A method for achieving ZVS and required power in WPT system using monotonic frequency modulation

Abstract

The present invention discloses a method for achieving ZVS and required power of a WPT system through monotonic frequency modulation, comprising constructing a circuit model of the WPT system, and determining different asymmetric coefficients τ according to the circuit model. c The ZPA boundary under the ZPA is used to determine the asymmetric coefficient τ. c The optimal choice; according to the asymmetric coefficient τ c The optimal selection is performed to obtain the power-frequency variation pattern of the WPT system. Based on the pattern in step S2, the frequency trajectory of the WPT system during the constant current and constant voltage phases is obtained. The frequency trajectory is used to analyze the constraints that satisfy the WPT system design, and the WPT system parameters are designed based on the constraints. Based on the designed parameters, the WPT system achieves monotonic frequency regulation during the constant current and constant voltage phases, meeting the required output power and achieving zero-voltage switching (ZVS). This method enables the WPT system to maintain its rated output voltage, and has the advantages of low implementation complexity and low cost.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless power transmission, and in particular to a method for achieving ZVS and required power in a WPT system through monotonic frequency modulation. Background Art

[0002] Wireless power transfer (WPT), a promising technology, has been widely adopted in consumer electronics, medical devices, industrial robots, and electric vehicles. SS-type WPT (SS-WPT) systems are widely used due to their simple structure and high efficiency. However, variations in parameters such as the coupling coefficient and load resistance in SS-WPT systems can affect the system's output power and the achievement of zero voltage switching (ZVS). Traditional WPT systems typically use additional DC / DC converters to maintain the rated output voltage, but this increases system complexity and cost. If the system uses a phase shifting approach, this increases the difficulty of achieving ZVS. In contrast, frequency regulation can achieve ZVS while still delivering the desired power. Summary of the Invention

[0003] The present invention aims to provide a method for achieving ZVS and the required power in a WPT system using monotonic frequency modulation. Specifically, the method achieves monotonic frequency regulation during both the constant current (CC) and constant voltage (CV) phases of the lithium battery charging process. This method can accommodate variations in the coupling coefficient and equivalent load of the wireless power transmission system, meet the required output power, and simultaneously achieve ZVS.

[0004] The technical solution of the present invention is a method for achieving ZVS and required power in a WPT system through monotonic frequency modulation, comprising the following steps:

[0005] S1. Construct a circuit model of the WPT system and determine different asymmetric coefficients τ based on the circuit model. c The ZPA boundary under the ZPA is used to determine the asymmetric coefficient τ. c The best choice;

[0006] S2, according to the asymmetric coefficient τ c The optimal choice of , and obtain the law of power variation of WPT system with frequency;

[0007] S3. According to the rule in step S2, obtain the frequency trajectory of the WPT system in the constant current stage and the constant voltage stage;

[0008] S4. Analyze the constraints of the WPT system design based on the frequency trajectory and design the WPT system parameters according to the constraints;

[0009] S5. According to the designed parameters, the WPT system can achieve monotonic frequency regulation in the constant current stage and the constant voltage stage to meet the required output power and achieve ZVS at the same time.

[0010] In the above method, in step S1, the circuit model includes an input DC voltage source V DC , primary coil L1, secondary coil L2, primary compensation capacitor C1, secondary compensation capacitor C2, primary parasitic resistance R1, secondary parasitic resistance R2 and DC load resistance R L，DC The fundamental wave equivalent circuit of the circuit model includes a sinusoidal input voltage V in and AC load resistance R L ; Input impedance Z in The expression is:

[0011]

[0012] Where ω=2πf, ω is the system angular frequency; f is the WPT system frequency; X i =ωL i -1 / ωC i , i = 1, 2; j is M is the mutual inductance between the primary and secondary coils; k is the coupling coefficient; R L =8R L，DC / π 2 ;

[0013] Ignoring the effects of the primary parasitic resistance R1 and the secondary parasitic resistance R2 on the system, the ZPA boundary is:

[0014]

[0015] Among them, f p is the primary side resonant frequency; f s is the secondary side resonant frequency.

[0016] In the above method, in step S1, the asymmetric coefficient τ c The definition of is:

[0017]

[0018] The asymmetric coefficient τ c >1 is the best choice.

[0019] In the aforementioned method, in step S2, the expression of the WPT system power P is:

[0020]

[0021] Formula (7) is derived with respect to f, and the derivative is made equal to 0. Then, the values ​​of f and R when the WPT system power P reaches the maximum or minimum can be obtained. L The equation of , that is, the PB_f curve, is shown in formula (8):

[0022]

[0023] According to formula (7) and formula (8), the WPT system power P is plotted against the WPT system frequency f and the AC load resistance R L Three-dimensional graph of changes;

[0024] According to the three-dimensional graph, when R L When the WPT system power P changes with the WPT system frequency f, the curve is called the P(f) curve.

