Actual source code: ex9adj.c
petsc-3.8.3 2017-12-09
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;
42: PetscErrorCode PostStepFunction(TS ts)
43: {
44: PetscErrorCode ierr;
45: Vec U;
46: PetscReal t;
47: const PetscScalar *u;
50: TSGetTime (ts,&t);
51: TSGetSolution (ts,&U);
52: VecGetArrayRead (U,&u);
53: PetscPrintf (PETSC_COMM_SELF ,"delta(%3.2f) = %8.7f\n" ,(double)t,(double)u[0]);
54: VecRestoreArrayRead (U,&u);
55:
56: return (0);
57: }
59: /*
60: Defines the ODE passed to the ODE solver
61: */
62: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
63: {
64: PetscErrorCode ierr;
65: PetscScalar *f,Pmax;
66: const PetscScalar *u;
69: /* The next three lines allow us to access the entries of the vectors directly */
70: VecGetArrayRead (U,&u);
71: VecGetArray (F,&f);
72: 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 */
73: else Pmax = ctx->Pmax;
74:
75: f[0] = ctx->omega_b*(u[1] - ctx->omega_s);
76: f[1] = (-Pmax*PetscSinScalar(u[0]) - ctx->D*(u[1] - ctx->omega_s) + ctx->Pm)*ctx->omega_s/(2.0*ctx->H);
78: VecRestoreArrayRead (U,&u);
79: VecRestoreArray (F,&f);
80: return (0);
81: }
83: /*
84: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian () for the meaning of a and the Jacobian.
85: */
86: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,AppCtx *ctx)
87: {
88: PetscErrorCode ierr;
89: PetscInt rowcol[] = {0,1};
90: PetscScalar J[2][2],Pmax;
91: const PetscScalar *u;
94: VecGetArrayRead (U,&u);
95: 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 */
96: else Pmax = ctx->Pmax;
98: J[0][0] = 0; J[0][1] = ctx->omega_b;
99: 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);
101: MatSetValues (B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES );
102: VecRestoreArrayRead (U,&u);
104: MatAssemblyBegin (A,MAT_FINAL_ASSEMBLY );
105: MatAssemblyEnd (A,MAT_FINAL_ASSEMBLY );
106: if (A != B) {
107: MatAssemblyBegin (B,MAT_FINAL_ASSEMBLY );
108: MatAssemblyEnd (B,MAT_FINAL_ASSEMBLY );
109: }
110: return (0);
111: }
113: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx0)
114: {
116: PetscInt row[] = {0,1},col[]={0};
117: PetscScalar J[2][1];
118: AppCtx *ctx=(AppCtx*)ctx0;
121: J[0][0] = 0;
122: J[1][0] = ctx->omega_s/(2.0*ctx->H);
123: MatSetValues (A,2,row,1,col,&J[0][0],INSERT_VALUES );
124: MatAssemblyBegin (A,MAT_FINAL_ASSEMBLY );
125: MatAssemblyEnd (A,MAT_FINAL_ASSEMBLY );
126: return (0);
127: }
129: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,AppCtx *ctx)
130: {
131: PetscErrorCode ierr;
132: PetscScalar *r;
133: const PetscScalar *u;
136: VecGetArrayRead (U,&u);
137: VecGetArray (R,&r);
138: r[0] = ctx->c*PetscPowScalarInt(PetscMax (0., u[0]-ctx->u_s),ctx->beta);
139: VecRestoreArray (R,&r);
140: VecRestoreArrayRead (U,&u);
141: return (0);
142: }
144: static PetscErrorCode DRDYFunction(TS ts,PetscReal t,Vec U,Vec *drdy,AppCtx *ctx)
145: {
146: PetscErrorCode ierr;
147: PetscScalar *ry;
148: const PetscScalar *u;
151: VecGetArrayRead (U,&u);
152: VecGetArray (drdy[0],&ry);
153: ry[0] = ctx->c*ctx->beta*PetscPowScalarInt(PetscMax (0., u[0]-ctx->u_s),ctx->beta-1);
154: VecRestoreArray (drdy[0],&ry);
155: VecRestoreArrayRead (U,&u);
156: return (0);
157: }
159: static PetscErrorCode DRDPFunction(TS ts,PetscReal t,Vec U,Vec *drdp,AppCtx *ctx)
160: {
161: PetscErrorCode ierr;
162: PetscScalar *rp;
163: const PetscScalar *u;
166: VecGetArrayRead (U,&u);
167: VecGetArray (drdp[0],&rp);
168: rp[0] = 0.;
169: VecRestoreArray (drdp[0],&rp);
170: VecGetArrayRead (U,&u);
171: return (0);
172: }
174: PetscErrorCode ComputeSensiP(Vec lambda,Vec mu,AppCtx *ctx)
