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📄 fm_upfc.m

📁 电力系统的psat
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  t316 = 1./t12;  t318 = sqrt(t315.*t316);  t319 = t318.*t59;  t320 = Xt+Xse;  t321 = 1./V2;  t325 = omega.*Imd;  t328 = 1./omega;  t330 = t62-t320.*(x2+Kp.*(t204.*t321-Imq)+t325).*t328;  t335 = omega.*Imq;  t339 = t68-t59.*V2-t320.*(x1+Kp.*(t171.*t321-Imd)-t335).*t328;  t340 = 1./t339;  t342 = atan(t330.*t340);  t343 = theta2-t342;  t344 = cos(t343);  t347 = t5-t7-t319.*t344./2;  t349 = t3.^2;  t350 = t320.^2;  t352 = 1./(t349+t350);  t354 = sin(theta2);  t355 = V2.*t354;  t356 = sin(t343);  t359 = t2-t355-t319.*t356./2;  t362 = t3.*t347.*t352+t320.*t359.*t352;  t365 = 1./t318.*t59;  t366 = t365.*t344;  t401 = -4.*t271.*t35+2.*t68.*t65-2.*t62.*t70-4.*t272.*t81+2.*t194.*t87-2.*t62.*t101-4.*t272.*t104+2.*t194.*t107+4.*t78.*t274-2.*t85.*t196+2.*t68.*t200+4.*t78.*t288-2.*t85.*t282+2.*t62.*t301+2.*t62.*t297+2.*t68.*t75+2.*t68.*t97;  t403 = t401.*t314.*t316;  t408 = t339.^2;  t409 = 1./t408;  t410 = t330.*t409;  t412 = -t60.*t32.*t340-t410.*t62;  t414 = t330.^2;  t417 = 1./(1+t414.*t409);  t421 = -t2-t366.*t403./4-t319.*t356.*t412.*t417./2;  t424 = t365.*t356;  t431 = t5-t424.*t403./4+t319.*t344.*t412.*t417./2;  t434 = t3.*t421.*t352+t320.*t431.*t352;  t440 = -t320.*t347.*t352+t3.*t359.*t352;  t446 = -t320.*t421.*t352+t3.*t431.*t352;  t451 = sqrt(6);  t452 = t451.*m;  t453 = Vdc.*Gsh;  t454 = cos(alpha);  t458 = Vdc.*Bsh;  t459 = sin(alpha);  t467 = t59.*t61;  t468 = t467.*t12;  t472 = t59.*t32;  t473 = t472.*t12;  t476 = t32.*V2;  t477 = t476.*omega;  t488 = t61.*V2;  t489 = t488.*omega;  t490 = t114.*Qref;  t498 = t132.*Qref;  t516 = -4.*t32.*t34.*t9-2.*t468.*t79.*x2-2.*t473.*t111-4.*t477.*t115+2.*t473.*t87-2.*t473.*t122-4.*t477.*t133+2.*t473.*t107-4.*t489.*t490+2.*t468.*t196-2.*t468.*t91.*x2-4.*t489.*t498+2.*t468.*t282+4.*V1.*t12.*t9+2.*t473.*t257+2.*t473.*t254-2.*t468.*t253.*Imd-2.*t468.*t236.*Imd;  t518 = t516.*t314.*t316;  t523 = t467.*t340-t410.*t472;  t528 = t4-t366.*t518./4-t319.*t356.*t523.*t417./2;  t537 = t1-t424.*t518./4+t319.*t344.*t523.*t417./2;  t540 = t3.*t528.*t352+t320.*t537.*t352;  t547 = -t320.*t528.*t352+t3.*t537.*t352;  t551 = -t401.*t314.*t316;  t555 = 1+t412.*t417;  t559 = t355-t366.*t551./4+t319.*t356.