Mathematical Model of Dual Three-Phase Permanent Magnet Synchronous Motor Considering Electromagnetic-Thermal Coupling Effect

Abstract

The present invention discloses a mathematical model of a dual three-phase permanent magnet synchronous motor considering the electromagnetic-temperature coupling effect. Based on the finite element calculation results of the electromagnetic field and combined with mathematical methods such as multi-dimensional interpolation and inversion, a high-precision mathematical model of the electromagnetic module of the dual three-phase permanent magnet synchronous motor is established, which can fully consider the magnetic saturation, harmonic magnetic field and rotor position influence in the actual operation of the motor. On this basis, based on the finite element calculation results of the temperature field and using the linear system identification method, a fast and high-precision calculation matrix from various losses to the temperature rise of multiple motor components is established to realize the fast and high-precision calculation of the motor temperature rise, achieving the coupling from electromagnetic to temperature; further, the influence of temperature on the electromagnetic characteristics of the motor is analyzed and calculated, and it is fed back to the electromagnetic module of the motor to realize the coupling from temperature to electromagnetic. The model of the present invention has better fidelity and can provide a more accurate controlled object for high-quality motor control strategies.

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, specifically to a high-precision electromagnetic-temperature coupling mathematical model of a dual three-phase permanent magnet synchronous motor established based on finite element calculation results and multi-dimensional interpolation. Background Technique

[0002] Permanent magnet synchronous motors have been widely used in the fields of production and life due to their advantages such as small volume, high power density, simple structure, and stable operation. Among them, dual three-phase permanent magnet synchronous motors have attracted much attention because of their advantages such as low voltage and high power, low torque ripple, and fault tolerance performance. However, due to the presence of two sets of three-phase windings in dual three-phase motors, the electromagnetic coupling relationship inside them is extremely complex, which makes the mathematical modeling of dual three-phase permanent magnet synchronous motors extremely complex. The currently commonly used modeling method is to regard a dual three-phase motor as the combination of two three-phase motors and model the two three-phase motors separately. However, this method ignores the electromagnetic coupling between the two sets of three-phase windings, resulting in a low-precision mathematical model of the dual three-phase motor. At the same time, the general modeling method ignores the electromagnetic-temperature coupling effect of the motor and only considers the modeling of the electromagnetic part, resulting in the established mathematical model not conforming to the actual situation and being unable to accurately simulate the actual situation, leading to problems in motor control. 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 considering the electromagnetic-temperature coupling effect, which not only considers the temperature rise of the motor caused by the losses generated during motor operation, but also considers the change in the electromagnetic characteristics of the motor caused by the temperature rise of the motor, and can comprehensively consider the effect of the electromagnetic-temperature coupling of the motor in both directions. Compared with the existing mathematical models, this model can consider the influence of magnetic saturation, electromagnetic coupling, harmonic magnetic field, and rotor position, has higher accuracy and fidelity, and considers the temperature rise caused by motor losses and the change in electromagnetic performance caused by the temperature rise of the motor, and can simulate the motor operation under real conditions with higher accuracy and has higher control accuracy.

[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 the electromagnetic-temperature coupling effect is modeled according to the following steps:

[0006] Step 1: Perform finite element modeling on the target dual three-phase permanent magnet synchronous motor, apply multiple sets of d-axis currents i d1 and multiple sets of q-axis currents i q1 to the first set of three-phase windings A1B1C1, and apply i d2 = 0, i q2With a current of 0, perform finite element calculations of the electromagnetic field to solve the magnetic flux linkage and torque calculation results;

[0007] Step 2. Take i d1 , i q1 and the rotor electrical angle position θ as independent variables, and take the d-axis magnetic flux linkage ψ d1 in the first set of three-phase windings A1B1C1, the q-axis magnetic flux linkage ψ q1 and the d-axis magnetic flux increment Δψ d2 in the second set of three-phase windings A2B2C2, and the q-axis magnetic flux increment Δψ q2 as dependent variables to establish 4 groups of relationships between magnetic 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, shift 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) by 30°, and 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:

[0009] ψ d2 (i d2 , i q2 , θ) = ψ d1 (i d1 , iq1 , θ - 30°);

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

[0013] When operating in dual three - phase, 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:

[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 = ψq2 (i d2 ,i q2 ,θ)+Δψ q2 (i d1 ,i q1 ,θ);

