Permanent magnet synchronous motor current harmonic suppression method based on model predictive control

Abstract

The invention discloses a permanent magnet synchronous motor current harmonic suppression method based on model prediction control, and the method comprises the following steps: S1, building a mathematical model of a permanent magnet synchronous motor in a rotating coordinate system, and carrying out the discretization through an Euler discretization method, and obtaining a prediction model for predicting the state of the permanent magnet synchronous motor at a future moment; s2, designing and constructing a cost function including a fundamental current tracking item and a high-order current harmonic suppression item in the prediction model; calculating a current harmonic term factor; s3, traversing voltage vectors corresponding to all switching states of the inverter, calculating predicted current and a cost function under the action of the voltage vectors, selecting an optimal voltage vector enabling the cost function to be minimum, and generating a switching signal to drive the permanent magnet synchronous motor to operate; according to the method, the prediction model containing fundamental wave tracking and high-order harmonic suppression is constructed, and the harmonic suppression factor is optimized in real time by using the Lagrange multiplier method, so that current harmonic suppression and system loss reduction are realized.

Description

Technical Field

[0001] This invention relates to the field of high-performance motor control technology, and more specifically to a method for suppressing current harmonics in permanent magnet synchronous motors based on model predictive control. Background Technology

[0002] Model predictive control (MPC) has attracted widespread attention due to its simple algorithm and multi-objective control capabilities. It can be divided into finite control set MPC (FCS-MPC) and continuous control set MPC (CCS-MPC). Because FCS-MPC has excellent adaptability to the finite switching combinations of three-phase inverter equipment, it is widely used in motor control algorithms. Although the FCS-MPC control algorithm is simple and has good dynamic performance, its steady-state performance is poor. The main factors affecting its steady-state performance are the periodic and aperiodic harmonics introduced by the nonlinearity of the motor and inverter.

[0003] To improve the stability of model prediction algorithms and achieve better control performance, researchers have proposed a number of patents related to harmonic suppression.

[0004] Chinese invention patent publication number CN115037204B proposes a method for suppressing current harmonics in permanent magnet synchronous motors. This method achieves online identification of time-varying parameters such as stator resistance and inductance by designing a model reference adaptive system, thereby improving the robustness of the control algorithm to parameter fluctuations. Furthermore, a harmonic injection system is designed for the 6x±1st order current harmonics, effectively suppressing current harmonics and reducing vibration and noise during motor operation. However, this method does not provide a detailed explanation of the parameter identification effect and current harmonic suppression effect of the adaptive algorithm during dynamic motor operation.

[0005] Chinese invention patent publication number CN114679111B proposes a method for suppressing harmonic current in a permanent magnet synchronous motor. This method constructs a repetitive extended state observer, defines d-axis and q-axis disturbances as new state variables, and combines them with a repetitive active disturbance rejection controller to compensate for harmonic disturbances. The control strategy of this method is highly versatile and can adapt to harmonic disturbances caused by various factors such as parameter fluctuations and load changes in the motor drive system. However, the repetitive extended state observer involved in this method involves multivariate coupling, resulting in a large computational load. Under high-requirement operating conditions, a trade-off between computational accuracy and system response speed is necessary. Summary of the Invention

[0006] The purpose of this invention is to provide a method for suppressing current harmonics in permanent magnet synchronous motors based on model predictive control. By constructing a predictive model that includes fundamental wave tracking and higher-order harmonic suppression, and using the Lagrange multiplier method to optimize the harmonic suppression factor in real time, the optimal voltage vector can be selected in finite set model predictive control to achieve current harmonic suppression and system loss reduction.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for suppressing current harmonics in a permanent magnet synchronous motor based on model predictive control includes the following steps:

[0009] S1. Establish a mathematical model of the permanent magnet synchronous motor in the rotating coordinate system, and discretize it using the Euler discretization method. Considering one-step delay compensation, we obtain a prediction model for the state of the permanent magnet synchronous motor at future moments.

[0010] S2. Design and construct a cost function in the prediction model that includes a fundamental current tracking term and a higher-order current harmonic suppression term; and calculate the current harmonic term factor in the cost function in real time using the Lagrange multiplier method; wherein, the higher-order current harmonic suppression term targets non-even and non-third harmonics; the current harmonic term factor is determined based on the deviation between the harmonic components of the predicted current and the reference current.

[0011] S3. Using a finite set model predictive control algorithm, the voltage vectors corresponding to all switching states of the inverter are traversed, the predicted current and cost function under the action of the voltage vector are calculated, the optimal voltage vector that minimizes the cost function is selected, and the switching signal is generated to drive the permanent magnet synchronous motor to achieve current harmonic suppression and system loss reduction.

