J. Cent. South Univ. (2020) 27: 490-499

DOI: https://doi.org/10.1007/s11771-020-4311-4

Multi-component opportunistic maintenance optimization for wind turbines with consideration of seasonal factor

SU Chun(苏春), HU Zhao-yong(胡照勇), LIU Yang(刘洋)

School of Mechanical Engineering, Southeast University, Nanjing 211189, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract: Aiming at wind turbines, the opportunistic maintenance optimization is carried out for multi-component system, where minimal repair, imperfect repair, replacement as well as their effects on component’s effective age are considered. At each inspection point, appropriate maintenance mode is selected according to the component’s effective age and its maintenance threshold. To utilize the maintenance opportunities for the components among the wind turbines, opportunistic maintenance approach is adopted. Meanwhile, the influence of seasonal factor on the component’s failure rate and improvement factor’s decrease with the increase of repair’s times are also taken into account. The maintenance threshold is set as the decision variable, and an opportunistic maintenance optimization model is proposed to minimize wind turbine’s life-cycle maintenance cost. Moreover, genetic algorithm is adopted to solve the model, and the effectiveness is verified with a case study. The results show that based on the component’s inherent reliability and maintainability, the proposed model can provide optimal maintenance plans accordingly. Furthermore, the higher the component’s reliability and maintainability are, the less the times of repair and replacement will be.

Key words: wind turbine; reliability; seasonal factor; multi-component maintenance; opportunistic maintenance

Cite this article as: SU Chun, HU Zhao-yong, LIU Yang. Multi-component opportunistic maintenance optimization for wind turbines with consideration of seasonal factor [J]. Journal of Central South University, 2020, 27(2): 490-499. DOI: https://doi.org/10.1007/s11771-020-4311-4.

1 Introduction

The problem of environmental pollution and ecological damage has become more serious than ever before. Therefore, the development of renewable energy, such as wind energy, solar energy, and hydropower, has attracted much attention. Up to now, wind energy has become the second largest renewable energy just behind the hydropower around the world [1].

Wind turbine is the key subsystem of wind power generation system, and it is composed of various electromechanical components. Moreover, wind farms usually locate in remote areas, and wind turbines need to work in wild environment throughout the year. Therefore, the maintenance cost and logistics cost are quite high. It is reported that during the 20-year life, the wind turbine’s operation and maintenance (O&M) cost accounts for about 25%-30% of the total generation output, or nearly 75%-90% investment cost of the wind farm [2]. Obviously, maintenance plays an important role in the operation of wind farm.

Scientific maintenance plans can improve system’s reliability and reduce the maintenance cost effectively [3, 4]. FANG et al [5] discussed the preventive maintenance (PM) and replacement policy for repairable system, and the vector Markov process method was adopted to solve the maintenance model. NILSSON et al [6] analyzed the maintenance cost of offshore wind turbines with the method of life-cycle cost analysis. SORENSEN [7] proposed an optimization strategy for wind turbines, and the Bayesian decision theory was adopted to acquire global maintenance optimization. JOSHI et al [8] proposed an approach to evaluate the failure rate and predict O&M cost for wind turbines, and optimal maintenance schedule was determined. SINHA et al [9] adopted the approach of failure modes, effect and criticality analysis (FMECA), and the failure modes and their occurrence rules of wind turbines were obtained. The results show that wind turbine’s reliability has obvious regional and manufacturer characteristics. In terms of the wind turbine’s performance, SANTOS et al [10] compared the corrective maintenance (CM) based on replacement and age-dependent preventive maintenance (PM) with imperfect repair. NGUYEN et al [11] proposed a dynamic maintenance strategy, and the aim was to improve the cost-effectiveness of the off shore wind turbines.

Opportunistic maintenance refers to maintain a component together with the other components so as to meet some maintenance requirements [12]. In this way, high fixed maintenance cost (including logistics cost, downtime loss, cost for disassembly and assembly, etc) can be shared and reduced. Wind turbines are typical multi-component systems, therefore the opportunistic maintenance policies should be effective for them. Up to now, some studies have been done on the opportunistic maintenance optimization for wind turbines, and the corresponding optimal maintenance plans were obtained, including SARKER et al [13], ZHAO et al [14] and LU et al [15]. DING et al [16] proposed three kinds of opportunistic maintenance models for wind turbines, where perfect maintenance, imperfect maintenance and two-level action were considered in the PM model respectively. The results show that two-level action is an effective method to reduce the maintenance cost. Taking wind turbine’s gearbox, bearing, rotor and engine as the objects of study, SU et al [17] proposed an opportunistic maintenance model to minimize the total maintenance cost. By using reliability-based imperfect repair, ZHANG et al [18] developed an opportunistic maintenance strategy for wind turbines. It is found that by adopting opportunistic maintenance, the maintenance cost can be reduced effectively.

