A Novel Approach for Identifying Electromagnetic Space–Time Coupling Load of Wind Turbine

An Electromagnetic Load Identification Method Based on the Polynomial Structure Selection Technique

“…Combine ϕ * o together with the equivalent concentrated dynamic load shown in Figure 5 into the modal transformation to calculate the 39th, 80th, 81th, 105th, and 117th efective modal electromagnetic load, as shown in Figure 6. Te coefcient C2 � −0.1992 in the proposed method is diferent from the coefcient C1 � 0.3997 in literature [19] due to the diferent signifcant mode shape matrix ϕ * o corresponding to fve concentrated load nodes 12, 13, 14, 15, and 16. Te signifcant mode shape matrix ϕ * o in literature [19] is reconstructed coming from directly selecting the 12th, 13th, 14th, 15th, and 16th order relative modal shapes instead of the 39th, 80th, 81th, 105th, and 117th order relative efective modal shapes by the polynomial selection technique.…”

“…Te coefcient C2 � −0.1992 in the proposed method is diferent from the coefcient C1 � 0.3997 in literature [19] due to the diferent signifcant mode shape matrix ϕ * o corresponding to fve concentrated load nodes 12, 13, 14, 15, and 16. Te signifcant mode shape matrix ϕ * o in literature [19] is reconstructed coming from directly selecting the 12th, 13th, 14th, 15th, and 16th order relative modal shapes instead of the 39th, 80th, 81th, 105th, and 117th order relative efective modal shapes by the polynomial selection technique. Both methods can accurately reconstruct the time history, which shows that the selection of modal shape does not afect the time-history function identifcation.…”

“…Te electromagnetic load can be transformed into a series of concentrated dynamic loads, which have the same timehistory form at each action point. Terefore, the dynamic diferential equation [19] of the wind turbine rotor under the electromagnetic load can be similar to the dynamic diferential equation under the concentrated dynamic load, expressed as shown in the following equation:…”

“…Te numerical example (Table 1 and Figure 3) coming from the literature [19] is given to examine the proposed identifcation method. Te electromagnetic loads acting vertically along the axis 335 mm-495 mm is selected as (z) � (z − 3)(z − 2), z ∈ [335, 495]mm, and l(t) � 3 sin(60πt) + 2 sin(90πt), t ∈ [0, 0.1]s. Te six terms of Chebyshev orthogonal polynomials (R 1 2.…”

“…Jiang et al [18] reconstructed the space-time coupling distributed load combining modal transformation together with orthogonal decomposition. Mao et al [19] reconstructed the space-time independent electromagnetic load combining the equivalented concentrated dynamic load with basis function ftting. Zhang et al [12] transformed distributed dynamic loads to equivalented concentrated loads acting on appropriate locations according to the strain modal theory.…”