永磁同步电机控制原理

1、永磁同步电机控制原理-yyc1永磁同步电机原理1.1永磁同步电机基本结构永磁同步电机转子是永磁铁，定子是三柑绕组。 假设1）定子绕组为Y形接法，三相绕组对称分布。2）忽略定子绕组的齿槽对气隙磁场分布的影响。3）忽略铁心损失4）忽略电动机参数（绕组电阻和绕组电感等）的变化。 三相两极永磁同步电机的结构：a)b)a）定子绕组分布图b）定子绕组示意图1.2永磁同步电机动态数学模型ABC三项绕组的磁链可以拆分为2部分，定子绕组自感互感产生的磁链和转子永磁体产生的 磁链。aa Lab Lac中4mba Lbb Lbc+屮BmCA “B Lgic定子绕组对称分布S = LS-Lm cos(20)Lbb =

2、 G + Lm cos(2(8 27r/3)Lee = G + Lm cos(2(0 + 2tt/3)Ls为三相绕组自感平均值Lm为三相绕组自感二次谐波幅值B为转子电角度电角阪=N%N为极对数叫为机械角度定子绕组互感Lca = Lac = 一M$ Lm cos(2 (% + 石 + 2w/3)注意，这堅1忖定义的是负号,跟有的书上不一样。转子永磁体在三相绕组产生的磁链与电流无关，仅与电角度冇关屮4m = Wm COS(0)屮Bm =屮mCOS(& -2兀/3)屮Cm=屮m COS(& + 27T/3)永磁同步电机模型的表达关键在于磁链数据，现在磁链数据表达为4个参数Lm Ms i|/m 转矩方

3、程化简表达式:Matlab 代码:syns thetasms L_AA L_AB L_AC L_BA L_BB L_BC L_CA L_CB L_CC Ls Lm MsL-AA = Ls +Ln*cos(2*theta);L_BB Ls 4Ln*cos(2*(theta-2*pi/3);L_CC = Ls *Ln*cos(2*(theta*2*pi/3):L_AB = -Ms - Lu*cos(2*(theta + pl/6);L.BC = -Ms - Ln*cos(2*(theta + pi/6 - 2*pi/3):L_CA = -Ms - Lii*cos (2* (theta pi/6 土

4、 2*pi/3):L_BA 二 L-AB;L.CB - L_BC：L_AC = L_CA：syns L.ABC 1_A1_Ci_ABC = Ci_A： i.B： i_C：L_ABC = L_AA L_AB L_AC； L_BA L_BB L_BC： L_CA L_CB L_CC；syns phi_Aa phi_Bm phi_Cx phi_Mphi.Am = phi_M*cos(theta):phl.Bm = phl_Mcoslthea-2*pl/3):phi.Cm = phi_M*cos(.theta*2*pi/3);syns phi.ABCnphl_A3Cn = phi_Am： phi_Bm

5、： phiCmJ:syras Te NTe = N/2*(i_ABC. *J*diff(L.ABC theta)*i_ABC * (i.ABC. )*diff(phi-ABCm, theta): slnpllfy(Te|)1.3坐标变换由前面推导发现在ABC三相坐标下磁链往往都相互耦合，与三相电流，角度都相关，表达式 很复杂，因此想到坐标变换。a) 3s坐标系b) 2s坐标系c) 2r坐标系电动机内的气隙磁场是进行电磁能量传递的媒介，定转子之间的能量传递是靠气隙磁场 来进行的，不同类型的绕组进行变换时，需要保持它们的总磁动势不变。嚟=“3 ( +滋片喑=比仏+ 4力）/嚟表示3 s坐标绕组产生

