Series winding nine-phase double-stator motor copper loss minimum torque control method

Abstract

The invention relates to the technical field of motors, in particular to a series winding nine-phase double-stator motor copper loss minimum torque control method, which comprises the following steps of: converting a voltage equation into a voltage equation under a rotating coordinate system; establishing an electromagnetic torque equation output by the rotor; a motor copper loss calculation equivalent formula and a Lagrange function equation with the minimum copper loss as the target under the constraint condition of the electromagnetic torque equation are obtained; calculating current reference values under different cup-shaped rotor structures according to different inner and outer side structures of the cup-shaped rotor; the current reference values under different cup-shaped rotor structures are given to a current inner ring of the series winding nine-phase double-stator motor, and copper loss minimum torque control of the series winding nine-phase double-stator motor is achieved. According to the method provided by the invention, the operation efficiency of the series winding nine-phase double-stator motor is improved while the wide torque range stable output of the series winding nine-phase double-stator motor is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of electric motors, and in particular to a method for controlling the copper loss of a series-wound nine-phase dual-stator motor with a minimum torque. Background Art

[0002] With the continuous development of materials and manufacturing processes, new structural designs of motors have gradually received widespread attention. Among them, dual-stator motors have been deeply studied by scholars at home and abroad due to their high power density, large torque range and flexible structural design.

[0003] How to view the relationship between the inner and outer stators of a dual-stator motor is one of the key issues in studying dual-stator motors.

[0004] On the other hand, with the rapid development of power electronics technology and microprocessors and the increasing requirements for motor performance in specific applications, multi-phase motors have been continuously developed and applied due to their strong fault tolerance, high power density, and small output torque pulsation. Compared with three-phase motors, multi-phase motors have not only the fundamental wave plane involved in energy conversion, but also mutually orthogonal harmonic planes; usually the harmonic plane is used to control the harmonic current to obtain better motor performance, but from the perspective of power output, when the air gap magnetomotive force is sinusoidally distributed, the magnetic flux and torque output of the rotor are independent of the harmonic plane components, that is, there are redundant degrees of freedom that are not used. Therefore, according to the multi-phase multi-motor series decoupling control theory, the traditional dual-stator motor structure in which the inner and outer stators each use a separate inverter is abandoned, and the inner stator three-phase winding and the outer stator six-phase winding are connected in series according to the multi-phase multi-motor series theory. The inner and outer stator decoupling control of the dual-stator motor can be realized using a single six-phase inverter.

[0005] However, the torque output by the rotor is the superposition of the combined effects of the inner and outer stators. Therefore, how to distribute the limited current to the inner and outer stators is a key problem that needs to be solved in the nine-phase dual-stator motor with series winding. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a method for controlling the copper loss of a nine-phase dual-stator motor with series windings with minimum torque. By establishing the voltage equation of the nine-phase dual-stator motor with series windings and the motor torque equation under different cup-type rotors, the Lagrangian extreme value function is constructed in combination with the copper loss calculation equivalent formula. The copper loss of the motor is minimized while ensuring the torque output, thereby achieving efficient operation of the motor.

[0007] The present invention is achieved through the following technical solutions: A method for controlling the copper loss of a nine-phase dual-stator motor with series windings to minimize torque comprises the following steps: S1: According to the multi-phase multi-motor series connection theory and coordinate change theory, the voltage equation of the series winding nine-phase double-stator motor is transformed from the six-phase stationary coordinate system to the voltage equation of the series winding nine-phase double-stator motor in the rotating coordinate system; S2: Based on the voltage equation of the nine-phase dual-stator motor with series winding in the rotating coordinate system, the electromagnetic torque equation of the rotor output is established according to the total electromagnetic torque output by the rotor being the superposition of the internal and external stators. S3: According to the multi-phase multi-motor series connection theory, the inner and outer stator windings are connected in series, and the equivalent formula for calculating the copper loss of the nine-phase double-stator motor with series windings and the Lagrangian function equation with the goal of minimizing the copper loss under the constraint condition of satisfying the electromagnetic torque equation of the rotor output are obtained; S4: According to the different inner and outer structures of the cup-shaped rotor, a Lagrangian function equation with the goal of minimizing copper loss under different cup-shaped rotor structures is established, and the current reference value under different cup-shaped rotor structures is calculated; S5: The current reference values ​​under different cup-shaped rotor structures are given to the current inner loop of the series-wound nine-phase dual-stator motor to achieve copper loss minimum torque control of the series-wound nine-phase dual-stator motor.

[0008] Furthermore, the voltage equation of the nine-phase dual-stator motor with series windings in the rotating coordinate system in step S1 is formula (1): (1); in: It represents the direct-axis voltage reference value of the fundamental wave plane of the nine-phase double-stator motor with series winding, It represents the quadrature axis voltage reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, It represents the direct-axis voltage reference value of the harmonic plane of the nine-phase double-stator motor with series windings, It represents the quadrature axis voltage reference value of the harmonic plane of the nine-phase dual-stator motor with series winding, represents the equivalent phase resistance of the outer stator winding, represents the equivalent phase resistance of the inner stator winding, It represents the direct axis current reference value of the fundamental wave plane of the nine-phase double-stator motor with series winding, It represents the quadrature axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, It represents the direct axis current reference value of the harmonic plane of the nine-phase double-stator motor with series winding, It represents the quadrature axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding, It represents the air gap flux between the outer stator and the direct axis of the fundamental wave plane of the nine-phase double-stator motor with series windings, It represents the air gap flux between the outer stator and the quadrature axis of the fundamental wave plane of the nine-phase double-stator motor with series windings. Represents the air gap flux between the inner stator and the direct axis of the harmonic plane of the nine-phase double-stator motor with series windings, It represents the air gap flux between the inner stator and the quadrature axis of the harmonic plane of the nine-phase double-stator motor with series windings. represents the electrical angular velocity of the external air gap magnetic field rotation, It represents the electrical angular velocity of the internal air gap magnetic field rotation.

