In order to make the linearisation azimuth independent, the following sources of periodic loading are turned off in all linearisation calculations:
- Gravity
- Tilt
- Imbalances
The wind field is uniform horizontal without shear, tower shadow or wake. All wave loading and currents are turned off. The external controller or any internal control dynamics are not used in any linearisation calculations.
The Campbell diagram calculates the coupled modes of the complete aeroelastic system and their properties such as frequency, damping and their composition in terms of blade modes, tower modes and other states of the system. The coupled mode frequencies are plotted against rotor speed.
There are three main modes of operation:
- Power production – Wind speed can be ramped from cut-in to cut-out and the steady state controller is used to determine the operating conditions at each speed.
- Idling – A range of rotor speeds are chosen and a wind speed is found in order to produce these rotor speeds given the idling pitch angle.
- Parked – The turbine is analysed with wind speed of zero. This can be useful to determine the pure elastodynamic coupled modes of the turbine.
In cases where there are a lot of high frequency modes in the system (e.g. multi-part blades), high frequency modes can be excluded from the plot by setting the maximum frequency for plot. The rotating modes (i.e. blade modes) can be transformed into the non-rotating frame. This will generate forward and backward whirling modes in the output.
Model linearisation generates input and state perturbations, and records the resulting variations in the state derivatives and the selected outputs. This is done for a series of steady-state power production operating points. The Linear Model 8.19 post-processing calculation is then able to derive a linearised model of the turbine in state-space form. This is of particular value for designing controllers.
The possible input perturbations are wind speed, collective pitch angle demand, generator torque. Optionally, linear horizontal and vertical shear and pitch angle demand on each blade can be perturbed. These are particularly useful for individual pitch control design. In the advanced fields, the user can change perturbation magnitudes. This might be useful if it is found that the perturbations are too large and are therefore include too much non-linear response.
Model linearisation can also be performed over a range of azimuth angles for each wind speed. This is usually necessary only for one or two bladed turbines where the structural coupling has a strong azimuthal dependence.
The blade stability analysis feature performs a frequency domain analysis of the turbine rotor in steady state. The analysis provides outputs of damping and frequency of all the coupled rotor or blade modes plotted against wind speed. It is a similar analysis to the Campbell diagram but the main differences are:
Only the rotor is modelled
Allowing analysis over a wide range of inflow conditions rather than being constrained to normal operating conditions
Improved initial condition finding suitable for extreme conditions.
For outputs, the blade stability analysis produces a Campbell diagram plot and frequency and damping curves of all coupled modes. It is primarily the damping curves that will be of most interest as this allows the user to detect possible instabilities by finding damping curves that have negative damping.
The coupled mode frequencies and dampings are plotted against wind speed, but can also be plotted against rotor speed by using an output channel as the x-axis in the data viewer.
There are two modes of operation for the blade stability analysis: tip-speed ratio tracking and parked, which are described in the sections below.
In this setup, the user chooses a range of wind speeds, in response to which the rotor will have a certain speed. The pitch angle is usually at fine or at an operational pitch angle in these simulations.
At very high rotor speeds, it often becomes difficult to find initial conditions. If the analysis reaches this point, it will complete without analysing the last few points. This allows the user to set the upper wind speed with some freedom.
The user can specify a ‘torque speed gain’ which determines an opposition torque applied against the rotor aerodynamic torque (in a gearless case this is equivalent to a generator torque and otherwise equivalent to a generator torque applied on the high-speed side of the gearbox). The torque speed gain is defined as:
In order to follow the optimal mode tip-speed ratio, the torque speed gain can be set as:
The user can perform a parked analysis where the rotor speed is locked at zero. Because the rotor freedom is disabled, only one blade is analysed as it is assumed that the blades do not couple. The user can select the wind direction and a range of wind speeds to do the analysis.
Linear model (see 8.19) to convert the output of the Model Linearisation (see 7.11) calculation into a state-space model suitable for control design, for example using Matlab [2]
This calculation is available for users with a licence for the Control module. It converts the output of a Model Linearisation (see 7.11) calculation into a state-space model, in a form which is suitable for controller design and is directly compatible with Matlab [2]. A state space model has the following form:
First click Select… to define which variables from the Model linearisation results are required as model outputs. **The model states will depend on the dynamics which were selected in the turbine model for that calculation**, and the inputs will include wind speed, pitch angle demand and generator torque demand. The state space matrix coefficients are calculated as the slope of a best fit line through a number of points generated by perturbations of different sizes away from the steady state condition.
The Minimum acceptable correlation coefficient defines whether a best fit will be accepted or not. If the correlation is poorer than this, that particular matrix coefficient is set to zero. A value of $0.5\,-\,0.8\$ is generally suitable.
Two output files are created in the selected output directory, using the selected run name and the following file extensions:
RunName .mat This is a ‘.mat’ file suitable for reading directly into Matlab [2].
RunName.$m2 This is an ASCII text file, also suitable for reading into Excel, containing the same information.
RunName .mat 这是一个‘.mat’文件，可直接导入Matlab读取 [2]。
RunName.$m2 这是一个ASCII文本文件，也可导入Excel读取，其中包含相同信息。
Each file contains the four state space matrices for each operating point, and also wind speeds and rotor azimuths defining the operating points. There are also vectors containing the steady state values of all inputs, states and outputs at each operating point, as well as some additional information which may be of use in controller design such as the gearbox ratio, number of blades, and nominal speed and torque values.
In the.mat file, the variable names used are fairly self-explanatory, except that the state space matrices and the names of the inputs, states and outputs are all stored in a structure called SYSTURB. The elements of SYSTURB are:
inputname The names of the input variables (character array)
outputname The names of the output variables (character array)
statename The names of the state variables (character array)
输入变量名 输入变量的名称 (字符数组)
输出变量名 输出变量的名称 (字符数组)
状态变量名 状态变量的名称 (字符数组)
A, B, C, D Arrays of the state-space matrices for the different operating points; thus $\mathsf{A}(\mathsf{i},\mathsf{j},\mathsf{k},\mathsf{l})$ is the $i,\mathtt{j}^{\mathtt{t h}}$ element of the A matrix (i.e. row I, column j), for the $k^{\mathrm{th}}$ wind speed and the $\vert t\vert$ rotor azimuth angle.
This structure can readily be converted to a Matlab lti model array using the single Matlab command:
${\sf S Y S}={\sf s s}$ (SYSTURB.A, SYSTURB.B, SYSTURB.C, SYSTURB.D, … 'inputname', cellstr(SYSTURB.inputname), … 'outputname', cellstr(SYSTURB.outputname), … 'statename', cellstr(SYSTURB.statename));
Diagnostic plots may be generated for all matrix coefficients, or for all matrix coefficients whose correlation coefficients fall within a specified range of values. Note: Diagnostic plots cause a much slower calculation, and may generate very large numbers of plot files; these are stored as enhanced metafiles in the selected run output directory, with the following naming convention:
