Active fault tolerant control for twin wind turbine subject to asymmetric fault

Active fault‐tolerant control based on sparse recovery diagnosis: The twin wind turbines case

“…The goal of the fault estimation problem is to solve the algebraic system of $$$ p $$$ equations, given by (6), with $$$ q $$$ unknowns terms. Obviously the particular case $$$ p=q $$$ is immediately solved by inverting the matrix $$$ \mathrm{LF}\left(x,u,\dot{u},\dots, {u}^{\left(n-1\right)}\right) $$$ if it's invertible (this case is treated in References 14 and 15). For $$$ p>q $$$, the system of equations is solved based on the dimension reduction.…”

“…The model of the healthy TWT is given in detail in previous works. 10,12,14 In this section, the model of the faulty PMSM while considering two types of electrical faults is investigated: stator ITSC and demagnetization fault. Here, the case when the faults affect on only one electrical machine (related to a single turbine) is considered.…”

“…The advantage of this structure is that its orientation in front of wind requires no actuator. The model of the healthy TWT is given in detail in previous works 10,12,14 . In this section, the model of the faulty PMSM while considering two types of electrical faults is investigated: stator ITSC and demagnetization fault.…”

“…Compared to Reference 14, the AFTC has 7 objectives to reach instead of 5. Two additional outputs $$$ {i}_{h1}=\frac{1}{3}\left({x}_5+{x}_6+{x}_7\right) $$$ and $$$ {i}_{h2}=\frac{1}{3}\left({x}_9+{x}_{10}+{x}_{11}\right) $$$ are used to correct the asymmetry of phases.…”

“…In order to respect the Kirchhoff laws, the direct current $$$ {i}_{di};i=1,2 $$$ as well as the zero sequence component (the homopolar component) ($$$ {i}_{hi}=\frac{1}{3}\left({i}_{ai}+{i}_{bi}+{i}_{ci}\right);i=1,2 $$$) must be assigned to zero. In the previous works, 12,14 an incipient fault (insulation degradation fault) of low severity (4%) appearing in only one phase, precisely in the $$$ a $$$‐phase, has been considered to test the robustness of the passive control based on HOSM. By changing the severity of the same fault, it was proved that once it exceeds 8%, the control is not enough robust to achieve all the objectives.…”