Actual source code: ex9busadj.c

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

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

 12:    \dot{x} = f(x,y,t)
 13:      0     = g(x,y,t)

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

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

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

 26:    where:
 27:     I(x,y) is the current injected from generators and loads.
 28:       Y    is the admittance matrix, and
 29:       V    is the voltage vector
 30: */

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

 46: #define freq 60
 47: #define w_s (2*PETSC_PI*freq)

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

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

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

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

 96:     Note: All loads have the same characteristic currently.
 97: */
 98: const PetscScalar PD0[3] = {1.25,0.9,1.0};
 99: const PetscScalar QD0[3] = {0.5,0.3,0.35};
100: const PetscInt    ld_nsegsp[3] = {3,3,3};
101: const PetscScalar ld_alphap[3] = {1.0,0.0,0.0};
102: const PetscScalar ld_betap[3]  = {2.0,1.0,0.0};
103: const PetscInt    ld_nsegsq[3] = {3,3,3};
104: const PetscScalar ld_alphaq[3] = {1.0,0.0,0.0};
105: const PetscScalar ld_betaq[3]  = {2.0,1.0,0.0};

107: typedef struct {
108:   DM          dmgen, dmnet; /* DMs to manage generator and network subsystem */
109:   DM          dmpgrid; /* Composite DM to manage the entire power grid */
110:   Mat         Ybus; /* Network admittance matrix */
111:   Vec         V0;  /* Initial voltage vector (Power flow solution) */
112:   PetscReal   tfaulton,tfaultoff; /* Fault on and off times */
113:   PetscInt    faultbus; /* Fault bus */
114:   PetscScalar Rfault;
115:   PetscReal   t0,tmax;
116:   PetscInt    neqs_gen,neqs_net,neqs_pgrid;
117:   PetscBool   alg_flg;
118:   PetscReal   t;
119:   IS          is_diff; /* indices for differential equations */
120:   IS          is_alg; /* indices for algebraic equations */
121: } Userctx;


124: /* Converts from machine frame (dq) to network (phase a real,imag) reference frame */
127: PetscErrorCode dq2ri(PetscScalar Fd,PetscScalar Fq,PetscScalar delta,PetscScalar *Fr, PetscScalar *Fi)
128: {
130:   *Fr =  Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
131:   *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
132:   return(0);
133: }

135: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
138: PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd, PetscScalar *Fq)
139: {
141:   *Fd =  Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
142:   *Fq =  Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
143:   return(0);
144: }

148: PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
149: {
151:   Vec            Xgen,Xnet;
152:   PetscScalar    *xgen,*xnet;
153:   PetscInt       i,idx=0;
154:   PetscScalar    Vr,Vi,IGr,IGi,Vm,Vm2;
155:   PetscScalar    Eqp,Edp,delta;
156:   PetscScalar    Efd,RF,VR; /* Exciter variables */
157:   PetscScalar    Id,Iq;  /* Generator dq axis currents */
158:   PetscScalar    theta,Vd,Vq,SE;

161:   M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
162:   D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];

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

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

169:   /* Generator subsystem initialization */
170:   VecGetArray(Xgen,&xgen);
171:   VecGetArray(Xnet,&xnet);

173:   for (i=0; i < ngen; i++) {
174:     Vr  = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
175:     Vi  = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
176:     Vm  = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
177:     IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
178:     IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;

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

182:     theta = PETSC_PI/2.0 - delta;

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

187:     Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
188:     Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);

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

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

195:     /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
196:     xgen[idx]   = Eqp;
197:     xgen[idx+1] = Edp;
198:     xgen[idx+2] = delta;
199:     xgen[idx+3] = w_s;

201:     idx = idx + 4;

203:     xgen[idx]   = Id;
204:     xgen[idx+1] = Iq;

206:     idx = idx + 2;

208:     /* Exciter */
209:     Efd = Eqp + (Xd[i] - Xdp[i])*Id;
210:     SE  = k1[i]*PetscExpScalar(k2[i]*Efd);
211:     VR  =  KE[i]*Efd + SE;
212:     RF  =  KF[i]*Efd/TF[i];

214:     xgen[idx]   = Efd;
215:     xgen[idx+1] = RF;
216:     xgen[idx+2] = VR;

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

220:     idx = idx + 3;
221:   }

223:   VecRestoreArray(Xgen,&xgen);
224:   VecRestoreArray(Xnet,&xnet);

