# Improving the Strategy of Maintaining Offshore Wind Turbines through Petri Net Modelling
## 4 Dynamic PN Modelling of the O&M of an Offshore Wind Turbine
### Operation Petri Net (OPN)  
As shown in Figure 4, the OPN is developed to simulate the normal operation and periodic maintenance of an OWT.  
Figure 3: Connections between PNs.  
Figure 2: Example of an enabled transition.  
In the figure, the PN on the top governs the normal operation of the wind turbine within the design life. Transition \"S1\" indicates the design life of the wind turbine, which is set to be 30 years in this study. Once Transition \"S1\" fires, a token will be produced in Place \"End of design life\", indicating the completion of the life of the wind turbine. Then, the instant transition, \"S2\", is enabled, thereby firing immediately and a token will be produced in Place \"End of one simulation\", and the simulation will be terminated.  
The PNs at the bottom, labelled \"periodic maintenance\" and \"weather condition\", are used to simulate the periodic maintenance of the wind turbine. As mentioned earlier, the periodic maintenance in this study includes two levels of services. The \"basic service\", BS for short in the figure for simplification, is for checking and fixing non-major issues; the \"advanced service\", AS for short, is for checking the key wind turbine components and finding the faults not detected by the CMS. The two levels of the services are conducted at different frequencies according to the reliability features of individual components. Once one or more faults are detected during \"advanced service\", maintenance will be planned and conducted to fix the faults. Due to the \"advanced service\" inspecting key wind turbine components, more maintenance resources (e.g., a bigger maintenance team, a larger vessel, longer service time, etc.) are required than for \"basic service\". In the OPN, the firing times of Transitions \"PM1\" and \"PM3\" are the time intervals of the two levels of services. A token produced in Places \"BS starts\" and \"AS starts\" means that periodic service is about to begin. A token in Place \"need inspection\" determines that a full inspection of the turbine should be conducted. The firing times of Transitions \"PM2\" and \"PM5\" are assumed to be one day and two days, respectively, indicating the duration of \"basic service\" and \"advanced service\" of each turbine every time. It should be noted that the turbine will be stopped during maintenance.  
In addition, as maintenance is not allowed in bad weather, Transitions \"PM2\" and \"PM5\" are inhibited if a token is in Place \"Bad weather\". In the existing maintenance models, the time taken waiting for favourable weather to enable maintenance to take place is usually represented by a mathematical function of sea conditions and the maximum wave height and wind speed that the maintenance is allowed to be conducted in [18,19]. In the current study, for simplicity, Transitions \"C1\" and \"C2\" are designed to describe the alternation between good and bad weather. The delay time due to weather conditions  
Figure 4: Operation Petri Net (OPN).  
is governed by a Weibull distribution function. The Weibull distribution function for C1 is characterised by \(\beta=3.2\) and \(\eta=42\) days; and the Weibull distribution function for C2 is characterised by \(\beta=3.2\) and \(\eta=7\) days, respectively. Here, \(\beta\) and \(\eta\) are the shape factor and the scale parameter of the distribution. These values of \(\beta\) and \(\eta\) can be easily modified based on the actual environmental situation in the offshore wind farm. Once Transitions \"PM2\" or \"PMS\" fire, a token will be produced in Place \"BS completed\" or \"AS completed\", respectively, which indicates the completion of the periodic maintenance. If a token is produced in Place \"AS completed\", the RMPN will be embedded into the model for preparing and conducting the maintenance if any fault was detected during the periodic maintenance. Finally, the token produced will be removed from either Place \"BS completed\" or Place \"AS completed\".