CN114301361A - Control method of electrolytic capacitor-free permanent magnet synchronous motor driving system based on bus current control - Google Patents
Control method of electrolytic capacitor-free permanent magnet synchronous motor driving system based on bus current control Download PDFInfo
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Abstract
The invention discloses a control method of a driving system of a permanent magnet synchronous motor without electrolytic capacitor based on bus current control, which comprises the following steps: directly calculating a given value of the q-axis voltage of the motor according to a constraint condition between the bus current instruction value and the motor variable; based on the Lyapunov stability theory, carrying out convergence judgment on the motor current under the q-axis given voltage, if the judgment is non-convergence, obtaining a motor q-axis current instruction value according to an approximate relation between a bus current instruction value and the motor q-axis current, and calculating the motor q-axis voltage given value based on a feedback linearization idea; and carrying out coordinate transformation on the given voltage of the d-q axis of the motor and outputting the coordinate transformation to the motor through the SVPWM module. The method has the advantages of high motor efficiency, high network side power factor, easy realization of control strategy and strong system robustness, and the control effect of the network side power factor is less influenced by system parameter errors.
Description
Technical Field
The invention belongs to the field of motor control, and particularly relates to a control technology of a driving system of a permanent magnet synchronous motor without electrolytic capacitor.
Background
Permanent magnet synchronous motors are widely used in industry and home appliances due to their high efficiency, high power density, and other characteristics. However, the dc bus electrolytic capacitor used in the conventional ac-dc-ac permanent magnet synchronous motor variable frequency driving system may reduce the system reliability and deteriorate the grid-side input power factor. In order to meet the requirement of network side input power, a power factor correction circuit is required to be added. Therefore, research for improving the grid-side input power factor by using a thin film capacitor instead of a bus electrolytic capacitor and adopting a control strategy has received much attention.
The existing control method for the driving system of the permanent magnet synchronous motor without the electrolytic capacitor realizes the control of power and current by adopting a repetitive controller, a proportional resonant controller and the like so as to improve the power factor of a network side, but has the problems of poor control effect, difficult parameter setting of the controller and lower motor efficiency.
Disclosure of Invention
In order to solve the technical problem, the invention provides a control method of a driving system of a permanent magnet synchronous motor without electrolytic capacitor based on bus current control, which directly controls bus current based on system convergence analysis, has low system complexity and strong robustness, can realize network side high power factor, calculates a d-axis current instruction of the motor based on a minimum copper loss principle, and effectively improves the motor efficiency.
The purpose of the invention is realized by the following technical scheme: a control method of a driving system of a permanent magnet synchronous motor without electrolytic capacitor based on bus current control comprises the following steps:
according to the bus current instruction value
Obtaining a given value of the q-axis voltage of the motor by constraint conditions between the motor variables
And then, based on the Lyapunov stability theory, setting the q-axis voltage of the motor
Carrying out convergence analysis on the motor current; if the judgment is convergence, adopting the given value of the q-axis voltage of the motor
If the bus current instruction value is judged to be non-convergence, the bus current instruction value is judged to be non-convergence
Obtaining the q-axis current instruction value of the motor by the approximate relation between the q-axis current and the motor
And obtaining the given value of the q-axis voltage of the motor based on the feedback linearization idea
Finally, d-axis voltage of the motor is given
q-axis voltage setting
Coordinate transformation is carried out to obtain a voltage given value under a static two-phase coordinate system
And then outputs the voltage to the motor.
Further, the bus current command value
And obtaining the voltage phase of the grid side according to the output value of the speed regulator and the capacitance value of the bus.
Further, the bus current command value
The calculation method comprises the following steps:
firstly, the voltage waveform of the network side is phase-locked to obtain the phase angle theta of the voltage of the network sides；
Then the motor rotating speed instruction value is differed from the actual rotating speed, and the motor rotating speed instruction value is output through a speed regulator and then input into a current instruction amplitude value at the network side
Combined net side voltage phase angle thetasObtaining instantaneous value of network side input current instruction
Finally, inputting the instantaneous value of the current instruction to the network side
Subtracting the instantaneous value i of the capacitor currentcObtaining the bus current instruction value
Further, the d-axis current command value
Based on the calculation of the minimum copper loss principle, the d-axis voltage given value
Obtained from a current regulator.