226:   /* VecView(Xgen,0); */
227:   DMCompositeGather(user->dmpgrid,X,INSERT_VALUES,Xgen,Xnet);
228:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
229:   return(0);
230: }

232: /* Computes F = [f(x,y);g(x,y)] */
235: PetscErrorCode ResidualFunction(SNES snes,Vec X, Vec F, Userctx *user)
236: {
238:   Vec            Xgen,Xnet,Fgen,Fnet;
239:   PetscScalar    *xgen,*xnet,*fgen,*fnet;
240:   PetscInt       i,idx=0;
241:   PetscScalar    Vr,Vi,Vm,Vm2;
242:   PetscScalar    Eqp,Edp,delta,w; /* Generator variables */
243:   PetscScalar    Efd,RF,VR; /* Exciter variables */
244:   PetscScalar    Id,Iq;  /* Generator dq axis currents */
245:   PetscScalar    Vd,Vq,SE;
246:   PetscScalar    IGr,IGi,IDr,IDi;
247:   PetscScalar    Zdq_inv[4],det;
248:   PetscScalar    PD,QD,Vm0,*v0;
249:   PetscInt       k;

252:   VecZeroEntries(F);
253:   DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
254:   DMCompositeGetLocalVectors(user->dmpgrid,&Fgen,&Fnet);
255:   DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
256:   DMCompositeScatter(user->dmpgrid,F,Fgen,Fnet);

258:   /* Network current balance residual IG + Y*V + IL = 0. Only YV is added here.
259:      The generator current injection, IG, and load current injection, ID are added later
260:   */
261:   /* Note that the values in Ybus are stored assuming the imaginary current balance
262:      equation is ordered first followed by real current balance equation for each bus.
263:      Thus imaginary current contribution goes in location 2*i, and
264:      real current contribution in 2*i+1
265:   */
266:   MatMult(user->Ybus,Xnet,Fnet);

268:   VecGetArray(Xgen,&xgen);
269:   VecGetArray(Xnet,&xnet);
270:   VecGetArray(Fgen,&fgen);
271:   VecGetArray(Fnet,&fnet);

273:   /* Generator subsystem */
274:   for (i=0; i < ngen; i++) {
275:     Eqp   = xgen[idx];
276:     Edp   = xgen[idx+1];
277:     delta = xgen[idx+2];
278:     w     = xgen[idx+3];
279:     Id    = xgen[idx+4];
280:     Iq    = xgen[idx+5];
281:     Efd   = xgen[idx+6];
282:     RF    = xgen[idx+7];
283:     VR    = xgen[idx+8];

285:     /* Generator differential equations */
286:     fgen[idx]   = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i];
287:     fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i];
288:     fgen[idx+2] = -w + w_s;
289:     fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i];

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

294:     ri2dq(Vr,Vi,delta,&Vd,&Vq);
295:     /* Algebraic equations for stator currents */

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

299:     Zdq_inv[0] = Rs[i]/det;
300:     Zdq_inv[1] = Xqp[i]/det;
301:     Zdq_inv[2] = -Xdp[i]/det;
302:     Zdq_inv[3] = Rs[i]/det;

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

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

310:     fnet[2*gbus[i]]   -= IGi;
311:     fnet[2*gbus[i]+1] -= IGr;

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

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

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

322:     idx = idx + 9;
323:   }

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

335:     /* Load currents */
336:     IDr = (PD*Vr + QD*Vi)/Vm2;
337:     IDi = (-QD*Vr + PD*Vi)/Vm2;

339:     fnet[2*lbus[i]]   += IDi;
340:     fnet[2*lbus[i]+1] += IDr;
341:   }
342:   VecRestoreArray(user->V0,&v0);

344:   VecRestoreArray(Xgen,&xgen);
345:   VecRestoreArray(Xnet,&xnet);
346:   VecRestoreArray(Fgen,&fgen);
347:   VecRestoreArray(Fnet,&fnet);

349:   DMCompositeGather(user->dmpgrid,F,INSERT_VALUES,Fgen,Fnet);
350:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
351:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Fgen,&Fnet);
352:   return(0);
353: }

355: /* \dot{x} - f(x,y)
356:      g(x,y) = 0
357:  */
360: PetscErrorCode IFunction(TS ts,PetscReal t, Vec X, Vec Xdot, Vec F, Userctx *user)
361: {
362:   PetscErrorCode    ierr;
363:   SNES              snes;
364:   PetscScalar       *f;
365:   const PetscScalar *xdot;
366:   PetscInt          i;

