Method for calculating capacitance between stator coil and stator core of permanent magnet synchronous motor

Abstract

The application relates to a calculation method of the capacitance between a permanent magnet synchronous motor stator coil and a stator core. N winding coils of the same size arranged side by side in front of the stator core are regarded as ideal cylindrical conductors, one of the conductors and other two conductors adjacent to the one conductor are taken as a model for calculating the capacitance value between a single winding coil and the stator core, and the three adjacent conductors are conductor 1, conductor 2 and conductor 3 in turn. The calculation process comprises the following steps: step 1, calculating the coordinates of equivalent line charges of the three conductors; step 2, calculating the spatial potential distribution in the region x<‑D based on the mirror charge method and the superposition theorem; step 3, calculating the potential on the surface of the conductors; step 4, calculating the capacitance value of the conductor 2 to the stator core in the three-conductor model; and step 5, calculating the total capacitance of the winding to the stator core. The calculation method is simple, and the calculation result can be used as a supplement and a comparison of the calculation result of the commercial software without the need of purchasing and learning the commercial software.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of electronic power technology, and particularly relates to a calculation method of capacitance between a stator coil and a stator core of a permanent magnet synchronous motor. BACKGROUND

[0002] The permanent magnet synchronous motor is a kind of motor widely used at present. In use, the PWM mode is often adopted to realize the control of the permanent magnet synchronous motor. Due to the development of power electronic technology in recent years, in order to realize more fine control of the motor, the switching frequency of the power electronic device is continuously improved, the common-mode voltage generated thereby can form a coupling path through the stray capacitance in the motor, and shaft voltage and shaft current are generated on the motor shaft, which in turn causes damage to the motor. The common-mode current generated by the high-frequency common-mode voltage can flow into the ground through the grounded stator shell, and harmonic interference is brought. The capacitance between the stator coil and the stator core of the permanent magnet synchronous motor is an important component of the stray capacitance in the coupling path, and the numerical calculation thereof is of great significance to the suppression of the common-mode voltage and the common-mode current.

[0003] At present, the calculation of the capacitance between the stator coil and the stator core of the permanent magnet synchronous motor mainly adopts the following two methods:

[0004] 1. The capacitance between the stator coil and the stator core is regarded as a flat plate capacitance for calculation, and the medium therebetween is the slot insulation, as shown in FIG. 1. Figure 1

[0005] 2. A commercial software is used for modeling and calculation.

[0006] The winding in the stator slot is actually a conductor in the shape of a cylinder, and if the whole winding is regarded as a rectangle for calculation, the calculation is relatively simple, but the shape of the winding conductor and the influence of the air gap in the slot are ignored, and in some cases, the calculation result deviates greatly from the actual value. The commercial software is expensive and has certain difficulty and learning cost. SUMMARY

[0007] The purpose of the present application is to provide a calculation method of the capacitance between the stator coil and the stator core of the permanent magnet synchronous motor, the stator winding in the slot is regarded as a conductor in the shape of a cylinder, the capacitance between each winding and the stator core is calculated respectively, and the slot insulation layer and the air gap in the slot are taken into account, so as to improve the accuracy of the calculation result.

[0008] The present application provides a calculation method of the capacitance between the stator coil and the stator core of the permanent magnet synchronous motor, characterized in that n winding coils of the same size arranged side by side in front of the stator core are regarded as ideal cylindrical conductors, the air and the insulation layer are arranged between the stator core and the winding;

[0009] ​Take one of the conductors and the other two conductors adjacent to it as a model for calculating the capacitance value between a single winding coil and the stator core, and the three adjacent conductors are conductor 1, conductor 2 and conductor 3 in turn;

[0010] Take the surface of the stator core as the y-axis, take the straight line passing through the center of conductor 2 and perpendicular to the surface of the core as the x-axis, and take the intersection of the x-axis and the y-axis as the origin to establish a rectangular coordinate system; the model is divided into three regions according to the different media, including the region of x<-D, the region of -D<x<0 and the region of 0<x, and the relative dielectric constants of the three regions are ε1, ε2 and ε3 respectively, and D is the thickness of the insulation layer;

[0011] The calculation process is as follows:

[0012] Step 1, calculate the coordinates of the equivalent line charges of the three conductors:

[0013] Let the coordinates of the equivalent line charges of the three conductors be E1(E 1x ,E 1y ), E2(E 2x ,E 2y ) and E3(E 3x ,E 3y ), where,

[0014]

[0015]

[0016] E 2y =0, (Formula 3)

[0017]

[0018] Where d3 is the distance between the centers of the conductors, r is the radius of the conductor, and d is the distance from the center of the conductor to the surface of the stator core.