Further, the d-axis current command value
The d-axis current command constant value is obtained based on the principle of minimum copper loss because the q-axis current of the motor of the electrolytic-capacitor-free driving system is a periodic sine wave
The calculation method comprises the following steps:
first making a Lagrange function
Wherein:
then let the Lagrangian function F (i)d,iqrms,iqav,λ1,λ2) The first partial derivative for each variable is equal to zero, resulting in:
finally, the d-axis current i corresponding to the minimum copper loss control can be solved by five equation sets in the formula (1)dAnd using it as d-axis command value
The expression is as follows:
further, obtaining the given value of the q-axis voltage of the motor
The method comprises the following steps:
firstly, an inverter modulation ratio function under a static three-phase coordinate system is expressed as follows:
in the formula: a. themFor inverter modulation ratio amplitude, θeThe angle value of the phase axis of the motor a is advanced by the shaft d of the motor;
outputting an angle value of a phase angle leading motor d shaft for the inverter;
motor voltage u under static three-phase coordinate systema、ub、ucUsing inverter transfer function FdAnd bus voltage udcExpressed as:
[ua ub uc]T＝Fd·udc (3)；
motor current i in static three-phase coordinate systema、ib、icAnd inverter transfer function FdWill bus current idcExpressed as:
idc＝Fd T·[ia ib ic]T (4)；
the motor voltage u under the rotating coordinate system is obtained after the constant amplitude value transformation from the static three-phase coordinate system to the rotating two-phase coordinate system of the formula (3) and the formula (4)d-qBus current idcVector of modulation ratio with inverter
The relationship between them is:
in the formula: i ismIs the motor current amplitude;
the phase angle of the motor current leads the angle value of the d axis of the motor;
is a motor current vector; a. thed、AqRespectively inverter modulation ratio vector
Components in a d-q coordinate system;
then, a map is constructed from equation (6) to obtain a modulation ratio vector
In the motor current vector
The calculation formula of the projection length L is as follows:
modulation ratio vector
The coordinate values of the intersection points of the perpendicular line and the d-q axis coordinate system are respectively as follows:
finally, the modulation ratio vector is obtained by the formula (5)
D-axis component of
According to the relation of similar triangles
Obtaining the given value of the q-axis voltage of the motor according to the formula (5)
Further, the method for judging the convergence of the motor current comprises the following steps:
firstly, respectively expressing voltage equations of the permanent magnet synchronous motor under a d-q coordinate system as follows:
in the formula: r is a stator resistor; omegaeIs the electrical angular velocity of the motor.
Then, the calculated q-axis voltage of the motor is given
The motor voltage equation (9) is substituted, and simplified to obtain:
simplifying according to the d-q axis current relationship of the motor to obtain a state variable equation of the q axis current of the motor as follows:
analyzing the stability of a nonlinear equation shown in formula (11) based on a Lyapunov direct method: order to
Equal to zero, two balance points exist in the system, which are respectively:
for convenient analysis, let y be iq-iq_0And substituting the equation to change the balance point into a state space zero point to obtain a transformed equation:
the formula (11) is simplified to the formula (13):
constructing positive definite lyapunov functions
Easy and appropriate y > -iq_0Derivative of the Schleipunuo function
The constant value is less than zero, so that the stable operation of the system can be ensured;
if the system is not satisfied
And y > -iq_0Under the two convergence conditions, the q-axis current instruction value of the motor is obtained according to the approximate relation between the q-axis current of the motor and the bus current
The motor q-axis voltage equation (9) is rewritten as:
according to the idea of feedback linearization, order
And the voltage equation of the q axis of the motor is introduced, and the q axis is simplified to obtain
Reissue control rate
Is simple and easy to obtain
Wherein a is a normal number,
for the current error, it is known that the error between the current command and the actual current converges to zero over time.
Further, the d-axis voltage of the motor is finally given
q-axis voltage setting
Coordinate transformation is carried out to obtain a voltage given value under a static two-phase coordinate system
And then the voltage is output to the motor through the SVPWM module.
