# Nonlinear Maximum Power Point Tracking Control Method for Wind Turbines Considering Dynamics
## 1 Introduction  
Variable-speed wind turbines (VSWTs) have been dominating the wind power market for decades, resulting in the emergence of effective strategies to improve its power coefficient (\(C_{\text{p}}\)). Maintaining the optimal tip speed ratio (TSR) by adjusting the rotor speed dynamically will contribute to maximum \(C_{\text{p}}\) in the variable speed region. The strategies to maintain \(C_{\text{p}}\) or power close to its maximum value (TSR to optimal TSR) is known as maximum power point tracking (MPPT). There are four main categories of the MPPT methods: power signal feedback (PSF) control, perturbation and observation (P&O) control, tip-speed ratio (TSR) control, and optimal torque (OT) control [1; 2; 3]. PSF control and OT control are similar in performance and commonly used in large-scale wind turbines [4]. This paper focuses on the OT control method. The conventional OT control method has a good performance in small-scale wind turbines since the dynamic response of small-scale wind turbines is swift enough. Regardless of the dynamic transient behavior of VSWTs, the conventional OT control method is based on the steady optimal generator torque versus the generator speed curve. However, there is no absolute steady-state for VSWTs due to the stochastic nature of the wind speed under real conditions. Unfortunately, the increasing tendency in size and capacity of VSWTs will aggravate the conflict between the rapid wind variations (especially for the wind conditions with a low average value and high turbulent density) and the slow dynamic response of wind turbines owing to the large inertia of the rotor and generator. Previous research [5; 6; 7; 8; 9]has demonstrated that the slow dynamic response resulting from large inertia of VSWTs leads to the power loss of MPPT. The frequency of the wind speed variations and the average value of wind speed also play a great role in power loss [6; 7; 8]. Therefore, it is vital and valuable to find a novel MPPT method to enable large-scale VSWTs to respond better to the rapid wind variations. [PERSON] et al. [10] focused on the short-term maximum energy optimization instead of the instantaneous maximum power capture. They used semi-definite programming (SDP) to execute the optimal reference command in an intelligent way considering the short-term wind speed prediction, maximum short-term energy, and wind turbine dynamic response collectively. Nevertheless, the time period for the short-term maximum energy optimization hasn't been adjusted corresponding to the nonlinear dynamics of VSWTs. Some system correction methods, including the differential control based on rotor speed and feed-forward control based on aerodynamic torque and generator torque, have been applied to MPPT control by previous researchers [11; 12; 13]. However, previous research [11; 12; 13] didn't figure out the method to design the proportional gain in the correction path. [PERSON] et al. [14] reduced the MPPT tracking range considering the dynamic wind performance (mean wind speed, turbulence intensity, and turbulence frequency), which improved the ability of MPPT to track varying turbulent wind at the expense of power loss under low-speed wind conditions. [PERSON] et al. [15] proposed an adaptive robust control (ARC) method to overcome the power reduction resulting from uncertain factors, including wind variations. [PERSON] et al. [16] found that regulating the blade-pitch angle dynamically within a slight range, according to instantaneous TSR could increase the power by 0.2% to 3.4% in the MPPT region. However, [PERSON] et al. didn't provide the method to estimate TSR. [PERSON] et al. [17; 18] proposed a multi-point method for aerodynamic optimization of VSWT blades considering the distribution of operational TSR and an inverse aerodynamic optimization to focus on determining an appropriate design TSR. The aerodynamic optimization focusing on blade remolding may cost a lot of money.