A cascaded predictive torque control method for permanent magnet synchronous motor

Abstract

This invention relates to the field of motor control technology, and in particular to a cascaded predictive torque control method for permanent magnet synchronous motors (PMSMs). The method includes the following steps: establishing an OEW-PMSM mathematical model; discretizing the OEW-PMSM mathematical model; constructing cost functions for electromagnetic torque and flux linkage respectively; determining the number of finite lumped voltage vectors in each layer; selecting the optimal voltage vector through the electromagnetic torque cost function and the flux linkage cost function; and finally, applying the selected optimal voltage vector to the inverter to input into the PMSM to control the motor's torque and flux linkage. By introducing a cascaded predictive torque control method, utilizing its hierarchical optimization approach, the introduction of weighting factors is directly avoided. Furthermore, by eliminating elements that generate large common-mode voltage amplitudes, zero-sequence current can be further suppressed, and the load can be reduced.

Description

Technical Field

[0001] This invention relates to the field of motor control technology, and in particular to a cascaded predictive torque control method for permanent magnet synchronous motors. Background Technology

[0002] Open-winding permanent magnet synchronous motor systems have gained favor among researchers due to their higher power density, greater low-speed output torque, higher high-speed output power, better field weakening characteristics, and smaller phase current, leading to their rapid promotion and application in high-power applications.

[0003] High-performance AC speed control methods generally include Field-Oriented Control (FOC), Direct Torque Control (DTC), and Model Predictive Control (MPC). FOC can achieve good torque and flux control of the motor, but its internal current loop requires complex tuning. DTC has a simple control structure and can achieve fast dynamic response, but its torque ripple is relatively large. MPC has advantages such as fast dynamic response and good control effect, but MPC requires simultaneous tuning of the stator flux weighting factor and the zero-sequence current weighting factor, which is cumbersome, computationally burdensome, and not conducive to practical applications.

[0004] In view of this, the applicant has conducted in-depth research on the above-mentioned issues, which led to this case. Summary of the Invention

[0005] The purpose of this invention is to provide a predictive torque control method for cascaded permanent magnet synchronous motors that helps reduce computational burden.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A cascaded predictive torque control method for permanent magnet synchronous motors includes the following steps:

[0008] S1: Establish the OEW-PMSM mathematical model;

[0009] S2: Discretize the OEW-PMSM mathematical model to obtain the stator flux linkage ψ. s Stator current i s and stator voltage u s The measured value;

[0010] S3: Predict the zero-sequence current i at time k+1 using the measurement value from step 2. s0 (k+1), electromagnetic torque T e (k+1) and stator flux linkage ψ s (k+1), where k is the current time;

[0011] S4: Regarding the electromagnetic torque T e (k+1) Construct the electromagnetic torque cost function JΔTe And the stator flux linkage ψ s (k+1) Construct the flux linkage cost function J Δψ ;

[0012] S5: List the electromagnetic torque cost function J ΔTe and the magnetic flux cost function J Δψ All hierarchical orders of the two cost functions are analyzed through simulation, and the electromagnetic torque cost function J is selected. ΔTe -The magnetic flux cost function J Δψ J, as the magnetic torque cost function ΔTe and the magnetic flux cost function J Δψ Hierarchical optimization order for two cost functions;

[0013] S6: Based on the zero-sequence current i in step 3 s0 The positive and negative values ​​of (k+1) are divided into two initial finite sets, and the electromagnetic torque cost function J is determined. ΔTe and the magnetic flux cost function J Δψ The number of voltage vectors in each finite set is determined by the following steps:

[0014] S6-1: Calculate the magnitude of the common-mode voltage U0 generated by each voltage vector in the finite set;

[0015] S6-2: Determine the zero-sequence current i predicted in step 3. s0 The value of (k+1), the zero-sequence current i s0 When (k+1) is greater than or equal to 0, then select the voltage vectors that generate common-mode voltage U0 less than or equal to 0 to form a finite set; the zero-sequence current i s0 When (k+1) is less than 0, select the voltage vectors that generate common-mode voltage U0 greater than 0 to form a finite set;

