Actual source code: ex9opt.c

petsc-3.12.1 2019-10-22
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  2: static char help[] = "Basic equation for generator stability analysis.\n";


\begin{eqnarray}
\frac{d \theta}{dt} = \omega_b (\omega - \omega_s)
\frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - P_max \sin(\theta) -D(\omega - \omega_s)\\
\end{eqnarray}



Ensemble of initial conditions
./ex2 -ensemble -ts_monitor_draw_solution_phase -1,-3,3,3 -ts_adapt_dt_max .01 -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly

Fault at .1 seconds
./ex2 -ts_monitor_draw_solution_phase .42,.95,.6,1.05 -ts_adapt_dt_max .01 -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly

Initial conditions same as when fault is ended
./ex2 -u 0.496792,1.00932 -ts_monitor_draw_solution_phase .42,.95,.6,1.05 -ts_adapt_dt_max .01 -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly


 25: /*
 26:    Include "petscts.h" so that we can use TS solvers.  Note that this
 27:    file automatically includes:
 28:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 29:      petscmat.h - matrices
 30:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 31:      petscviewer.h - viewers               petscpc.h  - preconditioners
 32:      petscksp.h   - linear solvers
 33: */

 35: #include <petsctao.h>
 36: #include <petscts.h>

 38: typedef struct {
 39:   TS          ts;
 40:   PetscScalar H,D,omega_b,omega_s,Pmax,Pm,E,V,X,u_s,c;
 41:   PetscInt    beta;
 42:   PetscReal   tf,tcl,dt;
 43: } AppCtx;

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

 48: /*
 49:      Defines the ODE passed to the ODE solver
 50: */
 51: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
 52: {
 53:   PetscErrorCode    ierr;
 54:   PetscScalar       *f,Pmax;
 55:   const PetscScalar *u;

 58:   /*  The next three lines allow us to access the entries of the vectors directly */
 59:   VecGetArrayRead(U,&u);
 60:   VecGetArray(F,&f);
 61:   if ((t > ctx->tf) && (t < ctx->tcl)) Pmax = 0.0; /* A short-circuit on the generator terminal that drives the electrical power output (Pmax*sin(delta)) to 0 */
 62:   else Pmax = ctx->Pmax;

 64:   f[0] = ctx->omega_b*(u[1] - ctx->omega_s);
 65:   f[1] = (-Pmax*PetscSinScalar(u[0]) - ctx->D*(u[1] - ctx->omega_s) + ctx->Pm)*ctx->omega_s/(2.0*ctx->H);

 67:   VecRestoreArrayRead(U,&u);
 68:   VecRestoreArray(F,&f);
 69:   return(0);
 70: }

 72: /*
 73:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
 74: */
 75: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,AppCtx *ctx)
 76: {
 77:   PetscErrorCode    ierr;
 78:   PetscInt          rowcol[] = {0,1};
 79:   PetscScalar       J[2][2],Pmax;
 80:   const PetscScalar *u;

 83:   VecGetArrayRead(U,&u);
 84:   if ((t > ctx->tf) && (t < ctx->tcl)) Pmax = 0.0; /* A short-circuit on the generator terminal that drives the electrical power output (Pmax*sin(delta)) to 0 */
 85:   else Pmax = ctx->Pmax;

 87:   J[0][0] = 0;                                  J[0][1] = ctx->omega_b;
 88:   J[1][1] = -ctx->D*ctx->omega_s/(2.0*ctx->H);  J[1][0] = -Pmax*PetscCosScalar(u[0])*ctx->omega_s/(2.0*ctx->H);

 90:   MatSetValues(A,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
 91:   VecRestoreArrayRead(U,&u);

 93:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 94:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 95:   if (A != B) {
 96:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 97:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
 98:   }
 99:   return(0);
100: }

102: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx0)
103: {
105:   PetscInt       row[] = {0,1},col[]={0};
106:   PetscScalar    J[2][1];
107:   AppCtx         *ctx=(AppCtx*)ctx0;

110:   J[0][0] = 0;
111:   J[1][0] = ctx->omega_s/(2.0*ctx->H);
112:   MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
113:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
114:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
115:   return(0);
116: }

118: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,AppCtx *ctx)
119: {
120:   PetscErrorCode    ierr;
121:   PetscScalar       *r;
122:   const PetscScalar *u;

125:   VecGetArrayRead(U,&u);
126:   VecGetArray(R,&r);
127:   r[0] = ctx->c*PetscPowScalarInt(PetscMax(0., u[0]-ctx->u_s),ctx->beta);
128:   VecRestoreArray(R,&r);
129:   VecRestoreArrayRead(U,&u);
130:   return(0);
131: }

