Maintenance Schedule

When using the FSMPOW model to analyse a real world scenario, the preventive maintenance schedule should be based on many dissimilar considerations, such as the type of wind turbines, accessibility, weather conditions, etc. (Vatn, 2011). These are all important factors for a real case offshore wind farm, but of less sig- nificance when creating a preventive maintenance schedule simply to evaluate the model. By relaxing these criteria, it is possible to generate preventive maintenance schedules with the FSMPOW_generator, only knowing the number of wind turbines at each wind farm, and the frequency at which preventive maintenance should be executed.

The FSMPOW_generator creates a maintenance schedule in three steps. This is done for the number of wind farms given as input to the application.

1. First, the application generates the preventive maintenance schedule for each wind turbine. And allocates this to all the third stage nodes. Given the assumption of two operations per wind turbine per year, the application selects two random "optimal" points in the time horizon, for each wind turbine and each farm, at which the operation should be executed. When this has been done for all the wind turbines, there will be a number of preventive maintenance activities evenly spread out throughout the time horizon (given that the number of wind turbines is relatively large).

Based on the optimal execution point and the expected execution time of a given preventive maintenance operation, a time interval in which the opera-

tion must be completed is calculated. The completion time is rounded up to the closest integer period, before the FSMPOW_generator adds two times the adjusted completion time on each side of the optimal starting point. This process results in two randomly placed time intervals, for each wind turbine, in which the preventive maintenance operation has to be completed. These intervals represent the hard time window for the activities.

We will illustrate this process with an example. First, a random optimal starting point is selected within the total number of periods. Assume that the optimal starting point is in period 20. If the activity takes 15 hours, the adjusted completion time becomes one period (period 20), and the hard time window is then to include the optimal starting period ± 2 periods, which is two times the adjusted completion time for the optimal starting point. The result of this example gives us a hard time window starting in 18 and ending in 22. In the case of larger completion time, the time windows would have been longer.

2. Second, for each farm, the generated preventive maintenance schedule is sorted from the first starting hard time window to the last.

The FSMPOW_generator then checks if the first operation has an overlapping time interval with the next three operations in the sorted list. If any of the following operations have an overlapping time interval with the first, they are merged into a bundle. The time interval for this bundle activity will be set to the periods in which the underlying activities are overlapping. If a bundle is created, the application continues with the first preventive operation not yet in a bundle, and repeats the process. For safety reasons, an activity bundle will include a maximum of four maintenance activities. For simplicity we have assumed that one activity only can appear in one bundle. If no overlapping periods are found between the active and the following activities, the application will jump to the next activity in the sorted list. The FSMPOW_generator stops the bundling when it has checked all the preventive maintenance operations on each farm. While generating the activity bundles, a set is created for each preventive maintenance activity, including the activity bundle that activity i is included in. This set is known as AB

if n in the model formulation. In addition, a set including all the activity bundles on wind farm f is created. This set is known as AB_{f n} in the model formulation.

3. Third, a given number of corrective maintenance scenarios are generated and allocated to their respective nodes, as illustrated in Figure 30. In each sce- nario, for each farm and each wind turbine and corrective maintenance activ- ity type, the FSMPOW_generator generates a uniformly distributed random number in the interval [0,1], and adds the corrective maintenance operation if the number is less than the expected failure rate, given in Table 4, for the given operation. If an operation is added, a random point of occurrence is generated. The operation is then split into the respective activities, all with the same point of occurrence. The hard time windows for all the belonging activities of an operation is created by taking the period of occurrence and adding the 9 subsequent periods. Hence, the FSMPOW_generator generates

7.2 The Generation of Scenarios and Pre-Processing of Input Data 71

between 0 and 4 different corrective maintenance operations for each wind turbine, consisting of up to 3 activities, each with associated time windows. When the three steps have been completed, the FSMPOW_generator has created a complete maintenance schedule for each third stage node, consisting of preventive and corrective maintenance activities, in addition to the bundle activities. If the application is run for more than one wind farm a complete maintenance schedule is generated for each wind farm. The maintenance schedule is referred to as PA

f in in the model formulation. Figure 34 illustrates possible composition of a maintenance schedule over a 8 period planning horizon.

Figure 34: An example of a maintenance schedule