CN106487308A - The input of series electric motor drive system lacks a phase error-tolerance type Direct Torque Control - Google Patents

Abstract

The present invention relates to a kind of series electric motor drive system input lacks a phase error-tolerance type Direct Torque Control, be applied particularly to single inverter power six phase permanent-magnet synchronous motor series connection three-phase permanent magnet synchronous motor drive system, purpose is to realize two motor transient electromagnetic torque decouplers in the case of the scarce phase of input side in this kind of bi-motor tandem drive system using remaining 5 phase inverter bridge to control, to improve the reliability of this kind of tandem drive system.

Description

The input of series electric motor drive system lacks a phase error-tolerance type Direct Torque Control

Technical field

The six phase permanent-magnet synchronous motor series connection three-phase permanent magnet synchronous motor drivetrain the present invention relates to a kind of single inverter is powered System input lacks a phase error-tolerance type Direct Torque Control.

Background technology

Close with aerospace propulsion system, full warship electric power promotion, electric locomotive traction, electronic/fuel combination Automobile drive etc. The high speed development in key field, it has harsher requirement to the weight and volume of drive system, and lightweight, high power are close Degree, the power-driven system of low cost will be important developing direction.Single inverter power multiple electric motors composition series connection Drive system is an important research direction, compared with the three-phase drive system of the one-to-one power supply of inverter-motor, advantage It is：The quantity of inverter leg decreases；All series electric motors just can be carried out by uneoupled control by a set of DSP control platform. Single inverter power six phase permanent-magnet synchronous motor series connection three-phase permanent magnet synchronous motor drive system be multiple electric motors tandem drive system Typical case in system, this drive system utilizes two winding current opposite in phase characteristics of six-phase motor electricity space mutual deviation 180 degree, by six Connect with a phase winding in three phase electric machine again, thus realizing three after two winding tail end parallel connections of phase motor electricity space mutual deviation 180 degree Electromagnetic torque decoupling between phase motor control and six-phase motor control.Power due to employing single inverter, improve and be The reliability of system, reduces the cost of system；Further, since adopting permanent magnet excitation, two motor operation efficiency highs.

In order to improve further above-mentioned tandem drive system reliability it is desirable to six-phase motor one phase winding open circuit or inversion Under one brachium pontis failure condition of bridge, remain able to realize the electromagnetic torque between two motors using remaining 5 inverter bridge legs Uneoupled control.The no matter open circuit of six-phase motor one phase winding or one brachium pontis fault of inverter bridge, six-phase motor only has five phase winding works Make, flow in the winding being connected with fault brachium pontis or breaking winding disappearance, with the phase winding of disappearance phase winding electricity space symmetr The electric current crossed is identical with corresponding three-phase windings electric current.For lacking the six-phase motor of a phase, with disappearance phase winding electricity The phase winding of space symmetr is uncontrollable；And, other electric currents in two windings of electric space symmetr no longer keep inverted relationship, So destroy the electromagnetic torque decoupling between two motors.How to realize the synchronous electricity of six-phase permanent-magnet that single inverter lacks a phase The electromagnetic torque uneoupled control that machine is connected between three-phase permanent magnet synchronous motor drive system is the problem in science that must solve.For This, patent of the present invention proposes single inverter six phase permanent-magnet synchronous motor series connection three-phase permanent magnet synchronous motor drive system of powering and lacks one Phase error-tolerance type Direct Torque Control.

Content of the invention

Present invention aims to the deficiencies in the prior art, a kind of single inverter is provided to power the synchronous electricity of six-phase permanent-magnet Machine series connection three-phase permanent magnet synchronous motor drive system input lacks a phase error-tolerance type Direct Torque Control it is therefore an objective to utilize remaining 5 phase inverter bridge realize this kind of bi-motor tandem drive system occur input side lack a phase in the case of two motor transient electromagnetics turn Square uneoupled control, to improve the reliability of this kind of tandem drive system.

For achieving the above object, the technical scheme is that：It is mutually fault-tolerant that a kind of series electric motor drive system input lacks one Type Direct Torque Control, be applied particularly to single inverter power six phase permanent-magnet synchronous motor series connection three-phase permanent magnet synchronous motor Drive system, the method comprises the steps,

S1：Using T₆Orthogonal transform matrix, will include six input current i of disappearance phase_sA～i_sFIt is transformed in α β coordinate i_αi_βAnd i in xy coordinate system_xi_y：

Wherein, i_o1、i_o2For two zero-sequence currents；Because six-phase motor lacks a phase, and three-phase windings have central point, Two motor driven systems of all series connection only have 4 degree of freedom can control, due to needing the stator magnetic linkage to two motors, electricity Magnetic torque carries out closed loop control, occupies 4 degree of freedom, so variable is uncontrolled in two zero sequence shaftings；

S2：Using formula (2), i_αi_β, six-phase motor rotor flux ψ_f1And six-phase motor rotor position angle θ_r1Calculate α β Plane six-phase motor stator magnetic linkage ψ_sαψ_sβ；

L_sm1=0.5 (L_dm1+L_qm1), L_rs1=0.5 (L_dm1-L_qm1), L_dm1、L_qm1It is respectively six-phase motor phase winding main magnetic circuit Straight, quadrature axis inductance, L_sσ1For six-phase motor phase winding leakage inductance；

Using formula (3), i_xi_y, three phase electric machine rotor flux ψ_f2And three phase electric machine rotor position angle θ_r2Calculate x/y plane Three-phase motor stator magnetic linkage ψ_sxψ_sy：

L_sm2=0.5 (L_dm2+L_qm2), L_rs2=0.5 (L_dm2-L_qm2), L_dm2、L_qm2It is respectively three phase electric machine phase winding main magnetic circuit Straight, quadrature axis inductance, L_sσ2For three phase electric machine phase winding leakage inductance；

S3：Judge α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβα β plane sector number θ residing for vector_1si；Judge that xy puts down Face three-phase motor stator magnetic linkage ψ_sxψ_syX/y plane sector number θ residing for vector_2si；

S4：According to α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβAnd stator magnetic linkage amplitude givesThrough six-phase motor magnetic Chain hysteresis comparator, the variable φ of output control α β plane six-phase motor stator magnetic linkage amplitude_e1：