[0025] The above method, wherein the frequency trajectory of the WPT system in the constant current stage and the constant voltage stage is obtained includes obtaining the AC load resistance R during the charging process. L The relationship between and WPT system frequency f:

[0026] Let formula (8) equal to 0, and get formula (9):

[0027]

[0028] Among them, f τPH PB_f curve and R L = the frequency of one of the intersection points of the 0 curve; f τPL It is a non-real number and has no actual physical meaning; f τZL and f τZH All are R L is the frequency of the ZPA boundary when , and

[0029] According to formula (9), when the ZPA boundary intersects the PB_f curve, the frequency of the intersection point is shown in formula (10):

[0030]

[0031] Among them, f τML is the frequency of the intersection of the ZPA boundary and the PB_f curve; f τMH It is a non-real number and has no actual physical meaning;

[0032] According to formula (10), when f is equal to f τML When R L As shown in formula (11):

[0033]

[0034] Among them, ω p is the angular frequency of the primary resonant frequency, ω p =2πf p ;ω s is the angular frequency of the secondary resonant frequency, ω s =2πfs ;

[0035] During charging, R L The relationship between and f is shown in formula (12):

[0036]

[0037] Among them, I cc is a constant current; U cv is a constant voltage;

[0038] After simplification, the AC load resistance R is as follows L And the relationship between WPT system frequency f:

[0039]

[0040] The aforementioned method, wherein the frequency trajectory of the WPT system in the constant current stage and the constant voltage stage is obtained, further comprises drawing the curves of ZPA, PB_f, the constant current stage and the constant voltage stage according to formula (2), formula (7), formula (8) and formula (13), thereby obtaining the frequency trajectory of the system in the constant current stage and the constant voltage stage; the frequency trajectory includes point A (R LA , f A ), point B(R LB , f B ), point C(R LC , f C ), point D(R LD , f D ), point E(R LE , f E ), point V(R LV , f V )、Point A1(R LA , f A1 ) and point B1(R LB , f B1 );

[0041] The point A(R LA , f A ) and point B(R LB , f B ) are the starting points of the constant current stage and the constant voltage stage respectively; the point C (R LC , f C ) is the end point of the constant pressure stage; the point A1 (R LA , f A1 ) is located on the PB_f curve; the point B1 (R LB , f B1 ) is located on the ZPA boundary; the point A1 (R LA , f A1 ) and point A(R LA, f A ) of the equivalent load is the same; the point B1 (R LB , f B1 ) and point B(R LB , f B ) of the same equivalent load; the point D(R LD , f D ) and point V(R LV , f V ) of the WPT system frequency; the point E(R LE , f E ) is the intersection of the ZPA boundary and the PB_f curve.

[0042] In the aforementioned method, in step S4, the process of satisfying the WPT system design constraints based on the frequency trajectory analysis is as follows:

[0043] For the frequency trajectory of the constant current stage, as R L As the frequency of the WPT system decreases, the constant current stage curve approaches the peak value of the PB_f curve, and the power of the WPT system increases; R LA =R LA 1 ≤R LV When f A Close to f s , which is beneficial to improving system efficiency; and R LA ≥R LV When f A Much larger than f s , greatly reducing the system efficiency; therefore, point A is located to the lower left of point V;

[0044] For the frequency trajectory of the constant voltage stage, let R L Taking the derivative of f, we get:

[0045]

[0046] in,

[0047]

[0048] The positive or negative value of formula (14) is determined by the value of H, which is affected by L1. p When L1 is larger, H2 is positive and H1 is negative; the larger L1 is, the smaller H is, the easier it is to be negative, and the easier it is for formula (14) to be positive; different L1s will produce three cases of constant voltage stage curves; according to whether the WPT system frequency of the constant voltage stage curve is monotonic, these three cases can be divided into the following two categories:

[0049] Constant pressure stage 1: When the constant pressure stage curve and the PB_f curve intersect at points I1 and I2, according to formula (8) and formula (13), formula (16) can be obtained:

[0050]

[0051] From formula (14) and formula (16), we can know that the intersection of the constant pressure stage curve and the PB_f curve is =0; therefore, after the constant voltage stage curve passes through point I1, the WPT system frequency f continues to increase, and the WPT system power P increases; while during the constant voltage stage charging process, the WPT system power P should decrease monotonically as the WPT system frequency f increases; therefore, the constant voltage stage 1 curve is not applicable to the constant voltage stage charging process;

[0052] Constant voltage stage 2 and constant voltage stage 3: R L As and f increase simultaneously, the WPT system power P gradually decreases, which can meet the requirement of monotonic frequency modulation in the constant voltage stage charging process; and the constant voltage stage 2 curve is the critical case for meeting the above requirements;

[0053] According to formula (13), the constant pressure stage curve only exists in a specific interval, as shown in formula (17):

[0054]

[0055] The larger L1 is, the smaller the specific interval is; therefore, for some large L1, there exists f C <f V situation;

[0056] The two intersection points of the PB_f curve and the constant voltage stage 1 curve are represented as points I1 (R LI1 , f I1 ) and point I2(R LI2 , f I2 ).