[0009] Furthermore, the electromagnetic torque equation of the rotor output established in step S2 is formula (2): (2); in: Represents the electromagnetic torque output by the rotor, Indicates the number of permanent magnet pole pairs on the outer side of the cup-shaped rotor, represents the direct-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series windings, represents the quadrature-axis inductance of the fundamental-wave plane of the nine-phase dual-stator motor with series windings, represents the equivalent permanent magnet flux of the external air gap, Indicates the number of permanent magnet poles on the inner side of the cup-shaped rotor, represents the direct-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series windings, represents the quadrature-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series windings, Represents the equivalent permanent magnet flux within the air gap.

[0010] Furthermore, in step S3, the equivalent formula for calculating the copper loss of the nine-phase dual-stator motor with series windings is formula (3): (3); in: Indicates the copper loss of a nine-phase double-stator motor with series windings, represents the equivalent phase resistance of the outer stator winding, represents the equivalent phase resistance of the inner stator winding, It represents the effective value of the current in the fundamental wave plane of the nine-phase double-stator motor with series windings. It represents the effective value of current in the harmonic plane of the nine-phase double-stator motor with series winding.

[0011] Furthermore, in step S3, the Lagrangian function equation for minimizing copper loss under the torque constraint condition is formula (4): (4); in: represents the Lagrangian function with the goal of minimizing copper loss under torque constraints, represents the Lagrange multiplier, Represents the reference electromagnetic torque output by the rotor.

[0012] Further, in step S4, when both the inner and outer sides of the cup-shaped rotor are of hidden pole type, the current reference value is calculated according to the following method: S411: When both the inner and outer sides of the cup-shaped rotor are hidden pole type, the direct-axis inductance of the fundamental wave plane of the series winding nine-phase dual-stator motor is equal to the quadrature-axis inductance of the fundamental wave plane of the series winding nine-phase dual-stator motor, and the direct-axis inductance of the harmonic plane of the series winding nine-phase dual-stator motor is equal to the quadrature-axis inductance of the harmonic plane of the series winding nine-phase dual-stator motor. The direct-axis current reference value of the fundamental wave plane of the series winding nine-phase dual-stator motor and the direct-axis current reference value of the harmonic plane of the series winding nine-phase dual-stator motor are both zero control. The corresponding Lagrangian function equation with the minimum copper loss as the target under the torque constraint condition is formula (5): (5); in: It represents the Lagrangian function with the goal of minimizing copper loss under torque constraints when both the inner and outer sides of the cup-type rotor are non-hidden poles; S412: According to formula (5), the partial derivatives of the quadrature-axis current reference value of the fundamental plane of the nine-phase dual-stator motor with series winding and the quadrature-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding are calculated and both are equal to zero, and the Lagrange multiplier is eliminated to obtain formula (6): (6); S413: Taking the PI output of the speed outer loop as the reference electromagnetic torque output by the rotor, the quadrature-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor and the quadrature-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor are calculated according to formula (6).

[0013] Further, in step S4, when the inner side of the cup-shaped rotor is a hidden pole type and the outer side is a salient pole type, the current reference value is calculated according to the following method: S421: When the inner side of the cup-shaped rotor is a hidden pole type and the outer side is a salient pole type, the direct-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding is equal to the quadrature-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding, and the direct-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding is not equal to the quadrature-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding. The corresponding Lagrangian function equation with the minimum copper loss as the goal under the torque constraint condition is formula (7): (7); in: It represents the Lagrangian function with the goal of minimizing copper loss under torque constraints when the inner side of the cup-shaped rotor is a hidden pole type and the outer side is a salient pole type; S422: According to formula (7), the direct axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, the quadrature axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, and the quadrature axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding are calculated and the partial derivatives are all equal to zero, and the Lagrange multiplier is eliminated to obtain formula (8): (8); S423: The PI output of the speed outer loop is used as the quadrature axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding. The direct axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding is obtained according to the maximum torque current ratio. Then, the quadrature axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding is calculated according to formula (8). The harmonic plane of the nine-phase dual-stator motor with series winding adopts the direct axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding as zero control.

