A distributed transmitting coil structure applied to a three-phase dynamic wireless power supply system

Abstract

The present invention provides a distributed transmitting coil structure applied to a three-phase dynamic wireless power supply system. By optimizing different structures of the coil, the structure of the present invention uses a distributed transmitting coil to eliminate the harmonic traveling wave magnetic field generated by the three-phase transmitting coil, so that the plane where the receiving end is located mainly contains a fundamental wave traveling wave magnetic field, and the amplitude of the induced voltage of the receiving coil is basically unchanged during the movement, thereby effectively suppressing the voltage fluctuation in the three-phase dynamic wireless power supply system and realizing the constancy of the output voltage.

Description

Technical Field

[0001] The present invention belongs to the technical fields of wireless power transmission and rail transit, and particularly relates to a distributed transmitting coil structure applied to a three-phase dynamic wireless power supply system. Background Art

[0002] Due to the characteristic of non-contact energy transmission, the wireless power supply method has greatly improved the problems of poor electrical safety and poor flexibility of the traditional wired power supply method. The new power supply method can be divided into a static wireless power supply method and a dynamic wireless power supply method according to whether the receiving side can move.

[0003] For the dynamic wireless power supply method, the receiving side can achieve uninterrupted energy transmission during the movement process, and currently has great application prospects in the field of electric vehicles. Research institutions at home and abroad have conducted many studies on the dynamic wireless power supply system. For the dynamic wireless power supply system, it will move continuously during the charging process, resulting in a change in the mutual inductance between the transmitting coil and the receiving coil, and further causing fluctuations in the output power. When the traveling wave magnetic field generated at the transmitting end only contains the fundamental wave traveling wave magnetic field, the output voltage at the receiving end is constant and independent of the position of the receiving end. Therefore, improving the output power fluctuation in the dynamic wireless power supply system can be transformed into improving the harmonic magnetic field component in the traveling wave magnetic field. Large output power fluctuations will have a huge negative impact on the device stress and system stability at the receiving end. Therefore, this is a problem that needs to be solved urgently at present.

[0004] The distributed transmitting coil structure described in the present invention can suppress the harmonic components of the traveling wave magnetic field generated at the receiving end plane of the three-phase dynamic wireless power supply system by reasonably designing the length value of the spacing between the transmitting coils, and can achieve the stability of the system output power, fundamentally solving the problems caused by the power fluctuation. Summary of the Invention

[0005] The purpose of the present invention is to solve the problem of large output power fluctuations in the current three-phase dynamic wireless power supply system, and a distributed transmitting coil structure applied to the three-phase dynamic wireless power supply system is proposed.

[0006] The present invention is realized through the following technical solutions. The present invention proposes a distributed transmitting coil structure applied to a three-phase dynamic wireless power supply system. Each phase of the distributed transmitting coil structure is composed of multiple coils. The multiple coils are connected together in a series connection manner at the end sides, which can ensure that the same current passes through. The multiple coils parallel to the x-axis direction are tightly connected, and for the multiple coils parallel to the y-axis, they are distributed at a distance of △x along the x-axis direction T and are equidistant from each other; by reasonably designing the spacing △x between two adjacent turns of coils in the distributed transmitting coil T, eliminating the harmonic traveling wave magnetic field of the transmitting coil, to achieve the purpose of suppressing the fluctuation of the output power in the three-phase dynamic wireless power supply system.

[0007] Furthermore, the distance △x between two adjacent turns of the distributed transmitting coil T The design method is specifically as follows:

[0008] Taking the A-phase coil in the three-phase distributed structure as an example, when a direct current i a = I0 is passed through the A-phase coil, a fundamental magnetic field is generated in the receiving end plane. The fundamental magnetic fields generated by each turn of the coil have the same amplitude B z-1 and pole pitch τ, but are spatially separated by a distance △x T along the x-axis direction;

[0009] The fundamental magnetic fields generated by each turn of the coil differ in phase by γ1, where γ1 is related to △x T and satisfies:

[0010]

[0011] The total fundamental magnetic field B generated by the A-phase coil z-A1 is equal to the phasor sum of the fundamental magnetic fields generated by each turn of the coil. From the geometric relationship in the phasor diagram, it can be seen that the amplitude of the total fundamental magnetic field B z-A1 satisfies:

[0012]

[0013] where k dT The expression of -1 satisfies:

[0014]

[0015] It is easy to prove that k dT-1 ≤ 1. Define k dT -1 as the fundamental wave distribution coefficient at the transmitting end, which is used to represent the amplitude attenuation of the fundamental magnetic field B z-A1 after the transmitting coil adopts the distributed structure; where the subscript dT represents Distributed transmitter coil, that is, the distributed transmitting coil, and the number represents the harmonic order of the traveling wave magnetic field;

[0016] The i-th harmonic magnetic fields generated by each turn of the coil are still spatially separated by a distance △x T along the x-axis direction. However, since the pole pitch τ i of the i-th harmonic magnetic field is only 1 / i of the fundamental pole pitch τ, the i-th harmonic magnetic fields generated by each turn of the coil differ in phase by γ i which is i times that of the fundamental wave, that is:

[0017]

[0018] From the geometric relationship in the phasor diagram, the amplitude of the i-th harmonic magnetic field B z -Ai satisfies:

[0019]

[0020] where k dT-i The expression of satisfies:

[0021]

[0022] Correspondingly, k dT -i is defined as the i-th harmonic distribution coefficient at the transmitting end, which is used to represent the amplitude attenuation of the i-th harmonic magnetic field B z-Ai in the distributed transmitting coil;

[0023] In order to make the amplitude of the i-th harmonic magnetic field B z-Ai be 0, the i-th harmonic distribution coefficient k dT-i at the transmitting end satisfies:

[0024] k dT -i = 0 (7)

[0025] Substituting equations (4) and (6) into equation (7) and solving, we get:

[0026]

[0027] In summary, by reasonably designing the inter-turn distance △x of the distributed transmitting coil T , the purpose of eliminating the i-th harmonic magnetic field is achieved.

[0028] Furthermore, if it is necessary to eliminate the fifth harmonic magnetic field generated by the transmitting coil, the distance △x between two adjacent coils carrying the same current in this structure T is designed as: where k = 1, 2, 3…n, and n is a positive integer greater than or equal to 1.

[0029] Furthermore, if it is necessary to eliminate the seventh harmonic magnetic field generated by the transmitting coil, the distance △x between two adjacent coils carrying the same current in this structure T is designed as: where k = 1, 2, 3…n, and n is a positive integer greater than or equal to 1.

[0030] Furthermore, if it is necessary to weaken the fifth harmonic magnetic field and the seventh harmonic magnetic field generated by the transmitting coil, the distance △x between two adjacent coils carrying the same current in this structure T is designed as: where k = 1, 2, 3…n, and n is a positive integer greater than or equal to 1.

[0031] Furthermore, to maximize the output voltage, the fundamental distribution coefficient k dT-1 is maximized. By setting k = 1 in the above turn spacing expression, i.e., the turn spacing △x T is designed as

[0032] Advantages of the present invention:

[0033] (1) The structure of the present invention can ensure that the third harmonic of the traveling wave magnetic field generated in space is zero;

[0034] (2) If the spacing △x between two adjacent coils passing the same current in this structure T is designed as: where k = 1, 2, 3…n, and n is a positive integer greater than or equal to 1. At this time, the amplitude of the fifth harmonic of the traveling wave magnetic field in the plane where the receiving coil is located is 0, then the fifth harmonic magnetic field generated in the receiving end plane can also be eliminated. During the movement of the receiving end with the charging device, the induced electromotive force no longer contains the fifth harmonic content, and the output voltage of the system is more stable;

[0035] (3) If the spacing △x between two adjacent coils passing the same current in this structure T is designed as: where k = 1, 2, 3…n, and n is a positive integer greater than or equal to 1. At this time, the amplitude of the seventh harmonic of the traveling wave magnetic field in the plane where the receiving coil is located is 0, then the seventh harmonic magnetic field generated in the receiving end plane can also be eliminated. During the movement of the receiving end with the charging device, the induced electromotive force no longer contains the seventh harmonic content, and the output voltage of the system is more stable;

[0036] (4) If the spacing △x between two adjacent coils passing the same current in this structure T is designed as: where k = 1, 2, 3…n, and n is a positive integer greater than or equal to 1. At this time, the amplitude of the seventh harmonic of the traveling wave magnetic field in the plane where the receiving coil is located is 0, then the fifth and seventh harmonic magnetic fields generated in the receiving end plane can be simultaneously suppressed. During the movement of the receiving end with the charging device, the fifth harmonic content and the seventh harmonic content of the induced electromotive force both decrease, and the output voltage of the system is more stable. Description of the Drawings

[0037] Figure 1(a) is a single-phase transmitting coil with N T = 3.