[0057] In the aforementioned method, in step S4, the constraint conditions are as follows:

[0058] P B1 ≥P rate Among them, P B1 is the power at point B1, P rate is the rated power at point B;

[0059] P A1 ≤P start Among them, P A1 is the power at point A1, P start is the starting power at point A;

[0060] R LD ≥R LV or f C ≤f V ;

[0061] RLA 1 ≤R LV .

[0062] In the above method, in step S4, the design of the WPT system parameters is carried out according to the following conditions: when designing the system parameters, the smaller k is, the greater the WPT system power at the peak of the PB_f curve is, and the WPT system frequency in the constant current stage tends to move away from the peak and focus on [f p , f s ] between; τ c The smaller it is, the closer the WPT system frequency in the constant current stage is to f s , the higher the system efficiency.

[0063] Compared with the prior art, the present invention constructs a circuit model of the WPT system and determines different asymmetric coefficients τ by the circuit model. c The ZPA boundary under the ZPA is used to determine the asymmetric coefficient τ. c The optimal choice; according to the asymmetric coefficient τ c The optimal selection is performed to obtain the power-frequency variation pattern of the WPT system. Based on the pattern in step S2, the frequency trajectory of the WPT system during the constant current and constant voltage phases is obtained. The frequency trajectory is used to analyze the constraints that satisfy the WPT system design, and the WPT system parameters are designed based on the constraints. Based on the designed parameters, the WPT system achieves monotonic frequency regulation during the constant current and constant voltage phases, meeting the required output power and achieving zero-voltage switching (ZVS). This method enables the WPT system to maintain its rated output voltage, and has the advantages of low implementation complexity and low cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 Schematic diagram of the circuit model of a two-coil WPT system;

[0065] Figure 2 is the fundamental wave equivalent circuit;

[0066] Figure 3 is τ c ZPA boundary when <1;

[0067] Figure 4 is τ c =1 when the ZPA boundary;

[0068] Figure 5 is τ c >ZPA boundary when 1;

[0069] Figure 6 The WPT power surface, PB_f curve and different R L The corresponding P(f) curve;

[0070] Figure 7 It is the constant current stage curve;

[0071] Figure 8 This is the constant pressure stage 1 curve;

[0072] Figure 9 This is the constant pressure stage 2 curve;

[0073] Figure 10 This is the constant pressure stage 3 curve;

[0074] Figure 11 The constraint curve and the overall diagram of the formation area when τ = 1.03;

[0075] Figure 12 The constraint curve and the local enlarged view of the formation area when τ = 1.03;

[0076] Figure 13 The theoretical and actual frequency values ​​are when k = 0.1 and k = 0.3;

[0077] Figure 14 is the system efficiency when k = 0.1 and k = 0.3;

[0078] Figure 15 This is the waveform diagram at 3.3kW when k = 0.3;

[0079] Figure 16 This is the waveform diagram at 3.3kW when k=0.1. DETAILED DESCRIPTION

[0080] The present invention will be further described below with reference to the embodiments and drawings, but they are not intended to limit the present invention.

[0081] Embodiment: A method for achieving ZVS and required power in a WPT system through monotonic frequency modulation. The method can achieve monotonic frequency regulation in both the constant current (CC) and constant voltage (CV) phases of a lithium battery charging process to cope with changes in the coupling coefficient and equivalent load of the wireless power transmission system, meet the required output power, and simultaneously achieve ZVS. The method comprises the following steps:

[0082] S1. Construct a circuit model of the WPT system and determine different asymmetric coefficients τ based on the circuit model. c The ZPA boundary under the ZPA is used to determine the asymmetric coefficient τ. c The best choice.

[0083] The circuit model of the SSWPT system is as follows Figure 1 As shown, the circuit model includes an input DC voltage source V DC , primary coil L1, secondary coil L2, primary compensation capacitor C1, secondary compensation capacitor C2, primary parasitic resistance R1, secondary parasitic resistance R2 and DC load resistance R L，DC .

[0084] The fundamental wave equivalent circuit of the circuit model is as follows Figure 2 As shown, the fundamental wave equivalent circuit of the circuit model includes a sinusoidal input voltage V in and AC load resistance R L ; Input impedance Z in The expression is:

[0085]

[0086] Where ω=2πf, ω is the system angular frequency; f is the WPT system frequency; X i =ωL i -1 / ωC i , i = 1, 2; j is M is the mutual inductance between the primary and secondary coils; k is the coupling coefficient; R L =8R L，DC / π 2 ;

[0087] Ignoring the effects of the primary parasitic resistance R1 and the secondary parasitic resistance R2 on the system, the ZPA boundary is:

[0088]

[0089] Among them, f p is the primary side resonant frequency; f s is the secondary side resonant frequency.

