Dynamic Torque Modeling Method of Single-Winding BL-PMSM with Unilateral Injection at Winding Midpoint

Abstract

Dynamic torque modeling method for single-winding BL-PMSM with single-sided injection at the winding midpoint, specifically including the following steps: Step 1, construct the structure of single-winding BL-PMSM with single-sided injection of floating current at the winding midpoint and its connection topology of dual three-phase inverters; Step 2, according to the structure of single-winding BL-PMSM with single-sided injection of floating current at the winding midpoint and its connection topology of dual three-phase inverters in Step 1, define the reference positive directions of the currents of each half-winding when the floating current at the winding midpoint is injected unidirectionally; Step 3, establish the current, flux linkage and voltage model expressions of single-winding BL-PMSM with single-sided injection of floating current at the winding midpoint; Step 4, use vector transformation to obtain the corresponding current components and flux linkage expressions in the synchronous rotating coordinate system; Step 5, obtain the torque model of single-winding bearingless permanent magnet motor with single-sided injection at the winding midpoint. The accurate electromagnetic torque calculation formula of this method can provide a technical model basis for the controllable torque calculation of MPSC-UI type single-winding BL-PMSM and the dynamic coupling torque calculation with the "double-frequency" characteristic.

Description

Technical Field

[0001] The present invention relates to the technical field of novel special AC motors and their drive control technologies, specifically to a dynamic torque modeling method for a single-winding BL-PMSM with unilateral injection at the winding midpoint Background Art

[0002] Bearingless motors have broad application prospects in fields such as advanced manufacturing, high-speed flywheel energy storage, aerospace, and biology and life sciences. Technical research has been carried out on "bearingless permanent magnet synchronous motors" (BL-PMSM) with a dual-winding structure at home and abroad. The main problems are as follows: Although the dual-winding structure facilitates the independent regulation of current, the independent suspension winding occupies the slot space of the torque winding, reduces the power density of the BL-PMSM, and reduces the working reliability of the motor. Therefore, it is an inevitable trend in the development of BL-PMSM technology to adopt a single-winding structure, that is, to make a single set of stator windings generate electromagnetic torque and suspension force simultaneously by providing torque current components and suspension current components. The single-winding structure of bearingless motors mainly includes several types such as polyphase windings, parallel windings, and midpoint injection windings.

[0003] The results of literature and patent searches show that in the existing control technology for single-winding BL-PMSM with midpoint injection, the suspension current is superimposed and injected into the lower half winding of each phase through the midpoint of each phase winding. The unbalanced injection of the suspension current will cause obvious torque dynamic coupling. However, the existing literature does not give a dynamic torque control model for single-winding BL-PMSM with midpoint injection considering the influence of suspension current coupling, which brings a lot of inconvenience to the implementation of compensation control for coupling torque ripple from the technical mechanism. Summary of the Invention

[0004] To solve this technical problem, the present invention provides a dynamic torque modeling method for a single-winding BL-PMSM with unilateral injection at the winding midpoint.

[0005] To achieve the above technical objectives, the technical solution adopted is: The dynamic torque modeling method for a single-winding BL-PMSM with unilateral injection at the winding midpoint specifically includes the following steps:

[0006] Step 1: Construct the structure of a single-winding BL-PMSM with unilateral injection of suspension current at the winding midpoint and its dual-three-phase inverter connection topology;

[0007] Each phase winding of the BL-PMSM is divided into two series-connected half windings with the midpoint as the boundary; two three-phase inverters are respectively connected to the three-phase winding output terminals and the midpoint of each phase winding. The three-phase windings are connected in a Y shape. It is set that the upper half windings of the three phases form an upper three-phase half winding, and the lower half windings of the three phases form a lower three-phase half winding;

[0008] Step 2: According to the winding midpoint floating current single-sided injection type single-winding BL-PMSM structure and its dual three-phase inverter connection topology in Step 1, define the positive reference direction of the half-winding current of each phase of the stator when the winding midpoint floating current is injected unidirectionally.

[0009] Only the torque current is passed through the upper three-phase half-windings, flowing out from the outgoing terminal, passing through the half-winding and entering the midpoint of each phase winding. The lower three-phase half-windings pass the torque current and the floating current with the same reference direction, flowing from the midpoint of each phase winding through the half-winding and entering the neutral point.

[0010] Step 3: Establish the half-winding current equation and flux linkage equation of the single-winding BL-PMSM with single-sided injection of winding midpoint floating current.

