Actual source code: ex9opt.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: ./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
14: Fault at .1 seconds
15: ./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
17: Initial conditions same as when fault is ended
18: ./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
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 <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: PetscScalar *f, Pmax;
51: const PetscScalar *u;
53: PetscFunctionBegin;
54: /* The next three lines allow us to access the entries of the vectors directly */
55: PetscCall(VecGetArrayRead(U, &u));
56: PetscCall(VecGetArray(F, &f));
57: 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 */
58: else Pmax = ctx->Pmax;
60: f[0] = ctx->omega_b * (u[1] - ctx->omega_s);
61: f[1] = (-Pmax * PetscSinScalar(u[0]) - ctx->D * (u[1] - ctx->omega_s) + ctx->Pm) * ctx->omega_s / (2.0 * ctx->H);
63: PetscCall(VecRestoreArrayRead(U, &u));
64: PetscCall(VecRestoreArray(F, &f));
65: PetscFunctionReturn(PETSC_SUCCESS);
66: }
68: /*
69: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
70: */
71: static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat A, Mat B, AppCtx *ctx)
72: {
73: PetscInt rowcol[] = {0, 1};
74: PetscScalar J[2][2], Pmax;
75: const PetscScalar *u;
77: PetscFunctionBegin;
78: PetscCall(VecGetArrayRead(U, &u));
79: 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 */
80: else Pmax = ctx->Pmax;
82: J[0][0] = 0;
83: J[0][1] = ctx->omega_b;
84: J[1][1] = -ctx->D * ctx->omega_s / (2.0 * ctx->H);
85: J[1][0] = -Pmax * PetscCosScalar(u[0]) * ctx->omega_s / (2.0 * ctx->H);
87: PetscCall(MatSetValues(A, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
88: PetscCall(VecRestoreArrayRead(U, &u));
90: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
91: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
92: if (A != B) {
93: PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
94: PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
95: }
96: PetscFunctionReturn(PETSC_SUCCESS);
97: }
99: static PetscErrorCode RHSJacobianP(TS ts, PetscReal t, Vec X, Mat A, void *ctx0)
100: {
101: PetscInt row[] = {0, 1}, col[] = {0};
102: PetscScalar J[2][1];
103: AppCtx *ctx = (AppCtx *)ctx0;
105: PetscFunctionBeginUser;
106: J[0][0] = 0;
107: J[1][0] = ctx->omega_s / (2.0 * ctx->H);
108: PetscCall(MatSetValues(A, 2, row, 1, col, &J[0][0], INSERT_VALUES));
109: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
110: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
111: PetscFunctionReturn(PETSC_SUCCESS);
112: }
114: static PetscErrorCode CostIntegrand(TS ts, PetscReal t, Vec U, Vec R, AppCtx *ctx)
115: {
116: PetscScalar *r;
117: const PetscScalar *u;
119: PetscFunctionBegin;
120: PetscCall(VecGetArrayRead(U, &u));
121: PetscCall(VecGetArray(R, &r));
122: r[0] = ctx->c * PetscPowScalarInt(PetscMax(0., u[0] - ctx->u_s), ctx->beta);
123: PetscCall(VecRestoreArray(R, &r));
124: PetscCall(VecRestoreArrayRead(U, &u));
125: PetscFunctionReturn(PETSC_SUCCESS);
126: }
128: static PetscErrorCode DRDUJacobianTranspose(TS ts, PetscReal t, Vec U, Mat DRDU, Mat B, AppCtx *ctx)
129: {
130: PetscScalar ru[1];
131: const PetscScalar *u;
132: PetscInt row[] = {0}, col[] = {0};
134: PetscFunctionBegin;
135: PetscCall(VecGetArrayRead(U, &u));
136: ru[0] = ctx->c * ctx->beta * PetscPowScalarInt(PetscMax(0., u[0] - ctx->u_s), ctx->beta - 1);
137: PetscCall(VecRestoreArrayRead(U, &u));
138: PetscCall(MatSetValues(DRDU, 1, row, 1, col, ru, INSERT_VALUES));
139: PetscCall(MatAssemblyBegin(DRDU, MAT_FINAL_ASSEMBLY));
140: PetscCall(MatAssemblyEnd(DRDU, MAT_FINAL_ASSEMBLY));
141: PetscFunctionReturn(PETSC_SUCCESS);
142: }
144: static PetscErrorCode DRDPJacobianTranspose(TS ts, PetscReal t, Vec U, Mat DRDP, AppCtx *ctx)
145: {
146: PetscFunctionBegin;
147: PetscCall(MatZeroEntries(DRDP));
