Development of a Novel Efficient Maximum Power Extraction Technique for Grid-Tied VSWT System

The growing tendency of wind energy technology usage has induced researchers to seek more studies on the improvement of wind energy harvesting systems with highly reliable power injected into the electric grid. The amount of extracted wind energy by a wind turbine depends on the accuracy of the maximum power point tracking (MPPT) algorithm associated with the control scheme of the wind energy conversion system (WECS). This paper aims to present a novel development of MPPT algorithm based on parabolic prediction techniques (PPT) for variable speed wind turbines (VSWT) so as to achieve maximum wind power extraction and efficiency enhancement. The developed PPT-MPPT algorithm uses parabolic convex functions to estimate the parabola wind turbine output curve and locate the maximum power point on that curve. Simultaneously the algorithm establishes a systematic procedure for adjusting the concavity and the optimal part of the estimated parabola curve to make sure that the proposed technique is in continuous convergence. The feasibility of the developed PPT-MPPT algorithm has been validated under rapid and random changing wind speed profiles via the MATLAB/Simulink environment. The performance of the proposed PPT-MMPT algorithm is evaluated by comparing the simulation finding to those obtained using the benchmark perturb and observe(P&O) algorithms. The simulation outcomes affirm that the proposed PPT-MPPT algorithm outperformed the other algorithms in terms of tracking efficiency and extracted power which can be regarded as an efficacious manner to improve the VSWT system.

is regarded as one of the most effective and sturdy means 23 of reducing environmental pollution and contributing to 24 The associate editor coordinating the review of this manuscript and approving it for publication was Nagesh Prabhu . the production of clean electrical energy [2]. As a result, 25 the capacity of installed wind energy conversion systems 26 (WECS) has risen from a few megawatts to hundreds of 27 gigawatts within the last few decades and is expected to 28 produce 29.1 % of global energy by 2030 [3], [4]. The wind 29 turbine (WT) is regarded as the primary component of WECS 30 and is classified into fixed speed WT (FSWT) and variable 31 speed WT (VSWT) [5]. The VSWT based on the perma-32 nent magnet synchronous generator (PMSG) with a full-scale 33 power converters (FSPC) topology has been espoused by 34 anemometer for measuring wind speed that in turn increases 91 the cost, in addition to using a fixed forward step-size that 92 creates undesirable oscillations around the MPP. In [34], 93 a new approach combining the use of synthetic curves and 94 ratios is introduced to adeptly adjust the SS according to 95 power variations, estimated wind speed and generator rota-96 tional speed. Despite tracking performance being improved, 97 the algorithm complexity is significantly increased. In [35], 98 the authors presented an updated traditional P&O-MPPT 99 algorithm in which the SS is altered according to the distance 100 between the estimated and measured generator's rotational 101 speed. In spite of the fact that tracking speed has improved, 102 this method is solely reliant on the first SS. In [36] and [37], 103 an advanced P&O-MPPT algorithm of the multi-operation 104 zone is proposed. In this approach, the power vs. rotating 105 speed (P − ω) curve is divided into four zones. Consequently, 106 the selection of the suitable SS is related to the closeness of 107 the operating zone to the MPP. For the two zones close to the 108 MPP, a small SS is applied. Otherwise, the algorithm uses a 109 big SS. However, this strategy comprises a restricted operat-110 ing zone, in addition to using an anemometer for measuring 111 wind speed. Furthermore, choosing SS poses a significant 112 challenge to reach proper and fast speed tracking with lesser 113 oscillations. Moreover, the approach in [38] is developed 114 to increase the applied SS number and operating zone via 115 adopting a synthesized ratio that corresponds to the nominal 116 optimal power. Nevertheless, the limits of the operating zone 117 and associated SS are retained constant even when the wind 118 speed changes. This in turn causes undesirable swinging 119 around the MPP at low wind speed profiles. Therefore, there 120 is still a need to develop a new effective MPPT algorithm that 121 can get rid of the limitation of the existing algorithms and add 122 more enhancement to the performances of WECS. 123 This work aims at introducing a new efficient senseless 124 MPPT technique that eliminates the limitation of the existing 125 D-MPPT and I-MPPT algorithms as well as extracting the 126 maximum wind power effectively. The proposed technique is 127 developed based on the concept of the downward parabola 128 curve and is named the parabolic prediction technique (PPT). 129 Then, by a progressive renewal of the operating points and 130 their corresponding parabola, the WT optimal rotational 131 speed and the corresponding power can be obtained. The 132 proposed PPT-MPPT algorithm has the following features 133 and advantages over the existing MPPT algorithms: 134 • In comparison to the P&O-MPPT algorithms, the pro-135 posed PPT-MPPT algorithm instantly finds the maxi-136 mum power point using parabolic function arithmetic. 137 The properties and constraints of the estimated parabola 138 shape for guaranteeing convergence conditions are eas-139 ily marked from introductory arithmetic. This results in 140 quicker MPPT hunting speed and eliminating oscillation 141 of operating point around the MPP.