369:   user->t = t;

371:   TSGetSNES(ts,&snes);
372:   ResidualFunction(snes,X,F,user);
373:   VecGetArray(F,&f);
374:   VecGetArrayRead(Xdot,&xdot);
375:   for (i=0;i < ngen;i++) {
376:     f[9*i]   += xdot[9*i];
377:     f[9*i+1] += xdot[9*i+1];
378:     f[9*i+2] += xdot[9*i+2];
379:     f[9*i+3] += xdot[9*i+3];
380:     f[9*i+6] += xdot[9*i+6];
381:     f[9*i+7] += xdot[9*i+7];
382:     f[9*i+8] += xdot[9*i+8];
383:   }
384:   VecRestoreArray(F,&f);
385:   VecRestoreArrayRead(Xdot,&xdot);
386:   return(0);
387: }

389: /* This function is used for solving the algebraic system only during fault on and
390:    off times. It computes the entire F and then zeros out the part corresponding to
391:    differential equations
392:  F = [0;g(y)];
393: */
396: PetscErrorCode AlgFunction(SNES snes, Vec X, Vec F, void *ctx)
397: {
399:   Userctx        *user=(Userctx*)ctx;
400:   PetscScalar    *f;
401:   PetscInt       i;

404:   ResidualFunction(snes,X,F,user);
405:   VecGetArray(F,&f);
406:   for (i=0; i < ngen; i++) {
407:     f[9*i]   = 0;
408:     f[9*i+1] = 0;
409:     f[9*i+2] = 0;
410:     f[9*i+3] = 0;
411:     f[9*i+6] = 0;
412:     f[9*i+7] = 0;
413:     f[9*i+8] = 0;
414:   }
415:   VecRestoreArray(F,&f);
416:   return(0);
417: }

421: PetscErrorCode PreallocateJacobian(Mat J, Userctx *user)
422: {
424:   PetscInt       *d_nnz;
425:   PetscInt       i,idx=0,start=0;
426:   PetscInt       ncols;

429:   PetscMalloc1(user->neqs_pgrid,&d_nnz);
430:   for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
431:   /* Generator subsystem */
432:   for (i=0; i < ngen; i++) {

434:     d_nnz[idx]   += 3;
435:     d_nnz[idx+1] += 2;
436:     d_nnz[idx+2] += 2;
437:     d_nnz[idx+3] += 5;
438:     d_nnz[idx+4] += 6;
439:     d_nnz[idx+5] += 6;

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

444:     d_nnz[idx+6] += 2;
445:     d_nnz[idx+7] += 2;
446:     d_nnz[idx+8] += 5;

448:     idx = idx + 9;
449:   }

451:   start = user->neqs_gen;

453:   for (i=0; i < nbus; i++) {
454:     MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL);
455:     d_nnz[start+2*i]   += ncols;
456:     d_nnz[start+2*i+1] += ncols;
457:     MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL);
458:   }

460:   MatSeqAIJSetPreallocation(J,0,d_nnz);

462:   PetscFree(d_nnz);
463:   return(0);
464: }

466: /*
467:    J = [-df_dx, -df_dy
468:         dg_dx, dg_dy]
469: */
472: PetscErrorCode ResidualJacobian(SNES snes,Vec X,Mat J,Mat B,void *ctx)
473: {
474:   PetscErrorCode    ierr;
475:   Userctx           *user=(Userctx*)ctx;
476:   Vec               Xgen,Xnet;
477:   PetscScalar       *xgen,*xnet;
478:   PetscInt          i,idx=0;
479:   PetscScalar       Vr,Vi,Vm,Vm2;
480:   PetscScalar       Eqp,Edp,delta; /* Generator variables */
481:   PetscScalar       Efd; /* Exciter variables */
482:   PetscScalar       Id,Iq;  /* Generator dq axis currents */
483:   PetscScalar       Vd,Vq;
484:   PetscScalar       val[10];
485:   PetscInt          row[2],col[10];
486:   PetscInt          net_start=user->neqs_gen;
487:   PetscScalar       Zdq_inv[4],det;
488:   PetscScalar       dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
489:   PetscScalar       dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
490:   PetscScalar       dSE_dEfd;
491:   PetscScalar       dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
492:   PetscInt          ncols;
493:   const PetscInt    *cols;
494:   const PetscScalar *yvals;
495:   PetscInt          k;
496:   PetscScalar       PD,QD,Vm0,*v0,Vm4;
497:   PetscScalar       dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
498:   PetscScalar       dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;

