Mathematical model of dual three-phase permanent magnet synchronous motor considering electromagnetic-pressure coupling effect

Abstract

The present invention discloses a mathematical model of a dual three-phase permanent magnet synchronous motor that takes into account the electromagnetic-pressure coupling effect. Based on the results of electromagnetic field finite element calculations, combined with mathematical methods such as multi-dimensional interpolation and inversion, the establishment of a high-precision mathematical model of the electromagnetic module of the dual three-phase permanent magnet synchronous motor is realized, which can fully consider the influence of magnetic saturation, harmonic magnetic field and rotor position in the actual operation of the motor. On this basis, the model is established based on the calculation results under multiple pressures, and combined with the interpolation in the pressure dimension, the influence of pressure on the electromagnetic characteristics of the motor can be obtained. In summary, the electromagnetic-temperature coupled dual three-phase permanent magnet synchronous motor high-precision mathematical model established by the present invention can fully consider the influence of magnetic saturation, harmonic magnetic field, rotor position in the operation of the motor, and the changes in electromagnetic performance caused by the external environment pressure during the operation of the motor. Compared with the existing motor mathematical models, the present invention is more comprehensive and has better fidelity.

Description

Technical Field

[0001] The present invention belongs to the field of motors and relates to a mathematical model of a dual three-phase permanent magnet synchronous motor, and specifically to a high-precision electromagnetic-pressure coupling mathematical model of a dual three-phase permanent magnet synchronous motor established based on finite element calculation results and multidimensional interpolation. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) have gained widespread application in production and life due to their small size, high power density, simple structure, and smooth operation. Dual three-phase PMSMs, in particular, have attracted considerable attention due to their low-voltage, high-power, low-torque ripple, and fault-tolerant performance. However, due to the complex electromagnetic coupling within dual three-phase motors, the motors have two sets of three-phase windings, making their mathematical modeling extremely complex. Currently, a common modeling approach treats dual three-phase motors as two combined three-phase motors, modeling each motor separately. However, this approach ignores the electromagnetic coupling between the two three-phase windings, resulting in a low-accuracy mathematical model for the dual three-phase motor. Furthermore, these approaches typically only consider the electromagnetic modeling while neglecting the effects of external pressure on the motor. This results in a mathematical model that is inconsistent with actual conditions and cannot accurately simulate the actual situation, leading to motor control issues. Summary of the Invention

[0003] The purpose of the present invention is to provide a mathematical model of a dual three-phase permanent magnet synchronous motor that takes into account the electromagnetic-pressure coupling effect. The model can take into account the influence of magnetic saturation, electromagnetic coupling, harmonic magnetic field and rotor position, and has higher accuracy and fidelity. It also takes into account the influence of the ambient pressure in which the motor is located on the electromagnetic performance of the motor. It can simulate the operation of the motor under realistic conditions with higher accuracy and has higher control accuracy, providing a means for calculating the motor characteristics in abnormal pressure environments such as space, deep sea, and deep earth.

[0004] The purpose of the present invention is achieved through the following technical solutions:

[0005] A mathematical model of a dual three-phase permanent magnet synchronous motor considering electromagnetic-pressure coupling effects is built according to the following steps:

[0006] Step 1: Perform finite element modeling on the target dual three-phase permanent magnet synchronous motor and apply multiple sets of d-axis currents i to the first three-phase winding A1B1C1. d1 and multiple sets of q-axis currents i q1 , apply i to the second set of three-phase windings A2B2C2 d2 =0, i q2 = 0, perform electromagnetic field finite element calculation, and solve the magnetic flux and torque calculation results;

[0007] Step 2: i d1 、iq1 and the rotor electrical angle position θ as independent variables, and the d-axis flux ψ in the first set of three-phase windings A1B1C1 obtained after calculation d1 , q-axis magnetic flux ψ q1 And the d-axis flux increment Δψ in the second three-phase winding A2B2C2 d2 , q-axis flux increment Δψ q2 As the dependent variable, establish the relationship between 4 sets of flux linkage and current ψ d1 (i d1 ,i q1 ,θ),ψ q1 (i d1 ,i q1 ,θ)、Δψ d2 (i d1 ,i q1 ,θ)、Δψ q2 (i d1 ,i q1 ,θ);

