WO2022257258A1 - 适用于永磁同步电机高速区运行的预测电流增量控制方法 - Google Patents

适用于永磁同步电机高速区运行的预测电流增量控制方法 Download PDF

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WO2022257258A1
WO2022257258A1 PCT/CN2021/110342 CN2021110342W WO2022257258A1 WO 2022257258 A1 WO2022257258 A1 WO 2022257258A1 CN 2021110342 W CN2021110342 W CN 2021110342W WO 2022257258 A1 WO2022257258 A1 WO 2022257258A1
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current
increment
stator
permanent magnet
time
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PCT/CN2021/110342
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English (en)
French (fr)
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史婷娜
李晨
阎彦
夏长亮
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浙江大学先进电气装备创新中心
浙江大学
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Priority to US17/794,986 priority Critical patent/US11811339B2/en
Publication of WO2022257258A1 publication Critical patent/WO2022257258A1/zh

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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0085—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for high speeds, e.g. above nominal speed
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0017—Model reference adaptation, e.g. MRAS or MRAC, useful for control or parameter estimation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/18—Estimation of position or speed
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/22—Current control, e.g. using a current control loop
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
    • H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation
    • H02P27/12—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation pulsing by guiding the flux vector, current vector or voltage vector on a circle or a closed curve, e.g. for direct torque control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/34—Modelling or simulation for control purposes
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

Definitions

  • the invention relates to a control prediction method of a permanent magnet synchronous motor, in particular to a prediction current increment control method for improving the current control performance under the high-speed operation condition of the motor.
  • Electric vehicles have higher requirements on the drive motors used due to the limitations of their space and use environment. Due to the advantages of high power density, high efficiency, and wide speed regulation range, permanent magnet synchronous motors have become the main target of research and application of electric vehicle companies, such as Nissan's Leaf and Toyota's RAVE EV. Since the permanent magnet synchronous motor is a typical nonlinear system, compared with the linear current control method (such as PI control), the nonlinear control method can obtain better control performance in the drive of the built-in permanent magnet synchronous motor, such as fuzzy control, Sliding mode control, predictive control, etc. Among them, predictive control has become a control method with great development prospects due to its advantages of flexible control mode, multivariable control, and fast dynamic response.
  • Predictive control is a model-based control method. Most of the existing predictive control methods use a simple first-order forward Euler discrete method to establish a predictive model. This model ignores the change of the rotor position within a control cycle and is only suitable for low-speed applications. occasions. However, motors in applications such as electric vehicles require good high-speed performance. When the motor is running in the high-speed area, the rotor position changes greatly within a control cycle, which leads to a large deviation between the discrete values of the d and q-axis stator voltages used for control and the actual value, thereby deteriorating the control performance of predictive control.
  • the motor parameters will change due to the influence of factors such as motor current and equipment temperature, which will cause errors in the prediction results.
  • the dead zone effect will cause an error between the actual output voltage of the inverter and the reference voltage, which will lead to the deterioration of the current control performance. Therefore, the prior art lacks a predictive control method that can improve the predictive accuracy and reduce the sensitivity of the system parameters in the high-speed operating region of the motor.
  • the technical problem to be solved by the present invention is to provide a predictive current incremental control method suitable for the operation of the permanent magnet synchronous motor in the high-speed region.
  • the reference current increment is converted from a preset reference torque (control target).
  • u d (t) and u q (t) represent the d-axis voltage and q-axis voltage of the permanent magnet synchronous motor respectively;
  • T s represents the control cycle;
  • u d, k represent the d-axis of the stator voltage vector at kT s Components,
  • u q, k respectively represent the q-axis component of the stator voltage vector at kT s time, where the subscript d represents the d-axis, the subscript q represents the q-axis, and the subscript k represents the ordinal number of the control cycle;
  • ⁇ r represents the motor rotor Rotational electrical angular velocity, k represents the ordinal number of the control cycle, and t represents the current moment.
  • the discrete current prediction model is specifically:
  • i s (k+1) A 0 (k)i s (k)+B 0 (k)u s (k)+D 0 (k)
  • i s (k+1) represents the predicted current vector at (k+1)T s time
  • i s (k) represents the stator current vector at kT s time
  • u s (k) represents the stator voltage at kT s time Vector
  • a 0 (k) represents the coefficient matrix of the i s (k) term
  • B 0 (k) represents the coefficient matrix of the u s (k) term
  • D 0 (k) represents the coefficient matrix of the back EMF term
  • ⁇ r,k Indicates the electrical angular velocity of the motor rotor at time kT s
  • r indicates the sign of variables related to the rotor
  • k indicates the ordinal number of the control cycle
  • r s0 , L d0 , L q0 and ⁇ f0 respectively indicate the stator resistance, d-axis stator inductance, q Nominal values for shaft stator inductance and permanent magnet flux linkage.
  • ⁇ i s (k+1) A 0 (k) ⁇ i s (k)+B 0 (k) ⁇ u s (k)
  • ⁇ i s (k+1) represents the predicted current increment calculated by the current increment prediction model
  • ⁇ i s (k) represents the stator current increment from (k-1) T s time to kT s time
  • ⁇ u s (k) represents the stator voltage increment from (k-1)T s time to kT s time
  • i s (k-1) represents the stator current vector at (k-1)T s time
  • u s (k-1 ) represents the stator voltage vector at (k-1) T s time
  • a 0 (k) represents the coefficient matrix of the item i s (k)
  • B 0 (k) represents the coefficient matrix of the item u s (k).