[0090] In step S1, the asymmetric coefficient τ c The definition of is:

[0091]

[0092] The ZPA boundary is calculated based on the asymmetry coefficient τ c The values ​​of can be divided into Figure 3 、 Figure 4 and Figure 5 Three different situations are shown. Figure 3 、 Figure 4 and Figure 5 In the shaded area, ZVS can be achieved. c =1, f p =f s =f0, that is:

[0093]

[0094] Among them, f τZL and f τZH All are R L The frequency of the ZPA boundary when it is 0;

[0095] The system efficiency is:

[0096]

[0097] By taking the derivative of formula (5) with respect to f and making the derivative equal to 0, we can obtain the optimal frequency of the system to achieve the highest efficiency, that is:

[0098]

[0099] There are two requirements for the frequency trajectory of the system:

[0100] 1) According to formula (6), R L When the value is small, the optimal frequency of the system is close to f s In the constant current stage, the WPT system frequency should also be close to f s .

[0101] 2) During the entire charging process (including the constant current (CC) stage and the constant voltage (CV) stage), the WPT system frequency should be able to be continuously adjusted within the shadow area.

[0102] Therefore, in τ c <1, it cannot meet the requirement of continuous adjustment of the WPT system frequency f, so it is abandoned; and when τ c = 1, the frequency trajectory of the system needs to pass through the ZPA boundary intersection point. The R of the ZPA boundary intersection point under different k values L Different, corresponding power requirements are also different, which makes the system parameters difficult to design, so it is abandoned; therefore, τ c >1 is the optimal choice for the system.

[0103] S2. Plot the WPT system power P versus the WPT system frequency f and AC load resistance R L The three-dimensional graph of the change is R L The curve of WPT system power P changing with WPT system frequency f when the power is constant.

[0104] The present invention adjusts the WPT system power by FM. It is necessary to study the influence of the WPT system frequency f on the WPT system power P. After ignoring the power loss of R1 and R2, the WPT system power P is

[0105]

[0106] Formula (7) is derived with respect to f, and the derivative is made equal to 0. Then, the values ​​of f and R when the WPT system power P reaches the maximum or minimum can be obtained. L The equation of PB_f curve is shown in formula (8):

[0107]

[0108] From formula (8), the WPT system frequency f at the beginning of the constant current (CC) phase is A The equivalent load R LA Satisfy: f A ≤f V , R LA ≤R LV , where f V and R LV are the frequency and equivalent load at the vertex V of the power peak-valley curve respectively.

[0109] Let formula (8) equal to 0, we can get formula (9):

[0110]

[0111] Among them, f τPH PB_f curve and R L =0One of the intersection points of the curve (such as Figure 7 、 Figure 8 、 Figure 9 、 Figure 10 shown) frequency;

[0112] According to formula (9), f τPL It is not a real number and has no actual physical meaning, but f τPH Close to f s When the ZPA boundary intersects the PB_f curve, the frequency of the intersection is given by formula (10):

[0113]

[0114] Among them, f τML is the frequency of the intersection of the ZPA boundary and the PB_f curve (i.e. Figure 7 、 Figure 8 、 Figure 9 、 Figure 10 f at midpoint E E );

[0115] Likewise, f τMH There is no actual physical meaning. τMH When R L As shown in formula (11):

[0116]

[0117] Among them, ω p is the angular frequency of the primary resonant frequency, that is, ω p =2πf p ;ω s is the angular frequency of the secondary resonant frequency, ω s =2πf s ;

[0118] During charging, R L The relationship between and f is shown in formula (12):

[0119]

[0120] Among them, I cc is a constant current; U cv is a constant voltage.

[0121] After simplification, we can get:

[0122]

[0123] According to formula (7) and formula (8), the WPT system power P can be plotted against the WPT system frequency f and the AC load resistance R. L A three-dimensional graph of changes, such as Figure 6 As shown, R L When the WPT system power P changes with the WPT system frequency f, the curve formed is the P(f) curve.

[0124] According to R L The P(f) curve can be divided into three categories based on its value: the curve formed by the maximum value point on the P(f) curve is the PB_f(Peak) curve; similarly, the curve formed by the minimum value point on the P(f) curve is the PB_f(Bottom) curve; point V is the intersection of the PB_f(Peak) curve and the PB_f(Bottom) curve, that is, the vertex V of the power peak-valley curve;

[0125] According to the number of extreme points of the P(f) curve, the P(f) curve can be divided into the following two categories:

[0126] P(f)(case1):R L <R LV When (R LV is the equivalent load value of point V), the P(f) curve is "M"-shaped, reaching a maximum value at the two intersections with the PB_f(Peak) curve and a minimum value at the intersection with the PB_f(Bottom) curve.

