CN112953329B - Copper consumption minimum control system and method for non-salient pole type hybrid excitation motor - Google Patents
Copper consumption minimum control system and method for non-salient pole type hybrid excitation motor Download PDFInfo
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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
- H02P21/0017—Model reference adaptation, e.g. MRAS or MRAC, useful for control or parameter estimation
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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
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/16—Estimation of constants, e.g. the rotor time constant
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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
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/20—Estimation of torque
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- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
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Abstract
The invention discloses the field of motor controlIn the control system and the method, the feedback rotating speed is used as the first input of a torque observation module, the given rotating speed is used as the second input of the torque observation module, and the output of the torque observation module is a set torque value T eg Given value of torque T eg As the input of the copper consumption minimum current distribution module, the q-axis current given value i is output after being processed qg With given value of exciting current i fg (ii) a The torque observation module designed by adopting the active disturbance rejection control idea does not depend on a specific motor parameter model, can estimate the required electromagnetic torque only according to the error between the given rotating speed and the feedback rotating speed, takes the minimum copper consumption as a target, takes the given torque as an equality constraint condition, adopts a sequence quadratic programming algorithm to distribute the problem to solve the optimal solution, avoids the problem that the traditional Newton-Lagrange extreme value solving problem can cause unstable numerical value in the iteration process, and realizes the purpose of the minimum copper consumption current distribution of the motor.
Description
Technical Field
The invention belongs to the field of motor control, and particularly relates to a control system and a control method for minimizing copper consumption of a non-salient pole type hybrid excitation motor, which are suitable for electric automobiles.
Background
The non-salient pole type hybrid excitation motor is a novel motor with high torque density and wide speed regulation range, and has wide application prospect in the field of electric automobiles. Because a set of excitation winding is introduced on the basis of the traditional permanent magnet synchronous motor, the non-salient pole type hybrid excitation motor has the problem that armature current and excitation current work cooperatively. In order to solve the problem, a hybrid excitation synchronous motor torque estimation method is proposed in the document with chinese patent publication No. CN111697890A, a given dq axis current and an excitation current are obtained by a table lookup method according to a given target torque, but the table lookup method does not relate to how to determine the given target torque, and the table lookup method depends on a large amount of simulation data. The document with chinese patent publication No. CN105281632A proposes a current coordination control method for a hybrid excitation motor, which obtains multiple sets of data by calculating output mechanical power and mechanical rotation speed, where each set of data includes three variables, namely armature current, internal power factor angle, and excitation current, then calculates electromagnetic loss of each set of data, and selects a set with the smallest loss. The document with chinese patent publication No. CN103401506A proposes a method for controlling direct torque of a non-salient pole type hybrid excitation motor for an electric vehicle, which calculates a given torque according to a given rotation speed and a feedback rotation speed, but does not relate to how to calculate the given torque, because how to obtain the given torque is a crucial step as an equality constraint condition of current distribution, and the proposed control strategy does not consider the problem of copper consumption of the motor. Although the problem of motor loss is considered, the problem of extreme value calculation by using a mathematical method of Newton-Lagrange extreme value calculation has the defects of large calculated amount, complex calculation and unstable numerical value in an iterative solution process.
Disclosure of Invention
The invention aims to provide a system and a method for controlling the minimum copper loss of a non-salient pole type hybrid excitation motor in order to solve the problems that the given torque in the control strategy of the non-salient pole type hybrid excitation motor is unknown, the copper loss and the current distribution of the motor are not considered, and the algorithm is complex.
In order to achieve the purpose, the technical scheme of the minimum control system for the copper consumption of the non-salient pole type hybrid excitation motor is as follows: three-phase current i of non-salient pole type hybrid excitation motor a 、i b 、i c Inputting the current feedback value into a first coordinate transformation module, and transforming the current feedback value into a dq-axis current feedback value i through coordinate transformation df 、i qf Speed n of feedback line of non-salient pole type mixed excitation motor f Input into a speed conversion module to be converted into a feedback rotating speed w f Feedback of the rotational speed w f As a first input to the torque monitoring module, a given rotational speed w g As a second input of the torque monitoring module, the torque monitoring module outputs a given torque value T eg Given value of torque T eg Used as the input of the copper loss minimum current distribution module, and outputs a q-axis current given value i after being processed qg With given value of exciting current i fg (ii) a The given value of q-axis current i qg And q-axis current feedback value i qf The q-axis current difference obtained by difference is input into a first PI regulating module, and q-axis given voltage u is obtained through PI regulation qg (ii) a The d-axis current given value i qg And d-axis current feedback value i df D-axis current difference obtained by difference is input into a second PI regulation module, and d-axis given voltage u is obtained through PI regulation dg (ii) a The d-axis given voltage u dg And q-axis given voltage u qg The output end of the second coordinate transformation module is sequentially connected with the SVPWM modulation module, the armature circuit power transformation module and the non-salient pole type hybrid excitation motor in series; output exciting current feedback value i of non-salient pole type mixed excitation motor ff Feedback value of exciting current i ff With said given value of exciting current i fg The difference value of the exciting current obtained by difference is input into a third PI regulating module, and the given value u of the exciting voltage is obtained by PI regulation fg Given value u of excitation voltage fg The PWM modulation module generates PWM wave as the input of the excitation circuit power conversion module, and the excitation circuit power conversion module outputs excitation voltage u f A non-salient pole type hybrid excitation motor is provided.
