Mechatronics seminar 1 Electromechanical System Electric Machines and

Mechatronics seminar 1 Electromechanical System, Electric Machines, and Applied Mechatronics CONTENTS 7. 4 Conventional three-phase syncronous machines; Dynamics in the machine variables, and in the rotor And syncronous reference frames 7. 4. 1 Dynamics of synchronous machines in the machine variables 7. 4. 2 Mathematical models of synchronous macines in the rotor and synchronous reference frames Changwon National Univ. ECAD Lab.

Mechatronics seminar 2 7. 4. 1 Dynamics of snchronous machines in the machine variavles, and in the rotor and synchronous reference frame Changwon National Univ. ECAD Lab.

Mechatronics seminar 3 Ø Voltage equation for stator windings and rotor windings Stator windings Rotor windings Uas, ubs, and ucs, are the phase voltages in the stator windings as, bs, and cs, respectively Ias, ibs, and ics, are the phase currents in the stator windings as, bs, and cs, respectively are the stator flux linkages Ufr is the exitation voltage applide to the rotor winding fr is the rotor flux linkage rs and rr are the resistances of the stator and rotor windings, respectively Changwon National Univ. ECAD Lab.

Mechatronics seminar 4 Ø Stator and Rotor flux linkages Self component Changwon National Univ. ECAD Lab.

Mechatronics seminar Ø Define 5 , 1. Salient type 2. Round-rotor type The magnetic paths in the quadrature and direct magnetic axes are idntical Changwon National Univ. ECAD Lab.

Mechatronics seminar 6 ØMatrix of self-and mutual Inductances Self inductance Changwon National Univ. ECAD Lab.

Mechatronics seminar 7 Ø Vector Matrix of flux linkage Changwon National Univ. ECAD Lab.

Mechatronics seminar 8 Ø Voltage equation for stator windings and rotor windings Changwon National Univ. ECAD Lab.

Mechatronics seminar 9 Changwon National Univ. ECAD Lab.

Mechatronics seminar 10 Changwon National Univ. ECAD Lab.

Mechatronics seminar 11 Ø The torsional-mechanical equation Changwon National Univ. ECAD Lab.

Mechatronics seminar 12 Ø Relation of mechanical(wrm) and electrical velocity (wrm) according to Pole number Changwon National Univ. ECAD Lab.

Mechatronics seminar 13 Ø The electromagnetic Torque Changwon National Univ. ECAD Lab.

Mechatronics seminar 14 Ø The torsional-mechanical equation Changwon National Univ. ECAD Lab.

Mechatronics seminar 15 Ø The nonlinear differential equations to map the transient dynamics of three-phase synchronous motors Changwon National Univ. ECAD Lab.

Mechatronics seminar 16 Changwon National Univ. ECAD Lab.

Mechatronics seminar 17 Ø Torque equation except viscous friction coefficient (Bm) Changwon National Univ. ECAD Lab.

Mechatronics seminar 18 Ø Typical torque-speed characteristic curves of synchronous motors Changwon National Univ. ECAD Lab.

Mechatronics seminar 19 Ø Example 7. 6 Model a three-phase, two-pole synchronous motor with following parameters 값 단위 Rs 0. 25 [ohm] Rr 0. 47 [H] Lls 0. 0001 [H] Lmq 0. 00095 [H] Lmd 0. 00095 [H] Llf 0. 00022 [H] Lmf 0. 0001 [H] Lmd 0. 00035 [H] J 0. 003 [Kg-m 2] Bm 0. 00072 [N-m-s-rad-1] Changwon National Univ. ECAD Lab.

Mechatronics seminar 20 The field voltage is ufr=5 V The load conditions are specified as Changwon National Univ. ECAD Lab.

Mechatronics seminar 21 MATLAB script crm_01. m tspan=[0 0. 5]; y 0=[0 0 0 0]'; options=odeset('Rel. Tol', 5 e-3, 'Abs. Tol', [1 e-4 1 e-4]); [t, y] = ODE 45('crm_02', tspan, y 0, options); subplot(3, 2, 1); plot(t, y(: , 1)); ylabel('ias'); axis([0, 0. 3, -500, 500]); grid; subplot(3, 2, 3); plot(t, y(: , 2)); ylabel('ibs'); axis([0, 0. 3, -500, 500]); grid; subplot(3, 2, 5); plot(t, y(: , 3)); ylabel('ics'); axis([0, 0. 3, -500, 500]); grid; subplot(3, 2, 2); plot(t, y(: , 4)); ylabel('ifr'); axis([0, 0. 3, -200, 200]); grid; subplot(3, 2, 4); plot(t, y(: , 5)); ylabel('wr'); axis([0, 0. 3, 0, 400]); grid; subplot(3, 2, 6); plot(t, y(: , 6)); ylabel('Q'); axis([0, 0. 3, 0, 200]); grid; Changwon National Univ. ECAD Lab.

