Actual source code: ex9busopt_fd.c

petsc-3.6.4 2016-04-12
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  1: static char help[] = "Power grid stability analysis of WECC 9 bus system.\n\
  2: This example is based on the 9-bus (node) example given in the book Power\n\
  3: Systems Dynamics and Stability (Chapter 7) by P. Sauer and M. A. Pai.\n\
  4: The power grid in this example consists of 9 buses (nodes), 3 generators,\n\
  5: 3 loads, and 9 transmission lines. The network equations are written\n\
  6: in current balance form using rectangular coordiantes.\n\n";

  8: /*
  9:    The equations for the stability analysis are described by the DAE

 11:    \dot{x} = f(x,y,t)
 12:      0     = g(x,y,t)

 14:    where the generators are described by differential equations, while the algebraic
 15:    constraints define the network equations.

 17:    The generators are modeled with a 4th order differential equation describing the electrical
 18:    and mechanical dynamics. Each generator also has an exciter system modeled by 3rd order
 19:    diff. eqns. describing the exciter, voltage regulator, and the feedback stabilizer
 20:    mechanism.

 22:    The network equations are described by nodal current balance equations.
 23:     I(x,y) - Y*V = 0

 25:    where:
 26:     I(x,y) is the current injected from generators and loads.
 27:       Y    is the admittance matrix, and
 28:       V    is the voltage vector
 29: */

 31: /*
 32:    Include "petscts.h" so that we can use TS solvers.  Note that this
 33:    file automatically includes:
 34:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 35:      petscmat.h - matrices
 36:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 37:      petscviewer.h - viewers               petscpc.h  - preconditioners
 38:      petscksp.h   - linear solvers
 39: */
 40: #include <petsctao.h>
 41: #include <petscts.h>
 42: #include <petscdm.h>
 43: #include <petscdmda.h>
 44: #include <petscdmcomposite.h>

 46: PetscErrorCode FormFunction(Tao,Vec,PetscReal*,void*);

 48: #define freq 60
 49: #define w_s (2*PETSC_PI*freq)

 51: /* Sizes and indices */
 52: const PetscInt nbus    = 9; /* Number of network buses */
 53: const PetscInt ngen    = 3; /* Number of generators */
 54: const PetscInt nload   = 3; /* Number of loads */
 55: const PetscInt gbus[3] = {0,1,2}; /* Buses at which generators are incident */
 56: const PetscInt lbus[3] = {4,5,7}; /* Buses at which loads are incident */

 58: /* Generator real and reactive powers (found via loadflow) */
 59: PetscScalar PG[3] = { 0.69,1.59,0.69};
 60: /* PetscScalar PG[3] = {0.716786142395021,1.630000000000000,0.850000000000000};*/
 61: const PetscScalar QG[3] = {0.270702180178785,0.066120127797275,-0.108402221791588};
 62: /* Generator constants */
 63: const PetscScalar H[3]    = {23.64,6.4,3.01};   /* Inertia constant */
 64: const PetscScalar Rs[3]   = {0.0,0.0,0.0}; /* Stator Resistance */
 65: const PetscScalar Xd[3]   = {0.146,0.8958,1.3125};  /* d-axis reactance */
 66: const PetscScalar Xdp[3]  = {0.0608,0.1198,0.1813}; /* d-axis transient reactance */
 67: const PetscScalar Xq[3]   = {0.4360,0.8645,1.2578}; /* q-axis reactance Xq(1) set to 0.4360, value given in text 0.0969 */
 68: const PetscScalar Xqp[3]  = {0.0969,0.1969,0.25}; /* q-axis transient reactance */
 69: const PetscScalar Td0p[3] = {8.96,6.0,5.89}; /* d-axis open circuit time constant */
 70: const PetscScalar Tq0p[3] = {0.31,0.535,0.6}; /* q-axis open circuit time constant */
 71: PetscScalar M[3]; /* M = 2*H/w_s */
 72: PetscScalar D[3]; /* D = 0.1*M */

 74: PetscScalar TM[3]; /* Mechanical Torque */
 75: /* Exciter system constants */
 76: const PetscScalar KA[3] = {20.0,20.0,20.0};  /* Voltage regulartor gain constant */
 77: const PetscScalar TA[3] = {0.2,0.2,0.2};     /* Voltage regulator time constant */
 78: const PetscScalar KE[3] = {1.0,1.0,1.0};     /* Exciter gain constant */
 79: const PetscScalar TE[3] = {0.314,0.314,0.314}; /* Exciter time constant */
 80: const PetscScalar KF[3] = {0.063,0.063,0.063};  /* Feedback stabilizer gain constant */
 81: const PetscScalar TF[3] = {0.35,0.35,0.35};    /* Feedback stabilizer time constant */
 82: const PetscScalar k1[3] = {0.0039,0.0039,0.0039};
 83: const PetscScalar k2[3] = {1.555,1.555,1.555};  /* k1 and k2 for calculating the saturation function SE = k1*exp(k2*Efd) */

 85: PetscScalar Vref[3];
 86: /* Load constants
 87:   We use a composite load model that describes the load and reactive powers at each time instant as follows
 88:   P(t) = \sum\limits_{i=0}^ld_nsegsp \ld_alphap_i*P_D0(\frac{V_m(t)}{V_m0})^\ld_betap_i
 89:   Q(t) = \sum\limits_{i=0}^ld_nsegsq \ld_alphaq_i*Q_D0(\frac{V_m(t)}{V_m0})^\ld_betaq_i
 90:   where
 91:     ld_nsegsp,ld_nsegsq - Number of individual load models for real and reactive power loads
 92:     ld_alphap,ld_alphap - Percentage contribution (weights) or loads
 93:     P_D0                - Real power load
 94:     Q_D0                - Reactive power load
 95:     V_m(t)              - Voltage magnitude at time t
 96:     V_m0                - Voltage magnitude at t = 0
 97:     ld_betap, ld_betaq  - exponents describing the load model for real and reactive part