*t555./2;  t567 = -t7-t424.*t551./4-t319.*t344.*t555./2;  t570 = t3.*t559.*t352+t320.*t567.*t352;  t576 = -t320.*t559.*t352+t3.*t567.*t352;  t579 = t15.*V2;  t584 = t11.*V2;  t597 = V2.*Xse;  t600 = V2.*t9;  t613 = t584.*Xse;  t616 = V2.*Kp;  t617 = t616.*Imd;  t623 = t271.*omega;  t626 = 2.*t19.*t579+2.*t10.*t579+2.*t10.*t584-0.12e2.*t33.*t73+2.*t38.*t579+2.*t40.*t579+2.*t38.*t584+2.*t40.*t584+4.*t50.*t597-4.*t62.*t600.*t96+0.8e1.*t35+4.*t68.*t600.*t300+4.*t68.*t600.*t296-0.8e1.*t170.*t136+4.*t22.*t613-4.*t186.*t617+4.*t69.*Xse.*t142-4.*t623.*t498;  t627 = V2.*omega;  t630 = t171.*Imd;  t638 = t127.*Imq;  t645 = t627.*Imq;  t670 = t579.*Xse;  t673 = 0.8e1.*t627.*t133-2.*t40.*t630+2.*t54.*t217-4.*t62.*t627.*t199-2.*t268.*t638+2.*t19.*t584+2.*t225.*t217-4.*t139.*t645+2.*t139.*t142-4.*t623.*t490-0.8e1.*t203.*t291-4.*t62.*t600.*t74+0.8e1.*t203.*t92+2.*t148.*V2+4.*t156.*V2.*t9+2.*t152.*V2+2.*t162.*V2+2.*t166.*V2+4.*t236.*t670;  t679 = t114.*t59;  t686 = t60.*t476;  t692 = t60.*t488;  t698 = t204.*Imq;  t703 = t59.*t12;  t712 = t33.*omega;  t717 = t703.*omega;  t724 = -0.8e1.*t170.*t264+4.*t22.*t670-4.*t679.*t181.*t335-4.*t68.*t627.*t69+4.*t686.*t87-4.*t68.*t627.*t100+4.*t692.*t196-4.*t180.*t212.*Imq-2.*t40.*t698+4.*t686.*t107+6.*t703.*t111+0.8e1.*t627.*t115+4.*t43.*t597-2.*t38.*t698-4.*t712.*t133-2.*t38.*t630-6.*t717.*t119+6.*t703.*t122+2.*t186.*t142;  t725 = t616.*Imq;  t735 = t627.*Imd;  t740 = t241.*Imd;  t770 = -4.*t225.*t725-4.*t139.*t617+4.*t679.*t212.*t325-4.*t186.*t645+4.*t225.*t735+4.*t236.*t613+2.*t268.*t740+4.*t54.*t735-4.*t54.*t725-4.*t62.*t627.*t64-6.*t717.*t136-6.*t703.*t254-6.*t703.*t257+4.*t692.*t282-4.*t712.*t115-2.*t126.*t638+2.*t126.*t740+4.*t64.*Xse.*t217-4.*t180.*t181.*Imd;  t778 = (t626+t673+t724+t770).*t314.*t316-2.*t315./t34;  t783 = t320.*Kp.*t59;  t793 = t783.*Qref.*t316.*t328.*t340-t410.*(-t59+t783.*Pref.*t316.*t328);  t798 = -t6-t365.*t344.*t778./4-t319.*t356.*t793.*t417./2;  t808 = -t354-t365.*t356.*t778./4+t319.*t344.*t793.*t417./2;  t811 = t3.*t798.*t352+t320.*t808.*t352;  t817 = -t320.*t798.*t352+t3.*t808.*t352;  DAE.J11 = DAE.J11 + sparse(bus1,bus1, -t2.*t362+t5.*t434+t5.*t440+t2.*t446,Bus.n,Bus.n);  DAE.J12 = DAE.J12 + sparse(bus1,bus1, 2.*V1.*Gsh-t452.*t453.*t454./4-t452.*t458.*t459./4+t4.*t362+t5.*t540+t1.*t440+t2.