[0011] First, when the winding midpoint floating current is injected unidirectionally, based on the current superposition theory, establish the half-winding current equation of the single-winding BL-PMSM with single-sided injection of winding midpoint floating current.

[0012] Then, based on the self-inductance L 1 of each half-winding, the mutual inductance M 1 between two adjacent half-windings, the mutual inductance M 2 between two half-windings with a spatial position difference of 180°, the mutual inductance M 3 between two half-windings with a spatial position difference of 120°, the amplitude ψ f of the coupled flux linkage of the permanent magnet on each half-winding, and the position angle α of the permanent magnet rotor in the electrical space, establish the half-winding flux linkage equation of the single-winding BL-PMSM with single-sided injection of winding midpoint floating current.

[0013] Step 4: For the half-winding current equation of the single-winding BL-PMSM with single-sided injection of winding midpoint floating current and the half-winding flux linkage equation of the single-winding BL-PMSM with single-sided injection of winding midpoint floating current, respectively, perform vector transformation from the three-phase stationary coordinate system to the synchronous placement coordinate system using the overall vector coordinate transformation matrix to obtain the corresponding current components and flux linkage expressions in the synchronous rotating coordinate system.

[0014] Step 5: Combine the half-winding current equation of the single-winding BL-PMSM with single-sided injection of winding midpoint floating current, the corresponding current components and flux linkage expressions in the synchronous rotating coordinate system, establish the motor magnetic field energy storage calculation formula including the magnetic field energy storage of the stator winding and the magnetic field energy of the rotor equivalent excitation winding, and according to the principle of electromechanical energy conversion, combine the corresponding current component expressions in the synchronous rotating coordinate system and the rotor magnetic field orientation angle to obtain the torque model of the single-winding bearingless permanent magnet motor with single-sided injection at the winding midpoint.

[0015]

[0016] where P T is the number of pole pairs of the torque system. is the initial phase angle of the torque current; ψ f is the amplitude of the magnetic flux linkage coupled by the permanent magnet magnetic field on each half winding, I T and I S are the amplitudes of the torque current and the suspension current respectively, ω is the current angular frequency, and are the initial phase angles of the torque current and the suspension current respectively; the first term in the torque model is the controllable torque expression, and the second term is the dynamic coupling torque expression generated by the injected single-sided suspension current and having the "double-frequency" characteristic.

[0017] The specific construction method of the single-winding BL-PMSM structure with single-sided injection of the suspension current at the winding midpoint is as follows:

[0018] First, construct the single-winding BL-PMSM structure with single-sided injection of the suspension current at the winding midpoint;

[0019] Adopt a surface-mounted parallel magnetized four-pole permanent magnet rotor structure; evenly arrange 6 stator teeth / slots on the stator core, and number the stator teeth in counterclockwise order as tooth U1, tooth V2, tooth W1, tooth U2, tooth V1, tooth W2. The angular pitch between adjacent two stator teeth is 60 degrees; adopt a parallel stator tooth structure; take the number of each tooth coil to be the same as the number of the stator tooth where it is located, that is, in counterclockwise order, they are tooth U1 coil, tooth V2 coil, tooth W1 coil, tooth U2 coil, tooth V1 coil, tooth W2 coil respectively. Connect the three-phase windings in Y shape, and the neutral point is N; mark the outgoing ends of the three-phase windings as terminal U1, terminal W1, and terminal V1 according to the tooth coil numbers of their upper half windings; each phase winding of the stator is composed of two upper and lower tooth coils connected in series; according to the reference direction of the torque current, the upper and lower half windings of each phase together form a four-pole torque winding structure; lead out the connection points of the upper and lower half windings and mark them as Mu, Mv, and Mw respectively;

[0020] Then, construct the three-phase half-winding structure of the single-winding BL-PMSM with single-sided injection of the suspension current at the winding midpoint; set that the tooth U1 coil, tooth V1 coil, and tooth W1 coil of the upper half windings of phases U, V, and W form the first group of three-phase symmetric half-winding structure, called the upper three-phase half-winding; the tooth U2 coil, tooth V2 coil, and tooth W2 coil of the lower half windings of phases U, V, and W form the second group of three-phase symmetric half-winding structure, called the lower three-phase half-winding.