 99:     Note: All loads have the same characteristic currently.
100: */
101: const PetscScalar PD0[3] = {1.25,0.9,1.0};
102: const PetscScalar QD0[3] = {0.5,0.3,0.35};
103: const PetscInt    ld_nsegsp[3] = {3,3,3};
104: const PetscScalar ld_alphap[3] = {1.0,0.0,0.0};
105: const PetscScalar ld_betap[3]  = {2.0,1.0,0.0};
106: const PetscInt    ld_nsegsq[3] = {3,3,3};
107: const PetscScalar ld_alphaq[3] = {1.0,0.0,0.0};
108: const PetscScalar ld_betaq[3]  = {2.0,1.0,0.0};

110: typedef struct {
111:   DM          dmgen, dmnet; /* DMs to manage generator and network subsystem */
112:   DM          dmpgrid; /* Composite DM to manage the entire power grid */
113:   Mat         Ybus; /* Network admittance matrix */
114:   Vec         V0;  /* Initial voltage vector (Power flow solution) */
115:   PetscReal   tfaulton,tfaultoff; /* Fault on and off times */
116:   PetscInt    faultbus; /* Fault bus */
117:   PetscScalar Rfault;
118:   PetscReal   t0,tmax;
119:   PetscInt    neqs_gen,neqs_net,neqs_pgrid;
120:   Mat         Sol; /* Matrix to save solution at each time step */
121:   PetscInt    stepnum;
122:   PetscBool   alg_flg;
123:   PetscReal   t;
124:   IS          is_diff; /* indices for differential equations */
125:   IS          is_alg; /* indices for algebraic equations */
126:   PetscReal   freq_u,freq_l; /* upper and lower frequency limit */
127:   PetscInt    pow; /* power coefficient used in the cost function */
128:   Vec         vec_q;
129: } Userctx;


132: /* Converts from machine frame (dq) to network (phase a real,imag) reference frame */
135: PetscErrorCode dq2ri(PetscScalar Fd,PetscScalar Fq,PetscScalar delta,PetscScalar *Fr, PetscScalar *Fi)
136: {
138:   *Fr =  Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
139:   *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
140:   return(0);
141: }

143: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
146: PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd, PetscScalar *Fq)
147: {
149:   *Fd =  Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
150:   *Fq =  Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
151:   return(0);
152: }

156: PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
157: {
159:   Vec            Xgen,Xnet;
160:   PetscScalar    *xgen,*xnet;
161:   PetscInt       i,idx=0;
162:   PetscScalar    Vr,Vi,IGr,IGi,Vm,Vm2;
163:   PetscScalar    Eqp,Edp,delta;
164:   PetscScalar    Efd,RF,VR; /* Exciter variables */
165:   PetscScalar    Id,Iq;  /* Generator dq axis currents */
166:   PetscScalar    theta,Vd,Vq,SE;

169:   M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
170:   D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];

172:   DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);

174:   /* Network subsystem initialization */
175:   VecCopy(user->V0,Xnet);

177:   /* Generator subsystem initialization */
178:   VecGetArray(Xgen,&xgen);
179:   VecGetArray(Xnet,&xnet);

181:   for (i=0; i < ngen; i++) {
182:     Vr  = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
183:     Vi  = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
184:     Vm  = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
185:     IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
186:     IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;

188:     delta = atan2(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */

190:     theta = PETSC_PI/2.0 - delta;

192:     Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
193:     Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */

195:     Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
196:     Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);

198:     Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
199:     Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */

201:     TM[i] = PG[i];

203:     /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
204:     xgen[idx]   = Eqp;
205:     xgen[idx+1] = Edp;
206:     xgen[idx+2] = delta;
207:     xgen[idx+3] = w_s;

209:     idx = idx + 4;

211:     xgen[idx]   = Id;
212:     xgen[idx+1] = Iq;

214:     idx = idx + 2;

216:     /* Exciter */
217:     Efd = Eqp + (Xd[i] - Xdp[i])*Id;
218:     SE  = k1[i]*PetscExpScalar(k2[i]*Efd);
219:     VR  =  KE[i]*Efd + SE;
220:     RF  =  KF[i]*Efd/TF[i];

222:     xgen[idx]   = Efd;
223:     xgen[idx+1] = RF;
224:     xgen[idx+2] = VR;

226:     Vref[i] = Vm + (VR/KA[i]);

228:     idx = idx + 3;
229:   }

231:   VecRestoreArray(Xgen,&xgen);
232:   VecRestoreArray(Xnet,&xnet);

234:   /* VecView(Xgen,0); */
235:   DMCompositeGather(user->dmpgrid,X,INSERT_VALUES,Xgen,Xnet);
236:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
237:   return(0);
238: }

240: /* Computes F = [-f(x,y);g(x,y)] */
243: PetscErrorCode ResidualFunction(SNES snes,Vec X, Vec F, Userctx *user)
244: {
246:   Vec            Xgen,Xnet,Fgen,Fnet;
247:   PetscScalar    *xgen,*xnet,*fgen,*fnet;
248:   PetscInt       i,idx=0;
249:   PetscScalar    Vr,Vi,Vm,Vm2;
250:   PetscScalar    Eqp,Edp,delta,w; /* Generator variables */
251:   PetscScalar    Efd,RF,VR; /* Exciter variables */
252:   PetscScalar    Id,Iq;  /* Generator dq axis currents */
253:   PetscScalar    Vd,Vq,SE;
254:   PetscScalar    IGr,IGi,IDr,IDi;
255:   PetscScalar    Zdq_inv[4],det;
256:   PetscScalar    PD,QD,Vm0,*v0;
257:   PetscInt       k;