*t547,Bus.n,Bus.n);  DAE.J11 = DAE.J11 + sparse(bus1,bus2, t5.*t570+t2.*t576,Bus.n,Bus.n);  DAE.J12 = DAE.J12 + sparse(bus1,bus2, t5.*t811+t2.*t817,Bus.n,Bus.n);  DAE.J21 = DAE.J21 + sparse(bus1,bus1, t5.*t362+t2.*t434+t2.*t440-t5.*t446,Bus.n,Bus.n);  DAE.J22 = DAE.J22 + sparse(bus1,bus1, -2.*V1.*Bsh+t452.*t458.*t454./4-t452.*t453.*t459./4+t1.*t362+t2.*t540-t4.*t440-t5.*t547,Bus.n,Bus.n);  DAE.J21 = DAE.J21 + sparse(bus1,bus2, t2.*t570-t5.*t576,Bus.n,Bus.n);  DAE.J22 = DAE.J22 + sparse(bus1,bus2, t2.*t811-t5.*t817,Bus.n,Bus.n);  DAE.J11 = DAE.J11 + sparse(bus2,bus1, -t7.*t434-t355.*t446,Bus.n,Bus.n);  DAE.J12 = DAE.J12 + sparse(bus2,bus1, -t7.*t540-t355.*t547,Bus.n,Bus.n);  DAE.J11 = DAE.J11 + sparse(bus2,bus2, t355.*t362-t7.*t570-t7.*t440-t355.*t576,Bus.n,Bus.n);  DAE.J12 = DAE.J12 + sparse(bus2,bus2, -t6.*t362-t7.*t811-t354.*t440-t355.*t817,Bus.n,Bus.n);  DAE.J21 = DAE.J21 + sparse(bus2,bus1, -t355.*t434+t7.*t446,Bus.n,Bus.n);  DAE.J22 = DAE.J22 + sparse(bus2,bus1, -t355.*t540+t7.*t547,Bus.n,Bus.n);  DAE.J21 = DAE.J21 + sparse(bus2,bus2, -t7.*t362-t355.*t570-t355.*t440+t7.*t576,Bus.n,Bus.n);  DAE.J22 = DAE.J22 + sparse(bus2,bus2, -t354.*t362-t355.*t811+t6.*t440+t7.*t817,Bus.n,Bus.n); case 3 % Differential Equations  t1 = V1.^2;  t3 = sqrt(6);  t5 = t3.*m.*Vdc;  t6 = V1.*Gsh;  t7 = cos(alpha);  t11 = V1.*Bsh;  t12 = sin(alpha);  t16 = t1.*Gsh-t5.*t6.*t7./4-t5.*t11.*t12./4;  t17 = 1./Cdc;  t19 = 1./Vdc;  t21 = cos(theta1);  t22 = V1.*t21;  t23 = cos(theta2);  t24 = V2.*t23;  t25 = t22-t24;  t27 = sin(theta1);  t28 = V1.*t27;  t29 = sin(theta2);  t30 = V2.*t29;  t31 = t28-t30;  t33 = Kp.^2;  t34 = Xt.*t33;  t35 = Qref.^2;  t39 = Pref.^2;  t43 = theta2-theta1;  t44 = cos(t43);  t45 = V1.*t44;  t46 = V2.^2;  t47 = t46.*V2;  t48 = omega.^2;  t52 = Xse.^2;  t53 = t52.*t33;  t54 = Imq.^2;  t55 = t54.*t46;  t57 = Xt.^2;  t58 = t57.*x2;  t59 = t46.*omega;  t60 = t59.*Imd;  t63 = t57.*t33;  t65 = x2.^2;  t67 = t46.*Xse;  t70 = Imd.^2;  t71 = t70.*t46;  t73 = Xt.*Kp;  t74 = sqrt(2);  t75 = t74.*Pref;  t77 = Xse.*omega;  t78 = Imq.*V2;  t82 = t74.*V1;  t83 = t82.*t44;  t84 = t46.*t48;  t90 = t46.^2;  t93 = x1.^2;  t97 = t57.*t48;  t99 = t74.*t47;  t100 = t99.*omega;  t107 = t52.*t48;  t112 = t82.*t44.*t46;  t113 = omega.*Xt;  t114 = Kp.*Imd;  t118 = 4.*t34.*t35.*Xse+4.