CN112968535B - Load coil position detection method for omnidirectional wireless power transmission system - Google Patents
Load coil position detection method for omnidirectional wireless power transmission system Download PDFInfo
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- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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- Y02T10/00—Road transport of goods or passengers
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Abstract
The invention provides a load coil position detection method for an omnidirectional wireless power transmission system, which converts the problem of load coil position detection in a two-dimensional and three-dimensional omnidirectional WPT system into the problem of input power maximization search of the omnidirectional WPT system after mathematical modeling analysis. The optimal step angle is calculated based on the gradient descent method of the Barz i a i-Borwe i n method, so that the optimal step angle in each iteration process can be realized, the iteration times are reduced, the current injected into the three-phase orthogonal transmitting coil is rapidly disturbed, the rapid search of the maximum input power is realized, the purpose of rapidly positioning the position of the load coil is achieved, and the maximum transmission efficiency is realized.
Description
Technical Field
The invention belongs to the technical field of wireless power transmission, and relates to a load coil position detection method for an omnidirectional wireless power transmission system.
Background
Wireless power transfer (Wireless Power Transfer, WPT) technology has become an emerging solution for charging electronic devices due to its convenience and security. With the gradual use of WPT, more and more electronic products, such as smartphones, smartwatches, tablet computers, and notebook computers, support wireless charging. In general, mobile electronic products such as mobile phones and smart watches need to be fixed on a charging board during charging, and users cannot freely use equipment during charging, which is inconvenient in practical use, unlike users hope, and the mobile electronic products can still freely use equipment during charging in the same way as traditional wired charging.
To solve the above problems, more and more students are beginning to pay attention to the problem of spatial freedom of WPT system. For the WPT system with the conventional two-coil and four-coil structure, the generated magnetic field points to a specific direction, and if the receiving coil is shifted in position or rotated, the transmission efficiency is greatly reduced, so that the conventional two-coil and four-coil structure is not suitable for application occasions with high requirements on movement, particularly for intelligent wearable equipment. In order to improve the space freedom of the wireless power transmission system, an effective solution is to use a multiphase orthogonal transmitting coil, generate an omnidirectional magnetic vector by using a current control method, and obtain omnidirectional wireless power transmission capability regardless of whether the wireless power transmission system moves or not. Studies have shown that transmitting wireless power directly to a target load is the most energy efficient method, rather than transmitting power in all directions. Therefore, in order to improve the transmission efficiency and reduce the charging time, the difficulty of the solution is that in practical application, it is difficult to obtain the position information of the load coil (i.e. the receiving coil) in real time, and directional transmission of the wireless power to the load coil cannot be guaranteed, so that the highest transmission efficiency of the system cannot be realized. Current amplitude modulation in the existing current control method is most suitable for realizing directional transmission of wireless power to a load coil. Based on the current control method, the current method for detecting the position of the load coil is to inject current into three orthogonal transmitting coils to sequentially generate a plurality of magnetic vectors, each magnetic vector is coupled with the magnetic field of the load coil, all the magnetic vectors are scanned once, a distorted spherical surface is generated, and the position corresponding to the magnetic vector added when the distortion degree is maximum is the position where the load coil is located. It can be seen that a large number of magnetic vectors need to be scanned once each time a load coil position detection is performed, so this approach is not suitable for frequently moving load coil position detection.
It is noted that this section is intended to provide a background or context for the embodiments of the invention that are recited in the claims. The description herein is not admitted to be prior art by inclusion in this section.
Disclosure of Invention
The invention aims to provide a load coil position detection method for an omnidirectional wireless power transmission system, which can rapidly position the load coil position and realize maximum transmission efficiency.
