Variable frequency motor air gap length optimization method and electromagnetic design parameter determination method

Abstract

The invention relates to a variable frequency motor air gap length optimization method and an electromagnetic design parameter determination method, and the method comprises the steps: firstly obtaining an air gap length theoretical optimal solution, which comprises the steps: building a binary relational expression between the total loss of a variable frequency motor and the air gap length, introducing a Newton-Raphson method, constructing an air gap length function, and constructing a Newton-Raphson formula; the method comprises the following steps: selecting operation efficiency, obtaining an initial air gap length by using an air gap length calculation formula of a common induction motor, substituting the initial air gap length into a Newton-Raphson formula to carry out iterative calculation to obtain a final value of the air gap length, calculating a power factor by using the obtained final value of the air gap length, and if the calculated power factor meets a design requirement, determining that the power factor is a power factor. The final value of the air gap length obtained by iteration is the theoretical optimal solution of the air gap length; and then, a whole set of relatively accurate electromagnetic design parameters is calculated based on an air gap length theory optimal solution, so that harmonic loss caused by an intelligent speed regulation driver is reduced, insulation damage is reduced, and the service life of the motor is prolonged.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic design of variable frequency motors, and in particular relates to a method for optimizing the air gap length of a variable frequency motor and a method for determining electromagnetic design parameters. Background Art

[0002] With the rapid development of power electronics technology and new semiconductor devices, AC speed regulation technology has been continuously improved and enhanced. The gradually improved intelligent speed regulation driver has been widely used in AC motors due to its excellent performance. However, it will generate harmonic voltage and current of varying degrees during its operation. When used in ordinary motors, it will cause an increase in motor temperature rise and a decrease in efficiency. Therefore, it is particularly important to design a suitable variable frequency motor.

[0003] At present, the electromagnetic design of variable frequency motors is generally based on the classic magnetic circuit design method to obtain the initial key dimensions and parameters, and then some parameters are appropriately changed, which often fails to obtain relatively accurate key dimensions.

[0004] In order to reduce the loss caused by the harmonic waveform of the intelligent speed control drive, it is an essential part of the variable frequency motor design to appropriately increase the motor air gap length. However, for motors with different powers and pole numbers, it is often impossible to calculate the appropriate air gap length in the early electromagnetic design. An inappropriate air gap length will cause the motor temperature to rise too high, which will not only reduce the motor's operating efficiency, but also cause motor insulation damage and reduce the motor's service life.

[0005] Calculating the theoretical optimal solution for the air gap length of the motor is the key to the electromagnetic design of the variable frequency motor. For this, there is currently no better design method in the existing technology. Summary of the invention

[0006] The technical problem to be solved by the present invention is to make up for the deficiencies of the prior art and to provide a method for optimizing the air gap length of a variable frequency motor and a method for determining electromagnetic design parameters.

[0007] To solve the above technical problems, the technical solution of the present invention is: A method for optimizing the air gap length of a variable frequency motor comprises the following steps: Step 1: Establish the total loss and air gap length of the variable frequency motor The binary relation ; Step 2: Based on the relationship between the total loss of the variable frequency motor and the air gap length, the Newton-Raphson method is introduced to construct the air gap length function: (1); Step 3: Construct the Newton-Raphson formula based on the air gap length function: (2); Step 4: Select the operating efficiency ; Use the common induction motor air gap length calculation formula to get the initial air gap length : ; Step 5: Set the initial air gap length Substitute into the Newton-Raphson formula for iterative calculation, when When , the iteration operation ends and the final value of the air gap length is obtained. ; Step 6: Based on the final value of the air gap length obtained in step 6 Calculate the power factor; If the calculated power factor does not meet the design requirements, adjust the operating efficiency , repeat step 5; If the calculated power factor meets the design requirements, the final value of the air gap length obtained in step 5 is This is the theoretical optimal solution for the air gap length.

[0008] Furthermore, in step 1, the total loss of the variable frequency motor includes stator copper loss , rotor copper loss Iron loss and ventilation losses , respectively establish the stator copper loss, rotor copper loss, iron loss and ventilation loss and air gap length The binary relation of is: , , and , then the total loss of the variable frequency motor is expressed as: (3).