[0008] Step 3: According to the symmetry and periodicity of the dual three-phase motor structure, d1 (i d1 ,i q1 ,θ),ψ q1 (i d1 ,i q1 ,θ)、Δψ d2 (i d1 ,i q1 ,θ)、Δψ q2 (i d1 ,i q1 ,θ) is phase-shifted by 30°, and ψ d2 (i d2 ,i q2 ,θ),ψ q2 (i d2 ,i q2 ,θ)、Δψ d1 (i d2 ,i q2 ,θ)、Δψ q1 (i d2 ,i q2 ,θ), that is:

[0009] ψ d2 (i d2 ,i q2 ,θ)=ψ d1 (i d1 ,i q1 ,θ-30°);

[0010] ψ q2 (i d2 ,iq2 , θ) = ψ q1 (i d1 , i q1 , θ - 30°);

[0011] Δψ d1 (i d2 , i q2 , θ) = Δψ d2 (i d1 , i q1 , θ - 30°);

[0012] Δψ q1 (i d2 , i q2 , θ) = Δψ q2 (i<着 d1 , i q1 , θ - 30°);

[0013] When operating in a dual-three-phase mode, the d-axis flux linkage ψ of the first set of three-phase windings A1B1C1 d1s and the q-axis flux linkage ψ q1s , the d-axis flux linkage ψ of the second set of three-phase windings A2B2C2 d2s and the q-axis flux linkage ψ q2s are as follows: <着

[0014] ψ d1s = ψ d1 (i d1 , i q1 , θ) + Δψ d1 (i d2 , i q2 , θ);

[0015] ψ q1s = ψ q1 (i d1 , i q1 , θ) + Δψ q1 (i d2 , i q2 , θ);

[0016] ψ d2s = ψ d2 (i d2 , i q2 , θ) + Δψ d2 (i d1 , i q1 , θ);

[0017] ψ q2s = ψ q2 (i d2 , i q2 , θ) + Δψ q2 (i d1 , iq1 ,θ);

[0018] Step 4: ψ d1 (i d1 ,i q1 ,θ),ψ q1 (i d1 ,i q1 ,θ) is inverted to obtain the current i d1 、i q1 and magnetic flux ψ d1 , ψ q1 The relationship between the rotor position θi d1 (ψ d1 ,ψ q1 ,θ) and i q1 (ψ d1 ,ψ q1 ,θ); According to the symmetry and periodicity of the dual three-phase motor structure, i d1 (ψ d1 ,ψ q1 ,θ) and i q1 (ψ d1 ,ψ q1 ,θ) is phase shifted by 30°, and i is obtained d2 (ψ d2 ,ψ q2 ,θ) and i q2 (ψ d2 ,ψ q2 ,θ), that is:

[0019] i d2 (ψ d2 ,ψ q2 ,θ)=i d1 (ψ d1 ,ψ q1 ,θ-30°);

[0020] i q2 (ψ d2 ,ψ q2 ,θ)=i q1 (ψ d1 ,ψ q1 ,θ-30°);

[0021] Step 5: i d1 、i q1 As well as the rotor electrical angle position θ as the independent variable, the calculated torque is used as the dependent variable to obtain the relationship between torque, current and rotor electrical angle position T e1 (i d1 ,i q1 ,θ), according to the symmetry and periodicity of the dual three-phase motor structure, the torque generated by the second set of three-phase windings A2B2C2 when working is determined by T e1(i d1 ,i q1 ,θ) is shifted by 30°, that is:

[0022] T e2 (i d2 ,i q2 ,θ)=T e1 (i d1 ,i q1 ,θ-30°);

[0023] Among them, T e1 With T e2 The torque is when a single set of windings is running, which can be expressed as:

[0024] T e1 =1.5p[ψ d1 (i d1 ,i q1 ,θ)i q1 -ψ q1 (i d1 ,i q1 ,θ)i d1 ];

[0025] T e2 =1.5p[ψ d2 (i d2 ,i q2 ,θ)i q2 -ψ q2 (i d2 ,i q2 ,θ)i d2 ];

[0026] When the motor runs in dual three-phase state, its total torque is:

[0027] T s =1.5p[ψ d1s i q1 -ψ q1s i d1+ ψ d2s i q2 -ψ q2s i d2 ]

[0028] =T e1 +T e2 +1.5p[Δψ d1 i q1 -Δψ q1 i d1 +Δψ d2 i q2 -Δψ q2 i d2 ];

[0029] Where p is the number of pole pairs of the permanent magnet;

[0030] According to the torque, calculate the motor electrical angular velocity ω e :

[0031] ω e =∫[(T s -T L ) / J]dt;

[0032] Among them, T L is the load torque of the motor, and J is the moment of inertia of the motor.

[0033] According to the motor electrical angular velocity ω e , calculate the motor rotor position electrical angle θ:

[0034] θ=∫ω e dt;

[0035] Step 6: According to the input voltage u of the motor d1 、u q1 、u d2 、u q2 Calculate magnetic linkage:

[0036] ψ d1s =∫(u d1 -i d1 R+ω e ψ q1s )dt;

[0037] ψ q1s =∫(u q1 -i q1 R-ω e ψ d1s )dt;

[0038] ψ d2s =∫(u d2 -i d2 R+ω e ψ q2s )dt;

[0039] ψ q2s =∫(u q2 -i q2 R-ω e ψ d2s )dt;

[0040] Where R is the stator winding resistance, ω e is the electrical angular velocity of the motor;

[0041] This completes the establishment of the mathematical model of the electromagnetic characteristics of the dual three-phase permanent magnet synchronous motor;

[0042] Step 7. According to actual needs, set n groups of pressure environments in which the motor is located, and use the methods of steps 1 to 6 to establish a mathematical model of the electromagnetic characteristics of the dual-three-term permanent magnet synchronous motor under different pressures. Based on the calculation results of the motor characteristics under these n groups of different pressures, establish an interpolation model on the pressure gradient, that is, realize the establishment of a mathematical model of the dual-three-term permanent magnet synchronous motor with electromagnetic-pressure coupling effect.

[0043] The larger the value of n, the higher the computational effort required to build the model and the more accurate the model. Conversely, the smaller the value, the lower the computational effort and the lower the accuracy of the model. To ensure the accuracy of the established model, the value of n should be no less than 5.

[0044] Compared with the prior art, the present invention has the following advantages:

[0045] Based on the results of electromagnetic field finite element calculations, the present invention combines mathematical methods such as multi-dimensional interpolation and inversion to achieve the establishment of a high-precision mathematical model of the electromagnetic module of a dual three-phase permanent magnet synchronous motor, which can fully consider the influence of magnetic saturation, harmonic magnetic field and rotor position in the actual operation of the motor. On this basis, the model is established based on the calculation results under multiple pressures, and combined with the interpolation in the pressure dimension, the influence of pressure on the electromagnetic characteristics of the motor can be obtained. In summary, the electromagnetic-temperature coupled dual three-phase permanent magnet synchronous motor high-precision mathematical model established by the present invention can fully consider the influence caused by magnetic saturation, harmonic magnetic field, rotor position in the operation of the motor, and the changes in electromagnetic performance caused by the external environment pressure during the operation of the motor. Compared with the existing motor mathematical model, the present invention is more comprehensive and has better fidelity, and can provide an analytical means for the calculation of motor performance in extreme pressure environments such as space, deep sea, and deep earth. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a structural diagram of a dual three-phase permanent magnet synchronous motor, where: 1-1 is the permanent magnet, 1-2 is the motor rotor, 1-3 is the motor stator, 1-4 is the first set of three-phase windings A1B1C1, and 1-5 is the second set of three-phase windings A2B2C2.