[0127] P(f)(case2) and P(f)(case3): R L ≥R LV When f increases, P(f) first increases and then decreases, reaching a maximum value at the intersection of the PB_f(Peak) curve and the PB_f(Peak) curve. At point V, the slope of the derivative of the P(f) curve with respect to f is exactly 0.

[0128] S3. According to the ZPA boundary and the curve of the WPT system power P changing with the WPT system frequency f, the frequency trajectory of the system in the constant current stage and the constant voltage stage is obtained.

[0129] In step S3, according to formula (2), formula (7), formula (8) and formula (13), the curves of ZPA, PB_f, constant current stage and constant voltage stage are drawn, thereby obtaining the frequency trajectory of the constant current stage and constant voltage stage system; the frequency trajectory includes point A (R LA , f A ), point B(R LB , f B ), point C(R LC , f C ), point D(R LD , f D ), point E(R LE , f E ), point V(R LV , f V )、Point A1(R LA , f A1 ), point B1(R LB , f B1 ), point I1(R LI1 , f I1 ) and point I2(R LI2 , f I2 ); respectively as Figures 7 to 10 shown. Figure 6 The PB_f(Peak) curve, PB_f(Bottom) curve and point V in Figures 7 to 10 correspond.

[0130] Points A and B are the starting points of the constant current and constant voltage phases, respectively, while Point C is the end point of the constant voltage phase. Point A1 is on the PB_f curve, while Point B1 is on the ZPA boundary. Point A1 and Point A have the same equivalent load. Similarly, Point B1 and Point B have the same equivalent load. Points I1 and I2 are the intersections of the PB_f curve and the CV (case 1) curve. Point D is on the CV (case 3) curve and has the same f as Point V. Point E is the intersection of the ZPA boundary and the PB_f curve. Figures 7 to 10 The AC load resistance R at each point L and WPT system frequency f are respectively represented by point A(R LA , f A ), point B(R LB , f B ), point C(R LC , f C ), point D(R LD , f D ), point E(R LE , fE ), point V(R LV , f V )、Point A1(R LA , f A1 ), point B1(R LB , f B1 ), point I1(R LI1 , f I1 ) and point I2(R LI2 , f I2 ). The equivalent load resistance at point E is given by formula (11), and f E =f τML According to the different number of intersections between the constant pressure stage curve and the PB_f curve in the region, it can be divided into three cases. To compare these three cases, let R L Taking the derivative of f, we get:

[0131]

[0132] in,

[0133]

[0134] The positive or negative value of formula (14) is determined by the value of H, which is affected by L1. p When L1 is larger, H2 is positive and H1 is negative; the larger L1 is, the smaller H is, the easier it is to be negative, and the easier it is for formula (14) to be positive; different L1s will produce three cases of constant voltage stage curves; according to whether the WPT system frequency of the constant voltage stage curve is monotonic, these three cases can be divided into the following two categories:

[0135] 1) CV (case 1): When the constant pressure stage curve and the PB_f curve intersect at points I1 and I2, formula (16) can be obtained according to formula (8) and formula (13).

[0136]

[0137] From formula (14) and formula (16), we can know that the intersection of the constant pressure stage curve and the PB_f curve is =0. Therefore, after the constant voltage phase curve passes point I1, f continues to increase, moving away from the PB_f (Bottom) curve and closer to the PB_f (Peak) curve, and the WPT system power P increases. However, during the constant voltage phase charging process of the present invention, the WPT system power P should decrease monotonically as the WPT system frequency f increases. These two factors contradict each other, and therefore the CV (case 1) curve is not applicable to the constant voltage phase charging process of the present invention.

[0138] 2) CV(case2) and CV(case3): R LAs both ρ and f increase, the constant voltage phase curve moves away from the PB_f(Peak) curve below, and the WPT system power P gradually decreases, meeting the monotonic frequency modulation requirement of the constant voltage charging process. CV (case 2) is a critical case that just meets these requirements.

[0139] According to formula (13), the constant pressure stage curve only exists in a specific interval (i.e., the domain of definition), as shown in formula (17). The larger L1 is, the smaller the specific interval is; therefore, for some larger L1, there exists f c <f v situation.

[0140]

[0141] S4. Obtain the constraints that meet the system design based on the system's frequency trajectory and design the system parameters.

