# A Maximum Power Point Tracking Control Method Based on Rotor Speed PDF Shape for Wind Turbines
## Abbreviations  
MPPT Maximum power point tracking  
PMSG Permanent magnet synchronous generator  
MPP Maximum power point  
LLS Linear least square  
FPK Fokker-Planck-Kolmogorov  
PDF Probability density function  
HCS Hill climbing search  
P&O Perturb and observe  
PSF Power signal feedback  
OT Optimal torque  
\(\omega_{max}\) Limited rotational speed (rad/s)  
\(P_{t}\) Mechanical power of the turbine (W)  
\(P_{t\ opt}\) Optimal mechanical power of the turbine (W)  
\(T_{t}\) Mechanical torque of the turbine (N-m)  
\(T_{t\ opt}\) Optimal mechanical torque of the turbine (N-m)  
\(T_{g}\) Electromagnetic torque of the turbine (N-m)  
\(T_{g}\)\({}^{*}\) Reference electromagnetic torque of the turbine (N-m)  
\(K_{opt}\) Optimum torque coefficient  
\(\rho\) Air density (kg/m\({}^{3}\))  
\(R\) Radius of the wind wheel (m)  
\(v\) Incoming wind speed (m/s)  
\(\lambda\), TSR Blade tip speed ratio  
\(\lambda_{opt}\) Optimal tip speed ratio  
\(\beta\) Pitch angle (degree)  
\(C_{p\ max}\) Maximum power coefficient of wind turbine  
\(C_{p}\) Power coefficient of wind turbine  
\(\overset{\wedge}{\lambda}\) Estimated value of blade tip speed ratio  
\(\overset{\wedge}{T}_{t}\) Estimated value of aerodynamic torque (N-m)  
\(C_{p}(\overset{\wedge}{\lambda},\beta)\) Estimated value of power coefficient  
\(C_{T}(\overset{\wedge}{\lambda},\beta)\) Estimated value of aerodynamic torque coefficient  
\(\omega_{t}\) Rotor speed of turbine (rad/s)  
\(\omega_{g}\) Rotor speed of generator (rad/s)  
\(J\) Moment of inertia of the wind turbine (kg\(\cdot\)m\({}^{2}\))  
\(K_{s}\) Stiffness of rotor (N-m/rad)  
\(l\) Order of controller  
\(p_{trf}\), \(p_{tr}(x)\) PDF of the system's state variable  
\(p_{trf}^{\infty}\), \(p_{trf}^{\infty}(x)\) Approximate PDF solved by FPK equation  
\(x(t)\) System status variable  
\(x(t_{0})\) Initial state variable of the system  
\(\varphi(x)\) System function  
\(u(x)\) Control function of the system  
\(F(x)\) Nonlinear part of the system  
\(G(x)\) Diffusion coefficient of stochastic dynamic equation  
\(\varepsilon(t)\) Stochastic input vector or interference vector  
\(S_{\mathrm{G1}}\) Power spectral density  
\(e(l)\) System tracking error  
\(p_{1}(x)\) One of the special solutions of \(p_{trf}^{\infty}(x)\)  
\(p_{2}(x)\) Another special solution of \(p_{trf}^{\infty}(x)\)  
\(c_{i}\) Exponential term coefficient of \(p_{trf}^{\infty}(x)\)  
\(\sigma\) Standard deviation of goal PDF in Gaussian distribution  
\(\mu\) Expectation of goal PDF in Gaussian distribution  
\(\sigma_{z}\) Standard deviation of goal PDF in multi-Gaussian distribution  
\(\mu_{z}\) Expectation of goal PDF in multi-Gaussian distribution  
\(w_{z}\) Weight coefficient of goal PDF in multi-Gaussian distribution  
\(C_{2}\), \(C_{5}\), \(C_{7}\), \(C_{10}\) Parametric set when the order of controller is 2, 5, 7, and 10  
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