148: PetscCall(MatAssemblyBegin(DRDP, MAT_FINAL_ASSEMBLY));
149: PetscCall(MatAssemblyEnd(DRDP, MAT_FINAL_ASSEMBLY));
150: PetscFunctionReturn(PETSC_SUCCESS);
151: }
153: PetscErrorCode ComputeSensiP(Vec lambda, Vec mu, AppCtx *ctx)
154: {
155: PetscScalar *y, sensip;
156: const PetscScalar *x;
158: PetscFunctionBegin;
159: PetscCall(VecGetArrayRead(lambda, &x));
160: PetscCall(VecGetArray(mu, &y));
161: sensip = 1. / PetscSqrtScalar(1. - (ctx->Pm / ctx->Pmax) * (ctx->Pm / ctx->Pmax)) / ctx->Pmax * x[0] + y[0];
162: y[0] = sensip;
163: PetscCall(VecRestoreArray(mu, &y));
164: PetscCall(VecRestoreArrayRead(lambda, &x));
165: PetscFunctionReturn(PETSC_SUCCESS);
166: }
168: int main(int argc, char **argv)
169: {
170: Vec p;
171: PetscScalar *x_ptr;
172: PetscMPIInt size;
173: AppCtx ctx;
174: Vec lowerb, upperb;
175: Tao tao;
176: KSP ksp;
177: PC pc;
178: Vec U, lambda[1], mu[1];
179: Mat A; /* Jacobian matrix */
180: Mat Jacp; /* Jacobian matrix */
181: Mat DRDU, DRDP;
182: PetscInt n = 2;
183: TS quadts;
185: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
186: Initialize program
187: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
188: PetscFunctionBeginUser;
189: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
190: PetscFunctionBeginUser;
191: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
192: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
194: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195: Set runtime options
196: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
197: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", "");
198: {
199: ctx.beta = 2;
200: ctx.c = PetscRealConstant(10000.0);
201: ctx.u_s = PetscRealConstant(1.0);
202: ctx.omega_s = PetscRealConstant(1.0);
203: ctx.omega_b = PetscRealConstant(120.0) * PETSC_PI;
204: ctx.H = PetscRealConstant(5.0);
205: PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL));
206: ctx.D = PetscRealConstant(5.0);
207: PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL));
208: ctx.E = PetscRealConstant(1.1378);
209: ctx.V = PetscRealConstant(1.0);
210: ctx.X = PetscRealConstant(0.545);
211: ctx.Pmax = ctx.E * ctx.V / ctx.X;
212: PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL));
213: ctx.Pm = PetscRealConstant(1.0194);
214: PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL));
215: ctx.tf = PetscRealConstant(0.1);
216: ctx.tcl = PetscRealConstant(0.2);
217: PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL));
218: PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL));
219: }
220: PetscOptionsEnd();
222: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
223: Create necessary matrix and vectors
224: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
225: PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
226: PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
227: PetscCall(MatSetType(A, MATDENSE));
228: PetscCall(MatSetFromOptions(A));
229: PetscCall(MatSetUp(A));
231: PetscCall(MatCreateVecs(A, &U, NULL));
233: PetscCall(MatCreate(PETSC_COMM_WORLD, &Jacp));
234: PetscCall(MatSetSizes(Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1));
235: PetscCall(MatSetFromOptions(Jacp));
236: PetscCall(MatSetUp(Jacp));
237: PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &DRDP));
238: PetscCall(MatSetUp(DRDP));
239: PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 2, NULL, &DRDU));
240: PetscCall(MatSetUp(DRDU));
242: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
243: Create timestepping solver context
244: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
245: PetscCall(TSCreate(PETSC_COMM_WORLD, &ctx.ts));
246: PetscCall(TSSetProblemType(ctx.ts, TS_NONLINEAR));
247: PetscCall(TSSetEquationType(ctx.ts, TS_EQ_ODE_EXPLICIT)); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
248: PetscCall(TSSetType(ctx.ts, TSRK));
249: PetscCall(TSSetRHSFunction(ctx.ts, NULL, (TSRHSFunction)RHSFunction, &ctx));