According to x/y plane three-phase motor stator magnetic linkage ψ_sxψ_syAnd stator magnetic linkage amplitude givesThrough three phase electric machine magnetic linkage Hysteresis comparator, the variable φ of output control x/y plane three-phase motor stator magnetic linkage amplitude_e2：

S5：Using formula (4), i_αi_βAnd ψ_sαψ_sβCalculate six-phase motor electromagnetic torque T_e1；

T_e1=p₁(ψ_sαi_β-ψ_sβi_α) (4)

Wherein, p₁For six-phase motor magnetic pole logarithm；

Using formula (5), i_xi_yAnd ψ_sxψ_syCalculate three phase electric machine electromagnetic torque T_e2；

T_e2=p₂(ψ_sxi_y-ψ_syi_x) (5)

Wherein, p₂For three phase electric machine magnetic pole logarithm；

S6：By six-phase motor electromagnetic torque T_e1And its set-pointGive six-phase motor torque hysteresis comparator, output Control six-phase motor electromagnetic torque variable τ_e1,

Wherein, ε_m1For six-phase motor torque stagnant ring ring width, its value can be according to actual six-phase motor direct torque error need Arrange；

By three phase electric machine electromagnetic torque T_e2And its set-pointGive three phase electric machine torque hysteresis comparator, output control Three phase electric machine electromagnetic torque variable τ_e2,

Wherein, ε_m2For three phase electric machine torque stagnant ring ring width, its value can be according to actual three phase electric machine direct torque error need Arrange；

S7：By τ_e1、φ_e1、θ_1si、τ_e2、φ_e2、θ_2siIt is simultaneously sent to optimized switching vector table, obtain one group of remaining healthy 5 phase Inverter bridge optimized switching combine, by inverter act on disappearance one mutually input six be in series three-phase permanent magnet synchronous motor drive System, realizing two stator flux of motor amplitude errors and electromagnetic torque error is 0 control targe.

In an embodiment of the present invention, in described step S6, six-phase motor electromagnetic torque set-pointDynamo-electric with three-phase electricity Magnetic torque set-pointDepending on concrete two motor control variables, specifically：If control is electromagnetic torque, system is straight Connect given；If control is rotating speed, two electric motor speed controller difference output torques giveWithIf control is Rotor position angle, then two motor position controller outputs are torque referenceWith

In an embodiment of the present invention, in described step S2, α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβWith x/y plane three Phase stator flux of motor ψ_sxψ_syAlso can be calculated using the voltage model of stator magnetic linkage, using the stator magnet of voltage model Chain typical calculation is as follows：

Step S21：Using T₆Orthogonal transform matrix, will include six input voltage u of disappearance phase_AO～u_FOIt is transformed to α β to sit U in mark_sαu_sβAnd u in xy coordinate system_sxu_sy：

Wherein, u_so1、u_so2For two residual voltages；

Step S22：According to formula (6), i_αi_βCalculate α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβ；

α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβ：

Wherein, R_s1For six-phase motor phase winding resistance；

According to formula (7), i_xi_yCalculate x/y plane three-phase motor stator magnetic linkage ψ_sxψ_sy；

X/y plane three-phase motor stator magnetic linkage ψ_sxψ_sy：

Wherein, R_s2For three phase electric machine phase winding resistance.

Compared to prior art, the invention has the advantages that：The single inverter of the present invention is powered and six is in series three Phase permagnetic synchronous motor lacks a phase error-tolerance type Direct Torque Control, solves the symmetrical winding permanent magnet of 60 degree six of biasing synchronous Motor series connection three-phase permanent magnet synchronous motor drive system two motors in the case of input disappearance one phase continue to decouple uninterrupted fortune A difficult problem for row, this control method has the advantage that：

1) consider the disappearance contribution to two motor mathematical models for the phase winding, two motor stator magnetic of disappearance phase will be included Chain control is circular, achieves the uneoupled control of two motor electromagnetic torques well；

2) permagnetic synchronous motor can produce reluctance torque using saliency, thus strengthening the load capacity of motor, and Control strategy of the present invention considers motor salient pole phenomenon, so when control object of the present invention is salient-pole permanent-magnet synchronous motor, Drive system output torque ability can effectively be strengthened；

3), after adopting the present invention, tandem drive system can be compatible to lacking one by winding normal non-fault situation fast transition Wrong running status, improves uninterrupted when series-connected double motors driving direct Torque Control winding open circuit or inverter bridge leg fault Reliability of operation.

Brief description

Fig. 1 single inverter power six phase permanent-magnet synchronous motor series connection three-phase permanent magnet synchronous motor input lack a phase error-tolerance type straight Connect torque-controlling structures figure.

Fig. 2 embodiments of the invention drive system hardware structure diagram.

Fig. 3 six phase permanent-magnet synchronous motor and three-phase permanent magnet synchronous motor series system.

Fig. 4 six phase permanent-magnet synchronous motor coordinate system defines.

Fig. 5 three-phase permanent magnet synchronous motor coordinate system defines.

The switching vector selector figure of α β plane, x/y plane after Fig. 6 phase shortage.

Synthesized voltage vector u in Fig. 7 alpha-beta plane_sα+ju_sβ.

Synthesized voltage vector u in Fig. 8 x-y plane_sx+ju_sy.

Specific embodiment

Below in conjunction with the accompanying drawings, technical scheme is specifically described.

When six symmetrical winding permanent magnet synchronous motor series connection three-phase permanent magnet synchronous motor drive system input sides lack a phase Afterwards, if not considering six in bi-motor tandem drive system mathematic model is set up and its error-tolerance type Strategy of Direct Torque Control builds In phase motor, the contribution of disappearance phase winding, so leads to the symmetry characteristic of original six-phase motor stator winding to go to pot, thus no Method searches out a set of effective coordinate transform and the six-phase motor lacking a phase is carried out decoupling modeling with three phase electric machine, finally cannot Realized using remaining 5 healthy inverter bridge leg output voltage vector between six-phase motor and the three phase electric machine of disappearance one phase Electromagnetic torque uneoupled control.In place of the deficiencies in the prior art, the present invention proposes a kind of consideration disappearance phase winding to fixed The six phase permanent-magnet synchronous motor series connection three-phase permanent magnet synchronous motor that the single inverter of sub- magnetic linkage modeling and control contribution is powered drives System lacks a phase error-tolerance type Direct Torque Control it is therefore an objective to realize this kind of bi-motor series connection using remaining 5 phase inverter bridge Two motor transient electromagnetic torque decouplers in the case of input side lacks a phase and controls, to improve this kind of tandem drive in drive system The reliability of system.