6、的磁动势在2s坐标中的衣达 珂：表示2s坐标绕组产生的磁动势在2s坐标中的表达 於:茨示2r坐标绕组产生的磁动势在2s坐标中的表达为了让推导出來的三相电流与两相电流幅值相等，取护=2/31 - 2V3-2_12V3_2同理得到:2宀2$ =cosOsin 3-shi 0cos 6 .C2sf2r =COS0一 sin 8sin 8cosJ1.4 dq坐标系的动态数学方程执行坐标变换ld1=2s2r3s2slALSKl=22山325Matlab代码syits thetaC.2s_2r = Leos(thetaj sin (theta): -sin(theta) cos(theta):C_cs_2

7、s = 2/3*L -1/2 -1/2： 0, sqrt(3)Z2 -sqrt /2;C.2s_3s = ：1 0;-l/2 sqrt(3) /2;l/2 -sqrt(3)/2;C_2r_2s = Icos I thetG -sin(theta; sin(theta) cos(theta); i_ABC C_2s_3s*C_2r_2s木i_d;i_Q】：u.ABC = C.2s.3s*C.2r_2s*u_d;u_q;phi.ABC = C_2s_3s*C_2r_2s* lphi_d; phi.q |;i_A = 1_ABC(1);u.A = u_ABC(l);phi_A = ohi_ABC(l

8、):得到：uA = ud cos 0 uq sin 0“ =id cos 3 iq sin 8= id cosO 一$ sin&带入A相电压方程:dA得到:iia cos 6 uq sin 0整理得到:才 d + R j COS 01 Uq ” $ CD书q RH I Sill 8 = 0对任惡角度&都满足，所以:ud = cod + Rlid+ 3书 q + R liq接下來就是求dQ的表达式，并且把它和前面4个参数0 Lm Ms屮m关联起來Matlab代码syms tlvtasyms L AA L AB L AC L BA L BB L BC L CA L CB L CC Ls Ln Ms

9、L.AA = Ls 45*cos(2theta)：L_BB = Ls LmcosCZ*(theta-2*pi/3):L-CC = Ls Hm*cos(2*(theta*2*pi/3):L_AB = -Ms - Lm*cos(2*(theta * pl/6)：L.BC =-Ms -Lm*cos(2*theta*pi/6-2*pi/3):L_CA -Ms -Lm*cos(2*(theta4pi/62*pi/3):L_BA =L_AB：L_CB =L_BC：L_AC =L_CA：syms L_ABC i_A i_B i_Csyms i_ABC i_d 1_qi_ABC = 1_A: i_B: i_C

10、：L.ABC = L_AA L_AB L_AC： L_BA L_B3 L_BC； L_CA L_CB L_CC： syms phi_Am phl.En phiCm phl.M phl_Ax 二 phl_M*oos (theta), phl_Bx = phlM*cos(theta-2*pl/3); phl_Cx 二 phl_M*cos(theta*2*pl/3);syms phl_ABCm phl.ABC phl.ABCo - phl.An, phl_Bn, pril_Cxl, phL.ABC 二 L-ABC*L-A3OphL.ABCm;C_2s_2r - cos(thete) sin(thet

11、aj, sin(theta) cos (theta)：,C_3s_2s = 2/3*l -1/2 -1/2; 0, sqrt(3)/2 -sqrt(3)/2j;C_2s_3s 三1 0-1/2 sqrt(3)/2; T/2 -sqrt (3)/21;C_2r_2s = Icos Ltheta) sin(theta/; sin(theta) cos(thwta)2, phi.dq = C_2s_2r*C_3s_2s*phi_ABC;i-ABC = C_2s-3s*C_2r_2s*i_d,i_q：;phi.dq = subs(phi_dq, (i.A, i.B i-C. (i.ABC(l), i_

12、ABC(2), i.ABC (3);| simplify (phidq)phi_M +(l_q*(2*Ls -3*Lm + 2*Ms) /2最终得到dq轴磁链表达式Ed &已经与角度无关了，JI互相解耦了Ld Lq与前面4个参数的关系如下3Lq = Ls + Ms - -LmLo = Ls - 2Ms最后，得出dq轴下转矩方程Te = 1.5N阳q - 忖d) = 15N(%4 + 仏 - Ljdij1.5永磁同步电机的稳态运行永磁同步电机稳态运行相量图。图中，R1和XI是电枢绕组上的阻抗和漏抗。Xad和Xaq是dq轴电枢反应电抗。 Xd和Xq足dq轴电枢同步电抗。Xd = X+Xad Xq