[0047] Figure 2 The four sets of flux linkages ψ are obtained by finite element calculation when the rotor position electrical angle θ = 0°. d1 , ψ q1 , Δψ d2 , Δψ q2 With current i d1 ,i q1 The relationship between them.

[0048] Figure 3 It is the mathematical model of the motor electromagnetic module.

[0049] Figure 4It is a mathematical model of electromagnetic-pressure coupling of permanent magnet synchronous motors established based on calculation results under multiple pressures.

[0050] Figure 5 is based on Figure 4 The torque waveform obtained by the model shown, the torque interpolation model, and the torque calculation results at 20 MPa. DETAILED DESCRIPTION

[0051] The technical solution of the present invention is further described below with reference to the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention that does not depart from the spirit and scope of the technical solution of the present invention should be included in the scope of protection of the present invention.

[0052] The present invention provides a mathematical model of a dual three-phase permanent magnet synchronous motor taking into account the electromagnetic-pressure coupling effect. The model is modeled according to the following steps:

[0053] 1) Perform finite element modeling on the target dual three-phase permanent magnet synchronous motor and apply multiple sets of d-axis currents i to the first three-phase winding A1B1C1 d1 and multiple sets of q-axis currents i q1 , apply i to the second set of three-phase windings A2B2C2 d2 =0, i q2 = 0, perform electromagnetic field finite element calculation, and solve the magnetic flux and torque calculation results.

[0054] 2) Change i d1 、i q1 and the rotor electrical angle position θ as independent variables, and the d-axis flux ψ in the first set of three-phase windings A1B1C1 obtained after calculation d1 , q-axis magnetic flux ψ q1 And the d-axis flux increment Δψ in the second three-phase winding A2B2C2 d2 , q-axis flux increment Δψ q2 As the dependent variable, the relationship between the four sets of magnetic flux and current can be established ψ d1 (i d1 ,i q1 ,θ),ψ q1 (i d1 ,i q1 ,θ)、Δψ d2 (i d1 ,i q1 ,θ)、Δψ q2 (i d1 ,i q1 ,θ), where ψ d1 (i d1 ,i q1 ,θ),ψ q1 (i d1,i q1 ,θ) reflects the dq axis cross coupling within the three phases, while Δψ d2 (i d1 ,i q1 ,θ)、Δψ q2 (i d1 ,i q1 ,θ) reflects the electromagnetic performance coupling between the two sets of three-phase windings.

[0055] 3) Due to the symmetry and periodicity of the dual three-phase motor structure, it is possible to d1 (i d1 ,i q1 ,θ),ψ q1 (i d1 ,i q1 ,θ)、Δψ d2 (i d1 ,i q1 ,θ)、Δψ q2 (i d1 ,i q1 ,θ) is phase-shifted by 30° to obtain ψ d2 (i d2 ,i q2 ,θ),ψ q2 (i d2 ,i q2 ,θ)、Δψ d1 (i d2 ,i q2 ,θ)、Δψ q1 (i d2 ,i q2 ,θ), that is:

[0056] ψ d2 (i d2 ,i q2 ,θ)=ψ d1 (i d1 ,i q1 ,θ-30°);

[0057] ψ q2 (i d2 ,i q2 ,θ)=ψ q1 (i d1 ,i q1 ,θ-30°);

[0058] Δψ d1 (i d2 ,i q2 ,θ)=Δψ d2 (i d1 ,i q1 ,θ-30°);

[0059] Δψ q1 (i d2 ,i q2 ,θ)=Δψ q2 (i d1 ,i q1 ,θ-30°).

[0060] During dual three-phase operation, the d-axis flux linkage ψ of the first three-phase winding A1B1C1 d1s and q-axis magnetic flux ψ q1s 、D-axis flux linkage ψ of the second three-phase winding A2B2C2 d2s and q-axis magnetic flux ψ q2s for:

[0061] ψ d1s =ψ d1 (i d1 ,i q1 ,θ)+Δψ d1 (i d2 ,i q2 ,θ);

[0062] ψ q1s =ψ q1 (i d1 ,i q1 ,θ)+Δψ q1 (i d2 ,i q2 ,θ);

[0063] ψ d2s =ψ d2 (i d2 ,i q2 ,θ)+Δψ d2 (i d1 ,i q1 ,θ);

[0064] ψ q2s =ψ q2 (i d2 ,i q2 ,θ)+Δψ q2 (i d1 ,i q1 ,θ).

