fm_upfc.m

电力系统的psat

  t213 = t134.*Imq;
  t216 = t85.*omega;
  t217 = t112.*Imd;
  t220 = V1.*t153;
  t221 = t220.*V2;
  t222 = Kp.*Qref;
  t223 = t86.*t222;
  t226 = Xse.*x2;
  t227 = t111.*t226;
  t231 = Kp.*t83;
  t232 = t231.*Pref;
  t236 = t152.*t99.*t40;
  t237 = Kp.*Imd;
  t238 = t86.*t237;
  t243 = t71.*t83;
  t245 = Pref.*Imd.*V2;
  t248 = t118.*t222;
  t251 = t104.*t83;
  t257 = t184.*t40+2.*t104.*t122+2.*t71.*t94+t190.*t40+2.*t104.*t94+4.*t194.*t134.*t195+2.*t40.*t16.*t42-4.*t202.*t203-4.*t206.*t207.*t208-4.*t212.*t213-2.*t216.*t217-4.*t221.*t223-2.*t154.*t227+2.*t46.*V2.*t232+2.*t236.*t238-2.*t216.*t203-2.*t243.*t245-4.*t221.*t248-2.*t251.*t245+2.*t68.*V2.*t232;
  t259 = t231.*Qref;
  t263 = Qref.*Imq.*V2;
  t266 = t118.*t237;
  t274 = t155.*V2;
  t275 = t83.*Qref;
  t279 = Qref.*Xse;
  t280 = Imq.*V2;
  t284 = t40.*t42;
  t285 = Xt.*Imq;
  t286 = t284.*t285;
  t289 = Xse.*Imq;
  t290 = t284.*t289;
  t294 = t45.*Kp.*t83;
  t295 = Pref.*omega;
  t296 = t295.*t280;
  t301 = t152.*t153.*t40;
  t302 = Kp.*Imq;
  t303 = t86.*t302;
  t306 = Xse.*Imd;
  t307 = t284.*t306;
  t310 = t118.*Imq;
  t313 = t118.*Imd;
  t316 = Xt.*Imd;
  t317 = t284.*t316;
  t321 = t67.*Kp.*t83;
  t322 = Qref.*omega;
  t323 = t322.*t208;
  t330 = t118.*t302;
  t341 = 2.*t301.*t303-2.*t154.*t307-4.*t202.*t310+4.*t212.*t313-2.*t154.*t317+2.*t321.*t323+4.*t112.*t275.*t118.*t208+2.*t301.*t330-2.*t321.*t296+2.*t294.*t323-4.*t112.*t195.*t118.*t280;
  t345 = 1./t42;
  t346 = (t116+t182+t257+2.*t51.*V2.*t259-2.*t243.*t263+2.*t236.*t266-2.*t251.*t263+2.*t91.*V2.*t259+4.*t274.*t134.*t275-4.*t206.*t279.*t280+2.*t159.*t286+2.*t159.*t290-2.*t294.*t296+t341).*t345;
  t347 = 1./t40;
  t349 = sqrt(t346.*t347);
  t350 = a2r.*t349;
  t351 = Xt+Xse;
  t352 = 1./V2;
  t356 = omega.*Imd;
  t359 = 1./omega;
  t361 = t154-t351.*(x2+Kp.*(t275.*t352-Imq)+t356).*t359;
  t366 = omega.*Imq;
  t370 = t159-t83.*V2-t351.*(x1+Kp.*(t195.*t352-Imd)-t366).*t359;
  t371 = 1./t370;
  t373 = atan(t361.*t371);
  t374 = theta2-t373;
  t375 = cos(t374);
  t376 = t83.*t375;
  t377 = t350.*t376;
  t379 = a2i.*t349;
  t380 = sin(t374);
  t381 = t83.*t380;
  t382 = t379.*t381;
  t384 = a1r.*t32-a1i.*t38+t377./2-t382./2;
  t385 = Rse+Rt;
  t386 = t349.*t83;
  t387 = t386.*t375;
  t389 = t29-t31-t387./2;
  t391 = t385.^2;
  t392 = t351.^2;
  t394 = 1./(t391+t392);
  t396 = t386.*t380;
  t398 = t35-t37-t396./2;
  t401 = t385.*t389.*t394+t351.*t398.*t394;
  t405 = t379.*t376;
  t407 = t350.*t381;
  t409 = a1i.*t32+a1r.*t38+t405./2+t407./2;
  t414 = -t351.*t389.*t394+t385.*t398.*t394;
  t423 = t7.*t4;
  t424 = t18.*t423;
  t426 = t3.*t8;
  t427 = t18.*t426;
