Actual source code: ex9opt.c


  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

 22: /*
 23:    Include "petscts.h" so that we can use TS solvers.  Note that this
 24:    file automatically includes:
 25:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 26:      petscmat.h - matrices
 27:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 28:      petscviewer.h - viewers               petscpc.h  - preconditioners
 29:      petscksp.h   - linear solvers
 30: */

 32: #include <petsctao.h>
 33: #include <petscts.h>

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

 42: PetscErrorCode FormFunction(Tao,Vec,PetscReal*,void*);
 43: PetscErrorCode FormGradient(Tao,Vec,Vec,void*);

 45: /*
 46:      Defines the ODE passed to the ODE solver
 47: */
 48: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
 49: {
 50:   PetscErrorCode    ierr;
 51:   PetscScalar       *f,Pmax;
 52:   const PetscScalar *u;

 55:   /*  The next three lines allow us to access the entries of the vectors directly */
 56:   VecGetArrayRead(U,&u);
 57:   VecGetArray(F,&f);
 58:   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 */
 59:   else Pmax = ctx->Pmax;

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

 64:   VecRestoreArrayRead(U,&u);
 65:   VecRestoreArray(F,&f);
 66:   return(0);
 67: }

 69: /*
 70:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
 71: */
 72: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,AppCtx *ctx)
 73: {
 74:   PetscErrorCode    ierr;
 75:   PetscInt          rowcol[] = {0,1};
 76:   PetscScalar       J[2][2],Pmax;
 77:   const PetscScalar *u;

 80:   VecGetArrayRead(U,&u);
 81:   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 */
 82:   else Pmax = ctx->Pmax;

 84:   J[0][0] = 0;                                  J[0][1] = ctx->omega_b;
 85:   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);

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

 90:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 91:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 92:   if (A != B) {
 93:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 94:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
 95:   }
 96:   return(0);
 97: }

 99: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx0)
100: {
102:   PetscInt       row[] = {0,1},col[]={0};
103:   PetscScalar    J[2][1];
104:   AppCtx         *ctx=(AppCtx*)ctx0;

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

115: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,AppCtx *ctx)
116: {
117:   PetscErrorCode    ierr;
118:   PetscScalar       *r;
119:   const PetscScalar *u;

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

130: static PetscErrorCode DRDUJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDU,Mat B,AppCtx *ctx)
131: {
132:   PetscErrorCode    ierr;
133:   PetscScalar       ru[1];
134:   const PetscScalar *u;
135:   PetscInt          row[] = {0},col[] = {0};

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

147: static PetscErrorCode DRDPJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDP,AppCtx *ctx)
148: {

152:   MatZeroEntries(DRDP);
153:   MatAssemblyBegin(DRDP,MAT_FINAL_ASSEMBLY);
154:   MatAssemblyEnd(DRDP,MAT_FINAL_ASSEMBLY);
155:   return(0);
156: }

158: PetscErrorCode ComputeSensiP(Vec lambda,Vec mu,AppCtx *ctx)
159: {
160:   PetscErrorCode    ierr;
161:   PetscScalar       *y,sensip;
162:   const PetscScalar *x;

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

174: int main(int argc,char **argv)
175: {
176:   Vec            p;
177:   PetscScalar    *x_ptr;
179:   PetscMPIInt    size;
180:   AppCtx         ctx;
181:   Vec            lowerb,upperb;
182:   Tao            tao;
183:   KSP            ksp;
184:   PC             pc;
185:   Vec            U,lambda[1],mu[1];
186:   Mat            A;             /* Jacobian matrix */
187:   Mat            Jacp;          /* Jacobian matrix */
188:   Mat            DRDU,DRDP;
189:   PetscInt       n = 2;
190:   TS             quadts;

192:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193:      Initialize program
194:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
195:   PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
197:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
198:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");

200:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
201:     Set runtime options
202:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
203:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
204:   {
205:     ctx.beta    = 2;
206:     ctx.c       = PetscRealConstant(10000.0);
207:     ctx.u_s     = PetscRealConstant(1.0);
208:     ctx.omega_s = PetscRealConstant(1.0);
209:     ctx.omega_b = PetscRealConstant(120.0)*PETSC_PI;
210:     ctx.H       = PetscRealConstant(5.0);
211:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
212:     ctx.D       = PetscRealConstant(5.0);
213:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
214:     ctx.E       = PetscRealConstant(1.1378);
215:     ctx.V       = PetscRealConstant(1.0);
216:     ctx.X       = PetscRealConstant(0.545);
217:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
218:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
219:     ctx.Pm      = PetscRealConstant(1.0194);
220:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
221:     ctx.tf      = PetscRealConstant(0.1);
222:     ctx.tcl     = PetscRealConstant(0.2);
223:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
224:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);

226:   }
227:   PetscOptionsEnd();

229:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
230:     Create necessary matrix and vectors
231:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
232:   MatCreate(PETSC_COMM_WORLD,&A);
233:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
234:   MatSetType(A,MATDENSE);
235:   MatSetFromOptions(A);
236:   MatSetUp(A);

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

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

249:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
250:      Create timestepping solver context
251:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
252:   TSCreate(PETSC_COMM_WORLD,&ctx.ts);
253:   TSSetProblemType(ctx.ts,TS_NONLINEAR);
254:   TSSetEquationType(ctx.ts,TS_EQ_ODE_EXPLICIT); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
255:   TSSetType(ctx.ts,TSRK);
256:   TSSetRHSFunction(ctx.ts,NULL,(TSRHSFunction)RHSFunction,&ctx);
257:   TSSetRHSJacobian(ctx.ts,A,A,(TSRHSJacobian)RHSJacobian,&ctx);
258:   TSSetExactFinalTime(ctx.ts,TS_EXACTFINALTIME_MATCHSTEP);