[0014] Further, in step S4, when the outer side of the cup-shaped rotor is a hidden pole type and the inner side is a salient pole type, the current reference value is calculated according to the following method: S431: When the cup-shaped rotor is of hidden pole type on the outside and salient pole type on the inside, the direct-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding is equal to the quadrature-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding, and the direct-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding is not equal to the quadrature-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding. The corresponding Lagrangian function equation with the minimum copper loss as the goal under the torque constraint condition is formula (9): (9); in: It represents the Lagrangian function with the goal of minimizing copper loss under torque constraints when the cup-shaped rotor has a hidden pole type on the outside and a salient pole type on the inside; S432: According to formula (9), the quadrature-axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, the direct-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding and the partial derivatives of the quadrature-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding are calculated and all are equal to zero, and the Lagrange multiplier is eliminated to obtain formula (10): (10); S433: The PI output of the speed outer loop is used as the quadrature-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor. The direct-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor is obtained according to the maximum torque current ratio. Then, the quadrature-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor is calculated according to formula (10). The fundamental wave plane of the series-wound nine-phase dual-stator motor adopts the direct-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor as zero control.

[0015] Further, when both the inner and outer sides of the cup-shaped rotor are salient poles in step S4, the current reference value is calculated as follows: S441: When both the inner and outer sides of the cup-shaped rotor are salient poles, the direct-axis inductance of the fundamental wave plane of the series-wound nine-phase dual-stator motor is not equal to the quadrature-axis inductance of the fundamental wave plane of the series-wound nine-phase dual-stator motor, and the direct-axis inductance of the harmonic plane of the series-wound nine-phase dual-stator motor is not equal to the quadrature-axis inductance of the harmonic plane of the series-wound nine-phase dual-stator motor. According to the maximum torque current ratio control, the relationship between the direct-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor and the quadrature-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor, and the direct-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor and the quadrature-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor is obtained as formula (11): (11); S442: The partial derivatives of the direct-axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding and the direct-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding are respectively calculated and are both equal to zero, and the Lagrange multiplier is eliminated by substituting formula (11) into the formula (12): (12); S443: Rearrange equation (12) to obtain equation (13), and then rearrange the right side of equation (13) to obtain equation (14): (13); (14); in: is the coefficient related to the motor parameters, ; S444: Combining equation (14) and equation (11), equation (13) is simplified to equation (15): (15); S445: The PI output of the speed outer loop is converted into the quadrature-axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding. The direct-axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding is obtained according to the maximum torque current ratio current relationship. Then, the quadrature-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding is solved according to formula (15). Finally, the direct-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding is obtained through the maximum torque current ratio relationship.

[0016] Further, in step S2, if the cup-shaped rotor is a hidden pole type on both the inner and outer sides, the electromagnetic torque equation of the rotor output is simplified to equation (16); if the cup-shaped rotor is a hidden pole type on the inner side and a salient pole type on the outer side, the electromagnetic torque equation of the rotor output is simplified to equation (17); if the cup-shaped rotor is a hidden pole type on the outer side and a salient pole type on the inner side, the electromagnetic torque equation of the rotor output is simplified to equation (18): (16); (17); (18).

[0017] Beneficial effects of the invention: The present invention provides a method for controlling the copper loss of a nine-phase dual-stator motor with series windings with minimum torque. The method calculates the current relationship between the inner and outer stator windings in an equivalent two-phase rotating coordinate system, obtains the magnitude of the reference value of the current of each axis under the minimum copper loss torque control of the nine-phase dual-stator motor with series windings, and provides a basis for the current distribution of the inner and outer stator windings of the dual-stator motor. While achieving stable output of the nine-phase dual-stator motor with series windings in a wide torque range, the high-efficiency operation of the nine-phase dual-stator motor with series windings is ensured. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic diagram of the process of the present invention.

[0019] Figure 2 The present invention is a schematic diagram of the series connection of the stator windings of the nine-phase double-stator motor with series windings.

[0020] Figure 3 It is a comparison diagram of the trajectory of current reference changing with torque between the method of the present invention and the traditional method.

[0021] Figure 4 It is a block diagram of the control system of the present invention.

[0022] Figure 5 It is a comparison diagram of copper loss in the full torque range under the condition that the current of the fundamental wave plane of the nine-phase dual-stator motor with series winding and the current of the harmonic plane of the nine-phase dual-stator motor with series winding are in a fixed ratio according to the method of the present invention.

[0023] In the figure: 1. Nine-phase dual-stator motor with series winding; 2. Position sensor; 3. Coordinate transformation module; 4. Copper loss minimum torque control module; 5. Sine pulse width modulation module; 6. Inverter; 7. PI controller; 8. External stator winding; 9. Internal stator winding. DETAILED DESCRIPTION