For wind turbines, their operating environment is usually harsh and challenging, and the seasonal factors (including wind speed, environmental temperature, etc.) may have great influence on wind turbine’s reliability and maintainability. Based on the data of a Denmark’s wind farm, TAVNER et al [19] concluded that geographical location and climate conditions have a significant impact on wind turbine’s failure rate. With the consideration of wind speed, SULAEMAN et al [20] assessed wind farm’s reliability and its output. Based on the data in a wind farm of Nordjylland, Denmark, SU et al [21] analyzed the correlation between failure rate and wind with the approach of time series. It shows that the failure rate of wind turbine has close relation with the wind speed. Furthermore, SU et al [22] established a reliability evaluation model with Bayesian network theory, where the influence of wind speed on wind turbine’s failure rate was taken into account. CHEN et al [23] proposed a multi-state reliability assessment model, where the uncertainty of wind speed and its influence on wind turbine’s failure rate were considered. The results show that the reliability of wind turbine has obvious seasonal characteristics. On the basis of the field operating data in a Chinese domestic wind farm, SU et al [24] analyzed the reliability characteristics of wind turbines and their components, the internal relation between the failure rate and environmental temperature was identified with the correlation function; and time series approach was applied to analyze the seasonal feature of the wind turbines’ failure rate.

The existing studies show that wind turbines’ failure rate changes with the season and wind speed regularly [19-24]. Moreover, the maintenance activities of wind turbines are also influenced by a variety of factors, including weather condition, the supply of spare parts, etc. Therefore, the maintenance activities should be carried out accordingly. However, up to now no studies are found on wind turbine’s maintenance optimization by considering the seasonal factors.

In this study, we take wind turbines as the object of study; the impact of seasonal factor on wind turbine’s failure rate is considered; and an opportunistic maintenance optimization model is established to minimize the life-cycle maintenance cost. Genetic algorithm (GA) is used to solve the optimization model and obtain the optimal maintenance plans. A case study is provided to illustrate the effectiveness of the proposed model. The major contributions of this study include:1) The multi-component maintenance optimization is carried out for wind turbines, where the seasonal factor is considered. To our best knowledge, this is one of the first studies of maintenance optimization by considering seasonal factors. 2) Based on the components’ inherent reliability and maintenance characteristics, the opportunistic maintenance policies are developed. 3) Maintenance mode at each inspection point is determined by considering both the effective age threshold and maintenance threshold.

The remaining parts of this paper are organized as follows. Section 2 defines the problem studied, and the maintenance cost model is established. In Section 3, the optimization solution is proposed on the basis of GA. In Section 4, a case study is provided to verify the validity of the proposed model. Section 5 concludes this study and suggests some directions for the future research.

2 Methodology

2.1 Maintenance policy

It is assumed that a wind turbine consists of I components in series; the life cycle of a wind turbine is divided into J inspection periods with equal inspection interval T. Let TL_i and TU_i denote the lower and upper bound of the repair threshold for component i respectively, and TU_i>TL_i (i=1, 2, …, I). Let X_{i, j} and Y_{i, j} denote the effective age of component i at the beginning and end of the jth inspection period respectively (i=1, 2, …, I; j=1, 2, …, J), and X_{i, 1} =0. Therefore, we have

    (1)

At the end of each inspection period, based on the effective age and repair threshold, we need to determine whether to perform PM for each component or not. At the end of the jth inspection period, for component i the maintenance options are as the follows:

(1) If Y_{i, j}i, component i does not require PM and will continue to operate.

(2) If TL_i≤Y_{i, j}i, component i will enter the state of waiting for opportunistic maintenance. At this time, if some other components require PM, they will be repaired simultaneously; otherwise, component i is not repaired and will continue to operate.

(3) If Y_i,j≥TU_i, component i enters the mandatory PM state. At this time, if some other components are also in the state of waiting for opportunistic maintenance or mandatory maintenance, they will be repaired simultaneously.

Here, PM includes imperfect repair and replacement. If X_i,j+1i, imperfect repair will be performed for component i; otherwise, replacement is performed. Furthermore, the improvement factor is used to describe the effect of imperfect repair. Let η_{i, k} (0<η_i,k<1) denote the improvement factor of component i during the kth imperfect repair in one replacement cycle. The higher η_i,k indicates that the effect of imperfect repair is better, and the effective age is reduced significantly. Hence, η_i,k can be expressed with Eq. (2) [25].

