A robust beamforming method for a three-way coil magnetic wireless power transmission system

Abstract

The present invention discloses a robust beamforming method for a three-way coil magnetic wireless power transmission system, which belongs to the field of frequency wireless power transmission, including: establishing a transmission power model and a receiving power model of the system according to the electrical parameters of the system; mutual inductance m in the electrical parameters k is the static mutual inductance and J k Hadamard, J. k is the column vector of the polarization factor coefficients between the transmitting coil and the kth receiving coil taking into account the unidirectional coil angle offset; the transmission power is minimized as the optimization goal, and the receiving power of each receiving coil is not less than the energy required by the receiving coil, and m k An initial optimization problem is established, with the constraint that the norm of the difference between the sum and the inductance does not exceed the mutual inductance change threshold. This problem is then restructured into a solvable final optimization problem. Solving the final optimization problem yields the current distribution vector for the transmitting coil, which is used to control the transmitting coil for beamforming. This method improves the robustness and energy transfer efficiency of wireless power transmission systems.

Description

Technical Field

[0001] The present invention belongs to the field of frequency wireless power transmission, and more particularly, relates to a robust beamforming method for a three-directional coil magnetic wireless power transmission system. Background Art

[0002] Magnetic induction transmission technology holds great promise for deploying underwater wireless sensor networks. Its advantages, such as low power consumption, low cost, and lack of multipath and Doppler effects, make it well-suited for communication in extreme environments. Sensors in magnetic induction communication networks in these environments often require difficult-to-replace batteries. Therefore, near-field wireless power transfer (WPT), which offers convenient and efficient power transmission, is considered a viable solution for power supply in challenging environments. WPT primarily includes inductive coupling, capacitive coupling, magnetodynamic coupling, and magnetic resonance coupling. Magnetic resonance coupling is widely used due to its long power transmission distance.

[0003] To achieve a more efficient wireless power transmission system, electrical parameters are usually changed, but the improvement is limited. To further improve system performance, multiple-input multiple-output technology (MIMO) is used in WPT systems in actual designs. However, such WPT systems often use single coils as transmitting and receiving coils, without considering the directional advantages of three coils. In addition, since the environment in actual applications is not constant, especially in underwater environments or pipeline environments, channel estimation errors caused by the offset of the coil angle are inevitable. The commonly used method now is to use channel estimation to obtain channel information and change the electrical parameters based on this information to improve the performance of the WPT system. However, considering the frequent changes in the environment, repeated channel estimation to obtain channel information will result in a large amount of energy consumption, resulting in poor system performance.

[0004] In summary, current WPT transmission performance optimization methods either consume significant energy resources due to the need for sampling or channel estimation, or only consider unidirectional coils as transmitting coils, failing to leverage the excellent directionality of three coils. Given the dynamic environmental changes and energy transfer performance challenges in wireless power transmission systems, it is necessary to develop a method that can simultaneously adapt to dynamic environmental changes and improve system energy transfer performance without significantly increasing system costs. Summary of the Invention

[0005] In response to the defects and improvement needs of the existing technology, the present invention provides a robust beamforming method for a three-directional coil magnetic wireless power transmission system, which aims to improve the robustness and energy transfer efficiency of the wireless power transmission system.

[0006] To achieve the above objectives, according to one aspect of the present invention, a robust beamforming method for a three-way coil magnetic wireless power transmission system is provided. The system uses multiple three-way coils as transmitting coils and multiple unidirectional coils as receiving coils. The method includes: establishing a transmitting power model and a receiving power model of the system based on the electrical parameters of the system; wherein m in the electrical parameters is k for and J k The Hadamard product, m k is the column vector of the mutual inductance coefficient between the transmitting coil and the kth receiving coil in a dynamic environment, is the column vector of the mutual inductance coefficient between the transmitting coil and the kth receiving coil at rest, J k is the column vector of the polarization factor coefficients between the transmitting coil and the kth receiving coil taking into account the unidirectional coil angle offset; the transmission power is minimized as the optimization goal, and the receiving power of each receiving coil is not less than the energy required by the receiving coil, and m k and An initial optimization problem is established with the constraint that the difference norm of the values ​​...

[0007] Furthermore, the transmission power model is:

[0008]

[0009] Among them, P T is the transmitting power, i is the distribution vector of the transmitting coil current, i H is the conjugate transpose of i, R T is the transmitting coil resistance, N R is the number of receiving coils, R R is the receiving coil resistance, ω is the carrier angular frequency, m k T is m k The transpose of .