[0024] The schematic diagram of the series connection of the stator windings of a nine-phase dual-stator motor with series windings is as follows Figure 2As shown in the figure, the comparison of the current reference trajectory with torque change of the copper loss minimum torque control method of the series winding nine-phase dual-stator motor and the traditional method is shown in the figure Figure 3 As shown, the inner stator winding of the series winding nine-phase double-stator motor includes three windings, the outer stator winding includes six windings, the inner stator winding 9 and the outer stator winding 8 are connected in series, and the flow chart of the copper loss minimum torque control method of the series winding nine-phase double-stator motor is as shown in Figure 1 As shown, the specific control process is completed by the copper loss minimum torque control module, which specifically includes the following steps: S1: According to the multi-phase multi-motor series connection theory and coordinate change theory, the voltage equation of the series winding nine-phase double-stator motor is transformed from the six-phase stationary coordinate system to the voltage equation of the series winding nine-phase double-stator motor in the rotating coordinate system; When the harmonic magnetic field is negligible, the magnetomotive force generated by the stator current and the rotor permanent magnet is sinusoidally distributed along the circumference of the air gap, and the outer stator of the series-wound nine-phase dual-stator motor is controlled by the fundamental plane, and the inner stator is controlled by the harmonic plane, which together provide an energy conversion path for the rotor, the voltage equation of the series-wound nine-phase dual-stator motor in the rotating coordinate system is formula (1): (1); in: It represents the direct-axis voltage reference value of the fundamental wave plane of the nine-phase double-stator motor with series winding, It represents the quadrature axis voltage reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, It represents the direct-axis voltage reference value of the harmonic plane of the nine-phase double-stator motor with series windings, It represents the quadrature axis voltage reference value of the harmonic plane of the nine-phase dual-stator motor with series winding, represents the equivalent phase resistance of the outer stator winding, represents the equivalent phase resistance of the inner stator winding, It represents the direct axis current reference value of the fundamental wave plane of the nine-phase double-stator motor with series winding, It represents the quadrature axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, It represents the direct axis current reference value of the harmonic plane of the nine-phase double-stator motor with series winding, It represents the quadrature axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding, It represents the air gap flux between the outer stator and the direct axis of the fundamental wave plane of the nine-phase double-stator motor with series windings, It represents the air gap flux between the outer stator and the quadrature axis of the fundamental wave plane of the nine-phase double-stator motor with series windings. Represents the air gap flux between the inner stator and the direct axis of the harmonic plane of the nine-phase double-stator motor with series windings, It represents the air gap flux between the inner stator and the quadrature axis of the harmonic plane of the nine-phase double-stator motor with series windings. represents the electrical angular velocity of the external air gap magnetic field rotation, It represents the electrical angular velocity of the internal air gap magnetic field rotation.

[0025] Among them , , , The magnetic flux equation is as follows: ; in: It represents the self-leakage inductance of each phase winding of the outer stator, which can usually be ignored. Combining the voltage equation and the flux equation, it can be seen that the harmonic plane of the nine-phase double-stator motor with series winding and the fundamental plane of the nine-phase double-stator motor with series winding are in a decoupled state, and the harmonic plane is only related to the phase resistance of the outer stator winding and the self-leakage inductance of each phase winding of the outer stator.

[0026] S2: Based on the voltage equation of the nine-phase dual-stator motor with series winding in the rotating coordinate system, the electromagnetic torque equation of the rotor output is established according to the total electromagnetic torque output by the rotor being the superposition of the internal and external stators. Specifically, the electromagnetic torque equation of the rotor output is established as formula (2): (2); in: Represents the electromagnetic torque output by the rotor, Indicates the number of permanent magnet pole pairs on the outer side of the cup-shaped rotor, represents the direct-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series windings, represents the quadrature-axis inductance of the fundamental-wave plane of the nine-phase dual-stator motor with series windings, represents the equivalent permanent magnet flux of the external air gap, Indicates the number of permanent magnet poles on the inner side of the cup-shaped rotor, represents the direct-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series windings, represents the quadrature-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series windings, Represents the equivalent permanent magnet flux within the air gap.

[0027] When the direct-axis current reference value of the harmonic plane of the series-wound nine-phase double-stator motor and the quadrature-axis current reference value of the harmonic plane of the series-wound nine-phase double-stator motor are 0, the series-wound nine-phase double-stator motor is operated only by the six phases of the outer stator; when the direct-axis current reference value of the fundamental wave plane of the series-wound nine-phase double-stator motor and the quadrature-axis current reference value of the fundamental wave plane of the series-wound nine-phase double-stator motor are 0, the series-wound nine-phase double-stator motor is operated only by the three phases of the inner stator; according to different distribution relationships of the direct-axis current reference value of the harmonic plane of the series-wound nine-phase double-stator motor, the quadrature-axis current reference value of the harmonic plane of the series-wound nine-phase double-stator motor, the direct-axis current reference value of the fundamental wave plane of the series-wound nine-phase double-stator motor and the quadrature-axis current reference value of the fundamental wave plane of the series-wound nine-phase double-stator motor, the inner and outer stator nine phases of the series-wound nine-phase double-stator motor can be operated together.

[0028] If the cup-shaped rotor is of hidden pole type on both the inner and outer sides, the electromagnetic torque equation of the rotor output is simplified to equation (16); if the cup-shaped rotor is of hidden pole type on the inner side and salient pole type on the outer side, the electromagnetic torque equation of the rotor output is simplified to equation (17); if the cup-shaped rotor is of hidden pole type on the outer side and salient pole type on the inner side, the electromagnetic torque equation of the rotor output is simplified to equation (18): (16); (17); (18).

[0029] S3: According to the multi-phase multi-motor series connection theory, the inner and outer stator windings are connected in series, and the equivalent formula for calculating the copper loss of the nine-phase double-stator motor with series windings and the Lagrangian function equation with the goal of minimizing the copper loss under the constraint condition of satisfying the electromagnetic torque equation of the rotor output are obtained; Specifically, the equivalent formula for calculating the copper loss of a nine-phase dual-stator motor with series windings is formula (3): (3); in: Indicates the copper loss of a nine-phase double-stator motor with series windings, represents the equivalent phase resistance of the outer stator winding, represents the equivalent phase resistance of the inner stator winding, It represents the effective value of the current in the fundamental wave plane of the nine-phase double-stator motor with series windings. It represents the effective value of current in the harmonic plane of the nine-phase double-stator motor with series winding.