The structured flowchart of the inventive method is as shown in Figure 1.Using T₆Orthogonal transform matrix mutually inputs include disappearance phase 6 Electric current i_sA～i_sFIt is transformed to i in α β coordinate plane_αi_βAnd i in xy coordinate plane_xi_y(formula (1)), thus two motors of control The current component of energy converting between mechanical projects respectively to α β coordinate plane and xy coordinate plane；Using formula (2), i_αi_βAnd six phases Permagnetic synchronous motor (this motor is abbreviated as PMSM6) rotor position angle θ_r1Calculate the six-phase permanent-magnet comprising to lack phase in α β plane Synchronous motor stator magnetic linkage ψ_sαψ_sβ；Using formula (3), i_xi_yAnd three-phase permanent magnet synchronous motor (this motor is abbreviated as PMSM3) turns Sub- angular position theta_r2Calculate three-phase permanent magnet synchronous motor stator magnetic linkage ψ in x/y plane_sxψ_sy；Using formula (4), i_αi_βAnd ψ_sαψ_sβ Calculate the six-phase motor electromagnetic torque T of disappearance one phase_e1；Using formula (5), i_xi_yAnd ψ_sxψ_syCalculate three phase electric machine electromagnetism to turn Square T_e2；Six-phase motor electromagnetic torque is givenAnd electromagnetic torque T_e1, give the output control of six-phase motor torque hysteresis comparator The τ of six-phase motor electromagnetic torque processed_e1Variable；Three phase electric machine electromagnetic torque is givenAnd electromagnetic torque T_e2, give three-phase electricity The τ of dynamo-electric magnetic torque hysteresis comparator output control three phase electric machine electromagnetic torque_e2Variable；In six-phase motor α β coordinate plane Stator magnetic linkage amplitude gives | ψ_s1|^*And stator magnetic linkage amplitude | ψ_s1|, give six-phase motor flux linkage hysteresis comparator device output control six The φ of the stator magnetic linkage amplitude in phase motor α β coordinate plane_e1Variable；Three phase electric machine xy coordinate plane inner stator magnetic linkage amplitude Given | ψ_s2|^*And stator magnetic linkage amplitude | ψ_s2|, give three phase electric machine flux linkage hysteresis comparator device output control three phase electric machine xy coordinate The φ of plane inner stator magnetic linkage amplitude_e2Variable；The stator magnetic linkage vector ψ in six-phase motor α β coordinate plane_s1Argument ∠ θ_ψs1 With the stator magnetic linkage vector ψ in three phase electric machine xy coordinate plane_s2Argument ∠ θ_ψs2Give respective Stator flux linkage sectors respectively and judge ring Section, exports sector number θ residing for two stator flux of motor vectors respectively_1si、θ_2si；The controlling electromagnetic torque of two motors is become Amount τ_e1τ_e2, stator magnetic linkage amplitude control variable φ_e1φ_e2And sector number θ_1siθ_2si, give optimized switching vector table and export one group Optimum five inverter bridge leg switch combinations of residue, thus adding an optimal voltage vector in remaining 5 phase inputs, to realize Two stator flux of motor amplitude errors and electromagnetic torque error are 0 control.Default due to calculating six-phase motor α β coordinate plane Sub- magnetic linkage formula 2 includes the contribution of disappearance phase winding so that obtaining decoupling between the electromagnetic torque of two motors, is so profit With remaining 5 inverter bridge legs, uneoupled control is carried out to two motor electromagnetic torques by stator magnetic linkage and creates precondition.? Using in the drive system of all-digitized demodulator, do not need in addition to add hardware using the present invention, you can realize two motors of series connection Lack any one input phase error-tolerance type Direct Torque Control, reduce the hardware cost of drive system.The method is implemented as follows,

S1：Using T₆Orthogonal transform matrix, will include six input current i of disappearance phase_sA～i_sFIt is transformed in α β coordinate i_αi_βAnd i in xy coordinate system_xi_y：

Wherein, i_o1、i_o2For two zero-sequence currents；Because six-phase motor lacks a phase, and three-phase windings have central point, Two motor driven systems of all series connection only have 4 degree of freedom can control, due to needing the stator magnetic linkage to two motors, electricity Magnetic torque carries out closed loop control, occupies 4 degree of freedom, so variable is uncontrolled in two zero sequence shaftings；

S2：Using formula (2), i_αi_β, six-phase motor rotor flux ψ_f1And six-phase motor rotor position angle θ_r1Calculate α β Plane six-phase motor stator magnetic linkage ψ_sαψ_sβ；

L_sm1=0.5 (L_dm1+L_qm1), L_rs1=0.5 (L_dm1-L_qm1), L_dm1、L_qm1It is respectively six-phase motor phase winding main magnetic circuit Straight, quadrature axis inductance, L_sσ1For six-phase motor phase winding leakage inductance, these inductance value can obtain from six-phase motor nameplate；

Using formula (3), i_xi_y, three phase electric machine rotor flux ψ_f2And three phase electric machine rotor position angle θ_r2Calculate x/y plane Three-phase motor stator magnetic linkage ψ_sxψ_sy：

L_sm2=0.5 (L_dm2+L_qm2), L_rs2=0.5 (L_dm2-L_qm2), L_dm2、L_qm2It is respectively three phase electric machine phase winding main magnetic circuit Straight, quadrature axis inductance, L_sσ2For three phase electric machine phase winding leakage inductance, these inductance value can obtain from six-phase motor nameplate；

S3：Judge α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβα β plane sector number θ residing for vector_1si；Judge that xy puts down Face three-phase motor stator magnetic linkage ψ_sxψ_syX/y plane sector number θ residing for vector_2si；

S4：According to α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβAnd stator magnetic linkage amplitude givesThrough six-phase motor magnetic Chain hysteresis comparator, the variable φ of output control α β plane six-phase motor stator magnetic linkage amplitude_e1：

According to x/y plane three-phase motor stator magnetic linkage ψ_sxψ_syAnd stator magnetic linkage amplitude givesThrough three phase electric machine magnetic linkage Hysteresis comparator, the variable φ of output control x/y plane three-phase motor stator magnetic linkage amplitude_e2：

