A large part of the operational cost for a wind farm is due to the cost of equipment maintenance, especially for offshore wind farms. How to reduce the maintenance cost, and hence increase profitability, is this article's focus. It presents a binary linear optimization model whose solution may inform the wind turbine owners about which components, and when, should undergo the next preventive maintenance (PM) replacements. The suggested short-term scheduling strategy takes into account eventual failure events of the multi-component system – in that after the failed system is repaired, the previously scheduled PM plan should be updated, assuming that the restored components are as good as new.

The optimization algorithm of this paper, NextPM, is tested through numerical case studies applied to a four-component model of a wind turbine. The first study addresses the important case of a single component system, used for parameter calibration purposes. The second study analyses the case of seasonal variations of mobilization costs, as compared to the constant mobilization cost setting. Among other things, this analysis reveals a 35 % cost reduction achieved by the NextPM model, as compared to the pure corrective maintenance (CM) strategy. The third case study compares the NextPM model with another optimization model – the preventive maintenance scheduling problem with interval costs (PMSPIC), which was the major source of inspiration for this article. This comparison demonstrates that the NextPM model is accurate and much faster in terms of computational time.

Wind energy is one of the lowest-priced renewable energy technologies available today; see

Typically, a maintenance model distinguishes between a corrective maintenance (CM) event, when a component should be attended after it breaks down, and a PM event, when one or several older components are renewed before they break down, see the recent survey

There is a multitude of papers devoted to the optimal PM scheduling for multi-component systems; see

The article

In

The preventive maintenance scheduling problem with interval costs (PMSPIC) model from

In this paper, we build on the state of the art with a new algorithm, NextPM. Given the current ages of the key components of the system, NextPM computes the best time to perform the next maintenance activity and determines which components should be replaced at that time. The algorithm can be solved in 1 s and thus has a potential for being used as a key module in a maintenance scheduling app for wind turbines.

The paper is organized as follows. Section

Flow diagram of the optimization algorithm involving NextPM as a major step.

The key ingredient of Algorithm 1, the NextPM optimization model, is carefully described in Sect.

Consider a system composed of

Suppose that the multi-component system is observed at some time

The NextPM model is the key module of the following Algorithm 1 aiming at the long-term PM scheduling until the end time

Algorithm 1 relies on a rescheduling procedure, where each NextPM step covering

This section sets up the optimization model NextPM, which is the key ingredient of Algorithm 1 summarized in Sect.

A flow diagram demonstrating how the PMSPIC calculates the objective function for a given feasible maintenance plan.

A flow diagram demonstrating how NextPM model calculates the objective function for a given feasible maintenance plan with

The main difference between PMSPIC and NextPM model is that while PMSPIC generates a maintenance plan for the whole lifetime of the wind turbine, the NextPM model produces an optimal schedule only for the next PM activity. To this end, PMSPIC looks into the total maintenance cost, while NextPM aims at minimizing the time average maintenance cost.

The purpose of the NextPM model is to produce an optimal PM plan for the period [

The NextPM optimization model is built around the objective function:

Let (

Here we deal with the term

To this end, consider

Treating

The expression (Eq.

The constraint (Eq.

Here we put together the complete optimization model of the NextPM step:

The NextOM step of Algorithm 1 is a specialized version of the NextPM step described above. The input vector of the NextOM algorithm

The NextOM optimization model uses the following modified version of the objective function (Eq.

The three case studies analyzed in this section treat a wind turbine as a system represented by four components. They are all based on the parameter values taken from the paper

Comparing the characteristics of four wind turbine components shown in Table

Key parameters for a four-component system.

All computational tests are performed on an Intel 2.40 GHz dual-core Windows PC with 16 GB RAM. The mathematical optimization models are implemented in AMPL IDE (version 3.5); the model components (Eqs.

If

Figure

Monthly maintenance cost for the gearbox with the mobilization cost

The same value

Now we are ready to explain how the results of our analysis justify the proposed value

The optimal next PM time

In this section, we study how different mobilization costs

Consider the simplest wind turbine maintenance strategy when the PM option is ignored and a CM activity is performed whenever a turbine component breaks down. This baseline case study will help us to evaluate how much can be saved by introducing PM planning.

Summary of the NextPM results for

The total cost associated with the pure CM strategy is estimated based on the random number of failures over the time interval [0,

To address the seasonal effects of the mobilization costs

If the wind turbine starts functioning in January, then the mobilization costs

If the wind turbine starts functioning in July, then the mobilization costs

This scenario has no seasonal effect in that for each month

In this section, the mobilization costs are halved to contrast the results of Part B, so that

Summary of the NextPM results for

According to Table

Outputs of the NextPM and PMSPIC models for

Outputs of the NextPM and PMSPIC models for

Outputs of the NextPM and PMSPIC models for

The optimal times for the next PM activity have landed in the range between 43 and 50 months and seem to be quite short. This is explained by the particular choice of the model parameters presented in Table

Comparison of the results of Part B and Part C with those of Part A shows that implementation of the PM planning reduces maintenance costs by 35 %.

In this case study, we compare the outputs of the NextPM model and the optimization model PMSPIC. A comparison of the NextPM model with the PMSPIC model is not a straightforward exercise, since the latter produces a maintenance plan for the whole lifespan [0,

Tables

For

This article introduces a new NextPM optimization model aiming at PM scheduling for a wind turbine viewed as a multi-component system. Which of the components should undergo PM replacements first is decided based on the information on the component ages. Compared to the PMSPIC model from

NextPM is tested with three case studies based on the data for four components of the wind turbine taken from

In this paper our NextPM model is applied to a system of four components belonging to a single wind turbine. However, we claim that our approach can handle the case of, say, 10 turbines with 80 components in total (the computational time required by our algorithm grows linearly with the increased number of components, while PMSPIC's computational time grows exponentially fast).

The notable limitation of our setting is that it neglects such important maintenance activities as inspections and minor and major repairs. By considering full replacements as the only kind of CM and PM activities allowed in the model, we were able to tame the mathematical challenge of the problem in hand. Still, even within this simplified model framework, our computational analysis may bring useful insights of more efficient PM planning, depending on a few key parameters of a concrete wind farm. Our results should be viewed as a first promising step towards a much more sophisticated mathematical optimization model that would take into account available condition monitoring data and even recognize the difference in the failure rates for minor repairs, major repairs, and component replacements.

The code used to calculate the parameters is in MATLAB; the code is available on

QY developed the theoretical formalism, performed the analytic calculations, and performed the numerical simulations. SS, QY, and MP contributed to the final version of the manuscript.

The authors declare that they have no conflict of interest.

We acknowledge the financial support from the Swedish Wind Power Technology Centre at Chalmers, from the Gothenburg University Library, and from the Swedish Research Council (grant no. 2014-5138). Special thanks to the director of SWPTC, Ola Carlson, for his constructive recommendations. The valuable comments of four reviewers helped considerably in improving the quality of our manuscript.

The article processing charges for this open-access publication were covered by the Gothenburg University Library.

This paper was edited by Katherine Dykes and reviewed by Jonas Kaczenski and Miriam Noonan.