# 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
### System Petri Net (SPN)  
As shown in Figure 5, the SPN is developed to simulate the degradation and the health state of the wind turbine subsystems over time, and the shutdown of the turbine due to failure.  
In the model, the natural degradation of the subsystems is indicated by three health states, namely \"Normal operation\", \"Subsystem fault\", and \"Subsystem failure\". The subsystems will initially operate normally without any fault, indicated by a token in Place \"Normal operation\" for each subsystem. Due to natural degradation, the subsystems may develop a fault, exhibiting abnormal features such as increased vibration and temperature, decreased efficiency, etc. In this case, the health state of the affected subsystem/subsystems  
Figure 5: System Petri Net (SPN).  
will be marked as \"Subsystem fault\". The degradation time from \"normal\" to \"fault\" is indicated by Transitions \"W1\" to \"W6\". Once a token is produced in any of the condition places \"Subsystem fault\", the DPN will be embedded into the model to simulate the fault detection by the CMS as required by the predefined condition. Once a subsystem fault is successfully detected by the CMS, the RMPN will be embedded into the model.  
However, if the subsystem fault was not detected by the CMS, the fault may continue to develop and eventually lead to the failure of the subsystem. The failure of the subsystem will cause the shutdown of the wind turbine. To enable simulation of the continual development of the fault, the predefined conditions, which embedding DPN into the model, will be removed from the corresponding places representing the subsystem faults and then these places will become normal places. The process of the undetected faults eventually leading to the shutdown of the turbine is modelled by Transitions \"W7\" to \"W12\". In the study, it is assumed that the times for Transitions \"W1\" to \"W12\" satisfy Weibull distributions characterised by the parameters listed in Table 1. In the table, the data has been estimated based on the wind turbine failure rate data published in the open literature [18,19]. In [19], the scale parameters \(\eta\) in the distributions for computing the times from normal to fault and failure are estimated based on the assumption that the time spans in the two scenarios will cover 80% and 20% of the Mean Time to Failure (MTTF) respectively of the corresponding subsystems. The MTTF is the inverse of the failure rate listed in Table 1. The shape parameters \(\beta\) in the distributions are assumed to be larger than 1 for all six subsystems in order to describe the increasing deterioration of the subsystems over time. In the model, it is assumed that the wind turbine will be shut down immediately as soon as any one of the six subsystems fails. This is modelled by Transitions \"W13\" to \"W18\". Once a token is produced in any one of Places \"Subsystem failure\", the wind turbine will be shut down and the RMPN will be embedded into the model.  
Once the failed subsystem is recovered, which will be modelled in the RMPN, a token will be passed to Place \"Wind turbine recovered\", and Transition \"W19\" will be activated hence starting the full inspection of the entire wind turbine system. Once any fault is detected (i.e., if there is a token in any one of Places \"Subsystem fault\"), the RMPN will be embedded into the model again.