[0010] Furthermore, the received power model is:

[0011]

[0012] Among them, P R,k is the receiving power of the kth receiving coil, R R is the receiving coil resistance, ω is the carrier angular frequency, R RL is the load resistance, i is the distribution vector of the transmitting coil current, iH is the conjugate transpose of i, m k T is m k The transpose of .

[0013] Furthermore, J k for:

[0014]

[0015] Among them, H k is the polarization factor change matrix, is the column vector of the polarization factor coefficients between the transmitting coil and the kth receiving coil at rest, Represents the Hadamard product.

[0016] Furthermore, when the main coil of the transmitting coil and the receiving coil are initially positioned in the same direction, H k for:

[0017]

[0018] Among them, H m,k is the polarization change column vector between the mth transmitting coil and the kth receiving coil, φ is the angle between the transmitting coil position vector and the positive Z-axis, θ is the angle between the projection vector of the transmitting coil position vector on the XY plane and the positive X-axis, and x, y, and z are the coordinates of the receiving coil direction vector.

[0019] Furthermore, the initial optimization problem is sequentially subjected to relaxation processing, S lemma reconstruction and penalty-based continuous convex approximation processing, specifically including: using a robust beamforming method that combines a semidefinite programming relaxation method and a penalty-based continuous convex approximation method to reconstruct the initial optimization problem into a first optimization problem; using the S lemma to reconstruct the first optimization problem into a second optimization problem; and using a penalty-based continuous convex approximation method to reconstruct the second optimization problem into the final optimization problem.

[0020] Furthermore, the final optimization problem is:

[0021]

[0022] C3:λ k ≥0,δ k ≥0,ξ k ≥0,k=1,...,N R

[0023]

[0024] Among them, tr() means finding the trace of the matrix, R T is the transmitting coil resistance, X is the current vector matrix, X=iiH , i is the distribution vector of the transmitting coil current, i H is the conjugate transpose of i, ξ k is the slack variable, N R is the number of receiving coils, μ is the penalty factor, || || * represents the kernel specification operation, X [l] is the X obtained in the first iteration, || ||2 represents the operation of spectrum specification, For X [l] The eigenvector corresponding to the maximum eigenvalue of for The conjugate transpose of C1, C2, C3 and C4 together constitute the constraints, Γ k (),Φ k () are the matrices reconstructed from the C1 and C2 constraints of the second optimization problem, respectively. k is the first parameter greater than 0, δ k The second parameter is greater than 0.

[0025] According to another aspect of the present invention, a robust beamforming device for a three-directional coil magnetic wireless power transmission system is provided. The system uses multiple three-directional coils as transmitting coils and multiple unidirectional coils as receiving coils. The device includes: a processor; and a memory storing a computer-executable program. When the program is executed by the processor, the processor executes the robust beamforming method for the three-directional coil magnetic wireless power transmission system as described above.

[0026] According to another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the program is executed by a processor, the robust beamforming method for the three-directional coil magnetic wireless power transmission system as described above is implemented.

[0027] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

[0028] (1) A robust beamforming method for a three-way coil magnetic wireless power transmission system is provided, and a multi-transmitter and multi-receiver magnetic-based wireless power transmission system with three-way coils as transmitting coils is designed. The designed system has better directivity. Furthermore, a robust beamforming method is designed for the system. When establishing the system receiving and transmitting power model, the influence of the unidirectional coil angle offset on the mutual inductance coefficient of the transmitting and receiving coils is considered. When establishing the constraint conditions of the optimization problem, the deviation of the mutual inductance coefficient of the transmitting and receiving coils in a dynamic environment relative to the mutual inductance coefficient of the transmitting and receiving coils in a static state is constrained. Therefore, a three-coil polarization factor model (i.e., optimization problem) is established in the scenario of imperfect magnetic mutual inductance information (MII). By introducing a norm-bounded MII error model, the problem is converted into a worst-case optimization problem, thereby improving the robustness and energy transfer efficiency of the wireless power transmission system.