  t429 = -t16.*Bsh+t424./4-t427./4;
  t432 = t2.*t423-t2.*t426;
  t436 = 1./t16;
  t438 = t436.*t14.*t12;
  t440 = t23.^2;
  t441 = t429.^2;
  t443 = Rsh.*(t440+t441);
  t447 = t401.^2;
  t448 = t414.^2;
  t454 = t1.*Vdc;
  t457 = -t454.*t5-t454.*t9;
  t463 = t454.*t423-t454.*t426;
  t469 = t427-t424;
  t473 = -t21-t19;
  t479 = 1./t349;
  t480 = a2r.*t479;
  t481 = t480.*t83;
  t488 = t45.*t40;
  t491 = Xt.*t40;
  t494 = t67.*t40;
  t497 = t111.*Xt;
  t500 = t111.*Xse;
  t507 = t45.*V2;
  t511 = Xt.*V2.*Xse;
  t514 = t67.*V2;
  t523 = 2.*t46.*t40+2.*t68.*t40+4.*t160.*t75-2.*t488.*t237-4.*t491.*t203-2.*t494.*t237-2.*t159.*t497-2.*t159.*t500+2.*t85.*t86+2.*t85.*t118+2.*t507.*t232+4.*t511.*t232+2.*t514.*t232-2.*t488.*t366-2.*t494.*t366-4.*t491.*t310;
  t525 = t345.*t347;
  t526 = t375.*t523.*t525;
  t529 = t370.^2;
  t530 = 1./t529;
  t531 = t361.*t530;
  t532 = t351.*t359;
  t533 = t361.^2;
  t536 = 1./(1+t533.*t530);
  t538 = t531.*t532.*t536;
  t541 = a2i.*t479;
  t542 = t541.*t83;
  t544 = t380.*t523.*t525;
  t551 = t479.*t83;
  t552 = t551.*t375;
  t554 = t523.*t345.*t347;
  t561 = t530.*t351.*t359.*t536;
  t564 = -t552.*t554./4-t386.*t380.*t361.*t561./2;
  t567 = t551.*t380;
  t574 = -t567.*t554./4+t386.*t375.*t361.*t561./2;
  t577 = t385.*t564.*t394+t351.*t574.*t394;
  t593 = -t351.*t564.*t394+t385.*t574.*t394;
  t602 = t12.*t14;
  t605 = Imd.*t40;
  t616 = t75.*Kp;
  t619 = t605.*Xse;
  t624 = t111.*t112;
  t627 = t111.*t134;
  t636 = 2.*t80.*t605+2.*t78.*t605+2.*t71.*t605+2.*t104.*t605-2.*t46.*t47-4.*t160.*t616+4.*t56.*t619-2.*t68.*t47+2.*t159.*t624+2.*t159.*t627-2.*t85.*t86.*Kp-2.*t85.*t118.*Kp;
  t637 = t195.*V2;
  t651 = t112.*t83;
  t652 = omega.*V2;
  t656 = t284.*Xse;
  t661 = t284.*Xt;
  t664 = t322.*V2;
  t669 = -2.*t71.*t637-4.*t206.*t207.*V2-2.*t104.*t637+2.*t51.*t111+4.*t129.*t619+2.*t91.*t111+4.*t651.*t279.*t652-2.*t154.*t656+4.*t155.*t500-2.*t154.*t661+2.*t321.*t664+2.*t294.*t664;
  t670 = t636+t669;
  t672 = t375.*t670.*t525;
  t675 = t350.*t83;
  t677 = t351.*Kp;
  t680 = -t351.*t371-t531.*t677.*t359;
  t682 = t380.*t680.*t536;
  t686 = t380.*t670.*t525;
  t689 = t379.*t83;
  t691 = t375.*t680.*t536;
  t697 = t670.*t345.*t347;
  t702 = -t552.*t697./4-t386.*t682./2;
  t709 = -t567.*t697./4+t386.*t691./2;
  t712 = t385.*t702.*t394+t351.*t709.*t394;
  t728 = -t351.*t702.*t394+t385.*t709.*t394;
  t767 = 2.*t51.*t40+2.*t91.*t40+4.*t155.*t75-2.*t488.*t302-4.*t491.*t213-2.*t494.*t302-2.*t154.*t497-2.*t154.*t500+2.*t507.*t259+4.*t511.*t259+2.*t514.*t259+2.*t488.*t356+2.*t494.*t356+4.*t491.*t313;
  t769 = t375.*t767.*t525;
  t773 = t532.*t371.*t536;