[0065] According to the above relationship, the excitation i can be applied based on only one set of three-phase windings A1B1C1. d1 ,i q1 Realize the mathematical modeling of the magnetic flux part of the two sets of three-phase windings A1B1C1 and A2B2C2 of the entire dual three-phase motor.

[0066] 4) Further study of ψ d1 (i d1 ,i q1,θ),ψ q1 (i d1 ,i q1 ,θ) is inverted to obtain the current i d1 、i q1 and magnetic flux ψ d1 , ψ q1 The relationship between the rotor position θi d1 (ψ d1 ,ψ q1 ,θ) and i q1 (ψ d1 ,ψ q1 ,θ). Similarly, according to the symmetry of the dual three-phase motor structure, we can d1 (ψ d1 ,ψ q1 ,θ) and i q1 (ψ d1 ,ψ q1 ,θ) phase shifted 30°, we get i d2 (ψ d2 ,ψ q2 ,θ) and i q2 (ψ d2 ,ψ q2 ,θ), that is:

[0067] i d2 (ψ d2 ,ψ q2 ,θ)=i d1 (ψ d1 ,ψ q1 ,θ-30°);

[0068] i q2 (ψ d2 ,ψ q2 ,θ)=i q1 (ψ d1 ,ψ q1 ,θ-30°).

[0069] 5) Change i d1 、i q1 As well as the rotor electrical angle position θ as the independent variable, the calculated torque is used as the dependent variable to obtain the relationship between torque, current and rotor electrical angle position T e1 (i d1 ,i q1 ,θ). According to the symmetry and periodicity of the dual three-phase motor structure, the torque generated by the second set of three-phase windings A2B2C2 when working can be expressed by T e1 (i d1 ,i q1 ,θ) is shifted by 30°, that is:

[0070] T e2(i d2 ,i q2 ,θ)=T e1 (i d1 ,i q1 ,θ-30°);

[0071] Among them, T e1 With T e2 The torque is when a single set of windings is running, which can be expressed as:

[0072] T e1 =1.5p[ψ d1 (i d1 ,i q1 ,θ)i q1 -ψ q1 (i d1 ,i q1 ,θ)i d1 ];

[0073] T e2 =1.5p[ψ d2 (i d2 ,i q2 ,θ)i q2 -ψ q2 (i d2 ,i q2 ,θ)i d2 ].

[0074] When the motor runs in dual three-phase state, its total torque is:

[0075] T s =1.5p[ψ d1s i q1 -ψ q1s i d1+ ψ d2s i q2 -ψ q2s i d2 ]

[0076] =T e1 +T e2 +1.5p[Δψ d1 i q1 -Δψ q1 i d1 +Δψ d2 i q2 -Δψ q2 i d2 ].

[0077] According to the torque, the motor electrical angular velocity ω can be calculated e Calculation:

[0078] ω e =∫[(Ts -T L ) / J]dt;

[0079] Among them, T L is the load torque of the motor, and J is the moment of inertia of the motor.

[0080] Furthermore, the electrical angle θ of the motor rotor position can be calculated:

[0081] θ=∫ω e dt.

[0082] 6) Since the input of the motor is voltage u d1 、u q1 、u d2 、u q2 , so it is necessary to calculate the flux linkage based on these four voltage inputs, namely:

[0083] ψ d1s =∫(u d1 -i d1 R+ω e ψ q1s )dt;

[0084] ψ q1s =∫(u q1 -i q1 R-ω e ψ d1s )dt;

[0085] ψ d2s =∫(u d2 -i d2 R+ω e ψ q2s )dt;

[0086] ψ q2s =∫(u q2 -i q2 R-ω e ψ d2s )dt;

[0087] Where R is the stator winding resistance, ω e is the electrical angular velocity of the motor.