[0016] S6-3: A threshold is preset to remove voltage vectors whose common-mode voltage U0 amplitude is greater than or equal to the threshold from a finite set;

[0017] S6-4: Final determination of the remaining electromagnetic torque cost function J after elimination. ΔTe and the flux linkage cost function J Δψ The number of voltage vectors in each finite set;

[0018] S7: The obtained finite lumped voltage vector is used to obtain the electromagnetic torque T at time k+2 through the delay compensation stage in the OEW-PMSM mathematical model. e The electromagnetic torque ψ at (k+2) and time k+2 s (k+2), predicting the electromagnetic torque T at time k+2. eSubstituting (k+2) into the electromagnetic torque cost function In the process, the stator flux linkage ψ at time k+2 will be predicted. s Substituting (k+2) into the stator flux cost function J Δψ In the process, select the appropriate voltage vector from m voltage vectors. The smallest n voltage vectors, then select the one from the n voltage vectors that makes J Δψ The minimum voltage vector, where m and n are both positive integers, is chosen to make J... Δψ The smallest voltage vector is selected as the optimal voltage vector in the final screening.

[0019] S8: The final selected optimal voltage vector is applied to the inverter and input into the open-winding permanent magnet synchronous motor to control the torque and flux linkage of the open-winding permanent magnet synchronous motor.

[0020] Furthermore, in step S2, the stator flux linkage ψ s The stator current i s and the stator voltage u s Specific acquisition methods:

[0021] Using constant power transformation, the OEW-PMSM mathematical model is transformed into a rotating coordinate system. In the rotating coordinate system, the stator flux linkage ψ s The expression is as follows:

[0022]

[0023] In a rotating coordinate system, the electromagnetic torque T of the motor e The expression is as follows:

[0024]

[0025] In a rotating coordinate system, the expression for the stator voltage balance equation is as follows:

[0026]

[0027] Where, ψ sd ,ψ sq ,ψ s0 The d-axis, q-axis, and 0-axis components of the stator flux linkage; u sd ,u sq ,u s0 The stator voltage consists of the d-axis, q-axis, and 0-axis components; i sd i sq i s0 Let ω be the d-axis, q-axis, and 0-axis components of the stator current, p be the differential operator, and ω be the q-axis component. r L is the motor speed. d For the d-axis inductance, Lq For the q-axis inductance, L sσ1 For motor leakage inductance, ψ f For the fundamental permanent magnet flux linkage, ψ 3f For the third harmonic component of the permanent magnet flux linkage, θ r R is the rotor position angle. s This is the stator resistance.

[0028] Furthermore, in step S3, the zero-sequence current i at time k+1 s0 (k+1), electromagnetic torque T e (k+1) and stator flux linkage ψ s The formula for calculating (k+1) is as follows:

[0029] The mechanical time constant is much larger than the electrical time constant, which affects the motor speed ω between two adjacent control cycles. r and rotor position angle θ r If we consider it invariant, the first-order Euler discretization expression is as follows:

[0030]

[0031] Calculate the stator flux linkage ψ at time k+1. s The amplitude of (k+1) is:

[0032]

[0033] Calculate the d-axis component i of the stator point current at time k+1. sd (k+1), q-axis component i of stator flux linkage sq (k+1) and the d-axis component i of the stator flux linkage s0 (k+1):

[0034]

[0035] The electromagnetic torque T at time k+1 is calculated using formula (6). e The amplitude of (k+1) is:

[0036]

[0037] Where, ψ sd (k+1) represents the d-axis component of the stator flux linkage at time k+1, ψ sq (k+1) is the q-axis component of the stator flux linkage at time k+1, ψ s0 (k+1) represents the zero-axis component of the stator flux linkage at time k+1, u sd (k) represents the d-axis component of the stator voltage at time k+1, T s To control the cycle.