175: {
176: PetscErrorCode ierr;
177: PetscScalar sensip;
178: const PetscScalar *x,*y;
179:
181: VecGetArrayRead (lambda,&x);
182: VecGetArrayRead (mu,&y);
183: sensip = 1./PetscSqrtScalar(1.-(ctx->Pm/ctx->Pmax)*(ctx->Pm/ctx->Pmax))/ctx->Pmax*x[0]+y[0];
184: PetscPrintf (PETSC_COMM_WORLD ,"\n sensitivity wrt parameter pm: %.7f \n" ,(double)sensip);
185: VecRestoreArrayRead (lambda,&x);
186: VecRestoreArrayRead (mu,&y);
187: return (0);
188: }
190: int main(int argc,char **argv)
191: {
192: TS ts; /* ODE integrator */
193: Vec U; /* solution will be stored here */
194: Mat A; /* Jacobian matrix */
195: Mat Jacp; /* Jacobian matrix */
197: PetscMPIInt size;
198: PetscInt n = 2;
199: AppCtx ctx;
200: PetscScalar *u;
201: PetscReal du[2] = {0.0,0.0};
202: PetscBool ensemble = PETSC_FALSE ,flg1,flg2;
203: PetscReal ftime;
204: PetscInt steps;
205: PetscScalar *x_ptr,*y_ptr;
206: Vec lambda[1],q,mu[1];
208: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209: Initialize program
210: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
211: PetscInitialize (&argc,&argv,(char*)0,help);if (ierr) return ierr;
212: MPI_Comm_size (PETSC_COMM_WORLD ,&size);
213: if (size > 1) SETERRQ (PETSC_COMM_WORLD ,PETSC_ERR_SUP,"Only for sequential runs" );
215: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
216: Create necessary matrix and vectors
217: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
218: MatCreate (PETSC_COMM_WORLD ,&A);
219: MatSetSizes (A,n,n,PETSC_DETERMINE ,PETSC_DETERMINE );
220: MatSetType (A,MATDENSE );
221: MatSetFromOptions (A);
222: MatSetUp (A);
224: MatCreateVecs (A,&U,NULL);
226: MatCreate (PETSC_COMM_WORLD ,&Jacp);
227: MatSetSizes (Jacp,PETSC_DECIDE ,PETSC_DECIDE ,2,1);
228: MatSetFromOptions (Jacp);
229: MatSetUp (Jacp);
231: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
232: Set runtime options
233: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
234: PetscOptionsBegin (PETSC_COMM_WORLD ,NULL,"Swing equation options" ,"" );
235: {
236: ctx.beta = 2;
237: ctx.c = 10000.0;
238: ctx.u_s = 1.0;
239: ctx.omega_s = 1.0;
240: ctx.omega_b = 120.0*PETSC_PI;
241: ctx.H = 5.0;
242: PetscOptionsScalar ("-Inertia" ,"" ,"" ,ctx.H,&ctx.H,NULL);
243: ctx.D = 5.0;
244: PetscOptionsScalar ("-D" ,"" ,"" ,ctx.D,&ctx.D,NULL);
245: ctx.E = 1.1378;
246: ctx.V = 1.0;
247: ctx.X = 0.545;
248: ctx.Pmax = ctx.E*ctx.V/ctx.X;;
249: PetscOptionsScalar ("-Pmax" ,"" ,"" ,ctx.Pmax,&ctx.Pmax,NULL);
250: ctx.Pm = 1.1;
251: PetscOptionsScalar ("-Pm" ,"" ,"" ,ctx.Pm,&ctx.Pm,NULL);
252: ctx.tf = 0.1;
253: ctx.tcl = 0.2;
254: PetscOptionsReal ("-tf" ,"Time to start fault" ,"" ,ctx.tf,&ctx.tf,NULL);
255: PetscOptionsReal ("-tcl" ,"Time to end fault" ,"" ,ctx.tcl,&ctx.tcl,NULL);
256: PetscOptionsBool ("-ensemble" ,"Run ensemble of different initial conditions" ,"" ,ensemble,&ensemble,NULL);
257: if (ensemble) {
258: ctx.tf = -1;
259: ctx.tcl = -1;
260: }
262: VecGetArray (U,&u);
263: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
264: u[1] = 1.0;
265: PetscOptionsRealArray ("-u" ,"Initial solution" ,"" ,u,&n,&flg1);
266: n = 2;
267: PetscOptionsRealArray ("-du" ,"Perturbation in initial solution" ,"" ,du,&n,&flg2);
268: u[0] += du[0];
269: u[1] += du[1];
270: VecRestoreArray (U,&u);
271: if (flg1 || flg2) {
272: ctx.tf = -1;
273: ctx.tcl = -1;
274: }
275: }
276: PetscOptionsEnd ();
278: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
279: Create timestepping solver context
280: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
281: TSCreate (PETSC_COMM_WORLD ,&ts);