13、=X“Xaq绕组不通电时转子产生的感应电动势叫空我反电动势E0 矩角定义为E0落后于电枢电压矢就U的角度.0可以看到U由几部分组成EO jiXl jIXaq IR1可以得到【dXd + IqR, = U COS 9 Eq-IdRi + lqXq = UsmO得到：rXq(7cose - Eo) -RosineIdR/+XqXd,_ Ri(/cos0 - EQ)-XdU sin 61lR/+XqXd stemPlnsical s stemReferenceGcncratucd rtfIPouer IonxertcrCurrentControllerVelocity(ontrollerPositi

14、on Sensor Signal ProcessingProteclion and auxilian* fiincdonsCurrent2.2永磁同步电机控制策略永磁同步电机控制，策略的不同主要体现在具体Id lq怎么控制，大体上有3类。FOC：定向磁场控制id = 0MTPA：最大化Tq/I弱磁査表：Id和lq通过査表来得到2.2.1 FOC2.2.2 MTPA2.2.3弱磁査表3永磁同步电机建模3.1永磁电机模型主要有2类模型，基于dq轴表达磁链和基于ABC坐咏表达磁链3.1.1基于dq轴坐标表达磁链的永磁同步电机模型1) Matlab Simscape Power SysteOm 工具箱

15、中的 Machines / Permanent Magnet Rotor 模块LibraryMachi nes / Perma nent Mag net Rotor磁链参数农达3 Block Parameters: Permanent Magnet Synchronous MotorXPennaiieiil Magnet Synchronous MolorThis block represents a penianent Magnet synchronous bio tor with sinusoidal flux distribuiio n.Righl-click on the block

16、and select Sinscape block choices to access variant impleraentations of this block.SettingsIk i nInit ial ConditionsNumber of pole pairs:Pcraancnt magnet flux linkage paia:neterization:PerfMnent wagnet flux linkage:S .fn! | ii meter /it ion:Srator d-axis inductance, Ld:Stator q axis inductance, La：S

17、:ator zero-sequenee induct anre. 1,0:Srator resistance per pliase, Rs:E3|ihqSpecify Ld, Lqt and LOHvgIIV*LO11v|RsOhir7Specify flux linkageUK | CancelHelpApp ly2) Matlab Powertrain Blockset 匸具箱中的 Interior PMSM block 模块Interior PMSMImplenGnt eynarrwes & an 应nor pormanem magno synchronous motorexpand a

18、l mpkeLibrory: Propulsion / Dectnc Motor?磁链参数表达O Elock Parameters: Interior PMSM SS SpdXInterior PMSM (mask) (link)Model the dynamics of a three-phase interior pern)anent magnet synchronous motor (BISM) vrith sinusoidal back electroti ve force.Block(Ht ionsPort Configuration: SpeedParameters ON Canc

19、el | Heh)它是通过引mulink而不是simscape来实现的.因此可以看到内部实现.相电压数据进来进行Clarke变换和Park变换.得到dq电压.在PMSM Equivalent Circuit子 系统中依据dq电压微分方程积分得出dq电流通过转矩方程计算转矩，通过逆Park变换和逆Clarke变换计算出相电流。3.1.2基于ABC坐标表达磁链的永磁同步电机模型Matlab Simsacpe Electronics 1】具箱中的 The FEM-Parameterized PMSM block 模块FEM-Parameterized PMSMPorma nont rnqgnot s

20、ynchro nous motor dofinod in terms of magn otic flux lin kageLibraryRotational Actuators它的磁链数据是通过矩阵来表达的，数据可以来源于冇限元仿真数据。磁链数据的表达形式有儿种2D数据模型，固定互感可 Block Parameters: FEM-Parameterized PMSMXFEM Piinimctcrizcd PMSM、block lupleoen Meclrical and aechaniral i*1* h i i u i m , wi. iwhI nugfi (motor ln limogji

