CN112016197A - Prediction method for harmonic current of permanent magnet motor - Google Patents
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Abstract
The invention discloses a prediction method of harmonic current of a permanent magnet motor. Establishing a motor magnetic field distribution model considering the saturation effect of the ferromagnetic material, wherein the input of the motor magnetic field distribution model is the harmonic current of the permanent magnet motor, and the output of the motor magnetic field distribution model is the terminal voltage of the permanent magnet motor; establishing a double Fourier series model of inverter output voltage harmonic waves based on space vector modulation of a modulation function, and inputting modulation depth to obtain the output voltage of the inverter; establishing a matching degree between the terminal voltage of the permanent magnet motor and the output voltage of the inverter as an optimization target, and providing a matching method of harmonic currents, namely performing global optimization on each order harmonic current of a motor magnetic field distribution model through an optimization algorithm, solving to obtain the amplitude and the phase of each order harmonic current, and further obtaining the harmonic current. The time for processing the harmonic current is shorter than that of a finite element processing mode, and the output result is consistent and accurate with the result calculated by a finite element.
Description
Technical Field
The invention relates to a permanent magnet motor parameter detection method in the field of motor electromagnetic performance analysis, in particular to a prediction method of harmonic current of a permanent magnet motor.
Background
Accurate and rapid analysis of the electromagnetic performance of the motor is the basis of the design of the high-performance permanent magnet motor. High-performance permanent magnet motors are generally driven by voltage source type inverters based on pulse width modulation, but the inherent switching process of the inverters can generate abundant magnetic field time harmonics in the motors, and the generated harmonic current can bring a series of damages to the motor performance, such as increase of torque ripple, electromagnetic loss, noise and vibration.
At present, a finite element method and an analytic method are generally adopted to analyze the harmonic current of a motor driven by an inverter. A combined simulation model containing the motor and the inverter can be established to analyze the harmonic current of the motor based on a finite element method, the calculation precision is high, the application range is wide, but the calculation speed is low, and dozens of hours are generally consumed. Analytic methods (typically, as in the papers w.liang, j.wang and w.fang, "Analytical Modeling of base Current Harmonic Components in Induction Machine Drive With Voltage Source Inverter by an SVM Technique," in IEEE reactions on Power Electronics, vol.28, No.11, pp.5372-5379, No. 2013.) directly derive Harmonic Current expressions for a specific type of motor based on a specific modulation strategy (e.g., space vector modulation), and the calculation speed is fast but the application range is narrow. And the derivation of the analytical method is based on a centralized parameter model of a certain specific motor, so that the influence of the saturation effect of ferromagnetic materials in the motor on the harmonic current calculation is difficult to accurately consider.
In the process of carrying and operating the high-performance permanent magnet motor under the driving of a voltage source type inverter, the saturation effect of ferromagnetic materials in the motor is ubiquitous.
Disclosure of Invention
In order to solve the problems in the prior art, the invention aims to provide a current harmonic prediction method which can accurately obtain the harmonic current of a permanent magnet motor driven by a voltage source type inverter. The method utilizes an optimization algorithm, takes the matching degree of the terminal voltage of the permanent magnet motor and the output voltage of the inverter as an optimization target, obtains each harmonic current through global optimization, and has the characteristics of high calculation precision and high calculation speed.
The invention adopts a technical scheme that:
1) establishing a motor magnetic field distribution model considering the saturation effect of the ferromagnetic material, wherein the motor magnetic field distribution model represents the relation between harmonic current and terminal voltage, the input of the motor magnetic field distribution model is the harmonic current of the permanent magnet motor, and the output of the motor magnetic field distribution model is the terminal voltage of the permanent magnet motor; specifically, air gap magnetic field distribution is obtained through calculation, and terminal voltage of the permanent magnet motor is obtained through further processing of the air gap magnetic field distribution of the permanent magnet motor.
