## 2 Background
### Lidar System Optimization for Control Applications
#### 2.4.1 Optimizing Lidars by Assessing Controller Performance  
While many lidar-assisted control studies rely on a single lidar scenario for simulations or field testing, some authors have directly analyzed the impact of different lidar configurations on controller performance. In an overview of the benefits of various LAC applications, [PERSON] et al. (2013) arrive at the general conclusion that both pulsed and CW lidars are suitable for control purposes, as long as they can measure roughly 10 points distributed around the rotor area upstream of the turbine every second while providing a few seconds of preview time. They claim that additional measurement points and faster sampling provide diminishing returns, and that a circular scan pattern is nearly as useful as more advanced scan patterns. The lidar model used in this study includes the spatial averaging, or \"range weighting\", along the beam that is inherent to both pulsed and CW lidars as well as the limitation to line-of-sight (LOS) velocity measurements (i.e., the projection of the three-dimensional wind vector onto the beam direction). The authors also find that the optimal scan configuration depends on the wind field parameter being estimated; large cone angles are beneficial for measuring wind direction, but harm the accuracy of rotor effective wind speed and wind shear estimates. Finally, the authors suggest that spatial averaging along the beam is helpful for estimating rotor effective wind quantities for control because it resembles the spatial averaging of the wind field by the rotor. Focusing on a circularly-scanning pulsed lidar, [PERSON] and [PERSON] (2011) discuss the potential for different LAC applications to reduce the cost of energy generated by a wind turbine. The authors investigate the impact of the number of beams (2, 4, 6, or 8) and the number of range gates (1-10) on rotor speed regulation and structural fatigue load reduction for a collective pitch feedforward controller. As expected, the study finds that the controller performance improves as the number of beams and range gates increases, with the largest improvement occurring when moving from two to four beams and diminishing returns beyond eight range gates. Although the authors do not reveal the specific range gate distances, for the maximum 10-range gate scenario, the range gates are roughly evenly spaced so that they span the entire rotor disk area when projected onto the rotor plane. It is concluded that coverage of the rotor plane area is the most important factor for the scan pattern. Finally, the authors show that sampling frequency has little impact on load reduction, as long as it is above 0.5 Hz. After first analyzing the influence of the scan pattern, spatial averaging, and LOS velocity limitations on overall measurement quality, researchers began to introduce models of wind evolution into LAC simulations. Wind evolution describes the change in turbulent structures as they advect from the measurement location downstream towards the turbine. This represents a deviation from [PERSON]'s frozen turbulence hypothesis ([PERSON], 2011), traditionally assumed during wind turbine simulation, which maintains that turbulent structures remain unchanged while traveling downstream at the mean wind speed. Wind evolution models are typically defined in terms of longitudinal spatial coherence (i.e., the correlation between wind speeds separated by different longitudinal distances as a function of frequency), with low frequency components of the turbulence remaining highly correlated as the wind travels downstream but high frequency components becoming decorrelated due to eddy decay ([PERSON], 2011). [PERSON] (2011) incorporated wind evolution into collective pitch LAC simulations using the theoretical [PERSON] wind evolution model ([PERSON], 2011), and found that evolving turbulence does notsignificantly impact the load reduction potential of LAC. [PERSON] et al. similarly included the [PERSON] wind evolution model while simulating lidar-assisted IPC for a 600 kW wind turbine.