CN110445438A - A kind of permanent magnet synchronous motor prediction flux linkage control method based on extension domination set - Google Patents
A kind of permanent magnet synchronous motor prediction flux linkage control method based on extension domination set Download PDFInfo
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- CN110445438A CN110445438A CN201910579131.2A CN201910579131A CN110445438A CN 110445438 A CN110445438 A CN 110445438A CN 201910579131 A CN201910579131 A CN 201910579131A CN 110445438 A CN110445438 A CN 110445438A
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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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
- H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
- H02P25/022—Synchronous motors
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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
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/34—Modelling or simulation for control purposes
Abstract
The invention discloses a kind of permanent magnet synchronous motors based on extension domination set to predict flux linkage control method, comprising: carries out mathematical modeling to permanent magnet synchronous motor；For the stator voltage vector in mathematical model, the borderline virtual voltage vector that endpoint is located at space voltage vector hexagon plane is obtained, constitutes extension domination set together with basic voltage vectors；Obtain the prediction magnetic linkage control model based on extension domination set, using stator magnetic linkage vector as control variable, influence according to domination sets different in the sampling period to stator magnetic linkage track constructs cost function, which has quantified the average value of sampling period an inner stator magnetic linkage reference locus and actual path error calculating by integration method；It determines optimal sector by the optimal solution of seeking of cost function, find optimal extension voltage vector in optimal sector and amplitude optimization is carried out to optimal extension voltage vector.
Description
Technical field
The present invention relates to electric system and control field more particularly to a kind of permanent magnet synchronous motors based on extension domination set
Predict flux linkage control method.
Background technique
Permanent magnet synchronous motor (PMSM) has the characteristics that high power density, high energy efficiency, compact-sized and torque current than high,
It is attracted wide attention in kinetic control system.In the past few decades, control algolithm has obtained extensive research.From
Model Predictive Control strategy is applied to power electronics and motor driven field to today for the first time before more than 20 years, and still temperature is not or not it
Subtract.Since it realizes simple, dynamic response is rapidly and by multiple control targets and the combined height of various constraint conditions
The remarkable advantages such as flexibility are spent, Model Predictive Control, especially its finite aggregate PREDICTIVE CONTROL branch have proved to be a kind of suitable
Effective control program, and it is considered as the scheme for most having prospect substitution mainstream Magnetic Field Oriented Control Strategies[1]。
When realizing the direct torque of permanent magnet synchronous motor using finite aggregate Model Predictive Control strategy, usually claimed
Stator-Quantities Control is predicted for finite aggregate.When the such controller of application, building is missed with torque error and magnetic linkage first
The relevant cost function of difference, then selects the optimal voltage vector for being minimized cost function as output[2].Obviously, this
The on-line optimization algorithm for binding directly controlled device solves the relevant issues such as current limit in which can be convenient[3]。
Although having advantage outstanding, finite aggregate prediction Stator-Quantities Control be there is also some problems, wherein most attaching most importance to
What is wanted is inevitably steady state torque to be caused to fluctuate.The reason is that finite aggregate prediction Stator-Quantities Control generally use it is constant
Sampling period, this algorithm all uses single switch state in the entire sampling period, and inverter can only be in sampling instant
Change its switch state.In addition, the domination set of this method is only made of six basic non-zero vectors and two Zero voltage vectors,
Amplitude and phase angle are all fixed values.These limitations will lead to torque and the control freedom degree of magnetic linkage and reduce, and eventually result in aobvious
The torque ripple of work[4].With the increase in sampling period, this phenomenon can be increasingly severe.
A kind of typical strategy for solving the problems, such as this is to adjust basic voltage vectors by insertion Zero voltage vector
Amplitude.It is minimized based on cost function, optimum voltage vector is selected from six basic vectors, and make itself and Zero voltage vector one
It reacts in algorithm.This is realized by introducing additional duty cycle analysis[5].The strategy can be such that inverter is sampling
Its switching state of any time changing in period, and not only in sampling instant.Therefore, torque control is predicted with traditional finite aggregate
Strategy processed is compared, and torque ripple opposite can be reduced.
In addition, in order to further suppress torque ripple, related researcher proposes the finite aggregate prediction of multivoltage vector
Stator-Quantities Control, it can neatly adjustment effect vector phase angle and amplitude, also have to torque ripple and more significantly change
It is kind.In order to further adjust the phase angle and amplitude of voltage vector, continuum predictive control strategy can be used[6].Pass through insertion one
A modulation module can obtain reference voltage more accurately, to accurately control torque and magnetic linkage.However, this control
Device usually requires to solve optimization problem offline.