  t777 = t380.*t767.*t525;
  t785 = t767.*t345.*t347;
  t790 = -t552.*t785./4+t396.*t773./2;
  t797 = -t567.*t785./4-t387.*t773./2;
  t800 = t385.*t790.*t394+t351.*t797.*t394;
  t816 = -t351.*t790.*t394+t385.*t797.*t394;
  t827 = Imq.*t40;
  t840 = t827.*Xse;
  t849 = t275.*V2;
  t855 = 2.*t78.*t827+2.*t80.*t827+2.*t71.*t827+2.*t104.*t827-2.*t51.*t47-4.*t155.*t616+4.*t56.*t840-2.*t91.*t47+2.*t154.*t624+2.*t154.*t627-2.*t71.*t849-4.*t206.*t279.*V2;
  t877 = t295.*V2;
  t882 = -2.*t104.*t849-2.*t46.*t111+4.*t129.*t840-2.*t68.*t111-2.*t85.*t146-2.*t85.*t129-4.*t160.*t500-4.*t651.*t207.*t652+2.*t159.*t661+2.*t159.*t656-2.*t294.*t877-2.*t321.*t877;
  t883 = t855+t882;
  t885 = t375.*t883.*t525;
  t888 = t359.*t371;
  t891 = t677.*t888-t531.*t351;
  t893 = t380.*t891.*t536;
  t897 = t380.*t883.*t525;
  t901 = t375.*t891.*t536;
  t907 = t883.*t345.*t347;
  t912 = -t552.*t907./4-t386.*t893./2;
  t919 = -t567.*t907./4+t386.*t901./2;
  t922 = t385.*t912.*t394+t351.*t919.*t394;
  t938 = -t351.*t912.*t394+t385.*t919.*t394;
  t949 = a1r.*V1;
  t951 = a1i.*V1;
  t987 = -4.*t220.*t101+2.*t159.*t156-2.*t154.*t161-4.*t221.*t166+2.*t301.*t238-2.*t154.*t172-4.*t221.*t177+2.*t301.*t266+4.*t164.*t223-2.*t236.*t303+2.*t159.*t227+4.*t164.*t248-2.*t236.*t330+2.*t154.*t286+2.*t154.*t290+2.*t159.*t307+2.*t159.*t317;
  t989 = t375.*t987.*t525;
  t995 = -t152.*t99.*t371-t531.*t154;
  t997 = t380.*t995.*t536;
  t1001 = t380.*t987.*t525;
  t1005 = t375.*t995.*t536;
  t1011 = t987.*t345.*t347;
  t1016 = -t35-t552.*t1011./4-t386.*t997./2;
  t1023 = t29-t567.*t1011./4+t386.*t1005./2;
  t1026 = t385.*t1016.*t394+t351.*t1023.*t394;
  t1044 = -t351.*t1016.*t394+t385.*t1023.*t394;
  t1056 = Vdc.*Gsh;
  t1060 = Vdc.*Bsh;
  t1064 = 2.*t3-t2.*t1056.*t4./4-t2.*t1060.*t8./4;
  t1072 = t83.*t153;
  t1073 = t1072.*t40;
  t1077 = t83.*t99;
  t1078 = t1077.*t40;
  t1081 = t99.*V2;
  t1082 = t1081.*omega;
  t1093 = t153.*V2;
  t1094 = t1093.*omega;
  t1095 = t112.*Qref;
  t1103 = t134.*Qref;
  t1121 = -4.*t99.*t84.*t42-2.*t1073.*t86.*x2-2.*t1078.*t87-4.*t1082.*t113+2.*t1078.*t238-2.*t1078.*t119-4.*t1082.*t135+2.*t1078.*t266-4.*t1094.*t1095+2.*t1073.*t303-2.*t1073.*t118.*x2-4.*t1094.*t1103+2.*t1073.*t330+4.*V1.*t40.*t42+2.*t1078.*t143+2.*t1078.*t147-2.*t1073.*t146.*Imd-2.*t1073.*t129.*Imd;
  t1123 = t375.*t1121.*t525;
  t1128 = t1072.*t371-t531.*t1077;
  t1130 = t380.*t1128.*t536;
  t1134 = t380.*t1121.*t525;
  t1138 = t375.*t1128.*t536;
  t1144 = t1121.*t345.*t347;
  t1149 = t28-t552.*t1144./4-t386.*t1130./2;
  t1156 = t34-t567.*t1144./4+t386.*t1138./2;
  t1159 = t385.*t1149.*t394+t351.*t1156.*t394;
  t1177 = -t351.*t1149.*t394+t385.*t1156.*t394;
