Method for optimizing distance between anchor points for safe operation of high-altitude tethered kites

Abstract

This invention provides a method for optimizing the anchor point spacing for safe operation of a high-altitude tethered kite, comprising: S1. Obtaining the wind speed of the operating environment of the high-altitude tethered kite, establishing a simulation model of the high-altitude tethered kite operation, and simulating the operating state of the high-altitude tethered kite under different wind speeds; S2. Determining the tangential velocity factor of the high-altitude tethered kite; S3. Constructing the control equations for the azimuth and pitch angles β of the high-altitude tethered kite based on the tangential velocity factor λ; S4. Determining the anchor point positions of the high-altitude tethered kite and constructing the minimum envelope ellipse of the high-altitude tethered kite. S5. Construct the coordinate equation of the high-altitude tethered kite based on the anchor point position, azimuth angle, and pitch angle β. S6. Determine whether a collision has occurred by using the coordinates of any two adjacent high-altitude tethered kites or the distance between the tethering lines of two adjacent high-altitude tethered kites. If so, change the anchor point spacing of the adjacent high-altitude kites and return to step S5. If not, use the minimum distance between the anchor points when no collision occurs as the anchor point spacing between the adjacent kites.

Description

Technical Field

[0001] This invention relates to a method for optimizing kite power generation, and more particularly to a method for optimizing the spacing between anchor points for safe operation of high-altitude tethered kites. Background Technology

[0002] Compared with traditional wind power generation technology, high-altitude wind energy systems have significant advantages in terms of infrastructure construction costs, achievable operating altitudes, and environmental impact control. They are especially suitable for areas with variable wind conditions or complex terrain. High-altitude wind energy systems are generally implemented using kite generators.

[0003] In kite wind farms, the safe operation and spatial layout of the units directly determine the overall power generation efficiency. Unlike traditional wind farms, the operation of high-altitude kite units is less affected by terrain and wake. The core challenge in their layout lies in how to define a safe and efficient three-dimensional operating airspace for each unit. The operating airspace of high-altitude tethered kites is a cone-shaped space with ground stations as anchor points. Therefore, selecting a reasonable anchor point distance is one of the key factors in avoiding collisions between high-altitude tethered kites. The collision of high-altitude tethered kites can be essentially attributed to the contact and entanglement between the traction rope and the tethered kite. In existing technologies, to avoid collisions between high-altitude tethered kites, a larger anchor point spacing is used. This method requires an open layout location and increases the cost of ground cable laying. When the ground area is small, not enough high-altitude tethered kites can be placed, resulting in insufficient output capacity of the entire kite wind farm. Moreover, in existing technologies, the influence of the kite's pitch and azimuth angles is not considered when selecting kite anchor points, leading to poor rationality in the final anchor point selection.

[0004] Therefore, in order to solve the above-mentioned technical problems, it is urgent to propose a new technical approach. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a method for optimizing the anchor point spacing for safe operation of high-altitude tethered kites. When optimizing the anchor point spacing, the time-domain variation characteristics of the pitch and azimuth angles of the high-altitude tethered kites are taken into account, thereby establishing a corresponding collision detection mechanism. This allows for the deployment of more kite-generated power equipment within a limited area while avoiding collisions between adjacent high-altitude tethered kites, without increasing the layout of ground cables and other facilities. This ensures both the safe operation of the kite-driven wind farm and sufficient power output, thereby improving wind energy utilization.

[0006] This invention provides a method for optimizing the anchor point spacing for safe operation of tethered kites, comprising the following steps:

[0007] S1. Obtain the wind speed of the high-altitude tethered kite operating environment, establish a simulation model of the high-altitude tethered kite operation, and simulate the operating status of the high-altitude tethered kite under different wind speeds;

[0008] S2. Determine the tangential velocity factor λ of the high-altitude tethered kite;

[0009] S3. Construct the governing equations for the azimuth angle Φ and pitch angle β of the high-altitude tethered kite based on the tangential velocity factor λ;

[0010] S4. Determine the anchor point of the high-altitude tethered kite and construct the high-altitude tethered kite with the smallest envelope ellipsoid; use the coordinates of the center of the smallest envelope ellipsoid as the coordinates of the high-altitude tethered kite.

[0011] S5. Construct the coordinate equation of the high-altitude tethered kite based on the anchor point location, azimuth angle Φ, and pitch angle β;

[0012] S6. Determine whether a collision has occurred by using the coordinates of any two adjacent high-altitude tethered kites or the distance between the tethering lines of two adjacent high-altitude tethered kites. If so, change the anchor point spacing of the adjacent high-altitude kites and return to step S5. If not, use the minimum distance between the anchor points when no collision occurs as the anchor point spacing between the adjacent kites.