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The PMSG converts mechanistic power into electrical power 200 even at a low angular rotating speed. It has the features of 201 high electrical power density, less copper loss due to the lack 202 of field coils, and a low cost, [44]. The revolving reference 203 frame's electrical voltages (dq − axis) supplied by the PMSG 204 are expressed as follows [41], [45]:  The PMSG's electromagnetic torque Te is figured by the 217 following equation [45], [46], [47]: Hence, the PMSG's dynamic model formula is expressed as 220 Equation (10), [45], [47].

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The VSWT-PMSG system is tied with UG terminals by 227 an FSPC [48]. The FSPC includes three major control 228 schemes namely the MPPT algorithm, the MSR, and the 229 GSI as depicted in Figure 1. The MPPT algorithm tracks 230 and provides the optimal angular rotating speed of the 231 best wind power extraction [49], [50]. The MSR con- MPP. This oscillation causes power loss in the WECS [53]. 335 For this reason, the VSSP&O-MPPT has been proposed by 336 many researchers. 337 2) VSSP&O-MPPT ALGORITHM

338
A VSSP&O-MPPT algorithm is intended to eliminate the 339 deficiencies of the FSS &O-MPPT approach by creating a 340 balance between tracking speed and oscillation challenge. 341 The operating principle of the VSS P&O-MPPT is that the 342 algorithm divides that P − ω curve into multiple zones and 343 each has a certain SS. This strategy is efficient for tracking 344 speed, nevertheless, it uses wind speed information to define 345 the curve which is in turn considered as the main limitation 346 of the I-MPPT algorithms. Besides, the number of operating 347 zones is limited and associated SS must be carefully tuned. 348 Therefore, the development of a new MPPT algorithm that 349 is not reliant on dividing the P − ω, hence picking a certain 350 perturbing SS or measuring wind speed is still required [54]. 351

352
The proposed work aims to develop a new MPPT algorithm 353 for the wind conversion system based on the parabolic predic-354 tion technique (PPT). The developed algorithm is intended 355 to address the most significant issues of the existing power 356 extraction algorithms. The concept of this algorithm comes 357 from the observation that the wind turbine power vs. rota-358 tional speed (P−ω) curve has a parabolic shape, characterised 359 by a single maximum point for each wind speed [55], [56], 360 [57], [58]. Therefore, strategies that are used to find the vertex 361 of a parabolic curve can be applied to search the MPP of a 362 wind turbine.

364
PPT is a parabola fitting technique used to find a maximum 365 point (vertex) of a parabola curve based on three given points 366 on that curve. One point must be taken from one side of the 367 curve and two-points are taken from the other side of the 368 curve as revealed in Figure 3. The standard formula, given 369 by Equation (12) where a, b, and c are numerical coefficients and x is an 373 unknown variable. The maximum point of the parabola curve 374 is called the vertex. By deriving the standard formula and 375 making the first derivative equal to zero, the vertex of the 376 To find the value of vertex, the numerical coefficients (a,  convergence, (ω 2 , P 2 ) must be higher than (ω 1 , P 1 ) and

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(ω 3 , P 3 ), as shown in Figure 4. Usually, the initial three points  rotational speed satisfy the convergence condition. With help 416 of the mathematics 1st derivative which state that, if P (ω) 417 varies from positive to negative on the interval of ω 1 and ω 3 , 418 then a ω max location is between ω 1 and ω 3 and can be found 419 by using PIP.

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Second case: when the ω 1 < ω 2 < ω 3 and the measured 421 power, P 3 , is a present largest output power. In this case, 422 the derivatives, P (ω 1 ) , P (ω 2 ) and P (ω 3 ), are positive (at 423 uphill side of the power curve of a wind turbine). This means 424 that the three measured powers do not satisfy the convergence 425 condition. Hence, extra consideration must be imposed to 426 have a successful convergence condition. In this case, a shift-427 ing procedure is performed in such a way that the rotational 428 speed ω 1 , ω 2 , and ω 3 are increased by a step size ( ω), 429 until the measured power, P 2 , becomes the highest. After it is 430 ensured the measured power at ω 2 is always the highest, the 431 PIP is applied. The concept of rotational speed adjustment to 432 the right is illustrated in Figure 5.

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Third case: when the ω 1 < ω 2 < ω 3 and the measured 434 power, P 1 , is the highest output power. In this case, the 435 derivatives, P (ω 1 ) , P (ω 2 ) and P (ω 3 ), are negative (at the 436 downhill side of the power curve of a wind turbine). This 437 means that the three measured powers do not satisfy the con-438 vergence conditions. Consequently, the shifting procedures 439 to the left must be performed in such a way that the rotating 440 speed ω 1 , ω 2 , and ω 3 are decreased by a step size ( ω), until 441 the measured power, P 2 , becomes the highest as shown in 442 Figure 6. Once making sure that the measured power P 2 is 443 the highest, the PIP is applied.