Different from above-mentioned control strategy, direct torque can also be improved by increasing limited domination set with more virtual vectors
Performance, this is known as extending domination set (ECS) control strategy.By using cascade optimization process, acted on by sector identification, vector
Assessment and amplitude optimization select optimal vector from extension domination set[7].Due to having used extension domination set strategy, control is certainly
It is improved by degree, it is often more important that, duty cycle signals can be directly determined during prediction, without additional modulated
Journey.However, in the case where torque is different with magnetic linkage dimension, being needed well-designed to realize while adjusting torque and magnetic linkage
Weight coefficient in cost function, a large amount of experimental data of the selected needs of this coefficient is as support.Further, since rotor speed
With the variation of load torque, the fixed weight coefficient determined under the conditions of offline is difficult to be all suitable under different operating conditions.It is especially fast
Degree Spline smoothing or load torque variation will lead to sector erroneous judgement, and then generate biggish torque ripple.
Therefore, in order to improve the control performance of controller, keep the tracking effect of magnetic linkage more accurate, and then reduce torque wave
It is dynamic, the control system of dynamic response faster, more stable is obtained, traditional model prediction Stator-Quantities Control is improved then
Seem particularly necessary.
Bibliography
[1]Xia C,Wang S,Wang Z,et al.Direct Torque Control for VSI–PMSMs
Using Four-Dimensional Switching-Table[J].IEEE Transactions on Power
Electronics,2016,31(8):5774-5785.
[2]J.Holtz and S.Stadtfeld,“A predictive controller for the stator
current vector of AC-machines fed from a switched voltage source,”in
Proc.Int.Power Electron.Conf.,vol.2,Tokyo,Japan,Mar.1983:1665–1675.
[3]Fuentes E J,Silva,César,Quevedo D E,et al.Predictive speed control
of a synchronous permanent magnet motor[C].IEEE International Conference on
Industrial Technology.IEEE,2009.
[4]Zhou Z,Xia C,Yan Y,et al.Torque Ripple Minimization of Predictive
Torque Control for PMSM with Extended Control Set[J].IEEE Transactions on
Industrial Electronics,2017,64(9):6930-6939.
[5]Davari S A,Khaburi D A,Kennel R.An Improved FCS–MPC Algorithm for
an Induction Motor With an Imposed Optimized Weighting Factor[J].IEEE
Transactions on Power Electronics,2012,27(3):0-1551.
[6]Morel F,Lin-Shi X,Retif J M,et al.A Comparative Study of
Predictive Current Control Schemes for a Permanent-Magnet Synchronous Machine
Drive[J].IEEE Transactions on Industrial Electronics,2009,56(7):2715-2728.
[7]Zhou Z,Xia C,Yan Y,et al.Torque Ripple Minimization of Predictive
Torque Control for PMSM with Extended Control Set[J].IEEE Transactions on
Industrial Electronics, 2017,64 (9): 6930-6939.
Summary of the invention
The present invention provides a kind of permanent magnet synchronous motors based on extension domination set to predict flux linkage control method, using stator
Flux linkage vector considers in the entire sampling interval different domination sets to magnetic as control variable in the construction process of cost function
The influence of chain locus is gone to calculate average magnetic linkage fluctuation, and the cascade synthesis process for passing through optimal stator voltage vector with integration method
Duty cycle signals are directly obtained, described below:
A kind of permanent magnet synchronous motor prediction flux linkage control method based on extension domination set, which comprises
Mathematical modeling is carried out to permanent magnet synchronous motor；
For the stator voltage vector in mathematical model, the boundary that endpoint is located at space voltage vector hexagon plane is obtained
On virtual voltage vector, with basic voltage vectors together constitute extension domination set；
The prediction magnetic linkage control model based on extension domination set is obtained, using stator magnetic linkage vector as control variable, root
Influence according to domination sets different in the sampling period to stator magnetic linkage track constructs cost function, which has quantified to pass through product
The average value of one sampling period inner stator magnetic linkage reference locus and actual path error of calculation of group dividing；
By cost function it is optimal seek solution determine optimal sector, find in optimal sector optimal extension voltage vector, with
And amplitude optimization is carried out to optimal extension voltage vector.