[0013] Furthermore, in step S5, the coordinate equation of the high-altitude tethered kite is constructed based on the anchor point position, azimuth angle Φ, and pitch angle β:

[0014] ;

[0015] in: Let represent the spherical coordinates of the i-th tethered kite at time t. Let represent the straight-line distance from the anchor point of the i-th tethered kite to the kite.

[0016] Furthermore, the azimuth angle Φ of the i-th kite at time t is determined by the following method:

[0017] ; This represents the factor that influences the trajectory of a tethered kite at high altitudes. The expression is:

[0018] ; This indicates the factor that caused the change in the trajectory of the tethered kite at the previous moment. This represents the change factor in the trajectory of the tethered kite at the current moment. This indicates the change in the trajectory variation factor of a high-altitude tethered kite;

[0019] ;

[0020] Among them, intermediate variables for:

[0021] ;

[0022] C represents the radial amplitude coefficient. Let dt represent the tangential velocity, r represent the length of the kite's tethering line, and dt represent the time step between the current moment and the previous moment. and This represents the horizontal amplitude coefficient.

[0023] Furthermore, the pitch angle β of the i-th kite at time t is determined by the following method:

[0024] Ascent Phase: ; This indicates the pitch angle of the tethered kite at the current moment. This indicates the pitch angle of the tethered kite in the air at the previous moment, representing the current moment.

[0025] Power generation stage: ; Indicates the heading angle; Indicates wind speed. This indicates the scaling factor for the kite during the power generation phase;

[0026] Recycling phase: ; This represents the kite scaling factor during the recovery phase.

[0027] Furthermore, the tangential velocity factor λ is determined using the following method:

[0028] ;

[0029] Where: a and b both represent intermediate variables;

[0030] ;

[0031] ;

[0032] k represents the lift-to-drag ratio. ; These represent the lift coefficient and drag coefficient of a kite, respectively. The heading angle of a high-altitude tethered kite is given by:

[0033] .

[0034] Furthermore, constructing a high-altitude tethered kite with a minimum envelope ellipsoid specifically includes:

[0035] Determine the external dimensions of the high-altitude tethered kite, with its length, width, and height representing 2m, 2m, and 2h, respectively;

[0036] The circumscribed ellipsoid of the high-altitude tethered kite is constructed as the minimum envelope ellipsoid, and the equation of the circumscribed ellipsoid is expressed as:

[0037] ;

[0038] in: .

[0039] Furthermore, determining whether a collision has occurred based on the coordinates of any two adjacent high-altitude tethered kites or the distance between the tethering lines of two adjacent high-altitude tethered kites specifically includes:

[0040] Determine the distance between the tethering lines of two adjacent high-altitude tethered kites:

[0041] The tethering rope of the high-altitude tethered kite is discretized into N nodes, and the coordinates of the i-th node are determined by the position of the anchor point. and the position of the kite Determine by performing linear interpolation:

[0042] ;

[0043] Any pair of nodes on the tethering lines of two adjacent high-altitude tethered kites The distance is:

[0044] ;

[0045] when or If two adjacent high-altitude tethered kites collide, the kites will be in flight.

[0046] The beneficial effects of this invention are as follows: By taking into account the temporal variation characteristics of the pitch and azimuth angles of high-altitude tethered kites when optimizing the anchor point spacing, a corresponding collision detection mechanism is established. This allows for the deployment of more kite power generation equipment within a limited area while avoiding collisions between adjacent high-altitude tethered kites, without increasing the layout of ground cables and other facilities. This ensures the safe operation of the kite wind farm while guaranteeing sufficient power output and improving wind energy utilization. Attached Figure Description

[0047] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0048] Figure 1 This is a schematic diagram of the process of the present invention.

[0049] Figure 2 This is a schematic diagram showing the speed breakdown of the high-altitude tethered kite according to the present invention.

[0050] Figure 3 This is a schematic diagram of the collision of the canopy of the high-altitude tethered kite according to the present invention.

[0051] Figure 4 This is a schematic diagram of the rope collision of the tethered kite of the present invention.