[0030] Under the torque constraint condition, that is, when the motor torque output is satisfied, the Lagrangian function equation for the current distribution on the fundamental plane and the harmonic plane of the series winding nine-phase dual-stator motor with the goal of minimizing copper loss is formula (4): (4); in: represents the Lagrangian function with the goal of minimizing copper loss under torque constraints, represents the Lagrange multiplier, Represents the reference electromagnetic torque output by the rotor.

[0031] Solving the partial derivatives for each variable and setting them to 0 gives the following formula: S4: According to the different inner and outer structures of the cup-shaped rotor, a Lagrangian function equation with the goal of minimizing copper loss under different cup-shaped rotor structures is established, and the current reference value under different cup-shaped rotor structures is calculated; When both the inner and outer sides of the cup-shaped rotor are hidden pole type, calculate the current reference value as follows: S411: When both the inner and outer sides of the cup-shaped rotor are hidden pole type, the direct-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding is equal to the quadrature-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding, and the direct-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding is equal to the quadrature-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding, that is, ; The direct axis current reference value of the fundamental wave plane of the series winding nine-phase dual-stator motor and the direct axis current reference value of the harmonic plane of the series winding nine-phase dual-stator motor are both zero control, and the corresponding Lagrangian function equation with the minimum copper loss as the goal under the torque constraint condition is formula (5): (5); in: It represents the Lagrangian function with the goal of minimizing copper loss under torque constraints when both the inner and outer sides of the cup-type rotor are non-hidden poles; S412: According to formula (5), the partial derivatives of the quadrature-axis current reference value of the fundamental plane of the nine-phase dual-stator motor with series winding and the quadrature-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding are calculated and both are equal to zero, and the Lagrange multiplier is eliminated to obtain formula (6): (6); S413: Taking the PI output of the speed outer loop as the reference electromagnetic torque output by the rotor, the quadrature-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor and the quadrature-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor are calculated according to formula (6).

[0032] Further, in step S4, when the inner side of the cup-shaped rotor is a hidden pole type and the outer side is a salient pole type, the current reference value is calculated according to the following method: S421: When the inner side of the cup-shaped rotor is a hidden pole type and the outer side is a salient pole type, the direct-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding is equal to the quadrature-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding, and the direct-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding is not equal to the quadrature-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding, that is, ; The corresponding Lagrangian function equation with the goal of minimizing copper loss under torque constraints is formula (7): (7); in: It represents the Lagrangian function with the goal of minimizing copper loss under torque constraints when the inner side of the cup-shaped rotor is a hidden pole type and the outer side is a salient pole type; S422: According to formula (7), the direct axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, the quadrature axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, and the quadrature axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding are calculated and the partial derivatives are all equal to zero, and the Lagrange multiplier is eliminated to obtain formula (8): (8); S423: The PI output of the speed outer loop is used as the quadrature axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding. The direct axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding is obtained according to the maximum torque current ratio. Then, the quadrature axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding is calculated according to formula (8). The harmonic plane of the nine-phase dual-stator motor with series winding adopts the direct axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding as zero control.

[0033] Further, in step S4, when the outer side of the cup-shaped rotor is a hidden pole type and the inner side is a salient pole type, the current reference value is calculated according to the following method: S431: When the cup-shaped rotor is of hidden pole type on the outside and salient pole type on the inside, the direct-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding is equal to the quadrature-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding, and the direct-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding is not equal to the quadrature-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding, then ; The corresponding Lagrangian function equation with the goal of minimizing copper loss under torque constraints is formula (9): (9); in: It represents the Lagrangian function with the goal of minimizing copper loss under torque constraints when the cup-shaped rotor has a hidden pole type on the outside and a salient pole type on the inside; S432: According to formula (9), the quadrature-axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, the direct-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding and the partial derivatives of the quadrature-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding are calculated and all are equal to zero, and the Lagrange multiplier is eliminated to obtain formula (10): (10); S433: The PI output of the speed outer loop is used as the quadrature axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding. The direct axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding is obtained according to the maximum torque current ratio. Then, the quadrature axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding is calculated according to formula (10). The fundamental wave plane of the nine-phase dual-stator motor with series winding adopts the direct axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding as zero control, that is, .

[0034] Further, when both the inner and outer sides of the cup-shaped rotor are salient poles in step S4, the current reference value is calculated as follows: S441: When both the inner and outer sides of the cup-shaped rotor are salient poles, the direct-axis inductance of the fundamental wave plane of the series-wound nine-phase dual-stator motor is not equal to the quadrature-axis inductance of the fundamental wave plane of the series-wound nine-phase dual-stator motor, and the direct-axis inductance of the harmonic plane of the series-wound nine-phase dual-stator motor is not equal to the quadrature-axis inductance of the harmonic plane of the series-wound nine-phase dual-stator motor. According to the maximum torque current ratio control, the relationship between the direct-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor and the quadrature-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor, and the direct-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor and the quadrature-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor is obtained as formula (11): (11); S442: The partial derivatives of the direct-axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding and the direct-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding are respectively calculated and are both equal to zero, and the Lagrange multiplier is eliminated by substituting formula (11) into the formula (12): (12); S443: Rearrange equation (12) to obtain equation (13), and then rearrange the right side of equation (13) to obtain equation (14): (13); (14); in: is the coefficient related to the motor parameters, ; S444: Combining equation (14) and equation (11), equation (13) is simplified to equation (15): (15); It can be seen from formula (15) that the quadrature-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor is not only related to the ratio of the direct-axis current reference value of the fundamental-wave plane of the series-wound nine-phase dual-stator motor and the quadrature-axis current reference value of the fundamental-wave plane of the series-wound nine-phase dual-stator motor, but also related to the motor parameters.