[0029] (2) Since the initial optimization problem (the model considering the worst-case non-perfect mutual inductance) is a non-rank-one problem with infinite constraints, the S lemma can transform the infinite constraints into a finite number of constraints, and the penalty-based continuous convex approximation method can effectively transform the non-rank-one problem into a rank-one problem. Through these two methods, the optimization problem can take into account the case of imperfect mutual inductance information, and the robustness of the system can be improved without increasing excessive energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 A flowchart of a robust beamforming method for a three-directional coil magnetic wireless power transmission system provided by an embodiment of the present invention;

[0031] Figure 2 A system model of a three-way coil magnetic wireless power transmission system provided in an embodiment of the present invention;

[0032] Figure 3 A power efficiency comparison chart of the robust beamforming method provided by an embodiment of the present invention, the traditional single-coil method, and the uniform distribution method;

[0033] Figure 4 A comparison chart of the power efficiency of the robust beamforming method provided by an embodiment of the present invention, the traditional non-robust method, and the uniform allocation method. DETAILED DESCRIPTION

[0034] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0035] In the present invention, the terms "first", "second", etc. (if any) in the present invention and the drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0036] Example 1

[0037] A robust beamforming method for a three-way coil magnetic wireless power transmission system, see Figure 1 , Figure 2-Figure 4 , the robust beamforming method of the three-directional coil magnetic wireless power transmission system in this embodiment is described in detail, and the method includes operations S1 to S4.

[0038] The three-way coil magnetic wireless power transmission system uses multiple three-way coils as transmitting coils and multiple unidirectional coils as receiving coils.

[0039] Since the three-way coil is larger than the unidirectional coil, it is suitable for placement on the transmitter side where miniaturization is not required. Therefore, the three-way coil is used as the transmitting coil and fixed on the power supply device, and the unidirectional coil is used as the receiving coil and placed on the terminal device. Due to environmental fluctuations, the unidirectional coil on the terminal device may produce an angle deviation, resulting in errors in the magnetic mutual induction information. Figure 2 As shown in the figure, the magnetic induction WPT system is taken as an example, where N T A three-way coil is used as the transmitting coil, N R A unidirectional coil is used as the receiving coil, all the transmitting coils are fixed at the same height, and the receiving coils are randomly distributed under the transmitting array. The current distribution of the transmitting coil is calculated to improve the system charging efficiency.

[0040] Operation S1: Establish a transmission power model and a receiving power model of the system according to the electrical parameters of the system; wherein m in the electrical parameters is k for and J k The Hadamard product, m k is the column vector of the mutual inductance coefficient between the transmitting coil and the kth receiving coil in a dynamic environment, is the column vector of the mutual inductance coefficient between the transmitting coil and the kth receiving coil at rest, J k is the column vector of the polarization factor coefficients between the transmitting coil and the kth receiving coil taking into account the unidirectional coil angle offset.

[0041] According to the equivalent circuit model, the circuit model of the magnetic induction WPT system is as follows: Figure 2 When the electrical parameters are known, the transmission power model is:

[0042]

[0043] Among them, P T is the transmitting power, i is the distribution vector of the transmitting coil current, iH is the conjugate transpose of i, R T is the transmitting coil resistance, N R is the number of receiving coils, R R is the receiving coil resistance, ω is the carrier angular frequency, m k T is m k The transpose of .

[0044] The received power model is:

[0045]

[0046] Among them, P R,k is the receiving power of the kth receiving coil, R RL is the load resistance.

[0047] m k By J k The influence of , there is the following relationship:

[0048]

[0049] in, In this embodiment, m=1,2,...,N T is the number of the transmitting coil, n = 1, 2, 3 is the number of the three coils in the three-way coil, k = 1, 2, ..., N R Number the receiving coil.

[0050] J k Controlled by the position and angle of the transceiver coil, J k The relationship with the position and angle of the transceiver coil is:

[0051]

[0052] in, For J k The 3(m-1)+n term is the polarization coefficient of coil number n in the mth three-way coil. Since the three transmitting coils are orthogonal to each other, assume that the direction vector of the first coil is o m,1 =[cosφ T sinθ T ,sinφ T sinθ T ,cosθ T ] T , then the direction vectors of the second and third coils are o m,2 =[-cosφ T cosθ T ,-sinφ Tcosθ T ,sinθ T ]、o m,3 =[-sinφ T ,-cosφ T ,cosθ T ]. Fix one of the transmitting coils so that its direction vector is in the same direction as the z-axis and name it the main coil.

[0053] Because of the angle offset, J k There will be errors. Assume that the stationary Then the offset J k Meeting and stillness There is an error, namely ΔJ k ,but The direction vector of the receiving coil is o k =[x k ,y k ,z k ],in z k =ξ1, ξ1 and ξ2 are variables used to measure the severity of the coil angle change. The larger the range of ξ1 and ξ2, the more severe the coil angle change.