260:   VecZeroEntries(F);
261:   DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
262:   DMCompositeGetLocalVectors(user->dmpgrid,&Fgen,&Fnet);
263:   DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
264:   DMCompositeScatter(user->dmpgrid,F,Fgen,Fnet);

266:   /* Network current balance residual IG + Y*V + IL = 0. Only YV is added here.
267:      The generator current injection, IG, and load current injection, ID are added later
268:   */
269:   /* Note that the values in Ybus are stored assuming the imaginary current balance
270:      equation is ordered first followed by real current balance equation for each bus.
271:      Thus imaginary current contribution goes in location 2*i, and
272:      real current contribution in 2*i+1
273:   */
274:   MatMult(user->Ybus,Xnet,Fnet);

276:   VecGetArray(Xgen,&xgen);
277:   VecGetArray(Xnet,&xnet);
278:   VecGetArray(Fgen,&fgen);
279:   VecGetArray(Fnet,&fnet);

281:   /* Generator subsystem */
282:   for (i=0; i < ngen; i++) {
283:     Eqp   = xgen[idx];
284:     Edp   = xgen[idx+1];
285:     delta = xgen[idx+2];
286:     w     = xgen[idx+3];
287:     Id    = xgen[idx+4];
288:     Iq    = xgen[idx+5];
289:     Efd   = xgen[idx+6];
290:     RF    = xgen[idx+7];
291:     VR    = xgen[idx+8];

293:     /* Generator differential equations */
294:     fgen[idx]   = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i];
295:     fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i];
296:     fgen[idx+2] = -w + w_s;
297:     fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i];

299:     Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
300:     Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */

302:     ri2dq(Vr,Vi,delta,&Vd,&Vq);
303:     /* Algebraic equations for stator currents */
304:     det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];

306:     Zdq_inv[0] = Rs[i]/det;
307:     Zdq_inv[1] = Xqp[i]/det;
308:     Zdq_inv[2] = -Xdp[i]/det;
309:     Zdq_inv[3] = Rs[i]/det;

311:     fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id;
312:     fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq;

314:     /* Add generator current injection to network */
315:     dq2ri(Id,Iq,delta,&IGr,&IGi);

317:     fnet[2*gbus[i]]   -= IGi;
318:     fnet[2*gbus[i]+1] -= IGr;

320:     Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq); Vm2 = Vm*Vm;

322:     SE = k1[i]*PetscExpScalar(k2[i]*Efd);

324:     /* Exciter differential equations */
325:     fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i];
326:     fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i];
327:     fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];

329:     idx = idx + 9;
330:   }

332:   VecGetArray(user->V0,&v0);
333:   for (i=0; i < nload; i++) {
334:     Vr  = xnet[2*lbus[i]]; /* Real part of load bus voltage */
335:     Vi  = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
336:     Vm  = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
337:     Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
338:     PD  = QD = 0.0;
339:     for (k=0; k < ld_nsegsp[i]; k++) PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
340:     for (k=0; k < ld_nsegsq[i]; k++) QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);

342:     /* Load currents */
343:     IDr = (PD*Vr + QD*Vi)/Vm2;
344:     IDi = (-QD*Vr + PD*Vi)/Vm2;

346:     fnet[2*lbus[i]]   += IDi;
347:     fnet[2*lbus[i]+1] += IDr;
348:   }
349:   VecRestoreArray(user->V0,&v0);

351:   VecRestoreArray(Xgen,&xgen);
352:   VecRestoreArray(Xnet,&xnet);
353:   VecRestoreArray(Fgen,&fgen);
354:   VecRestoreArray(Fnet,&fnet);

356:   DMCompositeGather(user->dmpgrid,F,INSERT_VALUES,Fgen,Fnet);
357:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
358:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Fgen,&Fnet);
359:   return(0);
360: }

362: /* \dot{x} - f(x,y)
363:      g(x,y) = 0
364:  */
367: PetscErrorCode IFunction(TS ts,PetscReal t, Vec X, Vec Xdot, Vec F, Userctx *user)
368: {
369:   PetscErrorCode    ierr;
370:   SNES              snes;
371:   PetscScalar       *f;
372:   const PetscScalar *xdot;
373:   PetscInt          i;

376:   user->t = t;

378:   TSGetSNES(ts,&snes);
379:   ResidualFunction(snes,X,F,user);
380:   VecGetArray(F,&f);
381:   VecGetArrayRead(Xdot,&xdot);
382:   for (i=0;i < ngen;i++) {
383:     f[9*i]   += xdot[9*i];
384:     f[9*i+1] += xdot[9*i+1];
385:     f[9*i+2] += xdot[9*i+2];
386:     f[9*i+3] += xdot[9*i+3];
387:     f[9*i+6] += xdot[9*i+6];
388:     f[9*i+7] += xdot[9*i+7];
389:     f[9*i+8] += xdot[9*i+8];
390:   }
391:   VecRestoreArray(F,&f);
392:   VecRestoreArrayRead(Xdot,&xdot);
393:   return(0);
394: }

396: /* This function is used for solving the algebraic system only during fault on and
397:    off times. It computes the entire F and then zeros out the part corresponding to
398:    differential equations
399:  F = [0;g(y)];
400: */
403: PetscErrorCode AlgFunction(SNES snes, Vec X, Vec F, void *ctx)
404: {
406:   Userctx        *user=(Userctx*)ctx;
407:   PetscScalar    *f;
408:   PetscInt       i;