  t1207 = a1r.*V2;
  t1209 = a1i.*V2;
  t1212 = -t375.*t987.*t525;
  t1216 = 1+t995.*t536;
  t1217 = t381.*t1216;
  t1221 = -t380.*t987.*t525;
  t1224 = t376.*t1216;
  t1230 = -t987.*t345.*t347;
  t1236 = t37-t552.*t1230./4+t386.*t380.*t1216./2;
  t1244 = -t31-t567.*t1230./4-t386.*t375.*t1216./2;
  t1247 = t385.*t1236.*t394+t351.*t1244.*t394;
  t1265 = -t351.*t1236.*t394+t385.*t1244.*t394;
  t1280 = t100.*omega;
  t1283 = t83.*t40;
  t1284 = t1283.*omega;
  t1289 = t220.*omega;
  t1302 = t322.*Imd;
  t1307 = t295.*Imq;
  t1314 = t62.*V2;
  t1319 = V2.*Xse;
  t1322 = t57.*V2;
  t1325 = -0.8e1.*t274.*t213-4.*t1280.*t113-6.*t1284.*t203-6.*t1284.*t217-4.*t1289.*t1095-4.*t1289.*t1103+4.*t160.*Xse.*t232+4.*t155.*Xse.*t259-0.8e1.*t194.*t310+2.*t294.*t1302+2.*t321.*t1302-2.*t321.*t1307+0.8e1.*t274.*t313-0.12e2.*t100.*t284+2.*t104.*t1314+2.*t71.*t1314+4.*t108.*t1319+2.*t104.*t1322;
  t1341 = V2.*Kp;
  t1342 = t1341.*Imd;
  t1348 = t1341.*Imq;
  t1354 = t1322.*Xse;
  t1368 = V2.*t42;
  t1372 = t1314.*Xse;
  t1378 = 2.*t71.*t1322+4.*t74.*t1319+2.*t78.*t1314+2.*t80.*t1314+2.*t80.*t1322+2.*t78.*t1322-4.*t159.*t652.*t171-4.*t46.*t1342-4.*t159.*t652.*t160-4.*t51.*t1348-4.*t154.*t652.*t155+4.*t56.*t1354-4.*t154.*t652.*t226+4.*t651.*t279.*t356-4.*t651.*t207.*t366-4.*t68.*t1342-4.*t154.*t1368.*t316+4.*t56.*t1372-4.*t154.*t1368.*t306;
  t1401 = t275.*Imq;
  t1404 = t195.*Imd;
  t1419 = t652.*Imq;
  t1424 = 4.*t159.*t1368.*t289+4.*t159.*t1368.*t285-4.*t91.*t1348+6.*t1283.*t87+6.*t1283.*t119+0.8e1.*t652.*t113+0.8e1.*t652.*t135+2.*t184.*V2-4.*t206.*t279.*Imq-2.*t71.*t1401-2.*t104.*t1404-2.*t104.*t1401+2.*t91.*t259+2.*t68.*t232-0.8e1.*t194.*t203-2.*t71.*t1404+2.*t46.*t232-4.*t46.*t1419+2.*t51.*t259;
  t1442 = t652.*Imd;
  t1456 = t152.*t1081;
  t1461 = t152.*t1093;
  t1467 = 2.*t190.*V2+2.*t180.*V2+4.*t129.*t1372-6.*t1283.*t147-4.*t1280.*t135+4.*t16.*V2.*t42+2.*t169.*V2-6.*t1283.*t143+4.*t51.*t1442-4.*t68.*t1419+4.*t129.*t1354+4.*t91.*t1442-4.*t206.*t207.*Imd-2.*t294.*t1307+4.*t1456.*t266+4.*t1456.*t238+4.*t1461.*t330+0.8e1.*t101+4.*t1461.*t303;
  t1475 = (t1325+t1378+t1424+t1467).*t345.*t347-2.*t346./t84;
  t1476 = t376.*t1475;
  t1479 = t677.*t83;
  t1480 = Qref.*t347;
  t1483 = Pref.*t347;
  t1488 = t1479.*t1480.*t888-t531.*(-t83+t1479.*t1483.*t359);
  t1490 = t380.*t1488.*t536;
  t1493 = t381.*t1475;
  t1497 = t375.*t1488.*t536;
  t1507 = -t30-t551.*t375.*t1475./4-t386.*t1490./2;
  t1515 = -t36-t551.*t380.*t1475./4+t386.*t1497./2;
  t1518 = t385.*t1507.*t394+t351.*t1515.*t394;
  t1536 = -t351.*t1507.*t394+t385.*t1515.*t394;
  t1547 = 1./Tmac;
  t1553 = 1./Tmdc;
  t1559 = Ki.*t83;
  t1561 = -K-Kp;

