CN117353617A - Closed loop non-inductive control method for DC brushless motor - Google Patents
Closed loop non-inductive control method for DC brushless motor Download PDFInfo
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Classifications
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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
- H02P21/22—Current control, e.g. using a current control loop
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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
- H02P21/05—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation specially adapted for damping motor oscillations, e.g. for reducing hunting
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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
- 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
- H02P27/085—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 wherein the PWM mode is adapted on the running conditions of the motor, e.g. the switching frequency
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Abstract
The invention relates to a closed-loop non-inductive control method of a direct-current brushless motor, which belongs to the technical field of permanent magnet synchronous motor control and comprises the following steps: sampling three-phase current of a motor to obtain Iu, iv and Iw; carrying out Clark transformation on Iu, iv and Iw to obtain Iα and Iβ; the Ialpha and the Ibeta are obtained by Park conversioni q ，i d The method comprises the steps of carrying out a first treatment on the surface of the Clicking actual parameters for identification; calculating the rotating speed of the motor to obtain the position of the rotor; setting PI parameters; correcting a current reference value of a given speed; obtaining an output control voltage V using the corrected current reference value q 、V d The method comprises the steps of carrying out a first treatment on the surface of the Vα, vβ are obtained by inverse PARK transformation; and synthesizing a voltage space vector by V alpha and V beta, and inputting the voltage space vector into the SVPWM module to modulate and drive the motor. The invention inputs the obtained parameter identification result into the current prediction control through parameter identification, and comprisesThe influence caused by parameter mismatch is effectively restrained, and the dynamic tracking effect of the system is improved.
Description
Technical Field
The invention belongs to the technical field of permanent magnet synchronous motor control, and particularly relates to a closed-loop non-inductive control method of a direct current brushless motor.
Background
Permanent magnet synchronous motors are widely used for various application requirements, such as various loads, constant loads and positioning applications in the fields of industrial control, automotive, aviation, automation systems, medical care equipment, household appliances and the like. In recent years, as the permanent magnet synchronous motor is developed on a large scale and the technology is mature gradually, the distribution range of a driving system in industrial production is also enlarged, and the development of industrial motors is gradually becoming the main stream.
However, in the current permanent magnet synchronous motor control strategy, rated load control cannot be realized under the condition of low rotation speed, and meanwhile, a Hall sensor is also required to be arranged for realizing feedback control, so that the cost is increased, and the closed-loop control process is reduced due to the open-loop strong dragging process.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a closed-loop non-inductive control method for a direct-current brushless motor, which can quickly estimate an electric angle to perform closed-loop control; the torque and the magnetic flux can be independent; capable of providing a smooth torque over the entire speed range; a rated torque can be provided at a low speed; the dynamic process of acceleration and deceleration can be quickened; because the current waveform of the control output is a sine wave, the mechanical vibration caused by torque fluctuation can be effectively reduced, so that noise is reduced, efficiency is improved, and comfort is improved.
The aim of the invention can be achieved by the following technical scheme:
a closed loop non-inductive control method of a DC brushless motor comprises the following steps:
s1, sampling three-phase current of a motor to obtain Iu, iv and Iw;
s2, sampling currents Iu, iv and Iw are subjected to Clark transformation to obtain Ialpha and Ibeta;
s3, performing Park conversion on the Ialpha and the Ibeta to obtaini q ，i d ；
S4, identifying initial values of the stator resistance and the rotor flux linkage under the condition of constant torque, then taking an identification result as a fixed value, carrying out online identification on the d-axis inductance and the q-axis inductance through a genetic particle swarm algorithm, and after the result is converged, identifying the stator resistance and the flux linkage by taking the identified d-axis inductance and q-axis inductance as fixed values;
s5, establishing a voltage equation of the motor under the condition that the motor current is a symmetrical three-phase sine wave, and acquiring a rotor position by calculating the motor rotating speed;
s6, setting PI parameters by utilizing the stator resistance and the inductance which are identified on line;
s7, correcting a current reference value of a given speed through the acquired rotating speed of the motor and the acquired actual current value;
s8, calculating a corrected current reference valuei q 、i d Errors Wq and Wd between the two are input into the PI controller to obtain an output control voltage V q 、V d For V q 、V d Performing anti-PARK transformation to obtain V alpha and V beta;
s9, synthesizing a voltage space vector by using V alpha and V beta, inputting the voltage space vector into an SVPWM module for modulation, and outputting the coded values of the state duty ratios of the three half-bridges at the current moment;
s10, controlling the MOS transistor switch of the three-phase inverter according to the output coding value, and driving the motor.