S5：Using formula (4), i_αi_βAnd ψ_sαψ_sβCalculate six-phase motor electromagnetic torque T_e1；

T_e1=p₁(ψ_sαi_β-ψ_sβi_α) (4)

Wherein, p₁For six-phase motor magnetic pole logarithm, can obtain from six-phase motor nameplate；

Using formula (5), i_xi_yAnd ψ_sxψ_syCalculate three phase electric machine electromagnetic torque T_e2；

T_e2=p₂(ψ_sxi_y-ψ_syi_x) (5)

Wherein, p₂For three phase electric machine magnetic pole logarithm, can obtain from six-phase motor nameplate；

S6：By six-phase motor electromagnetic torque T_e1And its set-pointGive six-phase motor torque hysteresis comparator, output Control six-phase motor electromagnetic torque variable τ_e1,

Wherein, ε_m1For six-phase motor torque stagnant ring ring width, its value can be according to actual six-phase motor direct torque error need Arrange；

By three phase electric machine electromagnetic torque T_e2And its set-pointGive three phase electric machine torque hysteresis comparator, output control Three phase electric machine electromagnetic torque variable τ_e2,

Wherein, ε_m2For three phase electric machine torque stagnant ring ring width, its value can be according to actual three phase electric machine direct torque error need Arrange；

S7：By τ_e1、φ_e1、θ_1si、τ_e2、φ_e2、θ_2siIt is simultaneously sent to optimized switching vector table, obtain one group of remaining healthy 5 phase Inverter bridge optimized switching combine, by inverter act on disappearance one mutually input six be in series three-phase permanent magnet synchronous motor drive System, realizing two stator flux of motor amplitude errors and electromagnetic torque error is 0 control targe.

In described step S6, six-phase motor electromagnetic torque set-pointWith three phase electric machine electromagnetic torque set-pointDepending on tool Depending on two motor control variables of body, specifically：If control is electromagnetic torque, system directly gives；If control is to turn Speed, then two electric motor speed controller difference output torques are givenWithIf control is rotor position angle, two electricity The output of machine positioner is torque referenceWith

In described step S2, α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβWith x/y plane three-phase motor stator magnetic linkage ψ_sxψ_sy Also can be calculated using the voltage model of stator magnetic linkage, the stator magnetic linkage typical calculation using voltage model is as follows：

Step S21：Using T₆Orthogonal transform matrix, will include six input voltage u of disappearance phase_AO～u_FOIt is transformed to α β to sit U in mark_sαu_sβAnd u in xy coordinate system_sxu_sy：

Wherein, u_so1、u_so2For two residual voltages；

Step S22：According to formula (6), i_αi_βCalculate α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβ；

α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβ：

Wherein, R_s1For six-phase motor phase winding resistance；

According to formula (7), i_xi_yCalculate x/y plane three-phase motor stator magnetic linkage ψ_sxψ_sy；

X/y plane three-phase motor stator magnetic linkage ψ_sxψ_sy：

Wherein, R_s2For three phase electric machine phase winding resistance.

It is below the specific embodiment of the present invention.

Embodiments of the invention drive system hardware configuration is as shown in Figure 2.Including：Rectification circuit, filter capacitor, six contraries Become device, 60 degree of six symmetrical winding permanent magnet synchronous motor of biasing, three-phase permanent magnet synchronous motor, six phase winding current collection circuits, Two motor rotor position angle Acquisition Circuit, isolation drive, central controller, man-machine interfaces etc..Can also adopt suitably straight Stream power supply provides six phase inverter DC bus-bar voltages.In inverter, power tube adopts IGBT or MOFET, and central controller adopts DSP or single-chip microcomputer.Winding current Acquisition Circuit is constituted with the operational amplifier mode of combining using Hall current sensor, also may be used Constituted so that the differential operational amplifier mode of combining is followed by using winding string power resistor.Can effectively be realized using Hall scheme Control loop and the electrical isolation of major loop, can reduce drive system cost using winding string power resistor scheme.Rotor position Angle setting Acquisition Circuit can be followed by level shifting circuit using rotary encoder and constitute, it would however also be possible to employ rotary transformer is followed by solving Code circuit is constituted, and wherein the former cost is relatively low, but position angle sampling precision is limited by encoder line number, and the latter is relatively costly, But position angle sampling precision is higher.Winding current Acquisition Circuit and the weak voltage signal of rotor position angle Acquisition Circuit deliver to central authorities' control Device A/D modular converter processed.Calculate and should send according to the error-tolerance type Strategy of Direct Torque Control of the signal obtaining and the present invention Control signal, goes to control the switch motion of the power switch pipe in inverter via isolation drive.

This system ultimate principle is described below：

Fig. 3 gives the connected mode of the six phase permanent-magnet synchronous motor series connection three-phase permanent magnet synchronous motor of the present invention. ABCDEF is six phase windings of six phase permanent-magnet synchronous motor, and UVW is three phase windings of three-phase permanent magnet synchronous motor.Normal six A phase current i in phase motor_sAWith D phase current i_sDAnti-phase, so being in series with three phase electric machine U again after A phase and the parallel connection of D phase tail end, To realize the decoupling in two motor controls, the connection of other phases is in the same manner.

Fig. 4 and Fig. 5 is the coordinate system that six phase permanent-magnet synchronous motor and three-phase permanent magnet synchronous motor realize energy converting between mechanical Definition.α β and xy is rest frame, d1q1 and d2q2 is rotor synchronous rotating frame.In the diagram, between d1 axle and α axle Angle be six-phase motor rotor position angle θ_r1, u_s1、i_s1、ψ_s1、ψ_r1It is respectively stator voltage vector, the electric current arrow of six-phase motor Amount, α β plane stator magnetic linkage vector and rotor flux linkage vector, projection on d1 axle, q1 axle, α axle, β axle for these vectors is used respectively Subscript " d1 ", " q1 ", " α ", " β " indicate.A～F is respectively six phase winding axis.ω_r1Electric angle for the rotation of six-phase motor rotor Speed.δ₁For the angle between six-phase motor α β plane stator magnetic linkage and rotor flux.In Figure 5, the folder between d2 axle and x-axis Angle is three phase electric machine rotor position angle θ_r2, u_s2、i_s2、ψ_s2、ψ_r2Be respectively the stator voltage vector of three phase electric machine, current phasor, X/y plane stator magnetic linkage vector and rotor flux linkage vector, these vectors are under the projection in d2 axle, q2 axle, x-axis, y-axis is used respectively Mark " d2 ", " q2 ", " x ", " y " indicate.U～W is respectively three-phase windings axis.ω_r2Electric angle speed for the rotation of three phase electric machine rotor Degree.δ₂Angle between x/y plane stator magnetic linkage for three phase electric machine and rotor flux.Except for controlling two in six-phase motor Freely it is outside one's consideration for 4 of platform motor energy converting between mechanical, also there are 2 degree of freedom, this two degree of freedom variables project to o respectively₁ And o₂Zero sequence shafting.