Mechatronics seminar 22 MATLAB script crm_02. m function yprime=difer(t, y); Lls=0. 0001; Lmqs=0. 00095; Lmds=0. 00095; Llf=0. 00022; Lmf=0. 0001; Lmd=0. 00035; Lmb=(Lmqs+Lmds)/3; rs=0. 25; rr=0. 47; J=0. 003; Bm=0. 00072; P=2; um=sqrt(2)*150; w=377; ufr=5; if t<=0. 2; T 1=0; else T 1=1; end Changwon National Univ. ECAD Lab.

Mechatronics seminar 23 uas=um*cos(w*t); ubs=um*cos(w*t-2*pi/3); ucs=um*cos(w*t+2*pi/3); Ld=2*Lls*Lmd^2; Ldr=2*Lls*Lmd; Lss=(-3*Lmb^2 -4*Lls^2 -8*Lls*Lmb)*(Lmf+Llf)+3*Lmd^2*Lmb+4*Lls*Lmd^2; Ldens=(2*Lls+3*Lmb)*((-2*Lls^2 -3*Lmb*Lls)*(Llf+Lmf)+3*Lmd^2*Lls); Ldenr=(-2*Lls^2 -3*Lmb*Lls)*(Llf+Lmf)+3*Lmd^2*Lls; Lms=(-3*Lmb^2 -2*Lls*Lmb)*(Lmf+Llf)+3*Lmd^2*Lmb+Lls*Lmd^2; Lrr=6*Lls*Lmd*Lmb+4*Lls^2*Lmd; Llr=-(2*Lls^2+3*Lmb*Lls); S 1=sin(y(6, : )); S 2=sin(y(6, : )-2*pi/3); S 3=sin(y(6, : )+2*pi/3); IUas=-rs*y(1, : )+uas; IUbs=-rs*y(2, : )+ubs; IUcs=-rs*y(3, : )+ucs; IUfr=-rr*y(4, : )+ufr; C 1=cos(y(6, : )); C 2=cos(y(6, : )-2*pi/3); C 3=cos(y(6, : )+2*pi/3); C 12=cos(2*y(6, : )); C 22=cos(2*y(6, : )-2*pi/3); C 32=cos(2*y(6, : )+2*pi/3); Nsts=(-6*Lmd^2*Lls*Lmb-4*Lmd^2*Lls^2)*y(5, : ). *(C 1. *y(1, : )+C 2. *y(2, : )+ C 3. *y(3, : )); Nstr=(3*Lmd*Lmb*Lls+2*Lmd*Lls^2)*y(5, : ). *(C 1. *y(1, : )+C 2. *y(2, : )+C 3. *y(3, : )); Nct=((6*Lmd*Lls*Lmb+4*Lmd*Lls^2)*(Llf+Lmf)-6*Lmd^3*Lls)*y(5, : ). *y(4, : ); Te=P*(Lmd*y(4, : ). *(y(1, : ). *C 1+y(2, : ). *C 2+y(3, : ). *C 3))/2; Changwon National Univ. ECAD Lab.

Mechatronics seminar 24 yprime=[((Lss+Ld*C 12). *IUas+(Lms+Ld*C 22). *IUbs+(Lms+Ld*C 32). *IUcs+Lrr*S 1. *IUfr+Nsts. *S 1+Nct. *C 1)/Ldens; . . . ((Lms+Ld*C 22). *IUas+(Lss+Ld*C 32). *IUbs+(Lms+Ld*C 12). *IUcs+Lrr*S 2. *IUfr+Nsts. *S 2+Nct. *C 2)/Ldens; . . . ((Lms+Ld*C 32). *IUas+(Lms+Ld*C 12). *IUbs+(Lss+Ld*C 22). *IUcs+Lrr*S 3. *IUfr+Nsts. *S 3+Nct. *C 3)/Ldens; . . . (Ldr*S 1. *IUas+Ldr*S 2. *IUbs+Ldr*S 3. *IUcs+Llr*IUfr+Nstr)/Ldenr; . . . (P*Te-2*Bm*y(5, : )-P*T 1)/(2*J); . . . y(5, : )]; Changwon National Univ. ECAD Lab.

Mechatronics seminar 25 Changwon National Univ. ECAD Lab.

Mechatronics seminar 26 Ø Dynamics of three-phase synchronous generators Changwon National Univ. ECAD Lab.

Mechatronics seminar 27 Ø Voltage equation for stator windings and rotor windings Stator windings Rotor windings Changwon National Univ. ECAD Lab.

Mechatronics seminar 28 Ø The nonlinear differential equations to map the transient dynamics of three-phase synchronous generators Changwon National Univ. ECAD Lab.

Mechatronics seminar 29 Changwon National Univ. ECAD Lab.

Mechatronics seminar 31 Ø The Park transformation Making use of the Park transformation The rotor reference frame Changwon National Univ. ECAD Lab.

Mechatronics seminar 32 Changwon National Univ. ECAD Lab.

Mechatronics seminar 33 Changwon National Univ. ECAD Lab.

Mechatronics seminar 34 Ø The electromagnetic torque by using the Park transformation The torsional-mechanical dynamics for conventional synchronous motors Changwon National Univ. ECAD Lab.