Actual source code: ex9adj.c


  2: static char help[] = "Basic equation for generator stability analysis.\n";

  4: /*F

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

 11:   Ensemble of initial conditions
 12:    ./ex9 -ensemble -ts_monitor_draw_solution_phase -1,-3,3,3 -ts_adapt_dt_max .01 -ts_monitor -ts_type rk -pc_type lu -ksp_type preonly

 14:   Fault at .1 seconds
 15:    ./ex9 -ts_monitor_draw_solution_phase .42,.95,.6,1.05 -ts_adapt_dt_max .01 -ts_monitor -ts_type rk -pc_type lu -ksp_type preonly

 17:   Initial conditions same as when fault is ended
 18:    ./ex9 -u 0.496792,1.00932 -ts_monitor_draw_solution_phase .42,.95,.6,1.05 -ts_adapt_dt_max .01 -ts_monitor -ts_type rk -pc_type lu -ksp_type preonly

 20: F*/

 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 <petscts.h>

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

 40: PetscErrorCode PostStepFunction(TS ts)
 41: {
 42:   Vec                U;
 43:   PetscReal          t;
 44:   const PetscScalar *u;

 46:   TSGetTime(ts, &t);
 47:   TSGetSolution(ts, &U);
 48:   VecGetArrayRead(U, &u);
 49:   PetscPrintf(PETSC_COMM_SELF, "delta(%3.2f) = %8.7f\n", (double)t, (double)u[0]);
 50:   VecRestoreArrayRead(U, &u);
 51:   return 0;
 52: }

 54: /*
 55:      Defines the ODE passed to the ODE solver
 56: */
 57: static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec U, Vec F, AppCtx *ctx)
 58: {
 59:   PetscScalar       *f, Pmax;
 60:   const PetscScalar *u;

 62:   /*  The next three lines allow us to access the entries of the vectors directly */
 63:   VecGetArrayRead(U, &u);
 64:   VecGetArray(F, &f);
 65:   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 */
 66:   else Pmax = ctx->Pmax;

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

 71:   VecRestoreArrayRead(U, &u);
 72:   VecRestoreArray(F, &f);
 73:   return 0;
 74: }

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

 85:   VecGetArrayRead(U, &u);
 86:   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 */
 87:   else Pmax = ctx->Pmax;

 89:   J[0][0] = 0;
 90:   J[0][1] = ctx->omega_b;
 91:   J[1][1] = -ctx->D * ctx->omega_s / (2.0 * ctx->H);
 92:   J[1][0] = -Pmax * PetscCosScalar(u[0]) * ctx->omega_s / (2.0 * ctx->H);

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

 97:   MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
 98:   MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
 99:   if (A != B) {
100:     MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY);
101:     MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY);
102:   }
103:   return 0;
104: }

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

113:   J[0][0] = 0;
114:   J[1][0] = ctx->omega_s / (2.0 * ctx->H);
115:   MatSetValues(A, 2, row, 1, col, &J[0][0], INSERT_VALUES);
116:   MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
117:   MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
118:   return 0;
119: }

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

126:   VecGetArrayRead(U, &u);
127:   VecGetArray(R, &r);
128:   r[0] = ctx->c * PetscPowScalarInt(PetscMax(0., u[0] - ctx->u_s), ctx->beta);
129:   VecRestoreArray(R, &r);
130:   VecRestoreArrayRead(U, &u);
131:   return 0;
132: }

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

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

149: static PetscErrorCode DRDPJacobianTranspose(TS ts, PetscReal t, Vec U, Mat DRDP, AppCtx *ctx)
150: {
151:   MatZeroEntries(DRDP);
152:   MatAssemblyBegin(DRDP, MAT_FINAL_ASSEMBLY);
153:   MatAssemblyEnd(DRDP, MAT_FINAL_ASSEMBLY);
154:   return 0;
155: }

