## 1 Introduction  
In recent years, wind power capacity is fast growing and there are increasing trends towards developing large scale offshore wind farms [1]. Due to the expensive installation and maintenance of offshore wind farms, the reliability issue has become more important [2; 3]. According to a field survey of wind turbine systems, the electrical parts have the highest failure rate (23%) compared to other parts like the plant control system (18%), sensors (10%), hydraulic system (9%), and yaw system (8%) [4]. It can be inferred that the lifetime of the power converter is the shortest and determines the lifetime of wind turbine systems. Meanwhile, the reliability issue in power electronics has been moved from a solely statistical approach to a more physics based approach, which involves not only considerations of the statistics but also the root causes behind the failures [5; 6; 7; 8; 9; 10]. Considerable numbers of reliability tests have been already carried out by leading power semiconductor manufacturers. In [11; 12], the power cycles to failure, which represent the lifetime expectation of a power device, are provided from a thermal stress point of view, and the most important factors affecting the lifetime are summarized in [13] (e.g., mean junction temperature, junction temperature fluctuation, the ON-state time duration of a periodical current, etc.). In a typical Doubly-Fed Induction Generator (DFIG) based wind turbine system, the back-to-back power converter consists of a Rotor-Side Converter (RSC) and a Grid-Side Converter (GSC). Focusing on the steady-state thermal cycles, the detailed method to estimate the lifetime expectation of both the GSC and the RSC are analyzed and presented in [2]. It can be seen that the lifetime expectancy of the RSC is significantly less than the GSC, which determines the lifetime of the overall DFIG power converter. In a wind farm, the wind turbine causes energy loss to a column of its downstream air flow, which is also known as the wake effect. The energy loss due to the wake effect in onshore wind farms accounts for about 5%-10% of the entire energy production [14], while the percentage reaches up to approximately 15% in offshore wind farms, because of its higher installation density compared to onshore wind farms [15; 16; 17]. Many wake models have been developed to estimate the energy loss [18; 19]. Based on the wake models, the downstream energy loss depends on the thrust coefficient of upstream wind turbines, which is a function of the pitch angle and the tip speed ratio. According to the aerodynamic model of wind turbines, the produced active power depends on the power coefficient, which is related to the pitch angle and to the tip speed ratio. With the wake model and the aerodynamic model, the optimal pitch angle and the tip speed ratio for each wind turbine are selected to maximize the total active power of the wind farm [17; 20]. With this approach, the downstream wind speed is calculated by the wake model with the ambient wind speed, which is also known as the freestream wind speed which is obtained from the mast outside the wind farm with no speed deficit due to the wake effect. In [21; 22], the online model free method is proposed, by which each wind turbine receives the control settings estimated based on the information received from its neighboring turbines. This method maximizes the total active power of the wind farm without the estimation of downstream wind speed deficit by a wake model. As mentioned in [17], the model-free approach would require steady state ideal wind conditions during long periods of time in order to be performed in actual wind farms. The widely implemented active power control method for DFIG wind turbines is the Maximum Power Point Tracking (MPPT) by which each individual wind turbine generates the maximum active power at specific wind speeds. With this method implemented, the wind turbine operates at the pitch angle of 0\({}^{\circ}\) and a fixed tip speed ratio to get the maximum power coefficient.