411:   ResidualFunction(snes,X,F,user);
412:   VecGetArray(F,&f);
413:   for (i=0; i < ngen; i++) {
414:     f[9*i]   = 0;
415:     f[9*i+1] = 0;
416:     f[9*i+2] = 0;
417:     f[9*i+3] = 0;
418:     f[9*i+6] = 0;
419:     f[9*i+7] = 0;
420:     f[9*i+8] = 0;
421:   }
422:   VecRestoreArray(F,&f);
423:   return(0);
424: }

428: PetscErrorCode PreallocateJacobian(Mat J, Userctx *user)
429: {
431:   PetscInt       *d_nnz;
432:   PetscInt       i,idx=0,start=0;
433:   PetscInt       ncols;

436:   PetscMalloc1(user->neqs_pgrid,&d_nnz);
437:   for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
438:   /* Generator subsystem */
439:   for (i=0; i < ngen; i++) {

441:     d_nnz[idx]   += 3;
442:     d_nnz[idx+1] += 2;
443:     d_nnz[idx+2] += 2;
444:     d_nnz[idx+3] += 5;
445:     d_nnz[idx+4] += 6;
446:     d_nnz[idx+5] += 6;

448:     d_nnz[user->neqs_gen+2*gbus[i]]   += 3;
449:     d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;

451:     d_nnz[idx+6] += 2;
452:     d_nnz[idx+7] += 2;
453:     d_nnz[idx+8] += 5;

455:     idx = idx + 9;
456:   }

458:   start = user->neqs_gen;

460:   for (i=0; i < nbus; i++) {
461:     MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL);
462:     d_nnz[start+2*i]   += ncols;
463:     d_nnz[start+2*i+1] += ncols;
464:     MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL);
465:   }

467:   MatSeqAIJSetPreallocation(J,0,d_nnz);

469:   PetscFree(d_nnz);
470:   return(0);
471: }

473: /*
474:    J = [-df_dx, -df_dy
475:         dg_dx, dg_dy]
476: */
479: PetscErrorCode ResidualJacobian(SNES snes,Vec X,Mat J,Mat B,void *ctx)
480: {
481:   PetscErrorCode    ierr;
482:   Userctx           *user=(Userctx*)ctx;
483:   Vec               Xgen,Xnet;
484:   PetscScalar       *xgen,*xnet;
485:   PetscInt          i,idx=0;
486:   PetscScalar       Vr,Vi,Vm,Vm2;
487:   PetscScalar       Eqp,Edp,delta; /* Generator variables */
488:   PetscScalar       Efd; /* Exciter variables */
489:   PetscScalar       Id,Iq;  /* Generator dq axis currents */
490:   PetscScalar       Vd,Vq;
491:   PetscScalar       val[10];
492:   PetscInt          row[2],col[10];
493:   PetscInt          net_start=user->neqs_gen;
494:   PetscScalar       Zdq_inv[4],det;
495:   PetscScalar       dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
496:   PetscScalar       dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
497:   PetscScalar       dSE_dEfd;
498:   PetscScalar       dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
499:   PetscInt          ncols;
500:   const PetscInt    *cols;
501:   const PetscScalar *yvals;
502:   PetscInt          k;
503:   PetscScalar       PD,QD,Vm0,*v0,Vm4;
504:   PetscScalar       dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
505:   PetscScalar       dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;

508:   MatZeroEntries(B);
509:   DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
510:   DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);

512:   VecGetArray(Xgen,&xgen);
513:   VecGetArray(Xnet,&xnet);

515:   /* Generator subsystem */
516:   for (i=0; i < ngen; i++) {
517:     Eqp   = xgen[idx];
518:     Edp   = xgen[idx+1];
519:     delta = xgen[idx+2];
520:     Id    = xgen[idx+4];
521:     Iq    = xgen[idx+5];
522:     Efd   = xgen[idx+6];

524:     /*    fgen[idx]   = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i]; */
525:     row[0] = idx;
526:     col[0] = idx;           col[1] = idx+4;          col[2] = idx+6;
527:     val[0] = 1/ Td0p[i]; val[1] = (Xd[i] - Xdp[i])/ Td0p[i]; val[2] = -1/Td0p[i];

529:     MatSetValues(J,1,row,3,col,val,INSERT_VALUES);

531:     /*    fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
532:     row[0] = idx + 1;
533:     col[0] = idx + 1;       col[1] = idx+5;
534:     val[0] = 1/Tq0p[i]; val[1] = -(Xq[i] - Xqp[i])/Tq0p[i];
535:     MatSetValues(J,1,row,2,col,val,INSERT_VALUES);

537:     /*    fgen[idx+2] = - w + w_s; */
538:     row[0] = idx + 2;
539:     col[0] = idx + 2; col[1] = idx + 3;
540:     val[0] = 0;       val[1] = -1;
541:     MatSetValues(J,1,row,2,col,val,INSERT_VALUES);

543:     /*    fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i]; */
544:     row[0] = idx + 3;
545:     col[0] = idx; col[1] = idx + 1; col[2] = idx + 3;       col[3] = idx + 4;                  col[4] = idx + 5;
546:     val[0] = Iq/M[i];  val[1] = Id/M[i];      val[2] = D[i]/M[i]; val[3] = (Edp + (Xqp[i]-Xdp[i])*Iq)/M[i]; val[4] = (Eqp + (Xqp[i] - Xdp[i])*Id)/M[i];
547:     MatSetValues(J,1,row,5,col,val,INSERT_VALUES);

549:     Vr   = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
550:     Vi   = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
551:     ri2dq(Vr,Vi,delta,&Vd,&Vq);