[0088] 7) In summary, the input of the mathematical model is the voltage u d1 、u q1 、u d2 、u q2 After step 6), the four flux linkages ψ corresponding to the two sets of three-phase windings are obtained. d1s , ψ q1s , ψ d2s , ψ q2s, and then decompose each flux linkage into two parts through step 3), and on this basis, solve the four currents i through step 4) d1 、i q1 、i d2 、i q2 , and then solve the torque based on step 5), and combine the motor's motion equation to calculate the motor's electrical angular velocity ω e So far, the electromagnetic part of the mathematical model of the dual three-phase permanent magnet synchronous motor proposed in the present invention has been established.

[0089] 8) Currently, the extreme pressure applications of motors are mainly in space (close to 0MPa), deep sea (close to 100MPa), and deep earth (140MPa). According to actual needs, set n groups of pressure environments in which the motor is located. The larger the value of n, the higher the amount of calculation required when establishing the model and the more accurate the model. Conversely, the lower the amount of calculation required and the lower the model accuracy. In order to ensure the accuracy of the established model, the value of n should be no less than 5. Use steps 1)-7) to establish a mathematical model of the electromagnetic characteristics of a dual-three-term permanent magnet synchronous motor under different pressures. Based on the calculation results of the motor characteristics under these n groups of different pressures, establish an interpolation model on the pressure gradient, that is, realize the establishment of a mathematical model of a dual-three-term permanent magnet synchronous motor with electromagnetic-pressure coupling effect.

[0090] Example 1:

[0091] Figure 1 This is a finite element model of a 22-pole, 24-slot, double-layer winding, dual-three-phase permanent magnet synchronous motor. The motor has a rated speed of 1800 r / min and a rated frequency of 330 Hz. It is controlled using the id=0 control method. Figure 1 The first three-phase winding A1B1C1 shown in the figure applies multiple sets of d-axis currents i d1 and multiple sets of q-axis currents i q1 , the range is -20A to 20A, and i is applied to another set of three-phase windings A2B2C2 d2 =0,i q2 = 0, perform electromagnetic field finite element calculation, and the solution is as follows Figure 2 The four sets of magnetic linkage relationships ψ d1 (i d1 ,i q1 ,θ)、 q1 (i d1 ,i q1 ,θ)、Δψ d2 (i d1 ,i q1 ,θ)、Δψ q2 (i d1 ,i q1 ,θ) and torque relationship T e1 (i d1,i q1 ,θ). Due to the symmetry of the two sets of three-phase windings of the dual three-phase motor, d1 (i d1 ,i q1 ,θ),ψ q1 (i d1 ,i q1 ,θ)、Δψ d2 (i d1 ,i q1 ,θ)、Δψ q2 (i d1 ,i q1 ,θ) and T e1 (i d1 ,i q1 ,θ) by phase shifting and transposing, we can get ψ d2 (i d2 ,i q2 ,θ),ψ q2 (i d2 ,i q2 ,θ)、Δψ d1 (i d2 ,i q2 ,θ)、Δψ q1 (i d2 ,i q2 ,θ) and T e2 (i d1 ,i q1 ,θ). Based on these relationships, the voltage equation and motion equation of the motor can be combined to make the following Figure 3 The mathematical model of the electromagnetic characteristics of the motor is established as shown.

