Dynamic Reliability and Availability Allocation of Wind Turbine Subassemblies Through Importance Measures

This paper illustrates the impact of wind turbine (WT) subassemblies’ availability on WTs’ performance. Complete and detailed reliability, availability, and maintainability (RAM) analysis of various subassemblies of WTs utilizing the Weibull probability density function (PDF) is also introduced. A modified dynamic important measures-based reliability and availability are presented to show the significant impact of various WT subassemblies on the overall system performance. This method is mainly utilized to rank the WT subassemblies regarding their impact on the system reliability and availability, identifying the subassemblies that the planned maintenance should focus on. Dynamic ranking of WT subassemblies is obtained to achieve the desired level of reliability and availability. The obtained results demonstrate the effectiveness and efficiency of the proposed approach that achieves the system’s secure operation and improves system reliability and availability.

isn't identified accurately and repaired or replaced in time, 40 other subassemblies or the whole system may be affected. 41 On the other hand, temporary random faults are defined as 42 temporary and short-term events caused by external factors. 43 Temporarily shutting down and restarting the faulty sub-44 assemblies or even the whole system may be the appropriate 45 action to clear these faults [2]. Unfortunately, in the case of 46 permanent faults, repairing or replacing the defective sub-47 assemblies cannot be performed for an extended period due 48 to inaccessibility issues. Thus, some subassemblies' failure 49 rates become more critical, making the developers select 50 systems with lower failure rates [3]. 51 System reliability is expressed as the probability of suc-52 cessful operation of a system, subsystem, or subassembly 53 to perform the required function acceptably for an intended 54 period. Reliability represents the wind energy systems' cru-55 cial issue in the planning and operational stages, which 56 enables predicting the system behavior over its operating 57 lifetime and contributes to setting appropriate maintenance 58 strategies. As a result, reliability may be used to control the 59 revenue losses [4], [5], [6]. On the other hand, the availability 60 of a system can be defined as the percentage of time that 61 the system remains available to achieve its required function. 62 Therefore, the system's availability depends on more factors 63 than reliability [4], [7], [8], [9]. Thus, the availability study 64 is necessary for assessing the system performance, especially 65 when accessibility is considered.

66
In the last decade, the reliability and availability of wind 67 energy conversion systems and their improvements represent 68 a main point of interest for many research and articles on 69 reliability and availability [4].

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Reliability and availability are considered good indicators 71 for evaluating a system's performance. Their values depend 72 on the reliability/availability of the subassembly and also on 73 the system structure. Of course, these values decrease with 74 increasing the subassembly ages [10]. Therefore, the main 75 requirements for operating complex systems are availability 76 and reliability. For the design stage, these requirements are 77 also very important to specify the appropriate subassem-78 blies' availability and reliability [11]. Some issues must be 79 resolved during both the design and operation phases to 80 improve the performance/availability of such systems. The 81 effect of improvements on the whole system availability after 82 identifying the system's weak points represents the most 83 important issue among them. More investigations have been 84 performed in availability studies about the problem of avail-85 ability allocation using various approaches [11], [12], [13], 86 [14], [15]. At the subassembly level, it is substantial to 87 consider the critical characteristics of reliability and main-88 tainability for the system to deal with the availability 89 allocation.

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Therefore, it is very important to point out that the 91 important measures based on reliability and maintainabil-92 ity must be considered to improve the existing availabil-93 ity characteristics. According to the concept of importance 94 measures (IMs), some subassemblies have more importance 95 than others in providing a particular system. The subassem-96 bly importance analysis, which represents the essential part 97 will be used in this paper, which plays a critical role in the Thus, the utilizing of Weibull PDF is more general and prac-122 tical than exponential PDF. Using the flexible Weibull PDF 123 with the important measures will give the dynamic ranking of 124 WT subassemblies that will be more realistic than the statistic 125 ranking.

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This paper presents a developed technique for reliability, 127 availability, and maintainability (RAM) analysis of wind sys-128 tem subassemblies using a Weibull distribution. This paper's 129 interests also extend to obtain the dynamic ranking of each 130 subassembly of the wind energy system from the reliability 131 and availability perspective based on reliability and availabil-132 ity IMs. Fig. 2 illustrates the work steps of this paper that 133 are carried out using MATLAB. Table 1 lists a Comparison 134 between the proposed work in this study and other related 135 studies.

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The rest of this paper is organized as follows. Section II 137 introduces and explains the reliability and maintenance of 138 WTs. Sections III and IV show the complete analysis and 139 result of RAM of WT subassemblies. Dynamic reliability 140 and availability IMs are proposed in section V. Results and 141 discussions are offered in Section VI. Finally, Section VII 142 provides the conclusions of this paper.