2) Establishing a double Fourier series model of inverter output voltage harmonic waves based on space vector modulation of a modulation function, and inputting modulation depth to obtain the output voltage of the inverter;
3) establishing a matching degree between the terminal voltage of the permanent magnet motor and the output voltage of the inverter according to the terminal voltage of the permanent magnet motor obtained in the step 1) and the output voltage of the inverter obtained in the step 2), and taking the matching degree as an optimization target, and providing a matching method of harmonic current, namely performing global optimization on each order harmonic current of the motor magnetic field distribution model in the step 1) through an optimization algorithm, and solving to obtain the amplitude and the phase I of each order harmonic currentv、
Then, the amplitude and phase I of each order harmonic current are utilizedv、
Calculating to obtain harmonic current; namely, when the terminal voltage of the permanent magnet motor is matched with the output voltage of the inverter, the harmonic current under the output voltage of the inverter is obtained.
The permanent magnet motor works under the drive of a voltage source type inverter.
The method can further calculate the iron loss in the permanent magnet motor by utilizing the harmonic current, and further obtain the motor performance according to the iron loss evaluation.
As shown in fig. 2, in step 1), neglecting the end effect of the permanent magnet motor, taking the induced voltage of the permanent magnet motor as the terminal voltage of the permanent magnet motor, and the magnetic field distribution model of the motor considering the saturation effect of the ferromagnetic material specifically includes:
Bs(t,Rs,α)＝(Fs(t,α)-Fr(t,α))·Λ(α)
wherein: b iss(t,RsAnd alpha) is the distribution of the air gap field at the angular position alpha on the circumference of the inner radius of the stator of the permanent magnet motor at the moment t, RsRepresenting the inner radius of the stator of the permanent magnet machine, Fs(t,α),Fr(t, α) are stator and rotor magnetomotive forces at time t and angular position α, respectively, t is time, α is the angular position on the stator circumference, and Λ (α) is the air gap flux guide at angular position α; n is a radical ofp(α) is the winding function of the permanent magnet machine, p is the pole pair number of the permanent magnet machine, iphThe harmonic current of the winding phase ph is expressed in a fourier series form, ph represents the phase of the permanent magnet motor, ph is a, B, C, A, B, C represent the three phases of the permanent magnet motor, k represents the phase corresponding to the three phases of the permanent magnet motor, and k is 1,2,3, i represents the phase corresponding to the three phases of the permanent magnet motorphRespectively correspond to iA,iB,iC(ii) a v represents the order of the harmonic current, Iv、
Amplitude and phase, N, of the v-th order harmonic current, respectivelycThe number of turns per slot of the permanent magnet motor, q is the number of slots per pole and phase, EpIs the induced voltage, omega, of a permanent magnet machinerMechanical angular velocity, l, for the rotation of the rotor of a permanent magnet machineefIs the effective length of the permanent magnet motor, alphaiIs the initial angle of the coil winding, τ is the winding span, kw(v) A winding coefficient for a v-th order harmonic current; u denotes the u-th antipole, Ψ, of the permanent magnet machinep(t) represents the flux linkage of the permanent magnet machine;
the key calculation domain of the motor magnetic field distribution model is the air gap circumference, the model input is the Fourier series form of the winding phase current, and the modeling is to respectively form the stator magnetomotive force Fs(t, α), rotor magnetomotive force Fr(t, alpha) and the magnetic conductance Lambda (t, theta) of the motor magnetic circuit, and the transient air gap flux density distribution B is obtained by calculation through a magnetic field formulas(Rsα), and thus a back-emf or terminal voltage. The motor magnetic field distribution model can effectively contain the saturation effect of ferromagnetic materials in the motor.