[0142] In summary, the system design has the following four constraints:

[0143] 1)P B1 ≥P rate Among them, P B1 is the power at point B1, P rate is the rated power at point B, which is 3.3 kW in this embodiment;

[0144] 2)P A1 ≤P start Among them, P A1 is the power at point A1, P start is the starting power at point A, which is 1.65 kW in this embodiment;

[0145] 3) R LD ≥R LV or f C ≤f V ;

[0146] 4) R LA 1 ≤R LV .

[0147] In this embodiment, f p Table 1 shows the system parameters.

[0148] parameter Numerical Rated power 3.3kW Input voltage 400V Output voltage 200-400V Output current 1.65-8.25A Load range 24.242-242.425Ω Coupling coefficient 0.1-0.3

[0149] Table 1

[0150] For [L1, L2, k, τ c] to determine whether each combination meets the requirements. Finite element simulation shows that the maximum self-inductance achieved with densely wound coils is approximately 813.6 μH. To simplify coil winding, L1 and L2 are both set to no more than 810 μH. The tested k values ​​are 0.1 and 0.3, respectively.

[0151] In the present invention, the system efficiency in the constant current stage should be as high as possible when the coupling coefficient k is minimum. The smaller k is, the greater the WPT system power at the peak of the PB_f curve is, and the WPT system frequency in the constant current stage tends to move away from the peak and focus on [f p , f s ]. c The smaller it is, the closer the WPT system frequency in the constant current stage is to f s , the higher the system efficiency. Therefore, τ c Parameter combination screening was carried out starting from 1.01. The results showed that τ c When τ is 1.01 or 1.02, there is no parameter combination that meets the requirements. c The different constraint condition curves and formation areas when is 1.03 are as follows: Figure 11 、 Figure 12 As shown in Figure 2, the three curves correspond exactly to the critical cases of the first three constraints of the system design. The shaded area surrounded by the constraint curves is the selected area that meets the requirements. Figure 12 exist Figure 11 On the basis of the added constraints of the coil self-inductance range. LA 1 ≤R LV , so R LV ≥19.65Ω. Figure 11 When L2 is less than 370μH at point P1, R LV <19.65Ω. Therefore, τ c =1.03, the system should satisfy L2≥370μH, which meets the fourth constraint.

[0152] The parameter combination that finally meets all requirements is as follows Figure 12 shown. Figure 12 In this example, L1 varies within the range of [763μH, 810μH], and L2 varies within the range of [605μH, 674μH]. Since the ranges of L1 and L2 are very small, the efficiency of different parameter combinations is almost the same. For simplicity, the number of turns of the coil wound within this parameter range is rounded to the nearest integer, and L1 is selected as 785μH and L2 as 635μH. It should be noted that other parameter combinations within this parameter range are also possible. The system parameters are shown in Table 2:

[0153]

[0154]

[0155] Table 2

[0156] In addition to achieving ZVS and rated output power within the load and coupling variation range, the system of this embodiment should also be able to achieve monotonic frequency regulation. To verify whether these three goals are achieved, this embodiment selects 20 operating points (10 for k = 0.3 operating point and 10 for k = 0.1 operating point). Among them, R L，DC is 48.485Ω, which is R L，rate . R at different working points L，DC 0.5R respectively L，rate , 0.6R L，rate , 0.7R L，rate , 0.8R L，rate , 0.9R L，rate 、R L，rate , 2R L，rate 、3R L，rate 、4R L，rate 、5R L，rate .

[0157] Figure 13 The comparison diagram of the theoretical frequency path and the frequency at the actual measurement point. In the constant voltage stage, the WPT system frequency f changes with R L The opposite is true during the constant current phase. Since Equation (7) does not include losses in the inverter, rectifier, and magnetic core, all measured frequencies are lower than the theoretical frequency. The lower the frequency, the closer the frequency path approaches the PB_f(Peak) curve, which is consistent with theory. When k = 0.1, the theoretical frequency decreases very little during the constant current phase. However, the switching frequency generated by the controller is discrete, so the frequencies at the actual measurement points have the same value.

[0158] Figure 14 is the measured efficiency at each working point. Figure 15 、 Figure 16 The following are the measured waveforms of the inverter output voltage and current at the rated power points of k = 0.3 and k = 0.1. Based on the measurement results, the following conclusions can be drawn:

[0159] a) The rated output power can be achieved at all operating points, which indicates that the design method proposed in the present invention can enable the system to achieve the rated output power requirement under a given coupling coefficient range and load resistance range;

[0160] b) The system can achieve ZVS in the entire coupling coefficient range and load resistance range;

[0161] c) The frequency of the WPT system can be monotonically adjusted in the constant current stage and the constant voltage stage respectively;

[0162] d) Within the operating region of the system, the measured DC-DC efficiency ranges from 81.2% to 97.2%.

[0163] In summary, the present invention can achieve monotonic frequency regulation in both the constant current (CC) stage and the constant voltage (CV) stage during the lithium battery charging process to cope with changes in the coupling coefficient and equivalent load of the wireless power transmission system, meet the required output power and achieve ZVS at the same time; it has the advantages of low implementation complexity and low cost.