133: static PetscErrorCode DRDUJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDU,Mat B,AppCtx *ctx)
134: {
135:   PetscErrorCode    ierr;
136:   PetscScalar       ru[1];
137:   const PetscScalar *u;
138:   PetscInt          row[] = {0},col[] = {0};

141:   VecGetArrayRead(U,&u);
142:   ru[0] = ctx->c*ctx->beta*PetscPowScalarInt(PetscMax(0., u[0]-ctx->u_s),ctx->beta-1);
143:   VecRestoreArrayRead(U,&u);
144:   MatSetValues(DRDU,1,row,1,col,ru,INSERT_VALUES);
145:   MatAssemblyBegin(DRDU,MAT_FINAL_ASSEMBLY);
146:   MatAssemblyEnd(DRDU,MAT_FINAL_ASSEMBLY);
147:   return(0);
148: }

150: static PetscErrorCode DRDPJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDP,AppCtx *ctx)
151: {

155:   MatZeroEntries(DRDP);
156:   MatAssemblyBegin(DRDP,MAT_FINAL_ASSEMBLY);
157:   MatAssemblyEnd(DRDP,MAT_FINAL_ASSEMBLY);
158:   return(0);
159: }

161: PetscErrorCode ComputeSensiP(Vec lambda,Vec mu,AppCtx *ctx)
162: {
163:   PetscErrorCode    ierr;
164:   PetscScalar       *y,sensip;
165:   const PetscScalar *x;

168:   VecGetArrayRead(lambda,&x);
169:   VecGetArray(mu,&y);
170:   sensip = 1./PetscSqrtScalar(1.-(ctx->Pm/ctx->Pmax)*(ctx->Pm/ctx->Pmax))/ctx->Pmax*x[0]+y[0];
171:   y[0] = sensip;
172:   VecRestoreArray(mu,&y);
173:   VecRestoreArrayRead(lambda,&x);
174:   return(0);
175: }

177: int main(int argc,char **argv)
178: {
179:   Vec            p;
180:   PetscScalar    *x_ptr;
182:   PetscMPIInt    size;
183:   AppCtx         ctx;
184:   Vec            lowerb,upperb;
185:   Tao            tao;
186:   KSP            ksp;
187:   PC             pc;
188:   Vec            U,lambda[1],mu[1];
189:   Mat            A;             /* Jacobian matrix */
190:   Mat            Jacp;          /* Jacobian matrix */
191:   Mat            DRDU,DRDP;
192:   PetscInt       n = 2;
193:   TS             quadts;

195:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196:      Initialize program
197:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
198:   PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
200:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
201:   if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");

203:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204:     Set runtime options
205:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
206:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
207:   {
208:     ctx.beta    = 2;
209:     ctx.c       = PetscRealConstant(10000.0);
210:     ctx.u_s     = PetscRealConstant(1.0);
211:     ctx.omega_s = PetscRealConstant(1.0);
212:     ctx.omega_b = PetscRealConstant(120.0)*PETSC_PI;
213:     ctx.H       = PetscRealConstant(5.0);
214:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
215:     ctx.D       = PetscRealConstant(5.0);
216:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
217:     ctx.E       = PetscRealConstant(1.1378);
218:     ctx.V       = PetscRealConstant(1.0);
219:     ctx.X       = PetscRealConstant(0.545);
220:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
221:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
222:     ctx.Pm      = PetscRealConstant(1.0194);
223:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
224:     ctx.tf      = PetscRealConstant(0.1);
225:     ctx.tcl     = PetscRealConstant(0.2);
226:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
227:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);

229:   }
230:   PetscOptionsEnd();

232:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
233:     Create necessary matrix and vectors
234:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
235:   MatCreate(PETSC_COMM_WORLD,&A);
236:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
237:   MatSetType(A,MATDENSE);
238:   MatSetFromOptions(A);
239:   MatSetUp(A);

241:   MatCreateVecs(A,&U,NULL);

243:   MatCreate(PETSC_COMM_WORLD,&Jacp);
244:   MatSetSizes(Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
245:   MatSetFromOptions(Jacp);
246:   MatSetUp(Jacp);
247:   MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,&DRDP);
248:   MatSetUp(DRDP);
249:   MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,&DRDU);
250:   MatSetUp(DRDU);

252:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
253:      Create timestepping solver context
254:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
255:   TSCreate(PETSC_COMM_WORLD,&ctx.ts);
256:   TSSetProblemType(ctx.ts,TS_NONLINEAR);
257:   TSSetEquationType(ctx.ts,TS_EQ_ODE_EXPLICIT); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
258:   TSSetType(ctx.ts,TSRK);
259:   TSSetRHSFunction(ctx.ts,NULL,(TSRHSFunction)RHSFunction,&ctx);
260:   TSSetRHSJacobian(ctx.ts,A,A,(TSRHSJacobian)RHSJacobian,&ctx);
261:   TSSetExactFinalTime(ctx.ts,TS_EXACTFINALTIME_MATCHSTEP);

263:   MatCreateVecs(A,&lambda[0],NULL);
264:   MatCreateVecs(Jacp,&mu[0],NULL);
265:   TSSetCostGradients(ctx.ts,1,lambda,mu);
266:   TSSetRHSJacobianP(ctx.ts,Jacp,RHSJacobianP,&ctx);

268:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
269:      Set solver options
270:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
271:   TSSetMaxTime(ctx.ts,PetscRealConstant(1.0));
272:   TSSetTimeStep(ctx.ts,PetscRealConstant(0.01));
273:   TSSetFromOptions(ctx.ts);

275:   TSGetTimeStep(ctx.ts,&ctx.dt); /* save the stepsize */

277:   TSCreateQuadratureTS(ctx.ts,PETSC_TRUE,&quadts);
278:   TSSetRHSFunction(quadts,NULL,(TSRHSFunction)CostIntegrand,&ctx);
279:   TSSetRHSJacobian(quadts,DRDU,DRDU,(TSRHSJacobian)DRDUJacobianTranspose,&ctx);
280:   TSSetRHSJacobianP(quadts,DRDP,(TSRHSJacobianP)DRDPJacobianTranspose,&ctx);
281:   TSSetSolution(ctx.ts,U);

283:   /* Create TAO solver and set desired solution method */
284:   TaoCreate(PETSC_COMM_WORLD,&tao);
285:   TaoSetType(tao,TAOBLMVM);

287:   /*
288:      Optimization starts
289:   */
290:   /* Set initial solution guess */
291:   VecCreateSeq(PETSC_COMM_WORLD,1,&p);
292:   VecGetArray(p,&x_ptr);
293:   x_ptr[0]   = ctx.Pm;
294:   VecRestoreArray(p,&x_ptr);

296:   TaoSetInitialVector(tao,p);
297:   /* Set routine for function and gradient evaluation */
298:   TaoSetObjectiveRoutine(tao,FormFunction,(void *)&ctx);
299:   TaoSetGradientRoutine(tao,FormGradient,(void *)&ctx);

301:   /* Set bounds for the optimization */
302:   VecDuplicate(p,&lowerb);
303:   VecDuplicate(p,&upperb);
304:   VecGetArray(lowerb,&x_ptr);
305:   x_ptr[0] = 0.;
306:   VecRestoreArray(lowerb,&x_ptr);
307:   VecGetArray(upperb,&x_ptr);
308:   x_ptr[0] = PetscRealConstant(1.1);
309:   VecRestoreArray(upperb,&x_ptr);
310:   TaoSetVariableBounds(tao,lowerb,upperb);

312:   /* Check for any TAO command line options */
313:   TaoSetFromOptions(tao);
314:   TaoGetKSP(tao,&ksp);
315:   if (ksp) {
316:     KSPGetPC(ksp,&pc);
317:     PCSetType(pc,PCNONE);
318:   }

320:   /* SOLVE THE APPLICATION */
321:   TaoSolve(tao);

323:   VecView(p,PETSC_VIEWER_STDOUT_WORLD);
324:   /* Free TAO data structures */
325:   TaoDestroy(&tao);
326:   VecDestroy(&p);
327:   VecDestroy(&lowerb);
328:   VecDestroy(&upperb);

330:   TSDestroy(&ctx.ts);
331:   VecDestroy(&U);
332:   MatDestroy(&A);
333:   MatDestroy(&Jacp);
334:   MatDestroy(&DRDU);
335:   MatDestroy(&DRDP);
336:   VecDestroy(&lambda[0]);
337:   VecDestroy(&mu[0]);
338:   PetscFinalize();
339:   return ierr;
340: }

342: /* ------------------------------------------------------------------ */
343: /*
344:    FormFunction - Evaluates the function

346:    Input Parameters:
347:    tao - the Tao context
348:    X   - the input vector
349:    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()

