Inclination rectification control method of active ballast water system for floating fan

Abstract

The invention discloses an inclination rectification control method for a floating fan by an active ballast water system, and the method specifically comprises the steps: building a power model of the floating fan: defining the degree of freedom of each part of a floating fan structure, calculating the kinetic energy of a floating fan system, and calculating the potential energy of the floating fan system; the external load of the structure is calculated, the wind load, the hydrodynamic load and the anchor chain load are considered, a power model of the floating type draught fan is established, then a servo system of the draught fan is added, and the complete draught fan power model is formed. Active ballast water system-rectification control: predicting the average wind speed and wind direction change in a few minutes in the future through a wind speed prediction method, calculating the ballast water variation of each cabin, and calculating the steady-state restoring force provided by seawater and an anchor chain; the gravity change generated by water allocation of each ballast tank is calculated through moment balance, then the change volume of water in each ballast tank is calculated through the change gravity, and then ballasting of each cabin is completed according to the set ballasting speed. According to the invention, the control efficiency of active ballast water is improved.

Description

Technical Field

[0001] This invention belongs to the field of offshore wind turbine technology, and particularly relates to a method for tilt control of floating wind turbines using an active ballast water system. Background Technology

[0002] According to data from the National Climate Center, the total deep-sea wind energy resources amount to approximately 1 billion kilowatts, equivalent to twice that of near-shore wind energy resources. Deep-sea areas with depths greater than 50 meters contain extremely rich wind energy reserves, and the wind power is stronger and more stable, making them ideal locations for large-scale development and utilization of next-generation marine wind energy. However, waves in the marine environment exert periodic impacts on the foundations and towers of wind turbines, subjecting them to continuous vibration loads, especially in deeper waters. Furthermore, changes in wind and waves can cause the floating foundations to tilt, leading to losses in wind energy capture by the turbine rotor, increased aerodynamic imbalance of the rotor, and consequently, reduced annual power generation and increased load.

[0003] Under the combined action of wind and waves, the floating body of a floating wind turbine tilts in both pitch and roll directions. This tilt angle consists of an average value and a fluctuating value. The average value is caused by the average component of the wind load, while the fluctuating value is caused by the fluctuating component of the wind load and wave loads. Currently, there are three main solutions to the tilting problem of the floating body of a floating wind turbine. The first is a passive control method, which can only reduce the fluctuating value. The second is to use pitch control technology to reduce the wind load acting on the wind turbine by changing the blade pitch angle in real time. However, this control effect comes at the cost of increasing the use of pitch actuators, and its control effect may be worse due to the strong coupling between the floating body's inherent modes and the wind turbine's pitch control loop. The third is to add water to the floating body through an active ballast water system, generating an anti-overturning moment to reduce the tilt angle, which has a significant control effect. However, many related studies only use sensors to measure the current tilt angle of the floating body for adding water, resulting in low control efficiency. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for correcting the tilt of a floating wind turbine using an active ballast water system. The aim is to improve the control efficiency of active ballast water systems.

[0005] The present invention provides a method for correcting the tilt of a floating wind turbine using an active ballast water system, specifically comprising:

[0006] A. Construct a dynamic model of the floating wind turbine, including:

[0007] Define the degrees of freedom of each component of the floating wind turbine structure.

[0008] Calculate the kinetic energy of the floating wind turbine system, taking into account the kinetic energy of the float, tower, nacelle, hub, and blades.

[0009] Calculate the potential energy of the floating wind turbine system, taking into account the potential energy of the float, tower, nacelle, hub, and blades.

[0010] The calculation of external loads on the structure takes into account wind loads, hydrodynamic loads, and anchor chain loads.

[0011] When calculating wind loads, the calculation is based on blade element momentum theory under operating conditions and on quasi-static field calculation under shutdown conditions; hydrodynamic loads are based on potential flow theory, taking into account wave force, radiation force and hydrostatic load; anchor chain force is calculated based on quasi-static assumptions.

[0012] A dynamic model of a floating wind turbine is established based on the Euler-Lagrange energy equation, and then a servo system of the wind turbine is added to form a complete wind turbine dynamic model.

[0013] B. Active Ballast Water System - Declination Correction Control.