     (2)

where a_i is the adjustment parameter of imperfect repair effect for component i, 0i<1/Cpm_i; Cpm_i is the single imperfect repair cost for component i; b_i is the adjustment parameter of the imperfect repair’s number for component i, and 0i<1.

It is assumed that at the end of the jth inspection period, component i has undergone k-1 times of imperfect repairs during the current replacement cycle, then the relationship between X_i,j+1 and Y_i,j is as the follows:

    (3)

In addition, considering that the component has a certain probability of sudden failure during the operation, minimal repair (MR) is carried out in that case. MR can restore the component to working state, and after MR the component’s effective age is not changed.

2.2 Analysis of maintenance cost

Here, the maintenance cost includes repair cost for sudden failure, cost for PM as well as the fixed maintenance cost. In addition, the cost for PM includes the imperfect repair cost and replacement cost. Either for single-component maintenance or for multi-component maintenance, at the inspection point if PM is carried out, only one time of fixed cost is incurred. However, a fixed cost is incurred for each repair of a sudden failure. In this study, the following maintenance cost is considered.

1) Maintenance cost for sudden failure

For wind turbines, sudden failure may occur with a certain probability during the operation. And at that case, MR will be carried out to restore the wind turbine to the state of as bad as old (ABAO). Long-term observation data indicate that the failure rate of wind turbine’s component is subject to Weibull distribution [26]. For component i, the failure rate at the effective age t, i.e. λ_i(t), can be expressed as:

  (4)

where β_i, m_i and δ_i are the shape parameter, scale parameter and positional parameter of the Weibull distribution for component i, respectively.

Therefore, for component i, the total number of sudden failures during the jth inspection period can be calculated as

As described above, seasonal factors have obvious influence on wind turbine’s failure rate. Therefore, the seasonal factors should be considered when calculating the failure times. In this study, seasonal factor θ is used to depict the influence of seasonal variations, and θ_j denotes the seasonal factor in the jth inspection period. For component i, the total number of sudden failures during the jth inspection period is

Assuming that for component i, its single MR cost is Cmr_i, thus during the jth inspection period the system’s total MR cost can be obtained:

             (5)

2) Cost of preventive maintenance

For component i, the single PM cost is Cpm_i. Therefore, for the wind turbine, the total PM cost during the jth inspection period, i.e. TCpm_j, can be expressed as:

                     (6)

where p_i,j is the decision variable of imperfect repair for component i at the end of the jth inspection period. The value of p_i,j is as follows:

                 (7)

For component i, the single replacement cost is Cr_i. Then, during the jth inspection period, the total replacement cost, i.e. TCr_j, can be expressed as:

                         (8)

where r_i,j is the decision variable of replacement for component i at the end of the jth inspection period. The value of r_i,j is as follows:

                    (9)

Considering that the imperfect repair and replacement will not be carried out simultaneously, p_i,j+r_i,j≤1. It can be seen from Eq. (3):

  (10)

3) Fixed maintenance cost

During the life cycle, if PM or MR is carried out, the fixed maintenance cost will be incurred. Assuming that the single fixed cost is Cf, then during the jth inspection period the fixed maintenance cost (i.e. TCf_j) can be obtained as:

 (11)

Thus, during the wind turbine’s life cycle, the total maintenance cost C_total can be obtained with:

                (12)

3 Optimization solution based on GA

Maintenance optimization needs to balance the maintenance requirement and corresponding resources. According to the effective age and maintenance thresholds, we can obtain the maintenance plan for each inspection period with Eq. (12). The maintenance plan will change with the threshold, and the total maintenance cost is also a function of TL_i and TU_i (i=1, 2, …, I), where I is the number of components in the system. Therefore, the corresponding solving process will become complicated when the number of inspection periods is large.

Here, we intend to optimize the total maintenance cost and determine the decision variables, i.e. TL_i and TU_i. The optimal model is as follows:

                         (13)

In this study, genetic algorithm (GA) is used to solve the optimization model. GA was first proposed by HOLLAND to study the adaptive behavior for natural and artificial systems [27]. It simulates the genetic and evolutionary mechanism of the biology to find the optimal solution; the main operators include duplication, crossover, mutation and selection. GA has good ability of global optimization. Figure 1 shows the basic optimization procedure for the optimization of maintenance decision-making.

When GA is applied to solving the above optimization model, the total maintenance cost under different thresholds corresponds to the fitness of GA. In this study, the optimization program is completed based on the toolbox of MATLAB.