The invention adopts the following technical scheme to realize the purposes:
the method for detecting the position of the load coil of the omnidirectional wireless power transmission system comprises the following steps:
s1: setting initial parameters
Establishing a mathematical model of an omnidirectional wireless power transmission system, and setting theta and thetaFor the physical angle of the synthesized current vector on the three-dimensional plane, the input power P in the initial state is obtained according to the sampled direct current voltage and direct current in (0, 0), proceeding to step S2; wherein θ is the current vector +.>Forward included angle with Z axis, +.>For current vector->The projection on the XOY plane forms an included angle with the positive X axis;
s2: calculating initial state information
Calculating information of an initial state based on a gradient descent method of a Barzilai-Borwein method;
s3: calculating the theta partial derivative of the objective function at the moment k;
calculating the given value of each phase transmitting coil current at the present moment, executing current control, and obtaining the input power at the k moment according to the sampled direct current voltage and direct current after the current is stabilizedThen calculate the target function of k momentPartial derivative of θ ->
calculating the given value of the current of each phase transmitting coil at the present moment, and executing current control; after the current is stabilized, obtaining the input power at the moment k according to the sampled direct current voltage and direct current Calculating the k moment objective function about +.>Partial derivative of>
S5: θ partial derivative sum based on k moment objective functionCalculating the optimal step length alpha by partial derivative;
s6: according to the calculated optimal step length alpha, theta (k+1) and theta (alpha+1) at the moment of k+1 are obtained
S7: the θ (k+1) at time k+1 is added toAssigning values to θ and +.>Calculating the current transmitting coilsThe current value, after the current is stable, the input power of k+1 moment is obtained according to the sampled direct current voltage and direct current>And will beAssign->
S8: saving information at the moment k, completing one iteration based on a Barzilai-Borwein method gradient descent method, adding 1 to iteration times N, and entering a step 9;
s9: if the maximum iteration number or the objective function value calculated by two iterations is reachedIf the set error requirement is met, ending the iteration and outputting theta (k) and +.>The actual physical position of the load coil; if none of them meets the setting error requirement, θ (k) and +.>Assigning values to θ and +.>And returning to the step S3.
Further, the step S2 specifically includes:
s201: calculating the partial derivative of the initial state objective function;
calculating the given value of the current of the three-phase transmitting coil at the present moment according to the formula (20), performing current control, and obtaining the input power P in the initial state according to the sampled direct current voltage and the sampled direct current after the current is stabilized in (Δθ, 0), and P in (Δθ, 0) is given to F (Δθ, 0);
from equation (21), the partial derivative of the initial state objective function with respect to θ can be calculatedAnd assign it +.>
calculating a given value of the current of the three-phase transmitting coil at the present moment according to a formula (22), and executing current control; after the current is stabilized, obtaining the input power in the initial state according to the sampled direct current voltage and direct currentAnd will beAssign->
From equation (23), the initial state objective function is calculatedPartial derivative of>And assign it +.>
Calculating the given value of the current of each phase transmitting coil at the next moment according to the formula (24), and executing current control; after the current is stabilized, obtaining the input power at the next moment according to the sampled direct current voltage and direct currentAnd will beAssign->
Storing the current time information according to a formula (25), wherein alpha takes a value of 0.5; and sum θ (k) of the current timeAssigning values to θ and +.>Step S3 is entered;
further, the step S3 specifically includes:
calculating the given value of each phase transmitting coil current at the present moment according to the formula (26), performing current control, and obtaining the input power at the k moment according to the sampled direct current voltage and direct current after the current is stabilized/>
Calculating the partial derivative of the objective function at the moment k with respect to θ from the equation (27)And assign it +.>Step S4 is entered;
further, the step S4 specifically includes:
calculating the given value of the current of each phase transmitting coil at the present moment according to the formula (28), and executing current control; after the current is stabilized, obtaining the input power at the moment k according to the sampled direct current voltage and direct currentAnd will beAssign->
Further, the step S5 specifically includes:
definition of s according to the Barzilai-Borwein method k 、z k :
Wherein s is k The vector difference, denoted as search points at time k and time k-1; z k The gradient difference of the search point vector is expressed as k time and k-1 time; x is x k A vector denoted as search point at time k; x is x k-1 A vector denoted as the search point at time k-1;a gradient denoted as a search point vector at time k; />A gradient denoted as a search point vector at time k-1;
calculating the optimal step length alpha according to the formula (31), and entering a step S6;
further, the step S6 specifically includes:
from the calculated optimal step alpha, the k+1 time θ (k+1) and the k+1 time θ can be calculated from the equation (32)And proceeds to step S7; />
Further, the step S8 specifically includes:
storing information at the k moment according to a formula (33), completing one iteration of a gradient descent method based on a Barzilai-Borwein method, adding 1 to iteration times N, and entering a step S9;
the invention has the beneficial effects that:
the load coil position detection method for the omnidirectional wireless power transmission system is suitable for the two-dimensional and three-dimensional omnidirectional WPT system, and converts the problem of load coil position detection in the two-dimensional and three-dimensional omnidirectional WPT system into the problem of input power maximization search of the omnidirectional WPT system after mathematical modeling analysis. The optimal step angle is calculated based on the gradient descent method of the Barzilai-Borwein method, so that the optimal step angle in each iteration process can be realized, the iteration times are reduced, the current injected into the three-phase orthogonal transmitting coil is rapidly disturbed, the rapid search of the maximum input power is realized, the purpose of rapidly positioning the position of the load coil is achieved, and the maximum transmission efficiency is realized.