The rotor magnetomotive force Fr(t, α) was modeled as follows:
the invention takes the magnetic conductivity of an ideal silicon steel sheet as positive infinity, magnetic induction lines are all orthogonal to materials, namely the surface magnetic potential is kept constant, and then the magnetic potential Ur generated by the induction of the stator magnetomotive force in an air gap polar arc area when the rotor does not have a permanent magnet at the moment t is respectively obtaineds(t,α,θr) And the magnetic potential Ur generated by the action of the permanent magnets in the air gap pole arc area when only the rotor permanent magnet is arrangedpm(α,θr) And permanent magnet equivalent magnetic potential Fpm(α,θr) Further obtain the rotor magnetic potential Fr(t,α)。
Fr(t,α)＝Fpm(α,θr)-Urs(t,α,θr)-Urpm(α,θr)
Wherein: fpm(α,θr) Indicating the angular position of the rotor at thetarPermanent magnet equivalent magnetomotive force at angular position alpha, Urs(t,α,θr) Indicating that the rotor angular position is at theta at time trThe magnetomotive force, Ur, induced by the stator magnetomotive force at the angular position alpha of the air gap polar arc region when the rotor permanent magnet is not consideredpm(α,θr) Indicating the angular position of the rotor at thetarThe magnetomotive force R generated by the permanent magnet at the angular position alpha of the air gap polar arc region when only the rotor permanent magnet is positionedsIs the inner radius of the stator of the permanent magnet motorbarrierFor the magnetic conductance of the rotor magnetic isolation slot, the magnetic isolation slot (or called magnetic isolation magnetic bridge) is a structure on the rotor of the built-in permanent magnet motor, and the inside of the slot is usually air for reducing the magnetic flux leakage. LambdaσFor the leakage flux of the rotor magnetic-isolating slot, ΛpmFor rotor permanent magnet permeance, alphapThe angle occupied by the air gap polar arc region, HcCoercive force of permanent magnet, hpmIs the thickness of the permanent magnet, krIs the conversion coefficient, w, of the rotor structure of the built-in permanent magnet synchronous motorpmTotal length of permanent magnet, warcIs the air gap polar arc regionWidth, thetarFor the angular position of the rotor, thetar0Is the initial angular position of the rotor. Permanent magnets are typically located on the rotor to provide excitation for the motor. Motors excited by permanent magnets are collectively referred to as permanent magnet motors. The specific embodiment is an interior permanent magnet synchronous motor.
According to air gap flux density Bs(r, alpha) obtaining the magnetic densities of the stator tooth part, the stator yoke part, the rotor yoke part and the pole shoe part, obtaining the relative magnetic permeability of each part through a BH curve of a silicon steel sheet, further obtaining the magnetic resistance of each part, obtaining a saturation coefficient and correcting the air gap magnetic permeability, and iterating until the saturation coefficient is converged, namely calculating the air gap magnetic density under the saturation effect of the ferromagnetic material. Air gap flux density is used to characterize air gap magnetic field distribution, and B is useds(t,RsAnd alpha) is shown.
Lambda (alpha) is the air gap permeance considering the influence of the stator slot opening and introduces a saturation coefficient k based on an equivalent magnetic networkuTo incorporate the saturation effect of ferromagnetic materials into the magnetic field distribution model of the machine. The air gap permeance Lambda (alpha) is set by adopting the following formula:
wherein: lambda0Is a uniform air gap permeance, kuIs a saturation coefficient, θsFor stator slot opening arc, alpha0Is the radian between two adjacent slots of the stator, Rst、Rsy、Rrt、Rry、RairMagnetic resistances of the stator tooth portion, the stator yoke portion, the rotor yoke portion, the pole shoe portion and the air gap, respectively; beta is arA coefficient for the air gap permeance obtained by conformal mapping is shown.
In the dual fourier series model in step 2), the modulation function of the inverter adopts the following manner:
wherein: v. ofsvm(ωmt) is the modulation function of the inverter, ωmFor modulating frequency, i.e. the electrical angular frequency of rotation, omega, of permanent-magnet machinescIs the carrier frequency, M is the modulation depth, UdcIs the dc bus voltage.
As shown in the specific implementation flow diagram of fig. 3, a differential evolution algorithm is used to perform global optimization.