21、ctic flux linkage depends nonlinearly on staler currents and rotur axiglc. Rigid click on the block and select SinsrapcdM) block choices to icccss Viiriant iBplrnh-ntiit ions.SettingsElectricalIron losses hanitdlParameterization:Current vector, i:Assuhc constant autual inductance - tabulate ith pha-

22、 rent and rotor angleRotor angle vector, theta:Flux liiikuxc partial drriviit ivc wrt currcnl. dPhi(ivthota)/di:Flux linluigc partial derivative rt angle. dPhi(i.theta)/dtheta:Gilculatc torque Matrix?:Inierpolat ion iwthod:|icc Ih xVec thdf luxdiU.it ri xTli. ASlblor rcsisiiuicc per phase Rs:CancelA

23、pplySuior Buluul induetuiicu.OK2D数据模型，正弦反电动势可 Blo|x*fids (kjiiI incarly on stator currents ssesParameieri2ation:Direct-axis current vector id:Qutdruiurc-uxis currcni vector iq:Ld Btitrix, I i. iq):Lq rntrix, llat ion nwthnd: Slttor resisluiice per pliase. Rs:UcctuihicdlAssune sinusoidal hack ewf Tab

24、ulate v th d and q axis currentsHCancelHelpApply4D数据模型% Block Parameters: FEM-Parameterized PMSMXFEM-Paranetcr i zed PMSMThis block implements the electrical and nechanical characteristics of a permanent naRnet synchronous inotor for which magnetic flux linkage depends nonlinearl on stator currents

25、and rotor angle Right-click on the block and select Si inscape(TM) block choices to access variant implementationsSettingsElectricalIron LossesMechanicalA-phasecurremvector.iA： -200. 0. 0. 0, 200. 0B phasecurrentvector,iB: |-200.0. 0.0, 200.0：C phasecurrentvector,iC:卜200000, 2000Rotor angle vector i

26、hna:|xVec t.hA-phasc flux linkage partial derivative wrt iA. dFhiA(iA. iBJC, theta)/diA:A phase flux linkage partial derivative wrt dPhi.4(iA. iBJC, theta)/dill:A-pliase flux linkdKe partial derivative wrt iC. dPhiA(iAt iB, iC, theta)/diC:A-phase flux Iinkagc partial derivative wrt angle.dPhiA(iA. i

27、B. iC. theta)/ dtheta:zeros (3. 3, 3t 4)zeros(3, 3, 3, 4)zeros (3. 3. 3. 1)Torque matrix, T(iA, iB, iC, theta):0.3, 0; 0, 0F 0, 0; 0, - 0.3t 0.3, 0 X*wInterpolation method:Stator resistance per phase, Rs:LinearOKCancelApply3D数据模型，使用Park变换加 Block Parameters: FEM Parameterized PMSMXFElbParamcteri zed

28、PUSHThis block iraplemcnts the electrical and mechanical characteristics of a Dcrmanent macnct syncluofious motor for which magnetic flux linkage depends nonl ineai ly on stator currents and rotor anglc. Right-click on the block and select Simscapc(TM)block choices to access variant ipleaienlations

29、SettingsEl cctricalron LossesMeehani caIDirect axis current vector. iD:Quadrature-axis current vector. iQ:Rotor angle vector, theta:A-phase flux linkage part ial derivative irt iA, dPhiAfiD. iQ. theta)/diA:A-phase flux linkage part ial derivative wrt iB, dPhiACiD. iQ. rhcta)/diB:A-phase flux linkage part ial derivative vrt iC, dPhiA(iD. iQ. theta)/diC:A-phase flux linkage part ial derivative iTt angle, dPhiA(iD, iQ. theta)/ tithe ta:Torque iwtrix, T(iD, iQ. theta):lnterp(jlation ix