[0092] Using the above method, a mathematical model of the electromagnetic characteristics of the motor under the six pressure states of 0MPa, 30MPa, 60MPa, 90MPa, 120MPa, and 150MPa is established, and the relevant results are calculated. Based on the calculation results under these six pressure states, an interpolation model in the pressure direction is established, which is as follows: Figure 4 The electromagnetic-pressure coupling mathematical model of the motor is shown in FIG. Then, the corresponding results are calculated from the interpolation model for the target pressure, and the electromagnetic performance of the motor corresponding to different pressures can be quickly calculated. Taking torque as an example, at the six pressures of 0MPa, 30MPa, 60MPa, 90MPa, 120MPa, and 150MPa, the motor has the following characteristics: d1 =i d2 =0A,i q1 =i q2 =10A) under the torque waveform is as follows Figure 5 As shown in (a), the cubic spline interpolation curve of the torque average value in the pressure dimension established based on these torque results is as follows Figure 5 As shown in (b), the torque waveform at 20MPa obtained by interpolation calculation and the torque waveform at 20MPa obtained by finite element calculation are as follows Figure 5 The torque waveform at 20 MPa calculated using this model is in good agreement with the finite element calculation results, demonstrating the excellent accuracy of the electromagnetic-pressure coupling mathematical model proposed in this invention.