501:   MatZeroEntries(B);
502:   DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
503:   DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);

505:   VecGetArray(Xgen,&xgen);
506:   VecGetArray(Xnet,&xnet);

508:   /* Generator subsystem */
509:   for (i=0; i < ngen; i++) {
510:     Eqp   = xgen[idx];
511:     Edp   = xgen[idx+1];
512:     delta = xgen[idx+2];
513:     Id    = xgen[idx+4];
514:     Iq    = xgen[idx+5];
515:     Efd   = xgen[idx+6];

517:     /*    fgen[idx]   = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i]; */
518:     row[0] = idx;
519:     col[0] = idx;           col[1] = idx+4;          col[2] = idx+6;
520:     val[0] = 1/ Td0p[i]; val[1] = (Xd[i] - Xdp[i])/ Td0p[i]; val[2] = -1/Td0p[i];

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

524:     /*    fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
525:     row[0] = idx + 1;
526:     col[0] = idx + 1;       col[1] = idx+5;
527:     val[0] = 1/Tq0p[i]; val[1] = -(Xq[i] - Xqp[i])/Tq0p[i];
528:     MatSetValues(J,1,row,2,col,val,INSERT_VALUES);

530:     /*    fgen[idx+2] = - w + w_s; */
531:     row[0] = idx + 2;
532:     col[0] = idx + 2; col[1] = idx + 3;
533:     val[0] = 0;       val[1] = -1;
534:     MatSetValues(J,1,row,2,col,val,INSERT_VALUES);

536:     /*    fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i]; */
537:     row[0] = idx + 3;
538:     col[0] = idx; col[1] = idx + 1; col[2] = idx + 3;       col[3] = idx + 4;                  col[4] = idx + 5;
539:     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];
540:     MatSetValues(J,1,row,5,col,val,INSERT_VALUES);

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

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

548:     Zdq_inv[0] = Rs[i]/det;
549:     Zdq_inv[1] = Xqp[i]/det;
550:     Zdq_inv[2] = -Xdp[i]/det;
551:     Zdq_inv[3] = Rs[i]/det;

553:     dVd_dVr    = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
554:     dVq_dVr    = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
555:     dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
556:     dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);

558:     /*    fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
559:     row[0] = idx+4;
560:     col[0] = idx;         col[1] = idx+1;        col[2] = idx + 2;
561:     val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0];  val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
562:     col[3] = idx + 4; col[4] = net_start+2*gbus[i];                     col[5] = net_start + 2*gbus[i]+1;
563:     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;
564:     MatSetValues(J,1,row,6,col,val,INSERT_VALUES);

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

574:     dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
575:     dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
576:     dIGr_dId    = PetscSinScalar(delta);  dIGr_dIq = PetscCosScalar(delta);
577:     dIGi_dId    = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);

579:     /* fnet[2*gbus[i]]   -= IGi; */
580:     row[0] = net_start + 2*gbus[i];
581:     col[0] = idx+2;        col[1] = idx + 4;   col[2] = idx + 5;
582:     val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
583:     MatSetValues(J,1,row,3,col,val,INSERT_VALUES);

585:     /* fnet[2*gbus[i]+1]   -= IGr; */
586:     row[0] = net_start + 2*gbus[i]+1;
587:     col[0] = idx+2;        col[1] = idx + 4;   col[2] = idx + 5;
588:     val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
589:     MatSetValues(J,1,row,3,col,val,INSERT_VALUES);

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

593:     /*    fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i]; */
594:     /*    SE  = k1[i]*PetscExpScalar(k2[i]*Efd); */
595:     dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);

597:     row[0] = idx + 6;
598:     col[0] = idx + 6;                     col[1] = idx + 8;
599:     val[0] = (KE[i] + dSE_dEfd)/TE[i];  val[1] = -1/TE[i];
600:     MatSetValues(J,1,row,2,col,val,INSERT_VALUES);

602:     /* Exciter differential equations */

604:     /*    fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i]; */
605:     row[0] = idx + 7;
606:     col[0] = idx + 6;       col[1] = idx + 7;
607:     val[0] = (-KF[i]/TF[i])/TF[i];  val[1] = 1/TF[i];
608:     MatSetValues(J,1,row,2,col,val,INSERT_VALUES);