[0035] S445: The PI output of the speed outer loop is converted into the quadrature-axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding. The direct-axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding is obtained according to the maximum torque current ratio current relationship. Then, the quadrature-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding is solved according to formula (15). Finally, the direct-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding is obtained through the maximum torque current ratio relationship.

[0036] S5: The current reference values ​​under different cup-shaped rotor structures are given to the current inner loop of the series-wound nine-phase dual-stator motor to achieve copper loss minimum torque control of the series-wound nine-phase dual-stator motor.

[0037] A normally operating salient-pole permanent magnet synchronous motor achieves maximum torque output with minimum current amplitude under maximum torque current ratio control. From the perspective of loss, a single AC-DC plane permanent magnet synchronous motor, while satisfying the torque output condition, lists and solves the Lagrangian function for minimum copper loss control. The obtained AC-DC axis nonlinear current trajectory coincides with the current trajectory controlled by maximum torque current ratio, so the maximum torque current ratio control also achieves the minimum motor copper loss.

[0038] The block diagram of the copper loss minimum torque control system of the series winding nine-phase dual-stator motor of the present invention is as follows: Figure 4 As shown in the figure Indicates the actual speed of the system feedback, Represents a given reference speed, the difference between the two is input into the PI controller 7, and after obtaining the current reference value or the electromagnetic torque reference value according to different rotor structures, it is output to the copper loss minimum torque control module 4; It represents the direct-axis feedback current of the fundamental wave plane of the nine-phase dual-stator motor with series winding, It represents the quadrature-axis feedback current of the fundamental wave plane of the nine-phase dual-stator motor with series windings, represents the direct-axis feedback current of the harmonic plane of the nine-phase dual-stator motor with series windings, The quadrature-axis feedback current of the harmonic plane of the nine-phase dual-stator motor with series winding is input into the PI controller after being subtracted from the corresponding reference current, and the , , , , then the reference voltage of each phase is obtained through the coordinate transformation module 3, and finally the inverter switching signal is obtained through the sinusoidal pulse width modulation module 5 and output to the inverter 6, Indicates the inverter DC bus voltage, and the six-phase current is obtained by the current sensor , and through the coordinate transformation module to obtain , and then the coordinate transformation module obtains the current fed back by the system , , , On the other hand, the cup rotor position angle is obtained by position sensor 2 And the actual speed feedback from the system , realizing closed-loop control of the series-winding nine-phase dual-stator motor 1.

[0039] Figure 5 The copper loss under the minimum copper loss torque control method of the present invention and the current of the fundamental wave plane of the nine-phase double-stator motor with series windings are Current in the harmonic plane of a nine-phase dual-stator motor with series windings A comparison diagram of copper loss in the full torque range under fixed ratio conditions is shown. It can be seen from the figure that the copper loss under the minimum copper loss torque control method of the present invention is much smaller under the same torque, which fully demonstrates the effectiveness of the copper loss minimum torque control method for the series winding nine-phase dual-stator motor of the present invention.

[0040] In summary, the present invention provides a method for controlling the copper loss of a nine-phase dual-stator motor with series windings at a minimum torque, calculates the current relationship between the inner and outer stator windings in an equivalent two-phase rotating coordinate system, and obtains the magnitude of the reference value of the current of each axis under the minimum copper loss torque control of the nine-phase dual-stator motor with series windings, thereby providing a basis for the current distribution of the inner and outer stator windings of the dual-stator motor, and improving the operating efficiency of the nine-phase dual-stator motor with series windings while achieving stable output of the nine-phase dual-stator motor with series windings in a wide torque range.

[0041] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for controlling the copper loss of a nine-phase dual-stator motor with series windings with minimum torque, characterized in that: The steps include: S1: According to the multi-phase multi-motor series connection theory and coordinate change theory, the voltage equation of the series winding nine-phase double-stator motor is transformed from the six-phase stationary coordinate system to the voltage equation of the series winding nine-phase double-stator motor in the rotating coordinate system; S2: Based on the voltage equation of the nine-phase dual-stator motor with series winding in the rotating coordinate system, the electromagnetic torque equation of the rotor output is established according to the total electromagnetic torque output by the rotor being the superposition of the internal and external stators. S3: According to the multi-phase multi-motor series connection theory, the inner and outer stator windings are connected in series, and the equivalent formula for calculating the copper loss of the nine-phase double-stator motor with series windings and the Lagrangian function equation with the goal of minimizing the copper loss under the constraint condition of satisfying the electromagnetic torque equation of the rotor output are obtained; S4: According to the different inner and outer structures of the cup-shaped rotor, a Lagrangian function equation with the goal of minimizing copper loss under different cup-shaped rotor structures is established, and the current reference value under different cup-shaped rotor structures is calculated; S5: The current reference values ​​under different cup-shaped rotor structures are given to the current inner loop of the series-wound nine-phase dual-stator motor to achieve copper loss minimum torque control of the series-wound nine-phase dual-stator motor.

