when the WS changes suddenly.

C. CASE 3: REAL FLUCTUATIONS OF WS
The feasibility of the studied control system to achieve MPPT is investigated in this part. with respect to genuine WS data measured in Ras Ghareb wind farm in the Gulf of Suez, Egypt, as seen in Fig. 10. The measured data is taken for 8 hours (480 mins) and reprocessed and scaled for 100 s to fit the simulation necessities. Three controllers (CPI, AFLC, and HHA-PI) are compared to prove the efficacy of the proposed control strategy. The portrayed WS profile is displayed as given away in Fig. 11(a). Fig. 11(b) as well as Fig. 11(c) demonstrate that the MPPT is attained since the λ and C P values are kept at their desired values, respectively. The proposed HHA-PIC for MPPT sustains the optimal C P more rapidly and maintains the optimal value of λ as perceived in Fig. 11(b). Fig. 11(d) displays the WSC's capacity to track the ω r with its reference value. The P m acquired by the WS is described in Fig. 11(e). From the simulated results, it can be said that the suggested HHA-PIC makes an available option for achieving MPPT under the high variability of WS and is superior to the compared controllers.

D. SYSTEM EFFICIENCY
The efficiency of the PMSWG system using the HHA-PIC, AFLC, and CPIC is shown in Fig. 12. As can be observed from Fig. 12 (a), the HHA-PIC system outperforms the CPIC, and AFLC in terms of improving the efficiency of a WT system. According to Fig. 12 (b), the average efficiency over this time period improved to 93.91% with HHA-PIC versus 85.44% with CPIC and 93.10% with AFLC. Table 4 compares this study's findings with previously published ones to demonstrate its originality and significance.

E. ERRORS OF HHA-PIC AND CPIC BASED ON MPPT CONTROLLERS
In addition, a quantitative comparison of tracking errors using the integral of time absolute error (ITAE) for the best evaluation of the HHA-PIC method is introduced as follows [63]: Table 5 illustrates a comparison of tracking errors of CPIC, AFLC, and HHA-PIC based on MPPT controllers. The HHA-PIC has the lowest error when compared with the other controllers. Consequently, the HHA-PIC is the best solution for achieving MPPT.

VI. CONCLUSION
This research examines a straightforward MPPT method to calculate WS without the need for any WS sensors in an effort to save installation costs and boost overall effectiveness. Additionally, the approximated WS is calculated using the ω r and I q feedbacks and depends on the Pm/torque. The PMSWG presents three SCL systems, the first using the CPIC, the second using AFLC, and the third using HHA-PIC. The system components and their control schemes are also presented. The CPIC at SCL is adjusted using the AFLC and HHA approaches to fix its flaws. To control the ω r with the required value, the HHA-PIC is implemented. The HHA-PIC, AFLC, and CPIC in SCL have been compared, and with the suggested controller, the WE system operates at Cp = 0.48 and λ = 8.1 in all working situations. The performance analysis demonstrates that HHA-PIC outperforms CPIC and AFLC when employing the WSE-MPPT method and suggests a significant fix for issues with traditional controllers. The overall system efficiency has been 85.44%, 93.10%, and 93.91% with the CPIC, AFLC, and HHA-PIC, respectively. Furthermore, the proposed scheme achieved higher efficiency with a negligible settling time (0.0086s). Finally, it can be said that the suggested technique improves the effectiveness and efficiency of WE systems and facilitates the production of cleaner energy.