Blade Stability Analysis

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

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 frequency and damping values are plotted against wind speed, but can also be plotted against rotor speed by selecting the appropriate 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 where a torque speed gain parameter is used to balance aerodynamic torque with generator torque, and
• parked which is described in the sections below.

For details of the the verification work that has been done on the new linearisation code.

Tip-speed ratio tracking

In this setup, the user chooses a range of wind speeds, in response to which the rotor will have a certain rotor 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 freedom.

The user can specify a torque speed gain \(K_{Q, \omega}\) which determines the counter torque applied against the rotor aerodynamic torque (in a direct-drive case this is equivalent to a generator torque or for a geared transmission equivalent to a generator torque applied on the high-speed side of the gearbox). The torque speed gain is defined as:

\[ \begin{equation} Q_\text{aero} = K_{Q, \omega} \omega_\text{rotor}^2 \end{equation} \]

In order to follow the optimal mode tip-speed ratio, the torque speed gain can be defined using the gear ratio \(G\) and optimal mode gain \(K_\text{opt}\) using

\[ \begin{equation} K_{Q, \omega} = K_\text{opt} G^3. \end{equation} \]

If the torque-speed gain is set at zero then the rotor will be in a free spin as no counter torque will be applied by the generator.

Parked analysis

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 pitch angle, wind direction and a range of wind speeds to do the analysis.

The multi-blade coordinate transform option cannot be used in this case. The transform is not relevant when the rotor is not rotating and so is not available.

Note

The user can freely set the maximum wind speed to a high value. When the turbine gets into very extreme operating conditions, at some point the turbine will fail to find adequate steady state conditions. At this point, Bladed will finish the blade stability analysis and proceed to complete the analysis with the wind speeds already analysed. The point of steady state failure typically happens at around twice the rated rotor speed.

Calculation Settings

The following additional inputs are now available:

• Minimum correlation coefficient: A user-specified threshold correlation coefficient value that must be exceeded in order for an entry in the state-space linear model matrices to be non-zero linear analysis.

• Maximum Frequency for plot: This controls the maximum frequency of modes that are plotted in the Campbell diagram. In case a model contains high-frequency blade or support structure modes, this setting can be useful to improve the responsiveness of the Campbell diagram view.

Last updated 10-09-2024