  DAE.Fx = DAE.Fx + sparse(Upfc.Vdc,Upfc.Vdc, t11.*t12.*t14./4-t23.*t12.*t26-(t384.*t401+t414.*t409).*t12.*t26-1./Rdc.*t12-2.*Rsh.*(t23.*t11./4+t429.*t432./4).*t438+t443.*t436.*t26.*t12+Rse.*(t447+t448).*t12.*t26,DAE.n,DAE.n);

  DAE.Fx = DAE.Fx + sparse(Upfc.Vdc,Upfc.x1, ((t481.*t526./4+t407.*t538./2-t542.*t544./4+t405.*t538./2).*t401+t384.*t577+(t542.*t526./4+t382.*t538./2+t481.*t544./4-t377.*t538./2).*t414+t409.*t593).*t12.*t14-2.*Rse.*(t401.*t577+t414.*t593).*t602,DAE.n,DAE.n);

  DAE.Fx = DAE.Fx + sparse(Upfc.Vdc,Upfc.x2, ((t481.*t769./4-t407.*t773./2-t542.*t777./4-t405.*t773./2).*t401+t384.*t800+(t542.*t769./4-t382.*t773./2+t481.*t777./4+t377.*t773./2).*t414+t409.*t816).*t12.*t14-2.*Rse.*(t401.*t800+t414.*t816).*t602,DAE.n,DAE.n);

