ANALYSIS OF THE DYNAMIC RESPONSE OF OFFSHORE FLOATING WIND POWER PLATFORMS IN WAVES

Floating wind power platforms are in constant motion due to waves when deployed at sea. This motion directly affects the stability and safety of the platform. Therefore, it is very important to study the laws governing the platform’s dynamic response. In this paper, the dynamic characteristics of an offshore floating wind power platform were analysed under nine different sets of operating conditions using a numerical calculation method. Following this, a scaled 1:50 platform model was tested in a tank. Model tests were carried out with different wave conditions, and dynamic response data for the platform were measured and analysed. The hydrodynamic variation rules of floating wind power generation platform in waves were obtained. Some effective measures for maintain the stability and safety of wind power platforms are put forward that can provide a reference for dynamic stability research and the design of floating wind power platforms in the future.


INTRODUCTION
At present, efficient equipment for the utilisation of offshore wind energy is being actively developed by scholars all over the world. In order to exploit the available wind energy in the South Baltic Sea region, Polish researchers have focused on exploring the safety and stability of 6 MW offshore wind turbines [7,8]. At Gdańsk University of Technology, scholars have studied the structural strength and parametric safety analysis of jack-up legs [7]. The stability of floating support structures for offshore wind turbines under towing, settlement and installation at sea has also been studied [8]. Iranian scholars have studied the laws governing the rise and fall of buoys of different shapes in association with offshore floating wind turbines, and the conversion efficiency of wave energy under normal wave conditions [3]. Floating wind power platforms have become the subject of intense research in many countries, and can undergo numerous types of movement when operating under various conditions at sea [1]. These movements will directly affect the safety of the wind power platform and the stability of power generation, and it is therefore very important to study the motion response of floating wind power platforms under the action of waves.
In this paper, a 800 kW floating wind power platform is selected as the research object, and the specific parameters for this platform are presented in Tables 1 and 2. First, the motion response of the floating wind power platform is calculated in the frequency domain using SESAM software (a strength analysis software developed by DNV in 1969), and a model pool test is then conducted to study the movement of the wind power platform under the action of wind and waves.

NUMERICAL SIMULATION
Under the action of waves, the wind power platform will be subject to both dynamic and static movements created by the fluid. The equation of motion of a floating body in the frequency domain is [4]: where M represents the mass matrix for the floating body, A(ω) represents the additional mass matrix, λ(ω) represents the damping matrix, C represents the hydrostatic recovery matrix, C m represents the restoring force matrix of the mooring system, and f represents the wave excitation.

ESTABLISHMENT OF THE FINITE ELEMENT MODEL
The model coordinate system is set up as follows. The origin is at the centre of the projection plane of the floating foundation, where the water-pressure plate is located. The coordinate system is arranged according to the right hand rule: the x-axis is parallel to the central axis of the connecting rod between the central buoy and the main buoy, where the direction from the centre of the supporting buoy towards the main buoy is positive; and the z-axis is along the axis of the tower, where upwards is positive.
SESAM software was used to carry out the modelling. First, the main buoy, the intermediate supporting buoy and the connecting body between the buoy and the tower were established based on the actual geometric size of the wind power platform. The tower was then divided into 10 sections to reflect the linear variation in the wall thickness. The wind turbine was placed on the top of the tower, and the weight of the cabin cover was taken as the weight of the whole cabin. The fan blades were simulated using a circular surface, so that the blades could fully withstand the wind load. Wadam of the HydroD module was used to calculate the motion response. The motion response was calculated using Wadam in Hydro-D module. The structure of the numerical calculation models is shown in Fig. 1.

BOUNDARY CONDITIONS
The boundary constraints of the model were set at the center points of the bottom of the three floating buckets, and different constraint conditions were assigned to these three nodes. Specific boundary conditions were shown in Table 3.

LOAD ANALYSIS
The main load on a floating wind power platform at sea arises from the wind and waves. A detailed analysis is presented below.
Under normal sea conditions, the average pressure on the whole turbine disk is calculated as [10]: where ρ represents the air density, C FB is a coefficient chosen according to the Bates formula, and V r is the wind speed. The formula used to calculate the horizontal wind load at the top of the turbine tower is [5]: The wind load on the tower is calculated as follows [5]: where k 1 represents the shape coefficient of the wind load, k 2 represents the variation coefficient for the air pressure height, a is the wind pressure coefficient, v t denotes the design wind speed within a given time t, and A w represents the area of headwind projection for the tower. The MacCamy-Fuchs equation is used to calculate the wave force on large diameter buoys. The formula for calculating the horizontal wave force is as follows [9]: where A(ka) is the horizontal amplitude of waves acting on large-scale structure at any height. The wave load dF on a small-scale member with unit length dz is calculated using the Morison formula [9]: where dF I represents the inertial force per unit length of a small scale member, dF D is the drag force per unit length on the small-scale components, ρ is the density of seawater, C M is the inertial coefficient, C A is the additional mass coefficient, C D is the drag coefficient, u represents the water particle velocity component perpendicular to the component axis, represents the water particle acceleration component perpendicular to the component axis, represents the velocity component perpendicular to the component axis, and represents the acceleration component perpendicular to the component axis.

Wind load
The wind load is calculated according to the change in the gradient of the wind pressure coefficient. Since the tower is a cylinder, the coefficient is 0.5, and the wind-affected area is half of the surface area of the tower. The parameters used to calculate the wind load within each gradient range of the tower are shown in Table 4. Eq. (4) is used to calculate the wind load at different heights, and the results are shown in Table 5. The application of wind load is shown in Fig. 2.

Wave load
The effective wavelength and height of the wave load were selected based on the main scale of the floating wind power platform. The specific wave parameters used are shown in Table 6.