4 Case study

In this section, we take the wind turbines of a wind farm in Jiangsu Province of China as an example. This batch of wind turbines belongs to the type of gear-driven, three-blade and horizontal axis; the rated wind speed is 12 m/s and the cut-in and cut-out wind speeds are 3 m/s and 20 m/s respectively. They are equipped with supervisory control and data acquisition (SCADA) system, which can collect real-time operation data of the wind turbines. Based on the field data collected from May of 2009 to July of 2013, the maintenance optimization of these wind turbines is studied.

Figure 1 Optimization procedure for maintenance decision

The design life of these wind turbines is 20 years (240 months), and the inspection period is one month. Here four types of major components are considered, that is I=4. The corresponding reliability and maintainability parameters are shown as in Table 1. The cost unit is Chinese Yuan (CNY).

Previous study shows that the seasonal fluctuation period for this batch of wind turbines is 12 months, and the seasonal factor θ_j has the following characteristics [24]:

           (14)

When the operational month is known, we can obtain the value of θ_j with Eq. (14) and Table 2.

To simplify the expression and its calculation, the wind turbines are supposed to be put into production from January 1st of a particular year. The parameters for genetic algorithm (GA) are set as follows: the number of individuals in the population is 80 and the crossover probability is 0.8. The adaptive mutation method and the roulette wheel selection approach are applied for individual selection. The termination condition is that the genetic generation reaches 800 generations or the fitness value does not change for 100 consecutive generations. The iterative process is shown in Figure 2.

Table 1 Reliability and maintainability parameters of components

Table 2 Seasonal factor in each month

From Figure 2, when the genetic generation reaches the 176th generation, the optimal fitness has not changed for 100 consecutive generations. Thus, the iteration is terminated, and the optimal fitness value is 2.00×10⁶ Yuan (RMB). The corresponding maintenance thresholds are as follows: TL=[19, 27, 38, 48], TU=[43, 60, 61, 100]. Under the thresholds, the change rules of the components’ effective age are presented in Figures 3-6, respectively.

Figure 2 Iterative process of GA

Figure 3 Effective age’s change of Component 1

Figure 4 Effective age’s change of Component 2

Figure 5 Effective age’s change of Component 3

Figure 6 Effective age’s change of Component 4

During the life cycle, the above four components are repaired with 6 times of PM. The details are as follows:

1) At the end of the 43th inspection period, Component 1 reaches its upper bound of the effective age threshold, and Components 2 and 3 are in the state of waiting for opportunistic maintenance. Therefore, PM is carried out for Components 1, 2 and 3 respectively. Imperfect repair is adopted, since it can reduce the components’ effective age to below their lower threshold bound.

2) At the end of the 80th inspection period, the effective age of Component 1 reaches its upper threshold bound, and Components 2, 3 and 4 are in the state of waiting for opportunistic maintenance. Thus, PM is carried out for the four components, and imperfect repair is adopted.

3) At the end of the 111th inspection period, the effective age of Component 1 reaches its upper threshold bound, and Components 2 and 3 are in the state of waiting for opportunistic maintenance. Therefore, PM is carried out for the above three components. For Component 1, imperfect repair can meet the maintenance requirement, while it is insufficient for Components 2 and 3. Thus, imperfect repair is performed for Component 1, and replacement is performed for Components 2 and 3.

4) At the end of the 137th inspection period, the effective age of Component 1 reaches its upper threshold bound, and Component 4 is in the state of waiting for opportunistic maintenance. Therefore, PM is carried out for Components 1 and 4. Imperfect repair can meet the maintenance requirement of Component 4, while it cannot meet the requirement of Component 1. Hence, imperfect repair is carried out for Component 4, and replacement is carried out for Component 1.

5) At the end of the 171th inspection period, the effective age of Component 2 reaches its upper threshold bound, and Components 1, 3 and 4 are in the state of waiting for opportunistic maintenance. Therefore, PM is carried out for the four components, and imperfect repair is adopted.

6) At the end of the 209th inspection period, the effective age of Component 1 reaches its upper threshold bound, and Components 2, 3 and 4 are in the state of waiting for opportunistic maintenance. Therefore, PM is carried out for the four components, and imperfect repair is adopted.

At the end of the 240th inspection period, the wind turbine reaches its design life. Among the four components, the PM’s number of Component 1 is the maximum. Its upper threshold bound has been reached for five times, and five times of imperfect repairs as well as one replacement are carried out. Both Component 2 and Component 3 are restored with four times of imperfect repairs and one replacement, wherein the effective age of Component 2 reaches its upper threshold bound for only one time, while Component 3 has not reached its upper threshold bound. Component 4 has undergone four times of imperfect repairs without replacement, and its effective age has never reached the upper threshold bound.