[0019]

[0020] Step 2, based on the mirror charge method and the superposition theorem, calculate the spatial potential distribution in the region x<-D:

[0021]

[0022] In the formula, ε0 is the dielectric constant of vacuum, λ1, λ2 and λ3 are the line charge densities of the equivalent line charges of the three conductors, and coefficients S and T can be calculated by formula 6 and formula 7;

[0023]

[0024]

[0025] ​where n, m are 1, 2 or 3, ε1, ε2 and ε3 are the relative dielectric constants of the regions of x<-D, -D<x<0 and 0<x respectively, S nm and T nm are the coefficients at the junction of the corresponding two regions; for example, the coefficients at the junction of the regions of -D<x<0 and 0<x are S 32 and T 32 ;

[0026] Step 3, calculate the potential of the surface of the conductor:

[0027] Three points are selected on the surface of the three conductors to calculate the potential of the conductors;

[0028]

[0029]

[0030]

[0031] where d3 is the distance between the centers of the conductors, r is the radius of the conductors, d is the distance from the center of the conductors to the surface of the stator core, and are the surface potentials of the three conductors respectively;

[0032] Step 4, calculate the capacitance of the conductor 2 to the stator core in the three-conductor model:

[0033] The simultaneous equations 8, 9 and 10 are as follows:

[0034]

[0035] Further, we can get

[0036]

[0037] The capacitance of the conductor 2 to the stator core is

[0038]

[0039] The capacitance c of a single coil to the stator core is approximately equal to c2, and the units of c and c2 are F / m;

[0040] where and are the surface potentials of the three conductors respectively, and λ1, λ2 and λ3 are the linear charge densities of the equivalent linear charges of the three conductors respectively;

[0041] Step 5, calculate the total capacitance of the winding to the stator core:

[0042] The total capacitance of the winding containing n coils to the stator core is:

[0043] c 总 = nc = nc2. (Equation 14)

[0044] With the above solution, through the calculation method of the capacitance between the stator coil and the stator core of the permanent magnet synchronous motor, the spatial structure in the stator slot is simplified into a "three-conductor model", and the spatial potential distribution of the "three-conductor model" is obtained by using the method of image charges. The capacitance of a single coil to the stator core is calculated, and then the total capacitance of the winding to the stator core is calculated. The calculation method is simple, and it can be calculated without purchasing and learning commercial software. The calculation results can be used as a supplement and comparison to the calculation results of commercial software.

[0045] The above description is only an overview of the technical solution of the present invention. In order to be able to understand the technical means of the present invention more clearly and implement it according to the content of the specification, the following takes the preferred embodiments of the present invention and combines with the drawings to describe in detail as follows. Brief Description of the Drawings

[0046] Figure 1 It is a schematic diagram of calculating the capacitance between the stator coil and the stator core of a permanent magnet synchronous motor by regarding the whole stator winding as a rectangle in the prior art, and regarding the capacitance between it and the stator core as a flat capacitor;

[0047] Figure 2 It is the spatial structure diagram of the stator core slot of the present invention;

[0048] Figure 3 It is the three-conductor model of the present invention. Detailed Embodiment

[0049] The following combines with the drawings and embodiments to further describe in detail the specific embodiments of the present invention. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0050] Refer Figure 2 As shown Figure 2 As shown, it is a part of the spatial structure in the stator core slot of a permanent magnet synchronous motor. n winding coils of the same size regarded as ideal cylindrical conductors are arranged side by side in front of the stator core. The space between the core and the winding is air and insulation layer. The coils, the core, and the insulation layer are regarded as infinitely extending in the direction perpendicular to the paper surface.

[0051] Take one of the conductors and the other two adjacent conductors to it as a model for calculating the capacitance value between a single winding coil and the stator core (abbreviated as three-conductor model), as Figure 3 . In the figure, d3 is the distance between the centers of each conductor, r is the radius of the conductor, d is the distance from the center of the conductor to the surface of the stator core (since each conductor is arranged side by side, d is equal for each conductor), and D is the thickness of the insulation layer.

[0052] For convenience of calculation, the surface of the stator core is taken as the y-axis, a straight line passing through the center of the conductor 2 and perpendicular to the surface of the core is taken as the x-axis, and a rectangular coordinate system is established with the intersection of the x-axis and the y-axis as the origin. The model shown in the figure can be divided into three regions according to the different media, and the relative dielectric constants of the regions where x<-D, -D<x<0 and 0<x are ε1, ε2 and ε3 respectively for convenience of calculation.

[0053] Since the coil, the core and the insulation layer are all considered to extend infinitely in the direction perpendicular to the paper, the influence of the z-axis is ignored in the calculation process, but it should be noted that the charge and the capacitance calculated are the values per unit length. In the calculation process, the core is grounded, and the calculation of the potential is all based on the potential of the core as the reference potential. The calculation process is as follows:

[0054] 1. Calculate the coordinates of the equivalent line charges of the three conductors.