Furthermore, the torque observation module consists of a linear control rate module, a state observer module and a limiting module, and the given rotating speed w g With feedback speed w f Is estimated value Z T1 Difference of rotation speed e T The total system disturbance estimated value Z output by the state observer module is used as the first input of the linear control rate module T2 As a second input to the linear control rate module, the linear control rate module outputs an initial estimate of the given torque T eg0 (ii) a The feedback rotating speed w f And given initial torque estimate T eg0 As two inputs to the state observer module, the state observer module output w f Is estimated value Z T1 And the total disturbance estimate Z of the system T2 (ii) a The amplitude limiting module is used for setting the initial estimated value T of the given torque eg0 Amplitude limiting to obtain the given torque value T eg 。
Furthermore, the copper consumption minimum current distribution module consists of a copper consumption calculation module, a torque calculation module, a subproblem conversion module and a subproblem iteration module, wherein the input of the copper consumption calculation module is the n-th iteration value i of the q-axis component of the armature current output by the subproblem iteration module qn And the nth iteration value i of the exciting current fn The output is the copper loss P of the nth iteration cu (i n ) The nth iteration value i of the q-axis component of the armature current qn And the nth iteration value i of the exciting current fn As two inputs to a torque calculation module, said given torque value T eg As a third input to the torque calculation module, the torque calculation module outputs the torque T of the nth iteration eg (i n ) (ii) a The copper loss P cu (i n ) And torque T eg (i n ) As two inputs to the subproblem transformation module, the subproblem transformation module transforms the sequence quadratic programming subproblem Q 3 And input into a sub-problem iteration module which performs sub-problem Q 3 Solving and outputting the optimal solution as (i) qg ,i fg )。
Furthermore, the subproblem conversion module is formed by connecting an equality constraint optimization problem conversion module, a Newton-Lagrange extreme value problem conversion module and a quadratic programming problem conversion module in series in sequence, and the equality constraint problem module uses copper consumption P cu (i n ) As an objective function, with a torque T eg (i n ) As an input to the constraint condition of the equation,at the moment of satisfying the torque T eg (i n ) Under the condition of calculating copper consumption P cu (i n ) The problem of minima is converted into an optimization problem Q that takes into account pure equality constraints 1 Optimization problem Q 1 Inputting the optimization problem Q into a Newton-Lagrange extremum problem conversion module 1 Conversion to newton-lagrange extremum problem Q 2 And inputting the data into a quadratic programming problem conversion module which solves the extreme value problem Q of Newton-Lagrange 2 Convert to said sequence quadratic programming subproblem Q 3
The technical scheme of the control method of the non-salient pole type hybrid excitation motor copper loss minimum control system comprises the following steps:
step 1: the state observer module is designed to expand a state observer into
e is Z T1 And w f An error of (2); beta is a T1 、β T2 Is the gain coefficient of the state observer, b is the compensation coefficient;
step 2: the discretized extended state observer is
h is the sampling period, w f (k) Is the feedback speed at time k, Z T1 (k) Is an estimate of the feedback speed at time k, Z T1 (k + 1) is a feedback rotation speed estimated value at the time of k +1, Z T2 (k) Is the total disturbance estimate of the system at time k, and e (k) is time Z at time k T1 (k) And w f (k) Error of (1), T eg0 (k) Is an initial estimate of the torque given at time k, Z T2 (k + 1) is the total disturbance estimate at time k +1, Z T1 (k + 1) as the feedback rotation speed w f State estimator Z T1 Output, Z T2 (k + 1) as the total disturbance estimate Z of the system T2 Outputting;
and 3, step 3: the amplitude limiting module initially estimates the value T for a given torque eg0 Comparing and judging when the electromagnetic torque estimated value T eg0 In the motor load range [ T ] min ，T max ]Internal time, T eg ＝T eg0 (ii) a When T is eg0 ≥T max ，T eg ＝T max (ii) a When T is eg0 ≤T min ，T eg ＝T min ，T max Is the limit value of the carrying capacity T when the motor rotates forwards min Is the limit value of the carrying capacity when the motor rotates reversely.
The technical scheme of the control method of the non-salient pole type hybrid excitation motor copper loss minimum control system comprises the following steps:
step 1): equality constraint problem model copper consumption P cu (i n ) As an objective function, with a torque T eg (i n ) As an equality constraint, an optimization problem Q is obtained 1 Comprises the following steps:
step 2): newton-Lagrange extreme value problem conversion module simplifies optimization problem Q 1 To obtain an optimization problem Q 1 Lagrange function L (i) n ,u n )＝P cu (i n )-u n H eq (i n )，u n Is the nth iteration Lagrangian multiplier, H eq (i n ) Is a torque-dependent constraint function;
step 3): solving the copper loss P cu (i n ) Gradient of (2)
And second derivative
And a constraint function H eq (i n ) Gradient of (2)
And second derivative
Thereby obtaining the Lagrangian function L (i) n ,u n ) First and second order derivatives ofThe number of the first and second groups is counted,
step 4): given an iteration point Z n ＝(i n ,u n ) Solving the problem of extreme value Q of Newton-Lagrange 2 Is composed of
The iteration points satisfy: z is a linear or branched member n+1 (i n+1 ,u n+1 )＝Z n (i n ,u n )+P n (d n ,v n )，d n Represents the current i n Micro increment of v n Representing lagrange multipliers u n In micro increments.