[0038] Furthermore, the d-axis component u of the stator voltage sd (k) The q-axis component u of the stator voltage sq (k) and the zero-axis component u of the stator voltage s0 The formula for calculating (k) is as follows:

[0039]

[0040] in, This is the stator voltage for the current control cycle.

[0041] Furthermore, the stator voltage of the current control cycle The calculation formula is as follows:

[0042]

[0043] Among them, T A1 T is the operating time of the A-phase upper transistor of inverter 1. A2 T is the operating time of the A-phase upper transistor of inverter 2. B1 T is the operating time of the upper transistor on phase B of inverter 1. B2 T is the operating time of the upper transistor on phase B of inverter 2. C1 T is the operating time of the C-phase upper transistor of inverter 1. C2 This refers to the operating time of the upper transistor on phase C of inverter 2.

[0044] Furthermore, in step S4, the electromagnetic torque evaluation function J ΔTe The expression is as follows:

[0045]

[0046] Magnetic flux linkage evaluation function J Δψ The expression is as follows:

[0047] J Δψ =||ψ s | * -|ψ s (k+2)|| 2 (11);

[0048] in, For the electromagnetic torque reference value, |ψ s | * This is the reference value for the stator flux linkage.

[0049] By adopting the above technical solution, the present invention has the following beneficial effects:

[0050] 1. By introducing a cascaded predictive torque control method, the hierarchical optimization idea is utilized to directly avoid the introduction of weighting factors. Furthermore, by eliminating elements that generate large common-mode voltage amplitudes, zero-sequence current can be further suppressed, and the burden can be reduced. It has the advantages of simple algorithm, good versatility, and easy implementation.

[0051] 2. By using the method of dividing into finite sets to suppress zero-sequence current and optimizing the number of vectors in each finite set layer, better control effect can be achieved, which can reduce the current ripple and zero-sequence current of the entire system. Attached Figure Description

[0052] Figure 1 The program execution flowchart provided for this invention. Detailed Implementation

[0053] The present invention will be further described below with reference to specific embodiments:

[0054] This embodiment provides a cascaded predictive torque control method for permanent magnet synchronous motors, such as... Figure 1 As shown, it includes the following steps:

[0055] S1: Establish the OEW-PMSM mathematical model.

[0056] S2: Discretize the OEW-PMSM mathematical model to obtain the stator flux linkage ψ s Stator current i s and stator voltage u s The measured value.

[0057] S3: Predict the zero-sequence current i at time k+1 using the measurement value from step 2. s0 (k+1), electromagnetic torque T e (k+1) and stator flux linkage ψ s (k+1), where k is the current time;

[0058] S4: Regarding the electromagnetic torque T e (k+1) Construct the electromagnetic torque cost function And the stator flux linkage ψ s (k+1) Construction of flux linkage cost function J Δψ .

[0059] S5: List the electromagnetic torque cost function and flux linkage cost function J Δψ In this embodiment, there are two possible hierarchical orders for the two cost functions. Simulation analysis is performed on each order, and the electromagnetic torque cost function minus the flux linkage cost function is selected as the magnetic torque cost function. and the magnetic flux cost function J ΔψHierarchical optimization order of two cost functions.

[0060] S6: Based on the zero-sequence current i in step 3 s0 The positive and negative values ​​of (k+1) are divided into two initial finite sets, and the electromagnetic torque cost function is determined. and the magnetic flux cost function J Δψ The steps to determine the number of finite concentrated voltage vectors in each layer are as follows:

[0061] S6-1: Taking a dual inverter as an example, calculate the magnitude of the common-mode voltage U0 generated by each voltage vector in the finite set, as shown in the table:

[0062]

[0063]

[0064] S6-2: Determine the zero-sequence current i predicted in step 3 s0 The value of (k+1), the zero-sequence current i s0 When (k+1) is greater than or equal to 0, then select the voltage vectors that generate common-mode voltage U0 less than or equal to zero to form a finite set; zero-sequence current i s0 When (k+1) is less than zero, select the voltage vectors that generate common-mode voltage U0 greater than 0 to form a finite set.