The prediction of the actual path of the stator magnetic linkage specifically:
As 0≤t≤τ7When,
ψsα=ψsα(k+1)+k7αt
Work as τ7<t≤τ7+τyWhen,
ψsα=ψsα(k+1)+k7ατ7+kyα(t-τ7)
Work as τ7+τy<t≤τ7+τy+τxWhen,
ψsα=ψsα(k+1)+k7ατ7+kyατy+kxα(t-τ7-τy)
Work as τ7+τy+τx<t≤TSWhen,
ψsα=ψsα(k+1)+k7ατ7+kyατy+kxατx+k0α(t-τ7-τy-τx)
Wherein, ψsαFor the stator magnetic linkage component of α axis；k7α、kyα、kxα、k0αRespectively in voltage vector V7, Vy, VxAnd V0Make
Under, ψsαDerivative；τ7、τy、τxRespectively voltage vector V7, VyAnd VxWorking time within a sampling period, x, y ∈
[1,2,3,4,5,6]。
The method also includes: provide the three-phase duty ratio for generating extension voltage vector.
The beneficial effect of the technical scheme provided by the present invention is that:
1, the present invention is used as control variable using stator magnetic linkage vector, can be to avoid the adjusting of sector erroneous judgement and weight coefficient
Process, and good torque and magnetic linkage control performance can be obtained under different operating conditions；
2, instantaneous error is minimized at the end of the sampling period different from traditional control method, the present invention is in cost function
Influence of the different domination sets to stator magnetic linkage track in the entire sampling period is considered in construction process, goes to calculate with integration method every
Average stator magnetic linkage undulate quantity in a sampling period, can further suppress torque and the steady-sxtate wave motion of stator magnetic linkage；
3, the present invention can directly obtain three-phase duty cycle signals by the cascade synthesis process of optimal stator voltage vector,
Space vector pulse width modulation process is not needed；
4, the present invention is based on extension domination set ECS to establish predictive controller, controls certainly compared with traditional predictive controller
Expanded by degree, therefore control performance has more apparent improvement.
Detailed description of the invention
Fig. 1 is that voltage source inverter extends domination set schematic diagram (by taking the I of sector as an example)；
(a) by taking the I of sector as an example, the extension domination set of voltage source inverter；(b) vector V is extended in the I of sectorex,ISynthesis
Schematic diagram.
Fig. 2 is to use V by taking the V of sector as an example1And V2The schematic diagram of synthesis extension vector；
Fig. 3 is the stator magnetic linkage vector locus schematic diagram for considering final tracking error；
Fig. 4 is the stator magnetic linkage vector locus schematic diagram for considering average tracking error；
Fig. 5 is to consider the stator magnetic linkage vector α track shaft schematic diagram of average tracking error under time domain；
Fig. 6 is switch state and corresponding duty ratio schematic diagram；
The direct flux linkage vector control system architecture figure that Fig. 7 is mentioned for the present invention.
Table 1 is the corresponding two non-zero vector V in each sectorxAnd VyValue；
Table 2 is to generate final stator voltage vector VsThree-phase duty ratio；
Table 3 for the mentioned algorithm of the present invention specific implementation process.
Specific embodiment
To make the object, technical solutions and advantages of the present invention clearer, embodiment of the present invention is made below further
Ground detailed description.
Embodiment 1
The embodiment of the present invention, as control variable, can be evaded using stator magnetic linkage vector and appear in traditional extension control
The sector collected in model prediction Stator-Quantities Control judges problem by accident, also avoids the process of weight coefficient adjusting；In cost function
Construction process in consider in the entire sampling period influence of the different domination sets to magnetic linkage track, go to calculate with integration method average
Stator magnetic linkage fluctuation, can further suppress torque and the steady-sxtate wave motion of stator magnetic linkage；Pass through the grade of optimal stator voltage vector
The process of being unified into can directly obtain duty cycle signals, not need space vector pulse width modulation process.The embodiment of the present invention
It is illustrated by following several parts:
101: to controlled device, i.e. permanent magnet synchronous motor carries out mathematical modeling；
102: for the stator voltage vector in mathematical model, segmenting outlet point and be located at space voltage vector hexagon plane
Borderline virtual voltage vector, together with 8 basic voltage vectors constitute extension domination set ECS, and provide generation extension
The three-phase duty ratio of voltage vector；
103: the prediction flux linkage control method based on extension domination set ECS is designed, using stator magnetic linkage vector as control
Variable considers influence design cost function of the different domination sets to stator magnetic linkage track, the cost function in the entire sampling period
The average value for having quantified sampling period an inner stator magnetic linkage reference locus and actual path error calculating by integration method, seeks
The optimal solution of cost function is asked to realize the minimum of Average stator magnetic linkage undulate quantity；
104: the selection and application of the optimal stator voltage vector that solution is determined to prediction magnetic linkage control, packet are sought by optimal solution
Include: the determination of optimal sector, found in selected sector optimal extension voltage vector and to selected extension voltage vector into
The optimization of row amplitude.