[0054] J k It can be expressed as:

[0055]

[0056] Among them, H k is the polarization factor change matrix, is the column vector of the polarization factor coefficients between the transmitting coil and the kth receiving coil at rest.

[0057] When the main coil of the transmitting coil and the receiving coil are initially in the same direction, H k for:

[0058]

[0059] Among them, H m,k is the polarization change column vector between the mth transmitting coil and the kth receiving coil, φ is the angle between the transmitting coil position vector and the positive Z-axis, θ is the angle between the projection vector of the transmitting coil position vector on the XY plane and the positive X-axis, and x, y, and z are the coordinates of the receiving coil direction vector.

[0060] Operation S2, with the minimum transmission power as the optimization goal, the receiving power of each receiving coil is not less than the energy required by the receiving coil, and m k and The difference norm is not higher than the mutual inductance change threshold as a constraint condition, and the initial optimization problem is established.

[0061] In practical applications, the real-time change in mutual inductance caused by angular offset will affect the design of magnetic beam forming. Therefore, this embodiment minimizes the total transmission power while taking into account the charging requirement constraints. After taking the offset of the angular polarization factor into account, the initial optimization problem of magnetic beam forming can be expressed as:

[0062]

[0063] C2:||Δm k ||≤ε k

[0064] Among them, b k The energy required by the receiving coil is determined by the energy storage capacity of the receiving coil and the energy consumed; ε k is the mutual inductance change threshold, Δm k is m k and Due to Δm k So there exists and in the case of finite angular displacement Δm k There is a threshold, namely ||Δm k ||≤ε k .

[0065] In operation S3, the initial optimization problem is sequentially subjected to relaxation processing, S-lemma reconstruction, and penalty-based continuous convex approximation processing to reconstruct the initial optimization problem into a final optimization problem.

[0066] Since the initial optimization problem constructed is a non-convex optimization problem that cannot be solved directly, it needs to be processed to convert it into an optimization problem that can be solved directly.

[0067] According to an embodiment of the present invention, the initial optimization problem is sequentially subjected to relaxation processing, S-lemma reconstruction, and penalty-based continuous convex approximation processing, specifically including the following sub-operations S31 to S33.

[0068] In sub-operation S31, the robust beamforming method combined with the semidefinite programming relaxation method is used to reconstruct the initial optimization problem into a first optimization problem:

[0069]

[0070] C3:||Δm k ||≤ε k

[0071] Among them, ξ k is the slack variable.

[0072] In sub-operation S32, the first optimization problem is reconstructed into a second optimization problem using the S-lemma.

[0073] Since ||Δm k ||≤ε k , so Δm k There are infinitely many implementations, which leads to an infinite number of constraints in the problem, making it difficult to solve. Therefore, in order to simplify the complex constraints, we further use the S lemma to restructure the first optimization problem into a second optimization problem:

[0074]

[0075] C3:λ k ≥0,δ k ≥0,ξ k ≥0,k=1,...,N R

[0076]

[0077] C5:rank(X)=1

[0078] Among them, Γ k (X,λ k ),Φ k (X,δ k ,ξ k ) are:

[0079]

[0080] In sub-operation S33 , the second optimization problem is reconstructed into a final optimization problem using a penalty-based continuous convex approximation method.

[0081] Since the rank-one constraint in the second optimization problem makes the problem non-convex, the penalty-based continuous convex approximation method is used to reformulate the second optimization problem into the final optimization problem:

[0082]

[0083] C3:λ k ≥0,δ k ≥0,ξ k ≥0,k=1,...,N R

[0084]

[0085] Among them, tr() means finding the trace of the matrix, R T is the transmitting coil resistance, X is the current vector matrix, X=ii H , i is the distribution vector of the transmitting coil current, i H is the conjugate transpose of i, ξ k is the slack variable, N Ris the number of receiving coils, μ is the penalty factor, || || * represents the kernel specification operation, X [l] is the X obtained in the first iteration, || ||2 represents the operation of spectrum specification, For X [l] The eigenvector corresponding to the maximum eigenvalue of for The conjugate transpose of C1, C2, C3 and C4 together constitute the constraints, Γ k (),Φ k () are the matrices reconstructed from the C1 and C2 constraints of the second optimization problem, respectively. k is the first parameter greater than 0, δ k The second parameter is greater than 0.

