# Optimal Power Dispatch of an Offshore Wind Farm under Generator Fault
## 1 Introduction
Another focus of this paper is WT fault. Many studies focused on the fault detection and prediction for various common faults, such as generator faults, gearbox faults, and blade damage [9; 10]. The fault characteristics are obtained by analyzing some physical signals of the system or using an additional detection device. Condition monitoring and fault diagnosis are the first steps in implementing fault accommodation. When a fault is detected or predicted, WTC and WFC can perform corresponding pre-set actions. Some studies used fault analysis methods such as Fault Tree Analysis (FTA) and Failure Mode and Effects Analysis (FMEA) to analyze the fault cause, process, and effect [11; 12]. These analysis results can be used to help the WTC and WFC design for fault accommodation. A test benchmark model for the fault detection and accommodation was proposed in [13]. The authors aimed at reducing the impact of the WT fault on the WF at the WF level, but focused on the blade erosion and debris build-up on the blades in [14]. The generator, which converts mechanical energy into electrical energy, is one of the most important components of the WT. Figure 1 shows the normalized failure rates and downtimes for main components in MW-class WTs [15]. It can be seen that, although the failure rate of the generator is not the highest, the downtime is quite long. Many generator faults are related to overheating, such as stator winding insulation faults. In general, at the beginning of the fault, it is just an inter-turn short circuit in a single-phase winding. However, as the fault progresses, the faulty phase current increases, which will lead to further damage of the insulation, and finally to a phase-to-phase short circuit or phase-to-ground short circuit. As a rule of thumb, the insulation lifetime is reduced by half for each 10 \({}^{\circ}\)C that the motor temperature exceeds its rated insulation temperature [16]. In addition, when the temperature of a generator exceeds a specific value, the WT will automatically shut down to protect the windings [17]. Therefore, the cooling system for generator windings is very important. When a cooling system fault occurs, the cooling capacity will be decreased. Long-term operation at high temperatures will lead to the aging of the windings' insulation. To avoid the damage of insulation under a cooling system fault, the phase current of the generator has to be reduced. That means the power of the faulty generator should be limited to reduce the heat generation and protect the generator. Because of this, fault protection and down-regulation can be linked. In the process of power dispatch, the power reference of a faulty turbine will be limited to a specific power value based on the severity of the fault. The contribution of this paper is to consider generator cooling system faults in the WF dispatch strategy. First, the safe operating power of the faulty WT is calculated based on the thermal model of the generator. Then, the safe operating power is taken as the power limit of this faulty WT. This will prevent the generator from operating under overheating conditions. According to [16], the insulation life of the generator windings will be reasonably protected. Considering the wake effect, this paper optimizes the multi-objectives through Particle Swarm Optimization (PSO): power tracking, power fluctuation and fault protection. Compared with the way that the WF usually handles the faulty WT, this method not only avoids the fault deterioration caused by the unreasonable operation in the fault state, but also reduces the power loss caused by direct shutdown. Compared with the Proportional Dispatch Strategy (PDS) that does not take the wake effect into account, the proposed strategy can better track the power demand from the TSO under the premise of protecting the faulty WT and obtain an efficient trade-off between fault protection and power tracking.