  • the cost function is established as:
  • ⁇ i s ref represents the reference current increment
  • P represents the weight factor, which determines the importance of the voltage increment
  • U max and I max represent the maximum current and voltage allowed by the motor drive system of the permanent magnet synchronous motor
  • T represents the matrix Transpose
  • Satisfy represents the constraint condition
  • ⁇ i s (k+2) represents the predicted current increment calculated by the current increment prediction model
  • ⁇ u s (k+1) represents the time from kT s to (k+1)T s
  • J represents the value of the cost function.
  • the optimal voltage increment is superimposed on the stator voltage of the current control cycle to obtain the optimal stator voltage of the next control cycle, specifically:
  • u s (k) represents the stator voltage at kT s time
  • u s opt (k+1) represents the optimal stator voltage at (k+1)T s time
  • ⁇ u s opt (k+1) represents (k +1) Optimal stator voltage increment at time T s .
  • the method of the present invention establishes a current increment prediction model by considering the change of the motor rotor position within a control cycle. Compared with the traditional current prediction model based on the first-order forward Euler approximation method, the current prediction result of the present invention is more accurate, and the current fluctuation of the prediction control method in the high-speed operation area of the motor is reduced.
  • the present invention uses the stator current increment as the state quantity and the stator voltage increment as the control quantity, so that the current tracking performance of the predictive current control method based on the current increment prediction model is affected by the motor parameter change and the inverter dead zone effect The effect is very small, and the influence of inductance change on the current fluctuation is also small during the actual operation of the motor.
  • Fig. 1 is a flow chart of the present invention's predictive current increment control method applicable to the high-speed zone operation of a permanent magnet synchronous motor;
  • Fig. 2 is a current simulation waveform diagram of the predictive current control method and the predictive current incremental control method based on the traditional current prediction model when the dead time is 3 ⁇ s;
  • Fig. 3 is the current prediction error waveform diagram of the current increment prediction model under different motor operating conditions when the inductance is mismatched;
  • Fig. 4 is the experimental waveform diagram of d, q-axis current and a-phase current of the predictive current control method and the predictive current incremental control method based on the traditional current prediction model under different motor operating conditions.
  • r s0 , L d0 , L q0 and ⁇ f0 represent the nominal values of stator resistance, d-axis stator inductance, q-axis stator inductance and permanent magnet flux linkage, respectively;
  • ⁇ r represents the electrical angular velocity of the motor rotor rotation;
  • a s represents the stator The coefficient matrix of the current term;
  • B s represents the coefficient matrix of the stator voltage term;
  • D s represents the coefficient matrix related to the back EMF;
  • i s (t) [i d (t), i q (t)] T , where i d (t) represents the component of the stator current on the d-axis, i q (t) represents the component of the stator current on the q-axis;
  • u s (t) [u d (t),u q (t)] T , Where u d (t) represents the component of the stator voltage on the d axi
  • T s represents the control period
  • I represents the identity matrix
  • the first-order forward Euler discretization method ignores the change of the rotor position within one control period, and linearizes the exponential function equivalently as e (t-kTs)As ⁇ (t-kT s )A s +I. Substituting the above approximate conditions into formula (2) and discretizing, the traditional current prediction model based on the first-order forward Euler discretization method can be obtained as:
  • i s (k+1) A c0 (k)i s (k)+B c0 (k)u s (k)+D c0 (k) (3)
  • u d,k , u q,k are d and q axis voltages at kT s time, respectively, kT s ⁇ t ⁇ (k+1)T s .
  • i s (k+1) A 0 (k)i s (k)+B 0 (k)u s (k)+D 0 (k) (5)
  • a 0 (k) represents the coefficient matrix of the stator current term at kT s time
  • B 0 (k) represents the coefficient matrix of the stator voltage term at kT s time
  • D 0 (k) represents the coefficient matrix of the stator voltage term at kT s time Matrix of coefficients related to back EMF.
  • formula (5) considers the influence of rotor position change on the actual trajectory of stator current and voltage in each control cycle, so it can more accurately reflect the change of stator current in each cycle. But dead zone effects and motor parameter mismatch still cause prediction errors.
  • the inverter output voltage error caused by the dead zone effect is related to the three-phase switch state of the inverter and the three-phase current direction.
  • the three-phase switching mode of the inverter is fixed, and the direction of the three-phase current does not change frequently, so the dead-zone voltage in two adjacent control cycles can be regarded as constant. Therefore, making the difference between the stator voltages at two adjacent moments can eliminate the voltage error caused by the dead zone to a certain extent.
  • the motor driver since the control period is very small, it can be considered that the motor rotor angular velocity ⁇ r is constant in two adjacent control periods. That is, A 0 (k), B 0 (k) and D 0 (k) in formula (5) are unchanged in two adjacent control periods. According to formula (5), the predicted current at two adjacent moments is subtracted, and the current increment prediction model suitable for high-speed working conditions can be obtained as follows:
  • ⁇ i s (k+1) A 0 (k) ⁇ i s (k)+B 0 (k) ⁇ u s (k) (6)
  • the control quantity in the current increment prediction model in formula (6) is the voltage increment ⁇ u s (k) at two adjacent moments, which enables the current increment prediction model to reduce the output voltage error caused by the dead zone of the inverter. Comparing formula (5) and formula (6), it can be seen that the coefficients of the two formulas are the same and have the same expression form. And formula (6) eliminates the permanent magnet flux linkage. Therefore, the current increment prediction model is only affected by the stator inductance of the motor, but not by the flux linkage of the permanent magnet.