[0009] Furthermore, the stator copper loss , rotor copper loss and air gap length The binary relationship is established as follows: First establish the stator current required for the magnetizing air gap and air gap length The binary relation ; Obtain circuit equivalent impedance based on the fundamental wave equivalent circuit of the variable frequency motor , Circuit Equivalent Resistance And circuit equivalent reactance : (4); (5); (6); in, is the fundamental voltage amplitude, is the fundamental stator current effective value, is the input power, is the power factor; (7); (8) Combining equations (7) and (8), we can get the circuit equivalent resistance and circuit equivalent reactance respectively: (9); in, is the stator resistance, is the stator leakage reactance, is the field resistance, is the magnetizing reactance, is the equivalent resistance of the rotor, is the rotor calculated equivalent leakage reactance; Combining equation (4) and equation (9), , , , , and Respectively transformed into The binary relation of is: (10) Since the fundamental stator current effective value The stator current required for the magnetizing air gap Approximately equal, let , then the fundamental stator current effective value and air gap length The binary relation is ; Then formula (10) can be rewritten as: (11); According to the harmonic equivalent circuit of the variable frequency motor, we can obtain: harmonic stator resistance , harmonic excitation resistance , stator harmonic leakage reactance , Rotor equivalent harmonic leakage reactance , Harmonic rotor equivalent resistance and kth harmonic inductance : (12); Where k represents the kth harmonic, is the resistance increase coefficient due to skin effect, is the kth harmonic winding factor; Substituting formula (11) into formula (12), we get: (13); According to the fundamental wave equivalent circuit of the variable frequency motor, the fundamental wave excitation current is obtained And the rotor equivalent current According to the harmonic equivalent circuit of the variable frequency motor, the harmonic excitation current is obtained Harmonic rotor equivalent current : (14); In the formula, for and The phase difference between (15); In the formula, for and The phase difference between (16); In the formula, for and The phase difference between (17); In the formula, for and The phase difference between Since the high-order harmonics have little impact on the operation of the motor, only the impact of the 5th and 7th harmonics is considered here, and the stator copper loss and rotor copper loss They are: (18); (19).

[0010] Furthermore, the stator current required to magnetize the air gap is and air gap length The binary relation is: (20); in, is the extreme logarithm; is the stator slot width; is the vacuum permeability; is the phase number; is the number of stator slots; is the inner diameter of the stator, , is the air gap diameter, , is the rated power, is the motor constant, is the aspect ratio of the equivalent axial length to the air gap diameter, and , is the synchronous speed in seconds, and , is the rated frequency; is the fundamental winding factor of the stator winding: , is the winding pitch, is the number of slots per pole per phase, is the pole distance, ; is the air gap flux density, The value range is [0.7, 0.9].

[0011] Furthermore, the iron loss and air gap length The binary relation for: (20); in is the fundamental iron loss, is the 5th harmonic iron loss, is the 7th harmonic iron loss; (twenty one); in, is the hysteresis loss coefficient, is the eddy current loss coefficient, is the stray loss coefficient, Fundamental angular frequency, is the kth harmonic voltage amplitude, is the stator outer diameter.

[0012] Furthermore, the ventilation loss and the air gap length The binary relation for: (twenty two); in, is the air density, is the flow resistance coefficient.

[0013] A method for determining electromagnetic design parameters of a variable frequency motor, using the above-mentioned variable frequency motor air gap length optimization method to obtain the theoretical optimal solution of the air gap length ,make , and substitute into equation (23)-(27) to calculate respectively: Stator inner diameter : (twenty three); Stator outer diameter : (twenty four), in, is the stator slot opening height, is the stator slot shoulder height, It is the stator slot shoulder. Stator slot winding trapezoidal height, is the stator slot insulation spacing, is the magnetic height of the stator yoke; Rotor outer diameter : (25); Rotor inner diameter : (26), in, is the rotor bar height, is the magnetic height of the rotor yoke; Stator and rotor core length : (27), ; Air gap magnetic flux : (28) in, is the number of parallel branches, is the back EMF, is the number of series turns, is the arithmetic mean coefficient of the flux density per pole The value range of is [0.6, 0.77]; First, from the corresponding value range, they are and Assign a proposed value to , ;Will and Substituting into formula (9), we can get: (29) For the calculated Rounding, we get ; make , and then substitute it into formula (9) to obtain the corrected air gap flux density .