The invention has the beneficial effects that:
1) The torque observation module designed by adopting the active disturbance rejection control idea can estimate the required electromagnetic torque only according to the error between the given rotating speed and the feedback rotating speed without depending on a specific motor parameter model.
2) The method takes the minimum copper loss as a target, takes the given torque as an equality constraint condition, adopts a sequential quadratic programming algorithm to calculate the optimal solution of the q-axis current and the exciting current, and effectively realizes the purpose of the minimum copper loss current distribution of the motor.
3) The method adopts the sequential quadratic programming algorithm to solve the current distribution problem, effectively avoids the situation that the numerical value is unstable in the iteration process in the traditional Newton-Lagrange extremum solving problem, and reduces the iteration times and the calculated amount due to higher convergence speed in the iteration process compared with the Newton-Lagrange extremum solving algorithm.
3) The PI regulator of the rotating speed ring is replaced by the torque observation module, so that the given electromagnetic torque can be estimated, and the total disturbance Z of the system can be estimated by the state observer T2 Therefore, the anti-interference capability of the system is improved, and the robustness of the system is enhanced.
4) The torque observation method based on the active disturbance rejection control technology and the current distribution method based on the sequence quadratic programming are simultaneously applied to the non-salient pole type hybrid excitation motor control strategy, and the defects of fuzzy torque observation and unstable current distribution iteration process in the traditional non-salient pole type hybrid excitation motor control scheme are overcome.
Drawings
In order that the invention may be more fully understood, reference is now made to the following detailed description of the invention taken in conjunction with the accompanying drawings in which:
fig. 1 is a structural block diagram of a copper consumption minimum control system of a non-salient pole type hybrid excitation motor according to the invention;
fig. 2 is a block diagram of the structure of the torque observation module 4 in fig. 1;
fig. 3 is a block diagram of the minimum copper current distribution module 10 in fig. 1;
fig. 4 is a block diagram of the sub-problem conversion module 7 in fig. 3;
FIG. 5 is a flow chart of an algorithm implementation of the subproblem iteration module 8 of FIG. 3;
in the figure: 1. a linear control rate module; 2. a state observer module; 3. an amplitude limiting module; 4. a torque observation module; 5. a copper consumption calculation module; 6. a torque calculation module; 7. a sub-problem conversion module; 8. a sub-problem iteration module; 9. a sequence quadratic programming module; 10. a copper consumption minimum current distribution module; 11. an equality constraint optimization problem conversion module; 12. a Newton-Lagrange extreme value problem conversion module; 13. a quadratic programming problem conversion module; 14. an armature circuit power conversion module; 15. an excitation circuit power conversion module; a PWM modulation module; 17. a speed conversion module; 18. a first PI regulation module; 19. a second PI regulation module; 20. a first coordinate transformation module; 21. a non-salient pole type hybrid excitation motor; 22. a second coordinate transformation module; 23, SVPWM module; 24. and the third PI regulation module.
Detailed Description
Referring to fig. 1, the minimum copper loss control system for a non-salient pole type hybrid excitation motor of the present invention is connected to a non-salient pole type hybrid excitation motor 21, and includes a PI regulation module, a coordinate transformation module, a speed conversion module 17, an SVPWM modulation module 23, an armature circuit power transformation module 14, and an excitation circuit power transformation module 15.
Feedback line speed n of non-salient pole type hybrid excitation motor 21 f Input into a speed conversion module 17, and converted into a feedback rotating speed w by the speed conversion module 17 f Feedback of the rotational speed w f As a first input to the torque observer module 4, a given rotational speed w g The output end of the torque observation module 4 is connected with a copper consumption minimum current distribution module 10 as a second input of the torque observation module 4, and the torque observation module 4 outputs a given torque value T eg . Given torque value T eg Used as the input of the copper consumption minimum current distribution module 10, and processed to output the given value i of the q-axis current qg With given value of exciting current i fg 。
Three-phase current i for detecting non-salient pole type hybrid excitation motor 21 a 、i b 、i c And apply three-phase current i a 、i b 、i c Input into a first coordinate transformation module 20, and transformed into dq-axis current feedback value i through coordinate transformation df 、i qf 。
Setting q-axis current to be a given value i qg And q-axis current feedback value i qf The difference is made and the resulting q-axis current difference is input to the first PI regulation module 18. Obtaining a given voltage u of a q axis through PI regulation qg 。
D-axis current set value i qg And d-axis current feedback value i df The difference is made, the obtained d-axis current difference value is input into a second PI regulation module 19, and d-axis given voltage u is obtained through PI regulation dg . Because the motor is a non-salient pole motor, the influence of d-axis current is ignored, so i is adopted qg Control strategy of = 0.
The output ends of the first PI regulation module 18 and the second PI regulation module 19 are connected with the input end of the second coordinate transformation module 22, and dq-axis given voltage u dg 、u qg Inputting into a second coordinate transformation module 22, transforming into α β axis voltage u α 、u β . The output end of the second coordinate transformation module 22 is sequentially connected in series with the SVPWM modulation module 23, the armature circuit power transformation module 14 and the non-salient pole type hybrid excitation motor 21. Alpha beta axis voltage u α 、u β The input SVPWM modulation module 23, the SVPWM modulation module 23 output SVPWM wave as the input signal of the armature circuit power conversion module 14, the armature circuit power conversion module 14 output three-phase armature voltage u a 、u b 、u c Driving non-salient poleHybrid excitation motor 21.
