MBC

A MATLAB®-based postprocessor for Multi-Blade Coordinate transformation of wind turbine state-space models

by Gungit Bir, NREL

MBC is a set of MatLab scripts that performs multi-blade coordinate transformation (MBC) on wind turbine system models. The dynamics of wind turbine rotor blades are conventionally expressed in rotating frames attached to the individual blades. The tower-nacelle subsystem sees the combined effect of all rotor blades, not the individual blades. This is because the rotor responds as a whole to excitations such as aerodynamic gusts, control inputs, and tower-nacelle motion—all of which occur in a nonrotating frame. MBC helps integrate the dynamics of individual blades and express them in a fixed (nonrotating) frame.

MBC is mandatory to controls and stability analyses—erroneous predictions can result otherwise. A novel feature of this MBC code is that it can handle variable-speed operation and turbines with dissimilar blades. Depending on the analysis objective, a user may generate system models either in the first-order (state-space) form or the second-order (physical-domain) form. MBC3 can handle both types of system models. Key advantages of MBC are: capturing cumulative dynamics of the rotor blades and its interaction with the tower-nacelle subsystem, well-conditioning of system matrices by eliminating non-essential periodicity, and filtering operation.

Usage

The MBC scripts were updated to functions and modified to deal with some changes in OpenFAST linearizaton for BeamDyn. The old scripts have been moved to the Source\old directory. The new functions can be called with

[mbc_data, matData, FAST_linData] = fx_mbc3( FileNames )

where the returned data structures are:

• mbc_data: the MBC3-transformed data
• matData: the data from calling fx_getMats
• FAST_linData: the raw data stored in the OpenFAST linearization files

After the MBC3 transformation, the campbell_diagram_data function can be called to help analyze modes:

[CampbellData] = campbell_diagram_data(mbc_data, BladeLen, TowerLen, xlsFileName)

Note that the blade and tower lengths are inputs to this function. Also, if the optional xlsFileName is used, the CampbellData is written to an Excel file, which can be useful for analyzing the results.