[0014] The beneficial effects that can be achieved by the present invention are as follows: by establishing a binary relationship between the total loss of the variable frequency motor and the air gap length, entering the Newton-Raphson method to construct the Newton-Raphson formula for iterative optimization, and taking the design operating efficiency and power factor of the variable frequency motor as design verification conditions, finally obtaining the theoretical optimal solution of the air gap length of the variable frequency motor design, so that based on the theoretical optimal solution of the air gap length, a complete set of relatively accurate electromagnetic design parameters can be calculated, thereby reducing the harmonic loss caused by the intelligent speed regulation drive, reducing insulation damage, and increasing the service life of the motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a cross-sectional view of the electromagnetic design of the variable frequency motor.

[0016] Figure 2 It is the fundamental wave equivalent circuit diagram of the variable frequency motor.

[0017] Figure 3 It is the harmonic equivalent circuit diagram of the variable frequency motor.

[0018] Figure 4 yes Figure 1 Part A in the middle is an enlarged and rotated image.

[0019] Figure 5 yes Figure 1 Part B in the middle is an enlarged and rotated image.

[0020] Figure 6 4 is a flow chart of a method for optimizing the air gap length of a variable frequency motor in an embodiment.

[0021] In the figure: 1-shaft, 2-rotor, 3-rotor slot, 4-stator slot, 5-stator DETAILED DESCRIPTION The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0022] 1 Using the classical electromagnetic design method, calculate the stator inner diameter , rotor outer diameter , equivalent axial length 、Air gap magnetic density , stator slot type and corresponding size, stator outer diameter wait: ①. Rated power according to motor design requirements , pole pairs Requirements and rated frequencies , Motor constant , get the air gap diameter of the asynchronous motor : (1) Among them, the aspect ratio of equivalent axial length to air gap diameter is , synchronous speed per second . Equivalent axial length : (2) ②、List the calculation formula of air gap length, stator inner diameter, rotor outer diameter, stator core length and air gap length: Depend on Figure 1 The inner diameter of the stator can be obtained and rotor outer diameter Dimensions: (3) (4) in, is the air gap length.

[0023] Assuming that no cooling channel is added in this design, the stator and rotor core lengths are You can get: (5) ③. Calculate the air gap magnetic flux density The fundamental winding factor of the stator winding is: (6) in, is the winding pitch, is the phase number, is the number of slots per pole per phase, is the polar distance; (7) Back EMF (Us is the effective value of the fundamental voltage), select the number of parallel branches , get the total number of series turns : (8) Number of conductors per slot : (9) in, is the air gap flux density, The value range of is [0.7, 0.9]; is the arithmetic mean coefficient of the flux density per pole The value range of is [0.6, 0.77]; is the number of stator slots.

[0024] From the corresponding value range, they are and Assign a proposed value to , ;Will and Substituting into formula (9), we can get: (10) For the calculated Rounding, we get ; make , and then substitute it into formula (9) to obtain the corrected air gap flux density .

[0025] ④. Establish the air gap length Relationship with the stator current Is required for the magnetizing air gap: Select stator slot width , then the equivalent slot width for: (11) The slot opening coefficient for: (12) Carter coefficient for: (13) The stator slot pitch , substituting into formula (13) we get: (14) Equivalent air gap The approximate formula is: (15) Air gap magnetic pressure drop for: (16) In the formula, is the air gap magnetic field strength, is the magnetic permeability of vacuum.

[0026] Assume that the air gap flux density of the motor is sinusoidally distributed along the pole shoe and the magnetic permeability of iron is Relative to vacuum permeability Infinite, so the magnetic resistance of the core part and the magnetic voltage drop of the core are both 0, so the entire stator current chain All are used to produce the required flux density in the air gap, so: (17) (18) (19) Substituting equation 12 and equation 14, we can simplify them to obtain: (20) The right side of the equation has the air gap length are all known values, then the stator current required to magnetize the air gap can be becomes a factor about the air gap length The equation is: (twenty one) ⑤. Calculate the stator conductor cross-sectional area through the stator current required for the magnetized air gap, determine the stator slot type and slot height, and Figure 1 and Figure 4 Thus, the stator outer diameter is calculated : Proposed stator current density and slot fill rate , stator conductor cross-sectional area and the area occupied by the winding in the slot for: (twenty two) (twenty three) Determine the stator slot type through the stator conductor cross-sectional area and calculate the stator slot size: stator slot width b s1 , stator slot winding shoulder width b s4c 、Stator slot shoulder width b s4 , stator slot winding fillet diameter b s5c , stator slot fillet diameter b s5 , stator slot opening height h s1 、Stator slot shoulder height h s2 , stator slot shoulder h s3 , stator slot winding height h s4 , stator slot winding trapezoidal height h s5 、Stator slot insulation spacing h s6 、Stator slot spacing h s ’ .

