Model predictive current control method suitable for dual three-phase permanent magnet synchronous motor

Abstract

The application discloses a high-precision model prediction current control method suitable for a dual three-phase permanent magnet synchronous motor, considers the change of a rotor position in a control period, deduces a current discrete model of the dual three-phase permanent magnet synchronous motor, constructs a candidate virtual voltage vector set composed of 24 virtual voltage vectors with voltage components of 0 on a voltage vector xy plane and zero vectors, takes the error square of dual three-phase permanent magnet synchronous motor dq axis currents and xy axis currents at the end of each control period as an evaluation index, constructs a cost function, evaluates the error of the dq axis currents and the xy axis currents corresponding to different voltage vectors in the candidate virtual voltage vector set at the end of each control period by using the cost function, and selects and outputs the voltage vector making the cost function minimum. The application has smaller dq axis current tracking error and electromagnetic torque tracking error when the motor operates under a low carrier ratio condition, and improves the steady-state performance of the motor operation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of motor control, and particularly relates to a high-precision model predictive current control method suitable for a dual three-phase permanent magnet synchronous motor. BACKGROUND

[0002] The increasing requirements of power density and reliability of motor drive systems in application fields such as aerospace, ship driving and electric vehicles make the limitations of ordinary three-phase motors gradually prominent, and multi-phase motors have attracted a lot of attention and research. The dual three-phase permanent magnet synchronous motor is one of the most widely researched multi-phase motors, which has the advantages of strong fault tolerance, high power density and small torque ripple, and is suitable for high-power traction and transmission systems; in order to reduce system loss, the switching frequency of the drive system needs to be appropriately reduced, which will make the motor operate in a low carrier ratio working condition, reducing the dynamic and steady-state performance of the motor.

[0003] In the process of realizing the predictive control of the motor through the digital controller, the existing predictive current control technology mostly adopts the forward Euler approximation method to discretize the motor model, such as the document [Y. Luo and C. Liu, "Multi-Vector-Based Model Predictive Torque Control for a Six-Phase PMSM Motor With Fixed Switching Frequency" in IEEE Transactions on Energy Conversion, vol. 34, no. 3, pp. 1369-1379, Sep. 2019] and the document [S. Liu and C. Liu, "Virtual-Vector-Based Robust Predictive Current Control for Dual Three-Phase PMSM" in IEEE Transactions on Industrial Electronics, vol. 68, no. 3, pp. 2048-2058, Mar. 2021], and then the current is predicted according to the candidate voltage vector, the optimal voltage vector is obtained by traversing and screening according to the cost function, and is output through the inverter. However, the predictive current control technology using the forward Euler approximation method assumes that the rotor position does not change within a control period, and when the motor speed is low or the control frequency is high, the technology can accurately realize the prediction and tracking control of the current; however, as the motor speed increases or the control frequency decreases, the rotor position changes greatly within a control period, the error caused by model discretization increases, and in addition, the control delay also increases, thereby causing problems such as the decrease of the motor current prediction accuracy and the dynamic and steady-state performance.

[0004] In summary, the current tracking performance and electromagnetic torque tracking performance of the prior art in the low carrier ratio operating condition of the dual three-phase permanent magnet synchronous motor still need to be improved. SUMMARY

[0005] In view of the above, the application provides a high-precision model predictive current control method suitable for a dual three-phase permanent magnet synchronous motor, which can improve the current and electromagnetic torque tracking performance of the motor in the low carrier ratio operating condition.

[0006] A high-precision model predictive current control method suitable for a dual three-phase permanent magnet synchronous motor, comprising the following steps:

[0007] (1) Considering the change of the rotor position in a control period, combining the dq-axis current free component and the forced component to establish a dq-axis current discrete model of the dual three-phase permanent magnet synchronous motor;

[0008] (2) According to the solving method of the first-order linear differential equation, an xy-axis current discrete model of the dual three-phase permanent magnet synchronous motor is established;

[0009] (3) A candidate voltage vector set is obtained by screening from all output voltage vectors of the motor inverter;

[0010] (4) The calculation expressions of the d-axis stator current i d k+2 and the q-axis stator current i q k+2 in the k+2 control period are determined according to the dq-axis current discrete model, k is a natural number, the calculation expressions of the x-axis stator current i x k+2 and the y-axis stator current i y k+2 in the k+2 control period are determined according to the xy-axis current discrete model, and then a cost function is constructed;

[0011] (5) The voltage vectors in the candidate voltage vector set are substituted into the cost function for calculation, and the voltage vector with the minimum corresponding function value is taken as the optimal voltage vector in the k+1 control period, and a group of PWM (pulse width modulation) signals are generated using the optimal voltage vector to control the on-off of the power switching devices in the motor inverter.