Using following T₆Matrix can be Transformation of Mathematical Model in natural system of coordinates to α β, xy, o₁o₂In rest frame：

Six-phase motor α β plane stator magnetic linkage ψ_sαψ_sβWith three phase electric machine x/y plane stator magnetic linkage ψ_sxψ_syAs follows respectively：

The electromagnetic torque of six phases and three phase electric machine is as follows respectively：

T_e1=p₁(ψ_sαi_β-ψ_sβi_α) formula 4

T_e2=p₂(ψ_sxi_y-ψ_syi_x) formula 5

αβ、xy、o₁o₂In rest frame, voltage balance equation is as follows respectively：

Contrast (formula 4～formula 8) can be seen that related to six-phase motor energy converting between mechanical in train Variable is only present on α β plane；In x/y plane, six-phase motor will produce leakage inductance pressure drop (L on three phase electric machine_sσ1*di_x/ dt、L_sσ1*di_y/ dt) and resistance drop (R_s1*i_x、R_s1*i_y), but leakage inductance and resistance very little, it is negligible, therefore should Only related to the three phase electric machine energy converting between mechanical variable of plane；o₁o₂Plane and the energy converting between mechanical variable of two motors All it doesn't matter, only relevant with the resistance of the stator winding of two motors and leakage inductance.Therefore, six-phase motor and three phase electric machine can So that decoupling independent control to be realized respectively on α β plane and x/y plane.

According to the definition of d1q1 in Fig. 4 and α β coordinate system, six-phase motor stator magnetic linkage and electromagnetic torque rotation transformation are arrived In d1q1 coordinate system：

T_e1=p₁(ψ_sd1i_q1-ψ_sq1i_d1) formula 10

Wherein, L_d1=L_sσ1+3L_sm1+3L_rs1, L_q1=L_sσ1+3L_sm1-3L_rs1It is respectively the straight of six-phase motor d1q1 coordinate system Quadrature axis inductance.

Obtained by Fig. 4：

ψ_sd1=| ψ_s1|cosδ₁Formula 11

ψ_sq1=| ψ_s1|sinδ₁Formula 12

Can be obtained according to formula (formula 9), (formula 11), (formula 12)

(formula 11)～(formula 14) is substituted into (formula 10) can derive：

Understood according to formula (formula 15), as stator magnetic linkage ψ_s1When amplitude is controlled to constant, want to control torque T_e1, only need Control angle δ₁.

In the same manner, three phase electric machine torque is it is also theorized that the expression formula similar to formula (formula 15) is as follows：

Wherein, L_d2=2L_sσ2+3L_sm2+3L_rs2, L_q2=2L_sσ2+3L_sm2-3L_rs2It is respectively three phase electric machine d2q2 coordinate system D-axis and q-axis inductance.Understood according to formula (formula 16), as stator magnetic linkage ψ_s2When amplitude is controlled to constant, want to control torque T_e2, only Angle δ need to be controlled₂.

Either six phase, or three phase electric machine, to by quick control δ₁Or δ₂, to realize quick to electromagnetic torque Control it is only necessary to the rotation of quick control stator magnetic linkage vector.So, realize uneoupled control between two motors it is important to How to utilize inverter output voltage vector to two stator flux of motor ψ_s1、ψ_s2Carry out uneoupled control.

From Fig. 3 connection figure, voltage u after six phase winding A phases are disconnected with inverter bridge_Ao～u_FoDerivation result is as follows：

Using T₆Premultiplication (formula 17) both sides obtain

According to (formula 18) visible, u_so1Naturally after being the open circuit of 0, A phase, and three-phase windings adopt star-like connection, so entirely Drive system only has 4 free variables controlled.Control six-phase motor and three phase electric machine electromechanics energy using α β plane, x/y plane respectively After total 4 free variables after amount conversion, on o2 axle, variable is uncontrollable.

Visible according to voltage, magnetic linkage relation, using suitable switch combination can control simultaneously six-phase motor α β plane, three Phase motor x/y plane inner stator magnetic linkage, thus realize to six phases and three phase electric machine electromagnetic torque uneoupled control.

Ignore u_AoAfter contribution to voltage vector in formula (formula 18), formula (formula 18) simplifies further

According to formula (formula 19), take different switch combination (S_b～S_f) one group of α β plane, the switch of x/y plane can be obtained Vector u_sα+ju_sβ、u_sx+ju_sy, draw α β plane, x/y plane switching vector selector figure as shown in Figure 6.

Can be according to the Direct Torque Control exporting a voltage vector in traditional one digital controlling cycle, directly It is connected on sectorization in α β plane and x/y plane, build optimized switching vector table.But this method can make optimized switching vector Table becomes very huge, reduces the real-time of Direct Torque Control.For this reason, the present invention adopts univoltage vector partial synthesis Voltage vector combines method, to build optimized switching vector table；α β plane and x/y plane are each divided into 90 degree of 4 spans Sector, respectively as shown in FIG. 7 and 8, the univoltage vector being adopted or synthesized voltage vector are on the border of sector.By following Mode resultant vector：81 (16,30), 82 (30,25), 83 (12,25), 84 (16,12), 85 (6,26), 87 (12,11), 89 (6, 19), 90 (15,19), 91 (15,1), 92 (6,1), 93 (19,20), 95 (9,13).Each resultant vector is by original two Nonzero voltage space vector respectively acts on half controlling cycle and produces, and such as resultant vector 85 is by original 6 vector 26 vector respectively Controlling cycle T of effect half_s/ 2 formation, its position, size and PWM sequential such as Fig. 7 and Fig. 8 institute on α β plane and x/y plane Show.Continuous for arrow number, in figures 7 and 8 original vector 10,4,27,21 again arrow number is 86,88, 94,96.Vector respective scattergram such as Fig. 7 and Fig. 8 on α β plane and x/y plane.Based on 81～96 vectors, build the present invention Optimized switching vector table method be elaborated as follows：

1) the synthesized voltage vector figure shown in Fig. 7, Fig. 8 is respectively divided into 4 sectors by figure mark, sector number is remembered respectively For θ_1siAnd θ_2si(i=1,2,3,4).90 ° of electrical angles of each sector span.