  • the square of the error between the preset reference current increment and the predicted current increment at the end of each control cycle is used as an evaluation index to construct a cost function, and the cost function is used to calculate the stator current increment corresponding to the stator voltage increment at the end of each control cycle. error is evaluated. Considering the delay compensation problem of predictive current control, the constructed cost function is
  • ⁇ i s ref represents the reference current increment
  • P represents the weight factor, which is used to determine the importance of the voltage increment
  • U max and I max represent the maximum current and voltage allowed by the motor drive system respectively
  • T represents the matrix transposition
  • Satisfy represents the constraints
  • ⁇ i s (k+2) represents the predicted current increment calculated by the current increment prediction model
  • ⁇ u s (k+1) represents the stator voltage from kT s time to (k+1)T s time Increment
  • J represents the value of the cost function. Adding the voltage increment into the cost function for evaluation can reduce the dynamic overshoot of the motor and prevent the motor and power switch tube from suffering voltage and current surges.
  • the optimal stator voltage for the next control cycle is obtained from the optimal voltage increment and the stator voltage of the current control cycle:
  • ⁇ us opt represents the optimal stator voltage increment.
  • the control block diagram of the specific implementation process of the present invention is shown in Figure 1.
  • the method improves the current prediction accuracy under the high-speed operation condition of the motor, and eliminates the use of the permanent magnet flux linkage in the realization process of the prediction current increment control method.
  • the present invention verifies the influence of the dead zone of the inverter on the current control performance of the predictive current control method based on the traditional current prediction model and the predictive current increment control method in the present invention through simulation.
  • the traditional current prediction model is the current prediction model in formula (3)
  • the control period T s is 200 ⁇ s
  • the dead time t d is set to 3 ⁇ s.
  • Figure 2 shows the preset d-axis current reference value id ref and d -axis current under different motor speed n and load torque T L for the predictive current control method and the predictive current incremental control method based on the traditional current prediction model Simulation waveforms of measured value id , q-axis current reference value i q ref , and q-axis current measured value i q .
  • the d-axis current of the predictive current control method based on the traditional current prediction model has obvious tracking error when n is 300r/min and T L is 64Nm, and the tracking performance is better under other working conditions; while The q-axis current has obvious tracking error under various working conditions.
  • Both the d and q axis currents of the predictive current control method based on the current increment prediction model can track their reference values more accurately.
  • Fig. 2 shows that the current increment prediction model proposed by the present invention can suppress the influence of the dead zone effect on the current tracking performance.
  • ⁇ i sp (k+1) represents the predicted current increment calculated considering the inductance error
  • e(k+1) represents the current prediction error vector caused by inductance mismatch
  • e(k+ 1) [e d,k+1 ,e q,k+1 ] T
  • e d,k+1 is the d-axis component of the current prediction error
  • e q,k+1 is the q-axis of the current prediction error Component
  • ⁇ i s (k+1) is shown in formula (5).
  • ⁇ L d represents the error between the actual value of the d-axis stator inductance and the nominal value of the d-axis stator inductance
  • ⁇ L q represents the error between the actual value of the q-axis stator inductance and the nominal value of the q-axis stator inductance
  • ⁇ A(k) represents the coefficient matrix of the stator current incremental term
  • ⁇ B(k) represents the coefficient matrix of the stator voltage incremental term.
  • the amplitude of the stator current is small, and the variation range of e d,k+1 and e q,k+1 is more obvious relative to the current amplitude, so the change of inductance has a greater influence on the current fluctuation; and Under heavy load conditions, the amplitude of the stator current becomes larger, and the variation ranges of e d,k+1 and e q,k+1 are small relative to the current amplitude. At this time, the same inductance change has a great influence on the current fluctuation. Small.
  • the inductance mismatch will affect the current fluctuation of the predictive current control method based on the current increment prediction model, but the influence is small, and the influence of inductance mismatch on the current tracking error of the predictive current control method based on the current increment prediction model The impact is also minimal.
  • the present invention is tested in a 20kW PMSM drive system to compare the steady-state performance of the predictive current control method based on the traditional current prediction model and the predictive current control method based on the current increment prediction model.
  • the motor parameters are shown in Table 1.
  • the motor speed n is 300r/min and 7500r/min respectively, and the output power of the motor is 20kW under the two speeds.
  • Figure 4 shows the d-axis current reference value id ref , the d -axis current measured value id , q of the predictive current control method based on the traditional current prediction model and the predictive current control method based on the current incremental prediction model under different working conditions
  • the steady-state experimental waveforms of axis current reference value i q ref , q-axis current measured value i q and a-phase current i a The steady-state experimental waveforms of axis current reference value i q ref , q-axis current measured value i q and a-phase current i a .
  • the model of each device is not limited unless otherwise specified, as long as the device can complete the above functions.