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There is an increasing need for complicated maintenance There is an increasing need for complicated maintenance 182 systems to achieve an acceptable level of reliability and avail-183 ability. This maintenance system generally relies on setting a 184 maintenance strategy for all subassemblies of the WT, which 185 will increase the maintenance cost of the WT. Therefore, if we 186 need to minimize this maintenance cost, we must determine 187 the subassemblies that have the most significant impact on 188 the reliability and availability of the WTs. In this case, the 189 maintenance strategies will focus only on these subassem-190 blies instead of all subassemblies. This maintenance will be 191 achieved by the dynamic reliability and availability proposed 192 in this paper.  Reliability is the probability of a system performing its 206 required function adequately for a specific time, t. The gen-207 eral reliability function R (t) can be expressed as follows:

ANALYSIS OF WIND TURBINES
Equation (1)   The various shapes achieve through different values of the 221 shape parameter. The 2-parameter Weibull PDF is given by: The Weibull reliability function is given by: where η and β represent the life and shape parameters, 226 respectively.

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When a failed item of a given system restores its normal 228 operating condition, this is known as maintainability. The 229 maintainability of a system, subsystem, or even subassembly 230 is the probability that it can be restored to a state in which 231 it can perform its intended function within a given time. hour, the probability that this item will be repaired is 90% 242 within an hour. MTTR represents the random variable in 243 maintainability, whereas MTBF is the random variable in 244 reliability. The maintainability equation M (t) for a system 245 where its repair times follow the Weibull distribution can be 246 written as: Availability is the percentage of time that the system is 249 available to perform its required function [35]. The time-250 dependent availability is expressed by: where λ and µ represent the failure and repair rates, 253 respectively.

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RAM analysis of any complex system is executed through 255 three steps. These steps are system decomposition, data col-256 lection, and modeling. The first step of RAM analysis decom-257 poses the whole wind energy system into subassemblies 258 according to their functions. The numbers of subassemblies 259 vary according to the type and size of WT. The main sub-260 assembly of a typical WT is illustrated in Fig. 4. As shown 261 in Fig. 4, the mechanical energy is transmitted by blades con-262 nected to the hub via a low-speed shaft to the gearbox's high-263 speed shaft. The main bearing supports the low-speed shaft, 264 while the gearbox is used to adjust speed. The converter is 265 utilized in some WTs to match the grid connection. The yaw 266 system is mounted on a bedplate or foundation at the top of a 267 tower. It is used to rotate the nacelle to control the alignment 268 of the direction of the wind. The pitch system (PS) mounted 269 in each blade acted as an aerodynamic brake and was used to 270 control the power input to the WT. The yaw, the brake, and 271 the PSs are controlled by a meteorological unit attached to 272 provide weather data (e.g., wind speed and direction). According to the WTs' types and sizes, the costs of all 274 of these subassemblies will vary. For instance, some WTs 275 do not have a gearbox in some configurations. Therefore, 276 depending on the configuration used, the costs of both gen-277 erators and converters will differ. Anyway, Fig. 5     . The application of 322 condition monitoring approaches can mitigate the reliability 323 issues of the gearbox that are attributable to the design and 324 manufacturing processes. Still, to minimize the downtime 325 of WTs, the enhancement of design and manufacturing pro-326 cesses is imperative. Table 2 lists the percentage reliability 327 of each subassembly after five and ten years of operation 328 utilizing Weibull PDF.     system is the most extended availability, followed by the 352 electrical controls. In contrast, the gearbox and the generator 353 are expected to have the least availability. Table 3 lists the percentage availability of each subassem-355 bly after five and ten years of operation utilizing Weibull PDF. 356

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Reliability allocation should execute in the initial stages of 359 systems design, which relates to setting the reliability objec-360 tives for the subsystems and/or subassemblies to achieve 361 the desired overall system reliability. The overall mission 362 requirements of the system are the basis of determining 363 the value of the system's reliability. There is an increasing 364 need for a proper method to determine the subassemblies' 365 VOLUME 10, 2022 reliability value to obtain the system reliability. As mentioned before, the predicted failure probability or the relia- where R i is the subassembly reliability, R s is the system 412 reliability, A i is the subassembly availability, and A s is the 413 system availability.

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IMs are utilized to specify the effect of each subassembly 415 reliability and availability of a system on the overall system 416 reliability and availability, respectively. The subassembly that 417 records the largest value of the IM is that it has the great-418 est effect on the whole system's reliability and availability.

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Consequently, it is essential to determine the value of the IM 420 of each subassembly of a system before taking any action 421 toward improving system reliability and availability. This 422 is to obtain the optimal results from improving the sys-423 tem reliability, availability and determine which subassembly 424 needs to be improved, hence obtaining the optimal results 425 from improving the system reliability and availability. The 426 improvement efforts should be concentrated on improving 427 the subassemblies that have the largest effect on system reli-428 ability and availability if each of those values needs more 429 improvement.