[0021] The specific method for constructing the connection topology between the winding midpoint floating current single-sided injection type single-winding BL-PMSM structure and the dual three-phase inverter is as follows: The stator winding of the winding midpoint floating current single-sided injection type single-winding BL-PMSM is powered by a dual "three-phase inverter". The first three-phase inverter is the main inverter, and the output terminals of its U, V, and W phases are respectively connected to the U1 terminal, W1 terminal, and V1 terminal of the three-phase winding. The second three-phase inverter is the floating inverter, its u output terminal is connected to the midpoint Mu of the phase winding of the stator U phase, and its v and w output terminals are respectively cross-connected to the midpoint Mw of the phase winding of the stator W phase and the midpoint Mv of the phase winding of the stator V phase.

[0022] The specific method for defining the reference positive direction of the half-winding current of each phase of the stator when the winding midpoint floating current is injected unidirectionally is as follows:

[0023] (1) For the U1 tooth coil, V1 tooth coil, and W1 tooth coil of the upper three-phase half-winding, only torque current is passed through, and the reference positive direction is from the outgoing end of each phase winding and then through the U1 tooth coil, V1 tooth coil, and W1 tooth coil into the midpoint of each phase winding; there is no superimposed injected floating current;

[0024] (2) For the U2 tooth coil, V2 tooth coil, and W2 tooth coil of the lower three-phase half-winding, the reference positive directions of their torque current and floating current are the same. Specifically, the reference positive directions of the torque current and floating current are both from the midpoint of each phase winding through the half-winding and then into the neutral point N of the three-phase winding.

[0025] The specific implementation method of Step Five is as follows: According to the current equation of the winding midpoint floating current single-sided injection type single-winding BL-PMSM and the magnetic flux expression in the synchronous rotating coordinate system, the magnetic field energy storage of the stator winding is obtained. According to the corresponding current components of the upper and lower three-phase half-windings in the synchronous coordinate system, the magnetic field energy of the rotor equivalent excitation winding is obtained. The magnetic field energy storage of the stator winding and the magnetic field energy of the rotor equivalent excitation winding are added to obtain the magnetic field energy storage expression inside the motor. According to the principle of electromechanical energy conversion, the electromagnetic torque is equal to the partial derivative of the motor magnetic field energy storage with respect to the rotor mechanical position angle θ m to obtain the torque expression, and then substituting the corresponding current component expressions in the synchronous rotating coordinate system and the rotor magnetic field orientation angle, the torque model of the single-winding bearingless permanent magnet motor with single-sided injection at the winding midpoint is obtained.

[0026] The beneficial effects of the present invention are:

[0027] 1) The accurate electromagnetic torque calculation formula of this method can provide a technical model basis for the real-time torque calculation of the MPSC-UI type single-winding BL-PMSM;

[0028] 2) The suspension current coupling torque model formula of this method can provide a model calculation basis for the coupling torque characteristic analysis of the MPSC-UI single-winding BL-PMSM and the implementation of torque decoupling compensation control technology;

[0029] 3) The accurate torque modeling method of this method can be extended and applied to the dynamic torque modeling of single-winding BL-PMSM with parallel winding structures, etc. Description of the Drawings

[0030] Figure 1 is the flowchart of the present invention;

[0031] Figure 2 is the structure of the winding midpoint suspension current single-sided injection single-winding BL-PMSM of the present invention;

[0032] Figure 3 is the connection topology of the winding midpoint suspension current single-sided injection single-winding BL-PMSM structure of the present invention and the dual three-phase inverter. Detailed Embodiments

[0033] A dynamic torque modeling method for a winding midpoint single-sided injection single-winding BL-PMSM. Specifically, according to the winding structure characteristics of the "winding midpoint (suspension current) single-sided injection" (MPSC-UI) single-winding BL-PMSM, establish the current equations of the "upper half winding" of each phase that only contain torque current, and the current equations of the "lower half winding" of each phase that contain both torque current and suspension current. Combine the self-inductance of the half winding and the mutual inductance parameters between the half windings to establish basic mathematical models such as the flux linkage equations of each half winding; then, according to the principle of electromechanical energy conversion, establish an accurate dynamic torque control model for the MPSC-UI single-winding BL-PMSM, so as to provide technical model support for the dynamic coupling characteristic analysis of the MPSC-UI single-winding BL-PMSM and the development of high-performance control systems. This patented technology belongs to the field of new special motors and their drive technologies, and is especially applicable to the high-speed magnetic suspension rotation drive technology field of MPSC-UI single-winding bearingless permanent magnet synchronous motors with high requirements for torque model accuracy and motor power density.

[0034] Principle basis of the present invention:

[0035] 1) Each phase winding of a bearingless three-phase permanent magnet synchronous motor (BL-PMSM) can be regarded as two series-connected half windings with the midpoint as the boundary; by connecting two three-phase inverters to the three-phase winding outlet ends and the midpoints of each phase winding respectively, three-phase symmetrical torque current and three-phase symmetrical suspension current can be superimposed and passed through each half-phase winding, so as to generate a (quadrupole or dipole) torque system magnetic field and a (dipole or quadrupole) suspension magnetic field with a difference of one pair of poles inside the motor.

[0036] 2) According to the principle of motor self-bearing, when the electrical angular frequencies of the torque current applied to the "upper and lower half windings" and the suspension current injected into the "lower half winding" are equal, and on the premise that the two sets of rotating magnetic fields differ by a pair of magnetic poles, a stable and controllable radial magnetic suspension force can be generated for the radial suspension motion control of the rotor; at the same time, the electromagnetic torque generated by the torque current is used for the rotational motion control of the rotor.

[0037] 3) Based on the winding midpoint suspension current single-sided injection (MPSC-UI) type single-winding BL-PMSM structure, the current equations and flux linkage equations of each half winding can be constructed. Then, combined with the inductance parameters and current equations of the half winding, the motor magnetic field energy storage calculation formula can be established. Furthermore, according to the principle of electromechanical energy conversion, an accurate torque control model of the MPSC-UI type single-winding BL-PMSM including torque current and suspension current can be obtained.

[0038] Dynamic torque modeling method for single-winding BL-PMSM with single-sided injection at the winding midpoint, attached Figure 1 The figure shows the flow chart of the modeling method. The specific steps are as follows:

[0039] 1) Construct the MPSC-UI type single-winding BL-PMSM structure and its connection with the dual three-phase inverter. Figure 2 is the basic structure diagram of the stator and rotor of the MPSC-UI type single-winding BL-PMSM, Figure 3 is the structure, current reference direction of the stator winding of the MPSC-UI type single-winding BL-PMSM and its connection topology diagram with the dual three-phase inverter. The specific steps of the modeling method are as follows:

[0040] First, construct the MPSC-UI type single-winding BL-PMSM structure. As Figure 2 shown, a surface-mounted parallel magnetized four-pole permanent magnet rotor structure is adopted; 6 stator teeth / slots are evenly arranged on the stator core, and the stator teeth are numbered U1 tooth, V2 tooth, W1 tooth, U2 tooth, V1 tooth, W2 tooth in counterclockwise order, and the angular distance between adjacent two stator teeth is 60 degrees; a parallel stator tooth structure is adopted; the numbers of each tooth coil are the same as those of the stator teeth where they are located, that is, the U1 tooth coil, V2 tooth coil, W1 tooth coil, U2 tooth coil, V1 tooth coil, W2 tooth coil in counterclockwise order. As Figure 3 shown, the stator three-phase (full) windings are connected in Y shape, and the neutral point is N; the outgoing ends of the stator three-phase windings are marked as U1 end, W1 end, V1 end respectively according to the tooth coil numbers of their upper half windings; each phase winding of the stator is composed of two half windings (tooth coils) in series; according to the torque current reference direction, the upper half winding and the lower half winding of each phase together form a four-pole torque winding structure; the midpoints of the U-phase winding, V-phase winding, and W-phase winding, that is, the connection points of their upper and lower half windings, are led out and marked as Mu, Mv, Mw respectively.

[0041] Then, construct the "three-phase half-winding" structure of the MPSC-UI type single-winding BL-PMSM. It is set that the upper half-windings (tooth coils) of phases U, V, and W are composed of tooth coils U1, V1, and W1 to form the first group of three-phase symmetrical half-winding structure, which is called the "upper three-phase half-winding"; the lower half-windings (tooth coils) of phases U, V, and W are composed of tooth coils U2, V2, and W2 to form the second group of three-phase symmetrical half-winding structure, which is called the "lower three-phase half-winding".

[0042] Finally, construct the connection topology between the stator winding of the MPSC-UI type single-winding BL-PMSM and the dual three-phase inverter. Use a dual "three-phase inverter" to supply power to the stator winding of the MPSC-UI type single-winding BL-PMSM; the first inverter is the main inverter, and the output terminals of its U, V, and W phases are respectively connected to the output terminals of the stator three-phase windings (that is, the output terminals of the upper three-phase half-winding); the second inverter is the floating inverter, its u output terminal is connected to the midpoint Mu of the phase winding of stator phase U (that is, the connection point of the upper and lower half-windings), and its v and w output terminals are respectively cross-connected to the midpoint Mw of the phase winding of stator phase W and the midpoint Mv of the phase winding of stator phase V.

[0043] 2) Define the reference positive direction of the half-winding current of each phase of the stator when using MPSC-UI. To account for the coupling effect of the floating current in the electromagnetic torque modeling process, according to Figure 2 the spatial positions of each half-winding (tooth coil) in Figure 3 and the connection methods of each half-winding (tooth coil) in

[0044] (1) For the tooth coils U1, V1, and W1 of the "upper three-phase half-winding", only torque current is passed through, and the reference positive direction is from the outgoing line end of each phase winding and then through the tooth coils U1, V1, and W1 and into the midpoint of each phase winding; there is no superimposed injected floating current.

[0045] (2) For the tooth coils U2, V2, and W2 of the "lower three-phase half-winding", the reference positive directions of their torque current and floating current are the same. Specifically, the reference positive directions of the torque current and floating current are both from the midpoint of each phase winding, passing through the half-winding, and then entering the neutral point N of the three-phase winding.

[0046] 3) Establish the current, flux linkage, and voltage equations of the MPSC-UI type single-winding BL-PMSM.

[0047] First, establish the half-winding current equation of the MPSC-UI type single-winding BL-PMSM. For example, define the number of pole pairs P of the torque magnetic field in this method T= 2, the number of pole pairs P of the suspension magnetic field S = 1. When the MPSC-UI method is adopted, using the idea of current superposition, the final matrix expressions of the currents supplied to each half-winding (tooth coil) from two three-phase inverters are as follows:

[0048]

[0049] In the formula: I T and I S are the amplitudes of the torque current and the suspension current respectively; ω is the current angular frequency; and are the initial phase angles of the torque current and the suspension current respectively.

[0050] Then, establish the half-winding flux linkage equation of the MPSC-UI type single-winding BL-PMSM. Define the self-inductance of each half-winding and the mutual inductance parameters between them (in Figure 1 ):

[0051] 1) The self-inductance of each half-winding is L 1 , L 1 = L mf + L l , where L mf and L l are the excitation inductance and leakage inductance of the half-winding respectively;

[0052] 2) The mutual inductance between two adjacent half-windings is M 1 (such as the mutual inductance between U 1 and V 2 and W 2 );

[0053] 3) The mutual inductance between two half-windings with a spatial position difference of 180° is M 2 (such as the mutual inductance between U 1 and U 2 );

[0054] 4) The mutual inductance between two half-windings with a spatial position difference of 120° is M 3 (such as the mutual inductance between U 1 and V 1 and W 1 ); Set: ψ f is the amplitude of the coupled magnetic flux of the permanent magnet (permanent magnetic field) on each half-winding; α is the position angle of the permanent magnet rotor in the electrical space.

[0055] According to the definition of the inductance parameters, the flux linkage equation of each half-winding in matrix form can be expressed as:

[0056]

[0057] Secondly, establish the phase voltage equation of the MPSC-UI type single-winding BL-PMSM. The voltage equations of each half-winding can be written as:

[0058] U = Ri + dψ / dt (1)

[0059] Where: R is the resistance matrix of each coil.

[0060] According to equations (2) and (3), the voltage equations of each half-phase winding can be obtained, where U 1 and U 2 The voltage equation of the coil (half-winding) is:

[0061]

[0062] Where: ω r is the rotor mechanical angular velocity.

[0063] According to Figure 3 When passing the torque current to the "upper three-phase half-winding" and "lower three-phase half-winding", and only superimposing and injecting the suspension current component to the "lower three-phase half-winding", considering the constraint conditions of "the sum of the three-phase torque currents is zero" and "the sum of the three-phase suspension currents is zero", adding the voltage expressions of U 1 , U 2 in the half-winding of equation (4), the U-phase voltage expression output by the inverter 1 can be obtained:

[0064]

[0065] According to equation (5): When adopting the MPSC-UI method, only inject the suspension current from the winding midpoint to the lower-side half-winding U 2 , and there is no corresponding balanced suspension current injection in the upper half-winding U 1 . Then, looking from the inverter 1 port to the winding neutral point, the induced electromotive force of the suspension current in the U 2 half-winding cannot be cancelled. Therefore, in the phase voltage output by the first inverter, there is not only the induced electromotive force related to the torque current, but also the induced electromotive force related to the suspension current. The expressions of the V-phase voltage and W-phase voltage output by the first inverter are similar to the U-phase voltage as:

[0066]

[0067] 4) Perform the vector coordinate transformation of the MPSC-UI type single-winding BL-PMSM.