*t34.*t39.*Xse-4.*t45.*t47.*t48+t53.*t55+2.*t58.*t60+t63.*t55+2.*Xt.*t65.*t67+t53.*t71-4.*t73.*t75.*t77.*t78+2.*t83.*t84.*Xt.*Imq+t63.*t71+2.*t90.*t48+2.*Xt.*t93.*t67+t97.*t71-2.*t100.*t73.*Imd+2.*t99.*t77.*x1+t107.*t71+t107.*t55+t97.*t55+2.*t112.*t113.*t114;  t128 = t57.*Kp.*t74;  t130 = Pref.*omega.*t78;  t133 = Xse.*Kp;  t137 = t133.*Imd;  t140 = Xt.*t48;  t141 = t71.*Xse;  t144 = t57.*x1;  t146 = Kp.*t74;  t147 = t146.*Pref;  t150 = Xt.*x1;  t155 = t63.*t74;  t157 = Pref.*Imd.*V2;  t160 = sin(t43);  t161 = t82.*t160;  t166 = Xt.*x2;  t167 = t166.*t46;  t171 = t52.*x2;  t174 = t45.*V2;  t175 = Kp.*Pref;  t179 = t34.*t74;  t181 = Imd.*V2;  t189 = t46.*Kp;  t190 = t189.*Imq;  t193 = t189.*Imd;  t196 = t52.*x1;  t200 = t53.*t74;  t207 = -2.*t83.*t59.*Xse.*x1+2.*t83.*t84.*Xse.*Imq-2.*t128.*t130+4.*t59.*t133.*Pref-2.*t100.*t137+2.*t140.*t141+2.*t144.*V2.*t147+4.*t150.*V2.*t133.*t75-2.*t155.*t157-2.*t161.*t84.*Xse.*Imd+4.*t167.*t77.*Imd+2.*t171.*t60-4.*t174.*t77.*t175-4.*t179.*Pref.*Xse.*t181-2.*t99.*t48.*Xse.*Imq-2.*t58.*t190-2.*t144.*t193+2.*t196.*V2.*t147-2.*t200.*t157-2.*t161.*t84.*Xt.*Imd;  t216 = t52.*Kp.*t74;  t220 = Qref.*omega.*t181;  t224 = V1.*t160.*V2;  t225 = Kp.*Qref;  t229 = t150.*t46;  t233 = t82.*t160.*t46;  t234 = Kp.*Imq;  t255 = t74.*Qref;  t275 = Qref.*Imq.*V2;  t278 = -2.*t99.*t140.*Imq+2.*t112.*t77.*t114-2.*t216.*t130+2.*t216.*t220-4.*t224.*t113.*t225-4.*t229.*t137+2.*t233.*t113.*t234+2.*t128.*t220-2.*t161.*t59.*Xse.*x2-2.*t196.*t193+2.*t34.*t141+2.*t1.*t46.*t48+t52.*t65.*t46+2.*t53.*t39+4.*t73.*t255.*t77.*t181+4.*t166.*V2.*t133.*t255-2.*t161.*t59.*t166-4.*t229.*t77.*Imq-4.*t179.*Qref.*Xse.*t78-2.*t155.*t275;  t283 = t146.*Qref;  t288 = t59.*Imq;  t294 = t55.*Xse;  t334 = -4.*t224.*t77.*t225-2.*t171.*t190+4.*t59.*t73.*Pref+2.*t63.*t39+t52.*t93.*t46+t57.*t93.*t46+2.*t63.*t35+t57.*t65.*t46+2.*t53.*t35+2.*t233.*t77.*t234+2.*t58.*V2.*t283;  t342 = sqrt((t118+t207+t278-2.*t83.*t59.*t150+2.*t171.*V2.*t283-2.*t200.*t275-2.*t196.*t288-4.*t174.*t113.*t175+2.*t140.*t294-2.*t144.*t288+2.*t34.*t294-4.*t167.*t133.*Imq+2.*t99.*t113.*x1+t334)./t48./t46);  t343 = a2r.*t342;  t344 = Xt+Xse;  t345 = 1./V2;  t347 = t255.*t345-Imq;  t348 = Kp.*t347;  t352 = 1./omega;  t357 = t75.*t345-Imd;  t358 = Kp.*t357;  t366 = atan((t161-t344.*(x2+t348+omega.*Imd).