[0012] Further, the expression of the dq-axis current discrete model is as follows:

[0013]

[0014] Wherein: i d k+1 and i qk+1 These are the d-axis stator current and q-axis stator current in the (k+1)th control cycle, respectively, i d k and i q k These are the d-axis stator current and q-axis stator current in the k-th control cycle, respectively, ω e Let ψ be the electric angular velocity of the motor. f For the permanent magnet flux linkage of the motor, L d and L q These are the d-axis stator inductance and q-axis stator inductance of the motor, respectively, T s To control the cycle, u d k and u q k These are the d-axis and q-axis components of the optimal voltage vector for the k-th control cycle, respectively.

[0015] Furthermore, the expression for the discrete model of the xy-axis current is as follows:

[0016]

[0017] Where: i x k+1 and i y k+1 These are the x-axis stator current and y-axis stator current of the motor in the (k+1)th control cycle, respectively, i x k and i y k These are the x-axis stator current and y-axis stator current of the motor in the k-th control cycle, respectively, R s L is the stator resistance. σ For stator leakage inductance, T s To control the cycle, u x k and u y k These are the x-axis and y-axis components of the optimal voltage vector for the k-th control cycle, respectively.

[0018] Further, in step (3), the output voltage vector of the motor inverter includes 60 effective vectors and 4 zero vectors. The 60 effective vectors are divided into 12 large vectors, 12 second-large vectors, 24 medium vectors, and 12 small vectors according to their amplitude. The large and second-large vectors with the same direction are selected on the αβ subplane to synthesize 12 virtual voltage vectors with 0 components on the xy subplane. The second-large and small vectors with the same direction are selected on the αβ subplane to synthesize another 12 virtual voltage vectors with 0 components on the xy subplane. Finally, these 24 virtual voltage vectors together with the zero vectors constitute a candidate voltage vector set.

[0019] Furthermore, in step (4), i d k+2 and i q k+2 The calculation expression is as follows:

[0020]

[0021] Where: i d k+1 and i q k+1 These are the d-axis stator current and q-axis stator current in the (k+1)th control cycle, respectively, ω e Let ψ be the electric angular velocity of the motor. f For the permanent magnet flux linkage of the motor, L d and L q These are the d-axis stator inductance and q-axis stator inductance of the motor, respectively, T s To control the cycle, u d k+1 and u q k+1 These are the d-axis and q-axis components of any voltage vector in the candidate voltage vector set, respectively.

[0022] Furthermore, in step (4), i x k+2 and i y k+2 The calculation expression is as follows:

[0023]

[0024] Where: i x k+1 and i y k+1 These are the x-axis stator current and y-axis stator current of the motor in the (k+1)th control cycle, respectively, R s L is the stator resistance. σ For stator leakage inductance, T s To control the cycle, u x k+1 and u y k+1 These are the x-axis and y-axis components of any voltage vector in the candidate voltage vector set, respectively.

[0025] Furthermore, the expression for the cost function is as follows:

[0026]

[0027] Where: g is the cost function, λ is the weighting coefficient, and i d * and i q* These are the reference values ​​for the d-axis stator current and the q-axis stator current, respectively. x * and i y * These are the reference values ​​for the x-axis stator current and the y-axis stator current, respectively.

[0028] Furthermore, the reference value i d * i x * and i y * All are set to 0, with reference value i. q * The error between the commanded motor speed and the actual speed is obtained after PI (proportional-integral) control.

[0029] A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the above-described high-precision model predictive current control method applicable to dual three-phase permanent magnet synchronous motors.

[0030] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described high-precision model predictive current control method applicable to dual three-phase permanent magnet synchronous motors.

[0031] Based on the above technical solution, the present invention has the following beneficial technical effects:

[0032] 1. This invention considers the change of the motor rotor position within a control cycle and derives a current prediction model for a dual three-phase permanent magnet synchronous motor. Compared with the traditional current prediction model based on the first-order forward Euler approximation method, the present invention has better dq-axis current tracking performance and electromagnetic torque tracking performance.