[0018] Step Four: Take the inverse of ψ d1 (i d1 ,i q1 ,θ), ψ q1 (i d1 ,i q1 ,θ) to obtain the relationships between the current i d1 、i q1 and the flux linkage ψ d1 、ψ q1 and the rotor position θ, i 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, shift i d1 (ψ d1 ,ψ q1 ,θ) and i q1 (ψ d1 ,ψ q1 ,θ) by 30°, to obtain i 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 Five: Take i d1 、i q1 and the rotor electrical angle position θ as independent variables, and take the calculated torque as the dependent variable, to obtain the relationship between the torque, the current and the rotor electrical angle position T e1 (id1 , i q1 , θ), according to the symmetry and periodicity of the double-three-phase motor structure, the torque generated when the second set of three-phase windings A2B2C2 operates is from T e1 (i d1 , i q1 , θ) 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 and T e2 are both torques when a single set of windings operates, and 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 operates in a double-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] Among them, p is the number of pole pairs of the permanent magnet;

[0030] Calculate the electrical angular velocity ω of the motor according to the torque 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] Calculate the electrical angle θ of the motor rotor position according to the electrical angular velocity ω of the motor e :

[0034] θ = ∫ω e dt;

[0035] Step 6. Calculate the magnetic flux according to the input voltages u d1 , u q1 , u d2 , u q2 of the motor:

[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] Among them, R is the resistance value of the stator winding, and ω e is the electrical angular velocity of the motor;

[0041] Thus, the establishment of the electromagnetic characteristic calculation model of the dual-three-phase permanent magnet synchronous motor is completed;

[0042] Step 7: Use the motor finite element to calculate the stator core loss P core and the permanent magnet eddy current loss P eddy under multiple operating conditions of a single three-phase winding A1B1C1. By calculating the stator core loss and the permanent magnet eddy current loss under multiple operating conditions, establish the relationship between the stator core loss P core and the permanent magnet eddy current loss P eddy and ω e , i d1 , i q1 . The copper loss is calculated using the following copper loss calculation formula: core (ω e , i d1 , i q1 ) and P eddy (ω e , i d1 , i q1 ). The copper loss calculation formula is as follows:

[0043] P cu = 0.5m(I d1 2 + I q1 2 )R s ;

[0044] where m is the number of phases and Rs is the phase resistance;

[0045] Step 8: Use the copper loss, stator core loss, and permanent magnet eddy current loss obtained in Step 7 as heat sources to calculate the motor temperature rise under several operating conditions, and extract the winding temperature rise T coil and the permanent magnet temperature rise T mag . For the concerned T coil and T mag , use the superposition principle to decompose them into the temperature rises caused by copper loss, stator core loss, and permanent magnet eddy current loss. Use a 2×3 transfer function matrix to represent the two temperature rises of the winding and the permanent magnet caused by copper loss, stator core loss, and permanent magnet eddy current loss:

[0046]

[0047] Step 9: Use linear system identification to identify the transfer functions in the 2×3 transfer function matrix. Start the identification from the low order, gradually increase the number of zeros and poles until the goodness of fit between the results calculated using the transfer function and the finite element calculation results meets the requirements. Use this 2×3 transfer function matrix to replace the temperature field finite element to calculate the motor winding temperature rise T coiland the temperature rise T of the permanent magnet mag for rapid calculation;

[0048] Step Ten: The main parameters affected by temperature are the remanence B of the permanent magnet r and the resistance value R s , and both change linearly with temperature:

[0049] B s1 = B s0 [1 + β(T1 - T0)];

[0050] R s1 = R s0 [1 + α(T1 - T0)];

[0051] where α and β are the temperature coefficients of the resistance value and the remanence respectively, T0 and T1 are two different temperatures, B s0 and R s0 are the remanence and the resistance value at temperature T0 respectively, B s1 and R s1 are the remanence and the resistance value at temperature T1 respectively;

[0052] By calculating the motor characteristics at two temperatures T0 and T1, two sets of motor electromagnetic characteristics can be obtained. Since the temperature has a linear effect on the resistance value and the remanence, other related characteristics also change linearly with temperature. Therefore, the slope on the temperature gradient can be solved using the electromagnetic characteristics at T0 and T1:

[0053]

[0054] where R s (T0), i d (T0), i q (T0) and T em (T0) are the motor phase resistance, d-axis current, q-axis current and torque at temperature T0 respectively, R s (T1), i d (T1), i q (T1) and T em (T1) are the motor phase resistance, d-axis current, q-axis current and torque at temperature T1 respectively, K R , K id , K iq and K Tem are the change rates of the motor phase resistance, d-axis current, q-axis current and torque on the temperature gradient respectively;

