Actual source code: ex9adj.c
petsc-3.7.1 2016-05-15
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
./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
Fault at .1 seconds
./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
Initial conditions same as when fault is ended
./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
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: */
34: #include <petscts.h>
36: typedef struct {
37: PetscScalar H,D,omega_b,omega_s,Pmax,Pm,E,V,X,u_s,c;
38: PetscInt beta;
39: PetscReal tf,tcl;
40: } AppCtx;
44: PetscErrorCode PostStepFunction(TS ts)
45: {
46: PetscErrorCode ierr;
47: Vec U;
48: PetscReal t;
49: const PetscScalar *u;
52: TSGetTime (ts,&t);
53: TSGetSolution (ts,&U);
54: VecGetArrayRead (U,&u);
55: PetscPrintf (PETSC_COMM_SELF ,"delta(%3.2f) = %8.7f\n" ,(double)t,(double)u[0]);
56: VecRestoreArrayRead (U,&u);
57:
58: return (0);
59: }
63: /*
64: Defines the ODE passed to the ODE solver
65: */
66: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
67: {
68: PetscErrorCode ierr;
69: PetscScalar *f,Pmax;
70: const PetscScalar *u;
73: /* The next three lines allow us to access the entries of the vectors directly */
74: VecGetArrayRead (U,&u);
75: VecGetArray (F,&f);
76: 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 */
77: else Pmax = ctx->Pmax;
78:
79: f[0] = ctx->omega_b*(u[1] - ctx->omega_s);
80: f[1] = (-Pmax*PetscSinScalar(u[0]) - ctx->D*(u[1] - ctx->omega_s) + ctx->Pm)*ctx->omega_s/(2.0*ctx->H);
82: VecRestoreArrayRead (U,&u);
83: VecRestoreArray (F,&f);
84: return (0);
85: }
89: /*
90: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian () for the meaning of a and the Jacobian.
91: */
92: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,AppCtx *ctx)
93: {
94: PetscErrorCode ierr;
95: PetscInt rowcol[] = {0,1};
96: PetscScalar J[2][2],Pmax;
97: const PetscScalar *u;
100: VecGetArrayRead (U,&u);
101: 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 */
102: else Pmax = ctx->Pmax;
104: J[0][0] = 0; J[0][1] = ctx->omega_b;
105: 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);
107: MatSetValues (B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES );
108: VecRestoreArrayRead (U,&u);
110: MatAssemblyBegin (A,MAT_FINAL_ASSEMBLY);
111: MatAssemblyEnd (A,MAT_FINAL_ASSEMBLY);
112: if (A != B) {
113: MatAssemblyBegin (B,MAT_FINAL_ASSEMBLY);
114: MatAssemblyEnd (B,MAT_FINAL_ASSEMBLY);
115: }
116: return (0);
117: }
121: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx0)
122: {
124: PetscInt row[] = {0,1},col[]={0};
125: PetscScalar J[2][1];
126: AppCtx *ctx=(AppCtx*)ctx0;
129: J[0][0] = 0;
130: J[1][0] = ctx->omega_s/(2.0*ctx->H);
131: MatSetValues (A,2,row,1,col,&J[0][0],INSERT_VALUES );
132: MatAssemblyBegin (A,MAT_FINAL_ASSEMBLY);
133: MatAssemblyEnd (A,MAT_FINAL_ASSEMBLY);
134: return (0);
135: }
139: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,AppCtx *ctx)
140: {
141: PetscErrorCode ierr;
142: PetscScalar *r;
143: const PetscScalar *u;
146: VecGetArrayRead (U,&u);
147: VecGetArray (R,&r);
148: r[0] = ctx->c*PetscPowScalarInt(PetscMax (0., u[0]-ctx->u_s),ctx->beta);
149: VecRestoreArray (R,&r);
150: VecRestoreArrayRead (U,&u);
151: return (0);
152: }
156: static PetscErrorCode DRDYFunction(TS ts,PetscReal t,Vec U,Vec *drdy,AppCtx *ctx)
157: {
158: PetscErrorCode ierr;
159: PetscScalar *ry;
160: const PetscScalar *u;
163: VecGetArrayRead (U,&u);
164: VecGetArray (drdy[0],&ry);
165: ry[0] = ctx->c*ctx->beta*PetscPowScalarInt(PetscMax (0., u[0]-ctx->u_s),ctx->beta-1);
166: VecRestoreArray (drdy[0],&ry);
167: VecRestoreArrayRead (U,&u);
168: return (0);
169: }
173: static PetscErrorCode DRDPFunction(TS ts,PetscReal t,Vec U,Vec *drdp,AppCtx *ctx)
174: {
175: PetscErrorCode ierr;