2) judge six-phase motor stator magnetic linkage ψ respectively_s1With three-phase motor stator magnetic linkage ψ_s2Residing sector, according to two Motor state in which, to select suitable voltage vector.For example, when the magnetic linkage of six-phase motor be in the first sector (as Fig. 7), Torque and magnetic linkage are required to increase；The sector of three phase electric machine is also at the first sector (as Fig. 8), torque and magnetic linkage and is also required to simultaneously Increase, then should select voltage vector 81.

3) combine 1) and 2) combined selection as a result, it is possible to obtain optimized switching vector table as shown in table 1, according to this table institute The inverter output voltage vector obtaining, can realize lacking simultaneously the six-phase motor of a phase and three phase electric machine electromagnetic torque and Stator magnetic linkage amplitude follows the tracks of set-point all the time, and two motors achieve uneoupled control.

Table 1 optimized switching vector table

In Table 1, τ_e1=1 and τ_e2=1 represents two motor torques all increases, τ_e1=-1 and τ_e2=-1 represents two electricity Machine torque all reduces.Ф_e1=1 and Ф_e2=1 represents two motor magnetic linkages all increases, Ф_e1=0 and Ф_e2=0 represents two motors Magnetic linkage all reduces

Work process comprises the steps：

(1) utilize T in formula 1₆Orthogonal transform matrix, will include six input current i of disappearance phase_sA～i_sFIt is transformed to α β I in coordinate_αi_βAnd i in xy coordinate system_xi_y；

(2) formula 2, i are utilized_αi_β, six-phase motor rotor flux ψ_f1And six-phase motor rotor position angle θ_r1Calculate α β to put down Face six-phase motor stator magnetic linkage ψ_sαψ_sβ；Using formula 3, i_xi_x, three phase electric machine rotor flux ψ_f2And three phase electric machine rotor position angle θ_r2Calculate x/y plane three-phase motor stator magnetic linkage ψ_sxψ_sy；

(3) judge α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβα β plane sector number θ residing for vector_1si；Judge that xy puts down Face three-phase motor stator magnetic linkage ψ_sxψ_syX/y plane sector number θ residing for vector_2si；

(4) according to α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβAnd stator magnetic linkage amplitude givesThrough six-phase motor magnetic Chain hysteresis comparator, the variable φ of output control α β plane six-phase motor stator magnetic linkage amplitude_e1；Fixed according to x/y plane three phase electric machine Sub- magnetic linkage ψ_sxψ_syAnd stator magnetic linkage amplitude givesThrough three phase electric machine flux linkage hysteresis comparator device, output control x/y plane three-phase The variable φ of stator flux of motor amplitude_e2；

(5) formula 4, i are utilized_αi_βAnd ψ_sαψ_sβCalculate six-phase motor electromagnetic torque T_e1；Using formula 5, i_xi_yAnd ψ_sxψ_syMeter Calculate three phase electric machine electromagnetic torque T_e2；

(6) by six-phase motor electromagnetic torque T_e1And its set-pointGive six-phase motor torque hysteresis comparator, output Control six-phase motor electromagnetic torque variable τ_e1；By three phase electric machine electromagnetic torque T_e2And its set-pointGive three phase electric machine to turn Square hysteresis comparator, output control three phase electric machine electromagnetic torque variable τ_e2；

(7) by τ_e1、φ_e1、θ_1si、τ_e2、φ_e2、θ_2siIt is simultaneously sent to optimized switching vector table, obtain one group of remaining healthy 5 phase Inverter bridge optimized switching combine, by inverter act on disappearance one mutually input six be in series three-phase permanent magnet synchronous motor drive System, realizing two stator flux of motor amplitude errors and electromagnetic torque error is 0 control targe.

Wherein in step (6), electromagnetic torque givesWithDepending on concrete two motor control variables.If controlling It is electromagnetic torque, then system directly gives this value；If control is rotating speed, (such as PI controls two electric motor speed controllers Device) respectively output torque giveWithIf control is rotor position angle, two motor position controller outputs are Torque referenceWith

α β plane six-phase motor stator magnetic linkage ψ wherein in step (2)_sαψ_sβWith x/y plane three-phase motor stator magnetic linkage ψ_sxψ_sy Can also be calculated using the voltage model of stator magnetic linkage.

It is more than presently preferred embodiments of the present invention, all changes made according to technical solution of the present invention, produced function is made With without departing from technical solution of the present invention scope when, belong to protection scope of the present invention.

Claims (3)

1. a kind of input of series electric motor drive system lack a phase error-tolerance type Direct Torque Control it is characterised in that：Specifically should Power six phase permanent-magnet synchronous motor series connection three-phase permanent magnet synchronous motor drive system for single inverter, the method includes walking as follows Suddenly,

S1：Using T₆Orthogonal transform matrix, will include six input current i of disappearance phase_sA～i_sFIt is transformed to i in α β coordinate_αi_βAnd I in xy coordinate system_xi_y：

$\left[\begin{array}{c}{i}_{\mathrm{\α}}\\ i_{\mathrm{\β}}\\ i_x\\ i_y\\ i_{o1}\\ i_{o2}\end{array}\right]=\frac{1}{\sqrt{3}}\left[\begin{array}{cccccc}1& \frac{1}{2}& -\frac{1}{2}& -1& -\frac{1}{2}& \frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& \frac{\sqrt{3}}{2}& 0& -\frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ 1& -\frac{1}{2}& -\frac{1}{2}& 1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}& 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}& -\frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& -\frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& -\frac{1}{\sqrt{2}}\end{array}\right]\left[\begin{array}{c}{i}_{sA}\\ i_{sB}\\ i_{sC}\\ i_{sD}\\ i_{sE}\\ i_{sF}\end{array}\right]---\left(1\right)$