[0065] S6-3: A threshold is preset to remove voltage vectors whose common-mode voltage U0 amplitude is greater than or equal to the threshold from a finite set. In this embodiment, the threshold is 2U. dc / 3, where U dc For bus voltage, i.e., excluding voltages with an amplitude of U dc and 2U dc / 3 of the voltage vectors, that is, the initial number of finite lumped vectors is 35;

[0066] S6-4: Final determination of the remaining electromagnetic torque cost function after elimination and the flux linkage cost function J Δψ The number of voltage vectors, in this embodiment, the electromagnetic torque cost function The finite set voltage vectors have 35 elements, and the flux linkage cost function J... Δψ The number of finite set voltage vectors is 7;

[0067] S7: The obtained finite lumped voltage vector is used to obtain the electromagnetic torque T at time k+2 through the delay compensation element in the mathematical model of the open-winding permanent magnet synchronous motor. e The electromagnetic torque ψ at (k+2) and time k+2 s (k+2), predicting the electromagnetic torque T at time k+2. eSubstituting (k+2) into the electromagnetic torque cost function In the process, the stator flux linkage ψ at time k+2 will be predicted. s Substituting (k+2) into the stator flux cost function J Δψ In the process, select the appropriate voltage vector from m voltage vectors. The smallest n voltage vectors, then select the one from the n voltage vectors that makes J Δψ The minimum voltage vector, where m and n are both positive integers, is chosen to make J... Δψ The smallest voltage vector is selected as the optimal voltage vector. It should be noted that the OEW-PMSM mathematical model has delay compensation, and the delay compensation is conventional, which will not be described in detail here.

[0068] S8: The final selected optimal voltage vector is applied to the inverter and input to the open-winding permanent magnet synchronous motor to control the torque and flux linkage of the open-winding permanent magnet synchronous motor.

[0069] In step S2, the stator flux linkage ψ s Stator current i s and stator voltage u s Specific acquisition methods:

[0070] Using constant power transformation, the OEW-PMSM mathematical model is transformed to a rotating coordinate system. In the rotating coordinate system (dq coordinate system), the stator flux linkage ψ s The expression is as follows:

[0071]

[0072] In a rotating coordinate system (dq coordinate system), the electromagnetic torque T of the motor e The expression is as follows:

[0073]

[0074] In the rotating coordinate system (dq coordinate system), the stator voltage balance equation is expressed as follows:

[0075]

[0076] Where, ψ sd ,ψ sq ,ψ s0 The d-axis, q-axis, and 0-axis components of the stator flux linkage; u sd ,u sq ,u s0 The stator voltage consists of the d-axis, q-axis, and 0-axis components; i sd i sq i s0Let ω be the d-axis, q-axis, and 0-axis components of the stator current, p be the differential operator, and ω be the q-axis component. r L is the motor speed. d For the d-axis inductance, L q For the q-axis inductance, L sσ1 For motor leakage inductance, ψ f For the fundamental permanent magnet flux linkage, ψ 3f For the third harmonic component of the permanent magnet flux linkage, θ r R is the rotor position angle. s This is the stator resistance.

[0077] In step S3, the zero-sequence current i at time k+1 s0 (k+1), electromagnetic torque T e (k+1) and stator flux linkage ψ s The formula for calculating (k+1) is as follows:

[0078] The mechanical time constant is much larger than the electrical time constant, which affects the motor speed ω between two adjacent control cycles. r and rotor position angle θ r If we consider it invariant, the first-order Euler discretization expression is as follows:

[0079]

[0080] Calculate the stator flux linkage ψ at time k+1. s The amplitude of (k+1) is:

[0081]

[0082] Calculate the d-axis component i of the stator point current at time k+1. sd (k+1), q-axis component i of stator flux linkage sq (k+1) and the d-axis component i of the stator flux linkage s0 (k+1):

[0083]

[0084] The electromagnetic torque T at time k+1 is calculated using formula (6). e The amplitude of (k+1) is:

[0085]

[0086] Where, ψ sd (k+1) represents the d-axis component of the stator flux linkage at time k+1, ψ sq (k+1) is the q-axis component of the stator flux linkage at time k+1, ψ s0 (k+1) represents the zero-axis component of the stator flux linkage at time k+1, u sd(k) represents the d-axis component of the stator voltage at time k+1, T s To control the cycle.