SIMULATED CONDITIONS
To reflect realistic conditions at sea, the rated wind speed for the wind power generation platform was 11 m/s, for a wind and wave direction of 180° and a water depth of 300 m. Nine different conditions of the floating wind power platform were considered, as shown in Table 7.

CALCULATION RESULTS
The results of the finite element calculation are shown in Tables 8-10.

TANK TEST TEST MODEL
The model test of the floating wind power platform involves both aerodynamics and hydrodynamics. When creating the test model, it is important to ensure that the blade tip speed ratios (TSRs) of the wind turbine blades are similar, and that the Froude number for the floating base model and the Reynolds number of the platform are similar. The scale of the selected model is 1:50.
The similarity conversion relation between the test model and the actual platform is shown in the following formula. The specific conversion relationship is shown in Table 11

TEST ENVIRONMENT AND MEASURING EQUIPMENT
The experiment was carried out in the hydrodynamic laboratory of Zhe Jiang Ocean University, and the main scale of the test pool is shown in Table 14 and Fig. 4. At the time of the experiment, the room temperature was 27°C and the water temperature was 25°C.
The measuring equipment used is listed in Table 15.

TESTING PROGRAM
The purpose of this experiment is to study the motion response of the floating wind power platform model under the action of regular waves.

Mooring model simulation
The arrangement of the mooring cables was as follows. Firstly, five weights were tied together to act as mooring points, and a variable pulley was set up at the mooring point. The mooring rope was then passed through the pulley, lifted out of the water, and connected to the pull sensor. It was then towed to the railings of the trailer, and finally, the other end of the mooring line was connected to the bottom of the bucket via the pulley.  In the experiment, three mooring ropes were first arranged using this method. Next, two motion sensors were placed on bucket No. 1 to measure the longitudinal and vertical acceleration of the wind power platform model. A tilt sensor was arranged at the top of the fan to measure the pitching angle of the model platform, as shown in Figs. 7 and 8.

Environmental load simulation
In the tank test, the environmental load mainly consisted of the wave load. Throughout the experiment, the motion response of the fan platform model was measured under different wave conditions, and the research is carried out from two aspects: wave height and wavelength. The PM spectrum was used to analyse the wave simulation, as shown in the formula below [11]:

Setting the test conditions
In order to ensure that the test conditions were consistent with the actual conditions, the wind speed was set to 1.56 m/s in the test, and the model rotor speed was set to 135 rpm based on the blade element momentum theory. Next, according to the wavelength selection principle for dangerous working conditions, the main scale length of the model was taken as the intermediate wavelength (2.1 m), and the arithmetic sequence was used to evaluate. The wave height was 6~14 cm with increments of 2 cm, as shown in Table 16.

TEST RESULTS
The acceleration of the longitudinal motion of the motion sensor, the acceleration of the heave motion and the angle of the pitching motion were recorded using the motion sensor. In this paper, the influence of wave height and wavelength on the motion response of the model wind power platform is studied based on regular wave conditions. The test data after application of the scale conversion ratio are shown in Tables 17 to 20.  where θ represents the angle between the combined wave and the main wave, in rad; H represents the significant wave height, in m; T 2 represents the period of the wave crossing zero, in s; ω represents the angular frequency of the wave, in rad/s.

RESULTS
By comparing the results of the numerical calculation with those of the experimental test and analysing them, a comparison of the dynamic characteristics of the platform under the action of waves could be obtained, as shown in Tables 21-23 and Figs. 10-12.

ANALYSIS OF RESULTS
According to the analysis in Tables 21-23, it can be seen that the results from the test data and the numerical calculation are very similar, and the error between them is not large, at around 20%. The dynamic characteristics produced by the two methods for the wind power platform in waves are essentially the same. The results show that the overall calculation scheme for the floating wind power platform is feasible. The following laws can be obtained from Figs. 10 to 12: (1) When the offshore wind speed is constant, the amplitude of the surge motion in the offshore motion response of the wind power platform is the largest, followed by the heave and pitch motion, and the various motion responses of the platform increase with the wave height. (2) When the wave height is constant, the surge motion slows down with an increase in the wavelength. When the wavelength exceeds 126 m, the amplitude of the surge motion tends to be stable. (3) When the wave height is constant, the heave and pitch motions of the platform first increase and then decrease with an increase in the wavelength. When the wavelength is close to the size of the platform, the motion reaches a peak.
(4) It can be seen from Figs. 8 and 11 that the amplitude of the mooring tension is largest when the motion of the platform is consistent with the direction of wave propagation, and reaches about eight times the mooring tension in the other two directions. (5) The mooring tension increases with an increase in the wind speed, and first increases and then decreases with an increase in the wavelength. When the wavelength is close to the scale of the platform, the mooring tension has the largest value.

CONCLUSIONS
The following conclusions can be drawn from our analysis of the experimental and numerical results presented here.
(1) Of the six degrees of freedom in the movement of the wind power platform, the amplitude of the surge motion is the largest. Hence, in order to ensure the safety of offshore floating wind power platforms and continuous power generation, the longitudinal stability of platforms is paramount. (2) The heave and pitch motions of the floating platform cannot be ignored. Before designing the layout of a wind farm, the sea conditions should be measured and investigated, and the wind power platform should not be placed in an area of the sea with a wavelength that is often close to the size of the platform. (3) The floating wind farm should be built in an area of the sea where the surface is gentle and there will be no high waves. (4) The wind at sea often causes waves from the same direction. When the wind direction and wave direction are the same, the wavelength is close to the scale of the platform length (in this paper, this specifically refers to the length of the triangle formed by the foundation of three floating bodies), and the hydrodynamic characteristics of the platform will be most affected. In this case, in addition to the wave suppression measures on the platform, the anchor mooring tension in the same direction as the waves must be monitored and protected.