In conclusion the embodiment of the present invention, which is based on extension domination set ECS, establishes prediction flux linkage control method, have with traditional
Limit domination set PREDICTIVE CONTROL method is expanded compared to control freedom degree, and considers the entire sampling period in building cost function
Influence of the interior difference domination set to stator magnetic linkage track, the Average stator magnetic linkage wave in each sampling period is realized using integration method
The minimum of momentum improves the steady-state performance of stator magnetic linkage and torque.In addition, due to only with stator magnetic linkage vector conduct
Variable is controlled, compared to being controlled simultaneously using traditional torque prediction that magnetic linkage amplitude and torque make variable, can be missed to avoid sector
Sentence the tuning process with weight coefficient, good torque and magnetic linkage control performance can be obtained under different operating conditions.
Embodiment 2
The scheme in embodiment 1 is further introduced below with reference to specific calculation formula, example, attached drawing, in detail
See below description:
One, permanent magnet synchronous motor models
The mathematical model of permanent magnet synchronous motor is established under two-phase stationary coordinate system, the embodiment of the present invention is carried out using vector
Variable expression, and by vector variable overstriking, such as: stator magnetic linkage vector is represented by ψs=ψsα+jψsβ, wherein ψsαIt is fixed for α axis
Sub- flux linkage vector component, ψsβFor β axis stator magnetic linkage vector component.Stator voltage equation and flux linkage equations may be expressed as:
In formula, RsAnd LsRepresent stator resistance and inductance；VsAnd isIndicate stator voltage vector and current phasor；ψsAnd ψrPoint
Stator magnetic linkage vector sum permanent magnet flux linkage vector is not represented.
Electromagnetic torque may be expressed as:
In formula, p is number of magnetic pole pairs.
ψrAnd ψsBetween angle thetaesIt can indicate are as follows:
In formula, ψsAnd ψrRespectively represent stator magnetic linkage and permanent magnet flux linkage amplitude.
Wherein, above-mentioned formula (1)-(3) constitute permanent magnet synchronous motor model.
Two, the building of domination set ECS is extended
Before introducing direct Flux estimation control, the concept of extension domination set is first introduced.Two level voltage source inventers
It can produce eight kinds of switch combinations, correspondingly can produce eight basic voltage vectors, comprising: two zero vectors and six non-null vectors
Amount.Six non-zero vectors may be expressed as:
In formula, VdcFor DC bus-bar voltage.This eight basic vectors constitute traditional limited domination set.
Using this six equally distributed non-zero vectors as boundary, voltage vector space complex plane can be divided into six fans
Area.In each sector, the borderline virtual voltage vector that outlet point is located at hexagonal area can further be segmented.These
Virtual voltage vector constitutes extension domination set together with eight basic vectors.By taking the I of sector as an example, in extension domination set, each
Extend vector Vex,IThe boundary vector V of sector I can be passed through1And V2To synthesize.It may be expressed as:
Vex,I=(1- λy)V1+λyV2 (5)
In formula, λyFor voltage vector V2Action time account for entire sampling period TSRatio.When its value is between 0 to 1
It can produce different extension vectors when variation.Normally, it needs in λyTwo neighboring value between fixed intervals are set.Such as Fig. 1
It is shown,
If using SA、SBAnd SCIt indicates the threephase switch state of inverter, then corresponds to each basic voltage vectors ViThree-phase
Switching vector selector is defined as Si=[SA SB SC].For example, S0=[0 0 0], S7=[1 1 1], bridge arm conducting, " 0 " in " 1 " expression
Indicate lower bridge arm conducting.Generate voltage vector Vex,IThree-phase duty ratio be defined as dex,I=[dA dB dC].According in formula (5)
Compositive relation, dex,IIt can state are as follows:
dex,I=(1- λy)S1+λyS2 (6)
What is interesting is six basic nonzero voltage space vectors can all pass through two voltage vector V1And V2And their combination letter
Changing indicates, as shown in formula (7):
Vi=λ1V1+λ2V2 (7)
In formula, λ1And λ2It indicates to be used for synthesized voltage vector ViCorresponding V1And V2Coefficient.In addition, every in voltage space
A voltage vector can use V1And V2Synthesis.As shown in Fig. 2, illustrating to synthesize by taking the extension voltage vector in the V of sector as an example
Journey, this can simplify the calculating of proposed algorithm, can mention in following content.