610:     /*    fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i]; */
611:     /* Vm = (Vd^2 + Vq^2)^0.5; */
612:     dVm_dVd    = Vd/Vm; dVm_dVq = Vq/Vm;
613:     dVm_dVr    = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
614:     dVm_dVi    = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
615:     row[0]     = idx + 8;
616:     col[0]     = idx + 6;           col[1] = idx + 7; col[2] = idx + 8;
617:     val[0]     = (KA[i]*KF[i]/TF[i])/TA[i]; val[1] = -KA[i]/TA[i];  val[2] = 1/TA[i];
618:     col[3]     = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
619:     val[3]     = KA[i]*dVm_dVr/TA[i];         val[4] = KA[i]*dVm_dVi/TA[i];
620:     MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
621:     idx        = idx + 9;
622:   }

624:   for (i=0; i<nbus; i++) {
625:     MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
626:     row[0] = net_start + 2*i;
627:     for (k=0; k<ncols; k++) {
628:       col[k] = net_start + cols[k];
629:       val[k] = yvals[k];
630:     }
631:     MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
632:     MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);

634:     MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
635:     row[0] = net_start + 2*i+1;
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+1,&ncols,&cols,&yvals);
642:   }

644:   MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
645:   MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);


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

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

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

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


677:     /*    fnet[2*lbus[i]]   += IDi; */
678:     row[0] = net_start + 2*lbus[i];
679:     col[0] = net_start + 2*lbus[i];  col[1] = net_start + 2*lbus[i]+1;
680:     val[0] = dIDi_dVr;               val[1] = dIDi_dVi;
681:     MatSetValues(J,1,row,2,col,val,ADD_VALUES);
682:     /*    fnet[2*lbus[i]+1] += IDr; */
683:     row[0] = net_start + 2*lbus[i]+1;
684:     col[0] = net_start + 2*lbus[i];  col[1] = net_start + 2*lbus[i]+1;
685:     val[0] = dIDr_dVr;               val[1] = dIDr_dVi;
686:     MatSetValues(J,1,row,2,col,val,ADD_VALUES);
687:   }
688:   VecRestoreArray(user->V0,&v0);

690:   VecRestoreArray(Xgen,&xgen);
691:   VecRestoreArray(Xnet,&xnet);

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

695:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
696:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
697:   return(0);
698: }

700: /*
701:    J = [I, 0
702:         dg_dx, dg_dy]
703: */
706: PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
707: {
709:   Userctx        *user=(Userctx*)ctx;

712:   ResidualJacobian(snes,X,A,B,ctx);
713:   MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
714:   MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);
715:   return(0);
716: }

718: /*
719:    J = [a*I-df_dx, -df_dy
720:         dg_dx, dg_dy]
721: */

725: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
726: {
728:   SNES           snes;
729:   PetscScalar    atmp = (PetscScalar) a;
730:   PetscInt       i,row;

733:   user->t = t;

735:   TSGetSNES(ts,&snes);
736:   ResidualJacobian(snes,X,A,B,user);
737:   for (i=0;i < ngen;i++) {
738:     row = 9*i;
739:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
740:     row  = 9*i+1;
741:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
742:     row  = 9*i+2;
743:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
744:     row  = 9*i+3;
745:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
746:     row  = 9*i+6;
747:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
748:     row  = 9*i+7;
749:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
750:     row  = 9*i+8;
751:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
752:   }
753:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
754:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
755:   return(0);
756: }

760: int main(int argc,char **argv)
761: {
762:   TS             ts;
763:   SNES           snes_alg;
765:   PetscMPIInt    size;
766:   Userctx        user;
767:   PetscViewer    Xview,Ybusview;
768:   Vec            X;
769:   Mat            J;
770:   PetscInt       i;
771:   /* sensitivity context */
772:   PetscScalar    *y_ptr;
773:   Vec            lambda[1];
774:   PetscInt       steps, total_steps = 0;
775:   PetscInt       *idx2;
776:   Vec            Xdot;
777:   Vec            F_alg;
778:   PetscInt       row_loc,col_loc;
779:   PetscScalar    val;
780: 
781:   PetscInitialize(&argc,&argv,"petscoptions",help);
782:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
783:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