Non salient pole type mixed excitation motor 21 outputs excitation current feedback value i ff Given value i of the exciting current output by the minimum current distribution module 10 fg With the excitation current feedback value i ff Performing difference, inputting the obtained excitation current difference value into a third PI regulation module 24, and performing PI regulation to obtain an excitation voltage given value u fg . The output end of the third PI regulation module 24 is sequentially connected with the PWM modulation module 16, the excitation circuit power conversion module 15 and the non-salient pole type hybrid excitation motor, and the given value u of the excitation voltage fg The PWM wave is inputted to a PWM modulation module 16, the generated PWM wave is inputted to an exciting circuit power conversion module 15, and the exciting circuit power conversion module 15 outputs an exciting voltage u f The magnetic field of the non-salient pole type hybrid excitation motor 21 is modulated.
Referring to fig. 2, based on the active disturbance rejection control technology, the torque observation module 4 is composed of a linear control rate module 1, a state observer module 2, and a limiting module 3. Given rotational speed w g Feedback speed w output by the state observer module 2 f Is estimated value Z T1 Making difference to obtain rotation speed difference e T ＝w g -Z T1 As a first input to the linear control rate module 1, the estimate Z of the total disturbance of the system output by the state observer module 2 T2 As a second input to the linear control rate module 1, the linear control rate module 1 provides an initial estimate T of torque eg0 Outputting as a compensation amount:
T eg0 ＝k p e T +z T2 (1)
wherein k is p Is a proportional gain coefficient, obtained by the state observer module 2.
Feedback speed w f As a first input to the state observer module 2, an initial estimate of torque T is given eg0 As a second input to the state observer module 2, the state observer module 2 outputs w f Is estimated value Z T1 And the total disturbance estimate Z of the system T2 . The control process of the state observer module 2 is as follows:
for the convenience of system design, the mechanical motion equation (2) of the non-salient pole type hybrid excitation motor 1 is rewritten into a first-order system expression (3):
in formulae (2) to (3), T L Is the load torque; j is the moment of inertia; b is the coefficient of friction.
For a first order system as shown in equation (3), let-B ω f the/J is regarded as internal disturbance; -T L treating/J as external disturbance; - (B omega) f +T L ) the/J is regarded as the total disturbance; can expand to a new state x 2 ＝-(Bω f +T L ) J; the original system formula (3) is changed into:
in the formula, x 2 Is a new state, considered as total disturbance; y is the output of the system expressed by equation (4) and is equal to the feedback rotation speed w f 。
For the system represented by equation (4), the following extended state observer is designed:
in which e is Z T1 And w f An error of (2); beta is a T1 、β T2 Is the gain coefficient of the state observer, related to the observer system bandwidth; and b is a compensation coefficient and is related to the controlled object model.
To facilitate the program implementation of the algorithm, equation (5) needs to be discretized, and the corresponding discrete form is:
in the formulas (5) to (6), h is a sampling period; after discretization, w f (k) The rotating speed is fed back at the moment k; z is a linear or branched member T1 (k) Is an estimated value of the feedback rotating speed at the k moment; z T1 (k + 1) is a feedback rotation speed estimation value at the k +1 moment; z is a linear or branched member T2 (k) Is the total disturbance estimated value of the system at the moment k; e (k) is time k Z T1 (k) And w f (k) An error of (2); t is eg0 (k) Setting an initial estimated value of torque at the moment k; z T2 (k + 1) is the total disturbance estimate at time k + 1; final Z T1 (k + 1) as the feedback rotation speed w f State estimator Z T1 Output, Z T2 (k + 1) as the total disturbance estimate Z of the system T2 And (6) outputting.
The amplitude limiting module 3 initially estimates the value T for the given torque eg0 Carrying out amplitude limiting treatment to obtain a final torque given value T eg . To prevent setting of the initial estimate T of torque eg0 Out of the range of motor load min ，T max ]It needs to be subjected to clipping processing. Wherein, T max Indicating a limit value of the load capacity, T, of the motor in forward rotation min Indicating the load capacity limit when the motor is rotating in reverse. Giving an initial estimated value T of torque eg0 Inputting the torque into a limiting module 3, and outputting a final torque set value T by the limiting module 3 eg ：
Initial estimation value T of given torque eg0 After the comparison and judgment of the amplitude limiting module 3, the final torque set value T is output eg . When electromagnetic torque estimated value T eg0 In the motor load range, T eg ＝T eg0 (ii) a When T is eg0 ≥T max ，T eg ＝T max (ii) a When T is eg0 ≤T min ，T eg ＝T min . Thus, the torque module 4 can effectively be based on a given rotational speed w g With feedback speed w f Given value of output torque T eg 。
Referring to fig. 3, the copper consumption minimum current distribution module 10 is shown asThe system comprises a copper consumption calculation module 5, a torque calculation module 6 and a sequence quadratic programming module 9, wherein the sequence quadratic programming module 9 is formed by connecting a sub-problem conversion module 7 and a sub-problem iteration module 8 in series. Wherein, the copper consumption calculation module 5 inputs the nth iteration value i of the q-axis component of the armature current fed back by the output of the subproblem iteration module 8 qn And the nth iteration value i of the exciting current fn The output is the copper loss P of the nth iteration cu (i n )：
In the formula, R s Is the armature winding resistance; r f Is the excitation winding resistance; i.e. i n ＝(i qn ,i fn ) Wherein i qn Is the nth iteration value of the q-axis component of the armature current; i.e. i fn Is the nth iteration value of the exciting current; p is cu (i n ) Is the copper loss for the nth iteration.