[0068] According to the definition of the reference positive direction of the aforementioned current variables, when adopting the MPSC-UI method, the instantaneous torque of the single-winding BL-PMSM is the sum of the torques generated by the currents of two groups of "three-phase half-windings".

[0069] Setting: d-q is the synchronous rotating coordinate system with the rotor permanent magnet magnetic field orientation; α is the electrical angular position of the permanent magnet rotor, that is, the rotor magnetic field orientation angle α = ωt. By performing vector coordinate transformation on the current equations and flux linkage equations of the two sets of "three-phase half windings" from the three-phase stationary coordinate system to the synchronous rotating coordinate system, the dynamic mathematical model in the d-q coordinate system can be obtained; the overall vector coordinate transformation matrix is:

[0070]

[0071] In the above formula (1), the current of the "upper three-phase half winding" only contains torque current, while the current of the "lower three-phase half winding" is composed of both torque current and suspension current; use the vector coordinate transformation matrix in formula (7) to perform the following coordinate transformation on formula (1):

[0072]

[0073] The expressions of the corresponding current components of the two sets of "three-phase half windings" in the synchronous coordinate system can be obtained as:

[0074]

[0075] The i d1 and i q1 in formulas (8)-(9) are the d-axis and q-axis current components of the "upper three-phase half winding", and their values are only related to the applied torque current and independent of the injected suspension current; i d2 and i q2 are the d-axis and q-axis current components of the "lower three-phase half winding", and their values are composed of both the applied torque current and the injected suspension current.

[0076] Similarly, through vector coordinate transformation, the flux linkage expressions in matrix form of the two sets of "three-phase half windings" in the d-q synchronous coordinate system can be obtained as:

[0077]

[0078] In the formula, L d and L q are the d-axis and q-axis inductance values of the half winding in the synchronous coordinate system, L d = L q = 3 / 2 * L mf , and the L mf in it is the excitation inductance of the half winding.

[0079] 5) Establish the electromagnetic torque model of the MPSC-UI type single-winding BL-PMSM.

[0080] According to the principles of electrical machinery, the magnetic field energy storage of the stator winding can be expressed as:

[0081]

[0082] The rotor permanent magnet flux linkage is equivalent to the exciting current \(i\) in the "rotor equivalent exciting winding" f , satisfying \(\psi\) f = \(L\) mf \(i\) f expression. According to the double reaction principle, the stator \(q\)-axis current always acts on the quadrature axis position and will not generate flux linkage in the "rotor equivalent exciting winding"; while the stator \(d\)-axis current always acts on the rotor direct axis position, will generate flux linkage in the "rotor equivalent exciting winding" and superimpose with the permanent magnet flux linkage; then the expression of the flux linkage of the "rotor equivalent exciting winding" is:

[0083]

[0084] The magnetic field energy of the rotor equivalent exciting winding is:

[0085]

[0086] Adding the magnetic field energies on the stator and rotor, the expression of the magnetic field energy storage inside the motor can be obtained as:

[0087]

[0088] According to the principle of electromechanical energy conversion, the electromagnetic torque is equal to the partial derivative of the motor magnetic field energy storage with respect to the rotor mechanical position angle \(\theta\) m , then there is:

[0089]

[0090] For the surface-mounted permanent magnet rotor structure, the \(d\)-axis inductance and \(q\)-axis inductance in the synchronous coordinate system are the same. Then there is:

[0091]

[0092] The \(p\) in the formula T is the number of pole pairs of the torque system, \(i\) q1 and \(i\) q2 are the \(q\)-axis current components of the "upper three-phase half winding" and "lower three-phase half winding" respectively, and the specific calculation expressions are shown in Equation (8).

[0093] Substituting Equation (9) into Equation (16) and replacing \(\alpha\) with \(\omega t\), the dynamic electromagnetic torque calculation formula can be obtained as:

[0094]

[0095] In Equation (17): \(P\) T is the number of pole pairs of the torque system, is the initial phase angle of the torque current; \(\psi\) f is the amplitude of the coupled flux linkage of the permanent magnet magnetic field on each half winding; \(I\) Tand I S are the amplitudes of the torque current and the suspension current respectively, ω is the current angular frequency, and are the initial phase angles of the torque current and the suspension current respectively;

[0096] The first part in the torque model of Equation (17) is the controllable torque expression, and the second part is the dynamic coupling torque expression generated by the injected unilateral suspension current and having the "double-frequency" characteristic (the alternating frequency of the coupling torque is twice the suspension current frequency).