[0012] Furthermore, in S1, the functional expression of the mathematical model is:

[0013]

[0014] Among them, i q Let u be the q-axis current. d For the d-axis voltage, u q R is the q-axis voltage. s L is the equivalent phase resistance. d L is the d-axis equivalent inductance. q ω is the q-axis equivalent inductance. e Let ψ be the electric angular velocity. f For permanent magnet flux linkage in motors.

[0015] Furthermore, in S1, the prediction model function expression is:

[0016]

[0017] in,

[0018] i d (k) represents the d-axis current in the k-th period, i d (k+1) represents the d-axis current in the (k+1)th period, u d(k) represents the d-axis voltage of the k-th period, u d (k+1) is the d-axis voltage of the (k+1)th period, i q (k) represents the q-axis current in the k-th period, i q (k+1) represents the q-axis current in the (k+1)th period, u q (k) is the q-axis voltage of the k-th period, u q (k+1) is the q-axis voltage of the (k+1)th period, T s To control the cycle, L d L represents the d-axis inductance of the motor. q ω represents the q-axis inductance of the motor. e This indicates the electric angular velocity of the motor.

[0019] Furthermore, the calculation process of the functional expression of the prediction model is as follows:

[0020] Electromagnetic torque T e The equation is:

[0021]

[0022] Based on the Euler discretization method, the mathematical model can be discretized as follows:

[0023]

[0024] Due to the existence of digital delay, one-beat delay compensation should be considered during the modeling process. Equation (1) can be further written as:

[0025]

[0026] Furthermore, in S2, the expression for the cost function is:

[0027]

[0028] in, To predict current harmonics, This represents the v-th current harmonic, where v represents the harmonic order, and ω represents the ω-th harmonic. v For current harmonic factors, Represents the reference current. This represents the predicted current.

[0029] Furthermore, in S2, the calculation process of the cost function is as follows:

[0030] In model predictive control, the traditional cost function is:

[0031]

[0032] Among them, i d(k+2) represents the d-axis current in the (k+2)th period, i q (k+2) represents the q-axis current in the (k+2)th period. Represents the d-axis reference current. Represents the q-axis reference current;

[0033] Predicting current under ideal conditions With reference current i s The same applies, but in practical applications, harmonics exist in the predicted current, therefore the predicted current... Represented as:

[0034]

[0035] in This represents the predicted current harmonics, where v represents the harmonic order. Represents the reference current, i s Represents the actual current; since the permanent magnet synchronous motor has three-phase symmetry and half-wave symmetry, there are no even-order and multiple-of-three harmonics in the stator winding, so equation (2) can be rewritten as:

[0036]

[0037] The new cost function considering current harmonics is:

[0038]

[0039] Where ω0 and ω v These are the coefficients of the fundamental current and the harmonic current, respectively.

[0040] When ω0 is 1, the cost function is rewritten as:

[0041]

[0042] Furthermore, in S3, the functional expression for the current harmonic term factor is:

[0043]

[0044] Where λ is the Lagrange factor.

[0045] Furthermore, in S3, the calculation process for the current harmonic term factor is as follows:

[0046] Find the expression for the proposed Lagrange function in terms of... The partial derivatives with respect to λ are specifically expressed as:

[0047]

[0048] Depend on The conclusion is

[0049] Therefore, equation (7) can be rewritten as:

[0050]

[0051] Solving the equations obtained from equations (7) and (8), it is obvious that... Setting equations (7) and (8) in the system of equations to 0, we can obtain the current harmonic term factor as follows:

[0052]

[0053] Due to the existence of the inverter dead time, the 5th and 7th harmonics in the stator phase current account for the majority of the total harmonics. Therefore, the current harmonic factor can be simplified as:

[0054]

[0055] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0056] This invention establishes a discretized prediction model of a permanent magnet synchronous motor in a rotating coordinate system and introduces a one-step delay compensation, significantly improving the accuracy and real-time performance of state prediction. It simultaneously incorporates a fundamental current tracking term and a high-order current harmonic suppression term targeting non-even and non-third harmonics into the cost function, and uses the Lagrange multiplier method to dynamically adjust the harmonic suppression factor in real time, enabling the system to adaptively optimize the control objective based on the deviation between the predicted current and the reference current. Finally, combined with a finite set model predictive control algorithm, by traversing the voltage vectors corresponding to all switching states of the inverter, the optimal voltage vector that minimizes the cost function is selected to generate the drive signal. This not only effectively suppresses specific high-order harmonic currents and reduces the current distortion rate, but also significantly reduces system losses, improves motor operating efficiency and stability, and possesses excellent dynamic response performance and engineering application value. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0058] The following description, in conjunction with the accompanying drawings, further illustrates a method for suppressing current harmonics in a permanent magnet synchronous motor based on model predictive control according to the present invention.