[0087] d-axis component u of stator voltage sd (k) q-axis component u of stator voltage sq (k) and the zero-axis component u of the stator voltage s0 The formula for calculating (k) is as follows:

[0088]

[0089] in, This is the stator voltage for the current control cycle.

[0090] Stator voltage in the current control cycle The calculation formula is as follows:

[0091]

[0092] Among them, T A1 T is the operating time of the A-phase upper transistor of inverter 1. A2 T is the operating time of the A-phase upper transistor of inverter 2. B1 T is the operating time of the upper transistor on phase B of inverter 1. B2 T is the operating time of the upper transistor on phase B of inverter 2. C1 T is the operating time of the C-phase upper transistor of inverter 1. C2 This refers to the operating time of the upper transistor on phase C of inverter 2.

[0093] The electromagnetic torque evaluation function J in step S4 ΔTe The expression is as follows:

[0094]

[0095] Magnetic flux linkage evaluation function J Δψ The expression is as follows:

[0096] J Δψ =||ψ s | * -|ψ s (k+2)|| 2 (11).

[0097] in, For the electromagnetic torque reference value, |ψ s | * This is the reference value for the stator flux linkage.

[0098] In summary, by introducing a cascaded predictive torque control method and utilizing its hierarchical optimization approach, the introduction of weighting factors is directly avoided. Furthermore, by eliminating elements that generate large common-mode voltage amplitudes, zero-sequence current can be further suppressed, and the load can be reduced. This method has advantages such as simple algorithm, good versatility, and ease of implementation, which is beneficial for practical applications. By using a finite set method to suppress zero-sequence current and optimizing the number of vectors in each finite set layer, better control performance can be achieved, reducing the current ripple and zero-sequence current of the entire open-winding permanent magnet synchronous motor system.

[0099] The present invention has been described in detail above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the above embodiments. Those skilled in the art can make various modifications to the present invention based on the prior art, and these modifications all fall within the protection scope of the present invention.

Claims

1. A cascaded predictive torque control method for permanent magnet synchronous motors, characterized in that, Includes the following steps: S1: Establish the OEW-PMSM mathematical model; S2: Discretize the OEW-PMSM mathematical model to obtain the stator flux linkage. Stator current and stator voltage The measured value; S3: Predict the zero-sequence current at time k+1 using the measurements from step 2. Electromagnetic torque and stator flux Where k is the current time; S4: Regarding the electromagnetic torque Constructing the electromagnetic torque cost function And the stator magnetic flux Constructing the flux linkage cost function ; S5: List the electromagnetic torque cost function. and the flux linkage cost function All hierarchical orders of the two cost functions are analyzed through simulation, and the electromagnetic torque cost function is selected. To the magnetic flux cost function As the magnetic torque cost function and the flux linkage cost function Hierarchical optimization order for two cost functions; S6: Based on the zero-sequence current in step 3 The positive and negative values ​​are divided into two initial finite sets, and the electromagnetic torque cost function is determined. and the flux linkage cost function The number of voltage vectors in each finite set is determined by the following steps: S6-1: Calculate the common-mode voltage generated by each voltage vector in the finite set. size; S6-2: Determine the zero-sequence current predicted in step 3. The value of the zero-sequence current If the value is greater than or equal to 0, then a common-mode voltage is selected. Voltage vectors less than or equal to 0 form a finite set; the zero-sequence current When the value is less than 0, select to generate common-mode voltage. Voltage vectors greater than 0 form a finite set; S6-3: A threshold is preset to remove common-mode voltages generated from a finite set. A voltage vector with an amplitude greater than or equal to the threshold; S6-4: Final determination of the remaining electromagnetic torque cost function after elimination. and the flux linkage cost function The number of voltage vectors in each finite set; S7: The obtained finite lumped voltage vector is used to obtain the electromagnetic torque at time k+2 through the delay compensation stage in the OEW-PMSM mathematical model. Electromagnetic torque at time k+2 The electromagnetic torque at time k+2 will be predicted. Substituting the electromagnetic torque cost function In the process, the stator flux linkage at time k+2 will be predicted. Substituting the stator flux cost function In the process, select the appropriate voltage vector from m voltage vectors. The smallest n voltage vectors, then select the smallest from the n voltage vectors. The minimum voltage vector, where m and n are both positive integers, is chosen to make... The smallest voltage vector is selected as the optimal voltage vector in the final screening. S8: The final selected optimal voltage vector is applied to the inverter and input into the open-winding permanent magnet synchronous motor to control the torque and flux linkage of the open-winding permanent magnet synchronous motor; Electromagnetic torque evaluation function in step S4 The expression is as follows: （10）； Magnet flux evaluation function The expression is as follows: （11）； in, This is the reference value for electromagnetic torque. This is the reference value for the stator flux linkage.