Copper loss P cu (i n ) As an objective function into the sub-problem transformation module 7 as a first input to the sub-problem transformation module 7.
Meanwhile, the nth iteration value i of the q-axis component of the armature current qn And the nth iteration value i of the exciting current fn As a first and a second input of the torque calculation module 6, a given torque value T eg As a third input of the torque calculation module 6, the torque T of the nth iteration is calculated eg (i n ) Is that;
in the formula, P is the pole number of the motor rotor;
indicating the permanent magnet flux linkage of the motor, L f Is the field winding inductance value.
Torque T eg (i n ) Is inputted into the subproblem conversion module 7 as a subproblem conversion module7, respectively.
The subproblem conversion module 7 receives the copper consumption P cu (i n ) And torque T eg (i n ) Converting the copper consumption minimum current distribution problem into a sequence quadratic programming subproblem Q 3 Sequence quadratic programming subproblem Q 3 The input is input into a subproblem iteration module 8, and the subproblem iteration module 8 processes the subproblem Q 3 And (5) carrying out iterative solution until an optimal solution (i) meeting the minimum copper loss is found qn ,i fn ) And assigns it as the final given current value to (i) qg ,i fg )，i qg As a given value of q-axis current, i fg As excitation current set value, optimal solution (i) qn ,i fn ) Output by the copper consumption minimum current distribution module 10.
Referring to fig. 4, the sub-problem transformation module 7 is formed by sequentially connecting an equality constraint optimization problem transformation module 11, a newton-lagrangian extreme value problem transformation module 12, and a quadratic programming problem transformation module 13 in series. Wherein the equation constraint problem module 11 is to use the copper loss P cu (i n ) As an objective function, with a torque T eg (i n ) As a constraint of equation, the torque T will be satisfied eg (i n ) Under the condition of calculating copper consumption P cu (i n ) The problem of minima is converted into an optimization problem Q that takes into account pure equality constraints 1 Optimization problem Q 1 The expression is as follows:
in the formula, min represents the minimum value, and st represents the limit; expression (10) shows the satisfaction of T eg (i n )-T eg Copper loss P of =0 constraint cu (i n ) Minimum value of (2), i.e. finding copper consumption P cu (i n ) Current sharing at minimum. Therefore, i output by the minimum copper consumption current distribution module 10 in the invention qg And i fg Not only can satisfy T eg And is the optimal solution for minimizing the copper loss of the motor.
Because the constraint condition T is satisfied eg (i n )-T eg Current (i) =0 qn ,i fn ) There are many combinations, so the invention uses the sequence quadratic programming algorithm to solve a group (i) qg ,i fg ) So that the current distribution satisfies both T in the formula (10) eg (i n )-T eg Torque request of =0, and the torque of equation (9) can be adjusted
The copper consumption is minimum, so that the minimum control of the copper consumption of the non-salient pole type hybrid excitation motor 1 is realized.
Optimization problem Q 1 Inputting the data into a Newton-Lagrange extremum problem transformation module 12, the Newton-Lagrange extremum problem transformation module 12 will optimize the problem Q 1 Conversion to newton-lagrange extremum problem Q 2 . Newton-lagrange extremum problem Q 2 Inputting the input into a quadratic programming problem conversion module 13, the quadratic programming problem conversion module 13 solving the extreme value problem Q of Newton-Lagrange 2 Conversion to sequential quadratic programming subproblem Q 3 。Q 2 To Q 3 The specific implementation method is as follows:
step 1: newton-lagrange extreme problem transformation module 12 simplifies problem Q 1 1.5R, 1 S Is marked as C 1 、R f Is marked as C 2 、
Notation C 3 、1.5PL f Is marked as C 4 And the formula (10) is briefly described as follows:
step 2: write the Lagrangian function L (i) of the problem (11) qn ,i fn U), the function is as follows:
in the formula u n Is the nth iteration lagrange multiplier; to facilitate problem analysis, equation (12) can be simplified as:
L(i n ,u n )＝P cu (i n )-u n H eq (i n ) (13)
wherein:
H eq (i n )＝C 3 i qn +C 4 i fn i qn -T eg (14)
in the formula, H eq (i n ) Representing a constraint function related to torque.
And 3, step 3: copper consumption P cu (i n ) As an objective function, solving the gradient of the objective function as:
in the formula (I), the compound is shown in the specification,
represents P cu (i n ) A gradient of (a); target function P cu (i) Are respectively corresponding to the gradient of i q And i f The derivation is carried out, and the derivation is carried out,
representing the target function P cu (i qn ) To i qn The first-order derivation is carried out,
representing the target function P cu (i qn ) To i fn A first derivative is performed.