2. The method for controlling the copper loss of a nine-phase dual-stator motor with series windings according to claim 1 is characterized in that: The voltage equation of the series winding nine-phase dual-stator motor in the rotating coordinate system in step S1 is formula (1): （1）； in: It represents the direct-axis voltage reference value of the fundamental wave plane of the nine-phase double-stator motor with series winding, It represents the quadrature axis voltage reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, It represents the direct-axis voltage reference value of the harmonic plane of the nine-phase double-stator motor with series windings, It represents the quadrature axis voltage reference value of the harmonic plane of the nine-phase dual-stator motor with series winding, represents the equivalent phase resistance of the outer stator winding, represents the equivalent phase resistance of the inner stator winding, It represents the direct axis current reference value of the fundamental wave plane of the nine-phase double-stator motor with series winding, It represents the quadrature axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, It represents the direct axis current reference value of the harmonic plane of the nine-phase double-stator motor with series winding, It represents the quadrature axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding, It represents the air gap flux between the outer stator and the direct axis of the fundamental wave plane of the nine-phase double-stator motor with series windings, It represents the air gap flux between the outer stator and the quadrature axis of the fundamental wave plane of the nine-phase double-stator motor with series windings. Represents the air gap flux between the inner stator and the direct axis of the harmonic plane of the nine-phase double-stator motor with series windings, It represents the air gap flux between the inner stator and the quadrature axis of the harmonic plane of the nine-phase double-stator motor with series windings. represents the electrical angular velocity of the external air gap magnetic field rotation, It represents the electrical angular velocity of the internal air gap magnetic field rotation.

3. The method for controlling the copper loss of a nine-phase dual-stator motor with series windings according to claim 2 is characterized in that: The electromagnetic torque equation of the rotor output established in step S2 is formula (2): （2）； in: Represents the electromagnetic torque output by the rotor, Indicates the number of permanent magnet poles on the outer side of the cup-shaped rotor, represents the direct-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series windings, It represents the quadrature-axis inductance of the fundamental-wave plane of the nine-phase dual-stator motor with series windings, represents the equivalent permanent magnet flux of the external air gap, Indicates the number of permanent magnet pole pairs inside the cup-shaped rotor, represents the direct-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series windings, represents the quadrature-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series windings, Represents the equivalent permanent magnet flux within the air gap.

4. The method for controlling the copper loss of a nine-phase dual-stator motor with series windings according to claim 1 is characterized in that: The equivalent formula for calculating the copper loss of the nine-phase dual-stator motor with series windings in step S3 is formula (3): （3）； in: Indicates the copper loss of a nine-phase double-stator motor with series windings, represents the equivalent phase resistance of the outer stator winding, represents the equivalent phase resistance of the inner stator winding, It represents the effective value of the current in the fundamental wave plane of the nine-phase double-stator motor with series windings. It represents the effective value of current in the harmonic plane of the nine-phase double-stator motor with series winding.

5. The method for controlling the copper loss of a nine-phase dual-stator motor with series windings according to claim 4 is characterized in that: In step S3, the Lagrangian function equation with the goal of minimizing copper loss under the torque constraint condition is formula (4): （4）； in: represents the Lagrangian function with the goal of minimizing copper loss under torque constraints, represents the Lagrange multiplier, Represents the reference electromagnetic torque output by the rotor.

6. The method for controlling the copper loss of a nine-phase dual-stator motor with series windings according to claim 5 is characterized in that: In step S4, when both the inner and outer sides of the cup-shaped rotor are hidden pole type, the current reference value is calculated according to the following method: S411: When both the inner and outer sides of the cup-shaped rotor are hidden pole type, the direct-axis inductance of the fundamental wave plane of the series winding nine-phase dual-stator motor is equal to the quadrature-axis inductance of the fundamental wave plane of the series winding nine-phase dual-stator motor, and the direct-axis inductance of the harmonic plane of the series winding nine-phase dual-stator motor is equal to the quadrature-axis inductance of the harmonic plane of the series winding nine-phase dual-stator motor. The direct-axis current reference value of the fundamental wave plane of the series winding nine-phase dual-stator motor and the direct-axis current reference value of the harmonic plane of the series winding nine-phase dual-stator motor are both zero control. The corresponding Lagrangian function equation with the minimum copper loss as the target under the torque constraint condition is formula (5): （5）； in: It represents the Lagrangian function with the goal of minimizing copper loss under torque constraints when both the inner and outer sides of the cup-type rotor are non-hidden poles; S412: According to formula (5), the partial derivatives of the quadrature axis current of the fundamental wave plane of the nine-phase dual-stator motor with series winding and the quadrature axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding are calculated and both are equal to zero, and the Lagrange multiplier is eliminated to obtain formula (6): （6）； S413: Taking the PI output of the speed outer loop as the reference electromagnetic torque output by the rotor, the quadrature-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor and the quadrature-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor are calculated according to formula (6).