Wherein, i_o1、i_o2For two zero-sequence currents；Because six-phase motor lacks a phase, and three-phase windings have central point, all strings Two motor driven systems of connection only have 4 degree of freedom can control, due to needing the stator magnetic linkage to two motors, electromagnetic torque Carry out closed loop control, occupy 4 degree of freedom, so variable is uncontrolled in two zero sequence shaftings；

S2：Using formula (2), i_αi_β, six-phase motor rotor flux ψ_f1And six-phase motor rotor position angle θ_r1Calculate α β plane Six-phase motor stator magnetic linkage ψ_sαψ_sβ；

$\left[\begin{array}{c}{\mathrm{\ψ}}_{s\mathrm{\α}}\\ {\mathrm{\ψ}}_{s\mathrm{\β}}\end{array}\right]=\left[\begin{array}{cc}{L}_{s\mathrm{\σ}1}+3L_{sm1}+3L_{rs1}\cos \left(2{\mathrm{\θ}}_{r1}\right)& 3L_{rs1}\sin \left(2{\mathrm{\θ}}_{r1}\right)\\ 3L_{rs1}\sin \left(2{\mathrm{\θ}}_{r1}\right)& L_{s\mathrm{\σ}1}+3L_{sm1}-3L_{rs1}\cos \left(2{\mathrm{\θ}}_{r1}\right)\end{array}\right]\left[\begin{array}{c}{i}_{\mathrm{\α}}\\ i_{\mathrm{\β}}\end{array}\right]+\sqrt{3}{\mathrm{\ψ}}_{f1}\left[\begin{array}{c}{\mathrm{cos\θ}}_{r1}\\ {\mathrm{sin\θ}}_{r1}\end{array}\right]---\left(2\right)$

L_sm1=0.5 (L_dm1+L_qm1), L_rs1=0.5 (L_dm1-L_qm1), L_dm1、L_qm1It is respectively six-phase motor phase winding main magnetic circuit Directly, quadrature axis inductance, L_sσ1For six-phase motor phase winding leakage inductance；

Using formula (3), i_xi_y, three phase electric machine rotor flux ψ_f2And three phase electric machine rotor position angle θ_r2Calculate x/y plane three-phase Stator flux of motor ψ_sxψ_sy：

$\left[\begin{array}{c}{\mathrm{\ψ}}_{sx}\\ {\mathrm{\ψ}}_{sy}\end{array}\right]=\left[\begin{array}{cc}2L_{s\mathrm{\σ}2}+3L_{sm2}+3L_{rs2}\cos \left(2{\mathrm{\θ}}_{r2}\right)& 3L_{rs2}\sin \left(2{\mathrm{\θ}}_{r2}\right)\\ 3L_{rs2}\sin \left(2{\mathrm{\θ}}_{r2}\right)& 2L_{s\mathrm{\σ}2}+3L_{sm2}-3L_{rs2}\cos \left(2{\mathrm{\θ}}_{r2}\right)\end{array}\right]\left[\begin{array}{c}{i}_x\\ i_y\end{array}\right]+\sqrt{3}{\mathrm{\ψ}}_{f2}\left[\begin{array}{c}{\mathrm{cos\θ}}_{r2}\\ {\mathrm{sin\θ}}_{r2}\end{array}\right]---\left(3\right)$

L_sm2=0.5 (L_dm2+L_qm2), L_rs2=0.5 (L_dm2-L_qm2), L_dm2、L_qm2It is respectively three phase electric machine phase winding main magnetic circuit Directly, quadrature axis inductance, L_sσ2For three phase electric machine phase winding leakage inductance；

S3：Judge α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβα β plane sector number θ residing for vector_1si；Judge x/y plane three-phase Stator flux of motor ψ_sxψ_syX/y plane sector number θ residing for vector_2si；

S4：According to α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβAnd stator magnetic linkage amplitude givesStagnant through six-phase motor magnetic linkage Ring comparator, the variable φ of output control α β plane six-phase motor stator magnetic linkage amplitude_e1：

${\mathrm{\&phi;}}_{e1}=\left\{\begin{array}{cc}1& \left|{\mathrm{\&psi;}}_{s1}^{*}\right|-\sqrt{{\mathrm{\&psi;}}_{s\mathrm{\&alpha;}}^2+{\mathrm{\&psi;}}_{s\mathrm{\&beta;}}^2}>0\\ 0& \left|{\mathrm{\&psi;}}_{s2}^{*}\right|-\sqrt{{\mathrm{\&psi;}}_{s\mathrm{\&alpha;}}^2+{\mathrm{\&psi;}}_{s\mathrm{\&beta;}}^2}<0\end{array}\right.$

According to x/y plane three-phase motor stator magnetic linkage ψ_sxψ_syAnd stator magnetic linkage amplitude givesThrough the stagnant chain rate of three phase electric machine magnetic linkage Compared with device, the variable φ of output control x/y plane three-phase motor stator magnetic linkage amplitude_e2：

${\mathrm{\&phi;}}_{e2}=\left\{\begin{array}{cc}1& \left|{\mathrm{\&psi;}}_{s2}^{*}\right|-\sqrt{{\mathrm{\&psi;}}_{sx}^2+{\mathrm{\&psi;}}_{sy}^2}>0\\ 0& \left|{\mathrm{\&psi;}}_{s2}^{*}\right|-\sqrt{{\mathrm{\&psi;}}_{sx}^2+{\mathrm{\&psi;}}_{sy}^2}<0\end{array}\right.$

S5：Using formula (4), i_αi_βAnd ψ_sαψ_sβCalculate six-phase motor electromagnetic torque T_e1；

T_e1=p₁(ψ_sαiβ-ψ_sβi_α) (4)

Wherein, p₁For six-phase motor magnetic pole logarithm；

Using formula (5), i_xi_yAnd ψ_sxψ_syCalculate three phase electric machine electromagnetic torque T_e2；

T_e2=p2 (ψ_sxi_y-ψ_syi_x) (5)

Wherein, p₂For three phase electric machine magnetic pole logarithm；

S6：By six-phase motor electromagnetic torque T_e1And its set-pointGive six-phase motor torque hysteresis comparator, output control six Phase motor electromagnetic torque variable τ_e1,