Solving an objective function P cu (i n ) Hesse array of (c):
in the formula (I), the compound is shown in the specification,
represents P cu (i n ) The second derivative of (a) is,
represents P cu (i n ) To i is to qn The second derivation is carried out to obtain the second derivative,
represents P cu (i n ) First to i qn Derivative and then pair i fn The derivation is carried out by taking the derivative,
is represented by P cu (i n ) To i fn The second derivation is carried out to obtain the second derivative,
represents P cu (i n ) First to i fn Derivative and then pair i qn And (6) derivation.
Solving a constraint function H eq (i n ) Gradient of (a):
in the formula (I), the compound is shown in the specification,
representing the first derivative of the constraint function, again for i separately qn And i fn The derivation is carried out, and the derivation is carried out,
representing a constraint function H eq To i qn The derivation is carried out, and the derivation is carried out,
representing a constraint function H eq To i fn And (6) carrying out derivation.
Solving a constraint function H eq (i n H of (A) to (B)An ese matrix:
in the formula (I), the compound is shown in the specification,
is represented by H eq (i n ) The second derivative of (a) is,
is represented by H eq (i n ) To i is to qn The second derivation is carried out to obtain the second derivative,
represents H eq (i n ) First to i qn Derivative and then pair i fn The derivation is carried out by the derivation,
is represented by H eq (i n ) To i fn The second derivation is carried out to obtain the second derivative,
is represented by H eq (i n ) First to i fn Derivative and then pair i qn And (6) derivation.
Solving the Lagrangian function L (i) n U) Jacobi matrix:
in the formula (I), the compound is shown in the specification,
representing the Lagrangian function L (i, u) n ) The first derivative of (a) needs to be respectively applied to i qn 、i fn 、u n Three variables are derived. Wherein
Show pulling oneLanri function L (i) n ,u n ) For current i n Making a derivative including L (i) n V) pairs of i qn Conducting derivation, L (i) n ,u n ) To i fn And (6) carrying out derivation.
Represents the Langeri function L (i) n ,u n ) The lagrange multiplier u is derived.
Solving the Lagrangian function L (i, u) n ) Hesse matrix of (1):
wherein:
in the formula (I), the compound is shown in the specification,
representing the Lagrangian function L (i) n ,u n ) The second derivative of (a); w (i) n ,u n ) Representing the Lagrangian function L (i) n ,u n ) For current i n Including the objective function P cu (i n ) Second derivative of (2)
And second derivative of the constraint function
To represent
Is transferred to
And step 3: combining equations (19) and (20), and giving an iteration point Z n ＝(i n ,u n ) Solving the problem of extreme value Q of Newton-Lagrange 2 The following:
and the iteration points satisfy:
Z n+1 (i n+1 ,u n+1 )＝Z n (i n ,u n )+P n (d n ,v n ) (23)
in the formula (d) n Represents the current i n Micro increment of v n Representing lagrange multipliers u n Is measured in increments of (a).
Problem of extreme value Q due to Newton-Lagrange 2 The values are not stable during the iteration process, so Q needs to be further adjusted 2 Conversion to strict convex quadratic programming problem Q 3 The implementation process of the quadratic programming problem conversion module 13 is as follows:
step 1: using positive definite matrix B n (i n ,u n ) In place of Z n (i n ,u n ) Wherein the parameter τ>0 and less than a set value, B n (i n ,u n ) Satisfies the following conditions:
step 2: by bringing formula (24) into formula (22):
in the formula, t n Satisfies the following conditions:
an essential condition for the establishment of the formula (26) is d n Satisfies the following conditions:
the equation described by equation (27) is the quadratic programming problem Q 3 Wherein q is n (d n ) Is about the current increment d n As a function of (c). The sub-problem Q3 is to find d satisfying the torque constraint condition k Is measured. If d is k Is small enough and smaller than the set value, meets the precision requirement, and then the corresponding (i) is obtained qn ,i fn ) Is an optimal solution that satisfies both the torque T eg (i n ) The requirement can also ensure that the copper consumption of the motor is P cu (i n ) And if not, re-iterating according to the flow shown in fig. 4 until an optimal solution is found.
Quadratic programming problem Q 3 The input is input into a subproblem iteration module 8, and the subproblem iteration module 8 represents a quadratic programming problem Q according to formula (27) 3 The calculation is performed, as shown in fig. 5, with the following specific steps:
step 1: given an initial value, i 0 、u 0 τ, ρ, γ, ε wherein i 0 ＝(i q0 ,i f0 ) For the initial set value of the current, and the other parameters are parameters used in the subsequent iteration process, wherein 0<ρ<1、0<γ<1、0<ε<<1、0<τ<<1。
Step 2: calculating P (i) n ,u n ) If P (i) n ,u n )<And epsilon, stopping calculation, turning to the step 6, and otherwise, turning to the step 3.
Wherein the penalty function P (i) n ,u n ) Is composed of
And step 3: solving a two-sequence quadratic programming subproblem Q 3 To obtain d n ,d n Substitution of formula (25) to t n Order:
and 4, step 4: determine i descending search direction, let m n Is the smallest non-negative integer m that makes the following inequality true:
P(i n +ρ m d n ,u n +p m v n )≤(1-γρ m )P(i n ,u n ) (30)
and 5: put alpha n ＝ρ mn Let i n+1 ＝i n +α n d n ，u n+1 ＝u n +α n ν n Let n = n +1, go to step 1.