The invention has the beneficial effects that: the invention can be used in all driving systems of the permanent magnet synchronous motor without electrolytic capacitor. Compared with the prior art, the method obtains the d-axis current of the motor based on the minimum copper loss principle, and improves the motor efficiency; the method has the advantages that the given value of the q-axis voltage of the motor is directly calculated according to the constraint condition between the bus current instruction value and the motor variable, the network side high power factor can be realized, the network side power factor control effect is slightly influenced by system parameter errors, the overall control strategy is easy to realize, and the system robustness is strong.
Drawings
FIG. 1 is a block diagram of a topology of a driving system without electrolytic capacitors in an embodiment of the invention;
FIG. 2 is a block diagram of inverter modulation ratio vector calculation according to an embodiment of the present invention;
FIG. 3 is a simulated d-q axis current waveform in accordance with an embodiment of the present invention;
FIG. 4 is a diagram illustrating an exemplary simulated net-side input current waveform.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings so that the objects and effects of the invention will become more apparent.
In one embodiment, a control method for a driving system of a permanent magnet synchronous motor without electrolytic capacitor based on bus current control is provided, and comprises the following steps:
according to the bus current instruction value
Obtaining a given value of the q-axis voltage of the motor by constraint conditions between the motor variables
Then, a q-axis voltage given value of the motor is determined based on the Lyapunov stability theory
Carrying out convergence analysis on the motor current; if the judgment is convergence, the given value of the q-axis voltage of the motor is adopted
If the bus current command value is judged to be non-convergence, the bus current command value is used for judging whether the bus current command value is non-convergence
And electricityObtaining the q-axis current instruction value of the motor by the approximate relation between the q-axis currents of the motor
And obtaining the given value of the q-axis voltage of the motor based on the feedback linearization idea
Finally, d-axis voltage of the motor is given
q-axis voltage setting
Coordinate transformation is carried out to obtain a voltage given value under a static two-phase coordinate system
And then outputs the voltage to the motor.
In one embodiment, the bus current command value
And obtaining the voltage phase of the grid side according to the output value of the speed regulator and the capacitance value of the bus.
In one embodiment, the bus current command value
The calculation method comprises the following steps:
firstly, the voltage waveform of the network side is phase-locked to obtain the phase angle theta of the voltage of the network sides；
Then the motor rotating speed instruction value is differed from the actual rotating speed, and the motor rotating speed instruction value is output through a speed regulator and then input into a current instruction amplitude value at the network side
Combined net side voltage phase angle thetasObtaining instantaneous value of network side input current instruction
Finally, inputting the instantaneous value of the current instruction to the network side
Subtracting the instantaneous value i of the capacitor currentcObtaining the bus current instruction value
In one embodiment, the d-axis current command value
Based on the calculation of the minimum copper loss principle, the d-axis voltage set value
Obtained from a current regulator.
Further, the d-axis current command value
The d-axis current command constant value is obtained based on the principle of minimum copper loss because the q-axis current of the motor of the electrolytic-capacitor-free driving system is a periodic sine wave
The calculation method comprises the following steps:
first making a Lagrange function
Wherein:
then let the Lagrangian function F (i)d,iqrms,iqav,λ1,λ2) The first partial derivative for each variable is equal to zero, resulting in:
finally, the d-axis current i corresponding to the minimum copper loss control can be solved by five equation sets in the formula (1)dAnd using it as d-axis command value
The expression is as follows:
in one embodiment, a given value of the q-axis voltage of the motor is obtained
The method comprises the following steps:
firstly, an inverter modulation ratio function under a static three-phase coordinate system is expressed as follows:
in the formula: a. themFor inverter modulation ratio amplitude, θeThe angle value of the phase axis of the motor a is advanced by the shaft d of the motor;
outputting an angle value of a phase angle leading motor d shaft for the inverter;
motor voltage u under static three-phase coordinate systema、ub、ucUsing inverter transfer function FdAnd bus voltage udcExpressed as:
[ua ub uc]T＝Fd·udc(3) (ii) a Motor current i in static three-phase coordinate systema、ib、icAnd inverter transfer function FdWill bus current idcExpressed as:
idc＝Fd T·[ia ib ic]T (4)；
the motor voltage u under the rotating coordinate system is obtained after the constant amplitude value transformation from the static three-phase coordinate system to the rotating two-phase coordinate system of the formula (3) and the formula (4)d-qBus current idcVector of modulation ratio with inverter
The relationship between them is:
in the formula: i ismIs the motor current amplitude;
the phase angle of the motor current leads the angle value of the d axis of the motor;
as a motor current vector；Ad、AqRespectively inverter modulation ratio vector
Components in a d-q coordinate system;
FIG. 2 is then plotted according to equation (6), and the modulation ratio vector from FIG. 2 is obtained
In the motor current vector
The calculation formula of the projection length L is as follows:
modulation ratio vector
The coordinate values of the intersection points of the perpendicular line and the d-q axis coordinate system are respectively as follows:
finally, the modulation ratio vector is obtained by the formula (5)
D-axis component of
According to the relation of similar triangles
Obtaining the given value of the q-axis voltage of the motor according to the formula (5)
In one embodiment, the method for determining convergence of motor current includes the following steps:
firstly, respectively expressing voltage equations of the permanent magnet synchronous motor under a d-q coordinate system as follows:
in the formula: r is a stator resistor; omegaeIs the electrical angular velocity of the motor.
