High-precision mathematical model for electromagnetic-thermal-pressure coupling of dual-three-phase motors

Abstract

The present invention discloses a high-precision mathematical model for the electromagnetic-temperature-pressure coupling of a dual-three-phase motor. The model not only considers the motor temperature rise caused by the losses generated during motor operation, but also takes into account the changes in the electromagnetic characteristics of the motor caused by the motor temperature rise, and can also account for the influence of the external environmental pressure on the motor characteristics. It can comprehensively consider the effect of the electromagnetic-temperature-pressure coupling of the motor and realize the establishment of a high-precision mathematical model for a dual-three-phase permanent magnet synchronous motor. 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 precision and fidelity, and takes into account the temperature rise caused by motor losses, the change in electromagnetic performance caused by motor temperature rise, and the influence of environmental pressure on motor performance. It can simulate the operation of the motor under real conditions with higher precision, has higher control precision, and also provides a method for calculating the operation performance of motors in extreme environments such as space, deep sea, and deep earth.

Description

Technical Field

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

[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, since the dual three-phase motor has two sets of three-phase windings, the electromagnetic coupling relationship inside it is extremely complex, which makes the mathematical modeling of the dual three-phase permanent magnet synchronous motor extremely complex. The currently commonly used modeling method is to regard the 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 coupling relationship between the electromagnetic characteristics of the motor and temperature and pressure, 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 invention is to provide a high-precision electromagnetic-temperature-pressure coupling mathematical model for a dual three-phase motor, 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 also take into account the influence of the external environmental pressure on the motor characteristics, and can comprehensively consider the effect of electromagnetic-temperature-pressure coupling of the motor to realize the establishment of a high-precision mathematical model of a dual three-phase permanent magnet synchronous motor. Compared with the existing mathematical model, this model can consider the influence of magnetic saturation, electromagnetic coupling, harmonic magnetic field, and rotor position, has higher precision and fidelity, and considers the temperature rise caused by motor losses, the change in electromagnetic performance caused by motor temperature rise, and the influence of environmental pressure on motor performance, and can simulate the motor operation under actual conditions with higher precision, has higher control precision, and also provides a method for calculating the motor operation performance in extreme environments such as space, deep sea, and deep earth.

[0004] The purpose of the invention is realized by the following technical solutions:

[0005] A high-precision electromagnetic-temperature-pressure coupling mathematical model of a dual three-phase motor is modeled 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 groups of d-axis currents i to the first set of three-phase windings A1B1C1 d1and multiple sets of q-axis currents i q1 , apply current i d2 = 0, i q2 = 0 to the second set of three-phase windings A2B2C2, and perform finite element electromagnetic field calculations to solve the magnetic flux 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 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 establish 4 groups of relationships between magnetic flux 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 (id2 , i q2 , θ) = ψ d1 (i d1 , i q1 , 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] During dual - three - phase operation, 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 , iq1 , θ);

[0017] ψ q2s = ψ q2 (i d2 , i q2 , θ) + Δψ q2 (i d1 , i q1 , θ);

[0018] Step Four: Invert 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 magnetic flux linkage ψ d1 , ψ q1 and the rotor position θ, i.e., 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), i.e.:

[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: Apply i d1 , i q1Taking the rotor electrical angle position θ as the independent variable and the calculated torque as the dependent variable, the relationship T between the torque, current, and rotor electrical angle position is obtained. e1 (i d1 ,i q1 ,θ). 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:

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

[0023] Among them, both T e1 and T e2 are 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 the 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] Calculate the electrical angular velocity ω of the motor according to the torque e :

[0031] ω e =∫[(T s -T L ) / J]dt;

[0032] where 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] wherein, 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 finite element of the motor to calculate the stator core loss P core and the permanent magnet eddy current loss P eddy under multiple working conditions of a single three-phase winding A1B1C1. 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 , that is, P core (ω e , i d1 , i q1 ) and P eddy (ω e , i d1 , i q1 ). The copper loss is calculated using the following copper loss calculation formula:

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

[0044] wherein, 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 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 them into the temperature rises caused by the 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 the copper loss, stator core loss, and permanent magnet eddy current loss:

[0046]

[0047] 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 temperature rise T of the motor winding coil and the temperature rise T of the permanent magnet body mag ;

[0048] Step 10: 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] Calculate the motor characteristics at two temperatures T0 and T1 to obtain two sets of motor electromagnetic characteristics. Since the temperature has a linear effect on the resistance value and the remanence, other related characteristics also change linearly with temperature. Then, 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 TemThey are the change rates of the motor phase resistance, d-axis current, q-axis current, and torque with respect to the temperature gradient, respectively;

[0055] Based on the slope of the temperature gradient and the electromagnetic characteristics at T0 obtained from the above calculations, the electromagnetic characteristics of the motor at any temperature rise T can be calculated. s The electromagnetic characteristics of the motor at temperature rise T are as follows:

[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 temperature rise Ts, respectively;

[0058] Step Eleven: Integrate the temperature rise caused by losses and the change in electromagnetic characteristics caused by temperature rise into the electromagnetic characteristic calculation model established in Step Six to obtain the electromagnetic-temperature coupling mathematical model of the dual three-phase permanent magnet synchronous motor;

[0059] Step Twelve: According to the actual operating environment of the motor, set the pressure environment in which h groups of motors are located. Respectively use the electromagnetic-temperature coupling mathematical models of the dual three-phase permanent magnet synchronous motor established in Steps One to Eleven at h pressures, and then based on the calculation results of these h models, combined with interpolation in the pressure direction, construct an interpolation model in the pressure dimension, which is the mathematical model of the dual three-phase permanent magnet synchronous motor considering the electromagnetic-temperature-pressure coupling effect.

[0060] Compared with the prior art, the present invention has the following advantages:

[0061] 1. Based on the finite element calculation results of the electromagnetic field, 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, 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 the coupling from electromagnetic to temperature is realized; 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. Furthermore, the electromagnetic-temperature coupling mathematical models of the dual three-phase permanent magnet synchronous motor under multiple groups of pressures are established, and based on the calculation results of multiple models, an interpolation model in the pressure dimension is constructed to realize the mutual coupling of electromagnetic-temperature-pressure.

[0062] 2. The high-precision mathematical model of the electromagnetic-temperature coupled 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 during motor operation, as well as the temperature rise of each part during motor operation and the change of the motor's electromagnetic performance caused by the temperature rise. It can also take into account the influence of environmental pressure on the motor's electromagnetic performance. Compared with the existing motor mathematical models, the present invention has a more comprehensive consideration, better fidelity, can provide a more accurate controlled object for high-quality motor control strategies, and also provides a method for calculating the motor performance in extreme environments such as space (low pressure and low temperature), deep sea (high pressure and low temperature), and deep earth (high pressure and high temperature). Description of the Drawings

[0063] Figure 1 is the structure 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;

[0064] Figure 2 is the relationship between the four groups of magnetic fluxes ψ d1 、ψ q1 、Δψ d2 、Δψ q2 and the currents i d1 、i q1 when the electrical angle θ of the rotor position is 0° obtained by finite element calculation;

[0065] 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;

[0066] 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;

[0067] Figure 5 is the process of calculating the motor temperature rise from the current, speed, and resistance of the motor;

[0068] Figure 6 is the mathematical model of the motor electromagnetic module affected by temperature;

[0069] Figure 7 is the electromagnetic-temperature-pressure coupled mathematical model established based on the electromagnetic-temperature coupled mathematical models under multiple pressures;

[0070] Figure 8 is based on Figure 7The torque waveforms, torque interpolation models, and torque calculation results at 20 MPa obtained from the model shown. Detailed implementation mode

[0071] 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.

[0072] The present invention provides a mathematical model of a dual three-phase permanent magnet synchronous motor considering the electromagnetic-temperature-pressure coupling effect. The model is built according to the following steps:

[0073] 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 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 magnetic flux and torque calculation results.

[0074] 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. Then, four groups of relationships between magnetic flux 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) can be established. Among them, ψ d1 (i d1 , i q1 , θ), ψ q1 (i d1 , i q1 , θ) reflect the dq-axis cross-coupling situation inside the three phases, 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.

[0075] 3) Due to the symmetry and periodicity of the double three-phase motor structure, by shifting 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:

[0076] ψ d2 (i d2 , i q2 , θ) = ψ d1 (i d1 , i q1 , θ - 30°);

[0077] ψ q2 (i d2 , i q2 , θ) = ψ q1 (i d1 , i q1 , θ - 30°);

[0078] Δψ d1 (i d2 , i q2 , θ) = Δψ d2 (i d1 , i q1 , θ - 30°);

[0079] Δψ q1 (i d2 , i q2 , θ) = Δψ q2 (id1 , i q1 , θ - 30°).

[0080] 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 , and 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:

[0081] ψ d1s = ψ d1 (i d1 , i q1 , θ) + Δψ d1 (i d2 , i q2 , θ);

[0082] ψ q1s = ψ q1 (i d1 , i q1 , θ) + Δψ q1 (i d2 , i q2 , θ);

[0083] ψ d2s = ψ d2 (i d2 , i q2 , θ) + Δψ d2 (i d1 , i q1 , θ);

[0084] ψ q2s = ψ q2 (i d2 , i q2 , θ) + Δψ q2 (i d1 , i q1 , θ).

[0085] According to the above relationships, the mathematical modeling of the flux linkages of the two sets of three-phase windings A1B1C1 and A2B2C2 of the entire dual three-phase motor can be achieved by only applying the excitation i d1 , i q1 to the first set of three-phase windings A1B1C1.

[0086] 4) Further, by taking the inverse of ψ d1 (i d1 , i q1 , θ), ψ q1 (i d1 , i q1 , θ), the currents i d1 , iq1 with the magnetic flux linkage ψ d1 , ψ q1 and the relationship between the rotor position θ and i 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, by shifting the phase of i d1 (ψ d1 , ψ q1 , θ) and i q1 (ψ d1 , ψ q1 , θ) by 30°, we can obtain i d2 (ψ d2 , ψ q2 , θ) and i q2 (ψ d2 , ψ q2 , θ), that is:

[0087] i d2 (ψ d2 , ψ q2 , θ) = i d1 (ψ d1 , ψ q1 , θ - 30°);

[0088] i q2 (ψ d2 , ψ q2 , θ) = i q1 (ψ d1 , ψ q1 , θ - 30°).

[0089] 5) Taking i d1 , i q1 and the rotor electrical angle position θ as independent variables, and the calculated torque as the dependent variable, we can obtain the relationship between the 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 when the second set of three-phase windings A2B2C2 operates can be obtained by shifting the phase of T e1 (i d1 , i q1 , θ) by 30°, that is:

[0090] T e2 (i d2 , i q2 , θ) = T e1 (i d1 , i q1, θ - 30°);

[0091] Among them, T e1 and T e2 are both torques during single - winding operation and can be expressed as:

[0092] T e1 = 1.5p[ψ d1 (i d1 , i q1 , θ)i q1 - ψ q1 (i d1 , i q1 , θ)i d1 ;

[0093] T e2 = 1.5p[ψ d2 (i d2 , i q2 , θ)i q2 - ψ q2 (i d2 , i q2 , θ)i d2 ;

[0094] When the motor operates in a dual - three - phase state, its total torque is:

[0095] T s = 1.5p[ψ d1s i q1 - ψ q1s i d1+ ψ d2s i q2 - ψ q2s i d2 ;

[0096] = T e1 + T e2 + 1.5p[Δψ d1 i q1 - Δψ q1 i d1 + Δψ d2 i q2 - Δψ q2 i d2 ;

[0097] Based on the torque, the electrical angular velocity ω e of the motor can be calculated as:

[0098] ω e = ∫[(T s - T L ) / J]dt;

[0099] Among them, T Lis the load torque of the motor, and J is the moment of inertia of the motor.

[0100] Furthermore, the electrical angle θ of the motor rotor position can be calculated as follows:

[0101] θ = ∫ω e dt.

[0102] 6) Since the input of the motor is voltage u d1 , u q1 , u d2 , u q2 , the flux linkage needs to be calculated based on these four voltage inputs, that is:

[0103] ψ d1s = ∫(u d1 - i d1 R + ω e ψ q1s )dt;

[0104] ψ q1s = ∫(u q1 - i q1 R - ω e ψ d1s )dt;

[0105] ψ d2s = ∫(u d2 - i d2 R + ω e ψ q2s )dt;

[0106] ψ q2s = ∫(u q2 - i q2 R - ω e ψ d2s )dt;

[0107] where R is the resistance of the stator winding, and ω e is the electrical angular velocity of the motor.