Step 6: output current (i) qn ,i fn ) The current is a current combination mode which satisfies the minimum copper loss, i qn Given value i as armature current q-axis component qg Output, will i fn As given component i of the excitation current fg And (6) outputting.
Referring to fig. 1, when the non-salient pole type hybrid excitation motor 1 performs the minimum copper loss control, the feedback linear velocity n of the motor f W is obtained by the speed conversion module 17 f The speed conversion module meets the following requirements:
feedback rotating speed w of non-salient pole type hybrid excitation motor 1 f With a given rotational speed w of the motor g As an input of the torque observation module 4, a final torque set value T is output eg 。T eg Inputting a copper loss minimum current distribution module 10 and outputting a q-axis current set value i qg With given value of exciting current i fg . Three-phase current i output by motor a 、i b 、i c A dq-axis current feedback value i is output through a first coordinate transformation module 20 df 、i qf While simultaneously outputting an exciting current feedback value i ff 。i qg And i qf Is input into the first PI regulation block 18 and outputs a q-axis given voltage u qg 。i dg And i df Is input into a second PI regulation module 19, outputs a d-axis given voltage u dg 。u qg And u dg Inputting the second coordinate transformation module 22 and outputting alpha and beta axis voltagesu α 、u β ；u α 、u β The input SVPWM modulation module 23 outputs SVPWM wave as the input signal of the armature circuit power conversion module 14, and the armature circuit power conversion module 14 outputs three-phase armature voltage u a 、u b 、u c The non-salient pole type hybrid excitation motor 21 is driven. i all right angle fg And i ff The error of the second PI regulation module 24 is output as an exciting current set value u fg 。u fg The output of the PWM modulation module 16 generates PWM wave as the exciting circuit power conversion module 15, and the exciting circuit power conversion module 15 outputs the exciting voltage u f The magnetic field of the non-salient pole type hybrid excitation motor 21 is modulated.
Claims (7)
1. A control system for minimizing copper consumption of non-salient pole type mixed excitation motor, three-phase current i of non-salient pole type mixed excitation motor a 、i b 、i c Input into a first coordinate transformation module (20) and transformed into a dq-axis current feedback value i through coordinate transformation df 、i qf Feedback line speed n of non-salient pole type hybrid excitation motor f Is input into a speed conversion module (17) and is converted into a feedback rotating speed w f Feedback of the rotational speed w f As a first input of the torque monitoring module (4), a predetermined rotational speed w is provided g As a second input to the torque monitoring module (4), characterized by: the torque observation module (4) outputs a given torque value T eg Given value of torque T eg Used as the input of a copper consumption minimum current distribution module (10) and processed to output a q-axis current set value i qg With given value of exciting current i fg (ii) a The given value of q-axis current i qg And q-axis current feedback value i qf The q-axis current difference obtained by the difference is input into a first PI regulation module (18) and is subjected to PI regulation to obtain a q-axis given voltage u qg (ii) a d-axis current set value i dg And d-axis current feedback value i df The d-axis current difference obtained by the difference is input into a second PI regulation module (19) and is regulated by a PI to obtain a d-axis given voltage u dg (ii) a The d-axis given voltage u dg And q-axis given voltage u qg Inputting the second coordinate transformation module (22), said second coordinate transformationThe output end of the switching module (22) is sequentially connected with the SVPWM modulation module (23), the armature circuit power conversion module (14) and the non-salient pole type hybrid excitation motor in series; output exciting current feedback value i of non-salient pole type hybrid excitation motor ff Feedback value of exciting current i ff With said given value of exciting current i fg The difference value of the exciting current obtained by difference is input into a third PI regulating module (24) and is regulated by PI to obtain the given value u of the exciting voltage fg Given value u of excitation voltage fg The PWM modulation module (16) generates PWM wave as the input of the excitation circuit power conversion module (15), and the excitation circuit power conversion module (15) outputs the excitation voltage u f Supplying a non-salient pole type hybrid excitation motor;
the torque observation module (4) consists of a linear control rate module (1), a state observer module (2) and an amplitude limiting module (3), and the given rotating speed w g With feedback speed w f Is estimated value Z T1 Difference of rotation speed e T The estimated value Z of the total system disturbance output by the state observer module (2) is used as a first input of the linear control rate module (1) T2 As a second input to the linear control rate module (1), the linear control rate module 1 outputs an initial estimate T of the given torque eg0 (ii) a The feedback rotating speed w f And given initial torque estimate T eg0 As two inputs to the state observer module (2), the state observer module (2) outputs w f Is estimated value Z T1 And the total disturbance estimate Z of the system T2 (ii) a Said limiter module (3) being adapted to determine an initial estimate T of said given torque eg0 Amplitude limiting to obtain the given torque value T eg ；