Figure 7 depicts four curves that the failure rates of the components vary over time without any maintenance. From Figure 7, the following conclusions can be drawn:

1) Compared with the other three components, the failure rate of Component 1 increases more rapidly, and its effective age reaches the upper threshold bound more frequently than the other components.

2) The failure rate of Component 4 increases with the slowest rate and its effective age has never reached the upper threshold bound when each PM is carried out.

3) The failure rates of Component 2 and Component 3 increase at a similar rate, which are lower than that of Component 1 and higher than that of Component 4. For Component 2 and Component 3, the total time of effective age reaching their upper threshold bound is only one time respectively.

Figure 7 Failure rate curves of four components

For the four components, the improvement factors of imperfect repair vary with the number of repairs as shown in Figure 8. The following conclusions can be drawn:

1) For Components 2 and 3, the improvement factors decrease rapidly, and after two imperfect repairs, one replacement will be carried out.

2) For Component 1, the improvement factor declines with the slowest speed, while its failure rate increases rapidly, and it will be replaced after three times of imperfect repairs.

3) For Component 4, the improvement factor decreases and the failure rate increases slowly, and it is not replaced throughout the lifecycle.

Figure 8 Improvement factor vs number of repairs

Obviously, when the component’s failure rate increases rapidly, maintenance is carried out frequently. Meanwhile, when the component’s improvement factor decreases with the increase of repair times, the frequency for the replacement will also be relatively high. Overall, the maintenance optimization model proposed in this study can make appropriate maintenance plans, according to the component’s inherent characteristics of reliability and maintainability.

To further investigate the behavior of the proposed model, the effect of parameters a_i and b_i on total maintenance cost is demonstrated in Figures 9 and 10, respectively.

Figure 9 Effect of a_i on C_total

Figure 10 Effect of b_i on C_total

From Figure 9, it can be found that with the increase of a_i, the system’s total maintenance cost shows a downward trend. At the beginning, the downward trend is sharp; while with the increase of a_i, the downward trend tends to be gentle. When a_i≥1.25×10^-8, the effect of a_i on the total maintenance cost is as follows, i.e., a₁>a₂>a₄>a₃.

As shown in Figure 10, with the increase of b_i, system’s maintenance cost shows an upward trend, and the upward trend tends to flatten gradually. When 0i≤0.025, the effect of b_i on the total maintenance cost is as follows, i.e., b₁>b₄>b₃>b₂; otherwise, b₁>b₄>b₂>b₃. Hence, under the condition of meeting the constraints of maintenance resources, the values of a_i and b_i need to be set reasonably, that is, a_i should be as large as possible, and b_i should be as small as possible.

5 Conclusions

Taking the wind turbine as the object of study, the opportunistic maintenance optimization is carried out for multi-component system, and the influence of seasonal factor on failure rate is considered. The threshold of component’s effective age is selected as the decision variable, and an optimization model of opportunistic maintenance is derived to minimize the maintenance cost. The results show that the proposed maintenance model can optimize the maintenance plans according to the component’s inherent characteristics of reliability and maintainability.

To obtain more accurate distributions as well as the parameters in the model, the field data collected by the wind turbine’s SCADA system can be used. Furthermore, the component’s performance degradation and its effect on maintenance plan can be integrated into the model, which is helpful to improve the quality of the maintenance decision- making.

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(Edited by YANG Hua)

中文导读

考虑季节因素的风力机多部件机会维修优化

摘要：以风力机为对象，考虑最小维修、不完全维修、更换等维修行为对部件有效年龄的影响，研究多部件系统机会维修优化问题。在每个检测点，根据部件的有效年龄和维修阈值选择适当的维修模式。为把握风力机多部件的维修机遇，采用机会维修方法。同时，考虑季节因素对零部件的故障率以及改善因子随维修次数的增加而降低的情况，将维修阈值作为决策变量，以风力机全寿命周期维修成本最低为目标，建立风力机多部件机会维修优化模型。采用遗传算法求解模型，通过实例验证模型的有效性。结果表明，该模型可以根据部件固有的可靠性和维修性特征，制定最优维修计划。此外，部件可靠性越高、维修性越好，维修和更换次数越少。

关键词：风力发电机；可靠性；季节因素；多部件维修；机会维修

Foundation item: Project(71671035) supported by the National Natural Science Foundation of China; Projects(ZK15-03-01, ZK16-03-07) supported by Open Fund of Jiangsu Wind Power Engineering Technology Center of China

Received date: 2019-04-03; Accepted date: 2019-11-18

Corresponding author: SU Chun, PhD, Professor; Tel: +86-13851875437; E-mail: suchun@seu.edu.cn; ORCID: 0000-0002-5523-1469