基于Markov模型的低风速地区风力发电机预防性维护优化策略

doi:10.15960/j.cnki.issn.1007-6093.2024.03.007

摘要/Abstract

摘要：

在“3060”双碳战略目标下, 随着风电产业的迅速发展, 预防性维护已然成为提高风力发电机运行可靠性的重要手段。关于复杂环境下风力发电机的运行管理尚存在对退化状态认识不充分、维修策略不可靠等问题。本文以期望成本最小化为目的, 考虑风力发电机关键部件退化过程与多阶段预防性维护策略的关系, 构建基于Markov状态转移的多阶段预防性维护成本模型。首先, 依据设备衰退规律, 利用Markov链的转移概率对退化状态、维护策略进行刻画。其次, 引入可靠度、故障率、役龄因子计算多阶段预防性维护时长和故障时长; 再进一步考虑天气条件对维护成本模型的影响, 构建风力发电机在整个维护周期内的期望成本模型。最后, 利用数值分析对模型进行求解。结果表明, 实施最小、更换维护策略的期望成本占据了总维护成本的80%以上, 相比之下, 采取预防性维护优化策略的期望成本则低于总维护成本的20%, 故该策略可为低风速地区的风电企业提供有效的决策参考, 提高风力发电机的运行可靠性。

关键词: 预防性维护, 风力发电机, 退化状态, Markov链, 期望成本

Abstract:

The wind power industry is rapidly developing under the '3060' dual-carbon strategy. Preventive maintenance has become crucial in improving the operational reliability of wind turbines. However, operational management of wind turbines in complex environments still lacks sufficient understanding of the degradation state and reliable maintenance strategies. This paper examines the relationship between the degradation process of wind turbine key components and a multi-stage preventive maintenance strategy. The objective is to minimize expected costs. Based on Markov degraded state transfer, a multi-stage preventive maintenance cost model is constructed. This paper describes a model that utilizes the equipment decline law and Markov chain to portray the degraded state and maintenance strategy. It also introduces reliability, failure rate, and service age factors to calculate multi-stage preventive maintenance and failure hours. Additionally, the model considers the influence of weather conditions on the maintenance cost of wind turbines throughout the maintenance cycle. Numerical simulation is used to solve and analyze the model. The results indicate that the minimum and replacement maintenance strategy accounts for over 80% of the total maintenance cost, while the preventive maintenance optimization strategy accounts for less than 20%. Therefore, wind power enterprises in low wind speed areas can use this strategy as a practical reference for decision-making to enhance the operational reliability of wind turbines.

Key words: preventive maintenance, wind turbine, degradation state, Markov chain, expected cost

中图分类号:

O221.2

张大永, 王红蕾. 基于Markov模型的低风速地区风力发电机预防性维护优化策略[J]. 运筹学学报（中英文）, 2024, 28(3): 108-120.

Dayong ZHANG, Honglei WANG. Optimization strategy for preventive maintenance of wind turbines in low wind speed areas based on Markov models[J]. Operations Research Transactions, 2024, 28(3): 108-120.

图/表 12

表1

参数与变量符号说明"

参数	描述	参数	描述
$ \Delta $	单个采样周期长度	$ D(\cdot) $	系统状态演化的随机过程
$ K $	采样周期总次数	$ p_{i, j}(s, n) $	第$ i $个退化状态$ Z_n $到第$ j $个状态$ Z_s $的转移概率
$ M $	维护策略集合
$ Re $	转移状态的吸收态	$ R(\cdot) $	系统在时刻$ t $的可靠度函数
$ A $	进行维护前的策略集合	$ \omega_{i, j}(\cdot) $	系统在第$ i $个阶段的第$ j $个预防性维护周期的故障率函数
$ B $	凝冻天气情况集合
$ \tau $	故障总次数	$ \lambda $	第3、4阶段预防性维护频率更新系数
$ \tau_i $	第$ i+1 $预防性阶段故障次数$ 1\leqslant i\leqslant 4 $	$ C_{\rm all} $	整个维护周期内的维护总成本
		$ C_M $	整个维修周期内的最小维护总成本
$ \tau_{\min} $	单次最小维护时长	$ C_{Pi} $	第$ i+1 $阶段内单次的预防性维护成本$ 0\leqslant i\leqslant 2 $
$ \tau_{pi} $	第$ i+1 $阶段的单次预防性维护时长$ 1\leqslant i\leqslant 3 $
		$ C_m $	单次最小维护成本
$ \tau_{d} $	单次更换时长	$ C_d $	为单位时间内的停机成本
$ S_k $	系统第$ k $周期的可列状态集	$ \psi(\cdot) $	出现凝冻天气的概率函数
$ C_R $	整个维修周期内的停机损失总成本	$ \varphi(\cdot) $	进行维护前的策略概率函数
		$ C_D $	整个维修周期内的更换总成本
$ T_{i, j} $	第$ i $个阶段采取第$ j $个预防性维护周期的时长	$ C_P $	整个维修周期内的预防性维护总成本
		$ p_{ij}(m, t) $	时刻$ t $状态$ i $到时刻$ t+1 $状态$ j $采取策略$ m $的概率
$ \xi_i $	第$ i+1 $阶段的役龄延长因子$ 1\leqslant i\leqslant 2 $
		$ T $ (决策变量)	第2阶段预防性维护时长
$ D_k(t_i) $	第$ k $个周期内时间为$ t_i $时刻的检测值	$ G_i $ (决策变量)	第$ i+1 $预测维护阶段的总次数$ 0\leqslant i\leqslant 2 $