Three, the direct flux linkage vector forecast Control Algorithm based on ECS
As it was noted above, the tracking performance of torque reference is realized by adjusting stator magnetic linkage vector.Torque reference
With the angle, θ between reference rotor magnetic linkagees,refIt is related.According to formula (3), θes,refIt can be obtained by following formula:
In formula, Te,refFor torque reference；ψs,refFor the amplitude with reference to stator magnetic linkage vector.
According to formula (1), stator voltage equation can be re-written as:
Ignore the influence of stator resistance, formula (9) becomes:
As can be seen from the above equation, stator voltage determines the variation of stator magnetic linkage.Within a sampling period, stator magnetic linkage
Track depends on the voltage vector of effect.
Since microprocessor calculates limited time, according to kTsThe duty cycle signals that the parameter of instance sample is calculated are wanted
To (k+1) TsMoment could be applied.This introduces the delay of a cycle in control process, is thus considered as prolonging accordingly
Compensation late.Therefore, in sampling period kTsTo (k+1) TsIn period, the prediction process of stator magnetic linkage track should be conceived to (k+1) Ts
To (k+2) TsPeriod.It should be noted that in sampling period kTsTo (k+1) TsIn period, stator magnetic linkage track is known
, because the duty cycle signals applied in this period were calculated in the last period.
In traditional control strategy, the effect of stator magnetic linkage actual path track reference track is commented at every sampling moment
Estimate, i.e., control purpose is the difference reduced between stator magnetic linkage reference locus and actual path at the end of each sampling period.
In other words, final tracking error is only considered in traditional control method, is determined between two neighbouring sample moment without considering
The sub- detailed variation track of magnetic linkage, at this moment stator magnetic linkage track is as shown in Figure 3.Assuming that including four voltages within a sampling period
Vector V7, Vy, VxAnd V0, wherein x, y ∈ [1,2,3,4,5,6], the action time of four vectors is respectively τ7, τy, τxAnd τ0.Ginseng
The track of stator magnetic linkage is examined (with L (ψs,ref) indicate) it is a standard round.Actual stator magnetic linkage track (uses L (ψs) indicate) along
Reference locus fluctuates up and down.Next (k+1) T is discussed in detailsTo (k+2) TsThe stator magnetic linkage pursuit path of period.
In (k+1) TsMoment, with reference to stator magnetic linkage vector position in point A.Then, it is moved along A-B-C-D-E,
Speed is equal to rotor electric angle frequencies omegae, point E represents the end of this sampling period internal reference stator magnetic linkage vector locus.In (k+
1)TsAt the moment, the position of actual stator flux linkage vector is in point Pfi.In voltage vector V7Effect during because zero vector is to stator
Flux linkage vector does not influence, so ψsIt is maintained at PfiPoint.As voltage vector VyWhen effect, ψsIt is moved to point Qfi, then switching is electric
Pressure vector makes vector VxEffect.In action time τxAfter, ψsPoint of arrival Sfi.Due to zero vector V0Effect, ψsIt is maintained at
Current location terminates until this sampling period.
In this traditional control algolithm, due to the ψ within a sampling periodsDetailed change procedure be ignored
Even if in terminal point E and point SfiBetween difference it is little, QfiPosition can may also much deviate desired track, in turn
Cause stator magnetic linkage fluctuation larger.In order to avoid this problem, this method focus is reference locus L (ψs,ref) and true rail
Mark L (ψs) between mean error, rather than only consider track final value error, as shown in figure 4, actual stator magnetic linkage track is pressed
According to Pav—Qav—SavTrail change.
It is clear from fig. 4 that with reference to stator magnet chain angle θs,refT changes at any time, change rate ωe.In (k+
1)TsMoment and (k+2) TsBetween moment, with reference to stator magnet chain angle θs,refIt may be expressed as:
θs,ref=θs,ref(k+1)+ωet (11)
=θe(k)+θes,ref(k)+ωeTs+ωet
In formula, θs,refAngle is referred to for stator magnetic linkage；θeFor rotor electrical angle, and 0≤t≤TS。
It can be indicated therewith with reference to stator magnetic linkage vector are as follows:
By coordinate transform, reference stator flux linkage vector be may be expressed as: under two-phase stationary coordinate system
ψsα,ref=ψs,refcos(θs,ref) (13)
ψsβ,ref=ψs,refsin(θs,ref)
In formula, ψsα,refAnd ψsβ,refThe respectively α axis and beta -axis component of reference stator flux linkage vector.