260:   MatCreateVecs(A,&lambda[0],NULL);
261:   MatCreateVecs(Jacp,&mu[0],NULL);
262:   TSSetCostGradients(ctx.ts,1,lambda,mu);
263:   TSSetRHSJacobianP(ctx.ts,Jacp,RHSJacobianP,&ctx);

265:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
266:      Set solver options
267:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
268:   TSSetMaxTime(ctx.ts,PetscRealConstant(1.0));
269:   TSSetTimeStep(ctx.ts,PetscRealConstant(0.01));
270:   TSSetFromOptions(ctx.ts);

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

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

280:   /* Create TAO solver and set desired solution method */
281:   TaoCreate(PETSC_COMM_WORLD,&tao);
282:   TaoSetType(tao,TAOBLMVM);

284:   /*
285:      Optimization starts
286:   */
287:   /* Set initial solution guess */
288:   VecCreateSeq(PETSC_COMM_WORLD,1,&p);
289:   VecGetArray(p,&x_ptr);
290:   x_ptr[0]   = ctx.Pm;
291:   VecRestoreArray(p,&x_ptr);

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

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

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

317:   /* SOLVE THE APPLICATION */
318:   TaoSolve(tao);

320:   VecView(p,PETSC_VIEWER_STDOUT_WORLD);
321:   /* Free TAO data structures */
322:   TaoDestroy(&tao);
323:   VecDestroy(&p);
324:   VecDestroy(&lowerb);
325:   VecDestroy(&upperb);

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

339: /* ------------------------------------------------------------------ */
340: /*
341:    FormFunction - Evaluates the function

343:    Input Parameters:
344:    tao - the Tao context
345:    X   - the input vector
346:    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()

348:    Output Parameters:
349:    f   - the newly evaluated function
350: */
351: PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
352: {
353:   AppCtx         *ctx = (AppCtx*)ctx0;
354:   TS             ts = ctx->ts;
355:   Vec            U;             /* solution will be stored here */
357:   PetscScalar    *u;
358:   PetscScalar    *x_ptr;
359:   Vec            q;

361:   VecGetArrayRead(P,(const PetscScalar**)&x_ptr);
362:   ctx->Pm = x_ptr[0];
363:   VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);

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

375:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
376:      Set initial conditions
377:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
378:   TSGetSolution(ts,&U);
379:   VecGetArray(U,&u);
380:   u[0] = PetscAsinScalar(ctx->Pm/ctx->Pmax);
381:   u[1] = PetscRealConstant(1.0);
382:   VecRestoreArray(U,&u);

384:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
385:      Solve nonlinear system
386:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
387:   TSSolve(ts,U);
388:   TSGetCostIntegral(ts,&q);
389:   VecGetArray(q,&x_ptr);
390:   *f   = -ctx->Pm + x_ptr[0];
391:   VecRestoreArray(q,&x_ptr);
392:   return 0;
393: }

395: PetscErrorCode FormGradient(Tao tao,Vec P,Vec G,void *ctx0)
396: {
397:   AppCtx         *ctx = (AppCtx*)ctx0;
398:   TS             ts = ctx->ts;
399:   Vec            U;             /* solution will be stored here */
401:   PetscReal      ftime;
402:   PetscInt       steps;
403:   PetscScalar    *u;
404:   PetscScalar    *x_ptr,*y_ptr;
405:   Vec            *lambda,q,*mu;

407:   VecGetArrayRead(P,(const PetscScalar**)&x_ptr);
408:   ctx->Pm = x_ptr[0];
409:   VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);

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

421:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
422:      Set initial conditions
423:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
424:   TSGetSolution(ts,&U);
425:   VecGetArray(U,&u);
426:   u[0] = PetscAsinScalar(ctx->Pm/ctx->Pmax);
427:   u[1] = PetscRealConstant(1.0);
428:   VecRestoreArray(U,&u);

430:   /* Set up to save trajectory before TSSetFromOptions() so that TSTrajectory options can be captured */
431:   TSSetSaveTrajectory(ts);
432:   TSSetFromOptions(ts);

434:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
435:      Solve nonlinear system
436:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
437:   TSSolve(ts,U);

439:   TSGetSolveTime(ts,&ftime);
440:   TSGetStepNumber(ts,&steps);

442:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
443:      Adjoint model starts here
444:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
445:   TSGetCostGradients(ts,NULL,&lambda,&mu);
446:   /*   Set initial conditions for the adjoint integration */
447:   VecGetArray(lambda[0],&y_ptr);
448:   y_ptr[0] = 0.0; y_ptr[1] = 0.0;
449:   VecRestoreArray(lambda[0],&y_ptr);
450:   VecGetArray(mu[0],&x_ptr);
451:   x_ptr[0] = PetscRealConstant(-1.0);
452:   VecRestoreArray(mu[0],&x_ptr);

454:   TSAdjointSolve(ts);
455:   TSGetCostIntegral(ts,&q);
456:   ComputeSensiP(lambda[0],mu[0],ctx);
457:   VecCopy(mu[0],G);
458:   return 0;
459: }

461: /*TEST

463:    build:
464:       requires: !complex

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

469:    test:
470:       suffix: 2
471:       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

473: TEST*/