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Abstract

提供一种适用于永磁同步电机高速区运行的预测电流增量控制方法。将定子电压在一个控制周期内的关系表达式代入连续时域电流模型并进行求解，得到离散电流预测模型和下一时刻的预测电流；将相邻两时刻的预测电流相减得到适用于永磁同步电机高速运行区的预测电流增量；根据预设的参考电流增量与预测电流增量构建成本函数，求解得到最优电压增量，并叠加得到下个控制周期的最优定子电压而施加控制。由此电流预测结果更加准确，降低了预测电流控制在电机高速运行区的电流波动，电流跟踪性能受电机参数变化和逆变器死区效应的影响很小，并且在电机实际运行过程中电感变化对电流波动的影响同样较小。

Description

适用于永磁同步电机高速区运行的预测电流增量控制方法 技术领域
本发明涉及一种永磁同步电机控制预测方法，特别是涉及一种在电机高速运行工况下，提高电流控制控制性能的预测电流增量控制方法。
背景技术
电动汽车由于其空间和使用环境的限制，对使用的驱动电机具有更高要求。永磁同步电机因高功率密度、高效率、宽调速范围等优势成为电动汽车企业研究与应用的主要目标，如Nissan公司的Leaf以及Toyota公司的RAVE EV等。由于永磁同步电机是典型的非线性系统，相比于线性电流控制方法(如PI控制)，非线性控制方法在内置式永磁同步电机驱动中可以获得更好的控制性能，如模糊控制、滑模控制、预测控制等。其中，预测控制以控制方式灵活、多变量控制、动态响应快等优点成为一种极具发展前景的控制方法。
预测控制是一种基于模型的控制方法，已有预测控制方法多数采用简单的一阶前向欧拉离散法建立预测模型，该模型忽略一个控制周期内转子位置的变化，只适用于转速不高的场合。但是电动汽车等应用场合中的电机要求具有良好的高速性能。当电机在高速区运行时一个控制周期内转子位置变化较大，这导致用于控制的d、q轴定子电压离散值与实际值偏差较大，从而恶化预测控制的控制性能。在永磁同步电机驱动系统的实际应用中，电机参数会因为电机电流、设备温度等因素的影响而变化，这会使预测结果产生误差。另外，死区效应会使逆变器实际输出电压与参考电压之间存在误差，从而导致电流控制性能的恶化。因此现有技术缺少了一种在电机高速运行区可以提高预测精度并降低系统参数敏感性的预测控制方法。
发明内容
本发明所要解决的技术问题是，提供一种适用于永磁同步电机高速区运行的预测电流增量控制方法。
本发明所采用的技术方案是：
1)根据一个控制周期内电机转子的位置变化，建立定子电压在一个控制周期内的关系表达式；
2)对永磁同步电机的连续时域模型求解处理得到永磁同步电机的连续时域电流模型；
3)忽略永磁同步电机的定子电阻压降，将定子电压在一个控制周期内的关 系表达式代入连续时域电流模型并进行求解，得到适用于永磁同步电机高速运行区的离散电流预测模型，利用离散电流预测模型处理获得下一时刻的预测电流；
4)将相邻两时刻的预测电流相减得到适用于永磁同步电机高速运行区的电流增量预测模型以及由电流增量预测模型计算得到的预测电流增量；
5)将预设的参考电流增量与预测电流增量在每个控制周期末的误差平方作为评价参数，构建成本函数，利用成本函数对定子电压增量对应的定子电流增量在每个控制周期末的误差进行评估；对成本函数采用凸优化求解方法进行求解，得到使成本函数最小的定子电压增量作为最优电压增量；
6)将最优电压增量叠加到当前控制周期的定子电压上得到下一个控制周期的最优定子电压，进而施加到永磁同步电机上进行控制。
所述的参考电流增量是由预设的参考转矩(控制目标)转换获得。
所述步骤1)中，所述定子电压在一个控制周期内的关系表达式是：
Figure PCTCN2021110342-appb-000001
式中，u d(t)、u q(t)分别表示永磁同步电机的d轴电压、q轴电压；T s表示控制周期；u d,k表示kT s时刻的定子电压矢量的d轴分量，u q,k分别表示kT s时刻的定子电压矢量的q轴分量，其中下标d表示d轴，下标q表示q轴，下标k表示控制周期的序数；ω r表示电机转子的旋转电角速度，k表示控制周期的序数，t表示当前时刻。
所述步骤3)中，所述的离散电流预测模型具体为：
i s(k+1)＝A 0(k)i s(k)+B 0(k)u s(k)+D 0(k)
Figure PCTCN2021110342-appb-000002
Figure PCTCN2021110342-appb-000003
Figure PCTCN2021110342-appb-000004
式中，i s(k+1)表示(k+1)T s时刻的预测电流矢量，i s(k)表示kT s时刻的定子电 流矢量；u s(k)表示kT s时刻的定子电压矢量；A 0(k)表示i s(k)项的系数矩阵；B 0(k)表示u s(k)项的系数矩阵；D 0(k)表示反电势项系数矩阵；ω r,k表示kT s时刻的电机转子旋转电角速度，r表示与转子相关的变量的标志，k表示控制周期的序数；r s0、L d0、L q0和ψ f0分别表示定子电阻、d轴定子电感、q轴定子电感和永磁体磁链的标称值。
所述步骤4)中，电流增量预测模型为：
Δi s(k+1)＝A 0(k)Δi s(k)+B 0(k)Δu s(k)
Δi s(k)＝i s(k)-i s(k-1)
Δu s(k)＝u s(k)-u s(k-1)