351:    Output Parameters:
352:    f   - the newly evaluated function
353: */
354: PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
355: {
356:   AppCtx         *ctx = (AppCtx*)ctx0;
357:   TS             ts = ctx->ts;
358:   Vec            U;             /* solution will be stored here */
360:   PetscScalar    *u;
361:   PetscScalar    *x_ptr;
362:   Vec            q;

364:   VecGetArrayRead(P,(const PetscScalar**)&x_ptr);
365:   ctx->Pm = x_ptr[0];
366:   VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);

368:   /* reset time */
369:   TSSetTime(ts,0.0);
370:   /* reset step counter, this is critical for adjoint solver */
371:   TSSetStepNumber(ts,0);
372:   /* reset step size, the step size becomes negative after TSAdjointSolve */
373:   TSSetTimeStep(ts,ctx->dt);
374:   /* reinitialize the integral value */
375:   TSGetCostIntegral(ts,&q);
376:   VecSet(q,0.0);

378:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
379:      Set initial conditions
380:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
381:   TSGetSolution(ts,&U);
382:   VecGetArray(U,&u);
383:   u[0] = PetscAsinScalar(ctx->Pm/ctx->Pmax);
384:   u[1] = PetscRealConstant(1.0);
385:   VecRestoreArray(U,&u);

387:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
388:      Solve nonlinear system
389:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
390:   TSSolve(ts,U);
391:   TSGetCostIntegral(ts,&q);
392:   VecGetArray(q,&x_ptr);
393:   *f   = -ctx->Pm + x_ptr[0];
394:   VecRestoreArray(q,&x_ptr);
395:   return 0;
396: }

398: PetscErrorCode FormGradient(Tao tao,Vec P,Vec G,void *ctx0)
399: {
400:   AppCtx         *ctx = (AppCtx*)ctx0;
401:   TS             ts = ctx->ts;
402:   Vec            U;             /* solution will be stored here */
404:   PetscReal      ftime;
405:   PetscInt       steps;
406:   PetscScalar    *u;
407:   PetscScalar    *x_ptr,*y_ptr;
408:   Vec            *lambda,q,*mu;

410:   VecGetArrayRead(P,(const PetscScalar**)&x_ptr);
411:   ctx->Pm = x_ptr[0];
412:   VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);

414:   /* reset time */
415:   TSSetTime(ts,0.0);
416:   /* reset step counter, this is critical for adjoint solver */
417:   TSSetStepNumber(ts,0);
418:   /* reset step size, the step size becomes negative after TSAdjointSolve */
419:   TSSetTimeStep(ts,ctx->dt);
420:   /* reinitialize the integral value */
421:   TSGetCostIntegral(ts,&q);
422:   VecSet(q,0.0);

424:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
425:      Set initial conditions
426:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
427:   TSGetSolution(ts,&U);
428:   VecGetArray(U,&u);
429:   u[0] = PetscAsinScalar(ctx->Pm/ctx->Pmax);
430:   u[1] = PetscRealConstant(1.0);
431:   VecRestoreArray(U,&u);

433:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
434:     Save trajectory of solution so that TSAdjointSolve() may be used
435:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
436:   TSSetSaveTrajectory(ts);

438:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
439:      Solve nonlinear system
440:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
441:   TSSolve(ts,U);

443:   TSGetSolveTime(ts,&ftime);
444:   TSGetStepNumber(ts,&steps);

446:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
447:      Adjoint model starts here
448:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
449:   TSGetCostGradients(ts,NULL,&lambda,&mu);
450:   /*   Set initial conditions for the adjoint integration */
451:   VecGetArray(lambda[0],&y_ptr);
452:   y_ptr[0] = 0.0; y_ptr[1] = 0.0;
453:   VecRestoreArray(lambda[0],&y_ptr);
454:   VecGetArray(mu[0],&x_ptr);
455:   x_ptr[0] = PetscRealConstant(-1.0);
456:   VecRestoreArray(mu[0],&x_ptr);

458:   TSAdjointSolve(ts);
459:   TSGetCostIntegral(ts,&q);
460:   ComputeSensiP(lambda[0],mu[0],ctx);
461:   VecCopy(mu[0],G);
462:   return 0;
463: }


466: /*TEST

468:    build:
469:       requires: !complex

471:    test:
472:       args: -viewer_binary_skip_info -ts_adapt_type none -tao_monitor -tao_gatol 0.0 -tao_grtol 1.e-3 -tao_converged_reason

474:    test:
475:       suffix: 2
476:       args: -viewer_binary_skip_info -ts_adapt_type none -tao_monitor -tao_gatol 0.0 -tao_grtol 1.e-3 -tao_converged_reason -tao_test_gradient

478: TEST*/