[0055] By using the slope of the temperature gradient obtained from the above calculation and the electromagnetic characteristics at T0, the motor electromagnetic characteristics at any temperature rise T s can be calculated:

[0056]

[0057] where Ts is an arbitrary temperature rise relative to temperature T0, and R s (T s )、i d (T s )、i q (T s ) and T em (T s ) are the motor phase resistance, d-axis current, q-axis current, and torque at the temperature rise Ts, respectively;

[0058] Step Eleven: Integrate the temperature rise caused by losses and the change in electromagnetic characteristics caused by the temperature rise into the electromagnetic characteristic calculation model established in Step Six to obtain a high-precision mathematical model of the dual three-phase permanent magnet synchronous motor that can comprehensively consider the electromagnetic-temperature coupling effect of the motor.

[0059] Compared with the prior art, the present invention has the following advantages:

[0060] Based on the finite element calculation results of the electromagnetic field and combined with mathematical methods such as multi-dimensional interpolation and inversion, the present invention realizes the establishment of a high-precision mathematical model of the electromagnetic module of the dual three-phase permanent magnet synchronous motor, which can fully consider the effects of magnetic saturation, harmonic magnetic field, and rotor position in the actual operation of the motor. On this basis, based on the finite element calculation results of the temperature field and using the linear system identification method, a fast and high-precision calculation matrix from various losses to the temperature rise of multiple motor components is established to realize the fast and high-precision calculation of the motor temperature rise and achieve the coupling from electromagnetic to temperature; further, the influence of temperature on the electromagnetic characteristics of the motor is analyzed and calculated and fed back into the motor electromagnetic module to achieve the coupling from temperature to electromagnetic. In summary, the high-precision mathematical model of the electromagnetic-temperature coupling dual three-phase permanent magnet synchronous motor established by the present invention can fully consider the effects of magnetic saturation, harmonic magnetic field, rotor position, and the temperature rise of each part during the operation of the motor and the change in the electromagnetic performance of the motor caused by the temperature rise. Compared with the existing motor mathematical models, the present invention considers more comprehensively, has better fidelity, and can provide a more accurate controlled object for high-quality motor control strategies. Description of the Drawings

[0061] Figure 1 is the structural diagram of the 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;

[0062] Figure 2 is the four groups of magnetic fluxes ψ obtained by finite element calculation when the electrical angle θ of the rotor position is 0°, d1 、ψq1 、 Δψ d2 、 Δψ q2 and the current i d1 , i q1 relationship;

[0063] Figure 3 is the process of obtaining the low-order transfer function G(s) that meets the accuracy requirements by performing linear system identification on the input loss S1 and output temperature rise O1 calculated by the finite element of the temperature field;

[0064] Figure 4 is the calculation result of the motor temperature rise corresponding to different numbers of zeros and poles obtained by using the linear system identification method;

[0065] Figure 5 is the process of calculating the motor temperature rise from the current, speed and resistance of the motor;

[0066] Figure 6 is the mathematical model of the motor electromagnetic module affected by temperature. Detailed implementation mode

[0067] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings, but it is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.

[0068] The present invention provides a mathematical model of a dual three-phase permanent magnet synchronous motor considering the electromagnetic temperature coupling effect. The mathematical model is modeled according to the following steps:

[0069] 1) Perform finite element modeling on the target dual three-phase permanent magnet synchronous motor, apply multiple sets of d-axis current i d1 and multiple sets of q-axis current i q1 to the first set of three-phase windings A1B1C1, and apply i d2 = 0, i q2 = 0 current to the second set of three-phase windings A2B2C2, perform electromagnetic field finite element calculation, and solve the magnetic flux and torque calculation results.

[0070] 2) Take i d1 , i q1 and the rotor electrical angle position θ as independent variables, and take the d-axis magnetic flux ψ d1 , q-axis magnetic flux ψ q1 in the first set of three-phase windings A1B1C1 and the d-axis magnetic flux increment Δψ d2 , q-axis magnetic flux increment Δψ q2 in the second set of three-phase windings A2B2C2 obtained after calculation as dependent variables, and 4 groups of relationships between magnetic flux and current ψ d1 (id1 , 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 situation inside the three-phase, while Δψ d2 (i d1 , i q1 , θ), Δψ q2 (i d1 , i q1 , θ) reflects the electromagnetic performance coupling between two sets of three-phase windings.