553:     det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];

555:     Zdq_inv[0] = Rs[i]/det;
556:     Zdq_inv[1] = Xqp[i]/det;
557:     Zdq_inv[2] = -Xdp[i]/det;
558:     Zdq_inv[3] = Rs[i]/det;

560:     dVd_dVr    = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
561:     dVq_dVr    = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
562:     dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
563:     dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);

565:     /*    fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
566:     row[0] = idx+4;
567:     col[0] = idx;         col[1] = idx+1;        col[2] = idx + 2;
568:     val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0];  val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
569:     col[3] = idx + 4; col[4] = net_start+2*gbus[i];                     col[5] = net_start + 2*gbus[i]+1;
570:     val[3] = 1;       val[4] = Zdq_inv[0]*dVd_dVr + Zdq_inv[1]*dVq_dVr; val[5] = Zdq_inv[0]*dVd_dVi + Zdq_inv[1]*dVq_dVi;
571:     MatSetValues(J,1,row,6,col,val,INSERT_VALUES);

573:     /*  fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
574:     row[0] = idx+5;
575:     col[0] = idx;         col[1] = idx+1;        col[2] = idx + 2;
576:     val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2];  val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
577:     col[3] = idx + 5; col[4] = net_start+2*gbus[i];                     col[5] = net_start + 2*gbus[i]+1;
578:     val[3] = 1;       val[4] = Zdq_inv[2]*dVd_dVr + Zdq_inv[3]*dVq_dVr; val[5] = Zdq_inv[2]*dVd_dVi + Zdq_inv[3]*dVq_dVi;
579:     MatSetValues(J,1,row,6,col,val,INSERT_VALUES);

581:     dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
582:     dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
583:     dIGr_dId    = PetscSinScalar(delta);  dIGr_dIq = PetscCosScalar(delta);
584:     dIGi_dId    = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);

586:     /* fnet[2*gbus[i]]   -= IGi; */
587:     row[0] = net_start + 2*gbus[i];
588:     col[0] = idx+2;        col[1] = idx + 4;   col[2] = idx + 5;
589:     val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
590:     MatSetValues(J,1,row,3,col,val,INSERT_VALUES);

592:     /* fnet[2*gbus[i]+1]   -= IGr; */
593:     row[0] = net_start + 2*gbus[i]+1;
594:     col[0] = idx+2;        col[1] = idx + 4;   col[2] = idx + 5;
595:     val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
596:     MatSetValues(J,1,row,3,col,val,INSERT_VALUES);

598:     Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq); Vm2 = Vm*Vm;

600:     /*    fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i]; */
601:     /*    SE  = k1[i]*PetscExpScalar(k2[i]*Efd); */

603:     dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);

605:     row[0] = idx + 6;
606:     col[0] = idx + 6;                     col[1] = idx + 8;
607:     val[0] = (KE[i] + dSE_dEfd)/TE[i];  val[1] = -1/TE[i];
608:     MatSetValues(J,1,row,2,col,val,INSERT_VALUES);

610:     /* Exciter differential equations */

612:     /*    fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i]; */
613:     row[0] = idx + 7;
614:     col[0] = idx + 6;       col[1] = idx + 7;
615:     val[0] = (-KF[i]/TF[i])/TF[i];  val[1] = 1/TF[i];
616:     MatSetValues(J,1,row,2,col,val,INSERT_VALUES);

618:     /*    fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i]; */
619:     /* Vm = (Vd^2 + Vq^2)^0.5; */
620:     dVm_dVd    = Vd/Vm; dVm_dVq = Vq/Vm;
621:     dVm_dVr    = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
622:     dVm_dVi    = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
623:     row[0]     = idx + 8;
624:     col[0]     = idx + 6;           col[1] = idx + 7; col[2] = idx + 8;
625:     val[0]     = (KA[i]*KF[i]/TF[i])/TA[i]; val[1] = -KA[i]/TA[i];  val[2] = 1/TA[i];
626:     col[3]     = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
627:     val[3]     = KA[i]*dVm_dVr/TA[i];         val[4] = KA[i]*dVm_dVi/TA[i];
628:     MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
629:     idx        = idx + 9;
630:   }


633:   for (i=0; i<nbus; i++) {
634:     MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
635:     row[0] = net_start + 2*i;
636:     for (k=0; k<ncols; k++) {
637:       col[k] = net_start + cols[k];
638:       val[k] = yvals[k];
639:     }
640:     MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
641:     MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);

643:     MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
644:     row[0] = net_start + 2*i+1;
645:     for (k=0; k<ncols; k++) {
646:       col[k] = net_start + cols[k];
647:       val[k] = yvals[k];
648:     }
649:     MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
650:     MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
651:   }

653:   MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
654:   MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);

656:   VecGetArray(user->V0,&v0);
657:   for (i=0; i < nload; i++) {
658:     Vr      = xnet[2*lbus[i]]; /* Real part of load bus voltage */
659:     Vi      = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
660:     Vm      = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm; Vm4 = Vm2*Vm2;
661:     Vm0     = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
662:     PD      = QD = 0.0;
663:     dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
664:     for (k=0; k < ld_nsegsp[i]; k++) {
665:       PD      += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
666:       dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
667:       dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
668:     }
669:     for (k=0; k < ld_nsegsq[i]; k++) {
670:       QD      += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
671:       dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
672:       dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
673:     }

675:     /*    IDr = (PD*Vr + QD*Vi)/Vm2; */
676:     /*    IDi = (-QD*Vr + PD*Vi)/Vm2; */

678:     dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
679:     dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;

681:     dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
682:     dIDi_dVi = (-dQD_dVi*Vr + dPD_dVi*Vi + PD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vi)/Vm4;