Claims

1. A method for constructing a mathematical model of a dual three-phase permanent magnet synchronous motor considering electromagnetic-pressure coupling effect, characterized in that The mathematical model of the dual three-phase permanent magnet synchronous motor is modeled according to the following steps: Step 1: Perform finite element modeling on the target dual three-phase permanent magnet synchronous motor and apply multiple sets of d-axis currents i to the first three-phase winding A1B1C1. d1 and multiple sets of q-axis currents i q1 , apply i to the second set of three-phase windings A2B2C2 d2 =0, i q2 = 0, perform electromagnetic field finite element calculation, and solve the magnetic flux and torque calculation results; Step 2: i d1 、i q1 and the rotor electrical angle position θ as independent variables, and the d-axis flux ψ in the first set of three-phase windings A1B1C1 obtained after calculation d1 , q-axis magnetic flux ψ q 1 And the d-axis flux increment Δψ in the second three-phase winding A2B2C2 d2 , q-axis flux increment Δψ q 2 As the dependent variable, establish the relationship between 4 sets of flux linkage and current ψ d1 (i d1 ,i q1 ,θ),ψ q 1 (i d1 ,i q1 ,θ)、Δψ d2 (i d1 ,i q1 ,θ)、Δψ q 2 (i d1 ,i q1 ,θ); Step 3: According to the symmetry and periodicity of the dual three-phase motor structure, d1 (i d1 ,i q1 ,θ),ψ q 1 (i d1 ,i q1 ,θ)、Δψ d2 (i d1 ,i q1 ,θ)、Δψ q 2 (i d1 ,i q1 ,θ) is phase-shifted by 30°, and ψ d2 (i d2 ,i q2 ,θ),ψ q 2 (i d2 ,i q2 ,θ)、Δψ d1 (i d2 ,i q2 ,θ)、Δψ q 1 (i d2 ,i q2 ,θ), that is: ψ d2 (i d2 ,i q2 ,θ)=ψ d1 (i d1 ,i q1 ,θ-30°); ψ q 2 (i d2 ,i q2 ,θ)=ψ q 1 (i d1 ,i q1 ,θ-30°); Δψ d1 (and d2 ,i q2 ,θ)=Δψ d2 (and d1 ,i q1 ,θ-30°); Δψ q 1 (and d2 ,i q2 ,θ)=Δψ q 2 (and d1 ,i q1 ,θ-30°); During dual three-phase operation, the d-axis flux linkage ψ of the first three-phase winding A1B1C1 d1 s and q-axis magnetic flux ψ q 1 s 、D-axis flux linkage ψ of the second three-phase winding A2B2C2 d2 s and q-axis magnetic flux ψ q 2 s for: ψ d1 s =ψ d1 (i d1 ,i q1 ,i)+Δψ d1 (i d2 ,i q2 ,i); ψ q 1 s =ψ q 1 (i d1 ,i q1 ,i)+Δψ q 1 (i d2 ,i q2 ,i); ψ d2 s =ψ d2 (i d2 ,i q2 ,i)+Δψ d2 (i d1 ,i q1 ,i); ψ q 2 s =ψ q 2 (i d2 ,i q2 ,i)+Δψ q 2 (i d1 ,i q1 ,i); Step 4: ψ d1 (i d1 ,i q1 ,θ),ψ q 1 (i d1 ,i q1 ,θ) is inverted to obtain the current i d1 、i q1 and magnetic flux ψ d1 , ψ q 1 The relationship between the rotor electrical angle position θi d1 (ψ d1 ,ψ q 1 ,θ) and i q1 (ψ d1 ,ψ q 1 ,θ); According to the symmetry and periodicity of the dual three-phase motor structure, i d1 (ψ d1 ,ψ q 1 ,θ) and i q1 (ψ d1 ,ψ q 1 ,θ) is phase shifted by 30°, and i is obtained d2 (ψ d2 ,ψ q 2 ,θ) and i q2 (ψ d2 ,ψ q 2 ,θ), that is: I d2 (ψ d2 ,ψ q 2 ,θ)=i d1 (ψ d1 ,ψ q 1 ,θ-30°); I q2 (ψ d2 ,ψ q 2 ,θ)=i q1 (ψ d1 ,ψ q 1 ,θ-30°); Step 5: i d1 、i q1 As well as the rotor electrical angle position θ as the independent variable, the calculated torque is used as the dependent variable to obtain the relationship between torque, current and rotor electrical angle position T e1 (i d1 ,i q1 ,θ), according to the symmetry and periodicity of the dual three-phase motor structure, the torque generated by the second set of three-phase windings A2B2C2 when working is determined by T e1 (i d1 ,i q1 ,θ) is shifted by 30°, that is: T e2 (i d2 ,i q2 ,θ)=T e1 (i d1 ,i q1 ,θ-30°); Among them, T e1 With T e2 All are the torques when a single set of windings is running; When the motor runs in dual three-phase state, its total torque is: T s =1.5p[ψ d1 s i q1 -ψ q 1 s i d1+ ψ d2 s i q2 -ψ q 2 s i d2 ] =T e1 +T e2 +1.5p[Δψ d1 i q1 -Δψ q 1 i d1 +Δψ d2 i q2 -Δψ q 2 i d2 ]; Where p is the number of pole pairs of the permanent magnet; According to the torque, calculate the motor electrical angular velocity ω e : ω e =∫[(T s -T L ) / J]dt; Among them, T L is the load torque of the motor, J is the moment of inertia of the motor; According to the motor electrical angular velocity ω e , calculate the motor rotor position electrical angle θ: θ=∫ω e dt; Step 6: According to the input voltage u of the motor d1 、u q1 、u d2 、u q2 Calculate magnetic linkage: ψ d1 s =∫(u d1 -i d1 R+ω e ψ q 1 s )dt; ψ q 1 s =∫(u q1 -i q1 R-ω e ψ d1 s )dt; ψ d2 s =∫(u d2 -i d2 R+ω e ψ q 2 s )dt; ψ q 2 s =∫(u q2 -i q2 R-ω e ψ d2 s )dt; Where R is the stator winding resistance, ω e is the electrical angular velocity of the motor; This completes the establishment of the mathematical model of the electromagnetic characteristics of the dual three-phase permanent magnet synchronous motor; Step 7. According to actual needs, set n groups of pressure environments in which the motor is located, and use the methods of steps 1 to 6 to establish a mathematical model of the electromagnetic characteristics of the dual-three-term permanent magnet synchronous motor under different pressures. Based on the calculation results of the motor characteristics under these n groups of different pressures, establish an interpolation model on the pressure gradient, that is, realize the establishment of a mathematical model of the dual-three-term permanent magnet synchronous motor with electromagnetic-pressure coupling effect.

2. The method for constructing a mathematical model of a dual three-phase permanent magnet synchronous motor considering electromagnetic-pressure coupling effect according to claim 1 is characterized in that The T e1 With T e2 Expressed as: T e1 =1.5p[ψ d1 (i d1 ,i q1 ,θ)i q1 -ψ q 1 (i d1 ,i q1 ,θ)i d1 ]; T e2 =1.5p[ψ d2 (i d2 ,i q2 ,θ)i q2 -ψ q 2 (i d2 ,i q2 ,θ)i d2 ]。

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