[0071] 3) Due to the symmetry and periodicity of the dual three-phase motor structure, by shifting the phase of 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) by 30°, we 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), that is:

[0072] ψ d2 (i d2 , i q2 , θ) = ψ d1 (i d1 , i q1 , θ - 30°);

[0073] ψ q2 (i d2 ,i q2 ,θ) = ψ q1 (i d1 ,i q1 ,θ - 30°);

[0074] Δψ d1 (i d2 ,i q2 ,θ) = Δψ d2 (i d1 ,i q1 ,θ - 30°);

[0075] Δψ q1 (i d2 ,i q2 ,θ) = Δψ q2 (i d1 ,i q1 ,θ - 30°).

[0076] When operating in 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:

[0077] ψ d1s = ψ d1 (i d1 ,i q1 ,θ) + Δψ d1 (i d2 ,i q2 ,θ);

[0078] ψ q1s = ψ q1 (i d1 ,i q1 ,θ) + Δψ q1 (i d2 ,i q2 ,θ);

[0079] ψ d2s = ψ d2 (i d2 ,i q2 ,θ) + Δψ d2 (i d1 ,i q1 ,θ);

[0080] ψ q2s = ψ q2 (i d2 ,iq2 , θ) + Δψ q2 (i d1 , i q1 , θ).

[0081] According to the above relationship, the excitation i can be applied only based on a set of three-phase windings A1B1C1 d1 , i q1 to achieve the mathematical modeling of the flux linkage part of the two sets of three-phase windings A1B1C1 and A2B2C2 of the entire dual three-phase motor.

[0082] 4) Further, by taking the inverse of ψ d1 (i d1 , i q1 , θ), ψ q1 (i d1 , i q1 , θ), the relationships between the current i d1 , i q1 and the flux linkages ψ d1 , ψ q1 and the rotor position θ, i d1 (ψ d1 , ψ q1 , θ) and i q1 (ψ d1 , ψ q1 , θ) can be obtained. Similarly, according to the symmetry of the dual three-phase motor structure, by shifting i d1 (ψ d1 , ψ q1 , θ) and i q1 (ψ d1 , ψ q1 , θ) by 30°, i d2 (ψ d2 , ψ q2 , θ) and i q2 (ψ d2 , ψ q2 , θ) can be obtained, that is:

[0083] i d2 (ψ d2 , ψ q2 , θ) = i d1 (ψ d1 , ψ q1 , θ - 30°);

[0084] i q2 (ψ d2 , ψ q2 , θ) = i q1 (ψ d1 , ψ q1 , θ - 30°).

[0085] 5) Substitute id1 , i q1 Taking the current i, the current i, and the rotor electrical angle position θ as independent variables, and the calculated torque as the dependent variable, the relationship between the torque and the current and the rotor electrical angle position T e1 (i d1 , i q1 , θ) can be obtained. According to the symmetry and periodicity of the dual-three-phase motor structure, the torque generated when the second set of three-phase windings A2B2C2 operates can be obtained by shifting T e1 (i d1 , i q1 , θ) by 30°, that is:

[0086] T e2 (i d2 , i q2 , θ) = T e1 (i d1 , i q1 , θ - 30°);

[0087] where T e1 and T e2 are both torques when a single set of windings operates and can be expressed as:

[0088] T e1 = 1.5p[ψ d1 (i d1 , i q1 , θ)i q1 - ψ q1 (i d1 , i q1 , θ)i d1 ;

[0089] T e2 = 1.5p[ψ d2 (i d2 , i q2 , θ)i q2 - ψ q2 (i d2 , i q2 , θ)i d2 ;

[0090] When the motor operates in the dual-three-phase state, its total torque is:

[0091] T s = 1.5p[ψ d1s i q1 - ψ q1s i d1+ ψ d2s i q2 - ψ q2s i d2

[0092] ​= T e1 + T e2 + 1.5p[Δψ d1 i q1 - Δψ q1 i d1 + Δψ d2 i q2 - Δψ q2 i d2 。

[0093] According to the torque, the electrical angular velocity ω of the motor can be calculated as follows: e :

[0094] ω e = ∫[(T s - T L ) / J]dt;

[0095] where T L is the load torque of the motor, and J is the moment of inertia of the motor.

[0096] Furthermore, the electrical angle θ of the motor rotor position can be calculated as follows:

[0097] θ = ∫ω e dt.

[0098] 6) Since the inputs to the motor are voltages u d1 , u q1 , u d2 , u q2 , the flux linkage needs to be calculated based on these four voltage inputs, i.e.:

[0099] ψ d1s = ∫(u d1 - i d1 R + ω e ψ q1s )dt;

[0100] ψ q1s = ∫(u q1 - i q1 R - ω e ψ d1s )dt;

[0101] ψ d2s = ∫(u d2 - i d2 R + ω e ψ q2s )dt;

[0102] ψ q2s = ∫(u q2 - i q2 R - ω e ψ d2s )dt;

[0103] wherein, R is the resistance of the stator winding, and ω e is the electrical angular velocity of the motor.