Drawings
Fig. 1 is an equivalent schematic diagram of a three-dimensional omnidirectional wireless power transmission system of the present invention;
FIG. 2 is a schematic diagram of the three-phase coil synthesis vector generation of the present invention;
fig. 3 is a flow chart of the present invention.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. However, the exemplary embodiments may be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the example embodiments to those skilled in the art. The described features or characteristics may be combined in any suitable manner in one or more embodiments.
Based on the current amplitude modulation principle and the mathematical model of the omnidirectional WPT system, for the system structure of the three-phase orthogonal transmitting coil and one load coil, the maximum load power P can be obtained simultaneously when the magnetic vector angle and the physical angle of the load coil are completely equal out Maximum input power P in And a maximum transmission efficiency η. It is therefore only necessary to search for the maximum input power by current amplitude modulation at the transmitting end, so that both maximum load power and maximum transmission efficiency can be achieved.
From the electromagnetic induction theorem, the magnetic vector angle (θ and θ are the two-dimensional omnidirectional WPT system and θ are the three-dimensional omnidirectional WPT system)) And the physical angle of the load coil (the two-dimensional omnidirectional WPT system is theta * The three-dimensional omnidirectional WPT system is theta * And->) When the magnetic fluxes obtained by the load coils are the largest when the magnetic fluxes are completely equal, and the load coils can receive the maximum power at the moment. Therefore, the corresponding magnetic vector angle when the maximum load power is realized is the physical angle of the load coil. Therefore, an optimal step angle is obtained by a gradient descent method based on a Barzilai-Borwein method, and the magnetic vector angle is disturbed by the optimal step angle, so that the current injected into the three-phase orthogonal transmitting coil is changed, the input power of the omnirange WPT system after the current is disturbed is detected, and the corresponding magnetic field is obtained when the input power reaches the maximumVector angle (two-dimensional omnidirectional WPT system is θ, three-dimensional omnidirectional WPT system is θ and +.>) I.e. the actual physical position of the load coil (two-dimensional omnidirectional WPT system is theta * The three-dimensional omnidirectional WPT system is theta * And->)。
The present invention will be described in detail with reference to the accompanying drawings and the detailed description.
Firstly, establishing a mathematical model of an omnidirectional wireless power transmission system, and obtaining an objective function. A three-dimensional omni-directional wireless power transmission system is exemplified here, but the method is equally applicable to a two-dimensional omni-directional wireless power transmission system.
Fig. 1 is an equivalent schematic diagram of a three-dimensional omnidirectional wireless power transmission system consisting of three orthogonal transmit coils and one receive coil. Wherein V is dc And I dc Respectively a direct current power supply voltage and a direct current power supply current; q (Q) 1 -Q 12 Switching tubes for three groups of single-phase bridge type inversion currents; l (L) 1 、L 2 、L 3 The inductance of each phase of transmitting coil is respectively; c (C) 1 、C 2 、C 3 Compensation capacitors of the transmitting coils of each phase respectively; r is R 1 、R 2 、R 3 Parasitic resistances of the transmitting coils of the phases respectively; l (L) 4 An inductance for the receiving coil; c (C) 4 A compensation capacitance for the receiving coil; r is R 4 Parasitic resistance of the receiving coil; r is R L Is an equivalent load resistance; m is M n4 (n=1, 2, 3) represents mutual inductance of each phase transmitting coil and receiving coil; m is M 12 、M 23 、M 13 Representing mutual inductance between the transmitting coils of each phase; u (U) 1 、U 2 、U 3 Respectively representing the bridge port output voltage of each phase of inverter; i 1 、I 2 、I 3 Respectively representing the current flowing into each phase of transmitting coil; i 4 Indicating the current flowing into the receiving coil.