[0097] Equation (17) shows that: when the MPSC-UI method is adopted, due to the suspension current components in i q1 and i q2 cannot be balanced and cancelled in the torque equation, the suspension current coupling electromagnetic torque will inevitably be generated; to achieve the dynamic decoupling control of the electromagnetic torque, the dynamic compensation of the suspension current coupling torque must be carried out.

Claims

1. A dynamic torque modeling method for a single-winding BL-PMSM with single-side injection at the winding midpoint, characterized by: The specific steps include: Step 1: construct a single-winding BL-PMSM structure with single-side injection of winding midpoint floating current and its dual three-phase inverter connection topology; Each phase winding of the BL-PMSM is divided into two half windings connected in series with the midpoint as the boundary; two three-phase inverters are respectively connected to the three-phase winding output terminal and the midpoint of each phase winding, and the three-phase winding is connected in a Y-type, and the upper half winding of the three-phase is set to constitute the upper three-phase half winding, and the lower half winding of the three-phase is set to constitute the lower three-phase half winding; Step 2: According to the winding midpoint floating current unilateral injection single-winding BL-PMSM structure and its dual three-phase inverter connection topology in step 1, define the reference positive direction of the stator phase half-winding current when the winding midpoint floating current is unilaterally injected; The upper three-phase half winding only carries the torque current, which flows out from the outlet terminal and enters the midpoint of each phase winding through the half winding. The lower three-phase half winding carries the torque current and the suspension current with the same reference direction, which flows from the midpoint of each phase winding through the half winding and enters the neutral point. Step 3, establish the half-winding current equation and flux equation of the single-winding BL-PMSM with single-side injection of winding midpoint suspension current; Firstly, when the winding midpoint suspension current is injected unilaterally, the half-winding current equation of the single-winding BL-PMSM with unilateral injection of the winding midpoint suspension current is established based on the current superposition theory. Then, based on the self-inductance L1 of each half winding, the mutual inductance M1 of two adjacent half windings, the mutual inductance M2 of two half windings with a spatial position difference of 180°, the mutual inductance M3 of two half windings with a spatial position difference of 120°, and the amplitude ψ of the coupling flux of the permanent magnet on each half winding, f , the position angle α of the permanent magnet rotor in the electrical space, establish the half-winding flux equation of the single-winding BL-PMSM with single-side injection of winding midpoint suspension current; Step 4, for the half-winding current equation of the single-winding BL-PMSM with unilateral injection of winding midpoint suspension current and the half-winding flux linkage equation of the single-winding BL-PMSM with unilateral injection of winding midpoint suspension current, respectively, the overall vector coordinate transformation matrix is ​​used to perform vector transformation from the three-phase static coordinate system to the synchronous placement coordinate system, and the corresponding current component expression and flux linkage expression in the synchronous rotating coordinate system are obtained; Step 5. Combine the half-winding current equation of the single-winding BL-PMSM with unilateral injection of the midpoint suspension current of the winding, the corresponding current component and flux linkage expression in the synchronous rotating coordinate system, and establish the motor magnetic field energy storage formula including the stator winding magnetic field energy storage and the rotor equivalent excitation winding magnetic field energy. According to the principle of electromechanical energy conversion, combined with the corresponding current component expression in the synchronous rotating coordinate system and the rotor magnetic field orientation angle, the torque model of the single-winding bearingless permanent magnet motor with unilateral injection of the midpoint of the winding is obtained. Among them, P T is the number of pole pairs of the torque system, is the initial phase angle of the torque current; ψ f is the amplitude of the coupling flux of the permanent magnetic field on each half winding, I T and I S are the amplitudes of torque current and suspension current respectively, ω is the current angular frequency, and are the initial phase angles of the torque current and the suspension current respectively; the first term in the torque model is the controllable torque expression, the second term The expression of dynamic coupling torque with "dual frequency" characteristics generated by the injected single-sided suspension current.