[0104] 7) As shown above, the inputs of the mathematical model are voltages u d1 , u q1 , u d2 , u q2 . After obtaining the four flux linkages ψ d1s , ψ q1s , ψ d2s , ψ q2s corresponding to the two sets of three-phase windings through step 6), each flux linkage is then decomposed into two parts through step 3). On this basis, four currents i d1 , i q1 , i d2 , i q2 are solved through step 4). Furthermore, the torque is solved based on step 5), and combined with the motion equation of the motor, the electrical angular velocity ω e and the electrical angular position θ are solved. Thus, the establishment of the electromagnetic part of the mathematical model of the dual three-phase permanent magnet synchronous motor proposed by the present invention is realized.

[0105] 8) The operating parameters of the motor can be used to calculate various losses of the motor. The stator core loss P core and the permanent magnet eddy current loss P eddy of a single three-phase winding A1B1C1 under multiple operating conditions of the motor are calculated using the finite element method of the motor. The given operating parameters include the rotational speed ω e of the motor and the currents i d1 , i q1 of the motor. By calculating the stator core loss and the permanent magnet eddy current loss under multiple operating conditions, the relationships P core and P eddy between the stator core loss P e , the permanent magnet eddy current loss P d1 , the currents i q1 and ω core (ω e , i d1 , i q1 ) and P eddy (ω e , i d1 , i q1 ) can be established. The copper loss can be calculated using the following copper loss calculation formula:

[0106] P cu = 0.5m(I d1 2 + I q1 2 )R s;

[0107] where m is the number of phases and Rs is the phase resistance.

[0108] 9) For any operating condition, there is a corresponding current i d1 、i q1 、i d2 、i q2 、rotational speed ω e and resistance R s , and the corresponding stator core loss P core and permanent magnet eddy current loss P eddy can be obtained by interpolation. The copper loss calculation formula in 8) can be used to calculate the copper loss P cu of the motor.

[0109] 10) Using the above copper loss, stator core loss and permanent magnet eddy current loss as heat sources, calculate the motor temperature rise under several operating conditions, and extract the winding temperature rise T coil and permanent magnet temperature rise T mag . Since the heat dissipation process of the motor is essentially the solution of a thermal resistance-capacitance network, and the thermal resistance-capacitance network is a linear system, the superposition principle applies. For the concerned T coil and T mag , the superposition principle can be used to decompose them into the temperature rises caused by copper loss, stator core loss and permanent magnet eddy current loss. Similarly, since the system is a linear system, the process of temperature rise caused by loss can be described by a transfer function. In summary, the two temperature rises of the winding and the permanent magnet caused by the three losses of copper loss, stator core loss and permanent magnet eddy current loss can be represented by a 2×3 transfer function matrix:

[0110]

[0111] 11) Use linear system identification to identify the transfer functions in the 2×3 transfer function matrix. Start the identification from the low order and gradually increase the number of zeros and poles until the goodness of fit between the result calculated by the transfer function and the result calculated by the finite element is greater than 0.95, which indicates that the calculation result of the transfer function has good accuracy compared with the result of the finite element. Then the 2×3 transfer function matrix can be used to quickly calculate the winding temperature rise T coil and permanent magnet temperature rise T mag of the motor.

[0112] 12) The main parameters affected by temperature are the remanence B r of the permanent magnet and the resistance value R s , and both change linearly with temperature:

[0113] B s1 = B s0[1 + β(T1 - T0)];

[0114] R s1 = R s0 [1 + α(T1 - T0)];

[0115] where α and β are the temperature coefficients of the resistance value and the remanence respectively. T0 and T1 are two different temperatures, B s0 and R s0 are the remanence and the resistance value at temperature T0 respectively, B s1 and R s1 are the remanence and the resistance value at temperature T1 respectively.

[0116] By calculating the motor characteristics at two temperatures T0 and T1, two sets of motor electromagnetic characteristics can be obtained. Since the temperature has a linear effect on the resistance value and the remanence, other related characteristics also change linearly with temperature. Therefore, the slope on the temperature gradient can be solved using the electromagnetic characteristics at T0 and T1:

[0117]

[0118] where R s (T0), i d (T0), i q (T0) and T em (T0) are the motor phase resistance, d-axis current, q-axis current and torque at temperature T0 respectively, R s (T1), i d (T1), i q (T1) and T em (T1) are the motor phase resistance, d-axis current, q-axis current and torque at temperature T1 respectively, K R , K id , K iq and K Tem are the change rates of the motor phase resistance, d-axis current, q-axis current and torque on the temperature gradient respectively.