(k+1) T in order to obtainsThe physical location of moment stator magnetic linkage obtains formula (10) discretization:
ψs(k+1)=ψs(k)+Vs(k)Ts (14)
According to formula (10), in (k+1) TsMoment is to (k+2) TsMoment stator magnetic linkage track L (ψs) can be predicted.Respectively to α
The stator magnetic linkage track of axis and β axis is predicted.The derivative of stator magnetic linkage may be expressed as: under α β coordinate system
In formula, ψsαAnd ψsβThe respectively stator magnetic linkage component of α axis and β axis；VsαAnd VsβThe respectively stator of α axis and β axis electricity
Press component；kαAnd kβThe respectively derivative of α axis and β axis stator magnetic linkage.
The prediction process of stator magnetic linkage is explained by taking α axis stator magnetic linkage as an example.In the time domain, ψsα,refAnd ψsαTrack such as
Shown in Fig. 5.In voltage vector V7, Vy, VxAnd V0Under effect, ψsαDerivative be respectively k7α, kyα, kxαAnd koα.Due to zero vector
Effect, k7αAnd koαEqual to zero.In t=0, ψsα,refAnd ψsαStarting point be ψ respectivelysα,ref(k+1) and ψsα(k+1).It is pre- at this
It surveys in the period,
When t meets 0≤t of condition≤τ7When, ψsαIt may be expressed as:
ψsα=ψsα(k+1)+k7αt (16)
When t meets condition τ7<t≤τ7+τyWhen, ψsαIt may be expressed as:
ψsα=ψsα(k+1)+k7ατ7+kyα(t-τ7) (17)
When t meets condition τ7+τy<t≤τ7+τy+τxWhen, ψsαIt may be expressed as:
ψsα=ψsα(k+1)+k7ατ7+kyατy+kxα(t-τ7-τy) (18)
When t meets condition τ7+τy+τx<t≤TSWhen, ψsαIt may be expressed as:
ψsα=ψsα(k+1)+k7ατ7+kyατy+kxατx (19)
+k0α(t-τ7-τy-τx)
When specific implementation, the prediction process of stator magnetic linkage beta -axis component is consistent with above-mentioned α axis, obtains ψsβExpression
With reference to formula (16)~(19), the embodiment of the present invention does not repeat them here this.
Four, the determination and application of optimal stator voltage vector
Stator magnetic linkage should be inhibited to fluctuate the tracking process of reference stator magnetic linkage.Actual stator magnetic linkage with refer to stator magnet
Difference between chain is defined as magnetic linkage fluctuation, usesTo indicate:
In embodiments of the present invention, main purpose is to reduce the fluctuation of Average stator magnetic linkage.The fluctuation of Average stator magnetic linkageIt can
It indicates are as follows:
By actual stator magnetic linkage and with reference to the integral process separate computations of stator magnetic linkage, ψsα,ref、ψsβ,ref、ψsαAnd ψsβ's
Integral result is by M (ψsα,ref)、M(ψsβ,ref)、M(ψsα) and M (ψsβ) respectively indicate.In order to quantify the fluctuation of Average stator magnetic linkageConstruct cost function:
Jav=[M (ψsα)-M(ψsα,ref)]2+[M(ψsβ)-M(ψsβ,ref)]2 (22)
According to formula (13), from (k+1) TsMoment is to (k+2) TsThe integral of the reference stator magnetic linkage at moment may be expressed as:
In order to minimize cost function (formula (22)), it should determine optimal synthesis stator voltage vector and a sampling period
The action time of the interior each voltage vector for synthesizing the vector.Obtain the mistake of optimal synthesis stator voltage vector and corresponding duty ratio
Journey can be divided into three steps.
(1) sector where best resultant vector is determined
It will be understood that an if synthesis stator voltage vector VSBest tracking performance can be obtained after effect, then,
With VSSimilar voltage vector can produce than with VSThe better tracking performance of the voltage vector of deviation.In other words, best synthesis
The function and effect of two boundary basic vectors of sector are more preferable than other four non-zero basic vectors where vector.So can
To determine best sector according to two optimal non-zero basic vectors.