176: PetscScalar *rp;
177: const PetscScalar *u;
180: VecGetArrayRead (U,&u);
181: VecGetArray (drdp[0],&rp);
182: rp[0] = 0.;
183: VecRestoreArray (drdp[0],&rp);
184: VecGetArrayRead (U,&u);
185: return (0);
186: }
190: PetscErrorCode ComputeSensiP(Vec lambda,Vec mu,AppCtx *ctx)
191: {
192: PetscErrorCode ierr;
193: PetscScalar sensip;
194: const PetscScalar *x,*y;
195:
197: VecGetArrayRead (lambda,&x);
198: VecGetArrayRead (mu,&y);
199: sensip = 1./PetscSqrtScalar(1.-(ctx->Pm/ctx->Pmax)*(ctx->Pm/ctx->Pmax))/ctx->Pmax*x[0]+y[0];
200: PetscPrintf (PETSC_COMM_WORLD ,"\n sensitivity wrt parameter pm: %.7f \n" ,(double)sensip);
201: VecRestoreArrayRead (lambda,&x);
202: VecRestoreArrayRead (mu,&y);
203: return (0);
204: }
208: int main(int argc,char **argv)
209: {
210: TS ts; /* ODE integrator */
211: Vec U; /* solution will be stored here */
212: Mat A; /* Jacobian matrix */
213: Mat Jacp; /* Jacobian matrix */
215: PetscMPIInt size;
216: PetscInt n = 2;
217: AppCtx ctx;
218: PetscScalar *u;
219: PetscReal du[2] = {0.0,0.0};
220: PetscBool ensemble = PETSC_FALSE ,flg1,flg2;
221: PetscReal ftime;
222: PetscInt steps;
223: PetscScalar *x_ptr,*y_ptr;
224: Vec lambda[1],q,mu[1];
226: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
227: Initialize program
228: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
229: PetscInitialize (&argc,&argv,(char*)0,help);
230: MPI_Comm_size (PETSC_COMM_WORLD ,&size);
231: if (size > 1) SETERRQ (PETSC_COMM_WORLD ,PETSC_ERR_SUP,"Only for sequential runs" );
233: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
234: Create necessary matrix and vectors
235: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
236: MatCreate (PETSC_COMM_WORLD ,&A);
237: MatSetSizes (A,n,n,PETSC_DETERMINE ,PETSC_DETERMINE );
238: MatSetType (A,MATDENSE );
239: MatSetFromOptions (A);
240: MatSetUp (A);
242: MatCreateVecs (A,&U,NULL);
244: MatCreate (PETSC_COMM_WORLD ,&Jacp);
245: MatSetSizes (Jacp,PETSC_DECIDE ,PETSC_DECIDE ,2,1);
246: MatSetFromOptions (Jacp);
247: MatSetUp (Jacp);
249: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
250: Set runtime options
251: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
252: PetscOptionsBegin (PETSC_COMM_WORLD ,NULL,"Swing equation options" ,"" );
253: {
254: ctx.beta = 2;
255: ctx.c = 10000.0;
256: ctx.u_s = 1.0;
257: ctx.omega_s = 1.0;
258: ctx.omega_b = 120.0*PETSC_PI;
259: ctx.H = 5.0;
260: PetscOptionsScalar ("-Inertia" ,"" ,"" ,ctx.H,&ctx.H,NULL);
261: ctx.D = 5.0;
262: PetscOptionsScalar ("-D" ,"" ,"" ,ctx.D,&ctx.D,NULL);
263: ctx.E = 1.1378;
264: ctx.V = 1.0;
265: ctx.X = 0.545;
266: ctx.Pmax = ctx.E*ctx.V/ctx.X;;
267: PetscOptionsScalar ("-Pmax" ,"" ,"" ,ctx.Pmax,&ctx.Pmax,NULL);
268: ctx.Pm = 1.1;
269: PetscOptionsScalar ("-Pm" ,"" ,"" ,ctx.Pm,&ctx.Pm,NULL);
270: ctx.tf = 0.1;
271: ctx.tcl = 0.2;
272: PetscOptionsReal ("-tf" ,"Time to start fault" ,"" ,ctx.tf,&ctx.tf,NULL);
273: PetscOptionsReal ("-tcl" ,"Time to end fault" ,"" ,ctx.tcl,&ctx.tcl,NULL);
274: PetscOptionsBool ("-ensemble" ,"Run ensemble of different initial conditions" ,"" ,ensemble,&ensemble,NULL);
275: if (ensemble) {
276: ctx.tf = -1;
277: ctx.tcl = -1;
278: }
280: VecGetArray (U,&u);
281: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
282: u[1] = 1.0;
283: PetscOptionsRealArray ("-u" ,"Initial solution" ,"" ,u,&n,&flg1);
284: n = 2;
285: PetscOptionsRealArray ("-du" ,"Perturbation in initial solution" ,"" ,du,&n,&flg2);
286: u[0] += du[0];
287: u[1] += du[1];
288: VecRestoreArray (U,&u);
289: if (flg1 || flg2) {
290: ctx.tf = -1;
291: ctx.tcl = -1;
292: }
293: }
294: PetscOptionsEnd ();
296: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
297: Create timestepping solver context