Firstly, according to the working condition requirement, obtaining the output voltage u of the inverter through a double Fourier series model of the harmonic wave of the output voltage of the invertersvm. Then, randomly generating a population P of the initial harmonic current matrix of the permanent magnet motor(0)For each individual harmonic current matrix I in the population of harmonic current matricesi,nAnd i is obtained by superposing Fourier series of the phase harmonic current of the three-phase windingphAnd inputting the motor magnetic field distribution model to obtain the corresponding terminal voltage u of the permanent magnet motorm。
P(n)＝[I1,n...Ii,n...INP,n]i＝1,...,NP；n＝0,...,G
The method comprises the following steps that NP is the number of groups of harmonic current matrixes of the permanent magnet motor, i represents the serial number of an individual in the groups of the harmonic current matrixes of the permanent magnet motor, G is the maximum evolution algebra, and n represents the group evolution algebra; p(n)Group representing harmonic current matrix of nth generation permanent magnet machine, I1,n...Ii,n...INP,nRespectively representing the first to Nth individuals in the group of the harmonic current matrix of the n-th generation permanent magnet motor Ii,nRepresenting the ith individual, I, in the population of the harmonic current matrix of the nth generation permanent magnet machine1～IvmaxRespectively representing the magnitudes of the 1 st through vmax order harmonic currents,
respectively representing the phases of the 1 st to vmax th harmonic currents
In the step 3), specifically, the terminal voltage u of the following permanent magnet motor is establishedmAnd the output voltage u of the invertersvmThe matching degree F:
where vmax is the maximum harmonic order number,
and
are respectively the output voltage u of the invertersvmAmplitude and phase, U, of the corresponding voltage harmonic of the v-th ordervAnd
respectively terminal voltage u of permanent magnet motormThe amplitude and phase of the corresponding v-th order voltage harmonic;
then, the matching degree maximization is taken as an optimization target, the harmonic current input by the motor magnetic field distribution model is subjected to global optimization solving through an optimization algorithm to obtain the amplitude and the phase I of each order harmonic current in the permanent magnet motorv、
Comparison usvmAnd umThe amplitude and the phase of each voltage harmonic are judged, and whether the amplitude and the phase are matched is judged. An embodied match may refer to usvmAnd umThe matching degree F of the amplitude and phase of the corresponding voltage harmonic is greater than a given value, such as 99.5%.
When terminal voltage u of permanent magnet motormAnd the output voltage u of the invertersvmWhen matching, optimizing is completed to obtain the power of the permanent magnet motor under the output voltage of the inverterA flow harmonic. If the two are not matched, forming a next generation population by adopting a difference mode, and repeating the operations until the two are matched.
The optimization algorithm in the step 3) includes, but is not limited to, an evolutionary algorithm, a group intelligence algorithm, a simulated annealing algorithm, a tabu search algorithm and a neural network algorithm.
The invention has the beneficial effects that:
1. the magnetic field distribution model of the permanent magnet motor adopts an analytic method model to effectively consider the saturation effect of the ferromagnetic material, the time for processing harmonic current is shorter than that of a finite element processing mode, and the output result is consistent and accurate with the result calculated by a finite element.
2. The invention provides a harmonic current matching and predicting method in an optimized mode, a magnetic field distribution model of the permanent magnet motor and an inverter output voltage harmonic model can be replaced, and the harmonic current predicting method for carrying out global optimization by adopting an optimization algorithm is wide in application range.
Drawings
FIG. 1 is a block diagram of an implementation flow of the present invention;
FIG. 2 is a block flow diagram of a magnetic field distribution model of the interior permanent magnet synchronous motor of the present invention considering the saturation effect of ferromagnetic materials;
FIG. 3 is a block diagram of a specific implementation of the method of the present invention based on matching;
FIG. 4 is a graph of inverter output voltage waveform under a given operating condition;
fig. 5 is a waveform diagram of harmonic current of the motor at the output voltage of the inverter.
Detailed Description
The invention is further described with reference to the accompanying drawings and examples so that the advantages and features of the invention may be more readily understood by those skilled in the art, and the scope of the invention will be more clearly and clearly defined.
As shown in fig. 1, the embodiment of the present invention is as follows:
inputting initial harmonic current into a magnetic field distribution model of the motor considering ferromagnetic material saturation effect to obtain the permanent magnet motorTerminal voltage u ofmAt the terminal voltage u of the permanent magnet machinemAnd the output voltage u of the invertersvmThe matching degree of the harmonic current is an optimization target, and the harmonic current of each order input by the magnetic field distribution model of the motor is globally optimized through an optimization algorithm. When the terminal voltage of the permanent magnet motor is matched with the output voltage of the inverter, optimization is completed, and motor current harmonic waves under the output voltage of the inverter are obtained.
Here, matching means terminal voltage u of the permanent magnet machinemAnd the output voltage u of the invertersvmThe degree of matching F is greater than a given value, in this case 99.5%. Terminal voltage u of permanent magnet machinemAnd the output voltage u of the invertersvmThe matching degree F is as follows:
where vmax is the maximum harmonic order number,
and
are respectively the output voltage u of the invertersvmAmplitude and phase, U, of the corresponding voltage harmonic of the v-th ordervAnd
respectively terminal voltage u of permanent magnet motormThe amplitude and phase of the corresponding v-th order voltage harmonic; the specific implementation mode and steps are as follows:
the following description will discuss a 6-pole 54-slot interior permanent magnet synchronous motor as an example.