[0119] With the slope of the temperature gradient obtained from the above calculations and the electromagnetic characteristics at T0, the motor electromagnetic characteristics at any temperature rise T s can be calculated:

[0120]

[0121] where Ts is an arbitrary temperature rise relative to temperature T0, R s (T s ), i d (T s ), i q (T s ) and T em(T s ) are the motor phase resistance, d-axis current, q-axis current, and torque at the temperature rise Ts, respectively.

[0122] 13) Integrate the temperature rise caused by the above losses and the change in electromagnetic characteristics caused by the temperature rise into the electromagnetic part of the dual three-phase permanent magnet synchronous motor mathematical model established in step 6), and a high-precision mathematical model of the dual three-phase permanent magnet synchronous motor that can comprehensively consider the electromagnetic-temperature coupling effect of the motor can be obtained.

[0123] Example 1:

[0124] Figure 1 It is a finite element model of a 22-pole 24-slot double-layer winding dual three-phase permanent magnet synchronous motor. The rated speed of the motor is 1800 r / min, the rated frequency is 330 Hz, and the control method of id = 0 is used for control. For Figure 1 the first set of three-phase windings A1B1C1 shown, apply multiple sets of d-axis current i d1 and multiple sets of q-axis current i q1 , with the range from -20 A to 20 A, and apply i d2 = 0, i q2 = 0 current to the other set of three-phase windings A2B2C2, and perform finite element calculation of the electromagnetic field to solve and obtain four sets of flux linkage relationships ψ Figure 2 shown as 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) 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, perform phase shift and transposition on 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) and T e1 (i d1 , i q1 , θ), and ψd2 (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, combined with the voltage equation and motion equation of the motor, the mathematical model of the electromagnetic characteristics of the motor can be established. Using the losses obtained from the finite element calculation of the electromagnetic field under multiple working conditions as heat sources, the finite element calculation of the temperature field is carried out to obtain the temperature rises of the windings and permanent magnets of the motor under multiple working conditions. Using the losses as input signals and the temperature rises as output signals, the method shown in Figure 3 is used for linear system identification to obtain the corresponding low-order transfer function. The calculated results of the constructed transfer function are closer to the calculation results of the finite element of the temperature field as the number of zeros and poles increases. As shown in Figure 4 , the transfer function G(s) between the copper loss and the winding temperature rise can already obtain a calculation result with a goodness of fit of up to 0.9949 when the pole n = 3 and the zero m = 2. Then, the transfer function characterizing the relationship between the copper loss and the winding temperature rise can be represented by this third-order transfer function. By using the same method, the 2×3 transfer function matrix of the three losses of copper loss, stator core loss, and permanent magnet eddy current loss corresponding to the two temperature rises of winding temperature rise and permanent magnet temperature rise can be solved, and this transfer function matrix can be used for rapid and high-precision calculation of the temperature rise. This process is the rapid temperature rise solving module of the motor, as shown in Figure 5 . Given two temperatures T0 and T1 for the calculation of the electromagnetic characteristics of the motor, since the influence of the temperature rise on the resistance value and the remanence shows a linear relationship, the slopes of the d-axis current, q-axis current, and torque T em in the temperature gradient can be solved to obtain Ki d , Ki q and KT em . When the motor is running, the winding temperature rise T coil will cause a change in the resistance value of the motor, while the permanent magnet temperature rise T mag will cause changes in the d-axis current, q-axis current, and torque T em . This change can be expressed in incremental form, that is, T mag Ki d , T mag Ki q and T mag KT em。Adding the increments caused by these temperature changes into the original mathematical model of the electromagnetic module, a high-precision model of the dual three-phase permanent magnet synchronous motor considering the temperature effect as shown in Figure 6 can be obtained. Combining with the rapid and high-precision calculation module of the motor temperature rise shown in Figure 5 , it is the complete high-precision mathematical model of the electromagnetic-temperature bidirectional coupling dual three-phase permanent magnet synchronous motor.

