Costoptimal spare parts inventory planning for wind energy systems
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Abstract
For safe and reliable machine operation, maintenance, repair and overhaul (MRO) activities are required. Spare parts demand forecasting and inventory planning, which is an important part of MRO activities, must be accurate to avoid costs because of surplus spare parts or machine downtimes. The restriction of reduced accessibility to wind turbines during the winter months also has to be taken into account when planning maintenance activities and spare part inventories for wind farms. The presented model provides the most economic stock quantity under given environmental conditions. It is based on the proportional hazards model, which is extended to calculate the remaining useful component life time and derive required spare parts inventory levels. The presented model is validated, using condition monitoring data and environmental data of an onshore wind farm. Comparison of the spare part inventory prediction to wind farm’s failure data proves the model’s accuracy. Parameter analyses show that the model can be applied for spare parts inventory planning under consideration of environmental conditions.
Keywords
Proportional hazards model Spare part Inventory planning MRO Wind turbine1 Problem statement
Maintenance, repair and overhaul (MRO) activities are necessary to ensure safe and reliable machine operation. For many MRO processes, spare parts are essential, because their nonavailability causes machine downtime. It is prolonged in case of long lead times that entail high operation costs. Hence, stock holding is necessary to achieve high service levels, allowing for short machine downtime. In contrast to high service levels and spare parts availability, inventory costs need to be considered to attain economic machine operation. There is a tradeoff between service and inventory costs. The point of costoptimal machine operation has to be determined.
For implementing weather restrictions, utilizing available information and achieving minimum operation and maintenance cost, mechanically stressed wind energy components have been investigated within the research project “EloWind”—service logistics for wind energy turbines. In the proposed method, a Weibull proportional hazards model (PHM) is combined with a Bernoulli approach. The spare demand is forecasted based on wind speeds and operating temperatures. A costoptimal inventory level of spare parts is derived, taking into account inventory costs of spare parts and downtime costs of wind energy turbines. The proposed method is validated with data of an onshore wind turbine farm.
2 State of the art
2.1 Maintenance costs

missing spare parts,

inclement weather conditions and

other missing maintenance resources, like maintenance personnel.
The inventory rate accumulates costs for personnel working in the inventory, costs for storage space and administrative costs, which are not directly linked to individual spare parts. If spare parts are expensive and stored for a long time, high stocking costs are incurred. These stocking cost are in conflict with the overall maintenance aim of minimal costs. The resulting tradeoff between low inventory costs and short machine downtime is addressed by spare parts and maintenance planning.
2.2 Spare parts planning
Spare parts replace worn and defective units, which are unable to fulfill their proposed function [5]. Systems without redundant units depend on spare parts in case of malfunctions. Predicting the amount of spare parts needed in the future is denoted as spare parts management or spare parts logistic. The field of spare parts logistic is split into the topics data preprocessing, inventory management and demand forecasting.
Data preprocessing is used to delete wrong data sets and to classify spare parts in correspondence to their demand pattern or according to their procurement costs, with the aim of grouping spare parts with similar properties [6]. Herewith, complexity of spare parts planning is reduced and demand prediction algorithms can be utilized according to their optimal field of application.
Inventory management as the second field of spare parts logistic aims at the most economic inventory level and the procurement strategy. Wellknown models of multiechelon inventory systems are the METRIC model by Sherbrooke or the model by Muckstadt [7, 8]. The objective of the current and future research is relaxing the restrictive assumptions of these two approaches. Examples are models taking into account lateral transshipments [9] or models assuming finite repair capacity in case of repairable item systems [10, 11]. Basten et al. and Kennedy et al. provide extensive reviews of latest and past inventory management models [12, 13].