[0027] Proposed stator yoke magnetic density , select the lamination coefficient k Fe , stator yoke magnetic height h ys for: (twenty four) Stator outer diameter D se for: (25) ⑥ Calculate the rotor bar current through the stator current, and then calculate the rotor bar cross-sectional area, determine the rotor slot type and slot height, and then calculate the rotor bar cross-sectional area through the stator current. Figure 1 and Figure 5 The inner diameter of the rotor is calculated : Proposed rotor current density J r , where the rotor bar current and rotor bar cross-sectional area are: (26) (27) in, is the power factor, is the number of rotor slots.

[0028] Determine the rotor slot type and calculate the rotor slot size by the rotor conductor cross-sectional area: rotor bar opening b r1 、Rotor bar shoulder width b r4 , rotor bar fillet diameter b r5 , rotor bar opening height h r1 、Rotor bar shoulder height h r2 , rotor bar height h rr .

[0029] Estimated magnetic density of rotor yoke , rotor yoke magnetic height h yr for: (28) Rotor inner diameter D ri for: (29) In this way, a complete set of magnetic circuit calculation parameters is obtained. The air gap length As an unknown variable, the optimal solution of the air gap length calculated by the algorithm can be used to obtain the entire set of magnetic circuit calculation parameters.

[0030] 2. The output voltage of the intelligent speed control drive is subjected to double Fourier series analysis. According to the Fourier series and Bessel function, the harmonic voltage expression is derived through the carrier and modulation wave expressions.

[0031] Output phase voltage of inverter circuit For harmonic analysis, the Fourier series expression is: (31) Where m zrepresents the harmonic order of the carrier wave, n represents the harmonic order of the modulating wave, Indicates the frequency of the sine wave angle n, U d is the DC bus voltage, J n is the Bessel function, M represents the modulation ratio, and N represents the carrier ratio.

[0032] Here we only consider the impact of harmonic power supply, without considering the impact of the configuration of intelligent speed control drive, and can transform equation 31 into: (32) In the formula, is the fundamental angular frequency, U k is the kth harmonic voltage amplitude, is the initial phase angle of the kth harmonic.

[0033] From this we can get the kth harmonic voltage U k Although higher harmonics have a greater impact on motor operation, because of their smaller amplitude, here we only consider the 5th and 7th harmonics, so the phase voltage can be approximated as the superposition of the fundamental voltage, the 5th harmonic voltage and the 7th harmonic voltage: (33) 3 Calculate the iron loss of the variable frequency motor: When using the harmonic analysis method, the iron loss can be expressed as: (34) In the formula, is the harmonic frequency, is the amplitude of the sinusoidal magnetic flux density.

[0034] Taking one phase of an induction motor as an example, ignoring the stator winding resistance voltage drop, the inverter circuit output phase voltage can be expressed as: (35) In the formula, is the winding flux, is the winding flux, and S is the cross-sectional area of ​​the stator core.

[0035] The Fourier decomposition of the magnetic flux density inside the motor is obtained: (36) In the formula, B k is the kth harmonic magnetic flux amplitude. Substituting equation (36) into equation (35), we get a value about B k Substituting the u(t) expression into equation (32), we can simplify it to obtain: (37) Substitution , then formula (34) can be transformed into: (38) Where Kh, Ke, and Kex are the hysteresis loss coefficient, eddy current loss coefficient, and stray loss coefficient, respectively. These three parameters can be obtained by consulting the manufacturer's manual based on the selected electrical steel model.