2. The method for dynamic torque modeling of a winding midpoint single-side injection single-winding BL-PMSM according to claim 1, characterized in that: The specific construction method of constructing a single-winding BL-PMSM structure with single-side injection of winding midpoint floating current is: Firstly, a single-winding BL-PMSM structure with single-side injection of winding midpoint floating current is constructed; A surface-mounted parallel magnetized four-pole permanent magnet rotor structure is adopted; 6 stator teeth / slots are evenly arranged on the stator core, and the stator teeth are numbered U1 tooth, V2 tooth, W1 tooth, U2 tooth, V1 tooth, and W2 tooth in counterclockwise order, and the spacing angle between two adjacent stator teeth is 60 degrees; a parallel stator tooth structure is adopted; the number of each tooth coil is the same as the number of the stator tooth where it is located, that is, in counterclockwise order, they are U1 tooth coil, V2 tooth coil, W1 tooth coil, U2 tooth coil, V1 tooth coil, and W2 tooth coil. Tooth coil, V1 tooth coil, W2 tooth coil, the three-phase winding is connected in Y shape, with the neutral point N; the three-phase winding output terminals are marked as U1 terminal, W1 terminal, and V1 terminal according to the tooth coil number of the upper half winding; each phase winding of the stator is composed of two upper and lower tooth coils connected in series; according to the reference direction of the torque current, the upper half winding and the lower half winding of each phase together constitute a four-pole torque winding structure; the connection points of the upper and lower half windings are drawn out and marked as Mu, Mv, and Mw respectively; Then, a three-phase half-winding structure of a single-winding BL-PMSM with single-sided injection of winding midpoint floating current is constructed; the U1 tooth coil, V1 tooth coil, and W1 tooth coil of the upper half winding of the U, V, and W phases are set to form the first group of three-phase symmetrical half-winding structures, called the upper three-phase half-winding; the U2 tooth coil, V2 tooth coil, and W2 tooth coil of the lower half winding of the U, V, and W phases constitute the second group of three-phase symmetrical half-winding structures, called the lower three-phase half-winding.

3. The dynamic torque modeling method of a winding midpoint single-side injection single-winding BL-PMSM according to claim 2, characterized in that: The specific method for constructing the connection topology of the winding midpoint floating current single-side injection single-winding BL-PMSM structure and the dual three-phase inverter is as follows: the dual "three-phase inverter" is used to power the stator winding of the winding midpoint floating current single-side injection single-winding BL-PMSM, the first three-phase inverter is the main inverter, and the output ends of its U, V, and W phases are respectively connected to the U1 end, W1 end, and V1 end of the three-phase winding; the second three-phase inverter is a floating inverter, and its u output end is connected to the midpoint Mu of the stator U phase phase winding, and its v and w output ends are cross-connected to the midpoint Mw of the stator W phase phase winding and the midpoint Mv of the stator V phase phase winding.

4. The method for dynamic torque modeling of a single-winding BL-PMSM with single-side injection at the winding midpoint according to claim 2, characterized in that: The specific method for defining the positive reference direction of the stator phase half winding current when the winding midpoint suspension current is injected unilaterally is: (1) For the U1 tooth coil, V1 tooth coil and W1 tooth coil of the upper three-phase half winding, only torque current is passed, and the reference positive direction is from the outlet end of each phase winding and then enters the midpoint of each phase winding through the U1 tooth coil, V1 tooth coil and W1 tooth coil; there is no superimposed injection of suspension current; (2) For the U2 tooth coil, V2 tooth coil and W2 tooth coil of the lower three-phase half winding, the reference positive directions of the torque current and the suspension current are the same. Specifically, the reference positive directions of the torque current and the suspension current are both from the midpoint of each phase winding through the half winding and then enter the neutral point N of the three-phase winding.

5. The method for dynamic torque modeling of a winding midpoint single-side injection single-winding BL-PMSM according to claim 1, characterized in that: The specific implementation method of step five is to obtain the stator winding magnetic field energy storage according to the current equation of the single-winding BL-PMSM with single-side injection of the winding midpoint suspension current and the magnetic flux expression in the synchronous rotating coordinate system, and obtain the magnetic field energy of the rotor equivalent excitation winding according to the corresponding current components of the upper and lower three-phase half windings in the synchronous coordinate system. The stator winding magnetic field energy storage and the rotor equivalent excitation winding magnetic field energy are added to obtain the motor internal magnetic field energy storage expression. According to the principle of electromechanical energy conversion, the electromagnetic torque is equal to the motor magnetic field energy storage to the rotor mechanical position angle θ m The partial derivative of is used to obtain the torque expression, which is then substituted into the corresponding current component expression in the synchronous rotating coordinate system and the rotor magnetic field orientation angle to obtain the torque model of the single-winding bearingless permanent magnet motor with single-side injection at the winding midpoint.

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