[0052] Figure 5 This is a schematic diagram of the trajectory of the tethered kite during its ascent phase according to the present invention. Detailed Implementation

[0053] The present invention will be further described in detail below:

[0054] This invention provides a method for optimizing the anchor point spacing for safe operation of tethered kites, comprising the following steps:

[0055] S1. Obtain the wind speed of the high-altitude tethered kite operating environment, establish a simulation model of the high-altitude tethered kite operation, and simulate the operating state of the high-altitude tethered kite under different wind speeds; in the simulation model, determine the initial anchor point spacing. The initial anchor point spacing should take into account factors such as the number of kite generator arrays, deployment cost, and output power. That is, the number of arrays should meet the total output power requirements, and the deployment cost should also be considered. For example, if 3 units are deployed, then cost is not a concern as long as the distance between the 3 kite generators is far enough. However, the cost of cables and other equipment will increase. Therefore, the spacing should be minimized while ensuring safety. In other words, during the simulation, multiple initial spacings are set, and simulations are performed at each spacing. Then, it is determined whether a collision occurs. If no collision occurs, the minimum spacing is selected as the final optimal anchor point spacing. The simulation model is implemented using existing simulation software, such as MATLAB.

[0056] S2. Determine the tangential velocity factor λ of the high-altitude tethered kite;

[0057] S3. Construct the governing equations for the azimuth angle Φ and pitch angle β of the high-altitude tethered kite based on the tangential velocity factor λ;

[0058] S4. Determine the anchor point of the high-altitude tethered kite and construct the high-altitude tethered kite with the smallest envelope ellipsoid; use the coordinates of the center of the smallest envelope ellipsoid as the coordinates of the high-altitude tethered kite.

[0059] S5. Construct the coordinate equation of the high-altitude tethered kite based on the anchor point location, azimuth angle Φ, and pitch angle β;

[0060] S6. Determine if a collision has occurred by using the coordinates of any two adjacent high-altitude tethered kites or the distance between their tethering lines. If so, change the anchor point spacing of the adjacent high-altitude kites and return to step S5. If not, use the minimum distance between the anchor points when no collision occurs as the anchor point spacing between the adjacent kites. This method considers the temporal variation characteristics of the pitch and azimuth angles of the high-altitude tethered kites when optimizing the anchor point spacing, thus establishing a corresponding collision detection mechanism. This avoids collisions between adjacent high-altitude tethered kites, allowing for the deployment of more kite-powered generators within a limited area without increasing the layout of ground cables and other facilities. This ensures the safe operation of the kite wind farm while guaranteeing sufficient power output and improving wind energy utilization.

[0061] In this embodiment, in step S5, the coordinate equation of the high-altitude tethered kite is constructed based on the anchor point position, azimuth angle Φ, and pitch angle β:

[0062] (1);

[0063] in: Let represent the spherical coordinates of the i-th tethered kite at time t. Let represent the straight-line distance from the anchor point of the i-th tethered kite to the kite, in spherical coordinates. This represents the pitch angle of the i-th kite. Let represent the azimuth angle of the i-th kite.

[0064] Specifically, the azimuth angle Φ of the i-th kite at time t is determined by the following method:

[0065] (2); This represents the factor that influences the trajectory of a tethered kite at high altitudes. This indicates the azimuth angle of the kite tethered in the air at the previous moment. The expression is:

[0066] ; This indicates the factor that caused the change in the trajectory of the tethered kite at the previous moment. This represents the change factor in the trajectory of the tethered kite at the current moment. This indicates the change in the trajectory variation factor of a high-altitude tethered kite;

[0067] (3);

[0068] Among them, intermediate variables for:

[0069] ;

[0070] C represents the radial amplitude coefficient. Indicates tangential velocity, , r represents the length of the kite's tethering line (this length is a variable that changes during the kite's ascent, power generation, and retrieval stages, and can also be determined directly using simulation software), and dt represents the time step between the current moment and the previous moment. and This represents the lateral amplitude coefficient. During the simulation of a tethered kite flying high altitude, and And parameter C can be determined directly through simulation software;

[0071] The pitch angle β of the i-th kite at time t is determined by the following method:

[0072] During the ascent phase, the kite climbs in a figure-eight pattern, with its heading angle changing according to the path. Figure 5 As shown, amplitude and This reflects the lateral width of the figure-eight path (i.e., the left and right sides of the middle of the figure-eight trajectory in the diagram; the left side (corresponding to the 8, the upper side is A1, and the lower side is A2) is A1, and the right side is A2), while C reflects the radial amplitude (i.e., the direction of rope extension):

[0073] (4); Indicates intermediate variables;

[0074] During the power generation phase, the heading angle is... The pitch angle decreases:

[0075] (5); Indicates the heading angle; This indicates the scaling factor for the kite during the power generation phase;

[0076] During the recovery phase, heading angle The pitch angle is reduced to its initial value:

[0077] (6); This represents the scaling factor during the kite recovery phase. Generally speaking, This allows for the rapid retrieval of the kite. At this time, due to The formula for the recovery stage is similar in form to that for the power generation stage, but the coefficients are different, i.e., the coefficients are independent, thus adapting to different recovery rate requirements.