[0036] pass Figure 1 It can be seen that the stator core area S is: (39) Substituting into formula (38) we can obtain: (40) From the analysis, we can see that except for the air gap length Except for the above, all are known values, then equation (38) can be used to obtain the core loss with respect to the air gap length: The binary relation , also considering only the 5th and 7th harmonics, the total core loss can be expressed as: (41) 4 Calculate the copper loss of the variable frequency motor: ① First, according to Figure 2 Fundamental frequency conversion motor equivalent circuit diagram to calculate the fundamental wave stator and rotor impedance parameters: (42) (43) (44) Among them, the circuit equivalent impedance is Z T , the circuit equivalent resistance is R T , the circuit equivalent reactance is X T , U 1 is the fundamental voltage amplitude, I 1 is the effective value of the fundamental stator current, P 1 is the input power, then the circuit impedance Z T The expression is: (45) Will Substituting in, we simplify the expressions for resistance and reactance: (46) In the formula, stator resistance R1, stator leakage reactance , Excitation resistance R m , excitation reactance X m , Rotor equivalent resistance , Rotor equivalent leakage reactance , s is the slip rate. When the speed of the variable frequency motor changes, different slip rates can be obtained. Substituting s=0, s=1, s=-1, the following six equations are constructed: When s=0, we get: (47) When s=1, we get: (48) When s=-1, we get: (49) From the analysis, we can see that the six equations include the stator resistance R 1 , stator leakage reactance , Excitation resistance R m , excitation reactance X m , Rotor equivalent resistance , Rotor equivalent leakage reactance , Fundamental stator current effective value I 1 Seven unknowns, here I 1 As a variable, if the matrix determinant of the coefficients before the unknowns in the calculation equations is not 0, then the stator resistance R 1 , stator leakage reactance , Excitation resistance R m , excitation reactance X m , Rotor equivalent resistance , Rotor equivalent leakage reactance They are transformed into binary equations about the fundamental stator current effective value I1: (50) Here the fundamental stator current effective value I 1 It is approximately equal to the stator current Is required for the magnetizing air gap calculated previously, so the equation for the fundamental stator current in the above formula can be converted into the equation for the air gap length The equation is: (51) ② First, according to Figure 3 Harmonic frequency conversion motor equivalent circuit diagram to calculate the harmonic stator and rotor impedance parameters: The parameters in the harmonic equivalent circuit can be calculated as follows: (52) In the above formula, R 1k is the harmonic stator resistance, is the stator harmonic leakage reactance, Calculate the equivalent harmonic resistance of the rotor, Calculate the equivalent harmonic leakage reactance of the rotor, When it is the fundamental wave, the rotor slot leakage reactance is is the harmonic leakage reactance, is the end leakage reactance, is the chute leakage reactance, K x K is the resistance increase coefficient due to skin effect. r is the leakage resistance reduction factor during skin effect, is the fundamental rotor bar resistance, is the fundamental wave end ring resistance. For the convenience of calculation, the rotor bar resistance is equal to the end ring resistance. Substituting in and performing approximate operations on the leakage reactance, equation (52) can be transformed into: (53) If the rotor slot is approximated as a rectangular slot, then taking the skin effect into account, the resistance increase factor and reactance reduction factor are: (54) (55) (56) In the formula is the rotor bar height, is the resistivity of cast aluminum, is the harmonic frequency, and the initial air gap length is selected before The rotor bar height is obtained , From this, we can get the harmonic resistance increase coefficient K rk Harmonic reactance reduction factor K xk . And because of the harmonic inductance , then the kth harmonic inductance , then the kth harmonic winding factor for: (57) The following formula is obtained: (58) Analyzing formula (58), it can be seen that the harmonic impedance in the formula can be obtained by multiplying the fundamental impedance and the corresponding coefficient. Substituting formula (51) into it, the equation for the air gap length can be obtained: (59) ③Analysis Figure 2 , Figure 3 , and obtain the fundamental excitation current, rotor equivalent current and harmonic excitation current, rotor equivalent current: (60) In the formula, for and The phase difference between them.

[0037] (61) In the formula, for and The phase difference between them. (62) In the formula, for and The phase difference between them.

[0038] (63) In the formula, for and The phase difference between them.