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

162:   VecGetArrayRead(lambda, &x);
163:   VecGetArrayRead(mu, &y);
164:   sensip = 1. / PetscSqrtScalar(1. - (ctx->Pm / ctx->Pmax) * (ctx->Pm / ctx->Pmax)) / ctx->Pmax * x[0] + y[0];
165:   PetscPrintf(PETSC_COMM_WORLD, "\n sensitivity wrt parameter pm: %.7f \n", (double)sensip);
166:   VecRestoreArrayRead(lambda, &x);
167:   VecRestoreArrayRead(mu, &y);
168:   return 0;
169: }

171: int main(int argc, char **argv)
172: {
173:   TS           ts, quadts; /* ODE integrator */
174:   Vec          U;          /* solution will be stored here */
175:   Mat          A;          /* Jacobian matrix */
176:   Mat          Jacp;       /* Jacobian matrix */
177:   Mat          DRDU, DRDP;
178:   PetscMPIInt  size;
179:   PetscInt     n = 2;
180:   AppCtx       ctx;
181:   PetscScalar *u;
182:   PetscReal    du[2]    = {0.0, 0.0};
183:   PetscBool    ensemble = PETSC_FALSE, flg1, flg2;
184:   PetscReal    ftime;
185:   PetscInt     steps;
186:   PetscScalar *x_ptr, *y_ptr;
187:   Vec          lambda[1], q, mu[1];

189:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190:      Initialize program
191:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
193:   PetscInitialize(&argc, &argv, (char *)0, help);
194:   MPI_Comm_size(PETSC_COMM_WORLD, &size);

197:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198:     Create necessary matrix and vectors
199:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
200:   MatCreate(PETSC_COMM_WORLD, &A);
201:   MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE);
202:   MatSetType(A, MATDENSE);
203:   MatSetFromOptions(A);
204:   MatSetUp(A);

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

208:   MatCreate(PETSC_COMM_WORLD, &Jacp);
209:   MatSetSizes(Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1);
210:   MatSetFromOptions(Jacp);
211:   MatSetUp(Jacp);

213:   MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &DRDP);
214:   MatSetUp(DRDP);
215:   MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 2, NULL, &DRDU);
216:   MatSetUp(DRDU);

218:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
219:     Set runtime options
220:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
221:   PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", "");
222:   {
223:     ctx.beta    = 2;
224:     ctx.c       = 10000.0;
225:     ctx.u_s     = 1.0;
226:     ctx.omega_s = 1.0;
227:     ctx.omega_b = 120.0 * PETSC_PI;
228:     ctx.H       = 5.0;
229:     PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL);
230:     ctx.D = 5.0;
231:     PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL);
232:     ctx.E    = 1.1378;
233:     ctx.V    = 1.0;
234:     ctx.X    = 0.545;
235:     ctx.Pmax = ctx.E * ctx.V / ctx.X;
236:     PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL);
237:     ctx.Pm = 1.1;
238:     PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL);
239:     ctx.tf  = 0.1;
240:     ctx.tcl = 0.2;
241:     PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL);
242:     PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL);
243:     PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL);
244:     if (ensemble) {
245:       ctx.tf  = -1;
246:       ctx.tcl = -1;
247:     }

249:     VecGetArray(U, &u);
250:     u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
251:     u[1] = 1.0;
252:     PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1);
253:     n = 2;
254:     PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2);
255:     u[0] += du[0];
256:     u[1] += du[1];
257:     VecRestoreArray(U, &u);
258:     if (flg1 || flg2) {
259:       ctx.tf  = -1;
260:       ctx.tcl = -1;
261:     }
262:   }
263:   PetscOptionsEnd();

265:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
266:      Create timestepping solver context
267:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
268:   TSCreate(PETSC_COMM_WORLD, &ts);
269:   TSSetProblemType(ts, TS_NONLINEAR);
270:   TSSetEquationType(ts, TS_EQ_ODE_EXPLICIT); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
271:   TSSetType(ts, TSRK);
272:   TSSetRHSFunction(ts, NULL, (TSRHSFunction)RHSFunction, &ctx);
273:   TSSetRHSJacobian(ts, A, A, (TSRHSJacobian)RHSJacobian, &ctx);
274:   TSCreateQuadratureTS(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);

279:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
280:      Set initial conditions
281:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
282:   TSSetSolution(ts, U);

284:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
285:     Save trajectory of solution so that TSAdjointSolve() may be used
286:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
287:   TSSetSaveTrajectory(ts);

289:   MatCreateVecs(A, &lambda[0], NULL);
290:   /*   Set initial conditions for the adjoint integration */
291:   VecGetArray(lambda[0], &y_ptr);
292:   y_ptr[0] = 0.0;
293:   y_ptr[1] = 0.0;
294:   VecRestoreArray(lambda[0], &y_ptr);

296:   MatCreateVecs(Jacp, &mu[0], NULL);
297:   VecGetArray(mu[0], &x_ptr);
298:   x_ptr[0] = -1.0;
299:   VecRestoreArray(mu[0], &x_ptr);
300:   TSSetCostGradients(ts, 1, lambda, mu);

302:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
303:      Set solver options
304:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
305:   TSSetMaxTime(ts, 10.0);
306:   TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP);
307:   TSSetTimeStep(ts, .01);
308:   TSSetFromOptions(ts);

310:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
311:      Solve nonlinear system
312:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
313:   if (ensemble) {
314:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
315:       VecGetArray(U, &u);
316:       u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
317:       u[1] = ctx.omega_s;
318:       u[0] += du[0];
319:       u[1] += du[1];
320:       VecRestoreArray(U, &u);
321:       TSSetTimeStep(ts, .01);
322:       TSSolve(ts, U);
323:     }
324:   } else {
325:     TSSolve(ts, U);
326:   }
327:   VecView(U, PETSC_VIEWER_STDOUT_WORLD);
328:   TSGetSolveTime(ts, &ftime);
329:   TSGetStepNumber(ts, &steps);

331:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
332:      Adjoint model starts here
333:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
334:   /*   Set initial conditions for the adjoint integration */
335:   VecGetArray(lambda[0], &y_ptr);
336:   y_ptr[0] = 0.0;
337:   y_ptr[1] = 0.0;
338:   VecRestoreArray(lambda[0], &y_ptr);

340:   VecGetArray(mu[0], &x_ptr);
341:   x_ptr[0] = -1.0;
342:   VecRestoreArray(mu[0], &x_ptr);

344:   /*   Set RHS JacobianP */
345:   TSSetRHSJacobianP(ts, Jacp, RHSJacobianP, &ctx);

347:   TSAdjointSolve(ts);

349:   PetscPrintf(PETSC_COMM_WORLD, "\n sensitivity wrt initial conditions: d[Psi(tf)]/d[phi0]  d[Psi(tf)]/d[omega0]\n");
350:   VecView(lambda[0], PETSC_VIEWER_STDOUT_WORLD);
351:   VecView(mu[0], PETSC_VIEWER_STDOUT_WORLD);
352:   TSGetCostIntegral(ts, &q);
353:   VecView(q, PETSC_VIEWER_STDOUT_WORLD);
354:   VecGetArray(q, &x_ptr);
355:   PetscPrintf(PETSC_COMM_WORLD, "\n cost function=%g\n", (double)(x_ptr[0] - ctx.Pm));
356:   VecRestoreArray(q, &x_ptr);

358:   ComputeSensiP(lambda[0], mu[0], &ctx);

360:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
361:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
362:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
363:   MatDestroy(&A);
364:   MatDestroy(&Jacp);
365:   MatDestroy(&DRDU);
366:   MatDestroy(&DRDP);
367:   VecDestroy(&U);
368:   VecDestroy(&lambda[0]);
369:   VecDestroy(&mu[0]);
370:   TSDestroy(&ts);
371:   PetscFinalize();
372:   return 0;
373: }

375: /*TEST

377:    build:
378:       requires: !complex

380:    test:
381:       args: -viewer_binary_skip_info -ts_adapt_type none

383: TEST*/