式中，Δi s(k+1)表示由电流增量预测模型计算得到的预测电流增量，Δi s(k)表示(k-1)T s时刻到kT s时刻的定子电流增量，Δu s(k)表示(k-1)T s时刻到kT s时刻的定子电压增量；i s(k-1)表示(k-1)T s时刻的定子电流矢量；u s(k-1)表示(k-1)T s时刻的定子电压矢量；A 0(k)表示i s(k)项的系数矩阵；B 0(k)表示u s(k)项的系数矩阵。
所述步骤5)中，成本函数建立为：
Figure PCTCN2021110342-appb-000005
Figure PCTCN2021110342-appb-000006
式中，Δi s ref表示参考电流增量，P表示权重因子，决定电压增量的重要性；U max与I max分别表示永磁同步电机的电机驱动系统允许的最大电流与电压，T表示矩阵转置；Satisfy表示约束条件；Δi s(k+2)表示由电流增量预测模型计算得到的预测电流增量，Δu s(k+1)表示kT s时刻到(k+1)T s时刻的定子电压增量；J表示成本函数的值。
所述步骤6)中，将最优电压增量叠加到当前控制周期的定子电压上得到下一个控制周期的最优定子电压，具体为：
u s opt(k+1)＝u s(k)+Δu s opt(k+1)
式中，u s(k)表示kT s时刻的定子电压，u s opt(k+1)表示(k+1)T s时刻的最优定子电压，Δu s opt(k+1)表示(k+1)T s时刻的最优定子电压增量。
本发明方法，具有如下有益效果：
1、本发明的方法通过考虑电机转子位置在一个控制周期内的变化建立电流增量预测模型。相比于基于一阶前向欧拉近似法的传统电流预测模型，本发明的电流预测结果更加准确，降低了预测控制方法在电机高速运行区的电流波动。
2、本发明将定子电流增量作为状态量，将定子电压增量作为控制量，使得 基于电流增量预测模型的预测电流控制方法的电流跟踪性能受电机参数变化和逆变器死区效应的影响很小，并且在电机实际运行过程中电感变化对电流波动的影响同样较小。
附图说明
图1是本发明一种适用于永磁同步电机高速区运行的预测电流增量控制方法的流程图；
图2是死区时间为3μs时的基于传统电流预测模型的预测电流控制方法与预测电流增量控制方法的电流仿真波形图；
图3是电感失配时不同电机运行工况下电流增量预测模型的电流预测误差波形图；
图4是不同电机运行工况下基于传统电流预测模型的预测电流控制方法与预测电流增量控制方法的d、q轴电流与a相电流实验波形图。
具体实施方式
下面结合实施例和附图对本发明的一种适用于永磁同步电机高速区运行的预测电流增量控制方法做出详细说明。
下面结合具体原理和情况对本发明的方法进行进一步地介绍：
一、建立永磁同步电机模型：
在以转子磁链定向的两相同步旋转坐标系中建立永磁同步电机的连续时域电压方程为：
Figure PCTCN2021110342-appb-000007
在式(1)中，
Figure PCTCN2021110342-appb-000008
其中，r s0、L d0、L q0和ψ f0分别表示定子电阻、d轴定子电感、q轴定子电感和永磁体磁链的标称值，ω r表示电机转子旋转电角速度；A s表示定子电流项的系数矩阵；B s表示定子电压项的系数矩阵；D s表示与反电势相关的系数矩阵；i s(t)＝[i d(t),i q(t)] T，其中i d(t)表示定子电流在d轴上的分量，i q(t)表示定子电流在q轴上的分量；u s(t)＝[u d(t),u q(t)] T，其中u d(t)表示定子电压在d轴上的分量，u q(t)表示定子电压在q轴上的分量；t表示时间。
对式(1)中的微分方程进行求解，得到永磁同步电机的连续时域电流模型为：
Figure PCTCN2021110342-appb-000009
在式(2)中，T s表示控制周期；I表示单位矩阵。
二、建立适用于永磁同步电机系统高速运行区的离散电流预测模型：
现有预测电流控制方法多数采用一阶前向欧拉离散法建立预测模型。一阶前向欧拉离散法忽略转子位置在一个控制周期内的变化，并将指数函数线性化等效为e (t-kTs)As≈(t-kT s)A s+I。将上述近似条件代入式(2)并进行离散化，可得基于一阶前向欧拉离散法的传统电流预测模型为：
i s(k+1)＝A c0(k)i s(k)+B c0(k)u s(k)+D c0(k)      (3)
Figure PCTCN2021110342-appb-000010
在式(3)中，i s(k+1)表示(k+1)T s时刻的预测电流矢量，并且，i s(k+1)＝[i d,k+1,i q,k+1] T，其中，i d,k+1为(k+1)T s时刻的预测电流矢量d轴分量，i q,k+1为(k+1)T s时刻的预测电流矢量q轴分量，其中，下标d表示d轴，下标q表示q轴，下标k+1表示第k+1个控制周期；i s(k)表示kT s时刻的定子电流矢量，并且，i s(k)＝[i d,k,i q,k] T，其中，i d,k为kT s时刻的定子电流矢量的d轴分量，i q,k为kT s时刻的定子电流矢量的q轴分量，其中，下标k表示第k个控制周期；；u s(k)表示kT s时刻的定子电压矢量，并且，u s(k)＝[u d,k,u q,k] T，其中，u d,k为kT s时刻的定子电压矢量的d轴分量，u q,k为kT s时刻的定子电压矢量的q轴分量；A c0(k)表示kT s时刻的定子电流项的系数矩阵；B c0(k)表示kT s时刻的定子电压项的系数矩阵；D c0(k)表示kT s时刻与反电势相关的系数矩阵；ω r,k表示kT s时刻的电机转子旋转电角速度，r表示与转子相关的变量的标志，k表示控制周期的序数。