[0078] In this embodiment, the tangential velocity factor λ is determined by the following method:

[0079] (7);

[0080] Where: a and b both represent intermediate variables;

[0081] (8);

[0082] (9);

[0083] k represents the lift-to-drag ratio. ; These represent the lift coefficient and drag coefficient of the kite, respectively. At the initial moment of kite launch, the initial values ​​of pitch and azimuth are detected and substituted into formulas (7)-(9) to determine the initial tangential velocity factor. During the ascent phase, at time t1, the initial tangential velocity factor is substituted into formulas (2) and (3) to determine the azimuth and pitch angles at time t1. The azimuth and pitch angles at time t1 are then substituted into formulas (7)-(9) to determine the tangential velocity factor at time t1. Then at time t2, the tangential velocity factor at time t1 is substituted into formulas (2) and (3) to determine the azimuth and pitch angles at time t2. The azimuth and pitch angles at time t2 are then substituted into formulas (7)-(9) to determine the tangential velocity factor at time t2. This process is repeated iteratively until... At the end of the ascent phase (the definition and determination process of the ascent phase, power generation phase and recovery phase of the high-altitude tethered kite are existing technologies and will not be elaborated here), the pitch angle and azimuth angle at the end of the ascent phase are substituted into formulas (7)-(9) to obtain the tangential velocity factor at the last moment of the ascent phase. At the initial moment of the power generation phase, the tangential velocity factor at the last moment of the ascent phase is substituted into the formulas for calculating the azimuth angle and pitch angle of the power generation phase, namely formulas (2) and (5). The azimuth angle, pitch angle and tangential velocity factor are calculated gradually according to the iterative method in the ascent phase. In the recovery phase, the azimuth angle and pitch angle are calculated using the tangential velocity factor at the end of the power generation phase, thereby obtaining several azimuth angles and pitch angles. The iterative calculation is still performed in the manner described above. By calculating several pitch and azimuth angles through the above iterations, and then substituting them into formula (1), the coordinates of the i-th high-altitude tethered kite can be obtained, that is, the coordinates of the geometric center of the minimum envelope ellipsoid. These coordinates reflect the coordinates of the i-th high-altitude tethered kite. Then, the coordinates of two adjacent high-altitude tethered kites (in formula (12), the superscripts (1) and (2) represent the two adjacent high-altitude tethered kites, and in formula (13), the subscripts 1 and 2 represent the two adjacent high-altitude tethered kites) are substituted into formula (13) to determine whether a collision has occurred. That is, the judgment condition must be met at any time to ensure the safe operation of the two adjacent kites.

[0084] in, This represents the winding factor, which is also determined based on the changes in pitch and azimuth angles, where:

[0085] Where A represents the reference area of ​​the tethered kite. Indicates wind pressure. , Indicates air density, ; This indicates the tension of the mooring rope (which can be determined by simulation software; this is existing technology).

[0086] In this embodiment, constructing a high-altitude tethered kite with a minimum envelope ellipsoid specifically includes:

[0087] Determine the external dimensions of the high-altitude tethered kite, with its length, width, and height representing 2m, 2m, and 2h, respectively;

[0088] The circumscribed ellipsoid of the high-altitude tethered kite is constructed as the minimum envelope ellipsoid, and the equation of the circumscribed ellipsoid is expressed as:

[0089] (10);

[0090] in: By using an circumscribed ellipsoid as the collision detection criterion, the collision risk oscillation caused by the curvature discontinuity resulting from the use of a cuboid envelope in traditional techniques can be avoided, thus making the collision detection more accurate.

[0091] In this embodiment, determining whether a collision has occurred based on the coordinates of any two adjacent high-altitude tethered kites or the distance between the tethering lines of two adjacent high-altitude tethered kites specifically includes:

[0092] Determine the distance between the tethering lines of two adjacent high-altitude tethered kites:

[0093] The tethering rope of the high-altitude tethered kite is discretized into N nodes, and the coordinates of the i-th node are determined by the position of the anchor point. and the position of the kite Determine by performing linear interpolation:

[0094] (11);

[0095] Any pair of nodes on the tethering lines of two adjacent high-altitude tethered kites The distance is:

[0096] (12);

[0097] when (This formula determines whether a rope collision has occurred) or (13) (This formula determines whether a collision occurs between the parachutes), then two adjacent high-altitude tethered kites will collide. Where D1 represents the parachute safety threshold and D2 represents the rope safety threshold.