  DAE.Fy = DAE.Fy + sparse(Upfc.Vdc,bus1, ((-t949.*t34-t951.*t28+t481.*t989./4+t675.*t997./2-t542.*t1001./4+t689.*t1005./2).*t401+t384.*t1026+(-t951.*t34+t949.*t28+t542.*t989./4+t689.*t997./2+t481.*t1001./4-t675.*t1005./2).*t414+t409.*t1044).*t12.*t14-2.*Rse.*(t401.*t1026+t414.*t1044).*t602,DAE.n,2*Bus.n);
  DAE.Fy = DAE.Fy + sparse(Upfc.Vdc,bus1+Bus.n, t1064.*t12.*t14+((a1r.*t28-a1i.*t34+t481.*t1123./4+t675.*t1130./2-t542.*t1134./4+t689.*t1138./2).*t401+t384.*t1159+(a1i.*t28+a1r.*t34+t542.*t1123./4+t689.*t1130./2+t481.*t1134./4-t675.*t1138./2).*t414+t409.*t1177).*t12.*t14-2.*Rsh.*(t23.*t1064+t429.*(-2.*t7+t2.*t1060.*t4./4-t2.*t1056.*t8./4)).*t438+2.*t443./t16./V1.*t14.*t12-2.*Rse.*(t401.*t1159+t414.*t1177).*t602,DAE.n,2*Bus.n);
  DAE.Fy = DAE.Fy + sparse(Upfc.Vdc,bus2, ((t1207.*t36+t1209.*t30+t481.*t1212./4-t350.*t1217./2-t542.*t1221./4-t379.*t1224./2).*t401+t384.*t1247+(t1209.*t36-t1207.*t30+t542.*t1212./4-t379.*t1217./2+t481.*t1221./4+t350.*t1224./2).*t414+t409.*t1265).*t12.*t14-2.*Rse.*(t401.*t1247+t414.*t1265).*t602,DAE.n,2*Bus.n);
  DAE.Fy = DAE.Fy + sparse(Upfc.Vdc,bus2+Bus.n, ((-a1r.*t30+a1i.*t36+t480.*t1476./4+t675.*t1490./2-t541.*t1493./4+t689.*t1497./2).*t401+t384.*t1518+(-a1i.*t30-a1r.*t36+t541.*t1476./4+t689.*t1490./2+t480.*t1493./4-t675.*t1497./2).*t414+t409.*t1536).*t12.*t14-2.*Rse.*(t401.*t1518+t414.*t1536).*t602,DAE.n,2*Bus.n);
  DAE.Fx = DAE.Fx + sparse(Upfc.Vmac,Upfc.Vmac, -t1547,DAE.n,DAE.n);
  DAE.Fy = DAE.Fy + sparse(Upfc.Vmac,bus1+Bus.n, Kmac.*t1547,DAE.n,2*Bus.n);
  DAE.Fx = DAE.Fx + sparse(Upfc.Vmdc,Upfc.Vdc, Kmdc.*t1553,DAE.n,DAE.n);
  DAE.Fx = DAE.Fx + sparse(Upfc.Vmdc,Upfc.Vmdc, -t1553,DAE.n,DAE.n);
  DAE.Fy = DAE.Fy + sparse(Upfc.x1,bus2+Bus.n, -t1559.*t1483,DAE.n,2*Bus.n);
  DAE.Fy = DAE.Fy + sparse(Upfc.x2,bus2+Bus.n, -t1559.*t1480,DAE.n,2*Bus.n);
  DAE.Gx = DAE.Gx + sparse(bus1,Upfc.Vdc, t11./4,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus1,Upfc.x1, t29.*t577+t35.*t593,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus1,Upfc.x2, t29.*t800+t35.*t816,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus1+Bus.n,Upfc.Vdc, t432./4,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus1+Bus.n,Upfc.x1, t35.*t577-t29.*t593,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus1+Bus.n,Upfc.x2, t35.*t800-t29.*t816,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus2,Upfc.x1, -t31.*t577-t37.*t593,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus2,Upfc.x2, -t31.*t800-t37.*t816,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus2+Bus.n,Upfc.x1, -t37.*t577+t31.*t593,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus2+Bus.n,Upfc.x2, -t37.*t800+t31.*t816,2*Bus.n,DAE.n);

