Accurate rotor data is notoriously hard to come by, since turbine manufacturers are reluctant to disclose detailed information, particularly for publication. That said, for the purposes of this research, the U.S. National Renewable Energy Laboratory (NREL) offshore baseline turbine — a fictional turbine — was used. It’s become the standard reference turbine for numerous studies, mainly due to the fact that its properties are freely available. Some of its parameters were arbitrarily selected using engineering judgment; others were selected to match those of a 5-MW turbine developed by REpower Systems SE, Hamburg, Germany.

The properties assigned to the NREL turbine represent the current state of the art for offshore wind turbines. This infers that its principal components are a conventional drivetrain with a three-stage gearbox and an asynchronous high-speed generator. For more information, see the NREL technical report.4

The nominal line pressure for dynamic loads on the hydrostatic transmission is set at 220 bar. This translates directly to a nominal torque of around 230 kNm. Maximum possible speed is approximately 31 rpm. These two conditions represent the limits for the operational range of the rotor simulation. When scaling down the rotor properties of the NREL turbine to match the transmission capability, the relation between power coefficient, CP, and tip speed ratio, λ, stays the same.

The maximum allowable rotor diameter is found by setting the torque and speed limits as rated power conditions of the wind-turbine rotor. Figure 8 shows the resulting optimal torque versus speed curve. Table 1 compares the rotor properties of the original NREL turbine with the version adapted to match the hydrostatic transmission.

Bladed wind-turbine-model simulation software

Obtaining a realistic response of the hydrostatic transmission requires accurate simulations of the aerodynamic rotor and wind conditions. In this regard, the multi-body dynamics software package “Bladed” from energy consultancy GL Garrad Hassan (Hamburg, Germany) is the industry-standard integrated software package for the design and certification of onshore and offshore turbines.5

One drawback when using Bladed involves creation of the transmission input; the software isn’t suited for interactive use, i.e. hardware-in-the-­loop. As a result, the drivetrain’s braking torque can’t be fed back into the program, which produces an unrealistic coupling between the simulated input and the transmission response. To make the coupling more realistic, the rotor-control settings are set to fixed-speed operation, Figure 9. This fixed speed is predetermined using the optimal tip speed ratio, λ, where the wind speed is the average taken from the wind file corresponding to the load case.

A wind file is required to run a simulation in Bladed (the software also creates these files). The nature of a wind file is determined by a number of user-selected settings, such as the mean wind speed, turbulence intensity, turbulence seed, yaw misalignment angle, inclusion of tower shadow (plus how it’s modeled), and the type of wind-shear profile. For more information on how this is achieved, see the Bladed manual.5 Output parameters of interest are the torque and angular velocity of the low-speed shaft versus time.

Adapt Bladed model results to a 50-m rotor

Results obtained from bladed model are scaled down to create the transmission’s input. They have to be translated from results of scaling from a 126 to a 50-m rotor diameter. Only steady-state relations are considered in this scenario, maintaining the same tip speed, vtip, and power coefficient, CP:

(1)   vtip = ω1 × R1 = ω2 × R2

(2)   CP = Protor/Pwind = (T1 × ω1)/(½ρ u3 × π R12) = (T2 × ω2)/(½ρ u3 × π R22)

where ρ = air density, kg/m3;

CP = power coefficient;  

Pwind = wind power through rotor area, W;  

Protor= wind power extracted by rotor, W;

T = torque (N-m).

These result in the following translations for speed and torque:

(3)    ω2 = ω1 × R1/R2

(4)    T2 = T1 × (R2/R1)2

The standard deviation of the torque with respect to the mean value is the same for both the original and the scaled rotor. This translation’s outcome doesn’t account for dynamic influence from changes in the rotor mass moment of inertia, dynamic stall, dynamic inflow, or Reynolds numbers.

Figures 10 through 13 reveal the scaled results from Bladed for fixed-speed simulation of NREL’s offshore baseline turbine for an extreme gust and wind with turbulence intensity of 16.3%.

Three different load cases show the effects of the control strategy, Figure 14. Load Case A is a simple torque step from 100 to 150 kNm. Case B is the torque curve of a gust of wind, also called a “Mexican Hat.” Case C is a 50-sec segment of real operation. The data for the two last files was generated in the Bladed software.