1) A magnetic field distribution model of the built-in permanent magnet synchronous motor considering the saturation effect of the ferromagnetic material is established based on a winding function theory so as to represent the nonlinear relation between the harmonic current of the permanent magnet motor and the terminal voltage of the permanent magnet motor. The input of the magnetic field distribution model is the harmonic current of the permanent magnet motor, the output is the terminal voltage of the permanent magnet motor, and the permanent magnet motor is obtained by modelingAir gap field distribution B of machines(t,Rsα), and thus a back-emf or terminal voltage.
The air gap field distribution of the permanent magnet motor is as follows:
Bs(t,Rs,α)＝(Fs(t,α)-Fr(t,α))·Λ(α)
wherein: b iss(t,RsAnd alpha) is the distribution of the air gap field at the angular position alpha on the circumference of the inner radius of the stator of the permanent magnet motor at the moment t, RsIs the inner radius of the stator of the permanent magnet motor, Fs(t,α)、FrAnd (t, alpha) are stator and rotor magnetomotive forces at time t and angular position alpha respectively, Λ (alpha) is air gap permeance at angular position alpha, t is time, and alpha is an angular position on the circumference of the stator.
And establishing the magnetomotive force of the stator double-layer short-distance distributed winding based on a winding function theory. Stator magnetomotive force FsThe fourier series expression of (t, α) is as follows:
wherein: n is a radical ofp(α) is the winding function of the permanent magnet machine, p is the pole pair number of the permanent magnet machine, iphThe harmonic current of the winding phase ph is expressed in a fourier series form, ph represents the phase of the permanent magnet motor, ph is a, B, C, A, B, C represent the three phases of the permanent magnet motor, k represents the phase corresponding to the three phases of the permanent magnet motor, and k is 1,2,3, i represents the phase corresponding to the three phases of the permanent magnet motorphRespectively correspond to iA,iB,iC(ii) a v represents the order of the harmonic current, Iv、
Amplitude and phase, ω, of the v-th order harmonic current, respectivelyrMechanical angular velocity, N, for the rotation of a rotor of a permanent magnet machinecIs the number of turns per slot of the permanent magnet motor, q is the number of slots per pole and phase, u represents the u-th counter-pole of the permanent magnet motor, kw(v) Is the winding coefficient of the v-th order harmonic current.
The rotor magnetomotive force is established based on the flux continuity theorem. Assuming that the permeability of ferromagnetic material (i.e. silicon steel sheet) is positive infinity, the magnetic induction lines are all orthogonal to the material, i.e. the surface magnetic potential remains constant. Then the magnetomotive force Ur induced by the stator magnetomotive force in the air gap polar arc area when the rotor permanent magnet is not considered at the moment t can be obtaineds(t,α,θr) And magnetomotive force Ur generated by action of permanent magnets in air gap pole arc area when only rotor permanent magnets are arrangedpm(α,θr) And permanent magnet equivalent magnetomotive force Fpm(α,θr) Further obtain the rotor magnetic potential Fr(t,α)。
Fr(t,α)＝Fpm(α,θr)-Urs(t,α,θr)-Urpm(α,θr)
θr＝θr0+ωrt
Wherein: fpm(α,θr) Indicating the angular position of the rotor at thetarPermanent magnet equivalent magnetomotive force at angular position alpha, Urs(t,α,θr) Indicating that the rotor angular position is at theta at time trThe magnetomotive force, Ur, induced by the stator magnetomotive force at the angular position alpha of the air gap polar arc region when the rotor permanent magnet is not consideredpm(α,θr) Indicating the angular position of the rotor at thetarThe magnetomotive force generated by the permanent magnet at the angle position alpha of the air gap pole arc area when only the rotor permanent magnet exists; lambdabarrierFor rotor flux-barrier slotsσFor the leakage flux of the rotor magnetic-isolating slot, ΛpmFor rotor permanent magnet permeance, alphapThe angle occupied by the air gap polar arc region, HcCoercive force of permanent magnet, hpmIs the thickness of the permanent magnet, wpmTotal length of permanent magnet, warcIs the width of the air gap polar arc region, krIs the conversion coefficient theta of the rotor structure of the built-in permanent magnet synchronous motorrFor the angular position of the rotor, thetar0Is the initial angular position of the rotor.