[0055] Let the coordinates of the equivalent line charges of the three conductors be E1(E 1x ,E 1y ), E2(E 2x ,E 2y ) and E3(E 3x ,E 3y ),

[0056] wherein,

[0057]

[0058]

[0059] E 2y = 0, (Equation 3)

[0060]

[0061] 2. Calculate the spatial potential distribution in the region x<-D based on the mirror charge method and the superposition theorem:

[0062]

[0063] In the formula, ε0 is the dielectric constant of vacuum, λ1, λ2 and λ3 are the line charge densities of the equivalent line charges of the three conductors, and the coefficients S and T can be calculated by Equations 6 and 7.

[0064]

[0065]

[0066] 3. Calculate the potential on the surface of the conductor. Since the surface potential of the conductor is equal in the electrostatic field, three points on the surface of the conductor can be selected for calculation of the potential of the conductor.

[0067]

[0068]

[0069]

[0070] 4、Calculate the capacitance of conductor 2 to the stator core in the three-conductor model. The following matrix can be obtained by combining equations 8, 9 and 10:

[0071]

[0072] Further, we can get

[0073]

[0074] The capacitance of conductor 2 to the stator core is

[0075]

[0076] It can be considered that Figure 2 The capacitance c of a single coil to the stator core is approximately equal to c2. It should be noted that the units of c and c2 are F / m.

[0077] 5、Calculate the total capacitance of the winding to the stator core. Since the winding coils are arranged side by side, the total capacitance of the winding containing n coils to the stator core is:

[0078] c 总 = nc = nc2. (Equation 14)

[0079] The method for calculating the capacitance between the stator coil and the stator core of the permanent magnet synchronous motor simplifies the spatial structure in the stator slot to a "three-conductor model", and uses the mirror charge method to obtain the spatial potential distribution of the "three-conductor model" The capacitance of a single coil to the stator core is calculated, and the total capacitance of the winding to the stator core is calculated. The calculation method is simple, and it can be calculated without purchasing and learning commercial software. The calculation result can be used as a supplement and comparison of the calculation result of commercial software.

[0080] The above only describes the preferred embodiments of the present application and is not used to limit the present application. It should be noted that for ordinary skilled persons in the art, without departing from the technical principles of the present application, several improvements and modifications can be made, and these improvements and modifications should be considered as the protection scope of the present application.

Claims

1. A method of calculating the capacitance between a permanent magnet synchronous motor stator coil and a stator core, characterized by, The n same size winding coils arranged side by side in front of the stator core are regarded as ideal cylindrical conductors, the core and the winding are air and insulation layer, the coil, the core and the insulation layer are all regarded as extending infinitely in the direction perpendicular to the paper; Take one of the conductors and the other two adjacent conductors as the model for calculating the capacitance value between the single winding coil and the stator core, the three adjacent conductors are conductor 1, conductor 2 and conductor 3 in turn; A rectangular coordinate system is established with the stator core surface as the y-axis, a straight line passing through the center of the conductor 2 and perpendicular to the core surface as the x-axis, and the intersection point of the x-axis and the y-axis as the origin; the model is divided into three regions according to the different media, including the region of the region of and the region of , and , is the thickness of the insulating layer; The calculation process is as follows: Step 1, calculate the coordinates of the equivalent line charge of the three conductors: Let the coordinates of the equivalent line charges of the three conductors be , and wherein, ... (Formula 1); ... (Formula 2); ,...... (Formula 3); ... (Formula 4); wherein is the distance between the centers of the conductors, is the radius of the conductors, is the distance from the center of the conductors to the surface of the stator core; Step 2. Calculate the spatial potential distribution in the region based on the image charge method, superposition theorem: Step 3. Calculate the spatial potential distribution in the region based on the image charge method, superposition theorem: ... (Formula 5); wherein is the vacuum permittivity, , and are the line charge densities of the equivalent line charges of the three conductors, the coefficients S and T are calculated from equation 6 and equation 7; ... (Formula 6); ... (Formula 7); wherein , the value of a is 1, 2 or 3, , and are the relative dielectric constants of the regions of , and , and are the coefficients at the interface of the respective two regions; Step 3, calculate the potential on the surface of the conductor: Select three points on the surface of the three conductors to calculate the potential of the conductors; ... (Formula 8); ... (Formula 9); ... (Formula 10); wherein , and are the surface potentials of the three conductors, respectively; Step 4, calculate the capacitance value of conductor 2 to the stator core in the three conductor model: The simultaneous equations 8, 9 and 10 are as follows: ... (Formula 11); Further ... (Formula 12); The conductor 2 has a capacitance value of ... (Formula 13) Capacitance of individual coils to stator core Approximately equal to , And The unit is ; Step 5, calculate the total capacitance of the winding to the stator core: The total capacitance of the stator core for a winding pair containing n coils is: ... (Equation 14).

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