[0033] 2. This invention considers the suppression of xy-plane current in a dual three-phase permanent magnet synchronous motor, has good versatility, and is applicable to any finite set model predictive control method that uses a current discrete model in a dual three-phase permanent magnet synchronous motor. Attached Figure Description

[0034] Figure 1 This is a block diagram of a dual three-phase permanent magnet synchronous motor control system based on the high-precision model prediction current control method of this invention.

[0035] Figure 2 This is a schematic diagram showing the distribution of the output voltage vector of a two-level six-phase inverter on the αβ and xy subplanes. The left side corresponds to the αβ subplane, and the right side corresponds to the xy subplane.

[0036] Figure 3This is a schematic diagram of the principle of virtual vector synthesis. The left side corresponds to the αβ subplane, and the right side corresponds to the xy subplane.

[0037] Figure 4 To achieve the desired effect in control period T, the high-precision current discretization model of this invention is compared with the traditional current discretization model. s The schematic diagram of the motor simulation waveform at 320μs is shown. The left side corresponds to the traditional current discretization model, and the right side corresponds to the high-precision current discretization model of this invention. Detailed Implementation

[0038] To describe the present invention in more detail, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] The principle and process of the high-precision model prediction current control method for dual three-phase permanent magnet synchronous motors of the present invention are as follows:

[0040] (1) Solve the high-precision dq plane current discrete model of the dual three-phase motor.

[0041] Since the voltage drop across the resistance of a dual three-phase permanent magnet synchronous motor is typically very small, and the control cycle is generally much smaller than the electrical time constant, the voltage drop across the resistance is usually ignored. Under this assumption, the dq-axis current equation of the dual three-phase permanent magnet synchronous motor can be established in a two-phase synchronous rotating coordinate system oriented by the rotor flux linkage as follows:

[0042]

[0043] In the formula: and i j (j=d,q) represents the stator voltage and stator current of the motor along the j-axis, L d and L q For the d-axis stator inductance and the q-axis stator inductance, ω e Let ψ be the electric angular velocity of the motor. f It is a permanent magnet flux linkage.

[0044] In the kth control cycle, i.e., kT s ≤t≤(k+1)T s The discrete solution of the free component of the dq plane current under zero control is obtained as follows:

[0045]

[0046] In the formula: T s To control the cycle, For kT s j-axis current at time For (k+1)T s The j-axis current at that time.

[0047] With control quantity u d and uq The relevant dq plane current forced component solution is:

[0048]

[0049] In the formula: For kT s The j-axis voltage at that time.

[0050] By combining the solutions of the free and forced components of the current in the dq plane, the high-precision discrete model of the current in the dq plane of a dual three-phase permanent magnet synchronous motor can be obtained as follows:

[0051]

[0052] (2) Solve the high-precision xy-plane current discrete model of the dual three-phase permanent magnet synchronous motor.

[0053] According to the solution method of the first-order linear differential equation, the discrete solution of the xy-axis current can be obtained as follows:

[0054]

[0055] In the formula: R s L is the stator resistance. σ For stator leakage, and For kT s j-axis current and voltage at time For (k+1)T s The j-axis current at that time.

[0056] (3) Construct a candidate voltage vector set.

[0057] The voltage vector plane of a dual three-phase permanent magnet synchronous motor driven by a two-level six-phase voltage source inverter has 60 effective vectors and 4 zero vectors. The voltage vector distributions in the αβ and xy subplanes are as follows: Figure 2 As shown, each voltage vector adopts the same expression as (S). A S B S C ) and (S D S E S F The binary equivalent of ) is used to number two decimal numbers, where S X (X = A, B, C, D, E, F) represents the switching state of the IGBT in the X-arm bridge. When the upper IGBT in the X-arm is turned on and the lower IGBT is turned off, S... X =1; conversely, S X =0; for example, the six-phase bridge arm switching state (S) corresponding to the voltage vector with serial number 46. A S B S C SD S E S F The magnitudes of the four vectors in the vector plane from the outside to the inside are (100110). The magnitudes of the largest vector |V| are... L |=0.644U dc Second largest vector |V ML |=0.471U dc , medium vector |V M |=0.333U dc and small vector |V S |=0.173U dc U dc This is the DC bus voltage.