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for optimizing the spacing of anchor points for safe operation of tethered kites at high altitudes, characterized in that: Includes the following steps: S1. Obtain the wind speed of the high-altitude tethered kite operating environment, establish a simulation model of the high-altitude tethered kite operation, and simulate the operating status of the high-altitude tethered kite under different wind speeds; S2. Determine the tangential velocity factor λ of the high-altitude tethered kite; S3. Construct the governing equations for the azimuth angle Φ and pitch angle β of the high-altitude tethered kite based on the tangential velocity factor λ; S4. Determine the anchor point of the high-altitude tethered kite and construct the high-altitude tethered kite with the smallest envelope ellipsoid; use the coordinates of the center of the smallest envelope ellipsoid as the coordinates of the high-altitude tethered kite. S5. Construct the coordinate equation of the high-altitude tethered kite based on the anchor point location, azimuth angle Φ, and pitch angle β; S6. Determine whether a collision has occurred by using the coordinates of any two adjacent high-altitude tethered kites or the distance between the tethering lines of two adjacent high-altitude tethered kites. If so, change the anchor point spacing of the adjacent high-altitude kites and return to step S5. If not, use the minimum distance between the anchor points when no collision occurs as the anchor point spacing between the adjacent kites.

2. The method for optimizing the anchor point spacing for safe operation of a high-altitude tethered kite according to claim 1, characterized in that: In step S5, the coordinate equation of the high-altitude tethered kite is constructed based on the anchor point position, azimuth angle Φ, and pitch angle β: ； in: Let represent the spherical coordinates of the i-th tethered kite at time t. Let represent the straight-line distance from the anchor point of the i-th tethered kite to the kite.

3. The method for optimizing the anchor point spacing for safe operation of high-altitude tethered kites according to claim 2, characterized in that: The azimuth angle Φ of the i-th kite at time t is determined by the following method: ; This represents the factor that influences the trajectory of a tethered kite at high altitudes. The expression is: ; This indicates the factor that caused the change in the trajectory of the tethered kite at the previous moment. This represents the change factor in the trajectory of the tethered kite at the current moment. This indicates the change in the trajectory variation factor of a high-altitude tethered kite; ； Among them, intermediate variables for: ； C represents the radial amplitude coefficient. Let dt represent the tangential velocity, r represent the length of the kite's tethering line, and dt represent the time step between the current moment and the previous moment. and This represents the horizontal amplitude coefficient.

4. The method for optimizing the anchor point spacing for safe operation of a high-altitude tethered kite according to claim 3, characterized in that: The pitch angle β of the i-th kite at time t is determined by the following method: Ascent Phase: ; This indicates the pitch angle of the tethered kite at the current moment. This indicates the pitch angle of the tethered kite in the air at the previous moment in the current time. Power generation stage: ; Indicates the heading angle; Indicates wind speed. This indicates the scaling factor for the kite during the power generation phase; Recycling phase: ; This represents the kite scaling factor during the recovery phase.

5. The method for optimizing the anchor point spacing for safe operation of a high-altitude tethered kite according to claim 3, characterized in that: The tangential velocity factor λ is determined using the following method: ； Where: a and b both represent intermediate variables; ； ； k represents the lift-to-drag ratio. ; These represent the lift coefficient and drag coefficient of a kite, respectively. The heading angle of a high-altitude tethered kite is represented by: 。 6. The method for optimizing the anchor point spacing for safe operation of a high-altitude tethered kite according to claim 2, characterized in that: Constructing a high-altitude tethered kite with a minimum envelope ellipsoid specifically includes: Determine the external dimensions of the high-altitude tethered kite, with its length, width, and height representing 2m, 2m, and 2h, respectively; The circumscribed ellipsoid of the high-altitude tethered kite is constructed as the minimum envelope ellipsoid, and the equation of the circumscribed ellipsoid is expressed as: ； in: .

7. The method for optimizing the anchor point spacing for safe operation of a high-altitude tethered kite according to claim 6, characterized in that: Determining whether a collision has occurred using the coordinates of any two adjacent high-altitude tethered kites or the distance between the tethering lines of two adjacent high-altitude tethered kites specifically includes: Determine the distance between the tethering lines of two adjacent high-altitude tethered kites: The tethering rope of the high-altitude tethered kite is discretized into N nodes, and the coordinates of the i-th node are determined by the position of the anchor point. and the position of the kite Determine by performing linear interpolation: ； Any pair of nodes on the tethering lines of two adjacent high-altitude tethered kites The distance is: ； when or If two adjacent high-altitude tethered kites collide, the kites will be in flight.

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