[0038] Figure 1(b) is a three-phase transmitting coil with N T = 3.

[0039] Figure 2 is an aerial view of a three-phase meandering structure.

[0040] Figure 3It is the fundamental wave magnetic field and the i-th wave magnetic field B generated by the A-phase distributed transmitting coil on the receiving end plane z-Ai The distribution and its phasor diagram. Among them, (a) is the distribution of the fundamental wave magnetic field B z-A1 and the phasor diagram of the fundamental wave magnetic field B z-A1 , (b) is the distribution of the i-th harmonic magnetic field B z-Ai and the phasor diagram of the harmonic magnetic field B z-Ai .

[0041] Figure 4 It is the relationship diagram of the distribution coefficient k T varying with the turn-to-turn distance △x dT-i under different numbers of turns N T . Among them, (a) is N T =3, (b) is N T =6.

[0042] Figure 5 It is the relationship diagram between the fundamental wave distribution coefficient k dT-1 and the number of turns N T of the coil when eliminating the 5th and 7th harmonic magnetic fields. Specific implementation manner

[0043] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0044] The present invention provides a distributed transmitting coil structure applied to a three-phase dynamic wireless power supply system that can generate a constant magnetic field amplitude. By optimizing different structures of the coil, the structure of the present invention uses a distributed transmitting coil to eliminate the harmonic traveling wave magnetic field generated by the three-phase transmitting coil, so that the plane where the receiving end is located mainly contains the fundamental wave traveling wave magnetic field, and the amplitude of the induced voltage of the receiving coil is basically unchanged during the movement, thereby effectively suppressing the fluctuation of the output voltage in the three-phase dynamic wireless power supply system and realizing the constancy of the output voltage.

[0045] The three-phase meandering coil is as Figure 2 shown, and its winding method is the tail-swinging method along the x-axis (traveling direction), and each phase is staggered from each other, and the staggered distance is one-third of the period. In the three-phase coil structure applicable to dynamic wireless power supply in the present invention, each phase is composed of multiple coils, and the multiple coils are connected together in a series connection manner at the end side, so that the same current can be ensured to pass through. The multiple coils parallel to the x-axis are tightly connected, while a certain distance should be left when laying the multiple coils parallel to the y-axis, and the multiple coils are equidistant from each other. By designing this distance, better performance can be obtained.

[0046] The distributed transmitting coil applied to the dynamic three-phase wireless power supply system described in the present invention includes, but is not limited to, being installed under the ground; the number of turns N T The shapes of the transmitting coils with 3 turns are shown in Figures 1(a) and 1(b), corresponding to the distributed single-phase transmitting coil and the distributed three-phase transmitting coil respectively. Each turn of the transmitting coil in the figure is numbered 1, 2, and 3 respectively, and the symbols after the numbers only represent the current direction along the y-axis.

[0047] Compared with Figure 2 the traditional three-phase meandering structure shown, the present invention proposes a distributed transmitting coil structure applied to the three-phase dynamic wireless power supply system. Each phase of the distributed transmitting coil structure is composed of multiple coils, and the multiple coils are connected together by end-side series connection, which can ensure that the same current is passed through. The multiple coils parallel to the x-axis direction are tightly connected, while the multiple coils parallel to the y-axis are placed at a distance difference of △x T along the x-axis direction, and the multiple coils are equidistant from each other; by reasonably designing the distance △x T between adjacent turns of the distributed transmitting coil, the harmonic traveling wave magnetic field of the transmitting coil is eliminated, and the purpose of suppressing the fluctuation of the output power in the three-phase dynamic wireless power supply system is achieved.