785:   user.neqs_gen   = 9*ngen; /* # eqs. for generator subsystem */
786:   user.neqs_net   = 2*nbus; /* # eqs. for network subsystem   */
787:   user.neqs_pgrid = user.neqs_gen + user.neqs_net;

789:   /* Create indices for differential and algebraic equations */
790:   PetscMalloc1(7*ngen,&idx2);
791:   for (i=0; i<ngen; i++) {
792:     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;
793:     idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
794:   }
795:   ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
796:   ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
797:   PetscFree(idx2);

799:   /* Read initial voltage vector and Ybus */
800:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
801:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);

803:   VecCreate(PETSC_COMM_WORLD,&user.V0);
804:   VecSetSizes(user.V0,PETSC_DECIDE,user.neqs_net);
805:   VecLoad(user.V0,Xview);

807:   MatCreate(PETSC_COMM_WORLD,&user.Ybus);
808:   MatSetSizes(user.Ybus,PETSC_DECIDE,PETSC_DECIDE,user.neqs_net,user.neqs_net);
809:   MatSetType(user.Ybus,MATBAIJ);
810:   /*  MatSetBlockSize(user.Ybus,2); */
811:   MatLoad(user.Ybus,Ybusview);

813:   /* Set run time options */
814:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Transient stability fault options","");
815:   {
816:     user.tfaulton  = 1.0;
817:     user.tfaultoff = 1.2;
818:     user.Rfault    = 0.0001;
819:     user.faultbus  = 8;
820:     PetscOptionsReal("-tfaulton","","",user.tfaulton,&user.tfaulton,NULL);
821:     PetscOptionsReal("-tfaultoff","","",user.tfaultoff,&user.tfaultoff,NULL);
822:     PetscOptionsInt("-faultbus","","",user.faultbus,&user.faultbus,NULL);
823:     user.t0        = 0.0;
824:     user.tmax      = 5.0;
825:     PetscOptionsReal("-t0","","",user.t0,&user.t0,NULL);
826:     PetscOptionsReal("-tmax","","",user.tmax,&user.tmax,NULL);
827:   }
828:   PetscOptionsEnd();

830:   PetscViewerDestroy(&Xview);
831:   PetscViewerDestroy(&Ybusview);

833:   /* Create DMs for generator and network subsystems */
834:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
835:   DMSetOptionsPrefix(user.dmgen,"dmgen_");
836:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
837:   DMSetOptionsPrefix(user.dmnet,"dmnet_");
838:   /* Create a composite DM packer and add the two DMs */
839:   DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
840:   DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
841:   DMCompositeAddDM(user.dmpgrid,user.dmgen);
842:   DMCompositeAddDM(user.dmpgrid,user.dmnet);

844:   DMCreateGlobalVector(user.dmpgrid,&X);

846:   MatCreate(PETSC_COMM_WORLD,&J);
847:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,user.neqs_pgrid);
848:   MatSetFromOptions(J);
849:   PreallocateJacobian(J,&user);


852:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
853:      Create timestepping solver context
854:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
855:   TSCreate(PETSC_COMM_WORLD,&ts);
856:   TSSetProblemType(ts,TS_NONLINEAR);
857:   TSSetEquationType(ts,TS_EQ_DAE_IMPLICIT_INDEX1);
858:   TSARKIMEXSetFullyImplicit(ts,PETSC_TRUE);
859:   TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&user);
860:   TSSetIJacobian(ts,J,J,(TSIJacobian)IJacobian,&user);
861:   TSSetApplicationContext(ts,&user);

863:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
864:      Set initial conditions
865:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
866:   SetInitialGuess(X,&user);
867:   /* Just to set up the Jacobian structure */
868:   VecDuplicate(X,&Xdot);
869:   IJacobian(ts,0.0,X,Xdot,0.0,J,J,&user);
870:   VecDestroy(&Xdot);

872:   /*
873:     Save trajectory of solution so that TSAdjointSolve() may be used
874:   */
875:   TSSetSaveTrajectory(ts);

877:   TSSetDuration(ts,1000,user.tfaulton);
878:   TSSetInitialTimeStep(ts,0.0,0.01);
879:   TSSetFromOptions(ts);

881:   user.alg_flg = PETSC_FALSE;
882:   /* Prefault period */
883:   TSSolve(ts,X);
884:   TSGetTimeStepNumber(ts,&steps);
885:   total_steps += steps;