444
In the PIP, the algorithm uses the information of the 445 three satisfying points to create equations of the estimated 446 parabolic curve as follows: After obtaining ω max , which produces P max , the values 464 of power become four different measured power points 465 P 1 , P 2 , P 3 , and P max . For the next iteration, the lowest power 466 is dropped out, and the three new points are launched until 467 the differences ( P max ) between the current P max and the 468 previous P max−1 is less than P thre . Then the algorithm 469 maintains that rotational speed to extract the MPP.  The dynamic response of the developed PPT-MPPT algo-475 rithm under dynamic-changing in wind speed can be analyzed 476 based on the effect of changes in wind speed on the measured 477 power P 2 position. In case, the measured power point P 2 at the 478 rotating speed ω 2 remains the largest, as shown in Figure 8. 479 This means that the change in wind speed has no effect on the 480 convergence condition and the three measured power points 481 are still satisfied to perform the PIP for finding ω max . Con-482 versely, in case, the change in wind speed has an influence on 483 the measured power points and changes the sorting patterns 484 of P 2 (P 2 is not the largest measured power), the algorithm 485 will give more time to the shifting procedure to rearrange the 486 rotational speed.

487
The rotational speed should be shifted to the right if the 488 values of power after changes in wind speed are on the left 489 side as portrayed in Figure 9. Otherwise, the rotational speed 490 should be shifted to the left when the values of power after 491 a change in wind speed are on the right side, as depicted in 492 FIGURE 8. Wind speed variation with no effect on power arrangement.   profile that changes every five seconds at the rate of 2 m/s 515 was applied as seen in Figure 11. Meanwhile, the optimal 516 rotational speed, the tip speed ratio, the power coefficient, and 517 the extracted power waveforms of the CP&O with a small and 518 big SS, VSP&O, and the proposed PPT-MPPT algorithms, 519 have been analysed and compared.

520
The analysis and comparison have been conducted via 521 evaluating the performances of all MPPT algorithms in 522 terms of oscillation rate, reaching time to optimal condi-523 tion and WECS efficiency indices. The WECS efficiency is 524 determined for each step changes during the entire period 525 so as to confirm the dynamic performance of the devel-526 oped control scheme. The efficiency η sys. is computed 527 as the ratio of the extracted output power (P ext ) of the 528 WECS to the nominal power (P nom ) using the formula of 529 η sys = t 0 P ext / t 0 P nom × 100%.

530
In this turn, Figure 12 (a) shows that with a small SS, 531 the reaching time to optimal rotational speed is longer and 532 the oscillation of operation point around the optimal value 533 is smaller when the wind speed changes quickly. Alterna-534 tively, using a big SS leads to a fast reaching to the optimal 535 rotational speed with large oscillations apparent when the 536 peak value is attained. The VSSP&O algorithm reduces the 537 reaching time but there are still some oscillations around the 538 maximum point; at steady state speed because of the strategy 539 used. In contrast, Figure 12 (a) proves that the developed 540 PPT-MPPT algorithm has a faster reaching time to the opti-541 mal rotational speed with zero oscillations around the maxi-542 mum point due to the features of the tracking mechanism. The 543 magnified views of the Figure 12 (a) shows that the Proposed 544 PPT-MPPT algorithm first sent three initial rotational speed 545 and then performed shifting procedure to satisfy the conver-546 gence condition. Consequently, the optimal rotational speed 547 that resulted in the maximum power is obtained by applying 548 the PIP procedure. The outcome showed that with the PPT-549 MMPT algorithm, the optimal rotational speed for the wind 550 speeds of 8,10 and 12 can be reached at 39 msec,25 msec and 551 10 msec respectively. Moreover, after the optimal value was 552 reached, the oscillation issue was totally eliminated which in 553 turn enhanced the overall system efficiency.

554
The comparison study including reaching time, oscillation 555 rate around optimal value and efficiency of the proposed 556 PPT-MPPT, CP&O and VSSP&O algorithms for wind speed 557 step change of 8 m/s 10 m/s and 12 m/s are provided and 558 listed in Table 1, Table 2 and Table 3 respectively. In view of 559 TSR, the outcomes shown in Figure 12     The power coefficient Cp is a crucial indicator of the 568 WECS conversion efficiency. In this study, the MPPT 569 algorithm must maintain the Cp at the optimal value of 570 0.44 regardless of the wind speed change to convert the 571 whole available wind energy into mechanical power. Zoomed 572 views in Figure 13 (a), reveals that the big SS-P&O and 573 PPT-MPPT algorithms attain the optimal Cp (0.44) faster than 574 both the small SS-P&O and the VSSP&O-MPPT algorithms. 575 Though, the big SSP&O has high steady-state oscillations 576 that have a negative impact on the converted mechanical 577   indicates that the amount of captured wind power utilising the 588 proposed PPT-MPPT algorithm under fast change wind speed 589 is higher and more efficient compared to the other algorithms 590 as portrayed in figure 13 (b).

591
To further demonstrate the performance of the proposed 592 PPT-MPPT under rapid change of wind speed, the significant 593 variables of GSI also have been analysed. The simulation 594 outcomes of active and reactive power under the given wind 595 speed profile for all algorithms are indicated in Figure 14. 596 Figure 14 (a) indicates that when the proposed PPT-MPPT 597 VOLUME 10, 2022