[0059] Figure 1 This is a flowchart illustrating the current harmonic suppression method for permanent magnet synchronous motors based on model predictive control in this invention.

[0060] Figure 2 This is a control block diagram of the model predictive control-based current harmonic suppression method for permanent magnet synchronous motors in this invention;

[0061] Figure 3 This is a topology diagram of the model predictive control circuit for the current harmonic suppression method of permanent magnet synchronous motor based on model predictive control in this invention.

[0062] Figure 4 This is a schematic diagram of the basic voltage vector of the model predictive control-based current harmonic suppression method for permanent magnet synchronous motors in this invention. Detailed Implementation

[0063] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0064] To better understand the purpose, structure, and function of this invention, the invention will be described in further detail below with reference to the accompanying drawings.

[0065] This invention provides a method for suppressing current harmonics in permanent magnet synchronous motors based on model predictive control, such as... Figure 1 As shown, it includes the following steps:

[0066] Step 1: First, analyze the mathematical model of the permanent magnet synchronous motor, such as... Figure 2 and 3 As shown, its mathematical model in the rotating coordinate system is:

[0067]

[0068] Among them, i d Let i be the d-axis current. q Let u be the q-axis current. d For the d-axis voltage, u q R is the q-axis voltage. s L is the equivalent phase resistance. d L is the d-axis equivalent inductance. q ω is the q-axis equivalent inductance. e Let ψ be the electric angular velocity. f For the motor body magnetic flux.

[0069] The electromagnetic torque equation is:

[0070]

[0071] Based on the Euler discretization method, its mathematical model can be discretized as follows:

[0072]

[0073] in,

[0074] i d (k) represents the d-axis current in the k-th period, i d (k+1) represents the d-axis current in the (k+1)th period, u d (k) represents the d-axis voltage of the k-th period, u d (k+1) is the d-axis voltage of the (k+1)th period, i q (k) represents the q-axis current in the k-th period, i q (k+1) represents the q-axis current in the (k+1)th period, u q (k) is the q-axis voltage of the k-th period, u q (k+1) is the q-axis voltage of the (k+1)th period, T s To control the cycle.

[0075] Due to the existence of digital latency, a one-beat delay compensation should be considered during the modeling process. The above formula can be further written as:

[0076]

[0077] Step 2: In model predictive control, the traditional cost function is... Predicting current under ideal conditions With reference current i s The same applies, but in practical applications, harmonics exist in the predicted current, therefore the predicted current will be... Represented as:

[0078]

[0079] in, Let represent the predicted current harmonics, and v represent the harmonic order. Since the permanent magnet synchronous motor has three-phase symmetry and half-wave symmetry, there are no even-order or multiple-of-three harmonics in the stator winding. Therefore, the above formula can be rewritten as:

[0080]

[0081] The new cost function considering current harmonics is:

[0082]

[0083] Where ω0 and ω v These are the coefficients of the fundamental current and harmonic current.

[0084] Step 3: Under normal circumstances, ω0 can be considered to be 1, so the cost function can be rewritten as:

[0085]

[0086] To obtain the coefficients of the current harmonic term, the Lagrangian function is introduced for solution, and its specific expression is as follows:

[0087]

[0088] Where λ is the Lagrange factor.

[0089] Step 4: Find the expression for the proposed Lagrange function in terms of... The partial derivatives with respect to λ are specifically expressed as:

[0090]

[0091] Depend on The conclusion is

[0092] Therefore, equation (7) can be rewritten as:

[0093]

[0094] Step 5: Solve the equations obtained from equations (7) and (8). Obviously, Setting equations (7) and (8) in the system of equations to 0, we can obtain the current harmonic term factor as follows:

[0095]

[0096] Due to the existence of the inverter dead time, the 5th and 7th harmonics in the stator phase current account for the majority of the total harmonics. Therefore, the current harmonic factor can be simplified as:

[0097]

[0098] like Figure 4 As shown, the finite set model predictive control algorithm is used to traverse the voltage vectors corresponding to all switching states of the inverter, calculate the predicted current and cost function under the action of the voltage vector, select the optimal voltage vector that minimizes the cost function, and generate a switching signal to drive the permanent magnet synchronous motor to achieve current harmonic suppression and system loss reduction.