298: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
299: TSCreate (PETSC_COMM_WORLD ,&ts);
300: TSSetProblemType (ts,TS_NONLINEAR);
301: TSSetType (ts,TSRK );
302: TSSetRHSFunction (ts,NULL,(TSRHSFunction)RHSFunction,&ctx);
303: TSSetRHSJacobian (ts,A,A,(TSRHSJacobian)RHSJacobian,&ctx);
304: TSSetExactFinalTime (ts,TS_EXACTFINALTIME_MATCHSTEP);
306: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
307: Set initial conditions
308: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
309: TSSetSolution (ts,U);
311: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
312: Save trajectory of solution so that TSAdjointSolve () may be used
313: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
314: TSSetSaveTrajectory (ts);
316: MatCreateVecs (A,&lambda[0],NULL);
317: /* Set initial conditions for the adjoint integration */
318: VecGetArray (lambda[0],&y_ptr);
319: y_ptr[0] = 0.0; y_ptr[1] = 0.0;
320: VecRestoreArray (lambda[0],&y_ptr);
322: MatCreateVecs (Jacp,&mu[0],NULL);
323: VecGetArray (mu[0],&x_ptr);
324: x_ptr[0] = -1.0;
325: VecRestoreArray (mu[0],&x_ptr);
326: TSSetCostGradients (ts,1,lambda,mu);
327: TSSetCostIntegrand (ts,1,(PetscErrorCode (*)(TS ,PetscReal ,Vec ,Vec ,void*))CostIntegrand,
328: (PetscErrorCode (*)(TS ,PetscReal ,Vec ,Vec *,void*))DRDYFunction,
329: (PetscErrorCode (*)(TS ,PetscReal ,Vec ,Vec *,void*))DRDPFunction,PETSC_TRUE ,&ctx);
331: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
332: Set solver options
333: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
334: TSSetDuration (ts,PETSC_DEFAULT ,10.0);
335: TSSetExactFinalTime (ts,TS_EXACTFINALTIME_STEPOVER);
336: TSSetInitialTimeStep (ts,0.0,.01);
337: TSSetFromOptions (ts);
339: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
340: Solve nonlinear system
341: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
342: if (ensemble) {
343: for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
344: VecGetArray (U,&u);
345: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
346: u[1] = ctx.omega_s;
347: u[0] += du[0];
348: u[1] += du[1];
349: VecRestoreArray (U,&u);
350: TSSetInitialTimeStep (ts,0.0,.01);
351: TSSolve (ts,U);
352: }
353: } else {
354: TSSolve (ts,U);
355: }
356: VecView (U,PETSC_VIEWER_STDOUT_WORLD );
357: TSGetSolveTime (ts,&ftime);
358: TSGetTimeStepNumber (ts,&steps);
360: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
361: Adjoint model starts here
362: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
363: /* Set initial conditions for the adjoint integration */
364: VecGetArray (lambda[0],&y_ptr);
365: y_ptr[0] = 0.0; y_ptr[1] = 0.0;
366: VecRestoreArray (lambda[0],&y_ptr);
368: VecGetArray (mu[0],&x_ptr);
369: x_ptr[0] = -1.0;
370: VecRestoreArray (mu[0],&x_ptr);
372: /* Set RHS JacobianP */
373: TSAdjointSetRHSJacobian (ts,Jacp,RHSJacobianP,&ctx);
375: TSAdjointSolve (ts);
377: PetscPrintf (PETSC_COMM_WORLD ,"\n sensitivity wrt initial conditions: d[Psi(tf)]/d[phi0] d[Psi(tf)]/d[omega0]\n" );
378: VecView (lambda[0],PETSC_VIEWER_STDOUT_WORLD );
379: VecView (mu[0],PETSC_VIEWER_STDOUT_WORLD );
380: TSGetCostIntegral (ts,&q);
381: VecView (q,PETSC_VIEWER_STDOUT_WORLD );
382: VecGetArray (q,&x_ptr);
383: PetscPrintf (PETSC_COMM_WORLD ,"\n cost function=%g\n" ,(double)(x_ptr[0]-ctx.Pm));
384: VecRestoreArray (q,&x_ptr);
386: ComputeSensiP(lambda[0],mu[0],&ctx);
388: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
389: Free work space. All PETSc objects should be destroyed when they are no longer needed.
390: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
391: MatDestroy (&A);
392: MatDestroy (&Jacp);
393: VecDestroy (&U);
394: VecDestroy (&lambda[0]);
395: VecDestroy (&mu[0]);
396: TSDestroy (&ts);
397: PetscFinalize ();
398: return (0);
399: }