Further, in the step S2, the formula of the Clark transformation is:
Iα=Iu；
；
Iu+Iv+Iw=0；
wherein Iu, iv, iw are current values in a three-phase 120-degree coordinate system; iα, iβ are current components in the stationary coordinate system.
Further, in the step S3, the Park transformation formula is:
i d = Iα·cos(φ)+ Iβ·sin(φ)；
i q = -Iα·sin(φ)+ Iβ·cos(φ)；
in the method, in the process of the invention,i d ，i q is a rotating coordinate systemd-qAn off-axis current component;φis the rotation angle.
Further, in the step S4, the parameter identification specifically includes the following steps:
s41, firstly, identifying initial values of stator resistance and rotor flux linkage, and constructing under constant torquei d =0 sumi d Not equal to 0:
wherein, psi is f0 Is thati d Permanent magnet flux linkage at time of =0,i q0 is thati d Q-axis current when=0,u q0 is thati d Q-axis voltage at=0, R s Is the stator resistance, w e Is the angular velocity of the rotor and,u d and u q respectively isi d The voltages of d-axis and q-axis are not equal to 0,i d andi q respectively isi d Current of d-axis and q-axis when not equal to 0;
s42, identifying initial values of permanent magnet flux linkage and stator resistance, and identifying d-axis inductance and q-axis inductance on line by adopting a genetic particle swarm algorithm:
generating chaotic particles based on chaotic mapping, combining the chaotic particles with the result of the previous parameter identification to generate an initialization population, and calculating the fitness value of each particle;
determining initial values of the historical optimal position and the global historical optimal position of the individual according to a calculation result of the particle fitness value in the initial population;
calculating a population evolution coefficient s and a dynamic inertia weight omega;
updating the speed vector and the position vector of each particle in the population according to the speed and position updating mode;
calculating the fitness value of each particle, and updating the individual historical optimal position and the global historical optimal position according to the fitness value;
if the convergence condition is met or the maximum iteration number is reached, outputting a global historical optimal position, and ending the algorithm; otherwise, the population evolution coefficient s and the dynamic inertia weight omega are recalculated and continuously executed according to the steps.
Further, in the step S42, the calculation formula of the population evolution coefficient S is:
；
wherein zbest (t) and zbest (t)-1) And respectively representing global historical optimal fitness values of the current iteration and the last iteration, wherein s varies within a range of 0-1.
Further, in the step S42, dynamic inertia weightωThe calculation formula is as follows:
ω=ω 0 -s a ω s ；
wherein omega is 0 As a result of the initial inertial weight coefficient,ais a positive integer for amplifying the influence of the variation of the population evolution coefficient s on the inertia weight coefficient omega s The inertia weight coefficient corresponding to the population evolution coefficient s.