[0048] The distance △x T between adjacent turns of the described distributed transmitting coil is designed as follows:

[0049] Taking the A-phase coil in the three-phase distributed structure as an example, when a direct current i a = I0 is passed through this coil, the A-phase coil generates a fundamental magnetic field on the receiving end plane, as shown in Figure 3 (a). The fundamental magnetic fields generated by each turn of the coil have the same amplitude B z-1 and pole pitch τ, but are distributed at a distance difference of △x T along the x-axis direction in space;

[0050] Figure 3 (a) also gives the phasor diagram of the fundamental magnetic field B z-A1 . The fundamental magnetic fields generated by each turn of the coil are out of phase by γ1, where γ1 is related to △x T and satisfies:

[0051]

[0052] The total fundamental magnetic field B z-A1 generated by the A-phase coil is equal to the phasor sum of the fundamental magnetic fields generated by each turn of the coil. From the geometric relationship in the phasor diagram, it can be known that the amplitude of the total fundamental magnetic field B z-A1 satisfies:

[0053]

[0054] where k dT-1 has an expression that satisfies:

[0055]

[0056] It is easy to prove that k dT-1 ≤ 1. Therefore, the amplitude of the fundamental magnetic field B z-A1 in the distributed transmitting coil will be reduced compared to the traditional meandering coil. Define k dT-1 as the fundamental distribution coefficient at the transmitting end, which is used to represent the amplitude attenuation of the fundamental magnetic field B z-A1 after the transmitting coil adopts a distributed structure. Here, the subscript dT represents Distributed transmitter coil, that is, the distributed transmitting coil, and the number represents the harmonic order of the traveling magnetic field;

[0057] Figure 3 (b) shows the distribution of the i-th order magnetic field B z-Ai generated by the A-phase distributed transmitting coil in the receiving end plane and its phasor diagram. The i-th harmonic magnetic fields generated by each turn of the coil still have a spatial phase difference of △x T along the x-axis direction. However, since the pole pitch τ i of the i-th harmonic magnetic field is only 1 / i of the fundamental pole pitch τ, the phase difference of the i-th harmonic magnetic fields generated by each turn of the coil is γ i which is i times that of the fundamental wave, that is:

[0058]

[0059] From the geometric relationship in the phasor diagram, it can be seen that the amplitude of the i-th harmonic magnetic field B z-Ai satisfies:

[0060]

[0061] where k dT-i has an expression that satisfies:

[0062]

[0063] Correspondingly, define k dT-i as the i-th harmonic distribution coefficient at the transmitting end, which is used to represent the amplitude attenuation of the i-th harmonic magnetic field B z-Ai in the distributed transmitting coil;

[0064] In order to make the amplitude of the i-th harmonic magnetic field B z-Ai equal to 0, the i-th harmonic distribution coefficient k dT-i at the transmitting end satisfies:

[0065] k dT-i = 0 (7)

[0066] Substitute Equation (4) and Equation (6) into Equation (7) and solve to obtain:

[0067]

[0068] In summary, by reasonably designing the inter-turn distance △x of the distributed emission coil T , the purpose of eliminating the i-th harmonic magnetic field is achieved.

[0069] As can be seen from Equation (3) and Equation (6), the inter-turn distance △x T affects the fundamental wave and harmonic distribution coefficients. The relationships between the distribution coefficients and the inter-turn spacing in the cases of 3 turns and 6 turns are shown in Figure 4 (a) and 4(b) respectively.

[0070] To maximize the output voltage and make the fundamental wave distribution coefficient k dT-1 maximum, in practical applications, k in the above inter-turn spacing expression should be set to 1, that is, the inter-turn spacing △x T should be designed as

[0071] In the three-phase meandering structure, the 5th and 7th harmonic magnetic fields B z-A5 , B z-A7 have the greatest impact on the output fluctuation. Figure 5 The relationships between the fundamental wave distribution coefficient k dT-5 and the number of turns N dT-7 of the emission coil are given respectively when eliminating the 5th and 7th harmonic magnetic fields (i.e., k dT-1 or k T = 0).

[0072] It can be seen from Figure 5 that as the number of turns N T increases, k dT-1 decreases. When N T ≥ 8, k dT-1 remains constant and is no longer affected by the number of turns. In addition, the lower the order i of the eliminated harmonic magnetic field, the smaller the fundamental wave distribution coefficient k dT-1 , that is, the attenuation of the induced electromotive force amplitude is more serious.