As shown in fig. 2, θ andis the physical angle of the composite current vector on the three-dimensional plane, where θ is the current vector +.>Forward included angle with Z axis, +.>For current vector->The projection on the XOY plane forms an included angle with the positive X axis; n is the iteration times of the gradient descent method; delta theta is the step length of theta in the gradient descent method; />Is>Is a step length of (2); alpha is the learning rate of the gradient descent method; θ (k) is the value of θ at time k; />For time k->Is a value of (2); θ (k-1) is the value of θ at time k-1; />Time k-1Is a value of (2); />The value of the objective function at the current moment; />Is->Fixing, wherein theta is provided with a corresponding objective function value of delta theta; />Is fixed by theta and is->With increment->Corresponding objective function values. />Time k-1Partial derivative with respect to θ; />For time k-1->About->Is a partial derivative of (2); />For time k->Partial derivative with respect to θ; />For time k->About->Is a partial derivative of (c).
For a single planar circular coil, the magnetic flux density at the center of the coil can be found by the Biot-Savart theoremIs that
In the method, in the process of the invention,and->Tangential unit vectors and radial unit vectors of the planar circular coils respectively; r is the radius of the coil; mu (mu) 0 Is vacuum magnetic permeability; n (N) P Is the number of turns of the coil. From the right-hand screw rule, +.>Perpendicular to the planar circular coil.
Similarly, the magnetic flux density at the center of the three-phase coilEqual to the magnetic flux density of the center of the respective coil>Vector sum of (i=1, 2, 3).
Wherein I is 1 、I 2 And I 3 Respectively representing the effective values of currents flowing into the three transmitting coils;the unit vectors of the X axis, the Y axis and the Z axis are respectively shown.
Three transmitting coils are provided and are powered by an in-phase and same-frequency alternating current power supply,and->The current vectors flowing into the transmitting coils of the respective phases are shown separately. According to the current amplitude control principle, the effective value I of the current flowing into three transmitting coils 1 、I 2 And I 3 Respectively is
Wherein θ andis the physical angle of the resultant current vector on the three-dimensional plane, as shown in FIG. 2, where θ is the resultant current vector +.>Forward included angle with Z axis, +.>For synthesizing current vector +.>The projection in the XOY plane is at an angle to the positive X-axis. Three current vectors>And->A resultant current vector can be generated>I is the resultant current vector->Is a function of the magnitude of (a). From the above analysis, it is known that the magnetic flux density at the center of the three-phase coil +.>And the combined current vector->In the same direction, the magnitude is proportional to the amplitude I, thus by varying θ and +.>Can change the magnetic flux density in the center of the three-phase coil>And provides an omnidirectional magnetic field in three dimensions.
Is provided withAnd->Is 0. According to FIG. 1, the KVL equation can be listed as shown in equation (4)
In the method, in the process of the invention,and->And the output voltage vectors of the bridge ports of the inverters of the respective phases are respectively shown. Three transmit coils are orthogonal to each other, thus M 12 =M 13 =M 23 =0. Therefore, the formula (4) can be simplified into
Wherein X is 1 、X 2 、X 3 、X 4 Represented by formula (6).
Effective value I of current flowing into receiving coil 4 Is that
Equation (7) characterizes the current flowing into the receiving coil, from equation (7) the power P received by the load can be calculated load Is that
Also, the power P received by the receiving coil out Is that
Input power P of DC source in Loss P including inverter inv Ohm of transmitting coilLoss P loss Received power P of receiving coil out . The ohmic losses of the transmitting coil include the ohmic losses P of the transmitting coil 1 loss1 Ohmic loss P of transmitting coil 2 loss2 And ohmic loss P of transmitting coil 3 loss3 . The loss of the three-phase transmitting coil can be calculated by equation (11).