[0039] ④. Using the previous current and impedance formula, the stator copper loss is obtained by considering only the 5th and 7th harmonics. and rotor copper loss : (64) (65) In the formula, is the effective value of the fifth harmonic stator current, is the fifth harmonic stator resistance, is the effective value of the seventh harmonic stator current, is the seventh harmonic stator resistance, is the fundamental-wave rotor equivalent current, is the equivalent resistance of the rotor, is the fifth harmonic rotor equivalent current, is the fifth harmonic rotor equivalent resistance, is the seventh harmonic rotor equivalent current, It is the seventh harmonic rotor calculated equivalent resistance.

[0040] 5Calculate ventilation loss: In addition to the copper loss and iron loss of the stator and rotor of the variable frequency motor, there are also friction loss and ventilation loss. Since the variable frequency motor here does not consider the ultra-high speed situation, the friction loss is ignored and only the ventilation loss is considered. Then the ventilation loss P w Calculate as follows: (66) In the formula is the flow resistance coefficient, is the air density, we can get: (67) Where ht is the height of the rotor surface protrusion, is the dynamic viscosity of the air; if the rotor non-convex groove structure is designed, the flow resistance coefficient can be simplified to: (68) 6 Calculate the relationship between the total loss of the variable frequency motor and the air gap length, and select the operating efficiency , we get a value for the air gap length Substituting the one-variable equation into the operating efficiency , the air gap length is calculated by the Newton-Raphson method The theoretical optimal solution is obtained and the value is substituted into the power factor calculation formula to determine whether it meets the design requirements: (69) Substitution , then formula (65) can be transformed into: (70) The Newton-Raphson method is introduced, and the air gap length function is for: (71) Take the first-order derivative of the above formula : (72) Construct the Newton-Raphson formula: (73) Using the common induction motor air gap length calculation formula, an initial air gap length is obtained : (74) Let variable air gap length , substituted into the Newton-Raphson formula, after several iterations, when the convergence judgment When , the iteration operation ends and we get The final value of .

[0041] Calculating Power Factor : (75) Using the Newton-Raphson formula, we get Substitute it into equation (74) to determine whether the calculated power factor meets the design requirements. If not, adjust the efficiency requirements until the power factor requirements are met. The air gap length obtained at this time is This is the theoretical optimal solution for variable frequency motor design.

[0042] 7 Substitute the newly obtained theoretical optimal air gap length of the variable frequency motor into the previous electromagnetic design, re-design the electromagnetic design, and obtain new electromagnetic design parameters to complete the electromagnetic design work: The optimal solution , substitute into the formulas in step 1 to obtain new electromagnetic design parameters, and finally complete the electromagnetic design under the optimal solution of air gap length.

Claims

1. A method for optimizing the air gap length of a variable frequency motor, characterized in that: The steps include: Step 1: Establish the total loss and air gap length of the variable frequency motor The binary relation ; Step 2: Based on the relationship between the total loss of the variable frequency motor and the air gap length, the Newton-Raphson method is introduced to construct the air gap length function: （1）； Step 3: Construct the Newton-Raphson formula based on the air gap length function: （2）； Step 4: Select the operating efficiency ; The initial air gap length is obtained by using the common induction motor air gap length calculation formula : ； Step 5: Set the initial air gap length Substitute into the Newton-Raphson formula for iterative calculation, when When , the iteration operation ends and the final value of the air gap length is obtained. ; Step 6: Based on the final value of the air gap length obtained in step 6 Calculate the power factor; If the calculated power factor does not meet the design requirements, adjust the operating efficiency , repeat step 5; If the calculated power factor meets the design requirements, the final value of the air gap length obtained in step 5 is This is the theoretical optimal solution for the air gap length.