685:     /*    fnet[2*lbus[i]]   += IDi; */
686:     row[0] = net_start + 2*lbus[i];
687:     col[0] = net_start + 2*lbus[i];  col[1] = net_start + 2*lbus[i]+1;
688:     val[0] = dIDi_dVr;               val[1] = dIDi_dVi;
689:     MatSetValues(J,1,row,2,col,val,ADD_VALUES);
690:     /*    fnet[2*lbus[i]+1] += IDr; */
691:     row[0] = net_start + 2*lbus[i]+1;
692:     col[0] = net_start + 2*lbus[i];  col[1] = net_start + 2*lbus[i]+1;
693:     val[0] = dIDr_dVr;               val[1] = dIDr_dVi;
694:     MatSetValues(J,1,row,2,col,val,ADD_VALUES);
695:   }
696:   VecRestoreArray(user->V0,&v0);

698:   VecRestoreArray(Xgen,&xgen);
699:   VecRestoreArray(Xnet,&xnet);

701:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);

703:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
704:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
705:   return(0);
706: }

708: /*
709:    J = [I, 0
710:         dg_dx, dg_dy]
711: */
714: PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
715: {
717:   Userctx        *user=(Userctx*)ctx;

720:   ResidualJacobian(snes,X,A,B,ctx);
721:   MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
722:   MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);
723:   return(0);
724: }

726: /*
727:    J = [a*I-df_dx, -df_dy
728:         dg_dx, dg_dy]
729: */

733: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
734: {
736:   SNES           snes;
737:   PetscScalar    atmp = (PetscScalar) a;
738:   PetscInt       i,row;

741:   user->t = t;

743:   TSGetSNES(ts,&snes);
744:   ResidualJacobian(snes,X,A,B,user);
745:   for (i=0;i < ngen;i++) {
746:     row = 9*i;
747:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
748:     row  = 9*i+1;
749:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
750:     row  = 9*i+2;
751:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
752:     row  = 9*i+3;
753:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
754:     row  = 9*i+6;
755:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
756:     row  = 9*i+7;
757:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
758:     row  = 9*i+8;
759:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
760:   }
761:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
762:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
763:   return(0);
764: }

768: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,Userctx *user)
769: {
770:   PetscErrorCode    ierr;
771:   PetscScalar       *r;
772:   const PetscScalar *u;
773:   PetscInt          idx;
774:   Vec               Xgen,Xnet;
775:   PetscScalar       *xgen;
776:   PetscInt          i;

779:   DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
780:   DMCompositeScatter(user->dmpgrid,U,Xgen,Xnet);

782:   VecGetArray(Xgen,&xgen);

784:   VecGetArrayRead(U,&u);
785:   VecGetArray(R,&r);
786:   r[0] = 0.;

788:   idx = 0;
789:   for (i=0;i<ngen;i++) {
790:     r[0] += PetscPowScalarInt(PetscMax(0.,PetscMax(xgen[idx+3]/(2.*PETSC_PI)-user->freq_u,user->freq_l-xgen[idx+3]/(2.*PETSC_PI))),user->pow);
791:     idx  += 9;
792:   }
793:   VecRestoreArray(R,&r);
794:   VecRestoreArrayRead(U,&u);
795:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
796:   return(0);
797: }

801: static PetscErrorCode MonitorUpdateQ(TS ts,PetscInt stepnum,PetscReal time,Vec X,void *ctx0)
802: {
804:   Vec            C,*Y;
805:   PetscInt       Nr;
806:   PetscReal      h,theta;
807:   Userctx        *ctx=(Userctx*)ctx0;
808: 
810:   theta = 0.5;
811:   TSGetStages(ts,&Nr,&Y);
812:   TSGetTimeStep(ts,&h);
813:   VecDuplicate(ctx->vec_q,&C);
814:   /* compute integrals */
815:   if (stepnum>0) {
816:     CostIntegrand(ts,time,X,C,ctx);
817:     VecAXPY(ctx->vec_q,h*theta,C);
818:     CostIntegrand(ts,time+h*theta,Y[0],C,ctx);
819:     VecAXPY(ctx->vec_q,h*(1-theta),C);
820:   }
821:   VecDestroy(&C);
822:   return(0);
823: }

827: int main(int argc,char **argv)
828: {
829:   Userctx            user;
830:   Vec                p;
831:   PetscScalar        *x_ptr;
832:   PetscErrorCode     ierr;
833:   PetscMPIInt        size;
834:   PetscInt           i;
835:   KSP                ksp;
836:   PC                 pc;
837:   PetscInt           *idx2;
838:   Tao                tao;
839:   TaoConvergedReason reason;
840:   Vec                lowerb,upperb;

842:   PetscInitialize(&argc,&argv,"petscoptions",help);
844:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
845:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

847:   VecCreateSeq(PETSC_COMM_WORLD,1,&user.vec_q);

849:   user.neqs_gen   = 9*ngen; /* # eqs. for generator subsystem */
850:   user.neqs_net   = 2*nbus; /* # eqs. for network subsystem   */
851:   user.neqs_pgrid = user.neqs_gen + user.neqs_net;

853:   /* Create indices for differential and algebraic equations */
854:   PetscMalloc1(7*ngen,&idx2);
855:   for (i=0; i<ngen; i++) {
856:     idx2[7*i]   = 9*i;   idx2[7*i+1] = 9*i+1; idx2[7*i+2] = 9*i+2; idx2[7*i+3] = 9*i+3;
857:     idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
858:   }
859:   ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
860:   ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
861:   PetscFree(idx2);