[0058] Traditional predictive current control models applied to dual three-phase permanent magnet synchronous motors only consider the voltage vector effect in the αβ subplane, neglecting the voltage vector effect in the xy subplane. This leads to relatively large 5th and 7th current harmonic components. To reduce current harmonics, this invention selects large and second-largest vectors with the same direction in the αβ subplane to synthesize 12 virtual voltage vectors, and selects second-largest and smallest vectors with the same direction to synthesize another 12 virtual voltage vectors. The large and second-largest vectors with the same direction in the αβ subplane correspond to vectors with opposite directions in the xy subplane, and the second-largest and smallest vectors in the αβ subplane also correspond to vectors with opposite directions in the xy subplane. By adjusting the vector's action time, the amplitude of the synthesized voltage vector in the xy subplane can be controlled to zero. Virtual vector VV1 is synthesized using the large vector 44 and the second-largest vector 65 adjacent to the α axis, and virtual vector VV is synthesized using the second-largest vector 65 and the smallest vector 56. 13 For example, the principle of virtual vector synthesis is as follows: Figure 3 As shown, the relationship between two vectors to form a virtual vector is:

[0059]

[0060] In the formula: T s To control the period, t1 and t2 are the large vector V L and the second largest vector V ML Duration of action, V αβ and V xy These are the components of the synthesized virtual vector in the αβ and xy subplanes. Let |V xy If |=0, we can solve for t1=0.732T. s and t2 = 0.268T s The magnitude of the synthesized virtual vector in the αβ subplane is 0.598U. dc Similarly, the duration of action when the second largest and smallest vectors are combined to form a virtual vector is 0.578T. s and 0.422T sThe magnitude of the synthesized virtual vector in the αβ subplane is 0.345U. dc .

[0061] (4) Construct the cost function.

[0062] Considering the delay compensation for predictive current control, the tracking errors of the dq-axis and xy-axis currents are taken into account in the cost function, which is expressed as:

[0063]

[0064] In the formula: This is the reference value for the j-axis current. For (k+2)T s The j-axis current is denoted by λ, where λ is the weighting coefficient. Since the candidate voltage vector set consists of virtual voltage vectors with zero components in the xy plane, the theoretical value of the xy-axis current error term is zero. The current discrete model of this invention is applicable to any finite set model predictive control method that uses a current discrete model in a dual three-phase permanent magnet synchronous motor. Therefore, this embodiment adopts a general cost function form.

[0065] The dual three-phase permanent magnet synchronous motor control system employing the high-precision model predictive current control method of this invention is as follows: Figure 1 As shown, this method reduces the dq axis current tracking error and electromagnetic torque tracking error of a dual three-phase permanent magnet synchronous motor under low carrier ratio operating conditions.

[0066] The feasibility and effectiveness of the method of the present invention are verified below using specific simulation data and comparison results.

[0067] To verify the feasibility and effectiveness of the method of this invention, a comparative analysis was conducted between the control strategy based on the high-precision current discrete model and the control strategy based on the traditional current discrete model. The motor parameters are shown in Table 1. The sampling period and carrier period of the control system are the same, set to 200μs, 320μs, and 400μs, respectively. The control strategies based on the high-precision current discrete model of this invention and the traditional current discrete model use the same controller parameters. The speed loop uses an anti-integral saturation PI controller with proportional, integral, and anti-integral saturation parameters of 0.1885, 1.1844, and 5.3052, respectively.

[0068] Table 1

[0069]

[0070] Figure 4 The waveforms of two discrete models under the condition of a step load torque are shown, from top to bottom: electromagnetic torque T e With load torque T L q-axis current actual value i qact Compared with reference value i q * Actual value of d-axis current i d act Compared with reference value i d * The motor operates under no-load conditions initially. After 1 second, the load torque jumps from 0 to 8 Nm, and after another 1 second, the load torque jumps to 16 Nm.

[0071] Depend on Figure 4 It is evident that the traditional method exhibits significant tracking errors in both the dq-axis current and electromagnetic torque. This is because the prediction error of the current at the next moment increases with the control cycle. The method of this invention significantly reduces the tracking errors of the dq-axis current and electromagnetic torque. The quantitative analysis results of the electromagnetic torque and current at a load torque of 16 Nm are shown in Table 2. In Table 2, the tracking errors of the dq-axis current and electromagnetic torque are expressed as the mean square root of the difference between the actual and reference values, σ. id σ iq and σ T Phase current quality is measured using the total harmonic distortion (THD).

[0072] Table 2

[0073]

[0074] As can be seen from Table 2, when T s At 320 μs, under low carrier ratio operating conditions, compared with the method based on the traditional current discrete model, the σ of the method of this invention is higher. id σ iq and σ T The reductions were 51.96%, 30.69%, and 13.68%, respectively, and the reduction effect became more pronounced as the control period increased. At the same time, the total harmonic distortion rate of the phase current was reduced by the method of the present invention.