[0099] The above description of the disclosed embodiments enables those skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for suppressing current harmonics in a permanent magnet synchronous motor based on model predictive control, characterized in that, Includes the following steps: S1. Establish a mathematical model of the permanent magnet synchronous motor in the rotating coordinate system, and discretize it using the Euler discretization method. Considering one-step delay compensation, we obtain a prediction model for the state of the permanent magnet synchronous motor at future moments. S2. Design and construct a cost function in the prediction model that includes a fundamental current tracking term and a higher-order current harmonic suppression term; and calculate the current harmonic term factor in the cost function in real time using the Lagrange multiplier method; wherein, the higher-order current harmonic suppression term targets non-even and non-third harmonics; the current harmonic term factor is determined based on the deviation between the harmonic components of the predicted current and the reference current. S3. Using a finite set model predictive control algorithm, the voltage vectors corresponding to all switching states of the inverter are traversed, the predicted current and cost function under the action of the voltage vector are calculated, the optimal voltage vector that minimizes the cost function is selected, and the switching signal is generated to drive the permanent magnet synchronous motor to achieve current harmonic suppression and system loss reduction.

2. The method for suppressing current harmonics in a permanent magnet synchronous motor based on model predictive control according to claim 1, characterized in that, In S1, the functional expression of the mathematical model is: Among them, i q Let u be the q-axis current. d For the d-axis voltage, u q R is the q-axis voltage. s L is the equivalent phase resistance. d L is the d-axis equivalent inductance. q ω is the q-axis equivalent inductance. e Let ψ be the electric angular velocity. f For permanent magnet flux linkage in motors.

3. The method for suppressing current harmonics in a permanent magnet synchronous motor based on model predictive control according to claim 1, characterized in that, In S1, the prediction model function expression is: in, i d (k) represents the d-axis current in the k-th period, i d (k+1) represents the d-axis current in the (k+1)th period, u d (k) represents the d-axis voltage of the k-th period, u d (k+1) is the d-axis voltage of the (k+1)th period, i q (k) represents the q-axis current in the k-th period, i q (k+1) represents the q-axis current in the (k+1)th period, u q (k) is the q-axis voltage of the k-th period, u q (k+1) is the q-axis voltage of the (k+1)th period, T s To control the cycle, L d L represents the d-axis inductance of the motor. q ω represents the q-axis inductance of the motor. e This indicates the electric angular velocity of the motor.

4. The method for suppressing current harmonics in a permanent magnet synchronous motor based on model predictive control according to claim 3, characterized in that, The calculation process of the function expression of the prediction model is as follows: Electromagnetic torque T e The equation is: Based on the Euler discretization method, the mathematical model can be discretized as follows: Due to the existence of digital delay, one-beat delay compensation should be considered during the modeling process. Equation (1) can be further written as:

5. The method for suppressing current harmonics in a permanent magnet synchronous motor based on model predictive control according to claim 1, characterized in that, In S2, the expression for the cost function is: in, To predict current harmonics, This represents the v-th current harmonic, where v represents the harmonic order, and ω represents the ω-th harmonic. v For current harmonic factors, Represents the reference current. This represents the predicted current.

6. The method for suppressing current harmonics in a permanent magnet synchronous motor based on model predictive control according to claim 5, characterized in that, In S2, the calculation process of the cost function is as follows: In model predictive control, the traditional cost function is: Among them, i d (k+2) represents the d-axis current in the (k+2)th period, i q (k+2) represents the q-axis current in the (k+2)th period. Represents the d-axis reference current. Represents the q-axis reference current; Predicting current under ideal conditions With reference current i s The same applies, but in practical applications, harmonics exist in the predicted current, therefore the predicted current... Represented as: in This represents the predicted current harmonics, where v represents the harmonic order. Represents the reference current, i s Represents the actual current; since the permanent magnet synchronous motor has three-phase symmetry and half-wave symmetry, there are no even-order and multiple-of-three harmonics in the stator winding, so equation (2) can be rewritten as: The new cost function considering current harmonics is: Where ω0 and ω v These are the coefficients of the fundamental current and the harmonic current, respectively. When ω0 is 1, the cost function is rewritten as:

7. The method for suppressing current harmonics in a permanent magnet synchronous motor based on model predictive control according to claim 1, characterized in that, In S3, the functional expression for the current harmonic term factor is: Where λ is the Lagrange factor.

8. The method for suppressing current harmonics in a permanent magnet synchronous motor based on model predictive control according to claim 7, characterized in that, In S3, the calculation process for the current harmonic term factor is as follows: Find the expression for the proposed Lagrange function in terms of... The partial derivatives with respect to λ are specifically expressed as: Depend on The conclusion is Therefore, equation (7) can be rewritten as: Solving the equations obtained from equations (7) and (8), it is obvious that... Setting equations (7) and (8) in the system of equations to 0, we can obtain the current harmonic term factor as follows: Due to the existence of the inverter dead time, the 5th and 7th harmonics in the stator phase current account for the majority of the total harmonics. Therefore, the current harmonic factor can be simplified as:

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