[0073] In the process of designing the distributed emission coil, in order to achieve the optimal output fluctuation suppression effect, the emission coil should be designed with the purpose of eliminating the 5th harmonic magnetic field, and the inter-turn distance satisfies: △x T = 2τ / 5·N T . At this time, the minimum value of k T under any number of turns N dT-1 is 0.936. In summary, the distributed emission coil can effectively eliminate the harmonic induced electromotive force and then suppress the output voltage fluctuation on the premise of very little weakening (less than 7%) of the fundamental wave output voltage.

[0074] When eliminating the 5th harmonic magnetic field generated in the receiving end plane, the spacing Δx between two adjacent turns of the coil T is designed as:

[0075] where k = 1, 2, 3…n, and n is a positive integer greater than or equal to 1; at this time, the amplitude of the 5th harmonic of the traveling wave magnetic field in the plane where the receiving coil is located is 0, and the 5th harmonic content in the induced electromotive force at the receiving end is zero. Mainly affected by the fundamental magnetic field, during the movement of the charging device at the receiving end, there is no longer 5th harmonic content in the induced electromotive force, and the output voltage of the system is more stable;

[0076] When eliminating the 7th harmonic magnetic field generated in the receiving end plane, the spacing Δx between two adjacent turns of the coil T is designed as: where k = 1, 2, 3…n, and n is a positive integer greater than or equal to 1; at this time, the amplitude of the 7th harmonic of the traveling wave magnetic field in the plane where the receiving coil is located is 0, and the 7th harmonic content in the induced electromotive force at the receiving end is zero. During the movement of the charging device at the receiving end, there is no longer 7th harmonic content in the induced electromotive force, and the output voltage of the system is more stable;

[0077] When simultaneously suppressing the 5th harmonic magnetic field and the 7th harmonic magnetic field generated by a single-phase transmitting coil, the spacing Δx between two adjacent turns of the coil T should be designed as At this time, both the 5th harmonic magnetic field and the 7th harmonic magnetic field generated by the distributed transmitting coil in the receiving end plane will be suppressed, and the harmonic induced voltage generated in the receiving coil will also be suppressed, thereby achieving the purpose of suppressing the output voltage fluctuation of the system; similarly, when the magnetic field generated by the single-phase transmitting coil contains only the i-th harmonic component and the (i + 2)-th harmonic component at the same time, the spacing Δx between two adjacent turns of the coil T should be designed as At this time, the distributed transmitting coil can simultaneously suppress the i-th harmonic magnetic field and the (i + 2)-th harmonic magnetic field generated in the receiving coil plane, achieving the purpose of suppressing the output voltage fluctuation of the system;

[0078] When the magnetic field generated by the single-phase transmitting coil contains harmonic components such as the i-th, (i + 2)-th, (i + 4)-th, (i + 6)-th, etc. at the same time, since the higher the harmonic order, the smaller the amplitude of the harmonic induced voltage generated by the harmonic magnetic field in the receiving coil, so when designing the spacing Δx between two adjacent turns of the coil T the main purpose should be to suppress the low-order harmonics, and the spacing Δx between two adjacent turns of the coil T should be designed as

[0079] In the process of designing the three-phase distributed transmitting coil of a wireless power supply system, in order to achieve the optimal output fluctuation suppression effect, the transmitting coil is generally designed to eliminate the 5th harmonic magnetic field. The length of the distributed transmitting coil affects both the amplitude of the harmonic magnetic field related to the output voltage fluctuation and the amplitude of the fundamental magnetic field. To maximize the output voltage, the fundamental distribution coefficient k dT-1 should be maximized. It can be seen from Figure 4 that in practical applications, k in the above turn spacing expression should be set to 1. For a three-phase distributed meandering transmitting coil with the number of turns N T , the adjacent turn spacing △x T should be designed as:

[0080]