  % m
  idx = find(m <= m_max & m >= m_min & (DAE.f(Upfc.m) ~= 0 | DAE.t == -1));
  if ~isempty(idx)
    DAE.Fx = DAE.Fx + sparse(Upfc.Vdc(idx),Upfc.m(idx), t457(idx).*t12(idx).*t14(idx)./4-2.*Rsh(idx).*(t23(idx).*t457(idx)./4+t429(idx).*t463(idx)./4).*t438(idx),DAE.n,DAE.n);
    DAE.Fx = DAE.Fx + sparse(Upfc.m(idx),Upfc.Vmac(idx), Kpac(idx).*t1547(idx)-Kiac(idx),DAE.n,DAE.n);
    DAE.Fy = DAE.Fy + sparse(Upfc.m(idx),bus1(idx)+Bus.n, -Kpac(idx).*Kmac(idx).*t1547(idx),DAE.n,2*Bus.n);
    DAE.Gx = DAE.Gx + sparse(bus1(idx),Upfc.m(idx), t457(idx)./4,2*Bus.n,DAE.n);
    DAE.Gx = DAE.Gx + sparse(bus1(idx)+Bus.n,Upfc.m(idx), t463(idx)./4,2*Bus.n,DAE.n);
  end
  idx = find((m >= m_max | m <= m_min) & DAE.f(Upfc.m) == 0);
  if ~isempty(idx)
    DAE.Fx = DAE.Fx + sparse(Upfc.m(idx),Upfc.m(idx),-1,DAE.n,DAE.n);
  end

  % alpha
  idx = find(alpha <= alpha_max & alpha >= alpha_min & (DAE.f(Upfc.alpha) ~= 0 | DAE.t == -1));
  if ~isempty(idx)
    DAE.Fx = DAE.Fx + sparse(Upfc.Vdc(idx),Upfc.alpha(idx), t469(idx).*t12(idx).*t14(idx)./4-2.*Rsh(idx).*(t23(idx).*t469(idx)./4+t429(idx).*t473(idx)./4).*t438(idx),DAE.n,DAE.n);
    DAE.Fx = DAE.Fx + sparse(Upfc.alpha(idx),Upfc.Vdc(idx), -Kpdc(idx).*Kmdc(idx).*t1553(idx),DAE.n,DAE.n);
    DAE.Fx = DAE.Fx + sparse(Upfc.alpha(idx),Upfc.Vmdc(idx), Kpdc(idx).*t1553(idx)-Kidc(idx),DAE.n,DAE.n);
    DAE.Gx = DAE.Gx + sparse(bus1(idx),Upfc.alpha(idx), t469(idx)./4,2*Bus.n,DAE.n);
    DAE.Gx = DAE.Gx + sparse(bus1(idx)+Bus.n,Upfc.alpha(idx), t473(idx)./4,2*Bus.n,DAE.n);
  end
  idx = find((alpha >= alpha_max | alpha <= alpha_min) & DAE.f(Upfc.alpha) == 0);
  if ~isempty(idx)
    DAE.Fx = DAE.Fx + sparse(Upfc.alpha(idx),Upfc.alpha(idx),-1,DAE.n,DAE.n);
  end