Claims

1. A modeling method for the mathematical model of a dual-three-phase permanent magnet synchronous motor considering the electromagnetic-temperature 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, apply multiple sets of d-axis currents i d1 and multiple sets of q-axis currents i q1 to the first set of three-phase windings A1B1C1, apply currents with i d2 = 0 and i q2 = 0 to the second set of three-phase windings A2B2C2, conduct finite element calculation of the electromagnetic field, and solve the calculation results of magnetic flux and torque; Step 2: Taking i d1 , i q1 and the rotor electrical angle position θ as independent variables, and taking the d-axis flux linkage ψ d1 , q-axis flux linkage ψ q1 in the first set of three-phase windings A1B1C1 and the d-axis flux linkage increment Δψ d2 , q-axis flux linkage increment Δψ q2 in the second set of three-phase windings A2B2C2 as dependent variables, establish 4 groups of relationships between 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); Step 3. According to the symmetry and periodicity of the dual-three-phase motor structure, shift the phases of 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) by 30°, and 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: ψ d2 (i d2 ,i q2 ,θ) = ψ d1 (i d1 ,i q1 ,θ - 30°); ψ q2 (i d2 ,i q2 ,θ) = ψ q1 (i d1 ,i q1 ,θ - 30°); Δψ d1 (i d2 ,i q2 ,θ) = Δψ d2 (i d1 ,i q1 ,θ - 30°); Δψ q1 (i d2 ,i q2 ,θ) = Δψ q2 (i d1 ,i q1 ,θ - 30°); When operating in 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: ψ d1s = ψ d1 (i d1 , i q1 , θ) + Δψ d1 (i d2 , i q2 , θ); ψ q1s = ψ q1 (i d1 , i q1 , θ) + Δψ q1 (i d2 , i q2 , θ); ψ d2s = ψ d2 (i d2 , i q2 , θ) + Δψ d2 (i d1 , i q1 , θ); ψ q2s = ψ q2 (i d2 , i q2 , θ) + Δψ q2 (i d1 , i q1 , θ); Step 4. Invert ψ d1 (i d1 ,i q1 ,θ), ψ q1 (i d1 ,i q1 ,θ) to obtain the relationships between the currents i d1 、i q1 and the fluxes ψ d1 、ψ q1 and the rotor position θ, i 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, shift i d1 (ψ d1 ,ψ q1 ,θ) and i q1 (ψ d1 ,ψ q1 ,θ) by 30°, to obtain i d2 (ψ d2 ,ψ q2 ,θ) and i q2 (ψ d2 ,ψ q2 ,θ), that is: i d2 (ψ d2 ,ψ q2 ,θ) = i d1 (ψ d1 ,ψ q1 ,θ - 30°); i q2 (ψ d2 ,ψ q2 ,θ) = i q1 (ψ d1 ,ψ q1 ,θ - 30°); Step 5: Taking i d1 , i q1 and the rotor electrical angle position θ as independent variables, and taking the calculated torque as the dependent variable, the relationship between the torque and the current and the rotor electrical angle position T e1 (i d1 , i q1 , θ) is obtained. According to the symmetry and periodicity of the dual three-phase motor structure, the torque generated when the second set of three-phase windings A2B2C2 operates is obtained by shifting T e1 (i d1 , i q1 , θ) by 30°, that is: T e2 (i d2 ,i q2 ,θ) = T e1 (i d1 ,i q1 , θ - 30°); Among them, T e1 and T e2 are both torques during single-winding operation; When the motor operates in the dual-three-phase state, its total torque is: T s = 1.5p[ψd 1s i q1 -ψ q1s id 1+ ψd 2s i q2 -ψ q2s id2] = T e1 + T e2 + 1.5p[Δψd1i q1 - Δψ q1 id1 + Δψd2i q2 - Δψ q2 id2]; Where p is the number of pole pairs of the permanent magnet; Calculate the electrical angular velocity ω of the motor based on the torque e : ω e = ∫[(T s - T L ) / J] dt; where T L is the load torque of the motor, and J is the moment of inertia of the motor; According to the electrical angular velocity ω of the motor e , calculate the electrical angle θ of the motor rotor position: θ = ∫ω e dt; Step 6. Calculate the magnetic flux based on the input voltages u d1 , u q1 , u d2 , u q2 : ψ d1s = ∫(u d1 - i d1 R + ω e ψ q1s )dt; ψ q1s = ∫(u q1 - i q1 R - ω e ψ d1s )dt; ψ d2s = ∫(u d2 - i d2 R + ω e ψ q2s )dt; ψ q2s = ∫(u q2 - i q2 R - ω e ψ d2s )dt; wherein, R is the resistance of the stator winding, and ω e is the electrical angular velocity of the motor; Thus, the establishment of the electromagnetic characteristic calculation model of the dual-three-phase permanent magnet synchronous motor is completed; Step 7: Use motor finite element to calculate the stator core loss P of a single three-phase winding A1B1C1 under multiple working conditions core and the permanent magnet eddy current loss P eddy . By calculating the stator core loss and the permanent magnet eddy current loss under multiple working conditions, establish the relationship between the stator core loss P core and the permanent magnet eddy current loss P eddy and ω e , i d1 , i q1 ; P core (ω e , i d1 , i q1 ) and P eddy (ω e , i d1 , i q1 ). Step 8: Using the copper loss, stator core loss, and permanent magnet eddy current loss as heat sources, calculate