Further, in the step S42, the range of the dynamic inertia weight ω is:
ω 0 -ω s <ω<1。
further, in the step S5, calculating the rotational speed of the motor to obtain the rotor position includes the following steps:
s51, neglecting core saturation and eddy current and hysteresis loss of the motor, and establishing a stator voltage equation:
；
；
wherein,u d and u q is a rotation coordinate systemd-qVoltage component under axis, R s Is stator resistance L d And L q Is thatd-qShaft inductance, w e Is the rotor angular velocity, ψ f Is a rotor flux linkage;
s52, obtaining through PID control of the current inner loopu d Andu q and (3) calculating back electromotive force:
e d =u d -R s ·i d +w e L q i q ；
e q = u q -R s ·i q -w e L d i d ；
in the formula e d And e q Is thatd-qA back EMF component under the shaft;
s53, calculating the actual rotation speed of the motor, and obtaining the rotor position by integrating the rotation speed of the motor:
w r =e/ψ f ；
wherein e is the back electromotive force, 。
further, in the step S6, the formula for PI parameter tuning is:
；
；
wherein K is pd 、K pq Proportional coefficients of d-axis and q-axis current loop controllers, R s Is stator resistance L d And L q Is thatd-qShaft inductance, K id 、K iq The d-axis and q-axis current loop controllers integrate coefficients, respectively.
Further, in the step S8, the inverse PARK transformation formula is:
Vα = V d ·cos(φ)- V q ·sin(φ)；
Vβ=V d ·sin(φ)+ V q ·cos(φ)；
wherein V is d 、V q Is the voltage component in the rotating coordinate system; vα, vβ are voltage components in the stationary coordinate system,φis the rotation angle.
The beneficial effects of the invention are as follows:
the invention can quickly estimate the electric angle to carry out closed-loop control; the torque and the magnetic flux can be independent; capable of providing a smooth torque over the entire speed range; a rated torque can be provided at a low speed; the dynamic process of acceleration and deceleration can be quickened; because the current waveform of the control output is a sine wave, the mechanical vibration caused by torque fluctuation can be effectively reduced, so that noise is reduced, efficiency is improved, and comfort is improved.
Drawings
The present invention is further described below with reference to the accompanying drawings for the convenience of understanding by those skilled in the art.
Fig. 1 is a schematic step diagram of a closed loop non-inductive control method for a brushless dc motor according to an embodiment of the present invention.
Detailed Description
In order to further describe the technical means and effects adopted by the invention for achieving the preset aim, the following detailed description is given below of the specific implementation, structure, characteristics and effects according to the invention with reference to the attached drawings and the preferred embodiment.
Referring to fig. 1, a closed loop non-inductive control method for a brushless dc motor includes the following steps:
s1, sampling three-phase current of a motor to obtain Iu, iv and Iw;
s2, carrying out Clark transformation on Iu, iv and Iw to obtain Ialpha and Ibeta;
Iα=Iu；
；
Iu+Iv+Iw=0；
wherein Iu, iv, iw are current values in a three-phase 120-degree coordinate system; iα, iβ are current components in a stationary coordinate system;
s3, performing Park conversion on the Ialpha and the Ibeta to obtaini q ，i d ；
i d = Iα·cos(φ)+ Iβ·sin(φ)；
i q = -Iα·sin(φ)+ Iβ·cos(φ)；
In the method, in the process of the invention,i d ，i q is a rotating coordinate systemd-qAn off-axis current component;φis the rotation angle;
s4, under the condition of constant torque, identifying initial values of the stator resistance and the rotor flux linkage, then taking an identification result as a fixed value, carrying out online identification on d-axis inductance and q-axis inductance through a genetic particle swarm algorithm, and after the result is converged, identifying the stator resistance and the flux linkage by taking the identified d-axis inductance and q-axis inductance as the fixed value; the method specifically comprises the following steps:
s41, firstly, identifying initial values of stator resistance and rotor flux linkage, and constructing under constant torquei d =0 sumi d Not equal to 0:
；
wherein, psi is f0 Is thati d Permanent magnet flux linkage at time of =0,i q0 is thati d Q-axis current when=0,u q0 is thati d Q-axis voltage at=0, R s Is the stator resistance, w e Is the angular velocity of the rotor and,u d and u q respectively isi d The voltages of d-axis and q-axis are not equal to 0,i d andi q respectively isi d When not equal to 0d-axis and q-axis currents.
