## 1 Introduction  
Wind energy is a foremost inexhaustible eco-friendly energy resource that can be considered a major power generating source in the future. The development of the wind energy industry accounts for a significant portion of the reduction in carbon emissions. Wind energy industries have the potential to provide a wide range of job opportunities in the future, including wind turbine manufacture, structural development, logistics, maintenance, and research and development. Operating wind turbines collectively as a wind farm is more beneficial and economical. However, the utmost pertaining concern in wind farms is the wake effect. When the wind turbine is in operation, it extracts energy from the wind, and a wake is thus developed behind the turbine that reduces the wind speed downstream. More specifically, it results in a reduction of the wind speed, an increase in turbulence, and finally a reduction in the overall wind farm power production [1]. This is illustrated in Figure 1.  
The wake developed throughout the wind farm can be characterised by its strength and direction. The downstream turbines' power generation may be hampered by the wake behind the upstream turbines, which results in reduced wind speed and turbulent wind flow [1, 2]. As a result, the overall power output is lowered, while the fatigue loading on the downstream turbines is increased [3, 4]. The flow field across the wind farm can be modified by managing the wake behind individual turbines, potentially boosting the wind farm's total energy generation [5]. Research on wind farm control for reducing the impact of the wake is attaining importance. The review [6] on wind farm control strategies deals with the following three main concepts: Power derating [7, 8, 9], yaw misalignment-based wake steering [10, 11, 12, 13] and turbine re-positioning [14, 15]. It is noted that the concept of power derating, wake redirection control (WRC), and turbine re-positioning [16] could result in a remarkable rise in power output. Power derating, also known as axial induction control (AIC) [17,18] is used to improve the efficiency of the downstream turbines by minimizing the strength of the wake by power derating the upstream turbines. This technique utilizes control of generator torque, pitch control of turbine blades, or turbine tilting to change the axial induction factor, \(a_{n}\). The turbine blade pitch control of upstream turbines reduces their power output, but the enhanced performance of downstream turbines could potentially improve the overall wind farm power output. When the axial induction method is used, some studies show significant power improvement [19,20], while other studies [17,18] do not demonstrate notable improvement in power production. When the WRC method [21,22] is used, the upstream wind turbine is steered away from the upcoming wind to redirect the wake. The upstream turbine's power output is reduced due to its steering, but the overall power output could be greatly improved by improving downstream turbine performance. Various studies [23,24] have found improvements and associated advantages of this method. Previous research on an optimization based wake steering approach evaluated on an operational wind farm found a power increase of 7-13% for site average wind speed and 28-47% for low wind speed, respectively [16]. The work carried out in [18] shows a 3.3% increase in the wind farm power production when the AIC is incorporated into the upstream turbines in a real-life wind farm in the UK. The preliminary investigation performed in [25] demonstrates further improvement when the WRC is incorporated into the turbines in a real-life wind farm in China. In this work, the Wind Farm Simulator (WFSim) is used for simulation studies. It is a dynamic wind farm control model developed by Delft University of Technology [26]. WFSim is implemented in MATLAB and it has two control variables, yaw angle and axial induction factor.