[0014] The average wind speed and wind direction changes over the next few minutes are predicted using wind speed prediction methods. The changes in ballast water in each compartment are then calculated. The specific calculation method is as follows:

[0015] The average tilt angles α and β of the floating body in roll and pitch are obtained from the average wind speed and wind direction information. Considering that the floating body is a 6-DOF model with 3 translational and 3 rotational degrees of freedom, the steady-state restoring force provided by the seawater and anchor chain is calculated.

[0016] The gravity change caused by the water distribution in each ballast tank is calculated by torque balance, and the change in water volume in each ballast tank is calculated by the change in gravity. Then, each compartment completes ballasting according to the set ballasting speed.

[0017] It is worth noting that the ballast water in each compartment is independently allocated, and there is no transfer of ballast water between ballast compartments.

[0018] Because there will be errors in the feedforward wind speed and direction, sensors such as gyroscopes are installed on the float to calculate the average value of the float's rolling over a period of time. When the average value is less than a set threshold, the tilt correction control is considered to be completed; if the average value is greater than the set threshold, the ballast water volume is recalculated based on the currently measured average tilt angle, and ballast is applied again.

[0019] Furthermore, step A specifically involves:

[0020] A1. Considering tip oscillation and flapping vibration q j and q j+3 j = 1, 2, 3, a total of 6 degrees of freedom; the top section of the tower considers longitudinal and transverse bending vibrations q7 and q8; the floating body considers translational and rotational motions in three directions q9~q8. 11 and q 12 ~q 14 The structural system has a total of 14 degrees of freedom.

[0021] A2. According to the Euler-Lagrange energy equations, the kinematic equations of the wind turbine system are expressed as:

[0022] ;

[0023] in, As the system's kinetic energy, For the system potential energy, For displacement of degrees of freedom, For the velocity of the degrees of freedom, For external loads with degrees of freedom.

[0024] A3. The kinetic energy of the floating wind turbine system is expressed as:

[0025] ;

[0026] in, The kinetic energy of the floating body includes translational and rotational kinetic energy; For the kinetic energy of the tower; The kinetic energy of the cabin includes translational and rotational kinetic energy; The kinetic energy of the wheel hub includes translational and rotational kinetic energy; This is the kinetic energy of the blade.

[0027] A4. The potential energy of a floating wind turbine system is expressed as:

[0028] ;

[0029] in, , , , and These represent the gravitational potential energy of the floating body, nacelle, hub, tower, and blades, respectively. The bending strain energy of the tower; It is the strain energy caused by the weight of the blades, nacelle, hub, and tower itself on the axial direction of the tower; The strain potential energy of the blade considering the effects of centrifugal force and gravity on stiffness.

[0030] A5. External loads on the structure should include wind loads, hydrodynamic loads, and anchor chain loads.

[0031] In wind load calculations, the lift and drag acting on the wind turbine blades during operation are calculated using blade element momentum theory, while the lift and drag during shutdown are calculated using quasi-steady field theory. Considering the relative velocity between the blade elements and the flow field, the blade aerodynamic load is also taken into account. The generalized wind load is expressed as:

[0032] ;

[0033] in, The transformation matrix for the floating body, tower, and blades; The wind load is given in the local coordinates of the blade. This represents the virtual displacement in global coordinates.

[0034] Hydrodynamic loads take into account wave forces, radiation forces, and hydrostatic loads.

[0035] The wave excitation force is considered only in its first order, determined by the incident force. and diffraction force Composition, represented as:

[0036] ;

[0037] in, and These are the amplitude and phase of the wave force transfer function; and The amplitude and phase of the wavefront elevation; The wave frequency.

[0038] Radiation It consists of radiation inertial force and radiation damping force, and is expressed as:

[0039] ;

[0040] in, It is a high-frequency additional quality matrix; , These are the displacement, velocity, and acceleration of the floating body; It is the pulse of the radiation load .

[0041] hydrostatic load Composed of still water restoring force and buoyancy, it is represented as:

[0042] ;

[0043] in, This is the hydrostatic stiffness recovery matrix. The density of water, It is the volume of water displaced by the floating body.

[0044] The calculation of anchor chain force is based on the quasi-static assumption, considering the geometric relationship between the guide chain end and the anchoring end under a given attitude of the floating body, and solving the anchor chain tension components through static equilibrium equations.

[0045] The servo control system of the wind turbine—pitch system, yaw system, and braking system—is then embedded to obtain the dynamic model of the floating wind turbine.