Then, the calculated q-axis voltage of the motor is given
The motor voltage equation (9) is substituted, and simplified to obtain:
simplifying according to the d-q axis current relationship of the motor to obtain a state variable equation of the q axis current of the motor as follows:
analyzing the stability of a nonlinear equation shown in formula (11) based on a Lyapunov direct method: order to
Equal to zero, two balance points exist in the system, which are respectively:
for convenient analysis, let y be iq-iq_0And substituting the equation to change the balance point into a state space zero point to obtain a transformed equation: will be provided with
The formula (11) is simplified to the formula (13):
constructing positive definite lyapunov functions
Easy and appropriate y > -iq_0Derivative of the Schleipunuo function
The constant value is less than zero, so that the stable operation of the system can be ensured;
if the system is not satisfied
And y > -iq_0Under the two convergence conditions, the q-axis current instruction value of the motor is obtained according to the approximate relation between the q-axis current of the motor and the bus current
The motor q-axis voltage equation (9) is rewritten as:
according to the idea of feedback linearization, order
And the voltage equation of the q axis of the motor is introduced, and the q axis is simplified to obtain
Reissue control rate
Is simple and easy to obtain
Wherein a is a normal number,
for the current error, it is known that the error between the current command and the actual current converges to zero over time.
In one embodiment, the motor d-axis voltage is finally given
q-axis voltage setting
Coordinate transformation is carried out to obtain a voltage given value under a static two-phase coordinate system
And then the voltage is output to the motor through the SVPWM module.
When the motor speed regulator works, the motor speed instruction value is differed from the actual speed to obtain a motor speed error, and the error value is used for obtaining a network side input current instruction amplitude value through the motor speed regulator
The speed regulator can adopt a PI regulator.
Network side input current instruction amplitude
Combined net side voltage phase angle thetasObtaining instantaneous value of network side input current instruction
Wherein, the grid side is electrifiedPhase angle of pressure thetasCan be obtained by using a second-order generalized integral phase-locked loop (SOGI-PLL), and the specific calculation formula of the input current instruction amplitude at the network side is
As can be seen from FIG. 1, the instantaneous value of the network-side input current command is
Subtracting the instantaneous value i of the capacitor currentcObtaining the bus current instruction value
Wherein the instantaneous value of the capacitance current
In the formula CdcIs a bus capacitance value; bus current command value
By the formula
Obtaining a d-axis current instruction value of the motor
Wherein, the average value i of the q-axis current of the motorqavAveraging with a sliding window filter yields:
where N is the number of samples in a bus voltage cycle, iq(k) Representing the q-axis current i of the kth sampleq。
The d-axis voltage set value is obtained by the current regulator after the d-axis current instruction value of the motor is differed from the actual current
The current regulator can adopt a PI regulator.