[0081] The above has introduced in detail a structure of a distributed transmitting coil applied to a three-phase dynamic wireless power supply system proposed by the present invention. Specific examples are used in this article to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A distributed transmitting coil structure applied to a three-phase dynamic wireless power supply system, characterized in that: Each phase of the distributed emission coil structure is composed of multiple coils. The multiple coils are connected together in a series connection mode at the end sides, which can ensure that the same current passes through them. The multiple coils parallel to the x-axis direction are tightly connected, while the multiple coils parallel to the y-axis are placed with a distance difference of Δx along the x-axis direction, and the multiple coils are equidistant from each other. By reasonably designing the spacing Δx between two adjacent turns of coils in the distributed emission coil, T the harmonic traveling wave magnetic field of the emission coil is eliminated, and the purpose of suppressing the fluctuation of the output power in the three-phase dynamic wireless power supply system is achieved. T ​ The distance Δx between two adjacent turns of the described distributed transmitting coil T The specific design method is as follows: For the phase-A coil in a three-phase distributed structure, when a direct current i a = I0 is passed through the coil, the phase-A coil generates a fundamental magnetic field in the receiving-end plane. The fundamental magnetic fields generated by each turn of the coil have the same amplitude B z-1 and pole pitch τ, but are spatially separated by a distance of Δx T along the x-axis direction; The fundamental magnetic fields generated by each turn of the coil differ in phase by γ1, where γ1 is related to △x T and satisfies: The total fundamental magnetic field B generated by the phase A coil z-A1 is equal to the phasor sum of the fundamental magnetic fields generated by each turn of the coil. From the geometric relationship in the phasor diagram, it can be seen that the total fundamental magnetic field B z-A1 has an amplitude that satisfies: where k dT-1 has an expression that satisfies: where k dT-1 ≤ 1, k dT-1 is defined as the fundamental wave distribution coefficient of the transmitting end, which is used to represent the amplitude attenuation of the fundamental wave magnetic field B z-A1 after the transmitting coil adopts a distributed structure; where the subscript dT represents Distributed transmitter coil, that is, a distributed transmitting coil, and the number represents the harmonic order of the traveling wave magnetic field; The i-th harmonic magnetic fields generated by each turn of the coil still have a spatial difference of △x along the x-axis T in distance distribution. Due to the pole pitch τ i of the i-th harmonic magnetic field being only 1 / i of the fundamental pole pitch τ, the i-th harmonic magnetic fields generated by each turn of the coil have a phase difference of γ i which is i times that of the fundamental wave, i.e.: As can be seen from the geometric relationship in the phasor diagram, the amplitude of the i-th harmonic magnetic field B z-Ai satisfies: where k dT-i has an expression that satisfies: Accordingly, define k dT-i as the i-th harmonic distribution coefficient of the transmitting end, which is used to represent the amplitude attenuation of the i-th harmonic magnetic field B z-Ai in the distributed transmitting coil; In order to make the amplitude of the i-th harmonic magnetic field B z-Ai be 0, the i-th harmonic distribution coefficient k dT-i at the transmitting end satisfies: k dT-i ＝0 (7) Substituting Equation (4) and Equation (6) into Equation (7) and solving, we get: By reasonably designing the inter-turn distance △x of the distributed emission coil T , the purpose of eliminating the i-th harmonic magnetic field is achieved.

2. The structure according to claim 1, characterized in that, If, in order to eliminate the fifth harmonic magnetic field generated by the transmitting coil, the spacing Δx between two adjacent coils carrying the same current in this structure T is designed as: where k = 1, 2, 3... n, and n is a positive integer greater than or equal to 1.

3. The structure according to claim 1, characterized in that, If, in order to eliminate the seventh harmonic magnetic field generated by the transmitting coil, the spacing Δx between two adjacent coils carrying the same current in this structure T is designed as: where k = 1, 2, 3…n, and n is a positive integer greater than or equal to 1.

4. The structure according to claim 1, characterized in that, If, in order to weaken the fifth-harmonic magnetic field and the seventh-harmonic magnetic field generated by the transmitting coil, the spacing Δx between two adjacent coils carrying the same current in this structure T is designed as: where k = 1, 2, 3…n, and n is a positive integer greater than or equal to 1.

5. The structure according to claim 1, characterized in that, To maximize the output voltage, make the fundamental wave distribution coefficient k dT-1 maximum. Let k = 1 in the above turn pitch expression, that is, the turn pitch △x T is designed to be

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