但是当电机高速运行时，上述的等效e (t-kTs)As≈(t-kT s)A s+I将不再成立，并且转子位置在一个控制周期内的变化不可忽略。本发明考虑转子位置在每个周期内的变化，将式(2)中一个控制周期内的定子电压u s(t)＝[u d(t),u q(t)] T表达为：
Figure PCTCN2021110342-appb-000011
在式(4)中，u d,k、u q,k分别为kT s时刻的d、q轴电压，kT s≤t≤(k+1)T s。
忽略电机定子电阻压降，并将式(4)代入式(2)，求解得到适用于永磁同步电机高速运行区的离散电流预测模型为：
i s(k+1)＝A 0(k)i s(k)+B 0(k)u s(k)+D 0(k)      (5)
Figure PCTCN2021110342-appb-000012
Figure PCTCN2021110342-appb-000013
在式(5)中，A 0(k)表示kT s时刻的定子电流项的系数矩阵；B 0(k)表示kT s时刻的定子电压项的系数矩阵；D 0(k)表示kT s时刻与反电势相关的系数矩阵。
相比于式(3)，式(5)考虑了每个控制周期内转子位置变化对定子电流与电压实际运行轨迹的影响，因此能更准确地反映定子电流在每个周期内的变化。但是死区效应与电机参数失配仍会造成预测误差。
三、建立适用于永磁同步电机系统高速运行区的电流增量预测模型：
死区效应造成的逆变器输出电压误差与逆变器三相开关状态和三相电流方向相关。逆变器的三相开关切换模式是固定的，并且三相电流的方向不会频繁变换，因此相邻两个控制周期内死区电压可以看作是不变的。因此，将相邻两时刻的定子电压做差可以在一定程度上消除死区造成的电压误差。在电机驱动器中，由于控制周期非常小，可以认为电机转子角速度ω r在相邻两个控制周期内是不变的。即式(5)中的A 0(k)、B 0(k)与D 0(k)在相邻两个控制周期内是不变的。根据式(5)，将相邻两时刻的预测电流相减，即可得到适用于高速工况下的电流增量预测模型为：
Δi s(k+1)＝A 0(k)Δi s(k)+B 0(k)Δu s(k)      (6)
在式(6)中，Δi s(k+1)表示由电流增量预测模型计算得到的预测电流增量，并且，Δi s(k+1)＝[Δi d,k+1,Δi q,k+1] T，其中，Δi d,k+1为预测电流增量的d轴分量，Δi q,k+1为预测电流增量的q轴分量；Δi s(k)表示(k-1)T s时刻到kT s时刻的定子电流增量，即Δi s(k)＝i s(k)-i s(k-1)，并且，Δi s(k)＝[Δi d,k,Δi q,k] T，其中，Δi d,k为(k-1)T s时刻到kT s时刻的定子电流增量的d轴分量，Δi q,k为(k-1)T s时刻到kT s时刻的定子电流增量的q轴分量，i s(k-1)表示(k-1)T s时刻的定子电流矢量；Δu s(k)表示(k-1)T s时刻到kT s时刻的定子电压增量，即Δu s(k)＝u s(k)-u s(k-1)，并且，Δu s(k)＝[Δu d,k,Δu q,k] T，其中，Δu d,k为(k-1)T s时刻到kT s时刻的定子电压增量的d轴分量，Δu q,k为(k-1)T s时刻到kT s时刻的定子电压增量的q轴分量，u s(k-1)表示(k-1)T s时刻的定子电压矢量。
式(6)中的电流增量预测模型中的控制量为相邻两时刻的电压增量Δu s(k)， 这使得电流增量预测模型可以降低逆变器死区造成的输出电压误差。对比式(5)与式(6)可以看出，两式系数相同，具有相同的表达形式。并且式(6)消去了永磁体磁链。因此，电流增量预测模型只受电机定子电感的影响，而不受永磁体磁链影响。
四、构建成本函数：
将预设的参考电流增量与预测电流增量在每个控制周期末的误差平方作为评价指标，构建成本函数，利用成本函数对定子电压增量对应的定子电流增量在每个控制周期末的误差进行评估。考虑预测电流控制的延时补偿问题，构建的成本函数为
Figure PCTCN2021110342-appb-000014
式中，Δi s ref表示参考电流增量；P表示权重因子，用来决定电压增量的重要性；U max与I max分别表示电机驱动系统允许的最大电流与电压；T表示矩阵转置；Satisfy表示约束条件；Δi s(k+2)表示由电流增量预测模型计算得到的预测电流增量，Δu s(k+1)表示kT s时刻到(k+1)T s时刻的定子电压增量；J表示成本函数的值。将电压增量加入成本函数中进行评估可以降低电机动态过冲，防止电机与功率开关管遭受电压、电流浪涌。
五、求解最优定子电压矢量：
将式(6)代入式(7)并进行整理，可得
Figure PCTCN2021110342-appb-000015
根据凸优化理论，对式(8)求关于Δu s(k)的导数，可以得到成本函数J的极值条件为：
Figure PCTCN2021110342-appb-000016
求解式(9)，可以得到使J的值最小的最优电压增量为：
Δu s opt＝[B 0 TB 0+P] -1B 0 T[Δi s ref-A 0Δi s(k+1)]      (10)
由最优电压增量与当前控制周期的定子电压得到下一个控制周期的最优定子电压为：
u s opt(k+1)＝u s(k)+Δu s opt(k+1)      (11)
式(11)中，Δu s opt表示最优的定子电压增量。
本发明的具体实施过程的控制框图如图1所示。该方法提高了电机高速运行工况下的电流预测精度，并消去了永磁体磁链在预测电流增量控制方法实现过程中的使用。
下面结合具体的仿真与实验数据、图2～图4对本发明方法进行可行性验证。