From the bus current command value
And the motor current amplitude ImObtaining a modulation ratio vector
In the motor current vector
The projection length L is calculated by
Obtaining modulation ratio vector by sine-cosine function relation
The coordinate values of the intersection points of the perpendicular line and the d-q axis coordinate system are respectively as follows:
given value by motor d-axis voltage
Obtaining a modulation ratio vector
D-axis component of
Obtaining the modulation ratio vector according to the similar triangular relation shown in FIG. 2
Q-axis component of
Finally by a modulation ratio vector
Q-axis component of
And bus voltage udcObtaining a given value of q-axis voltage
By passing
And y > -iq_0Two conditions determine whether the motor current converges. If the two formulas can not be satisfied simultaneously, the given value of the q-axis voltage needs to be changed
The specific method comprises the following steps:
obtaining a q-axis current instruction value according to the relation between the q-axis current of the motor and the bus current
Obtaining a given value of q-axis voltage according to a feedback linearization idea
Setting the d-axis voltage of the motor
q-axis voltage setting
Coordinate transformation is carried out to obtain a voltage given value under a static two-phase coordinate system
And then the given voltage is output to the motor through the SVPWM module.
The invention can be used in all driving systems of the permanent magnet synchronous motor without electrolytic capacitor. Compared with the prior art, the method obtains the d-axis current of the motor based on the minimum copper loss principle, and improves the motor efficiency; the method has the advantages that the given value of the q-axis voltage of the motor is directly calculated according to the constraint condition between the bus current instruction value and the motor variable, the network side high power factor can be realized, the network side power factor control effect is slightly influenced by system parameter errors, the overall control strategy is easy to realize, and the system robustness is strong. As shown in fig. 3 and 4, in the q-axis current convergence region, the grid-side input current is a standard sine wave, so that the grid-side power factor is maximized.
Claims (8)
1. A control method of a driving system of a permanent magnet synchronous motor without electrolytic capacitor based on bus current control is characterized by comprising the following steps:
according to the bus current instruction value
Obtaining a given value of the q-axis voltage of the motor by constraint conditions between the motor variables
And then, based on the Lyapunov stability theory, setting the q-axis voltage of the motor
Carrying out convergence analysis on the motor current; if the judgment is convergence, adopting the given value of the q-axis voltage of the motor
If the bus current instruction value is judged to be non-convergence, the bus current instruction value is judged to be non-convergence
Obtaining the q-axis current instruction value of the motor by the approximate relation between the q-axis current and the motor
And obtaining the given value of the q-axis voltage of the motor based on the feedback linearization idea
Finally, d-axis voltage of the motor is given
q-axis voltage setting
Coordinate transformation is carried out to obtain a voltage given value under a static two-phase coordinate system
And then outputs the voltage to the motor.
2. The method for controlling the driving system of the electrolytic capacitor-free permanent magnet synchronous motor based on the bus current control as claimed in claim 1, wherein the bus current command value
And obtaining the voltage phase of the grid side according to the output value of the speed regulator and the capacitance value of the bus.
3. The method for controlling the driving system of the electrolytic capacitor-free permanent magnet synchronous motor based on the bus current control as claimed in claim 2, wherein the bus current command value
The calculation method comprises the following steps: firstly, the voltage waveform of the network side is phase-locked to obtain the phase angle theta of the voltage of the network sides；
Then the motor rotating speed instruction value is differed from the actual rotating speed, and the motor rotating speed instruction value is output through a speed regulator and then input into a current instruction amplitude value at the network side
Combined net side voltage phase angle thetasObtaining instantaneous value of network side input current instruction
Finally, inputting the instantaneous value of the current instruction to the network side
Subtracting the instantaneous value i of the capacitor currentcObtaining the bus current instruction value
4. The method for controlling the driving system of the electrolytic capacitor-free permanent magnet synchronous motor based on the bus current control as claimed in claim 1, wherein the d-axis current command value
Based on the calculation of the minimum copper loss principle, the d-axis voltage given value
Obtained from a current regulator.