2. The method for optimizing the air gap length of a variable frequency motor according to claim 1, characterized in that: In step 1, the total loss of the variable frequency motor includes stator copper loss , rotor copper loss Iron loss and ventilation losses , respectively establish the stator copper loss, rotor copper loss, iron loss and ventilation loss and air gap length The binary relation of is: , , and , then the total loss of the variable frequency motor is expressed as: （3）。 3. The method for optimizing the air gap length of a variable frequency motor according to claim 2, characterized in that: The stator copper loss , rotor copper loss and air gap length The binary relationship is established as follows: First establish the stator current required for the magnetizing air gap and air gap length The binary relation ; Obtain circuit equivalent impedance based on the fundamental wave equivalent circuit of the variable frequency motor , Circuit Equivalent Resistance And the circuit equivalent reactance : （4）； （5）； （6）； in, is the fundamental voltage amplitude, is the fundamental stator current effective value, is the input power, is the power factor; （7）； （8） Combining equations (7) and (8), we can get the circuit equivalent resistance and circuit equivalent reactance respectively: （9）； in, is the stator resistance, is the stator leakage reactance, is the field resistance, is the magnetizing reactance, is the equivalent resistance of the rotor, is the rotor calculated equivalent leakage reactance; Combining equation (4) and equation (9), , , , , and Transformed into about The binary relation of is: （10） Since the fundamental stator current effective value The stator current required for the magnetizing air gap Approximately equal, let , then the fundamental stator current effective value and air gap length The binary relation is ; Then formula (10) can be rewritten as: （11）； According to the harmonic equivalent circuit of the variable frequency motor, we can obtain: harmonic stator resistance , harmonic excitation resistance , stator harmonic leakage reactance , Rotor equivalent harmonic leakage reactance , Harmonic rotor equivalent resistance and kth harmonic inductance : （12）； Where k represents the kth harmonic, is the resistance increase coefficient due to skin effect, is the kth harmonic winding factor; Substituting formula (11) into formula (12), we get: （13）； According to the fundamental wave equivalent circuit of the variable frequency motor, the fundamental wave excitation current is obtained And the rotor equivalent current According to the harmonic equivalent circuit of the variable frequency motor, the harmonic excitation current is obtained Harmonic rotor equivalent current : （14）； In the formula, for and The phase difference between （15）； In the formula, for and The phase difference between （16）； In the formula, for and The phase difference between （17）； In the formula, for and The phase difference between Since the high-order harmonics have little impact on the operation of the motor, only the impact of the 5th and 7th harmonics is considered here, and the stator copper loss and rotor copper loss They are: （18）； （19）。 4. The method for optimizing the air gap length of a variable frequency motor according to claim 3, characterized in that: Stator current required to magnetize the air gap and air gap length The binary relation is: （20）； in, is the extreme logarithm; is the stator slot width; is the vacuum permeability; is the phase number; is the number of stator slots; is the inner diameter of the stator, , is the air gap diameter, ， is the rated power, is the motor constant, is the aspect ratio of the equivalent axial length to the air gap diameter, and , is the synchronous speed in seconds, and , is the rated frequency; is the fundamental winding factor of the stator winding: ， is the winding pitch, is the number of slots per pole per phase, is the pole distance, ; is the air gap flux density, The value range is [0.7, 0.9].

5. The method for optimizing the air gap length of a variable frequency motor according to claim 2, characterized in that: The iron loss and air gap length The binary relation for: （20）； in is the fundamental iron loss, is the 5th harmonic iron loss, is the 7th harmonic iron loss; （21）； in, is the hysteresis loss coefficient, is the eddy current loss coefficient, is the stray loss coefficient, Fundamental angular frequency, is the kth harmonic voltage amplitude, is the stator outer diameter.

6. The method for optimizing the air gap length of a variable frequency motor according to claim 2, characterized in that: The ventilation loss and air gap length The binary relation for: （22）； in, is the air density, is the flow resistance coefficient.

7. A method for determining electromagnetic design parameters of a variable frequency motor, characterized in that: The optimal solution of the air gap length is obtained by using the method for optimizing the air gap length of the variable frequency motor as claimed in claim 1. ,make , and substitute into equation (23)-(27) to calculate respectively: Stator Inner Diameter : （23）； Stator outer diameter : （24）， in, is the stator slot opening height, is the stator slot shoulder height, It is the stator slot shoulder. Stator slot winding trapezoidal height, is the stator slot insulation spacing, is the magnetic height of the stator yoke; Rotor outer diameter : （25）； Rotor inner diameter : （26）， in, is the rotor bar height, is the magnetic height of the rotor yoke; Stator and rotor core length : （27）， ； Air gap magnetic flux : （28） in, is the number of parallel branches, is the back EMF, is the number of series turns, is the arithmetic mean coefficient of the flux density per pole The value range of is [0.6, 0.77]; First, from the corresponding value range, they are and Assign a proposed value to , ;Will and Substituting into formula (9), we can get: （29） For the calculated Rounding, we get ; make , and then substitute it into formula (9) to obtain the corrected air gap flux density .

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