为了验证本发明的一种基于电流增量预测模型的预测电流控制方法的可行性与有效性，在20kW的永磁同步电机系统中进行仿真与实验验证。电机参数如表1所示。在实验测试平台中，数字信号处理器(DSP)TMS320F28335进行方法的实现，测功机为感应电机，感应电机由西门子公司生产的S120进行控制。
表1
Figure PCTCN2021110342-appb-000017
一、死区效应对电流控制性能影响
为了避免参数失配的影响，本发明通过仿真验证逆变器死区分别对基于传统电流预测模型的预测电流控制方法与本发明中的预测电流增量控制方法的电流控制性能的影响。仿真中，传统电流预测模型为式(3)中的电流预测模型，控制周期T s为200μs，死区时间t d设为3μs。图2给出了基于传统电流预测模型的预测电流控制方法与预测电流增量控制方法在不同电机转速n与负载转矩T L下的预设的d轴电流参考值i d ref、d轴电流实测值i d、q轴电流参考值i q ref与q轴电流实测值i q的仿真波形。
由图2可以看出，基于传统电流预测模型的预测电流控制方法的d轴电流在n为300r/min、T L为64Nm时存在较明显跟踪误差，在其他工况下跟踪性能较好；而q轴电流在各种工况下均存在较明显的跟踪误差。基于电流增量预测模型的预测电流控制方法的d、q轴电流均可以较为准确地跟踪其参考值。图2表明本发明提出的电流增量预测模型能够抑制死区效应对电流跟踪性能的影响。
二、电感失配下电流预测误差分析
在电机实际控制过程中，电机实际电感与标称电感存在误差ΔL d与ΔL q。令 L d、L d为电感的实际值，将L d＝L d0+ΔL d、L q＝L q0+ΔL q代入式(5)，可得电流增量预测模型考虑电感误差的预测电流增量为：
Δi sp(k+1)＝Δi s(k+1)+e(k+1)      (12)
Figure PCTCN2021110342-appb-000018
在式(12)中，Δi sp(k+1)表示考虑电感误差的计算得到的预测电流增量；e(k+1)表示电感失配造成的电流预测误差矢量，并且，e(k+1)＝[e d,k+1,e q,k+1] T，其中，e d,k+1为电流预测误差的d轴分量，e q,k+1为电流预测误差的q轴分量；Δi s(k+1)参考式(5)所示。
在式(13)中，ΔL d表示d轴定子电感实际值与d轴定子电感标称值之间的误差；ΔL q表示q轴定子电感实际值与q轴定子电感标称值之间的误差；ΔA(k)表示定子电流增量项的系数矩阵；ΔB(k)表示定子电压增量项的系数矩阵。
式(13)可以看出，电流预测误差(e d,k+1、e q,k+1)的幅值与符号受状态量(Δi d,k、Δi q,k)、控制量(Δu d,k、Δu q,k)和电机转速的影响。为了直观说明电感失配对电流增量预测模型的电流预测误差的影响，图3绘制了不同电机转速n与负载转矩T L下传统电流预测模型和电流增量预测模型在L d与L q分别变化20％与50％时计算的e d,k+1与e q,k+1的波形。
对于电流增量预测模型，电感失配下的e d,k+1与e q,k+1始终围绕零点上下变化，如图3所示。这种电流预测误差主要会影响d、q轴电流的波动量，而对电流跟踪性能的影响很小。另外，e d,k+1与e q,k+1围绕零点上下变化的幅度越大，对d、q轴电流波动量的影响越大。由图3可以看出，在不同负载转矩下电流增量预测模型的e d,k+1与e q,k+1的变化幅度没有明显的变化。在轻载工况下，定子电流幅值较小，e d,k+1与e q,k+1的变化幅度相对于电流幅值较为明显，因此电感变化对电流波动的影响较大；而在重载工况下，定子电流幅值变大，e d,k+1与e q,k+1的变化幅 度相对于电流幅值很小，此时相同的电感变化对电流波动的影响很小。上述分析过程在不同负载工况下设置的电感变化是一致的(ΔL d＝20％L d0andΔL q＝50％L q0)，然而电机电感变化与d、q轴电流幅值呈正相关，即电感在轻载(电流幅值小)时的变化远小于上述设置。因此在电机实际运行过程中，电感变化对基于电流增量预测模型的预测电流控制方法的电流波动影响较小。
综上所述，电感失配会影响基于电流增量预测模型的预测电流控制方法的电流波动，但是影响较小，并且电感失配对基于电流增量预测模型的预测电流控制方法的电流跟踪误差的影响也很小。
三、稳态性能对比
本发明在20kW的PMSM驱动系统中进行实验，对比基于传统电流预测模型的预测电流控制方法与基于电流增量预测模型的预测电流控制方法的稳态性能，电机参数如表1所示。实验中，电机转速n分别为300r/min与7500r/min，两种转速下电机输出功率均为20kW。
图4给出了不同工况下基于传统电流预测模型的预测电流控制方法与基于电流增量预测模型的预测电流控制方法的d轴电流参考值i d ref、d轴电流实测值i d、q轴电流参考值i q ref、q轴电流实测值i q与a相电流i a的稳态实验波形。由实验波形可知，在电机运行在300r/min时，尽管电流增量预测模型忽略了定子电阻项，但是基于电流增量预测模型的预测电流控制方法电流波动并没有恶化，而当电机运行在7500r/min时，基于电流增量预测模型的预测电流控制方法的d、q电流波动均明显低于基于传统电流预测模型的预测电流控制方法。同时可以看出，基于电流增量预测模型的预测电流控制方法的i d、i q可以较好地跟踪其给定值，而基于传统电流预测模型的预测电流控制方法因死区效应与参数失配的影响，其i d与i q具有明显的跟踪误差。