2. The cascaded predictive torque control method for permanent magnet synchronous motors according to claim 1, characterized in that, In step S2, the stator magnetic flux The stator current and the stator voltage Specific acquisition methods: Using constant power transformation, the OEW-PMSM mathematical model is transformed to a rotating coordinate system. In the rotating coordinate system, the stator flux linkage... The expression is as follows: （1）； In a rotating coordinate system, the electromagnetic torque of the motor The expression is as follows: （2）； In a rotating coordinate system, the expression for the stator voltage balance equation is as follows: （3）； in, These are the d-axis, q-axis, and 0-axis components of the stator flux linkage; These are the d-axis, q-axis, and 0-axis components of the stator voltage. These represent the d-axis, q-axis, and 0-axis components of the stator current. For differential operators, This refers to the motor speed. For d-axis inductance, It is the q-axis inductance. For motor leakage inductance, For fundamental permanent magnet flux linkage, The third harmonic component of the permanent magnet flux linkage. The rotor position angle, This is the stator resistance.

3. The cascaded predictive torque control method for permanent magnet synchronous motors according to claim 2, characterized in that, In step S3, the zero-sequence current at time k+1 Electromagnetic torque and stator flux The calculation formula is as follows: The motor speed is adjusted between two adjacent control cycles. and rotor position angle If we consider it invariant, the first-order Euler discretization expression is as follows: （4）； Calculate the stator flux linkage at time k+1 Amplitude is: （5）； Calculate the d-axis component of the stator point current at time k+1. q-axis component of stator flux and the d-axis component of the stator flux linkage : （6）； The electromagnetic torque at time k+1 is calculated using formula (6). Amplitude is: （7）； in, Let be the d-axis component of the stator flux linkage at time k+1. Let be the q-axis component of the stator flux linkage at time k+1. Let be the 0-axis component of the stator flux linkage at time k+1. Let be the d-axis component of the stator voltage at time k+1. To control the cycle.

4. The cascaded predictive torque control method for permanent magnet synchronous motors according to claim 3, characterized in that, The d-axis component of the stator voltage The q-axis component of the stator voltage and the zero-axis component of the stator voltage The calculation formula is as follows: （8）； in, This is the stator voltage for the current control cycle.

5. The cascaded predictive torque control method for permanent magnet synchronous motors according to claim 4, characterized in that, The stator voltage of the current control cycle The calculation formula is as follows: （9）； in, The operating time of the A-phase upper transistor of inverter 1. The operating time of the A-phase upper transistor of inverter 2. The operating time of the upper transistor on phase B of inverter 1. The operating time of the upper transistor on phase B of inverter 2. The operating time of the upper transistor on phase C of inverter 1. This refers to the operating time of the upper transistor on phase C of inverter 2.

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