[0046] Furthermore, step B specifically involves:

[0047] B1. Under the combined action of wind and waves, the floating wind turbine will produce an angle of inclination in the pitch and roll directions. This angle of inclination consists of an average value and a pulsating value. The average value is caused by the average component of the wind load, while the pulsating value is caused by the pulsating component of the wind load and the wave load.

[0048] The ballast compartments of the floating wind turbine are arranged in the pontoons of the floating body. The angle between the lines connecting any two adjacent ballast compartments and the center of gravity of the floating body is 120 degrees, and the horizontal distance from the center of gravity of each ballast compartment to the center of gravity of the floating body is also 120 degrees. Therefore, in the local coordinate system xyz of the floating body, the centers of gravity of each ballast tank are respectively expressed as: and .

[0049] B2. Assume the floating body has [conditions] in the roll and pitch directions respectively. and If the angle of inclination is given, then the restoring force provided is expressed as:

[0050] ;

[0051] in, To recover the stiffness matrix in still water, Here is the anchor chain stiffness matrix.

[0052] B3. Each ballast tank generates a torque through independent water distribution to balance the restoring torque, allowing the buoy to return to a horizontal and stable state; the gravity changes generated by the water distribution in each ballast tank are set as follows: , and Since the ballast water system only affects the directions of heave, roll, and pitch, the equilibrium equations are derived as follows:

[0053] ;

[0054] in, , and Resilience The vertical force component and the horizontal rotation component.

[0055] B4. Calculate the change in water weight inside each buoy by solving the system of equations, and then... , That is, calculate the change in water volume in each ballast tank, where The density of seawater, This is the acceleration due to gravity.

[0056] B5. During the movement of the floating body, the center of gravity of the ballast tank changes in real time in the global coordinate system, thus causing a change in the lever arm of the ballast water force; the real-time center of gravity of each ballast tank is expressed as:

[0057] ;

[0058] in, Let be the transformation matrix of the floating body.

[0059] B6. Compile the ballast load of each ballast tank as it varies with the average wind speed and direction, and complete the tilt correction control.

[0060] The beneficial technical effects of this invention are as follows:

[0061] This invention establishes an integrated wind turbine model equipped with active ballast water, which can analyze and simulate the entire ballast water loading process and observe the dynamic response. After the active ballast water corrective control, the average values ​​of the roll and pitch angles return to around 0 degrees, and the maximum value of the rolling response is reduced. Because the pitch and roll directions of the floating body are strongly coupled with the front-to-back and lateral directions of the tower top, respectively, the average and maximum values ​​of the tower top displacement are also reduced. The control strategy is based on feedforward control, which reduces the coupling with other servo control systems of the wind turbine to a certain extent and greatly improves control efficiency. Through the above control strategy, the tower base bending moment is reduced, the service life of the tower is increased, and the power generation is improved. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the front elevation of a floating wind turbine.

[0063] Figure 2 This is a schematic diagram of the side elevation of a floating wind turbine.

[0064] Figure 3 This is a schematic diagram of a floating wind turbine tilting under the combined action of wind and waves.

[0065] Figure 4 This is a logic diagram for the active ballast water system - tilt correction control.

[0066] Figure 5 This is a top-view schematic diagram of the floating platform.

[0067] Figure 6 This is for the effect of correcting pitch and roll. Detailed Implementation

[0068] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0069] The present invention provides a method for correcting the tilt of a floating wind turbine using an active ballast water system, specifically comprising:

[0070] A. Construct a dynamic model of a floating wind turbine.

[0071] A1, See also Figure 1 , Figure 2 Schematic diagrams of the front and side elevations of a semi-submersible offshore wind turbine are presented. Tip twitching and flapping vibrations (q) are considered. j and qj+3 j = 1, 2, 3, a total of 6 degrees of freedom; the top section of the tower considers longitudinal and transverse bending vibrations q7 and q8; the floating body considers translational and rotational motions in three directions q9~q8. 11 and q 12 ~q 14 The structural system has a total of 14 degrees of freedom.

[0072] A2. According to the Euler-Lagrange energy equations, the kinematic equations of the wind turbine system are expressed as:

[0073] ;

[0074] in, As the system's kinetic energy, For the system potential energy, For displacement of degrees of freedom, For the velocity of the degrees of freedom, For external loads with degrees of freedom.