Cost function is initially used for determining optimal basic voltage vectors.By taking α axis stator magnetic linkage component as an example, when entire sampling
In period when the effect of only one basic voltage vectors, ψsαTrack may be expressed as:
ψsα=ψsα(k+1)+kiαt (24)
In formula, 0≤t≤TS；kiαFor basic voltage vectors ViThe derivative of α axis stator magnetic linkage component when effect.
In these cases, from (k+1) TsMoment is to (k+2) TsThe actual stator magnetic linkage integral representation at moment are as follows:
M(ψsα)=ψsα(k+1)Ts+0.5kiαTs 2 (25)
M(ψsβ)=ψsβ(k+1)Ts+0.5kiβTs 2
In formula, kiβFor basic voltage vectors ViThe derivative of β axis stator magnetic linkage component when effect.It will be recalled from above that any Vi
V can be passed through1And V2Synthesis, therefore only k1α、k1β、k2αAnd k2βIt needs to calculate in advance.
From i=1 to i=6, six basic voltage vectors are successively brought into cost function, keep cost function the smallest
Voltage vector is optimal voltage vector Vop, and the smallest voltage vector of cost function time is made to be defined as Vsec.With VopAnd VsecFor
The sector on boundary is optimal sector.
(2) optimal extension voltage vector is determined in selected sector
As described above, extension voltage vector is by boundary basic voltage vectors VopAnd VsecSynthesis.Two candidate vector Vop
And VsecTwo non-zero vector V as Part III introductionxAnd Vy, and the collective effect within a sampling period.According to inversion
Device switching rule, for the V of each candidate vectorxAnd VyThe distribution of numerical value can be determined according to table 1.When t meet 0≤t of condition≤
τyWhen, ψsαIt may be expressed as:
ψsα=ψsα(k+1)+kyαt (26)
In formula, kyαFor basic voltage vectors VyThe derivative of α axis stator magnetic linkage component when effect.
Work as τy≤t≤TSWhen, ψsαIt is represented by
ψsα=ψsα(k+1)+kyατy+kxα(t-τy) (27)
In formula, kxαIt is basic voltage vectors VxThe derivative of α axis stator magnetic linkage component when effect.It was found from formula (5):
τy=λyTs (28)
τx=(1- λy)Ts
According to formula (26)-(28), from (k+1) TsMoment is to (k+2) TsThe stator magnetic linkage integral at moment may be expressed as:
M(ψsα)=ψsα(k+1)Ts+λy(1-0.5λy)kyαTs 2+0.5(1-λy)2kxαTs 2 (29)
M(ψsβ)=ψsβ(k+1)Ts+λy(1-0.5λy)kyβTs 2+0.5(1-λy)2kxβTs 2
In formula, kxβAnd kyβRespectively indicate basic voltage vectors VxAnd VyUnder effect, the derivative of β axis stator magnetic linkage component.
Cost function J is being calculated according to formula (29)avAfterwards, so that cost function JavThe smallest λyOptimal extension arrow has been determined
Amount.Obviously, the precision and λ of optimal vectoryCandidate vector the proportional relationship of number.
(3) the amplitude optimization of optimal extension voltage vector
Optimal extension vector has been selected in previous step.However, during prediction, ψsTrack can be with VxOr Vy
Effect constantly change until action time end.Due to VxOr VyAdditional vector length, ψsIdeal position may be exceeded.
In order to further decrease torque and stator magnetic linkage fluctuation, zero vector V is introduced7And V0With VxAnd VyCollective effect, to adjust voltage arrow
Measure VxAnd VyAmplitude.The ratio of the zero vector added in a sampling period is by λ0It indicates, then the effect of four voltage vectors
Time can respectively indicate are as follows:
τ7=λ0λyTs (30)
τy=(1- λ0)λyTs
τx=(1- λ0)(1-λy)Ts
τ0=λ0(1-λy)Ts
In formula, 0≤λ0≤1。
In this case, from (k+1) TsMoment is to (k+2) TsThe stator magnetic linkage integral at moment may be expressed as:
Then, (31) are brought into (22) and go to calculate cost function Jav.Similar to λySelection course, λ0Value can
The selection in arithmetic progression { 0,1/8,1/4 ..., 1 }.So that cost function JavThe smallest λ0When effect for determining zero vector
Between.As shown in formula (30), action time τ7, τy, τxAnd τ0Parameter lambda can be usedyAnd λ0Indicate, thus can directly obtain A, B,
The duty ratio of C three-phase.By taking the I of sector as an example, V7, V2, V1And V0Will within a sampling period collective effect, as shown in Figure 6.Often
The ratio that the working time of a voltage vector accounts for the entire sampling period has marked, such as vector V7Action time accounts for a sampling
The ratio in period is λ0λy.Thus obtained threephase switch state is as shown, wherein indicate the switch state shade table of "ON"
Show.The final duty ratio of every phase is equal to the sum of shadow region ratio, for example, the duty ratio of A phase is equal to λ0λy、(1-λ0)λyWith (1-
λ0)(1-λyThe sum of).