[0086] In this way, the initial optimization problem is transformed into a final optimization problem that can be solved using existing optimization tools.

[0087] In operation S4, the final optimization problem is solved to obtain a distribution vector of the transmitting coil current, and the transmitting coil is controlled to perform beamforming according to the distribution vector of the transmitting coil current.

[0088] Specifically, the final optimization problem can be solved directly using the CVX toolbox. The resulting distribution vector i for the corresponding transmitting coil current can be obtained. Using this current as the transmitting current improves charging efficiency while accounting for angle offset.

[0089] The method is explained using two sets of transmitting coils, three sets of receiving coils, and a center frequency of 10MHz. Both the transmitting and receiving coils have a radius of 0.1m, 100 turns, and require the same power. The larger the v is, the greater the mutual inductance error caused by the angle offset is, and the channel information is less accurate.

[0090] Figure 4 The figure shows the variation of power efficiency with v for the non-robust solution, the same current solution, and the solution of the embodiment of the present invention when the battery capacity is different. Figure 4 As shown in the figure, when the maximum required power is five times the minimum required power, the MII estimation error for each receiving coil is compared to the uniform feeding scheme. When v = 0.2, the power efficiency of the embodiment of the present invention is 77.7%, while the power efficiencies of the same current and non-robust schemes are 51.5% and 70.4%, respectively. Numerically, the embodiment of the present invention can improve the power efficiency by 25.9% and 7.0%, respectively, compared to the same current and non-robust schemes.

[0091] The following describes the application of this method in an ideal situation (underground deployment where the coil angle hardly deviates and the mutual inductance information is considered accurate). For a system with accurate mutual inductance information, the current distribution of the beamforming is obtained using the formula, i.e., ε k = 0, the optimization problem is as follows:

[0092]

[0093] Let X = ii H 、 The above optimization problem can be equivalent to the SDP problem with constraint 1:

[0094]

[0095] C3:rank(X)=1

[0096] Among them, constraint C3 is to ensure that the unit module constraint of i can be recovered from X.

[0097] For the case of a known channel, the solution should be . However, the problem is non-convex due to the constraint C3. Removing the rank constraint can give the SDR problem. To solve this problem, the rank-one constraint C3 in the problem is transformed into the following form:

[0098]

[0099] For X∈Η m ,have λ i (X)≥||X||2=max i λ i holds, where λ i represents the i-th singular value of X. The equality relation holds if and only if X is a rank-one matrix. Therefore, the rank-one constraint C3 in the problem is equivalent to But the constraints is an affine-convex form. To overcome the non-convexity, we use a penalty method to transform the problem into the following problem:

[0100]

[0101] Among them, μ is used to punish the violation of constraints behavior.

[0102] In the case of 2 transmitters and 3 receivers, a center frequency of 10MHz, and a radius of 0.1m and 100 turns for both the transmitter and receiver coils, the power efficiency performance is as follows when the receiver coils are randomly distributed in a 1m×1m area and a 2m×2m area: Figure 3 shown.

[0103] See Figure 3 It can be seen that when channel information is known, the average performance of the embodiment of the present invention outperforms the most common single-coil beamforming solution and uniform feeding solution by 39.9% and 52.5%, respectively. When the receiving coils are distributed within a 2m×2m area, the average performance of the embodiment of the present invention outperforms the three-coil beamforming solution and uniform feeding solution by 15.8% and 17.6%, respectively. This information shows that the embodiment of the present invention offers significant performance improvements over current single-coil beamforming solutions, and the performance improvement is greater as the receiving coils are distributed more closely.

[0104] Example 2

[0105] A robust beamforming device for a three-way magnetic wireless power transmission system employs multiple three-way coils as transmitting coils and multiple unidirectional coils as receiving coils. The device includes a processor and a memory storing a computer-executable program. When executed by the processor, the program causes the processor to perform the robust beamforming method for the three-way magnetic wireless power transmission system. The related technical solutions are the same as those in Example 1 and are not further described here.

[0106] Example 3

[0107] A computer-readable storage medium stores a computer program that, when executed by a processor, implements the robust beamforming method for the three-way coil magnetic wireless power transmission system. The related technical solutions are the same as those in Example 1 and will not be described in detail here.