250: PetscCall(TSSetRHSJacobian(ctx.ts, A, A, (TSRHSJacobian)RHSJacobian, &ctx));
251: PetscCall(TSSetExactFinalTime(ctx.ts, TS_EXACTFINALTIME_MATCHSTEP));
253: PetscCall(MatCreateVecs(A, &lambda[0], NULL));
254: PetscCall(MatCreateVecs(Jacp, &mu[0], NULL));
255: PetscCall(TSSetCostGradients(ctx.ts, 1, lambda, mu));
256: PetscCall(TSSetRHSJacobianP(ctx.ts, Jacp, RHSJacobianP, &ctx));
258: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
259: Set solver options
260: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
261: PetscCall(TSSetMaxTime(ctx.ts, PetscRealConstant(1.0)));
262: PetscCall(TSSetTimeStep(ctx.ts, PetscRealConstant(0.01)));
263: PetscCall(TSSetFromOptions(ctx.ts));
265: PetscCall(TSGetTimeStep(ctx.ts, &ctx.dt)); /* save the stepsize */
267: PetscCall(TSCreateQuadratureTS(ctx.ts, PETSC_TRUE, &quadts));
268: PetscCall(TSSetRHSFunction(quadts, NULL, (TSRHSFunction)CostIntegrand, &ctx));
269: PetscCall(TSSetRHSJacobian(quadts, DRDU, DRDU, (TSRHSJacobian)DRDUJacobianTranspose, &ctx));
270: PetscCall(TSSetRHSJacobianP(quadts, DRDP, (TSRHSJacobianP)DRDPJacobianTranspose, &ctx));
271: PetscCall(TSSetSolution(ctx.ts, U));
273: /* Create TAO solver and set desired solution method */
274: PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
275: PetscCall(TaoSetType(tao, TAOBLMVM));
277: /*
278: Optimization starts
279: */
280: /* Set initial solution guess */
281: PetscCall(VecCreateSeq(PETSC_COMM_WORLD, 1, &p));
282: PetscCall(VecGetArray(p, &x_ptr));
283: x_ptr[0] = ctx.Pm;
284: PetscCall(VecRestoreArray(p, &x_ptr));
286: PetscCall(TaoSetSolution(tao, p));
287: /* Set routine for function and gradient evaluation */
288: PetscCall(TaoSetObjective(tao, FormFunction, (void *)&ctx));
289: PetscCall(TaoSetGradient(tao, NULL, FormGradient, (void *)&ctx));
291: /* Set bounds for the optimization */
292: PetscCall(VecDuplicate(p, &lowerb));
293: PetscCall(VecDuplicate(p, &upperb));
294: PetscCall(VecGetArray(lowerb, &x_ptr));
295: x_ptr[0] = 0.;
296: PetscCall(VecRestoreArray(lowerb, &x_ptr));
297: PetscCall(VecGetArray(upperb, &x_ptr));
298: x_ptr[0] = PetscRealConstant(1.1);
299: PetscCall(VecRestoreArray(upperb, &x_ptr));
300: PetscCall(TaoSetVariableBounds(tao, lowerb, upperb));
302: /* Check for any TAO command line options */
303: PetscCall(TaoSetFromOptions(tao));
304: PetscCall(TaoGetKSP(tao, &ksp));
305: if (ksp) {
306: PetscCall(KSPGetPC(ksp, &pc));
307: PetscCall(PCSetType(pc, PCNONE));
308: }
310: /* SOLVE THE APPLICATION */
311: PetscCall(TaoSolve(tao));
313: PetscCall(VecView(p, PETSC_VIEWER_STDOUT_WORLD));
314: /* Free TAO data structures */
315: PetscCall(TaoDestroy(&tao));
316: PetscCall(VecDestroy(&p));
317: PetscCall(VecDestroy(&lowerb));
318: PetscCall(VecDestroy(&upperb));
320: PetscCall(TSDestroy(&ctx.ts));
321: PetscCall(VecDestroy(&U));
322: PetscCall(MatDestroy(&A));
323: PetscCall(MatDestroy(&Jacp));
324: PetscCall(MatDestroy(&DRDU));
325: PetscCall(MatDestroy(&DRDP));
326: PetscCall(VecDestroy(&lambda[0]));
327: PetscCall(VecDestroy(&mu[0]));
328: PetscCall(PetscFinalize());
329: return 0;
330: }
332: /* ------------------------------------------------------------------ */
333: /*
334: FormFunction - Evaluates the function
336: Input Parameters:
337: tao - the Tao context
338: X - the input vector
339: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient()
341: Output Parameters:
342: f - the newly evaluated function
343: */
344: PetscErrorCode FormFunction(Tao tao, Vec P, PetscReal *f, void *ctx0)
345: {
346: AppCtx *ctx = (AppCtx *)ctx0;
347: TS ts = ctx->ts;
348: Vec U; /* solution will be stored here */
349: PetscScalar *u;
350: PetscScalar *x_ptr;
351: Vec q;
353: PetscFunctionBeginUser;
354: PetscCall(VecGetArrayRead(P, (const PetscScalar **)&x_ptr));
355: ctx->Pm = x_ptr[0];
356: PetscCall(VecRestoreArrayRead(P, (const PetscScalar **)&x_ptr));