863:   /* Set run time options */
864:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Transient stability fault options","");
865:   {
866:     user.tfaulton  = 1.0;
867:     user.tfaultoff = 1.2;
868:     user.Rfault    = 0.0001;
869:     user.faultbus  = 8;
870:     PetscOptionsReal("-tfaulton","","",user.tfaulton,&user.tfaulton,NULL);
871:     PetscOptionsReal("-tfaultoff","","",user.tfaultoff,&user.tfaultoff,NULL);
872:     PetscOptionsInt("-faultbus","","",user.faultbus,&user.faultbus,NULL);
873:     user.t0        = 0.0;
874:     user.tmax      = 5.0;
875:     PetscOptionsReal("-t0","","",user.t0,&user.t0,NULL);
876:     PetscOptionsReal("-tmax","","",user.tmax,&user.tmax,NULL);
877:     user.freq_u    = 61.0;
878:     user.freq_l    = 59.0;
879:     user.pow       = 2;
880:     PetscOptionsReal("-frequ","","",user.freq_u,&user.freq_u,NULL);
881:     PetscOptionsReal("-freql","","",user.freq_l,&user.freq_l,NULL);
882:     PetscOptionsInt("-pow","","",user.pow,&user.pow,NULL);

884:   }
885:   PetscOptionsEnd();

887:   /* Create DMs for generator and network subsystems */
888:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
889:   DMSetOptionsPrefix(user.dmgen,"dmgen_");
890:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
891:   DMSetOptionsPrefix(user.dmnet,"dmnet_");
892:   /* Create a composite DM packer and add the two DMs */
893:   DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
894:   DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
895:   DMCompositeAddDM(user.dmpgrid,user.dmgen);
896:   DMCompositeAddDM(user.dmpgrid,user.dmnet);

898:   /* Create TAO solver and set desired solution method */
899:   TaoCreate(PETSC_COMM_WORLD,&tao);
900:   TaoSetType(tao,TAOBLMVM);
901:   /*
902:      Optimization starts
903:   */
904:   /* Set initial solution guess */
905:   VecCreateSeq(PETSC_COMM_WORLD,3,&p);
906:   VecGetArray(p,&x_ptr);
907:   x_ptr[0] = PG[0]; x_ptr[1] = PG[1]; x_ptr[2] = PG[2];
908:   VecRestoreArray(p,&x_ptr);

910:   TaoSetInitialVector(tao,p);
911:   /* Set routine for function and gradient evaluation */
912:   TaoSetObjectiveRoutine(tao,FormFunction,(void *)&user);
913:   TaoSetGradientRoutine(tao,TaoDefaultComputeGradient,(void *)&user);

915:   /* Set bounds for the optimization */
916:   VecDuplicate(p,&lowerb);
917:   VecDuplicate(p,&upperb);
918:   VecGetArray(lowerb,&x_ptr);
919:   x_ptr[0] = 0.5; x_ptr[1] = 0.5; x_ptr[2] = 0.5;
920:   VecRestoreArray(lowerb,&x_ptr);
921:   VecGetArray(upperb,&x_ptr);
922:   x_ptr[0] = 2.0; x_ptr[1] = 2.0; x_ptr[2] = 2.0;
923:   VecRestoreArray(upperb,&x_ptr);
924:   TaoSetVariableBounds(tao,lowerb,upperb);

926:   /* Check for any TAO command line options */
927:   TaoSetFromOptions(tao);
928:   TaoGetKSP(tao,&ksp);
929:   if (ksp) {
930:     KSPGetPC(ksp,&pc);
931:     PCSetType(pc,PCNONE);
932:   }

934:   /* TaoSetTolerances(tao,1e-15,1e-15,1e-15,1e-15,1e-15); */
935:   /* SOLVE THE APPLICATION */
936:   TaoSolve(tao);
937:   /* Get information on termination */
938:   TaoGetConvergedReason(tao,&reason);
939:   if (reason <= 0){
940:     ierr=PetscPrintf(MPI_COMM_WORLD, "Try another method! \n");
941:   }

943:   VecView(p,PETSC_VIEWER_STDOUT_WORLD);
944:   /* Free TAO data structures */
945:   TaoDestroy(&tao);

947:   DMDestroy(&user.dmgen);
948:   DMDestroy(&user.dmnet);
949:   DMDestroy(&user.dmpgrid);
950:   ISDestroy(&user.is_diff);
951:   ISDestroy(&user.is_alg);

953:   return(0);
954: }

956: /* ------------------------------------------------------------------ */
959: /*
960:    FormFunction - Evaluates the function and corresponding gradient.

962:    Input Parameters:
963:    tao - the Tao context
964:    X   - the input vector
965:    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()

967:    Output Parameters:
968:    f   - the newly evaluated function
969: */
970: PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
971: {
972:   TS             ts;
973:   SNES           snes_alg;
975:   Userctx        *ctx = (Userctx*)ctx0;
976:   Vec            X;
977:   Mat            J;
978:   /* sensitivity context */
979:   PetscScalar    *x_ptr;
980:   PetscViewer    Xview,Ybusview;
981:   Vec            F_alg;
982:   Vec            Xdot;
983:   PetscInt       row_loc,col_loc;
984:   PetscScalar    val;

986:   VecGetArray(P,&x_ptr);
987:   PG[0] = x_ptr[0];
988:   PG[1] = x_ptr[1];
989:   PG[2] = x_ptr[2];
990:   VecRestoreArray(P,&x_ptr);

992:   ctx->stepnum = 0;

994:   VecZeroEntries(ctx->vec_q);

996:   /* Read initial voltage vector and Ybus */
997:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
998:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);