${\mathrm{\&tau;}}_{e1}=\left\{\begin{array}{cc}1& T_{e1}^{*}-T_{e1}\&GreaterEqual;+{\mathrm{\&epsiv;}}_{m1}\\ -1& T_{e1}^{*}-T_{e1}\&le;-{\mathrm{\&epsiv;}}_{m1}\end{array}\right.$

Wherein, ε_m1For six-phase motor torque stagnant ring ring width, its value can need set according to actual six-phase motor direct torque error Put；

By three phase electric machine electromagnetic torque T_e2And its set-pointGive three phase electric machine torque hysteresis comparator, output control three-phase Motor electromagnetic torque variable τ_e2,

${\mathrm{\&tau;}}_{e2}=\left\{\begin{array}{cc}1& T_{e2}^{*}-T_{e2}\&GreaterEqual;+{\mathrm{\&epsiv;}}_{m2}\\ -1& T_{e2}^{*}-T_{e2}\&le;-{\mathrm{\&epsiv;}}_{m2}\end{array}\right.$

Wherein, ε_m2For three phase electric machine torque stagnant ring ring width, its value can need set according to actual three phase electric machine direct torque error Put；

S7：By τ_e1、φ_e1、θ_1si、τ_e2、φ_e2、θ_2siIt is simultaneously sent to optimized switching vector table, obtain one group of remaining healthy 5 phase inversion Bridge optimized switching combines, and is in series three-phase permanent magnet synchronous motor drivetrain by inverter acts on that disappearance one mutually inputs six System, realizing two stator flux of motor amplitude errors and electromagnetic torque error is 0 control targe.

2. series electric motor drive system input according to claim 1 lacks a phase error-tolerance type Direct Torque Control, its It is characterised by：In described step S6, six-phase motor electromagnetic torque set-pointWith three phase electric machine electromagnetic torque set-pointDepending on Depending on concrete two motor control variables, specifically：If control is electromagnetic torque, system directly gives；If control is Rotating speed, then two electric motor speed controller difference output torques are givenWithIf control is rotor position angle, two Motor position controller output is torque referenceWith

3. series electric motor drive system input according to claim 1 lacks a phase error-tolerance type Direct Torque Control, its It is characterised by：In described step S2, α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβWith x/y plane three-phase motor stator magnetic linkage ψ_sxψ_sy Also can be calculated using the voltage model of stator magnetic linkage, the stator magnetic linkage typical calculation using voltage model is as follows：

Step S21：Using T₆Orthogonal transform matrix, will include six input voltage u of disappearance phase_AO～u_FOIt is transformed in α β coordinate u_sαu_sβAnd u in xy coordinate system_sxu_sy：

$\left[\begin{array}{c}{u}_{s\mathrm{\&alpha;}}\\ u_{s\mathrm{\&beta;}}\\ u_{sx}\\ u_{sy}\\ u_{so1}\\ u_{so2}\end{array}\right]=\frac{1}{\sqrt{3}}\left[\begin{array}{cccccc}1& \frac{1}{2}& -\frac{1}{2}& -1& -\frac{1}{2}& \frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& \frac{\sqrt{3}}{2}& 0& -\frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ 1& -\frac{1}{2}& -\frac{1}{2}& 1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}& 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}& -\frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& -\frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& -\frac{1}{\sqrt{2}}\end{array}\right]\left[\begin{array}{c}{u}_{AO}\\ u_{BO}\\ u_{CO}\\ u_{DO}\\ u_{EO}\\ u_{FO}\end{array}\right]$

Wherein, u_so1、u_so2For two residual voltages；

Step S22：According to formula (6), i_αi_βCalculate α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβ；

$\left[\begin{array}{c}{u}_{s\mathrm{\&alpha;}}\\ u_{s\mathrm{\&beta;}}\end{array}\right]=\left[\begin{array}{c}{R}_{s1}{i}_{\mathrm{\&alpha;}}\\ R_{s1}{i}_{\mathrm{\&beta;}}\end{array}\right]+\frac{d}{dt}\left[\begin{array}{c}{\mathrm{\&psi;}}_{s\mathrm{\&alpha;}}\\ {\mathrm{\&psi;}}_{s\mathrm{\&beta;}}\end{array}\right]---\left(6\right)$

α β plane six-phase motor stator magnetic linkage ψ_sαψ_sβ：

$\left\{\begin{array}{c}{\mathrm{\&psi;}}_{s\mathrm{\&alpha;}}=\&Integral;(u_{s\mathrm{\&alpha;}}-R_{s1}{i}_{\mathrm{\&alpha;}})dt\\ {\mathrm{\&psi;}}_{s\mathrm{\&beta;}}=\&Integral;(u_{s\mathrm{\&beta;}}-R_{s1}{i}_{\mathrm{\&beta;}})dt\end{array}\right.$

Wherein, R_s1For six-phase motor phase winding resistance；

According to formula (7), i_xi_yCalculate x/y plane three-phase motor stator magnetic linkage ψ_sxψ_sy；

$\left[\begin{array}{c}{u}_{sx}\\ u_{sy}\end{array}\right]=\left[\begin{array}{c}(R_{s1}+2R_{s2})i_x\\ (R_{s1}+2R_{s2})i_y\end{array}\right]+L_{s\mathrm{\&sigma;}1}\frac{d}{dt}\left[\begin{array}{c}{i}_x\\ i_y\end{array}\right]+\frac{d}{dt}\left[\begin{array}{c}{\mathrm{\&psi;}}_{sx}\\ {\mathrm{\&psi;}}_{sy}\end{array}\right]---\left(7\right)$

X/y plane three-phase motor stator magnetic linkage ψ_sxψ_sy：

$\left\{\begin{array}{c}{\mathrm{\&psi;}}_{sx}=-L_{s\mathrm{\&sigma;}1}{i}_x+\&Integral;\&lsqb;u_{sx}-(R_{s1}+2R_{s2})i_x\&rsqb;dt\\ {\mathrm{\&psi;}}_{sy}=-L_{s\mathrm{\&sigma;}1}{i}_y+\&Integral;\&lsqb;u_{sy}-(R_{s1}+2R_{s2})i_y\&rsqb;dt\end{array}\right.$

Wherein, R_s2For three phase electric machine phase winding resistance.