the motor temperature rise under several working conditions, and extract the winding temperature rise T coil and the permanent magnet temperature rise T mag . For the concerned T coil and T mag , use the superposition principle to decompose it into the temperature rises caused by copper loss, stator core loss, and permanent magnet eddy current loss, and use a 2×3 transfer function matrix to represent the two temperature rises of the winding and the permanent magnet caused by copper loss, stator core loss, and permanent magnet eddy current loss: Step 9: Identify the transfer functions in the 2×3 transfer function matrix using linear system identification. Start the identification from low order, gradually increase the number of zeros and poles until the goodness of fit between the results calculated using the transfer functions and the results of finite element calculation meets the requirements. Use this 2×3 transfer function matrix to replace the finite element of the temperature field for the rapid calculation of the motor winding temperature rise T coil and the permanent magnet temperature rise T mag ; Step Ten: The main parameters affected by temperature are the remanence B of the permanent magnet r and the resistance value R s , and both change linearly with temperature: B s1 = B s0 [1 + β(T1 - T0)]; R s1 = R s0 [1 + α(T1 - T0)]; where α and β are the temperature coefficients of the resistance value and the remanence respectively, T0 and T1 are two different temperatures, B s0 and R s0 are the remanence and the resistance value at temperature T0 respectively, B s1 and R s1 are the remanence and the resistance value at temperature T1 respectively; By calculating the motor characteristics at two temperatures T0 and T1, two sets of motor electromagnetic characteristics can be obtained. Since the temperature has a linear effect on the resistance value and the remanence, other related characteristics also change linearly with the temperature. Therefore, the electromagnetic characteristics at T0 and T1 can be used to solve the slope on the temperature gradient: Among them, R s (T0), i d (T0), i q (T0) and T em (T0) are the motor phase resistance, d-axis current, q-axis current, and torque at temperature T0 respectively. R s (T1), i d (T1), i q (T1) and T em (T1) are the motor phase resistance, d-axis current, q-axis current, and torque at temperature T1 respectively. K R , K id , K iq and K Tem are the change rates of the motor phase resistance, d-axis current, q-axis current, and torque on the temperature gradient respectively; Based on the slope of the temperature gradient obtained from the above calculations and the electromagnetic characteristics at T0, the electromagnetic characteristics of the motor at any temperature rise T can be calculated. s The electromagnetic characteristics of the motor at: where Ts is an arbitrary temperature rise relative to the temperature T0, R s (T s ), i d (T s ), i q (T s ), and T em (T s ) are the motor phase resistance, d-axis current, q-axis current, and torque at the temperature rise Ts, respectively; Step 11: Incorporate the temperature rise caused by losses and the change in electromagnetic characteristics caused by the temperature rise into the electromagnetic characteristic calculation model established in Step 6 to obtain a high-precision mathematical model of the dual-three-phase permanent magnet synchronous motor that can comprehensively consider the electromagnetic-temperature coupling effect of the motor.

2. The modeling method of the mathematical model of the dual three-phase permanent magnet synchronous motor considering the electromagnetic temperature coupling effect according to claim 1, characterized in that The said T e1 and T e2 is expressed as: T e1 = 1.5p[ψ d1 (i d1 , i q1 , θ)i q1 - ψ q1 (i d1 , i q1 , θ)i d1 ; T e2 = 1.5p[ψ d2 (i d2 ,i q2 ,θ)i q2 -ψ q2 (i d2 ,i q2 ,θ)i d2 .

3. The modeling method of the mathematical model of the dual three-phase permanent magnet synchronous motor considering the electromagnetic temperature coupling effect according to claim 1, characterized in that The copper loss is calculated using the following copper loss calculation formula: P cu = 0.5m(I d1 2 + I q1 2 )R s ; Where m is the number of phases and Rs is the phase resistance.

4. The modeling method of the mathematical model of the dual three-phase permanent magnet synchronous motor considering the electromagnetic temperature coupling effect according to claim 1, characterized in that The goodness of fit is greater than 0.95.

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