To simplify the analysis, the resistances of the three transmit coils are considered equal, satisfying the following equation:
R 1 =R 2 =R 3 =R (12)
thus, ohmic loss P of the transmitting coil can be calculated loss Is that
P loss =P loss1 +P loss2 +P loss3 =I 2 R (13)
Loss P of inverter inv Including the conduction loss and the switching loss of the power device, the loss P of the inverter can be calculated by the method (14) inv Is that
The combined formula (10), the formula (13) and the formula (14) can calculate the input power P of the direct current source in Is that
The transmission efficiency η can be calculated as
The input power P can be obtained by introducing variables K and gamma in Power P received by load load The expression of the transmission efficiency η is rewritten as
P load =I 2 R L Ksin 2 (θ+γ)
P in =P loss +P inv +I 2 (R 4 +R L )Ksin 2 (θ+γ) (17)
Wherein K and γ are represented by formula (18).
From equation (17), it can be seen that the conditions for achieving maximum load power, maximum input power, and maximum transmission efficiency are the same, and are only θ andrelated to the following. The maximum input power can be realized, and the maximum load power and the maximum transmission efficiency can be realized at the same time, so that the power flow control can be realized only by inputting power information. Similarly, the transmitting end detects the input power, and when the input power is maximum, the corresponding theta * And->I.e. the actual physical position of the load coil. The target equation is therefore the input power P in An expression.
From the formula (15), after the system is determined, P in The value of (2) depends only on θ andthe problem of the actual physical position detection of the load coil can thus be converted into a mathematical optimization problem, which can be described as:
when the system is in normal operation, the input power of the direct current source is required to be detected in real time, if the input power P is detected in Descent means that the position of the load coil changes and the position detection algorithm starts to be executed.
The following describes the solving of the mathematical optimization problem in steps using a gradient descent method based on the Barzilai-Borwein method.
Step 1: setting each initial parameter
Let θ sumThe initial values of (2) are all 0.Δθ and +.>Should be small enough so that the WPT system does not produce a large buffeting around the optimization point. But at the same time Δθ and +>But should also be large enough so that the sensor can detect the change. The invention suggests Δθ and +.>The value is between 0.001rad and 0.005 rad.
θ and according to initializationFrom equation (3), the given values of the three transmitting coil currents at the present time can be found, and current control is performed. After the current is stabilized, obtaining the input power P in an initial state according to the sampled direct current voltage and the sampled direct current in (0, 0), and will-P in (0, 0) is given to F (0, 0), and the process proceeds to step 2.
Step 2: calculating initial state information
The gradient descent method based on the Barzilai-Borwein method requires an additional calculation of a set of data, and thus requires calculation of information of an initial state.
1) Calculating the partial derivative of the initial state objective function with respect to θ
And calculating a given value of the current of the three-phase transmitting coil at the present moment according to the formula (20), and executing current control. After the current is stabilized, obtaining the input power P in an initial state according to the sampled direct current voltage and the sampled direct current in (Δθ, 0), and will be-P in (Δθ, 0) is given to F (Δθ, 0).
From equation (21), the partial derivative of the initial state objective function with respect to θ can be calculatedAnd assign it to
And calculating a given value of the current of the three-phase transmitting coil at the present moment according to the formula (22), and executing current control. After the current is stabilized, obtaining the input power in the initial state according to the sampled direct current voltage and direct currentAnd will beAssign->
From equation (23), the initial state objective function is calculatedPartial derivative of>And assign it +.>
The given value of the current of each phase transmitting coil at the next time is calculated according to the formula (24), and current control is performed. After the current is stabilized, obtaining the input power at the next moment according to the sampled direct current voltage and direct currentAnd will->Assign->
To this end, a first set of all data based on the Barzilai-Borwein method for optimal step size has been obtained. Next, the current time information is saved according to equation (25), where α takes a value of 0.5. And is combined withθ (k) sum of the current timeAssigning values to θ and +.>Step 3 is entered.