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Sets of IMs can also be specified with the DAIMs accord-431 ing to the relation between MTBF/MTTR and the system 432 availability as follows:  The MTBF/failure rate of a certain subassembly on the 436 overall system availability can be represented by the DAIMs 437 of MTBF/failure rate. The subassembly with the largest value 438 of DAIMs of MTBF/failure rate has the most significant 439 effect on the system's availability. It can be calculated by: However, the DAIMs of MTTR/repair rate is an indi-442 cator of the MTTR/repair rate of a subassembly effect on 443 the overall system availability. The high value of DAIMs 444 of MTTR/repair rate means a high effect on the system's 445 availability. It is calculated as follows: From the reliability theory point of view, the steady-448 state availability of a system that contains m-independent 449 subassemblies connected in series can be written as: The DAIMs of specific subassembly i in a series system 452 can be expressed as: The DAIMs of a specific subassembly is affected by 455 all subassemblies' availability except that subassembly. The 456 subassembly that records the minimum availability estimate 457 should greatly prioritize increasing the whole system's avail-458 ability. According to the availability characteristics of a sys-459 tem, various DAIMs types can be calculated by the following 460 equations:   The steady-state availability of a system that contains 464 m-independent subassemblies connected in parallel can be 465 expressed as: 467 The DAIMs of specific subassembly i in a parallel system 468 can be expressed as:

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The dynamic reliability and availability important measures 481 suggested in section V are utilized to find the weakest 482 subassembly that affects the overall system reliability and 483 availability. Fig. 13 shows the subassemblies' reliability and 484 availability collected together, representing the IMs stage's 485 input. The IMs stage's output representing the subassemblies' 486 ranking according to their influence on the overall system 487 reliability and availability is shown in Fig. 14 and Fig. 15, 488 respectively. It is found that the ranking of subassemblies 489 according to the impact on the overall performance of the WT 490 is a dynamic ranking. This means that this ranking varied (not 491 fixed) through the expected lifetime of the WT.

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The main reason behind this is using the flexible Weibull 493 PDF, which combines the permanent and intermittent faults 494 that make the availability vary through the lifetime of the 495 WT. Therefore, the priority of the subassemblies to enhance 496 the overall system performance is very short (each year). 497 As shown in Fig. 14, the generator has the greatest impact on 498 the overall reliability among the WT subassemblies for the 499 VOLUME 10, 2022 TABLE 2. Percentage reliability of wind turbine subassemblies after five and ten years of operation.     Thus, the importance or focus of one subassembly along the 506 total lifetime of the system and the consideration that its 507 improvement will enhance the overall system reliability must 508 be changed according to these findings. 509 Similarly, as shown in Fig. 15, the generator has the great-510 est impact on the overall availability among the WT sub-511 assemblies for the first five years. At the same time, rotor hub 512 subassembly recorded the first priority between all subassem-513 blies from year six to year nine. From year ten to year twelve, 514 the gearbox represents the first priority. For the last eight 515 years, the mechanical brake has been the greatest influence 516 on the overall system availability among all subassemblies 517 of WT. Thus, the importance or focus of one subassembly 518 along the system's total lifetime and the consideration that 519 its improvement will enhance the overall system availabil-520 ity must be changed according to these findings. It is very 521 important to point out that the proposed dynamic reliability 522 and availability IMs will generate another dynamic ranking 523 VOLUME 10, 2022    Fig. 14 and Fig. 15.

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This will help the operators and the developers of the WF to 530 identify the critical subassemblies that the maintenance will 531 be focused on.

532
As mentioned before, the system's availability depends on 533 more factors than reliability. Thus, availability improvement 534 is necessary for assessing the overall system performance. 535 System availability improvement will be excited by either 536 improving the MTBF or MTTR for the subassemblies that 537 have priority one in Fig. 15. Therefore, DAIMs for MTBF 538 and MTTR will be determined utilizing Equations (12) 539 and (13). Table 4 and Table 5 list the results of the dynamic 540 IMs for MTBF and MTTR of various WT subassemblies, 541  respectively. Fig. 16 illustrates the effect of the dynamic 542 MTBF-IMs and MTTR-IMs of various WT subassemblies to 543 improve overall system availability.

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Comparing the IMs of MTBF and MTTR of each sub-545 assembly can determine whether the MTBF or MTTR of 546 that subassembly has more influence on the WT availability. 547 VOLUME 10, 2022 needs to be improved, the efforts should be concentrated on 549 increasing the availability of the subassemblies that have the 550 first ranking (GE, RH, GB, and MB). Furthermore, it is better 551 to pay more attention to MTTR for those subassemblies; their 552 MTTR on the overall system availability is greater than the