5. The method for controlling the driving system of the electrolytic capacitor-free permanent magnet synchronous motor based on the bus current control as claimed in claim 4, wherein the d-axis current command value
The d-axis current command constant value is obtained based on the principle of minimum copper loss because the q-axis current of the motor of the electrolytic-capacitor-free driving system is a periodic sine wave
The calculation method comprises the following steps:
first making a Lagrange function
Wherein:
then let the Lagrangian function F (i)d,iqrms,iqav,λ1,λ2) The first partial derivative for each variable is equal to zero, resulting in:
finally, the d-axis current i corresponding to the minimum copper loss control can be solved by five equation sets in the formula (1)dAnd using it as d-axis command value
The expression is as follows:
6. the method for controlling the driving system of the electrolytic capacitor-free permanent magnet synchronous motor based on the bus current control as claimed in claim 5, wherein the given value of the q-axis voltage of the motor is obtained
The method comprises the following steps:
firstly, an inverter transfer function F under a static three-phase coordinate systemdExpressed as:
in the formula: a. themFor inverter modulation ratio amplitude, θeThe angle value of the phase axis of the motor a is advanced by the shaft d of the motor;
outputting an angle value of a phase angle leading motor d shaft for the inverter;
motor voltage u under static three-phase coordinate systema、ub、ucUsing inverter transfer function FdAnd bus voltage udcExpressed as:
[ua ub uc]T＝Fd·udc (3)；
motor current i in static three-phase coordinate systema、ib、icAnd inverter transfer function FdWill bus current idcExpressed as:
idc＝Fd T·[ia ib ic]T (4)；
a general formula (3) isThe motor voltage u under the rotating coordinate system is obtained after the constant amplitude value transformation from the static three-phase coordinate system to the rotating two-phase coordinate system in the formula (4)d、uqBus current idcVector of modulation ratio with inverter
The relationship between them is:
in the formula: i ismIs the motor current vector magnitude;
the phase angle of the motor current leads the angle value of the d axis of the motor;
is a motor current vector; a. thed、AqRespectively inverter modulation ratio vector
Components in a d-q coordinate system;
then, a map is constructed from equation (6) to obtain a modulation ratio vector
In the motor current vector
The calculation formula of the projection length L is as follows:
modulation ratio vector
The coordinate values of the intersection points of the perpendicular line and the d-q axis coordinate system are respectively as follows:
finally, the modulation ratio vector is obtained by the formula (5)
D-axis component of
According to the relation of similar triangles
Obtaining the given value of the q-axis voltage of the motor according to the formula (5)
7. The method for controlling the driving system of the electrolytic capacitor-free permanent magnet synchronous motor based on the bus current control as claimed in claim 6, wherein the method for judging the convergence of the motor current comprises the following steps:
firstly, respectively expressing voltage equations of the permanent magnet synchronous motor under a d-q coordinate system as follows:
in the formula: r is a stator resistor; omegaeIs the electrical angular velocity of the motor.
Then, the calculated q-axis voltage of the motor is given
The motor voltage equation (9) is substituted, and simplified to obtain:
simplifying according to the d-q axis current relationship of the motor to obtain a state variable equation of the q axis current of the motor as follows:
analyzing the stability of a nonlinear equation shown in formula (11) based on a Lyapunov direct method: order to
Equal to zero, two balance points exist in the system, which are respectively:
for convenient analysis, let y be iq-iq_0And substituting the equation to change the balance point into a state space zero point to obtain a transformed equation:
the combination formula (11) and the formula (13) are simplified into:
constructing positive definite lyapunov functions
Easy and appropriate y > -iq_0Derivative of the Schleipunuo function
The constant value is less than zero, so that the stable operation of the system can be ensured;
if the system is not satisfied
And y > -iq_0Under the two convergence conditions, the q-axis current instruction value of the motor is obtained according to the approximate relation between the q-axis current of the motor and the bus current
The motor q-axis voltage equation (9) is rewritten as:
according to the idea of feedback linearization, order
And the voltage equation of the q axis of the motor is introduced, and the q axis is simplified to obtain
Reissue control rate
Is simple and easy to obtain
Wherein a is a normal number,
for the current error, it is known that the error between the current command and the actual current converges to zero over time.
8. The method for controlling the driving system of the electrolytic capacitor-free permanent magnet synchronous motor based on the bus current control as claimed in claim 1, wherein the d-axis voltage of the motor is finally given
q-axis voltage setting
Coordinate transformation is carried out to obtain a voltage given value under a static two-phase coordinate system
And then the voltage is output to the motor through the SVPWM module.
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| CN115051608B (en) * | 2022-06-16 | 2024-03-08 | 西北工业大学 | Three-phase current reconstruction method based on new axial positioning coordinate transformation of bus current |
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