Lambda (alpha) is air gap permeance considering stator slot opening influence based on a conformal mapping method and introduces a saturation coefficient k based on an equivalent magnetic networkuTo incorporate the saturation effect of ferromagnetic materials into the motor field distribution model. According to the air-gap field distribution Bs(t,RsAnd alpha) calculating the magnetic densities of the stator tooth part, the stator yoke part, the rotor yoke part and the pole shoe part, obtaining the relative magnetic permeability of each part through a BH curve of a silicon steel sheet, further obtaining the magnetic resistance of each part, obtaining a saturation coefficient, correcting the air gap magnetic permeability, iterating until the saturation coefficient is converged, and calculating the air gap magnetic field distribution under the condition of considering the saturation effect of the ferromagnetic material.
Wherein: lambda0Is the permeance of a uniform air gap, g is the air gap length, kuIs a saturation coefficient, θsFor stator slot opening arc, alpha0Is the radian of the slot pitch between two adjacent slots of the stator, Rst、Rsy、Rrt、Rry、RairReluctance, β, of the stator teeth, stator yoke, rotor yoke, pole shoe parts and air gap, respectivelyrRepresenting a coefficient for the permeance of the air gap obtained by conformal mapping, vc and a being calculated as betarTwo intermediate parameters in the process.
So as to obtain the air gap magnetic field distribution B of the permanent magnet motors(t,RsAlpha) to further obtain the induction voltage E of the permanent magnet motorp. Neglecting the end effect, the induced voltage is the terminal voltage u of the permanent magnet motorm；
Wherein: epIs the induced voltage of a permanent magnet machinep(t) denotes the flux linkage of the permanent magnet machine, NcIs the number of turns per slot, l, of the permanent magnet motorefIs the effective length of the permanent magnet motor, alphaiFor the initial angle of the coil winding, τ is the winding span.
Fig. 2 is a block flow diagram of a magnetic field distribution model of the interior permanent magnet synchronous motor considering the saturation effect of the ferromagnetic material according to the present invention.
2) Building (2)The method is characterized in that a double Fourier series model of inverter output voltage harmonic waves based on space vector modulation of a modulation function is established, and the modulation function v with uniformly distributed zero vectors is adoptedsvm(ωmt) to obtain an inverter output voltage usvm(t)：
Wherein: v. ofsvm(ωmt) is the modulation function, ωmFor modulating frequency, omegacIs the carrier frequency, M is the modulation depth, UdcIs a DC bus voltage, A0,0、A0,n、Am,0、Am,nIs a cosine Fourier coefficient, B0,n、Bm,0、Bm,nIs a sine Fourier coefficient, x is omegact，y＝ωmt，q＝mp'+n，
3) Establishing a matching degree between the terminal voltage of the permanent magnet motor and the output voltage of the inverter obtained in the step 1) and taking the matching degree as an optimization target according to the terminal voltage of the permanent magnet motor obtained in the step 1) and the output voltage of the inverter obtained in the step 2), carrying out global optimization on the harmonic current of each order input by the motor magnetic field distribution model in the step 1) through a differential evolution algorithm, and solving to obtain the amplitude and the phase I of each order harmonic currentv、
Then, the amplitude and phase I of each order harmonic current are utilizedv、
And calculating to obtain the harmonic current. As shown in fig. 3, a detailed implementation flow diagram of a method for predicting the harmonic current of the permanent magnet motor is provided, which is based on a magnetic field distribution model of the interior permanent magnet synchronous motor that is established based on a winding function theory and takes the saturation effect of the ferromagnetic material into consideration and a differential evolution algorithm.