  % Imd
  DAE.Fx = DAE.Fx + sparse(Upfc.Vdc,Upfc.Imd, ((t481.*t672./4+t675.*t682./2-t542.*t686./4+t689.*t691./2).*t401+t384.*t712+(t542.*t672./4+t689.*t682./2+t481.*t686./4-t675.*t691./2).*t414+t409.*t728).*t12.*t14-2.*Rse.*(t401.*t712+t414.*t728).*t602,DAE.n,DAE.n);
  DAE.Fx = DAE.Fx + sparse(Upfc.Imd,Upfc.x1, 1,DAE.n,DAE.n);
  DAE.Fx = DAE.Fx + sparse(Upfc.Imd,Upfc.Imd, t1561,DAE.n,DAE.n);
  DAE.Fy = DAE.Fy + sparse(Upfc.Imd,bus2+Bus.n, -t231.*t1483,DAE.n,2*Bus.n);
  DAE.Fx = DAE.Fx + sparse(Upfc.x1,Upfc.Imd, -Ki,DAE.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus1,Upfc.Imd, t29.*t712+t35.*t728,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus1+Bus.n,Upfc.Imd, t35.*t712-t29.*t728,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus2,Upfc.Imd, -t31.*t712-t37.*t728,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus2+Bus.n,Upfc.Imd, -t37.*t712+t31.*t728,2*Bus.n,DAE.n);

  % Imq
  DAE.Fx = DAE.Fx + sparse(Upfc.Vdc,Upfc.Imq, ((t481.*t885./4+t675.*t893./2-t542.*t897./4+t689.*t901./2).*t401+t384.*t922+(t542.*t885./4+t689.*t893./2+t481.*t897./4-t675.*t901./2).*t414+t409.*t938).*t12.*t14-2.*Rse.*(t401.*t922+t414.*t938).*t602,DAE.n,DAE.n);
  DAE.Fx = DAE.Fx + sparse(Upfc.Imq,Upfc.x2, 1,DAE.n,DAE.n);
  DAE.Fx = DAE.Fx + sparse(Upfc.Imq,Upfc.Imq, t1561,DAE.n,DAE.n);
  DAE.Fy = DAE.Fy + sparse(Upfc.Imq,bus2+Bus.n, -t231.*t1480,DAE.n,2*Bus.n);
  DAE.Fx = DAE.Fx + sparse(Upfc.x2,Upfc.Imq, -Ki,DAE.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus1,Upfc.Imq, t29.*t922+t35.*t938,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus1+Bus.n,Upfc.Imq, t35.*t922-t29.*t938,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus2,Upfc.Imq, -t31.*t922-t37.*t938,2*Bus.n,DAE.n);
  DAE.Gx = DAE.Gx + sparse(bus2+Bus.n,Upfc.Imq, -t37.*t922+t31.*t938,2*Bus.n,DAE.n);

 case 5  % non-windup limits

  idx = find((alpha >= alpha_max | alpha <= alpha_min) & ...
             DAE.f(Upfc.alpha) == 0);
  if ~isempty(idx)
    k = Upfc.alpha(idx);
    DAE.tn(k) = 0;
    DAE.Ac(:,k) = 0;
    DAE.Ac(k,:) = 0;
    if Settings.octave
      DAE.Ac(k,k) = -eye(length(idx));
    else
      DAE.Ac(k,k) = -speye(length(idx));
    end
  end

  idx = find((m >= m_max | m <= m_min) & DAE.f(Upfc.m) == 0);
  if ~isempty(idx)
    k = Upfc.m(idx);
    DAE.tn(k) = 0;
    DAE.Ac(:,k) = 0;
    DAE.Ac(k,:) = 0;
    if Settings.octave
      DAE.Ac(k,k) = -eye(length(idx));
    else
      DAE.Ac(k,k) = -speye(length(idx));
    end
  end

  idx = find(Vdc <= 1e-6); % & DAE.f(Upfc.Vdc) == 0);
  if ~isempty(idx)
    k = Upfc.Vdc(idx);
    DAE.tn(k) = 0;
    DAE.Ac(:,k) = 0;
    DAE.Ac(k,:) = 0;
    if Settings.octave
      DAE.Ac(k,k) = -eye(length(idx));
    else
      DAE.Ac(k,k) = -speye(length(idx));
    end
  end

end