[0075] A3. The kinetic energy of the floating wind turbine system is expressed as:

[0076] ;

[0077] in, The kinetic energy of the floating body includes translational and rotational kinetic energy; For the kinetic energy of the tower; The kinetic energy of the cabin includes translational and rotational kinetic energy; The kinetic energy of the wheel hub includes translational and rotational kinetic energy; This is the kinetic energy of the blade.

[0078] A4. The potential energy of a floating wind turbine system is expressed as:

[0079] ;

[0080] in, , , , and These represent the gravitational potential energy of the floating body, nacelle, hub, tower, and blades, respectively. The bending strain energy of the tower; It is the strain energy caused by the weight of the blades, nacelle, hub, and tower itself on the axial direction of the tower; The strain potential energy of the blade considering the effects of centrifugal force and gravity on stiffness.

[0081] A5. External loads on the structure should include wind loads, hydrodynamic loads, and anchor chain loads.

[0082] In wind load calculations, the lift and drag acting on the wind turbine blades (in the local coordinate system of the blades) under operating conditions are calculated using blade element momentum theory, while the lift and drag under stopped conditions are calculated using quasi-fixed field theory. Considering the relative velocity between the blade elements and the flow field, the blade aerodynamic load is also taken into account. The generalized wind load is expressed as:

[0083] ;

[0084] in, The transformation matrix for the floating body, tower, and blades; The wind load is given in the local coordinates of the blade. This represents the virtual displacement in global coordinates.

[0085] Hydrodynamic loads take into account wave forces, radiation forces, and hydrostatic loads.

[0086] The wave excitation force is considered only in its first order, determined by the incident force. and diffraction force Composition, represented as:

[0087] ;

[0088] in, and These are the amplitude and phase of the wave force transfer function; and The amplitude and phase of the wavefront elevation; The wave frequency.

[0089] Radiation It consists of radiation inertial force and radiation damping force, and is expressed as:

[0090] ;

[0091] in, It is a high-frequency additional quality matrix; , These are the displacement, velocity, and acceleration of the floating body; It is the pulse of the radiation load .

[0092] hydrostatic load Composed of still water restoring force and buoyancy, it is represented as:

[0093] ;

[0094] in, This is the hydrostatic stiffness recovery matrix. The density of water, It is the volume of water displaced by the floating body.

[0095] The calculation of anchor chain force is based on the quasi-static assumption, considering the geometric relationship between the guide chain end and the anchoring end under a given attitude of the floating body, and solving the anchor chain tension components through static equilibrium equations.

[0096] The servo control system of the wind turbine—pitch system, yaw system, and braking system—is then embedded to obtain the dynamic model of the floating wind turbine.

[0097] B. Active Ballast Water System - Anti-steering Control, control logic as follows: Figure 4 As shown.

[0098] B1, such as Figure 3 As shown, under the combined action of wind and waves, the floating wind turbine produces an inclination angle in the pitch and roll directions. This inclination angle consists of an average value and a pulsating value. The average value is caused by the average component of the wind load, while the pulsating value is caused by the pulsating component of the wind load and the wave load.

[0099] See Figure 5 A top view of the floating structure of a semi-submersible wind turbine is given. The ballast compartments of the floating wind turbine are arranged in the pontoons of the floating body. The angle between the lines connecting any two adjacent ballast compartments and the center of gravity of the floating body is 120 degrees, and the horizontal distance from the center of gravity of each ballast compartment to the center of gravity of the floating body is also 120 degrees. Therefore, in the local coordinate system xyz of the floating body, the centers of gravity of each ballast tank are respectively expressed as: and .

[0100] B2. For a horizontally stable floating structure, when subjected to a constant bending moment (caused by the average component of wind load) in any horizontal direction, the floating body develops a tilt angle in that direction. This tilt angle is decomposed into two horizontally perpendicular rotational directions (roll and pitch). At this time, the seawater and anchor chain provide a restoring moment, bringing the floating body to a new equilibrium state (tilt). Let the floating body have [various forces] in the roll and pitch directions respectively. and If the angle of inclination is given, then the restoring force provided is expressed as:

[0101] ;

[0102] in, To recover the stiffness matrix in still water, Here is the anchor chain stiffness matrix.

[0103] B3. Each ballast tank generates a torque through independent water distribution to balance the restoring torque, allowing the buoy to return to a horizontal and stable state; the gravity changes generated by the water distribution in each ballast tank are set as follows: , and Since the ballast water system only affects the directions of heave, roll, and pitch, the equilibrium equations are derived as follows:

[0104] ;

[0105] in, , and Resilience The vertical force component and the horizontal rotation component.