S42, identifying initial values of permanent magnet flux linkage and stator resistance, and identifying d-axis inductance and q-axis inductance on line by adopting a genetic particle swarm algorithm:
generating chaotic particles based on chaotic mapping, combining the chaotic particles with the result of the previous parameter identification to generate an initialization population, and calculating the fitness value of each particle;
determining initial values of the historical optimal position and the global historical optimal position of the individual according to a calculation result of the particle fitness value in the initial population;
calculating a population evolution coefficient s and a dynamic inertia weight omega;
updating the speed vector and the position vector of each particle in the population according to the speed and position updating mode;
calculating the fitness value of each particle, and updating the individual historical optimal position and the global historical optimal position according to the fitness value;
if the convergence condition is met or the maximum iteration number is reached, outputting a global historical optimal position, and ending the algorithm; otherwise, the population evolution coefficient s and the dynamic inertia weight omega are recalculated and continuously executed according to the steps.
The calculation formula of the population evolution coefficient s is as follows:
；
wherein zbest (t) and zbest (t)-1) The global historical optimal fitness values of the current iteration and the last iteration are respectively represented, s varies within a range of 0-1, and the smaller s is, the faster the evolution speed is. When s is always 1 after a certain number of iterations, it means that the algorithm stops evolving.
The dynamic inertia weight omega calculation formula is as follows:
ω=ω 0 -s a ω s ；
wherein omega is 0 For initial inertial weight coefficient, 1, a is usually taken as a positive integer to amplify the influence of the variation of population evolution coefficient s on inertial weight coefficient omega s For the population evolution coefficient sThe corresponding inertial weight coefficient. Omega has the value of omega 0 -ω s <ω<1。
It should be noted that, during actual operation of the motor, the rotor flux is not usually a fixed value, and is affected by factors such as temperature. Therefore, to avoid the influence of rotor flux variations on the position estimation, it is necessary to first apply to the rotor flux, stator resistance and the motord-qThe shaft inductance is identified on line.
S5, establishing a voltage equation of the motor under the condition that the motor current is a symmetrical three-phase sine wave, and acquiring a rotor position by calculating the motor rotating speed; the method specifically comprises the following steps:
s51, neglecting core saturation and eddy current and hysteresis loss of the motor, and establishing a stator voltage equation:
；
；
wherein,u d and u q is a rotation coordinate systemd-qVoltage component under axis, R s Is stator resistance L d And L q Is thatd-qShaft inductance, w e Is the rotor angular velocity, ψ f Is a rotor flux linkage;
s52, obtaining through PID control of the current inner loopu d And u q and (3) calculating back electromotive force:
e d =u d -R s ·i d +w e L q i q ；
e q = u q -R s ·i q -w e L d i d ；
in the formula e d And e q Is thatd-qBack emf component under the shaft.
S53, calculating the actual rotation speed of the motor, and obtaining the rotor position by integrating the rotation speed of the motor:
w r =e/ψ f ；
wherein e is the back electromotive force,。
s6, setting PI parameters by using the stator resistance and the inductance which are identified on line, wherein the calculation formula is as follows:
；
；
wherein K is pd 、K pq Proportional coefficients of d-axis and q-axis current loop controllers, R s Is stator resistance L d And L q Is thatd-qShaft inductance, K id 、K iq The d-axis and q-axis current loop controllers integrate coefficients, respectively.
S7, correcting the current reference value of the given speed through the acquired rotating speed of the motor and the acquired actual current value.
The expected current reference value is compared with the actual current value, the current error is calculated, the current reference value is regulated according to the rotating speed error of the motor through the PI controller, the output of the PI controller is taken as the correction quantity of the current reference value, and the current reference value is corrected by adopting addition and subtraction operation.
S8, calculating a corrected current reference valuei q 、i d Errors Wq and Wd between the two are input into the PI controller to obtain an output control voltage V q 、V d For V q 、V d Performing anti-PARK transformation to obtain V alpha and V beta;
Vα = V d ·cos(φ)- V q ·sin(φ)；
Vβ=V d ·sin(φ)+ V q ·cos(φ)；
wherein V is d 、V q Is the rotation coordinatesA voltage component of the system; vα, vβ are voltage components in the stationary coordinate system,φis the rotation angle.