[0075] The above description of the embodiments is provided to enable those skilled in the art to understand and apply the present invention. Those skilled in the art can readily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made to the present invention by those skilled in the art based on the disclosure thereof should be within the scope of protection of the present invention.

Claims

1. A model predictive current control method for dual three-phase permanent magnet synchronous motor, comprising the following steps: (1) Considering the change of rotor position in a control period, combining the free component and forced component of dq plane current to establish the dq axis current discrete model of dual three-phase permanent magnet synchronous motor, the specific expression is as follows: wherein: i d k+1 and i q k+1 are the d-axis stator current and the q-axis stator current of the k+1th control period, respectively, i d k and i q k are the d-axis stator current and the q-axis stator current of the kth control period, respectively, ω e is the electrical angular velocity of the electric machine, ψ f is the permanent magnet flux linkage of the electric machine, L d and L q are the d-axis stator inductance and the q-axis stator inductance of the electric machine, respectively, T s is the control period, u d k and u q k are the d-axis component and the q-axis component of the optimal voltage vector of the kth control period, respectively; (2) According to the solving method of first-order linear differential equation, the xy axis current discrete model of dual three-phase permanent magnet synchronous motor is established, the specific expression is as follows: wherein: i x k+1 and i y k+1 are the x-axis stator current and the y-axis stator current of the motor in the k+1th control period, respectively, i x k and i y k are the x-axis stator current and the y-axis stator current of the motor in the kth control period, respectively, R s is the stator resistance, L σ is the stator leakage inductance, u x k and u y k are the x-axis component and the y-axis component of the optimal voltage vector in the kth control period, respectively; (3) Synthesizing the candidate voltage vector set from all output voltage vectors of motor inverter through screening; (4) determining a calculation expression of a d-axis stator current i d k+2 and a q-axis stator current i q k+2 according to the dq-axis current discrete model, k being a natural number, determining a calculation expression of a x-axis stator current i x k+2 and a y-axis stator current i y k+2 according to the xy-axis current discrete model, and further constructing a cost function; (5) The voltage vector in the candidate voltage vector set is substituted into the cost function for calculation, and the voltage vector with the minimum function value is taken as the optimal voltage vector of the k+1 control period, and a group of PWM signals is generated by using the optimal voltage vector to control the on-off of power switch devices in motor inverter.

2. The model predictive current control method of claim 1, wherein: The output voltage vectors of motor inverter in step (3) include 60 effective vectors and 4 zero vectors, and the 60 effective vectors are divided into 12 large vectors, 12 sub-large vectors, 24 medium vectors and 12 small vectors according to the amplitude; the large vectors and sub-large vectors with the same direction are selected in the αβ sub-plane to synthesize 12 virtual voltage vectors with 0 component in the xy sub-plane, and the sub-large vectors and small vectors with the same direction are selected in the αβ sub-plane to synthesize another 12 virtual voltage vectors with 0 component in the xy sub-plane, and finally the 24 virtual voltage vectors are combined with the zero vectors to form the candidate voltage vector set.

3. The model predictive current control method of claim 1, wherein: In step (4) i d k+2 and i q k+2 The calculation expression is as follows: where: u d k+1 and u q k+1 are the d- and q-axis components, respectively, of any voltage vector of the set of candidate voltage vectors.

4. The model predictive current control method of claim 1, wherein: The calculation expression of i in the step (4) is as follows: x k+2 and i y k+2 The calculation expression of i in the step (4) is as follows: where: u x k+1 and u y k+1 are the x- and y-axis components, respectively, of any voltage vector of the set of candidate voltage vectors.

5. The model predictive current control method of claim 1, wherein: The expression of the cost function is as follows: wherein: g is a cost function, λ is a weight coefficient, i d * and i q * are reference values for the d-axis stator current and the q-axis stator current, respectively, i x * and i y * are reference values for the x-axis stator current and the y-axis stator current, respectively.

6. The model predictive current control method of claim 5, wherein: The reference value i d * , i x * and i y * are all set to 0, and the reference value i q * is an error between the motor speed command value and the actual value after PI control.

7. A computer device comprising a memory and a processor, said memory having stored therein a computer program, characterized in that: The processor is used to execute the computer program to realize the model predictive current control method according to any one of claims 1-6.

8. A computer readable storage medium storing a computer program, characterized in that: The computer program is executed by the processor to realize the model predictive current control method according to any one of claims 1-6.

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