*t352)./(t83-t74.*V2-t344.*(x1+t358-omega.*Imq).*t352));  t367 = theta2-t366;  t368 = cos(t367);  t369 = t74.*t368;  t372 = a2i.*t342;  t373 = sin(t367);  t374 = t74.*t373;  t378 = Rse+Rt;  t379 = t342.*t74;  t382 = t22-t24-t379.*t368./2;  t384 = t378.^2;  t385 = t344.^2;  t387 = 1./(t384+t385);  t391 = t28-t30-t379.*t373./2;  t394 = t378.*t382.*t387+t344.*t391.*t387;  t407 = -t344.*t382.*t387+t378.*t391.*t387;  t415 = t16.^2;  t424 = (-t1.*Bsh+t5.*t11.*t7./4-t5.*t6.*t12./4).^2;  t431 = t394.^2;  t432 = t407.^2;  t440 = 1./Tmac;  t452 = 1./Tmdc;  DAE.f(Upfc.Vdc) = t16.*t17.*t19+((a1r.*t25-a1i.*t31+t343.*t369./2-t372.*t374./2).*t394+(a1i.*t25+a1r.*t31+t372.*t369./2+t343.*t374./2).*t407).*t17.*t19-Vdc./Rdc.*t17-Rsh.*(t415+t424)./t1.*t19.*t17-Rse.*(t431+t432).*t17.*t19;  DAE.f(Upfc.Vmac) = (-Vmac+Kmac.*V1).*t440;  DAE.f(Upfc.m) = (Kpac.*t440-Kiac).*Vmac+Kiac.*Vrefac-Kpac.*Kmac.*t440.*V1;  DAE.f(Upfc.Vmdc) = (-Vmdc+Kmdc.*Vdc).*t452;  DAE.f(Upfc.alpha) = (Kpdc.*t452-Kidc).*Vmdc+Kidc.*Vrefdc-Kpdc.*Kmdc.*t452.*Vdc;  DAE.f(Upfc.x1) = Ki.*t357;  DAE.f(Upfc.Imd) = x1-K.*Imd+t358;  DAE.f(Upfc.x2) = Ki.*t347;  DAE.f(Upfc.Imq) = x2-K.*Imq+t348;  for i = 1:Upfc.n    if DAE.x(Upfc.Vdc(i)) <= 1e-6      DAE.x(Upfc.Vdc(i)) = 1e-6;      if DAE.f(Upfc.Vdc(i)) < 0; DAE.f(Upfc.Vdc(i)) = 0; end    end    if DAE.x(Upfc.alpha(i)) >= alpha_max(i)      DAE.x(Upfc.alpha(i)) = alpha_max(i);      if DAE.f(Upfc.alpha(i)) > 0; DAE.f(Upfc.alpha(i)) = 0; end    end    if DAE.x(Upfc.alpha(i)) <= alpha_min(i)      DAE.x(Upfc.alpha(i)) = alpha_min(i);      if DAE.f(Upfc.alpha(i)) < 0; DAE.f(Upfc.alpha(i)) = 0; end    end    if DAE.x(Upfc.m(i)) >= m_max(i)      DAE.x(Upfc.m(i)) = m_max(i);      if DAE.f(Upfc.m(i)) > 0; DAE.f(Upfc.m(i)) = 0; end    end    if DAE.x(Upfc.m(i)) <= m_min(i)      DAE.x(Upfc.m(i)) = m_min(i);      if DAE.f(Upfc.m(i)) < 0; DAE.f(Upfc.m(i)) = 0; end    end  end  % wind-up limits  if Settings.init    DAE.x(Upfc.Imd) = max(I_min,DAE.x(Upfc.Imd));    DAE.x(Upfc.Imq) = max(I_min,DAE.x(Upfc.Imq));    DAE.x(Upfc.Imd) = min(I_max,DAE.x(Upfc.Imd));    DAE.x(Upfc.Imq) = min(I_max,DAE.x(Upfc.Imq));  end case 4 % Jacobians of state and service variables  t1 = sqrt(6);  t2 = t1.*m;  t3 = V1.*Gsh;  t4 = cos(alpha);  t5 = t3.*t4;  t7 = V1.*Bsh;  t8 = sin(alpha);  t9 = t7.