Firstly, according to the working condition requirement, obtaining the output voltage u of the inverter through a double Fourier series model of the harmonic wave of the output voltage of the invertersvm. Then, randomly generating a population P of the initial harmonic current matrix of the permanent magnet motor(0). For each individual I in the group of harmonic current matrix of the permanent magnet machinei,n(i.e., harmonic current vector including amplitude and phase of 1 st to vmax th harmonic current), and obtaining i by Fourier series superposition of the harmonic current of the three-phase winding phasephInputting the motor magnetic field distribution model to obtain the corresponding terminal voltage u of the permanent magnet motorm。
P(n)＝[I1,n...Ii,n...INP,n]i＝1,...,NP；n＝0,...,G
Comparing terminal voltages u of permanent magnet machinesmAnd the output voltage u of the invertersvmThe amplitude and the phase of each order voltage harmonic are calculated, and the matching degree F of the amplitude and the phase is calculated to judge whether the amplitude and the phase are matched. Here "matching" means the terminal voltage u of the permanent magnet machinemAnd the output voltage u of the invertersvmThe degree of matching F is greater than a given value, in this case 99.5%. Terminal voltage u of permanent magnet machinemAnd the output voltage u of the invertersvmHas a degree of matching F of
Where vmax is the maximum harmonic order number,
and
are respectively the output voltage u of the invertersvmAmplitude and phase, U, of the corresponding voltage harmonic of the v-th ordervAnd
respectively terminal voltage u of permanent magnet motormThe amplitude and phase of the corresponding v-th order voltage harmonic;
when terminal voltage u of permanent magnet motormAnd the output voltage u of the invertersvmWhen matching, optimizing is completed to obtain the amplitude and phase I of each order harmonic current of the permanent magnet motor under the output voltage of the inverterv、
Then, the amplitude and phase I of each order harmonic current are utilizedv、
Obtaining harmonic current i of the permanent magnet motor by superposing Fourier series of the harmonic currentph. If the two are not matched, forming a next generation population by adopting a difference mode, and repeating the operations until the two are matched.
As shown in fig. 4-5, fig. 4 is a waveform of an inverter output voltage under a given condition, and fig. 5 is a waveform of a harmonic current of a motor under the inverter output voltage, it can be seen that the harmonic current calculated by the method is consistent with a calculation result of a finite element, and the calculation time by the method is shorter than that by the finite element method.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.
Claims (7)
1. A prediction method for harmonic current of a permanent magnet motor is characterized by comprising the following steps:
1) establishing a motor magnetic field distribution model considering the saturation effect of the ferromagnetic material, wherein the input of the motor magnetic field distribution model is the harmonic current of the permanent magnet motor, and the output of the motor magnetic field distribution model is the terminal voltage of the permanent magnet motor;
2) establishing a double Fourier series model of inverter output voltage harmonic waves based on space vector modulation of a modulation function, and inputting modulation depth to obtain the output voltage of the inverter;
3) establishing a matching degree between the terminal voltage of the permanent magnet motor and the output voltage of the inverter according to the terminal voltage of the permanent magnet motor obtained in the step 1) and the output voltage of the inverter obtained in the step 2), and taking the matching degree as an optimization target, and providing a matching method of harmonic current, namely performing global optimization on each order harmonic current of the motor magnetic field distribution model in the step 1) through an optimization algorithm, and solving to obtain the amplitude and the phase I of each order harmonic currentv、
Then, the amplitude and phase I of each order harmonic current are utilizedv、
And calculating to obtain the harmonic current.
2. The method for predicting the harmonic current of the permanent magnet motor according to claim 1, wherein: in the step 1), the induced voltage of the permanent magnet motor is used as the terminal voltage of the permanent magnet motor, and the magnetic field distribution model of the motor considering the ferromagnetic material saturation effect is specifically as follows:
Bs(t,Rs,α)＝(Fs(t,α)-Fr(t,α))·Λ(α)
wherein: b iss(t,RsAnd alpha) is the distribution of the air gap field at the angular position alpha on the circumference of the inner radius of the stator of the permanent magnet motor at the moment t, RsRepresenting the inner radius of the stator of the permanent magnet machine, Fs(t,α),Fr(t, α) are stator and rotor magnetomotive forces at time t and angular position α, respectively, t is time, α is the angular position on the stator circumference, and Λ (α) is the air gap flux guide at angular position α; n is a radical ofp(α) is the winding function of the permanent magnet machine, p is the pole pair number of the permanent magnet machine, iphThe harmonic current of the winding phase ph is expressed in a fourier series form, ph represents the phase of the permanent magnet motor, ph is a, B, C, A, B, C represent the three phases of the permanent magnet motor, k represents the phase corresponding to the three phases of the permanent magnet motor, and k is 1,2,3, i represents the phase corresponding to the three phases of the permanent magnet motorphRespectively correspond to iA,iB,iC(ii) a v represents the order of the harmonic current, Iv、
Amplitude and phase, N, of the v-th order harmonic current, respectivelycThe number of turns per slot of the permanent magnet motor, q is the number of slots per pole and phase, EpIs the induced voltage, omega, of a permanent magnet machinerMechanical angular velocity, l, for the rotation of the rotor of a permanent magnet machineefIs the effective length of the permanent magnet motor, alphaiIs the initial angle of the coil winding, τ is the winding span, kw(v) A winding coefficient for a v-th order harmonic current; u denotes the u-th antipole, Ψ, of the permanent magnet machinep(t) represents the flux linkage of the permanent magnet machine.