7. The method for controlling the copper loss of a nine-phase dual-stator motor with series windings according to claim 5 is characterized in that: In step S4, when the inner side of the cup-shaped rotor is a hidden pole type and the outer side is a salient pole type, the current reference value is calculated according to the following method: S421: When the inner side of the cup-shaped rotor is a hidden pole type and the outer side is a salient pole type, the direct-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding is equal to the quadrature-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding, and the direct-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding is not equal to the quadrature-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding. The corresponding Lagrangian function equation with the minimum copper loss as the goal under the torque constraint condition is formula (7): （7）； in: It represents the Lagrangian function with the goal of minimizing copper loss under torque constraints when the inner side of the cup-shaped rotor is a hidden pole type and the outer side is a salient pole type; S422: According to formula (7), the direct axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, the quadrature axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, and the quadrature axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding are calculated and the partial derivatives are all equal to zero, and the Lagrange multiplier is eliminated to obtain formula (8): （8）； S423: The PI output of the speed outer loop is used as the quadrature-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor. The direct-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor is obtained according to the maximum torque current ratio. Then, the quadrature-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor is calculated according to formula (8). The harmonic plane of the series-wound nine-phase dual-stator motor adopts the direct-axis current of the harmonic plane of the series-wound nine-phase dual-stator motor to be zero control.

8. The method for controlling the copper loss of a nine-phase dual-stator motor with series windings according to claim 5 is characterized in that: In step S4, when the cup-shaped rotor is of hidden pole type on the outside and salient pole type on the inside, the current reference value is calculated as follows: S431: When the cup-shaped rotor is of hidden pole type on the outside and salient pole type on the inside, the direct-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding is equal to the quadrature-axis inductance of the fundamental wave plane of the nine-phase dual-stator motor with series winding, and the direct-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding is not equal to the quadrature-axis inductance of the harmonic plane of the nine-phase dual-stator motor with series winding. The corresponding Lagrangian function equation with the minimum copper loss as the goal under the torque constraint condition is formula (9): （9）； in: It represents the Lagrangian function with the goal of minimizing copper loss under torque constraints when the cup-shaped rotor has a hidden pole type on the outside and a salient pole type on the inside; S432: According to formula (9), the quadrature-axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding, the direct-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding and the partial derivatives of the quadrature-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding are calculated and all are equal to zero, and the Lagrange multiplier is eliminated to obtain formula (10): （10）； S433: The PI output of the speed outer loop is used as the quadrature-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor. The direct-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor is obtained according to the maximum torque current ratio. Then, the quadrature-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor is calculated according to formula (10). The fundamental wave plane of the series-wound nine-phase dual-stator motor adopts the direct-axis current of the fundamental wave plane of the series-wound nine-phase dual-stator motor to be zero control.

9. The method for controlling the copper loss of a nine-phase dual-stator motor with series windings according to claim 5 is characterized in that: When both the inner and outer sides of the cup-shaped rotor are salient poles in step S4, the current reference value is calculated as follows: S441: When both the inner and outer sides of the cup-shaped rotor are salient poles, the direct-axis inductance of the fundamental wave plane of the series-wound nine-phase dual-stator motor is not equal to the quadrature-axis inductance of the fundamental wave plane of the series-wound nine-phase dual-stator motor, and the direct-axis inductance of the harmonic plane of the series-wound nine-phase dual-stator motor is not equal to the quadrature-axis inductance of the harmonic plane of the series-wound nine-phase dual-stator motor. According to the maximum torque current ratio control, the relationship between the direct-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor and the quadrature-axis current reference value of the fundamental wave plane of the series-wound nine-phase dual-stator motor, and the direct-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor and the quadrature-axis current reference value of the harmonic plane of the series-wound nine-phase dual-stator motor is obtained as formula (11): （11）； S442: The partial derivatives of the direct-axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding and the direct-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding are respectively calculated and are both equal to zero, and the Lagrange multiplier is eliminated by substituting formula (11) into the formula (12): （12）； S443: Rearrange equation (12) to obtain equation (13), and then rearrange the right side of equation (13) to obtain equation (14): （13）； （14）； in: is the coefficient related to the motor parameters, ; S444: Combining equation (14) and equation (11), equation (13) is simplified to equation (15): （15）； S445: The PI output of the speed outer loop is converted into the quadrature-axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding. The direct-axis current reference value of the fundamental wave plane of the nine-phase dual-stator motor with series winding is obtained according to the maximum torque current ratio current relationship. Then, the quadrature-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding is solved according to formula (15). Finally, the direct-axis current reference value of the harmonic plane of the nine-phase dual-stator motor with series winding is obtained through the maximum torque current ratio relationship.

10. The method for controlling the copper loss of a nine-phase dual-stator motor with series windings according to claim 3 is characterized in that: In step S2, if the cup-shaped rotor is a hidden pole type on both the inner and outer sides, the electromagnetic torque equation of the rotor output is simplified to equation (16); if the cup-shaped rotor is a hidden pole type on the inner side and a salient pole type on the outer side, the electromagnetic torque equation of the rotor output is simplified to equation (17); if the cup-shaped rotor is a hidden pole type on the outer side and a salient pole type on the inner side, the electromagnetic torque equation of the rotor output is simplified to equation (18): （16）； （17）； （18）。

Images