S9, synthesizing a voltage space vector by using V alpha and V beta, inputting the voltage space vector into an SVPWM module for modulation, and outputting the coded values of the state duty ratios of the three half-bridges at the moment;
s10, controlling the MOS transistor switch of the three-phase inverter according to the output coding value, and driving the motor.
The invention can quickly estimate the electric angle to carry out closed-loop control; the torque and the magnetic flux can be independent; capable of providing a smooth torque over the entire speed range; a rated torque can be provided at a low speed; the dynamic process of acceleration and deceleration can be quickened; because the current waveform of the control output is a sine wave, the mechanical vibration caused by torque fluctuation can be effectively reduced, so that noise is reduced, efficiency is improved, and comfort is improved.
The present invention is not limited to the above embodiments, but is capable of modification and variation in detail, and other modifications and variations can be made by those skilled in the art without departing from the scope of the present invention.
Claims (10)
1. A closed loop non-inductive control method for a DC brushless motor is characterized in that: the method comprises the following steps:
s1, sampling three-phase current of a motor to obtain Iu, iv and Iw;
s2, sampling currents Iu, iv and Iw are subjected to Clark transformation to obtain Ialpha and Ibeta;
s3, performing Park conversion on the Ialpha and the Ibeta to obtaini q ，i d ；
S4, identifying initial values of the stator resistance and the rotor flux linkage under the condition of constant torque, then taking an identification result as a fixed value, carrying out online identification on the d-axis inductance and the q-axis inductance through a genetic particle swarm algorithm, and after the result is converged, identifying the stator resistance and the flux linkage by taking the identified d-axis inductance and q-axis inductance as fixed values;
s5, establishing a voltage equation of the motor under the condition that the motor current is a symmetrical three-phase sine wave, and acquiring a rotor position by calculating the motor rotating speed;
s6, setting PI parameters by utilizing the stator resistance and the inductance which are identified on line;
s7, correcting a current reference value of a given speed through the acquired rotating speed of the motor and the acquired actual current value;
s8, calculating a corrected current reference valuei q 、i d Errors Wq and Wd between the two are input into the PI controller to obtain an output control voltage V q 、V d For V q 、V d Performing anti-PARK transformation to obtain V alpha and V beta;
s9, synthesizing a voltage space vector by using V alpha and V beta, inputting the voltage space vector into an SVPWM module for modulation, and outputting the coded values of the state duty ratios of the three half-bridges at the current moment;
s10, controlling the MOS transistor switch of the three-phase inverter according to the output coding value, and driving the motor.
2. The method for closed loop non-inductive control of a brushless dc motor as claimed in claim 1, wherein: in the step S2, the formula of Clark transformation is:
Iα=Iu；
；
Iu+Iv+Iw=0；
wherein Iu, iv, iw are current values in a three-phase 120-degree coordinate system; iα, iβ are current components in the stationary coordinate system.
3. The method for closed loop non-inductive control of a brushless dc motor as claimed in claim 1, wherein: in the step S3, the Park transformation formula is:
i d = Iα·cos(φ)+ Iβ·sin(φ)；
i q = -Iα·sin(φ)+ Iβ·cos(φ)；
in the method, in the process of the invention,i d ，i q is a rotating coordinate systemd-qAn off-axis current component;φis the rotation angle.