*t8;  t11 = -t2.*t5-t2.*t9;  t12 = 1./Cdc;  t14 = 1./Vdc;  t16 = V1.^2;  t18 = t2.*Vdc;  t19 = t18.*t5;  t21 = t18.*t9;  t23 = t16.*Gsh-t19./4-t21./4;  t25 = Vdc.^2;  t26 = 1./t25;  t28 = cos(theta1);  t29 = V1.*t28;  t30 = cos(theta2);  t31 = V2.*t30;  t32 = t29-t31;  t34 = sin(theta1);  t35 = V1.*t34;  t36 = sin(theta2);  t37 = V2.*t36;  t38 = t35-t37;  t40 = V2.^2;  t41 = t40.^2;  t42 = omega.^2;  t45 = Xt.^2;  t46 = t45.*x1;  t47 = t40.*Kp;  t48 = t47.*Imd;  t51 = t45.*x2;  t52 = t47.*Imq;  t55 = Kp.^2;  t56 = Xt.*t55;  t57 = Imd.^2;  t58 = t57.*t40;  t59 = t58.*Xse;  t62 = Imq.^2;  t63 = t62.*t40;  t64 = t63.*Xse;  t67 = Xse.^2;  t68 = t67.*x1;  t71 = t45.*t55;  t73 = x1.^2;  t74 = Xt.*t73;  t75 = t40.*Xse;  t78 = t45.*t42;  t80 = t67.*t42;  t83 = sqrt(2);  t84 = t40.*V2;  t85 = t83.*t84;  t86 = omega.*Xt;  t87 = t86.*x1;  t91 = t67.*x2;  t94 = Pref.^2;  t98 = theta2-theta1;  t99 = cos(t98);  t100 = V1.*t99;  t101 = t84.*t42;  t104 = t67.*t55;  t107 = x2.^2;  t108 = Xt.*t107;  t111 = t40.*omega;  t112 = Xt.*Kp;  t113 = t112.*Pref;  t116 = 2.*t41.*t42-2.*t46.*t48-2.*t51.*t52+2.*t56.*t59+2.*t56.*t64-2.*t68.*t48+t71.*t58+2.*t74.*t75+t78.*t58+t80.*t58+t80.*t63+2.*t85.*t87+t78.*t63-2.*t91.*t52+4.*t56.*t94.*Xse-4.*t100.*t101+t104.*t63+t71.*t63+2.*t108.*t75+4.*t111.*t113;  t118 = omega.*Xse;  t119 = t118.*x1;  t122 = Qref.^2;  t126 = t111.*Imq;  t129 = Xt.*t42;  t134 = Xse.*Kp;  t135 = t134.*Pref;  t140 = t111.*Imd;  t143 = t129.*Imq;  t146 = t42.*Xse;  t147 = t146.*Imq;  t152 = t83.*V1;  t153 = sin(t98);  t154 = t152.*t153;  t155 = Xt.*x2;  t156 = t111.*t155;  t159 = t152.*t99;  t160 = Xt.*x1;  t161 = t111.*t160;  t164 = t100.*V2;  t165 = Kp.*Pref;  t166 = t86.*t165;  t169 = t67.*t107;  t171 = Xse.*x1;  t172 = t111.*t171;  t177 = t118.*t165;  t180 = t45.*t73;  t182 = t104.*t58+2.*t85.*t119+4.*t56.*t122.*Xse-2.*t68.*t126+2.*t129.*t64-2.*t46.*t126+4.*t111.*t135+2.*t129.*t59+2.*t51.*t140-2.*t85.*t143-2.*t85.*t147+2.*t91.*t140-2.*t154.*t156-2.*t159.*t161-4.*t164.*t166+t169.*t40-2.*t159.*t172+2.*t71.*t122-4.*t164.*t177+t180.*t40;  t184 = t45.*t107;  t190 = t67.*t73;  t194 = t160.*V2;  t195 = t83.*Pref;  t202 = t160.*t40;  t203 = t134.*Imd;  t206 = t56.*t83;  t207 = Pref.*Xse;  t208 = Imd.*V2;  t212 = t155.*t40;

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