1000:   VecCreate(PETSC_COMM_WORLD,&ctx->V0);
1001:   VecSetSizes(ctx->V0,PETSC_DECIDE,ctx->neqs_net);
1002:   VecLoad(ctx->V0,Xview);

1004:   MatCreate(PETSC_COMM_WORLD,&ctx->Ybus);
1005:   MatSetSizes(ctx->Ybus,PETSC_DECIDE,PETSC_DECIDE,ctx->neqs_net,ctx->neqs_net);
1006:   MatSetType(ctx->Ybus,MATBAIJ);
1007:   /*  MatSetBlockSize(ctx->Ybus,2); */
1008:   MatLoad(ctx->Ybus,Ybusview);

1010:   PetscViewerDestroy(&Xview);
1011:   PetscViewerDestroy(&Ybusview);

1013:   DMCreateGlobalVector(ctx->dmpgrid,&X);

1015:   MatCreate(PETSC_COMM_WORLD,&J);
1016:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,ctx->neqs_pgrid,ctx->neqs_pgrid);
1017:   MatSetFromOptions(J);
1018:   PreallocateJacobian(J,ctx);

1020:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1021:      Create timestepping solver context
1022:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1023:   TSCreate(PETSC_COMM_WORLD,&ts);
1024:   TSSetProblemType(ts,TS_NONLINEAR);
1025:   TSSetType(ts,TSCN);
1026:   TSSetIFunction(ts,NULL,(TSIFunction) IFunction,ctx);
1027:   TSSetIJacobian(ts,J,J,(TSIJacobian)IJacobian,ctx);
1028:   TSSetApplicationContext(ts,ctx);

1030:   TSMonitorSet(ts,MonitorUpdateQ,ctx,NULL);
1031:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1032:      Set initial conditions
1033:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1034:   SetInitialGuess(X,ctx);

1036:   VecDuplicate(X,&F_alg);
1037:   SNESCreate(PETSC_COMM_WORLD,&snes_alg);
1038:   SNESSetFunction(snes_alg,F_alg,AlgFunction,ctx);
1039:   MatZeroEntries(J);
1040:   SNESSetJacobian(snes_alg,J,J,AlgJacobian,ctx);
1041:   SNESSetOptionsPrefix(snes_alg,"alg_");
1042:   SNESSetFromOptions(snes_alg);
1043:   ctx->alg_flg = PETSC_TRUE;
1044:   /* Solve the algebraic equations */
1045:   SNESSolve(snes_alg,NULL,X);

1047:   /* Just to set up the Jacobian structure */
1048:   VecDuplicate(X,&Xdot);
1049:   IJacobian(ts,0.0,X,Xdot,0.0,J,J,ctx);
1050:   VecDestroy(&Xdot);

1052:   ctx->stepnum++;

1054:   TSSetDuration(ts,1000,ctx->tfaulton);
1055:   TSSetInitialTimeStep(ts,0.0,0.01);
1056:   TSSetFromOptions(ts);
1057:   /* TSSetPostStep(ts,SaveSolution); */

1059:   ctx->alg_flg = PETSC_FALSE;
1060:   /* Prefault period */
1061:   TSSolve(ts,X);

1063:   /* Create the nonlinear solver for solving the algebraic system */
1064:   /* Note that although the algebraic system needs to be solved only for
1065:      Idq and V, we reuse the entire system including xgen. The xgen
1066:      variables are held constant by setting their residuals to 0 and
1067:      putting a 1 on the Jacobian diagonal for xgen rows
1068:   */
1069:   MatZeroEntries(J);

1071:   /* Apply disturbance - resistive fault at ctx->faultbus */
1072:   /* This is done by adding shunt conductance to the diagonal location
1073:      in the Ybus matrix */
1074:   row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
1075:   val     = 1/ctx->Rfault;
1076:   MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1077:   row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
1078:   val     = 1/ctx->Rfault;
1079:   MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);

1081:   MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1082:   MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);

1084:   ctx->alg_flg = PETSC_TRUE;
1085:   /* Solve the algebraic equations */
1086:   SNESSolve(snes_alg,NULL,X);

1088:   ctx->stepnum++;

1090:   /* Disturbance period */
1091:   TSSetDuration(ts,1000,ctx->tfaultoff);
1092:   TSSetInitialTimeStep(ts,ctx->tfaulton,.01);

1094:   ctx->alg_flg = PETSC_FALSE;

1096:   TSSolve(ts,X);

1098:   /* Remove the fault */
1099:   row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1;
1100:   val     = -1/ctx->Rfault;
1101:   MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1102:   row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus;
1103:   val     = -1/ctx->Rfault;
1104:   MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);

1106:   MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1107:   MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);

1109:   MatZeroEntries(J);

1111:   ctx->alg_flg = PETSC_TRUE;

1113:   /* Solve the algebraic equations */
1114:   SNESSolve(snes_alg,NULL,X);

1116:   ctx->stepnum++;

1118:   /* Post-disturbance period */
1119:   TSSetDuration(ts,1000,ctx->tmax);
1120:   TSSetInitialTimeStep(ts,ctx->tfaultoff,.01);

1122:   ctx->alg_flg = PETSC_TRUE;

1124:   TSSolve(ts,X);
1125:   VecGetArray(ctx->vec_q,&x_ptr);
1126:   *f   = x_ptr[0];
1127:   VecRestoreArray(ctx->vec_q,&x_ptr);

1129:   MatDestroy(&ctx->Ybus);
1130:   VecDestroy(&ctx->V0);
1131:   SNESDestroy(&snes_alg);
1132:   VecDestroy(&F_alg);
1133:   MatDestroy(&J);
1134:   VecDestroy(&X);
1135:   TSDestroy(&ts);

1137:   return 0;
1138: }