4. The method for closed loop non-inductive control of a brushless dc motor as claimed in claim 1, wherein: in the step S4, the parameter identification specifically includes the following steps:
s41, firstly, identifying initial values of stator resistance and rotor flux linkage, and constructing under constant torquei d =0 sumi d Not equal to 0:
；
wherein, psi is f0 Is thati d Permanent magnet flux linkage at time of =0,i q0 is thati d Q-axis current when=0,u q0 is thati d Q-axis voltage at=0, R s Is the stator resistance, w e Is the angular velocity of the rotor and,u d and u q respectively isi d The voltages of d-axis and q-axis are not equal to 0,i d andi q respectively isi d Current of d-axis and q-axis when not equal to 0;
s42, identifying initial values of permanent magnet flux linkage and stator resistance, and identifying d-axis inductance and q-axis inductance on line by adopting a genetic particle swarm algorithm:
generating chaotic particles based on chaotic mapping, combining the chaotic particles with the result of the previous parameter identification to generate an initialization population, and calculating the fitness value of each particle;
determining initial values of the historical optimal position and the global historical optimal position of the individual according to a calculation result of the particle fitness value in the initial population;
calculating a population evolution coefficient s and a dynamic inertia weight omega;
updating the speed vector and the position vector of each particle in the population according to the speed and position updating mode;
calculating the fitness value of each particle, and updating the individual historical optimal position and the global historical optimal position according to the fitness value;
if the convergence condition is met or the maximum iteration number is reached, outputting a global historical optimal position, and ending the algorithm; otherwise, the population evolution coefficient s and the dynamic inertia weight omega are recalculated and continuously executed according to the steps.
5. The method for closed loop non-inductive control of a brushless dc motor as claimed in claim 4, wherein: in the step S42, the calculation formula of the population evolution coefficient S is as follows:
；
wherein zbest (t) and zbest (t)-1) And respectively representing global historical optimal fitness values of the current iteration and the last iteration, wherein s varies within a range of 0-1.
6. The method for closed loop non-inductive control of a brushless dc motor as claimed in claim 5, wherein: in the step S42, dynamic inertial weightωThe calculation formula is as follows:
ω=ω 0 -s a ω s ；
wherein omega is 0 As a result of the initial inertial weight coefficient,ais a positive integer for amplifying the influence of the variation of the population evolution coefficient s on the inertia weight coefficient omega s The inertia weight coefficient corresponding to the population evolution coefficient s.
7. The method for closed loop non-inductive control of a brushless dc motor as claimed in claim 6, wherein: in the step S42, the range of the dynamic inertia weight ω is:
ω 0 -ω s <ω<1。
8. the method for closed loop non-inductive control of a brushless dc motor as claimed in claim 1, wherein: in the step S5, calculating the rotational speed of the motor to obtain the rotor position includes the following steps:
s51, neglecting core saturation and eddy current and hysteresis loss of the motor, and establishing a stator voltage equation:
；
；
wherein,u d and u q is a rotation coordinate systemd-qVoltage component under axis, R s Is stator resistance L d And L q Is thatd-qShaft inductance, w e Is the rotor angular velocity, ψ f Is a rotor flux linkage;
s52, obtaining through PID control of the current inner loopu d Andu q and (3) calculating back electromotive force:
e d =u d -R s ·i d +w e L q i q ；
e q = u q -R s ·i q -w e L d i d ；
in the formula e d And e q Is thatd-qA back EMF component under the shaft;
s53, calculating the actual rotation speed of the motor, and obtaining the rotor position by integrating the rotation speed of the motor:
w r =e/ψ f ；
wherein e is the back electromotive force, 。
9. the method for closed loop non-inductive control of a brushless dc motor as claimed in claim 1, wherein: in the step S6, the formula for PI parameter tuning is:
；
；
wherein K is pd 、K pq Proportional coefficients of d-axis and q-axis current loop controllers, R s Is stator resistance L d And L q Is thatd-qShaft inductance, K id 、K iq The d-axis and q-axis current loop controllers integrate coefficients, respectively.
10. The method for closed loop non-inductive control of a brushless dc motor as claimed in claim 1, wherein: in the step S8, the inverse PARK transformation formula is:
Vα = V d ·cos(φ)- V q ·sin(φ)；
Vβ=V d ·sin(φ)+ V q ·cos(φ)；
wherein V is d 、V q Is the voltage component in the rotating coordinate system; vα, vβ are voltage components in the stationary coordinate system,φis the rotation angle.
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