Claims

1. A method for achieving ZVS and required power in a WPT system using monotonic frequency modulation, characterized by: The steps include: S1. Construct a circuit model of the WPT system and determine different asymmetric coefficients τ based on the circuit model. c The ZPA boundary under the ZPA is used to determine the asymmetric coefficient τ. c The best choice; The asymmetric coefficient τ c The definition of is: The asymmetric coefficient τ c >1 is the best choice; Where, f p is the primary side resonant frequency; f s is the secondary resonant frequency, L1 is the primary coil self-inductance, L2 is the secondary coil self-inductance, C1 is the primary compensation capacitor, and C2 is the secondary compensation capacitor; S2, according to the asymmetric coefficient τ c The optimal choice of , and obtain the law of power variation of WPT system with frequency; S3. According to the rule in step S2, obtain the frequency trajectory of the WPT system in the constant current stage and the constant voltage stage; The frequency trajectory of the WPT system is the AC load resistance R when the WPT system is working. L fR formed by the corresponding operating frequency f L curve; S4. Analyze the constraints of the WPT system design based on the frequency trajectory and design the WPT system parameters according to the constraints; The constraints are as follows: P B1 ≥P rate ; Among them, P B1 is the power at point B1, P rate is the rated power at point B; point B is the starting point of the constant voltage phase of the WPT system, and point B1 is located on the ZPA boundary and has the same equivalent load as point B; P A1 ≤P start Among them, P A1 is the power at point A1, P start is the starting power at point A; point A is the starting point of the constant current phase of the WPT system, and point A1 is where f and R are located when the power P of the WPT system reaches its maximum or minimum value. L The point on the equation curve with the same equivalent load as point A; when the WPT system power P reaches the maximum or minimum, f and R L The equation curve is the PB_f curve; R LD ≥R LV or f C ≤f V ; Among them, R LD is the AC load resistance value corresponding to point D, R LV is the AC load resistance value corresponding to point V; f C is the WPT system frequency corresponding to point C, f V is the WPT system frequency corresponding to point V; point C is the end point of the constant voltage phase of the WPT system, point V is the vertex of the PB_f curve, and point D is the point on the constant voltage phase curve with the same frequency value as point V; R LA1 ≤R LV , R LA1 is the AC load resistance value corresponding to point A1; S5. According to the designed parameters, the WPT system can achieve monotonic frequency regulation in the constant current stage and the constant voltage stage to meet the required output power and achieve ZVS at the same time.

2. The method according to claim 1, wherein: In step S1, the circuit model includes an input DC voltage source V DC , primary coil, secondary coil, primary compensation capacitor C1, secondary compensation capacitor C2, primary parasitic resistance R1, secondary parasitic resistance R2 and DC load resistance R L,DC The fundamental wave equivalent circuit of the circuit model includes a sinusoidal input voltage V in and AC load resistance R L ; Input impedance Z in The expression is: Where ω=2πf, ω is the system angular frequency; f is the WPT system frequency; X i =ωL i -1 / ωC i ,i=1,2;j is M is the mutual inductance between the primary and secondary coils; k is the coupling coefficient; R L =8R L,DC / π 2 ; L1 is the self-inductance of the primary coil, L2 is the self-inductance of the secondary coil; Ignoring the effects of the primary parasitic resistance R1 and the secondary parasitic resistance R2 on the system, the ZPA boundary is: Among them, f p is the primary side resonant frequency; f s is the secondary side resonant frequency.

3. The method according to claim 2, wherein: In step S2, the expression of the WPT system power P is: Formula (7) is derived with respect to f, and the derivative is made equal to 0. Then, the values ​​of f and R when the WPT system power P reaches the maximum or minimum can be obtained. L The equation of , that is, the PB_f curve, is shown in formula (8): According to formula (7) and formula (8), the WPT system power P is plotted against the WPT system frequency f and the AC load resistance R L Three-dimensional graph of changes; According to the three-dimensional graph, when R L When the WPT system power P changes with the WPT system frequency f, the curve is called the P(f) curve.