moving average,

exponential smoothing,

Crostons’ method or

regression analysis.
Time series analysis methods are applied if historical demand patterns are expected in the future. The algorithms try to recognize patterns in the demand history and extrapolate them into the future [16, 17, 18]. In addition to demand data only, life expectancy models also utilize information about lifetime of failed components and the current age of components. By that, they convey failure functions for the life cycle of component, which are used to predict the probability of failure at a given instance [19]. These models have also been extended to include more parameters, describing the probability of failure as a function of temperature, machine stress or surrounding conditions [20, 21, 22]. Heng et al. [23] provide a survey of reliabilitybased forecasting models.
Time series analysis methods are easy to apply, but do not offer the possibility of considering condition monitoring information, available in nearly every wind turbine. Therefore, advanced methods are used for failure prediction, which allow for consideration of information of logfiles and condition monitoring systems.
2.3 Proportional hazards model
The major assumption of the model is a constant hazard ration (h _{1}(t; z) and h _{2}(t; z)) during lifetime, meaning that a covariate like wind speed has the same influence on the probability of survival at two different instances of time.
The model is mainly applied in the field of medicine, whereupon it has also been used in the technical domain [25]. Lanza et al. and Abernethy extensively discuss different types of Weibull models for technical applications [19, 26]. Vlok utilizes the PHM in a technical domain and estimated the instant of maintenance [27]. Wang and Ghodrati realized spare parts prediction by means of a stochastic process based on the PHM [28, 29]. In contrast to them, Tracht et al. presented a method to preprocess condition monitoring and operational information and implemented them into an enhanced forecast model [28, 30]. The method proposed in this paper is an advancement of the model presented by Tracht. Demand levels are integrated into an inventory planning approach, but do not allow for integration of wavering surrounding conditions.
3 Approach
The output of the model is the most economic stock quantity under given environmental conditions, like increased wind speeds that will also increase machine breakdown costs. By comparing costs for surplus of stock and stockout costs, the costoptimal stock quantity can be calculated.
3.1 System analysis
From the functional system in Fig. 2, it can be concluded that availability of every component is crucial to system availability. If there were two redundant components, it would have been possible for the machine to operate, despite malfunction of one component. In the example presented, flawless operation of every component is necessary.
For components in stock, further classification steps will be conducted. They include classification regarding demand pattern, demand level and purchasing costs. Demand pattern can be analyzed by means of plotting historical data. This is necessary because time series analysis approaches have to take into account demand patterns for achieving low prediction errors.
3.2 Demand prediction
Therefore, it is possible to calculate stock out and surplus probability, which can be multiplied with the daily downtime and daily inventor cost, respectively.
3.3 Inventory planning
Stockout costs arise when inventory level is lower than demand. The first expression in Eq. 9 represents daily downtime cost, caused by missing material. In the second expression, the probability of surplus material is multiplied with the inventory cost per day. Minimizing this function leads to the costoptimal inventory level, because further cost parameter named in Eq. 1 cannot be influenced by means of increasing or lowering spare parts inventory level.
4 Results
4.1 Validation of demand forecasting
Demand data for validation
Year  1/2009  2/2009  1/2010  2/2010  1/2011  2/2011  1/2012  2/2012 

Number of requests  0  2  2  0  0  0  1  0 
Prognosis result of simple exponential smoothing
Point forecast  Forecast confidence level of 0.77  Forecast confidence level of 0.95  

Lower limit  Upper limit  Lower limit  Upper limit  
0.63 (1) part  −0.40 (0) parts  1.65 (2) parts  −1.05 (0) parts  2.30 (2) parts 
One demand is estimated by the point forecast for the following 6 months. For the upper threshold levels of the confidence intervals, two parts are estimated respectively. The forecast results are rounded, because spare parts can only be stored in entire pieces.
Weibull PHM parameter estimations
Parameter  Value 

Shape parameter  1.17 (–) 
Scale parameter  2667 days 
Regression parameter α  0.0138 (–) 
p value (χ ^{2} test)  0.0206 
The investigations were conducted using a Weibull PHM, which comprises a baseline hazard function. The baseline hazard function is determined based on failure probability data. The parameters impacting the hazard function—called covariates—can be the temperatures of the generator, the stator, the main bearing or the nominal power output. The amount of the impact of the covariates on the Weibull PHM is determined by regression parameters, which are calculated, applying the maximum likelihood approach.
The positive regression parameter shows the positive correlation between temperature exceedances and end of life. When utilizing these parameters for demand prediction, the condition information considered in the model also needs to be predicted. In this prediction scenario, the temperature of the stator during time of prognosis is assumed to rise forty times over the threshold of 100 °C. Therefore, the outcome of the Weibull PHM is inserted to formula 6 to calculate the failure probability of every single unit.
Comparison of conventional and proposed method
Method  Point forecast  Confidence levels of forecast  

Upper limit (0.77)  Upper limit (0.95)  
Exponential smoothing  0.63 (1) part  1.65 (2) parts  2.30 (2) parts 
Probabilistic method  0.64 (1) part  –  – 
Combined method (WPHM)  –  1 part  2 parts 
The results in Table 4 show that the proposed method leads to results comparable to conventional methods. The advantage of the combined method is the integration of information about the lifetime and condition monitoring data and, therefore, compensating missing demand history information. Furthermore, it is possible to determine the probability of occurrence and to assess the financial impact of stock outs and surplus material by considering environmental conditions in spare parts planning.
4.2 Dynamic inventory planning
Forecasting accuracy of the proposed method improves with the amount of available historical data for calculating the remaining useful lifetime. The method is not suitable for parts that only have a short lifetime in relation to the planning period, because the failure rate caused by a parameter (e.g., wind) has to remain constant during the planning period.
5 Summary
The research work conducted within the project EloWind made it possible to utilize information of condition monitoring systems already available and integrate them into a novel probabilistic planning approach. The planning approach has been evaluated and tested for slow moving, expensive spare parts of a power train. Above that, wavering surrounding conditions in terms of different wind speeds are considered in the developed model. It is the first model to allow for consideration of environmental conditions. Interdependencies between all relevant parameters are presented by means of parameter studies. Thereby, stock levels can be dynamically adjusted regarding the time of the year and lowering maintenance costs. This will reduce energy costs generated from wind turbines and will make renewable energy resources more competitive. The presented model is a first example of integrating surrounding conditions into a probabilistic planning approach. The example calculation shows very promising results. Further case studies and extensive laboratory experiments to analyze the impact of additional parameters will be conducted in the future.
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