It should be noted that λyAnd λ0Search interval can be adjusted according to the accuracy requirement of control performance.Use NVTable
Show the candidate vector number in arithmetic progression, it can be seen that the precision and N of finally obtained optimal voltage vectorVIt is proportional.So
And NVIncrease will lead to find optimal vector amount of calculation increase and Riming time of algorithm it is elongated.Therefore, NVChoosing
Needs are selected to be weighed between performance requirement and computation burden.Based on determining λyAnd λ0And sector auxiliary information, final three-phase
Duty ratio ds=[dA dB dC] as shown in table 2.The prediction magnetic linkage control block diagram based on ECS that the embodiment of the present invention is proposed is such as
Shown in Fig. 7.Assuming that having determined that sector III is optimal sector in the first step, determining final optimal is indicated in dotted line frame
The process of resultant vector.In order to which the algorithm that the embodiment of the present invention is proposed, the entire implementation process point of algorithm is more clearly presented
Step has been listed in table 3.
Table 1: the corresponding two non-zero vector V in each sectorxAnd VyValue
Table 2: final stator voltage vector V is generatedsThree-phase duty ratio
Table 3: the specific implementation process of this method
The embodiment of the present invention to the model of each device in addition to doing specified otherwise, the model of other devices with no restrictions,
As long as the device of above-mentioned function can be completed.
It will be appreciated by those skilled in the art that attached drawing is the schematic diagram of a preferred embodiment, the embodiments of the present invention
Serial number is for illustration only, does not represent the advantages or disadvantages of the embodiments.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all in spirit of the invention and
Within principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (3)
1. a kind of permanent magnet synchronous motor based on extension domination set predicts flux linkage control method, which is characterized in that the method packet
It includes:
Mathematical modeling is carried out to permanent magnet synchronous motor；
For the stator voltage vector in mathematical model, obtains endpoint and be located at the borderline of space voltage vector hexagon plane
Virtual voltage vector constitutes extension domination set with basic voltage vectors together；
The prediction magnetic linkage control model based on extension domination set is obtained, using stator magnetic linkage vector as control variable, according to adopting
Influence of the different domination sets to stator magnetic linkage track constructs cost function in the sample period, which has quantified to pass through integration method
The average value of sampling period an inner stator magnetic linkage reference locus and actual path error calculating；
It determines optimal sector by the optimal solution of seeking of cost function, find in optimal sector optimal extension voltage vector and right
Optimal extension voltage vector carries out amplitude optimization.
2. a kind of permanent magnet synchronous motor based on extension domination set according to claim 1 predicts flux linkage control method,
It is characterized in that, the prediction of the actual path of the stator magnetic linkage specifically:
As 0≤t≤τ7When,
ψsα=ψsα(k+1)+k7αt
Work as τ7<t≤τ7+τyWhen,
ψsα=ψsα(k+1)+k7ατ7+kyα(t-τ7)
Work as τ7+τy<t≤τ7+τy+τxWhen,
ψsα=ψsα(k+1)+k7ατ7+kyατy+kxα(t-τ7-τy)
Work as τ7+τy+τx<t≤TSWhen,
ψsα=ψsα(k+1)+k7ατ7+kyατy+kxατx+k0α(t-τ7-τy-τx)
Wherein, ψsαFor the stator magnetic linkage component of α axis；k7α、kyα、kxα、k0αRespectively in voltage vector V7, Vy, VxAnd V0Under effect,
ψsαDerivative；τ7、τy、τxRespectively voltage vector V7, VyAnd VxWorking time within a sampling period, x, y ∈ [1,2,3,
4,5,6]。
3. a kind of permanent magnet synchronous motor based on extension domination set according to claim 1 predicts flux linkage control method,
It is characterized in that, the method also includes: provide the three-phase duty ratio for generating extension voltage vector.
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