[0108] 7) In summary, the input of this mathematical model is voltage u d1 , u q1 , u d2 , u q2 . After step 6), four flux linkages ψ d1s , ψ q1s , ψ d2s , ψ q2s corresponding to two sets of three-phase windings are obtained. On this basis, through step 3), each flux linkage is decomposed into two parts, and then through step 4), 4 currents i d1 , i q1 , i d2 , iq2 , and then solve for the torque based on step 5), and combine with the motion equation of the motor to solve for the electrical angular velocity ω e and the electrical angular position θ. Thus, the establishment of the electromagnetic characteristic calculation model of the dual three-phase permanent magnet synchronous motor is completed.

[0109] 8) The operating parameters of the motor can be used to calculate various losses of the motor. Use the finite element of the motor 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. The given operating parameters include the rotational speed ω e and the current i d1 、i q1 . By calculating the stator core loss and the permanent magnet eddy current loss under multiple operating conditions, the relationship P core between the stator core loss P eddy and the permanent magnet eddy current loss P e 、i d1 、i q1 can be established as P core (ω e ,i d1 ,i q1 ) and P eddy (ω e ,i d1 ,i q1 ). The copper loss can be calculated using the following copper loss calculation formula:

[0110] P cu =0.5m(I d1 2 +I q1 2 )R s ;

[0111] where m is the number of phases and Rs is the phase resistance.

[0112] 9) For any operating condition, there are corresponding currents i d1 、i q1 、i d2 、i q2 、rotational speed ω e and resistance R s . Using interpolation, the corresponding stator core loss P core and the permanent magnet eddy current loss P eddy can be obtained, and the copper loss P cu of the motor can be calculated using the copper loss calculation formula in 8).

[0113] 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 the 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 is applicable. 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 this system is a linear system, the process of temperature rise caused by loss can be described using 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:

[0114]

[0115] 11) 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 result calculated using the transfer function and the result calculated by finite element is greater than 0.95. Then, this 2×3 transfer function matrix can be used to quickly calculate the motor winding temperature rise T coil and the permanent magnet temperature rise T mag .

[0116] 12) The main parameters affected by temperature are the permanent magnet remanence B r and the resistance value R s , and both change linearly with temperature:

[0117] B s1 = B s0 [1 + β(T1 - T0)];

[0118] R s1 = R s0 [1 + α(T1 - T0)];

[0119] 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 resistance value at temperature T0 respectively, and B s1 and R s1 are the remanence and resistance value at temperature T1 respectively.

[0120] The motor characteristics are calculated at two temperatures T0 and T1 to obtain two sets of motor electromagnetic characteristics. Since temperature has a linear effect on resistance and residual magnetism, other related characteristics also vary linearly with temperature. Therefore, the electromagnetic characteristics at T0 and T1 can be used to solve the slope on the temperature gradient:

[0121]

[0122] 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.

[0123] 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 s can be calculated:

[0124]

[0125] Among them, 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 temperature rise Ts respectively.

[0126] 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 the dual three-phase permanent magnet synchronous motor electromagnetic-temperature coupling mathematical model that can comprehensively consider the motor electromagnetic-temperature coupling effect can be obtained.

[0127] 14) Set the pressure environment of the h groups of motors according to the actual operating environment of the motors. Respectively, use steps 1)-13) to establish the electromagnetic-thermal coupling mathematical models of the dual three-phase permanent magnet synchronous motors under h pressures. Then, based on the calculation results of these h models and combined with the interpolation in the pressure direction, construct an interpolation model in the pressure dimension, which is the mathematical model of the dual three-phase permanent magnet synchronous motor considering the electromagnetic-thermal-pressure coupling effect. Calculate the corresponding results from the interpolation model for the target pressure, and the calculation results corresponding to the required pressure can be obtained.

[0128] Example 1:

[0129] 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. Apply multiple sets of d-axis currents i Figure 1 and multiple sets of q-axis currents i d1 with a range from -20 A to 20 A to the first set of three-phase windings A1B1C1 as shown. Apply currents of i q1 = 0 and i d2 = 0 to the other set of three-phase windings A2B2C2, and perform finite element calculations of the electromagnetic field. Solve to obtain four sets of magnetic flux relationships ψ q2 as shown in Figure 2 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, for 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, ψ can be obtained by performing phase shift and transposition on θ 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, 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 the heat source, the finite element calculation of the temperature field is carried out to obtain the temperature rise of the winding and permanent magnet of the motor under multiple working conditions. Using the loss as the input signal and the temperature rise as the output signal, the corresponding low-order transfer function is obtained by using the method shown in Figure 3 . As the number of zeros and poles of the constructed transfer function increases, the calculation result is closer to the calculation result of the finite element of the temperature field. 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 fast and high-precision calculation of the temperature rise. This process is the fast temperature rise solving module of the motor, as shown in Figure 5 . Given two temperatures T0 and T1, the electromagnetic characteristics of the motor are calculated. 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 on 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 Tmag KT em Add the increments caused by these temperature changes into the original mathematical model of the electromagnetic module, and 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 high-precision calculation module of the motor temperature rise as shown in Figure 5 results in a high-precision mathematical model of the electromagnetic-temperature two-way coupled dual three-phase permanent magnet synchronous motor.

[0130] Using the above method, establish the mathematical models of the electromagnetic characteristics part of the motor under 6 pressure states of 0 MPa, 30 MPa, 60 MPa, 90 MPa, 120 MPa, and 150 MPa, and calculate the relevant results. Based on the calculation results under these 6 pressure states, establish an interpolation model in the pressure direction, which is the electromagnetic-pressure coupled mathematical model of the motor as shown in Figure 4 . Then, calculate the corresponding results from the interpolation model for the target pressure, and the rapid calculation of the motor electromagnetic performance corresponding to different pressures can be realized. Taking torque as an example, at 6 pressures of 0 MPa, 30 MPa, 60 MPa, 90 MPa, 120 MPa, and 150 MPa, the torque waveforms of the motor under rated current (id1 = id2 = 0 A, iq1 = iq2 = 10 A) and steady-state temperature (Tmag = 26.8 °C, Tcoil = 52.4 °C) are as shown in Figure 8 (a). The cubic spline interpolation curve of the average torque in the pressure dimension established based on these torque results is as shown in Figure 8 (b). The torque waveforms at 20 MPa obtained by interpolation calculation and the torque waveforms at 20 MPa obtained by finite element calculation are as shown in Figure 8 (c). The torque waveform at 20 MPa calculated using this model is in good agreement with the finite element calculation results, which proves that the electromagnetic-temperature-pressure coupled mathematical model proposed in the present invention has excellent accuracy.

Claims

1. A method for constructing a high-precision mathematical model of electromagnetic-temperature-pressure coupling for a dual-three-phase motor, characterized in that The model 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: Take i d1 , i q1 , and the rotor electrical angle position θ as independent variables, and take 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, and establish the relationships between the four sets of flux linkages and currents 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 three-phase winding A1B1C1 d1s and the q-axis flux linkage ψ q1s , the d-axis flux linkage ψ of the second three-phase winding 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 flux linkages ψ d1 、ψ q1 and the rotor electrical angle 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 Five: 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 T e1 (i d1 , i q1 , θ) between the torque and the current and the rotor electrical angle position 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 the phase of 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 a 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 angular position θ of the motor rotor: 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 value 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 the motor finite element to calculate the stator core loss P of a single three-phase winding A1B1C1 under multiple operating 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 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 , that is, P core (ω e , i d1 , i q1 ) and P eddy (ω e , i d1 , i q1 ); Step 8: Use copper loss, stator core loss, and permanent magnet eddy current loss as heat sources to 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 disassemble 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 remanence, other related characteristics also vary linearly with 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 with respect to 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 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 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 the electromagnetic-temperature coupling mathematical model of the dual-three-phase permanent magnet synchronous motor; Step Twelve: According to the actual operating environment of the motor, set the pressure environment in which h groups of motors are located, and use the electromagnetic-temperature coupling mathematical models of the dual-three-phase permanent magnet synchronous motor at h pressures established in Steps One to Eleven respectively. Then, based on the calculation results of these h models and combined with interpolation in the pressure direction, construct an interpolation model in the pressure dimension, which is the mathematical model of the dual-three-phase permanent magnet synchronous motor considering the electromagnetic-temperature-pressure coupling effect.

2. The method for constructing a high-precision electromagnetic-temperature-pressure coupled mathematical model of a dual three-phase motor 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 method for constructing a high-precision mathematical model of electromagnetic-temperature-pressure coupling of a dual-three-phase motor 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 method for constructing a high-precision electromagnetic-temperature-pressure coupling mathematical model of a dual-three-phase motor according to claim 1, characterized in that The goodness of fit is greater than 0.95.

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