Step 3: calculating the partial derivative of the objective function at time k with respect to θ
And calculating the given value of the current of each phase transmitting coil at the present moment according to the formula (26), and executing current control. After the current is stabilized, obtaining the input power at the moment k according to the sampled direct current voltage and direct currentAnd will beAssign->
From equation (27), the partial derivative of the objective function at time k with respect to θ can be calculatedAnd assign it toStep 4 is entered.
And calculating the given value of the current of each phase transmitting coil at the present moment according to the formula (28), and executing current control. After the current is stabilized, obtaining the input power at the moment k according to the sampled direct current voltage and direct currentAnd will beAssign->
From equation (29), the k-time objective function can be calculatedPartial derivative of>And assign it +.> Step 5 is entered.
Step 5: calculating an optimal step size
The gradient method searches along the steepest descent direction, and is opposite to the gradient direction of the objective function. As long as the current iteration point is not a stationary point, a continued decrease of the objective function can be ensured. The convergence speed of the algorithm and the accuracy of the final result are greatly dependent on the step length alpha, and the larger the step length alpha is, the faster the convergence speed of the gradient descent method is, but the larger the oscillation is near the optimal value. Conversely, when the step length alpha is smaller, the more the iteration times of the gradient descent method are, the slower the convergence speed is. Therefore, the accuracy and convergence speed of the algorithm need to be weighed when setting the step size α.
Different step size selections result in different gradient algorithms. In recent years, a lot of research has been conducted on the selection of the step size by the gradient method. The main idea of the Barzilai-Borwein method is to use the information in the previous iteration to decide the step size in the current iteration. For the two-dimensional convex function problem, a specific choice of step sizes is given and demonstrated to ensure their super-linear convergence.
Defining s according to Barzilai-Borwein method k 、z k
Wherein s is k The vector difference, denoted as search points at time k and time k-1; z k The gradient difference of the search point vector is expressed as k time and k-1 time; x is x k A vector denoted as search point at time k; x is x k-1 A vector denoted as the search point at time k-1;a gradient denoted as a search point vector at time k; />Denoted as the gradient of the search point vector at time k-1.
Therefore, the optimum step size α can be calculated from the equation (31), and the process proceeds to step 6.
From the calculated optimal step alpha, the k+1 time θ (k+1) and the k+1 time θ can be calculated from the equation (32)And proceeds to step 7.
The θ (k+1) at time k+1 is added toAssigning values to θ and +.>And the current value of each transmitting coil is calculated according to the formula (3). After the current is stabilized, obtaining the input power at the moment k+1 according to the sampled direct current voltage and direct currentAnd will->Assign->Step 8 is entered.
Step 8: preserving k time information
Information at time k is stored according to equation (33). So far, one iteration of the gradient descent method based on the Barzilai-Borwein method is completed, the iteration number N is increased by 1, and the step 9 is entered to judge whether the iteration is completed or not.
Step 9: judging whether the iteration is finished
The maximum iteration number can be set, if the maximum iteration number or the objective function value calculated by two iterations is reachedMeets the error requirement, and outputs theta (k) and +.>I.e. the actual physical position of the load coil. If neither condition is satisfied, θ (k) and +.>Assigning values to θ and +.>Returning to the step 3.
Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.