The copper consumption minimum current distribution module (10) consists of a copper consumption calculation module (5), a torque calculation module (6), a sub-problem conversion module (7) and a sub-problem iteration module (8), wherein the input of the copper consumption calculation module (5) is an nth iteration value i of an armature current q-axis component output by the sub-problem iteration module (8) qn And the nth iteration value i of the exciting current fn The output is the copper loss P of the nth iteration cu (i n ) The nth iteration value i of the q-axis component of the armature current qn And the nth iteration value i of the exciting current fn As a rotationTwo inputs of a moment calculation module (6), the given value of the torque T eg As a third input of the torque calculation module (6), the torque calculation module (6) outputs the torque T of the nth iteration eg (i n ) (ii) a The copper loss P cu (i n ) And torque T eg (i n ) As two inputs to the subproblem transformation module (7), the subproblem transformation module (7) transforms the sequential quadratic programming subproblem Q 3 And input into a sub-problem iteration module (8), and the sub-problem iteration module (8) plans a sub-problem Q for the sequence twice 3 Solving and outputting the optimal solution as (i) qg ,i fg )。
2. The system for controlling the minimum copper loss of the non-salient pole type hybrid excitation motor according to claim 1, is characterized in that: the subproblem conversion module (7) is formed by sequentially connecting an equality constraint optimization problem conversion module (11), a Newton-Lagrangian extreme value solving problem conversion module (12) and a quadratic programming problem conversion module (13) in series, and the equality constraint optimization problem conversion module (11) uses copper consumption P cu (i n ) As an objective function, with a torque T eg (i n ) As an input to the equality constraint condition, when the torque T is satisfied eg (i n ) Under the condition of calculating copper consumption P cu (i n ) The problem of minima is converted into an optimization problem Q that takes into account pure equality constraints 1 Optimization problem Q 1 Inputting the data into a Newton-Lagrange extremum problem conversion module (12), and enabling the Newton-Lagrange extremum problem conversion module (12) to optimize a problem Q 1 Conversion to newton-lagrange extremum problem Q 2 And input into a quadratic programming problem conversion module (13), and the quadratic programming problem conversion module (13) solves the extreme value problem Q of Newton-Lagrange 2 Convert to said sequence quadratic programming subproblem Q 3 。
3. The system for controlling the minimum copper loss of the non-salient pole type hybrid excitation motor according to claim 1, is characterized in that: the initial estimation value T of the given torque eg0 ＝k p e T +z T2 ，k p Is a proportional gain factor.
4. The system for controlling the minimum copper loss of the non-salient pole type hybrid excitation motor according to claim 1, is characterized in that: said copper loss
The torque of the nth iteration
R s Is the resistance of the armature winding, R f Is the resistance value of the field winding, i n ＝(i qn ,i fn ) And P is the number of poles of the motor rotor,
indicating the permanent magnet flux linkage of the motor, L f Is the field winding inductance value.
5. A control method of the copper loss minimum control system of the non-salient pole type hybrid excitation motor as claimed in claim 2, which is characterized by comprising the following steps:
step 1): the equality constraint optimization problem conversion module (11) uses the copper consumption P cu (i n ) As an objective function, with a torque T eg (i n ) As an equality constraint, get an optimization problem Q 1 Comprises the following steps:
step 2): a Newton-Lagrange extremum problem transformation module (12) simplifies the optimization problem Q 1 To obtain an optimization problem Q 1 Lagrange function L (i) n ,u n )＝P cu (i n )-u n H eq (i n )，u n Is the nth iteration Lagrangian multiplier, H eq (i n ) Is a torque-related constraint function;
and step 3): solving for copper loss P cu (i n ) Gradient of (2)
And second derivative
And a constraint function H eq (i n ) Gradient of (2)
And second derivative
Thereby obtaining the Lagrangian function L (i) n ,u n ) The first and second derivatives of the first and second,
and step 4): given iteration point Z n ＝(i n ,u n ) To obtain the Newton-Lagrange extremum problem Q 2 Is composed of
The iteration points satisfy: z is a linear or branched member n+1 (i n+1 ,u n+1 )＝Z n (i n ,u n )+P n (d n ,v n )，d n Represents the current i n Micro increment of v n Representing lagrange multipliers u n In micro increments.
6. The control method according to claim 5, wherein: in step 4), solving the extreme value problem Q of Newton-Lagrange 2 Conversion to sequential quadratic programming subproblem Q 3 Using positive definite matrix first
In place of Z n (i n ,u n ) Then according to formula
Deriving a sequence quadratic programming subproblem Q 3 The method comprises the following steps:
q n (d n ) Is about the current increment d n A function of (a); if d is k If the current is less than the set value, the corresponding current (i) is at the moment qn ,i fn ) Is the optimal solution.
7. The control method according to claim 6, wherein: sub-problem iteration module (8) plans sub-problem Q for sequence quadratic 3 The treatment method comprises the following specific steps:
step (1): given an initial value, i 0 、u 0 τ, ρ, γ, ε, where i 0 ＝(i q0 ,i f0 ) For the initial set value of the current, and the other parameters are used in the subsequent iteration process, wherein 0<ρ<1、0<γ<1、0<ε<<1、0<τ<<1；
Step (2): calculating a penalty function
If P (i) n ,u n )<E, stopping calculation, turning to the step (6), and otherwise, turning to the step (3);
and (3): solving a sequential quadratic programming subproblem Q 3 To obtain d n And t n Let us order
And (4): determine i descending search direction, let m n Is such that the inequality P (i) n +ρ m d n ,u n +p m v n )≤(1-γρ m )P(i n ,u n ) Minimum non-negative integer m for true:
and (5): put alpha n ＝ρ mn Let i n+1 ＝i n +α n d n ，u n+1 ＝u n +α n ν n Turning to step (1) when n = n + 1;
and (6): output current (i) qn ,i fn )。
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