[0106] B4. Calculate the change in water weight inside each buoy by solving the system of equations, and then... , That is, calculate the change in water volume in each ballast tank, where The density of seawater, This is the acceleration due to gravity.

[0107] B5. During the movement of the floating body, the center of gravity of the ballast tank changes in real time in the global coordinate system, thus causing a change in the lever arm of the ballast water force; the real-time center of gravity of each ballast tank is expressed as:

[0108] ;

[0109] in, Let be the transformation matrix of the floating body.

[0110] B6. Based on the above calculation theory, consider that both wind and wave loads are incident at 0 degrees, where the wind load is the rated wind speed U. H =10.59 m / s, effective wave height of wave load is 1.625 m, and spectral peak period is 7.589 s.

[0111] See Figure 6 This paper presents a comparison of the time-history response of the buoy's pitch displacement with and without an active ballast water system. The inflow and outflow rates of the active ballast water system were both set to 20 m³ / s, and it was started at 50 s. It can be seen that after the active ballast water system was started, the buoy's pitch displacement response quickly returned to swaying around 0 degrees, and the maximum value decreased by 82.13%.

[0112] B7. The ballast load of each ballast tank is obtained by summing the data as a function of average wind speed and direction. The established integrated load analysis model can simulate the entire ballast water loading process and observe the dynamic response.

[0113] The above embodiments are only used to illustrate the technical solutions of the present invention more clearly, and are therefore only examples and should not be used to limit the scope of protection of the present invention.

Claims

1. A method for correcting the tilt of a floating wind turbine using an active ballast water system, characterized in that, Specifically: A. Construct a dynamic model of the floating wind turbine, including: Define the degrees of freedom of each component of the floating wind turbine structure; Calculate the kinetic energy of the floating wind turbine system, taking into account the kinetic energy of the floating body, tower, nacelle, hub, and blades; Calculate the potential energy of the floating wind turbine system, taking into account the potential energy of the floating body, tower, nacelle, hub, and blades; The calculation of external loads on the structure takes into account wind loads, hydrodynamic loads, and anchor chain loads. When calculating wind loads, the calculation is based on blade element momentum theory under operating conditions and on quasi-static field calculation under shutdown conditions; hydrodynamic loads are based on potential flow theory, taking into account wave force, radiation force and hydrostatic load; anchor chain force is calculated based on quasi-static assumptions. A dynamic model of a floating wind turbine is established based on the Euler-Lagrange energy equation, and then a servo system of the wind turbine is added to form a complete wind turbine dynamic model. B. Active Ballast Water System - Declination Correction Control; The average wind speed and wind direction changes over the next few minutes are predicted using wind speed prediction methods. The changes in ballast water in each compartment are then calculated. The specific calculation method is as follows: The average tilt angles α and β of the floating body in roll and pitch are obtained from the average wind speed and wind direction information. Considering that the floating body is a 6-DOF model with 3 translational and 3 rotational degrees of freedom, the steady-state restoring force provided by the seawater and anchor chain is calculated. The gravity change caused by the water distribution in each ballast tank is calculated by torque balance, and the change in water volume in each ballast tank is calculated by the change in gravity. Then each compartment completes ballasting according to the set ballasting speed. Because there may be errors in the feedforward wind speed and direction, sensors are installed on the float to calculate the average value of the float's rolling over a period of time. When the average value is less than a set threshold, the tilt correction control is considered complete; if the average value is greater than the set threshold, the ballast water volume is recalculated based on the currently measured average tilt angle, and ballast is applied again.