本发明对各器件的型号除做特殊说明的以外，其他器件的型号不做限制，只要能完成上述功能的器件均可。
本领域技术人员可以理解附图只是一个示意图，上述本发明实施例序号仅仅为了描述，不代表实施例的优劣。
以上所述仅为本发明的较佳实施例，并不用以限制本发明，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。

Claims (6)

  1. 一种适用于永磁同步电机高速区运行的预测电流增量控制方法，其特征在于，方法包括如下步骤：
    1)根据一个控制周期内电机转子的位置变化，建立定子电压在一个控制周期内的关系表达式；
    2)对永磁同步电机的连续时域模型求解处理得到永磁同步电机的连续时域电流模型；
    3)将定子电压在一个控制周期内的关系表达式代入连续时域电流模型并进行求解，得到适用于永磁同步电机高速运行区的离散电流预测模型，利用离散电流预测模型处理获得下一时刻的预测电流；
    4)将相邻两时刻的预测电流相减得到适用于永磁同步电机高速运行区的电流增量预测模型以及由电流增量预测模型计算得到的预测电流增量；
    5)将预设的参考电流增量与预测电流增量在每个控制周期末的误差平方作为评价参数，构建成本函数，对成本函数采用凸优化求解方法进行求解，得到使成本函数最小的定子电压增量作为最优电压增量；
    6)将最优电压增量叠加到当前控制周期的定子电压上得到下一个控制周期的最优定子电压，进而施加到永磁同步电机上进行控制。
  2. 根据权利要求1所述的一种适用于永磁同步电机高速区运行的预测电流增量控制方法，其特征在于：所述步骤1)中，所述定子电压在一个控制周期内的关系表达式是：
    Figure PCTCN2021110342-appb-100001
    式中，u d(t)、u q(t)分别表示永磁同步电机的d轴电压、q轴电压；T s表示控制周期；u d,k表示kT s时刻的定子电压矢量的d轴分量，u q,k分别表示kT s时刻的定子电压矢量的q轴分量，其中下标d表示d轴，下标q表示q轴，下标k表示控制周期的序数；ω r表示电机转子的旋转电角速度，k表示控制周期的序数，t表示当前时刻。
  3. 根据权利要求1所述的一种适用于永磁同步电机高速区运行的预测电流增量控制方法，其特征在于：所述步骤3)中，所述的离散电流预测模型具体为：
    i s(k+1)＝A 0(k)i s(k)+B 0(k)u s(k)+D 0(k)
    Figure PCTCN2021110342-appb-100002
    Figure PCTCN2021110342-appb-100003
    Figure PCTCN2021110342-appb-100004
    式中，i s(k+1)表示(k+1)T s时刻的预测电流矢量，i s(k)表示kT s时刻的定子电流矢量；u s(k)表示kT s时刻的定子电压矢量；A 0(k)表示i s(k)项的系数矩阵；B 0(k)表示u s(k)项的系数矩阵；D 0(k)表示反电势项系数矩阵；ω r,k表示kT s时刻的电机转子旋转电角速度，r表示与转子相关的变量的标志，k表示控制周期的序数；r s0、L d0、L q0和ψ f0分别表示定子电阻、d轴定子电感、q轴定子电感和永磁体磁链的标称值。
  4. 根据权利要求1所述的一种适用于永磁同步电机高速区运行的预测电流增量控制方法，其特征在于，所述步骤4)中，电流增量预测模型为：
    Δi s(k+1)＝A 0(k)Δi s(k)+B 0(k)Δu s(k)
    Δi s(k)＝i s(k)-i s(k-1)
    Δu s(k)＝u s(k)-u s(k-1)
    式中，Δi s(k+1)表示由电流增量预测模型计算得到的预测电流增量，Δi s(k)表示(k-1)T s时刻到kT s时刻的定子电流增量，Δu s(k)表示(k-1)T s时刻到kT s时刻的定子电压增量；i s(k-1)表示(k-1)T s时刻的定子电流矢量；u s(k-1)表示(k-1)T s时刻的定子电压矢量；A 0(k)表示i s(k)项的系数矩阵；B 0(k)表示u s(k)项的系数矩阵。
  5. 根据权利要求1所述的一种适用于永磁同步电机高速区运行的预测电流增量控制方法，其特征在于：所述步骤5)中，成本函数建立为：
    Figure PCTCN2021110342-appb-100005
    Figure PCTCN2021110342-appb-100006
    式中，Δi s ref表示参考电流增量，P表示权重因子；U max与I max分别表示永磁同步电机的电机驱动系统允许的最大电流与电压，T表示矩阵转置；Satisfy表示 约束条件；Δi s(k+2)表示由电流增量预测模型计算得到的预测电流增量，Δu s(k+1)表示kT s时刻到(k+1)T s时刻的定子电压增量；J表示成本函数的值。
  6. 根据权利要求1所述的一种适用于永磁同步电机高速区运行的预测电流增量控制方法，其特征在于：所述步骤6)中，将最优电压增量叠加到当前控制周期的定子电压上得到下一个控制周期的最优定子电压，具体为：
    u s opt(k+1)＝u s(k)+Δu s opt(k+1)
    式中，u s(k)表示kT s时刻的定子电压，u s opt(k+1)表示(k+1)T s时刻的最优定子电压，Δu s opt(k+1)表示(k+1)T s时刻的最优定子电压增量。
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