[0108] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A robust beamforming method for a three-way coil magnetic wireless power transmission system, characterized in that: The system uses multiple three-way coils as transmitting coils and multiple unidirectional coils as receiving coils. The method includes: The system's transmit power model and receive power model are established based on the system's electrical parameters. The transmit power model is: Among them, P T is the transmitting power, i is the distribution vector of the transmitting coil current, i H is the conjugate transpose of i, R T is the transmitting coil resistance, N R is the number of receiving coils, R R is the receiving coil resistance, ω is the carrier angular frequency, m k T is m k The transpose of; wherein, m in the electrical parameter k for and J k The Hadamard product, m k is the column vector of the mutual inductance coefficient between the transmitting coil and the kth receiving coil in a dynamic environment, is the column vector of the mutual inductance coefficient between the transmitting coil and the kth receiving coil at rest, J k is the column vector of the polarization factor coefficients between the transmitting coil and the kth receiving coil taking into account the unidirectional coil angle offset, Among them, H k is the polarization factor change matrix, is the column vector of the polarization factor coefficients between the transmitting coil and the kth receiving coil at rest, represents the Hadamard product; The optimization goal is to minimize the transmission power. The receiving power of each receiving coil is not less than the energy required by the receiving coil, and m k and The difference norm is not higher than the mutual inductance change threshold as a constraint condition, and the initial optimization problem is established; The initial optimization problem is subjected to relaxation processing, S-lemma reconstruction, and penalty-based continuous convex approximation processing in sequence to reconstruct the initial optimization problem into a final optimization problem. The final optimization problem is: C3:λ k ≥0,δ k ≥0,ξ k ≥0,k=1,...,N R Among them, tr() means finding the trace of the matrix, R T is the transmitting coil resistance, X is the current vector matrix, X=ii H , i is the distribution vector of the transmitting coil current, i H is the conjugate transpose of i, ξ k is the slack variable, N R is the number of receiving coils, μ is the penalty factor, || || * represents the kernel specification operation, X [l] is the X obtained in the first iteration, || ||2 represents the operation of spectrum specification, For X [l] The eigenvector corresponding to the maximum eigenvalue of for The conjugate transpose of C1, C2, C3 and C4 together constitute the constraints, Γ k (),Φ k () are the matrices reconstructed by the C1 and C2 constraints, respectively, k is the first parameter greater than 0, δ k is the second parameter greater than 0; The final optimization problem is solved to obtain a distribution vector of the transmitting coil current, and the transmitting coil is controlled to perform beamforming according to the distribution vector of the transmitting coil current.

2. The robust beamforming method for a three-way coil magnetic wireless power transmission system according to claim 1, wherein: The received power model is: Among them, P R,k is the receiving power of the kth receiving coil, R R is the receiving coil resistance, ω is the carrier angular frequency, R RL is the load resistance, i is the distribution vector of the transmitting coil current, i H is the conjugate transpose of i, m k T is m k The transpose of .

3. The robust beamforming method for a three-way coil magnetic wireless power transmission system according to claim 1, wherein: When the main coil of the transmitting coil and the receiving coil are initially in the same direction, H k for: Among them, H m,k is the polarization change column vector between the mth transmitting coil and the kth receiving coil, φ is the angle between the transmitting coil position vector and the positive Z-axis, θ is the angle between the projection vector of the transmitting coil position vector on the XY plane and the positive X-axis, and x, y, and z are the coordinates of the receiving coil direction vector.

4. The robust beamforming method for a three-way coil magnetic wireless power transmission system according to any one of claims 1 to 3, characterized in that: The initial optimization problem is subjected to relaxation processing, S-lemma reconstruction, and penalty-based continuous convex approximation processing in sequence, specifically including: Reconstructing the initial optimization problem into a first optimization problem using a robust beamforming method combined with a semidefinite programming relaxation method; Reconstruct the first optimization problem into a second optimization problem using the S lemma; The second optimization problem is reconstructed into the final optimization problem using a penalty-based continuous convex approximation method.

5. A robust beamforming device for a three-way coil magnetic wireless power transmission system, characterized in that: The system uses multiple three-way coils as transmitting coils and multiple unidirectional coils as receiving coils. The equipment includes: processor; A memory storing a computer-executable program, wherein when the program is executed by the processor, the processor executes the robust beamforming method for the three-directional coil magnetic wireless power transmission system according to any one of claims 1 to 4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the robust beamforming method of the three-directional coil magnetic wireless power transmission system is implemented according to any one of claims 1 to 4.

Images