887:   /* Create the nonlinear solver for solving the algebraic system */
888:   /* Note that although the algebraic system needs to be solved only for
889:      Idq and V, we reuse the entire system including xgen. The xgen
890:      variables are held constant by setting their residuals to 0 and
891:      putting a 1 on the Jacobian diagonal for xgen rows
892:   */
893:   VecDuplicate(X,&F_alg);
894:   SNESCreate(PETSC_COMM_WORLD,&snes_alg);
895:   SNESSetFunction(snes_alg,F_alg,AlgFunction,&user);
896:   MatZeroEntries(J);
897:   SNESSetJacobian(snes_alg,J,J,AlgJacobian,&user);
898:   SNESSetOptionsPrefix(snes_alg,"alg_");
899:   SNESSetFromOptions(snes_alg);

901:   /* Apply disturbance - resistive fault at user.faultbus */
902:   /* This is done by adding shunt conductance to the diagonal location
903:      in the Ybus matrix */
904:   row_loc = 2*user.faultbus; col_loc = 2*user.faultbus+1; /* Location for G */
905:   val     = 1/user.Rfault;
906:   MatSetValues(user.Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
907:   row_loc = 2*user.faultbus+1; col_loc = 2*user.faultbus; /* Location for G */
908:   val     = 1/user.Rfault;
909:   MatSetValues(user.Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);

911:   MatAssemblyBegin(user.Ybus,MAT_FINAL_ASSEMBLY);
912:   MatAssemblyEnd(user.Ybus,MAT_FINAL_ASSEMBLY);

914:   user.alg_flg = PETSC_TRUE;
915:   /* Solve the algebraic equations */
916:   SNESSolve(snes_alg,NULL,X);


919:   /* Disturbance period */
920:   TSSetDuration(ts,1000,user.tfaultoff);
921:   TSSetInitialTimeStep(ts,user.tfaulton,.01);

923:   user.alg_flg = PETSC_FALSE;

925:   TSSolve(ts,X);
926:   TSGetTimeStepNumber(ts,&steps);
927:   total_steps += steps;
928:   /* Remove the fault */
929:   row_loc = 2*user.faultbus; col_loc = 2*user.faultbus+1;
930:   val     = -1/user.Rfault;
931:   MatSetValues(user.Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
932:   row_loc = 2*user.faultbus+1; col_loc = 2*user.faultbus;
933:   val     = -1/user.Rfault;
934:   MatSetValues(user.Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);

936:   MatAssemblyBegin(user.Ybus,MAT_FINAL_ASSEMBLY);
937:   MatAssemblyEnd(user.Ybus,MAT_FINAL_ASSEMBLY);

939:   MatZeroEntries(J);

941:   user.alg_flg = PETSC_TRUE;

943:   /* Solve the algebraic equations */
944:   SNESSolve(snes_alg,NULL,X);

946:   /* Post-disturbance period */
947:   TSSetDuration(ts,1000,user.tmax);
948:   TSSetInitialTimeStep(ts,user.tfaultoff,.01);

950:   user.alg_flg = PETSC_TRUE;

952:   TSSolve(ts,X);
953:   TSGetTimeStepNumber(ts,&steps);
954:   total_steps += steps;

956:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
957:      Adjoint model starts here
958:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
959:   TSSetPostStep(ts,NULL);
960:   MatCreateVecs(J,&lambda[0],NULL);
961:   /*   Set initial conditions for the adjoint integration */
962:   VecZeroEntries(lambda[0]);
963:   VecGetArray(lambda[0],&y_ptr);
964:   y_ptr[0] = 1.0;
965:   VecRestoreArray(lambda[0],&y_ptr);
966:   TSSetCostGradients(ts,1,lambda,NULL);

968:   TSAdjointSolve(ts);

970:   PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: \n");
971:   VecView(lambda[0],PETSC_VIEWER_STDOUT_WORLD);
972:   VecDestroy(&lambda[0]);

974:   SNESDestroy(&snes_alg);
975:   VecDestroy(&F_alg);
976:   MatDestroy(&J);
977:   MatDestroy(&user.Ybus);
978:   VecDestroy(&X);
979:   VecDestroy(&user.V0);
980:   DMDestroy(&user.dmgen);
981:   DMDestroy(&user.dmnet);
982:   DMDestroy(&user.dmpgrid);
983:   ISDestroy(&user.is_diff);
984:   ISDestroy(&user.is_alg);
985:   TSDestroy(&ts);
986:   PetscFinalize();
987:   return(0);
988: }