# Improving the Strategy of Maintaining Offshore Wind Turbines through Petri Net Modelling
## 5 Simulation Results and Discussions
### Impact of Maintenance Strategy
#### 5.2.1 The Influence of the Time Interval of \"Advanced Service\"
In the calculation, both the costs of corrective maintenance and periodic maintenance are taken into account. The cost of corrective maintenance is dependent on the subsystem in which the fault occurs, fault severity, consequence (i.e., whether causing a subsystem failure), and the expense of the maintenance vessels. In this paper, two different types of vessels are used for different purposes. The first type of vessel is crew transfer vessel, which is used to transfer maintenance crews to the site to check and repair faults; the second type of vessel is a crane vessel, which is used to recover the failed subsystems. Therefore, the maintenance cost, \(C_{m}\), is calculated by  
\[C_{m}=N_{l}C_{I}+N_{S}C_{S}+\sum_{i=1}^{n}\bigl{(}N_{A_{i}}\bigl{(}C_{A_{i}}+C _{CT}N_{CT}\bigr{)}+N_{B_{i}}\bigl{(}C_{B_{i}}+C_{CV}N_{CV}\bigr{)}\bigr{)} \tag{1}\]  
where \(N_{l}\) is the number of \"advanced services\" performed, \(C_{I}=\ell 5600\) is the average cost of each \"advanced service\", \(N_{S}\) is the number of \"basic services\" performed, \(C_{S}=\ell 1400\) is the average cost of each \"basic service\". \(C_{A_{i}}\) and \(C_{B_{i}}\) are the average cost for repairing a fault in subsystem \(i\) and the average cost for recovering the subsystem \(i\) from failure respectively. They are listed in Table 4.  
Likewise, \(N_{A_{i}}\) and \(N_{B_{i}}\) are the average number of faults occurring in subsystem \(i\) and the average number of failures of subsystem \(i\) during the lifetime of the wind turbine respectively. \(C_{CV}=\ell 70,000/\text{day}\) and \(C_{CT}=\ell 7000/\text{day}\) are the charter rates of a typical crane vessel and a typical crew transfer vessel respectively. \(N_{CV}=7/\text{day}\) and \(N_{CT}=1/\text{day}\) are the number of days that the two types of vessels will be chartered every time. These values about the maintenance vessels are deduced based on [18; 19; 30]. Then, the maintenance costs in different scenarios are calculated using Equation (1), and the results are shown in Figure 11. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Subsystem** & \(C_{A_{i}}\) (\(\mathbf{\upalpha}\)) & \(C_{B_{i}}\) (\(\mathbf{\upalpha}\)) \\ \hline Rotor & 4000 & 200,000 \\ Drivetrain & 5000 & 402,000 \\ Power system & 10,000 & 201,000 \\ Bearing system & 8000 & 230,000 \\ Braking system & 1000 & 4000 \\ Structures & 20,000 & 200,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average costs \(C_{A_{i}}\) and \(C_{B_{i}}\)[19; 30; 31]. From Figure 11, it is found that
* After taking the proposed Measure (2), the resultant red dash line is clearly below the blue solid line if the time interval of \"advanced service\" is longer than one year. This proves the positive contribution of the new measure to the reduction of maintenance costs if the \"advanced service\" is conducted infrequently;
* As for the downtime shown in Figure 10, maintenance costs initially decrease and then increase with the increase of the time interval of \"advanced service\". However, Figure 11 shows that the minimum maintenance costs occur when the time interval of \"advanced service\" is 0.5 years, indicating that 0.5 years is the optimal time interval from the perspective of maintenance cost. This contradicts the optimal time interval obtained from the perspective of downtime in Figure 10.  
Then, which time interval is the optimal one? To answer this question, a new maintenance strategy assessment criterion, namely Cost for achieving turbine availability per day, is proposed. It is denoted by \(C_{available}\) and calculated by  
\[C_{available}=\frac{C_{m}}{L-T_{down}} \tag{2}\]  
where \(L\) refers to the design life of the wind turbine. This represents the cost of keeping the turbine running per day. Assume the design life of the turbine is 30 years and there are 365.25 days per year, then \(L=10,957.5\) days. \(T_{down}\) represents the total downtime of the wind turbine in its lifetime.