2. The method for correcting the tilt of a floating wind turbine using an active ballast water system according to claim 1, characterized in that, Step A specifically involves: A1. Considering tip oscillation and flapping vibration q j and q j+3 j = 1, 2, 3, a total of 6 degrees of freedom; the top section of the tower considers longitudinal and transverse bending vibrations q7 and q8; the floating body considers translational and rotational motions in three directions q9~q8. 11 and q 12 ~q 14 The structural system has a total of 14 degrees of freedom; A2. According to the Euler-Lagrange energy equations, the kinematic equations of the wind turbine system are expressed as: ； in, As the system's kinetic energy, For the system potential energy, For displacement of degrees of freedom, For the velocity of the degrees of freedom, External loads for degrees of freedom; A3. The kinetic energy of the floating wind turbine system is expressed as: ； in, The kinetic energy of the floating body includes translational and rotational kinetic energy; For the kinetic energy of the tower; The kinetic energy of the cabin includes translational and rotational kinetic energy; The kinetic energy of the wheel hub includes both translational and rotational kinetic energy; For the kinetic energy of the blades; A4. The potential energy of a floating wind turbine system is expressed as: ； in, , , , and These represent the gravitational potential energy of the floating body, nacelle, hub, tower, and blades, respectively. The bending strain energy of the tower; It is the strain energy caused by the weight of the blades, nacelle, hub, and tower itself on the axial direction of the tower; The strain potential energy of the blade considering the effects of centrifugal force and gravity on stiffness; A5. External loads on the structure should consider wind loads, hydrodynamic loads, and anchor chain loads. In wind load calculations, the lift and drag acting on the wind turbine blades during operation are calculated using blade element momentum theory, while the lift and drag during shutdown are calculated using quasi-steady field theory. Considering the relative velocity between the blade elements and the flow field, the blade aerodynamic load is also taken into account. The generalized wind load is expressed as: ； in, The transformation matrix for the floating body, tower, and blades; The wind load is given in the local coordinates of the blade. This represents the virtual displacement in global coordinates; Hydrodynamic loads take into account wave forces, radiation forces, and hydrostatic loads; The wave excitation force is considered only in its first order, determined by the incident force. and diffraction force Composition, represented as: ； in, and These are the amplitude and phase of the wave force transfer function; and The amplitude and phase of the wavefront elevation; The wave frequency; Radiation Composed of radiation inertial force and radiation damping force, it is expressed as: ； in, It is a high-frequency additional quality matrix; , These are the displacement, velocity, and acceleration of the floating body; It is the pulse of the radiation load ; hydrostatic load Composed of still water restoring force and buoyancy, it is represented as: ； in, This is the hydrostatic stiffness recovery matrix. The density of water, It is the volume of water displaced by the floating body; The calculation of anchor chain force is based on the quasi-static assumption, considering the geometric relationship between the guide chain end and the anchoring end under a given attitude of the floating body, and solving the anchor chain tension components through static equilibrium equations; The servo control system of the wind turbine—pitch system, yaw system, and braking system—is then embedded to obtain the dynamic model of the floating wind turbine.

3. The method for correcting the tilt of a floating wind turbine using an active ballast water system according to claim 2, characterized in that, Step B specifically involves: B1. Under the combined action of wind and waves, the floating wind turbine will produce an angle of inclination in the pitch and roll directions. This angle of inclination consists of an average value and a pulsating value. The average value is caused by the average component of the wind load, while the pulsating value is caused by the pulsating component of the wind load and the wave load. The ballast compartments of the floating wind turbine are arranged in the pontoons of the floating body. The angle between the lines connecting any two adjacent ballast compartments and the center of gravity of the floating body is 120 degrees, and the horizontal distance from the center of gravity of each ballast compartment to the center of gravity of the floating body is also 120 degrees. ; Therefore, in the local coordinate system xyz of the floating body, the centers of gravity of each ballast tank are respectively expressed as: and ; B2. Assume the floating body has [conditions] in the roll and pitch directions respectively. and If the angle of inclination is given, then the restoring force provided is expressed as: ； in, To recover the stiffness matrix in still water, Here is the anchor chain stiffness matrix; B3. Each ballast tank generates a torque through independent water distribution to balance the restoring torque, allowing the buoy to return to a horizontal and stable state; the gravity changes generated by the water distribution in each ballast tank are set as follows: , and Since the ballast water system only affects the directions of heave, roll, and pitch, the equilibrium equations are derived as follows: ； in, , and Resilience The vertical force component and the horizontal rotation component; B4. Calculate the change in water weight inside each buoy by solving the system of equations, and then... , That is, calculate the change in water volume in each ballast tank, where The density of seawater, It is the acceleration due to gravity; B5. During the movement of the floating body, the center of gravity of the ballast tank changes in real time in the global coordinate system, thus causing a change in the lever arm of the ballast water force; the real-time center of gravity of each ballast tank is expressed as: ； in, The transformation matrix for the floating body; B6. Compile the ballast load of each ballast tank as it varies with the average wind speed and direction, and complete the tilt correction control.

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