Claims (1)
1. A method for detecting the position of a load coil in an omnidirectional wireless power transmission system, comprising the steps of:
s1: setting initial parameters
Establishing a mathematical model of an omnidirectional wireless power transmission system, and setting theta and thetaFor the physical angle of the synthesized current vector on the three-dimensional plane, the input power P in the initial state is obtained according to the sampled direct current voltage and direct current in (0, 0), proceeding to step S2; wherein θ is the current vector +.>Forward included angle with Z axis, +.>For current vector->The projection on the XOY plane forms an included angle with the positive X axis;
s2: calculating initial state information
Calculating information of an initial state based on a gradient descent method of a Barzilai-Borwein method;
s201: calculating the partial derivative of the initial state objective function;
calculating the given value of the current of the three-phase transmitting coil at the present moment according to the formula (20), performing current control, and obtaining the input power P in the initial state according to the sampled direct current voltage and the sampled direct current after the current is stabilized in (. DELTA.θ, 0), and P in (. DELTA.θ, 0) is given to F (DELTA.θ, 0);
wherein, delta theta is the step length of theta in the gradient descent method;
from equation (21), the partial derivative of the initial state objective function with respect to θ can be calculatedAnd assign it toThe I represents synthetic electricityStream vector->The amplitude of said I 1 Representing the effective value of the current flowing into the transmitting coil 1, which acts on the Z-axis of the three-dimensional coordinate, said I 2 Representing the effective value of the current flowing into the transmitting coil 2, which acts on the Y-axis of the three-dimensional coordinates, said I 3 The effective value of the current flowing into the transmitting coil 3, which acts on the X-axis of the three-dimensional coordinates, is shown;
calculating a given value of the current of the three-phase transmitting coil at the present moment according to a formula (22), and executing current control; after the current is stabilized, obtaining the input power in the initial state according to the sampled direct current voltage and direct current And will beAssign->
from equation (23), the initial state objective function is calculatedPartial derivative of>And assign it to/>
Calculating the given value of the current of each phase transmitting coil at the next moment according to the formula (24), and executing current control; after the current is stabilized, obtaining the input power at the next moment according to the sampled direct current voltage and direct current And will beAssign->
Then, the current time information is stored according to a formula (25), wherein alpha takes a value of 0.5, and theta (k) at the current time is added withAssigning values to θ and +.>Step S3 is entered;
s3: calculating the theta partial derivative of the objective function at the moment k;
calculating the given value of each phase transmitting coil current at the present moment, executing current control, and obtaining the input power at the k moment according to the sampled direct current voltage and direct current after the current is stabilizedCalculating partial derivative +.about theta of the objective function at k moment>
Calculating the given value of each phase transmitting coil current at the present moment according to the formula (26), performing current control, and obtaining the input power at the k moment according to the sampled direct current voltage and direct current after the current is stabilized
Calculating the partial derivative of the objective function at the moment k with respect to θ from the equation (27)And assign it +.>Step S4 is entered;
calculating the given value of the current of each phase transmitting coil at the present moment, and executing current control; after the current is stabilized, obtaining the input power at the moment k according to the sampled direct current voltage and direct currentCalculating the k moment objective function about +.>Partial derivative of>/>
Calculating the given value of the current of each phase transmitting coil at the present moment according to the formula (28), and executing current control; after the current is stabilized, obtaining the input power at the moment k according to the sampled direct current voltage and direct current And will beAssign->
S5: θ partial derivative sum based on k moment objective functionCalculating the optimal step length alpha by partial derivative;
definition of s according to the Barzilai-Borwein method k 、z k :
Wherein s is k The vector difference, denoted as search points at time k and time k-1; z k The gradient difference of the search point vector is expressed as k time and k-1 time; x is x k Denoted as time-of-k searchVector of cable points; x is x k-1 A vector denoted as the search point at time k-1;a gradient denoted as a search point vector at time k; />A gradient denoted as a search point vector at time k-1;
calculating the optimal step length alpha according to the formula (31), and entering a step S6;
s6: according to the calculated optimal step length alpha, theta (k+1) and theta (alpha+1) at the moment of k+1 are obtained
From the calculated optimal step alpha, the k+1 time θ (k+1) and the k+1 time θ can be calculated from the equation (32)And proceeds to step S7;
s7: the θ (k+1) at time k+1 is added toAssigning values to θ and +.>Calculating the current value of each current transmitting coil, and obtaining the input power +.1 of the moment k+ according to the sampled direct current voltage and direct current after the current is stable>And will beAssign->
S8: saving information at the moment k, completing one iteration based on a Barzilai-Borwein method gradient descent method, adding 1 to iteration times N, and entering a step 9;
storing information at the k moment according to a formula (33), completing one iteration of a gradient descent method based on a Barzilai-Borwein method, adding 1 to iteration times N, and entering a step S9;
s9: if the maximum iteration number or the objective function value calculated by two iterations is reachedIf the set error requirement is met, ending the iteration and outputting theta (k) and +.>The actual physical position of the load coil; if none of them meets the setting error requirement, θ (k) and +.>Assigning values to θ and +.>And returning to the step S3./>
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