282: TSSetProblemType (ts,TS_NONLINEAR );
283: TSSetType (ts,TSRK );
284: TSSetRHSFunction (ts,NULL,(TSRHSFunction)RHSFunction,&ctx);
285: TSSetRHSJacobian (ts,A,A,(TSRHSJacobian)RHSJacobian,&ctx);
287: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
288: Set initial conditions
289: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
290: TSSetSolution (ts,U);
292: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
293: Save trajectory of solution so that TSAdjointSolve () may be used
294: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
295: TSSetSaveTrajectory (ts);
297: MatCreateVecs (A,&lambda[0],NULL);
298: /* Set initial conditions for the adjoint integration */
299: VecGetArray (lambda[0],&y_ptr);
300: y_ptr[0] = 0.0; y_ptr[1] = 0.0;
301: VecRestoreArray (lambda[0],&y_ptr);
303: MatCreateVecs (Jacp,&mu[0],NULL);
304: VecGetArray (mu[0],&x_ptr);
305: x_ptr[0] = -1.0;
306: VecRestoreArray (mu[0],&x_ptr);
307: TSSetCostGradients (ts,1,lambda,mu);
308: TSSetCostIntegrand (ts,1,NULL,(PetscErrorCode (*)(TS ,PetscReal ,Vec ,Vec ,void*))CostIntegrand,
309: (PetscErrorCode (*)(TS ,PetscReal ,Vec ,Vec *,void*))DRDYFunction,
310: (PetscErrorCode (*)(TS ,PetscReal ,Vec ,Vec *,void*))DRDPFunction,PETSC_TRUE ,&ctx);
312: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
313: Set solver options
314: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
315: TSSetMaxTime (ts,10.0);
316: TSSetExactFinalTime (ts,TS_EXACTFINALTIME_MATCHSTEP );
317: TSSetTimeStep (ts,.01);
318: TSSetFromOptions (ts);
320: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
321: Solve nonlinear system
322: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
323: if (ensemble) {
324: for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
325: VecGetArray (U,&u);
326: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
327: u[1] = ctx.omega_s;
328: u[0] += du[0];
329: u[1] += du[1];
330: VecRestoreArray (U,&u);
331: TSSetTimeStep (ts,.01);
332: TSSolve (ts,U);
333: }
334: } else {
335: TSSolve (ts,U);
336: }
337: VecView (U,PETSC_VIEWER_STDOUT_WORLD );
338: TSGetSolveTime (ts,&ftime);
339: TSGetStepNumber (ts,&steps);
341: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
342: Adjoint model starts here
343: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
344: /* Set initial conditions for the adjoint integration */
345: VecGetArray (lambda[0],&y_ptr);
346: y_ptr[0] = 0.0; y_ptr[1] = 0.0;
347: VecRestoreArray (lambda[0],&y_ptr);
349: VecGetArray (mu[0],&x_ptr);
350: x_ptr[0] = -1.0;
351: VecRestoreArray (mu[0],&x_ptr);
353: /* Set RHS JacobianP */
354: TSAdjointSetRHSJacobian (ts,Jacp,RHSJacobianP,&ctx);
356: TSAdjointSolve (ts);
358: PetscPrintf (PETSC_COMM_WORLD ,"\n sensitivity wrt initial conditions: d[Psi(tf)]/d[phi0] d[Psi(tf)]/d[omega0]\n" );
359: VecView (lambda[0],PETSC_VIEWER_STDOUT_WORLD );
360: VecView (mu[0],PETSC_VIEWER_STDOUT_WORLD );
361: TSGetCostIntegral (ts,&q);
362: VecView (q,PETSC_VIEWER_STDOUT_WORLD );
363: VecGetArray (q,&x_ptr);
364: PetscPrintf (PETSC_COMM_WORLD ,"\n cost function=%g\n" ,(double)(x_ptr[0]-ctx.Pm));
365: VecRestoreArray (q,&x_ptr);
367: ComputeSensiP(lambda[0],mu[0],&ctx);
369: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
370: Free work space. All PETSc objects should be destroyed when they are no longer needed.
371: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
372: MatDestroy (&A);
373: MatDestroy (&Jacp);
374: VecDestroy (&U);
375: VecDestroy (&lambda[0]);
376: VecDestroy (&mu[0]);
377: TSDestroy (&ts);
378: PetscFinalize ();
379: return ierr;
380: }