4. The method according to claim 3, wherein: The frequency trajectory of the WPT system in the constant current stage and the constant voltage stage is obtained by obtaining the AC load resistance R during the charging process. L The relationship between and WPT system frequency f: Let formula (8) equal to 0, and get formula (9): Among them, f τPH PB_f curve and R L = the frequency of one of the intersection points of the 0 curve; f τPL It is a non-real number and has no actual physical meaning; f τZL and f τZH All are R L is the frequency of the ZPA boundary when , and According to formula (9), when the ZPA boundary intersects the PB_f curve, the frequency of the intersection point is shown in formula (10): Among them, f τML is the frequency of the intersection of the ZPA boundary and the PB_f curve; f τMH It is a non-real number and has no actual physical meaning; According to formula (10), when f is equal to f τML When R L As shown in formula (11): Among them, ω p is the angular frequency of the primary resonant frequency, ω p =2πf p ;ω s is the angular frequency of the secondary resonant frequency, ω s =2πf s ; During charging, R L The relationship between and f is shown in formula (12): Among them, I cc is a constant current; U cv is a constant voltage; After simplification, the AC load resistance R is as follows L And the relationship between WPT system frequency f:

5. The method according to claim 4, characterized in that: The frequency trajectory of the WPT system in the constant current stage and the constant voltage stage is obtained by drawing the curves of ZPA, PB_f, the constant current stage and the constant voltage stage according to formula (2), formula (7), formula (8) and formula (13), thereby obtaining the frequency trajectory of the system in the constant current stage and the constant voltage stage; the frequency trajectory includes point A (R LA ,f A ), point B(R LB ,f B ), point C(R LC ,f C ), point D(R LD ,f D ), point E(R LE ,f E ), point V(R LV ,f V )、Point A1(R LA ,f A1 ) and point B1(R LB ,f B1 ); The point A(R LA ,f A ) and point B(R LB ,f B ) are the starting points of the constant current stage and the constant voltage stage respectively; the point C (R LC ,f C ) is the end point of the constant pressure stage; the point A1 (R LA1 ,f A1 ) is located on the PB_f curve; the point B1 (R LB1 ,f B1 ) is located on the ZPA boundary; the point A1 (R LA1 ,f A1 ) and point A(R LA ,f A ) of the equivalent load is the same; the point B1 (R LB1 ,f B1 ) and point B(R LB ,f B ) of the same equivalent load; the point D(R LD ,f D ) and point V(R LV ,f V ) of the WPT system frequency, point V is the vertex of the power peak-valley curve, and point D is the point on the constant voltage stage curve with the same frequency value as point V; the point E (R LE ,f E ) is the intersection of the ZPA boundary and the PB_f curve.

6. The method according to claim 5, characterized in that: In step S4, the process of satisfying the WPT system design constraints based on the frequency trajectory analysis is as follows: For the frequency trajectory of the constant current stage, as R L As the frequency of the WPT system decreases, the constant current stage curve approaches the peak value of the PB_f curve, and the power of the WPT system increases; R LA =R LA1 ≤R LV When R LA1 is the AC load resistance at point A1, f A Close to f s , which is beneficial to improving system efficiency; and R LA ≥R LV When f A Much larger than f s , greatly reducing system efficiency; Therefore, point A is located to the lower left of point V; For the frequency trajectory of the constant voltage stage, let R L Taking the derivative of f, we get: in, The positive or negative value of formula (14) is determined by the value of H, which is affected by L1; when f>f p When L1 is larger, H2 is positive and H1 is negative; the larger L1 is, the smaller H is, the easier it is to be negative, and the easier it is for formula (14) to be positive; different L1s will produce three cases of constant voltage stage curves; according to whether the WPT system frequency of the constant voltage stage curve is monotonic, these three cases are divided into the following two categories: Constant pressure stage 1: When the constant pressure stage curve and the PB_f curve intersect at points I1 and I2, according to formula (8) and formula (13), formula (16) can be obtained: From formula (14) and formula (16), we can know that the intersection of the constant pressure stage curve and the PB_f curve is is 0; Therefore, after the constant voltage stage curve passes through point I1, the WPT system frequency f continues to increase, and the WPT system power P increases; while during the constant voltage stage charging process, the WPT system power P should decrease monotonically as the WPT system frequency f increases; therefore, the constant voltage stage 1 curve is not applicable to the constant voltage stage charging process; Constant voltage stage 2 and constant voltage stage 3: R L As and f increase simultaneously, the WPT system power P gradually decreases, meeting the requirement of monotonic frequency modulation in the constant voltage stage charging process; and the constant voltage stage 2 curve is the critical case for meeting the above requirements; According to formula (13), the constant pressure stage curve only exists in a specific interval, as shown in formula (17): The larger L1 is, the smaller the specific interval is; therefore, for some large L1, there exists f C <f V situation; The two intersection points of the PB_f curve and the constant voltage stage 1 curve are represented as points I1 (R LI1 ,f I1 ) and point I2(R LI2 ,f I2 ).

7. The method according to claim 6, characterized in that: In step S4, the design of the WPT system parameters is carried out according to the following conditions: When designing the system parameters, the smaller k is, the greater the WPT system power at the peak of the PB_f curve is, and the WPT system frequency in the constant current stage tends to move away from the peak and focus on [f p , f s ] between; τ c The smaller it is, the closer the WPT system frequency in the constant current stage is to f s , the higher the system efficiency.

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