358: /* reset time */
359: PetscCall(TSSetTime(ts, 0.0));
360: /* reset step counter, this is critical for adjoint solver */
361: PetscCall(TSSetStepNumber(ts, 0));
362: /* reset step size, the step size becomes negative after TSAdjointSolve */
363: PetscCall(TSSetTimeStep(ts, ctx->dt));
364: /* reinitialize the integral value */
365: PetscCall(TSGetCostIntegral(ts, &q));
366: PetscCall(VecSet(q, 0.0));
368: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
369: Set initial conditions
370: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
371: PetscCall(TSGetSolution(ts, &U));
372: PetscCall(VecGetArray(U, &u));
373: u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax);
374: u[1] = PetscRealConstant(1.0);
375: PetscCall(VecRestoreArray(U, &u));
377: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
378: Solve nonlinear system
379: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
380: PetscCall(TSSolve(ts, U));
381: PetscCall(TSGetCostIntegral(ts, &q));
382: PetscCall(VecGetArray(q, &x_ptr));
383: *f = -ctx->Pm + x_ptr[0];
384: PetscCall(VecRestoreArray(q, &x_ptr));
385: PetscFunctionReturn(PETSC_SUCCESS);
386: }
388: PetscErrorCode FormGradient(Tao tao, Vec P, Vec G, void *ctx0)
389: {
390: AppCtx *ctx = (AppCtx *)ctx0;
391: TS ts = ctx->ts;
392: Vec U; /* solution will be stored here */
393: PetscReal ftime;
394: PetscInt steps;
395: PetscScalar *u;
396: PetscScalar *x_ptr, *y_ptr;
397: Vec *lambda, q, *mu;
399: PetscFunctionBeginUser;
400: PetscCall(VecGetArrayRead(P, (const PetscScalar **)&x_ptr));
401: ctx->Pm = x_ptr[0];
402: PetscCall(VecRestoreArrayRead(P, (const PetscScalar **)&x_ptr));
404: /* reset time */
405: PetscCall(TSSetTime(ts, 0.0));
406: /* reset step counter, this is critical for adjoint solver */
407: PetscCall(TSSetStepNumber(ts, 0));
408: /* reset step size, the step size becomes negative after TSAdjointSolve */
409: PetscCall(TSSetTimeStep(ts, ctx->dt));
410: /* reinitialize the integral value */
411: PetscCall(TSGetCostIntegral(ts, &q));
412: PetscCall(VecSet(q, 0.0));
414: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
415: Set initial conditions
416: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
417: PetscCall(TSGetSolution(ts, &U));
418: PetscCall(VecGetArray(U, &u));
419: u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax);
420: u[1] = PetscRealConstant(1.0);
421: PetscCall(VecRestoreArray(U, &u));
423: /* Set up to save trajectory before TSSetFromOptions() so that TSTrajectory options can be captured */
424: PetscCall(TSSetSaveTrajectory(ts));
425: PetscCall(TSSetFromOptions(ts));
427: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
428: Solve nonlinear system
429: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
430: PetscCall(TSSolve(ts, U));
432: PetscCall(TSGetSolveTime(ts, &ftime));
433: PetscCall(TSGetStepNumber(ts, &steps));
435: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
436: Adjoint model starts here
437: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
438: PetscCall(TSGetCostGradients(ts, NULL, &lambda, &mu));
439: /* Set initial conditions for the adjoint integration */
440: PetscCall(VecGetArray(lambda[0], &y_ptr));
441: y_ptr[0] = 0.0;
442: y_ptr[1] = 0.0;
443: PetscCall(VecRestoreArray(lambda[0], &y_ptr));
444: PetscCall(VecGetArray(mu[0], &x_ptr));
445: x_ptr[0] = PetscRealConstant(-1.0);
446: PetscCall(VecRestoreArray(mu[0], &x_ptr));
448: PetscCall(TSAdjointSolve(ts));
449: PetscCall(TSGetCostIntegral(ts, &q));
450: PetscCall(ComputeSensiP(lambda[0], mu[0], ctx));
451: PetscCall(VecCopy(mu[0], G));
452: PetscFunctionReturn(PETSC_SUCCESS);
453: }
455: /*TEST
457: build:
458: requires: !complex
460: test:
461: args: -viewer_binary_skip_info -ts_adapt_type none -tao_monitor -tao_gatol 0.0 -tao_grtol 1.e-3 -tao_converged_reason
463: test:
464: suffix: 2
465: 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
467: TEST*/