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表2

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表7

表8

表9

表10

图2

参考文献 18

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阶段	公式	时间段
0	$ \omega_{1, 1}(t) =\omega_0(t) $	$ 0\leqslant t\leqslant t_1 $
1	$\begin{gathered}\omega_{2, 1}(t)=\omega_0\left(t-\xi_1 T\right), \\\omega_{2, 2}(t)=\omega_0\left(t-2 \xi_1 T\right), \\\vdots \\\omega_{2, G_1}(t)=\omega_0\left(t-\xi_1 G_1 T\right)\end{gathered} $	$ 0\leqslant t\leqslant T_{2, j}(j=1, 2, \cdots, N_1) $
2	$ \begin{gathered}\omega_{3, 1}(t)=\omega_0\left(t-\xi_1 G_1 T-\xi_2 T\right) , \\\omega_{3, 2}(t)=\omega_0\left(t-\xi_1 G_1 T-2 \xi_2 T\right), \\\vdots \\\omega_{3, G_2}(t)=\omega_0\left(t-\xi_1 G_1 T-\xi_2 G_2 T\right)\end{gathered}$	$ 0\leqslant t\leqslant T_{3, j}(j=1, 2, \cdots, N_2) $
3	$ \begin{gathered}\omega_{4, 1}(t)=\omega_0\left(t-\xi_1 G_1 T-\xi_2 G_2 T-\xi_3 T\right), \\\omega_{4, 2}(t)=\omega_0\left(t-\xi_1 G_1 T-\xi_2 G_2 T-2 \xi_3 T\right) , \\\vdots \\\omega_{4, G_3}(t)=\omega_0\left(t-\xi_1 G_1 T-\xi_2 G_2 T-\xi_3 G_3 T\right)\end{gathered}$	$ 0\leqslant t\leqslant T_{4, j}(j=1, 2, \cdots, N_3) $

阶段	最小维护成本	预防性维护成本	更换成本	停机成本
0	$ \checkmark $	$ \checkmark $
1	$ \checkmark $	$ \checkmark $
2	$ \checkmark $	$ \checkmark $
3	$ \checkmark $	$ \checkmark $
4	$ \checkmark $		$ \checkmark $	$ \checkmark $

部件	$ \delta $	$ \varrho $	单位费用/美元						单位时间/天
部件	$ \delta $	$ \varrho $	$ C_m $	$ C_{P1} $	$ C_{P2} $	$ C_{P3} $	$ C_{R} $	$ C_{d} $	$ \tau_{d} $	$ \tau_{\min} $	$ \tau_{p1} $	$ \tau_{p2} $	$ \tau_{p3} $
轴承	3	3 750	2 000	2 500	2 800	3 000	60 000	350	3	3.5	4	4.5	7
齿轮箱	3	2 400	2 000	2 500	2 800	3 000	152 000	350	3	3.5	4	4.5	15

阶段	0	1	2	3	4
$ \varphi(-1) $	0.90	0.10	0.08	0.05	0.01
$ \varphi(0) $	0.05	0.80	0.90	0.95	0.00
$ \varphi(1) $	0.05	0.10	0.02	0.05	0.99

阶段	0	1	2	3	4	Re
0	0.95	0.05	0.00	0.00	0.00	0.00
1	0.80	0.10	0.05	0.02	0.01	0.00
2	0.60	0.20	0.15	0.03	0.02	0.00
3	0.05	0.00	0.00	0.85	0.10	0.00
4	0.01	0.00	0.00	0.00	0.99	0.00
Re	0.00	0.00	0.00	0.00	0.00	1.00