3. The method for predicting the harmonic current of the permanent magnet motor according to claim 2, wherein: the rotor magnetomotive force Fr(t, α) was modeled as follows:
Fr(t,α)＝Fpm(α,θr)-Urs(t,α,θr)-Urpm(α,θr)
wherein: fpm(α,θr) Indicating the angular position of the rotor at thetarPermanent magnet equivalent magnetomotive force at angular position alpha, Urs(t,α,θr) Indicating that the rotor angular position is at theta at time trThe magnetomotive force, Ur, induced by the stator magnetomotive force at the angular position alpha of the air gap polar arc region when the rotor permanent magnet is not consideredpm(α,θr) Indicating the angular position of the rotor at thetarThe magnetomotive force generated by the permanent magnet at the angular position alpha of the air gap pole arc area when only the rotor permanent magnet is positioned,Rsis the inner radius of the stator of the permanent magnet motorbarrierFor rotor flux-barrier slotsσFor the leakage flux of the rotor magnetic-isolating slot, ΛpmFor rotor permanent magnet permeance, alphapThe angle occupied by the air gap polar arc region, HcCoercive force of permanent magnet, hpmIs the thickness of the permanent magnet, krIs the conversion coefficient, w, of the rotor structure of the built-in permanent magnet synchronous motorpmTotal length of permanent magnet, warcIs the width of the air gap polar arc region, thetarFor the angular position of the rotor, thetar0Is the initial angular position of the rotor.
4. The method for predicting the harmonic current of the permanent magnet motor according to claim 2, wherein: the air gap permeance Lambda (alpha) is set by adopting the following formula:
wherein: lambda0Is a uniform air gap permeance, kuIs a saturation coefficient, θsFor stator slot opening arc, alpha0Is the radian between two adjacent slots of the stator, Rst、Rsy、Rrt、Rry、RairMagnetic resistances of the stator tooth portion, the stator yoke portion, the rotor yoke portion, the pole shoe portion and the air gap, respectively; beta is arA coefficient for the air gap permeance obtained by conformal mapping is shown.
5. The method for predicting the harmonic current of the permanent magnet motor according to claim 1, wherein: in the dual fourier series model in step 2), the modulation function of the inverter adopts the following manner:
wherein: v. ofsvm(ωmt) is the modulation function of the inverter, ωmFor modulating frequency, omegacIs the carrier frequency, M is the modulation depth, UdcIs the dc bus voltage.
6. The method for predicting the harmonic current of the permanent magnet motor according to claim 1, wherein: in the step 3), specifically, the terminal voltage u of the following permanent magnet motor is establishedmAnd the output voltage u of the invertersvmThe matching degree F:
where vmax is the maximum harmonic order number,
and
are respectively the output voltage u of the invertersvmAmplitude and phase, U, of the corresponding voltage harmonic of the v-th ordervAnd
respectively terminal voltage u of permanent magnet motormThe amplitude and phase of the corresponding v-th order voltage harmonic;
then, the matching degree maximization is taken as an optimization target, the harmonic current input by the motor magnetic field distribution model is subjected to global optimization solving through an optimization algorithm to obtain the amplitude and the phase I of each order harmonic current in the permanent magnet motorv、
7. The method for predicting the harmonic current of the permanent magnet motor according to claim 1, wherein: the optimization algorithm in the step 3) includes, but is not limited to, an evolutionary algorithm, a group intelligence algorithm, a simulated annealing algorithm, a tabu search algorithm and a neural network algorithm.
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