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: /* The next three lines allow us to access the entries of the vectors directly */
54: VecGetArrayRead(U, &u);
55: VecGetArray(F, &f);
56: 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 */
57: else Pmax = ctx->Pmax;
59: f[0] = ctx->omega_b * (u[1] - ctx->omega_s);
60: f[1] = (-Pmax * PetscSinScalar(u[0]) - ctx->D * (u[1] - ctx->omega_s) + ctx->Pm) * ctx->omega_s / (2.0 * ctx->H);
62: VecRestoreArrayRead(U, &u);
63: VecRestoreArray(F, &f);
64: return 0;
65: }
67: /*
68: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
69: */
70: static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat A, Mat B, AppCtx *ctx)
71: {
72: PetscInt rowcol[] = {0, 1};
73: PetscScalar J[2][2], Pmax;
74: const PetscScalar *u;
76: VecGetArrayRead(U, &u);
77: 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 */
78: else Pmax = ctx->Pmax;
80: J[0][0] = 0;
81: J[0][1] = ctx->omega_b;
82: J[1][1] = -ctx->D * ctx->omega_s / (2.0 * ctx->H);
83: J[1][0] = -Pmax * PetscCosScalar(u[0]) * ctx->omega_s / (2.0 * ctx->H);
85: MatSetValues(A, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES);
86: VecRestoreArrayRead(U, &u);
88: MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
89: MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
90: if (A != B) {
91: MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY);
92: MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY);
93: }
94: return 0;
95: }
97: static PetscErrorCode RHSJacobianP(TS ts, PetscReal t, Vec X, Mat A, void *ctx0)
98: {
99: PetscInt row[] = {0, 1}, col[] = {0};
100: PetscScalar J[2][1];
101: AppCtx *ctx = (AppCtx *)ctx0;
104: J[0][0] = 0;
105: J[1][0] = ctx->omega_s / (2.0 * ctx->H);
106: MatSetValues(A, 2, row, 1, col, &J[0][0], INSERT_VALUES);
107: MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
108: MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
109: return 0;
110: }
112: static PetscErrorCode CostIntegrand(TS ts, PetscReal t, Vec U, Vec R, AppCtx *ctx)
113: {
114: PetscScalar *r;
115: const PetscScalar *u;
117: VecGetArrayRead(U, &u);
118: VecGetArray(R, &r);
119: r[0] = ctx->c * PetscPowScalarInt(PetscMax(0., u[0] - ctx->u_s), ctx->beta);
120: VecRestoreArray(R, &r);
121: VecRestoreArrayRead(U, &u);
122: return 0;
123: }
125: static PetscErrorCode DRDUJacobianTranspose(TS ts, PetscReal t, Vec U, Mat DRDU, Mat B, AppCtx *ctx)
126: {
127: PetscScalar ru[1];
128: const PetscScalar *u;
129: PetscInt row[] = {0}, col[] = {0};
131: VecGetArrayRead(U, &u);
132: ru[0] = ctx->c * ctx->beta * PetscPowScalarInt(PetscMax(0., u[0] - ctx->u_s), ctx->beta - 1);
133: VecRestoreArrayRead(U, &u);
134: MatSetValues(DRDU, 1, row, 1, col, ru, INSERT_VALUES);
135: MatAssemblyBegin(DRDU, MAT_FINAL_ASSEMBLY);
136: MatAssemblyEnd(DRDU, MAT_FINAL_ASSEMBLY);
137: return 0;
138: }
140: static PetscErrorCode DRDPJacobianTranspose(TS ts, PetscReal t, Vec U, Mat DRDP, AppCtx *ctx)
141: {
142: MatZeroEntries(DRDP);
143: MatAssemblyBegin(DRDP, MAT_FINAL_ASSEMBLY);
144: MatAssemblyEnd(DRDP, MAT_FINAL_ASSEMBLY);
145: return 0;
146: }
148: PetscErrorCode ComputeSensiP(Vec lambda, Vec mu, AppCtx *ctx)
149: {
150: PetscScalar *y, sensip;
151: const PetscScalar *x;
153: VecGetArrayRead(lambda, &x);
154: VecGetArray(mu, &y);
155: sensip = 1. / PetscSqrtScalar(1. - (ctx->Pm / ctx->Pmax) * (ctx->Pm / ctx->Pmax)) / ctx->Pmax * x[0] + y[0];
156: y[0] = sensip;
157: VecRestoreArray(mu, &y);
158: VecRestoreArrayRead(lambda, &x);
159: return 0;
160: }
162: int main(int argc, char **argv)
163: {
164: Vec p;
165: PetscScalar *x_ptr;
166: PetscMPIInt size;
167: AppCtx ctx;
168: Vec lowerb, upperb;
169: Tao tao;
170: KSP ksp;
171: PC pc;
172: Vec U, lambda[1], mu[1];
173: Mat A; /* Jacobian matrix */
174: Mat Jacp; /* Jacobian matrix */
175: Mat DRDU, DRDP;
176: PetscInt n = 2;
177: TS quadts;
179: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
180: Initialize program
181: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
183: PetscInitialize(&argc, &argv, NULL, help);
185: MPI_Comm_size(PETSC_COMM_WORLD, &size);
188: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
189: Set runtime options
190: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
191: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", "");
192: {
193: ctx.beta = 2;
194: ctx.c = PetscRealConstant(10000.0);
195: ctx.u_s = PetscRealConstant(1.0);
196: ctx.omega_s = PetscRealConstant(1.0);
197: ctx.omega_b = PetscRealConstant(120.0) * PETSC_PI;
198: ctx.H = PetscRealConstant(5.0);
199: PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL);
200: ctx.D = PetscRealConstant(5.0);
201: PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL);
202: ctx.E = PetscRealConstant(1.1378);
203: ctx.V = PetscRealConstant(1.0);
204: ctx.X = PetscRealConstant(0.545);
205: ctx.Pmax = ctx.E * ctx.V / ctx.X;
206: PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL);
207: ctx.Pm = PetscRealConstant(1.0194);
208: PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL);
209: ctx.tf = PetscRealConstant(0.1);
210: ctx.tcl = PetscRealConstant(0.2);
211: PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL);
212: PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL);
213: }
214: PetscOptionsEnd();
216: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
217: Create necessary matrix and vectors
218: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
219: MatCreate(PETSC_COMM_WORLD, &A);
220: MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE);
221: MatSetType(A, MATDENSE);
222: MatSetFromOptions(A);
223: MatSetUp(A);
225: MatCreateVecs(A, &U, NULL);
227: MatCreate(PETSC_COMM_WORLD, &Jacp);
228: MatSetSizes(Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1);
229: MatSetFromOptions(Jacp);
230: MatSetUp(Jacp);
231: MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &DRDP);
232: MatSetUp(DRDP);
233: MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 2, NULL, &DRDU);
234: MatSetUp(DRDU);
236: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
237: Create timestepping solver context
238: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
239: TSCreate(PETSC_COMM_WORLD, &ctx.ts);
240: TSSetProblemType(ctx.ts, TS_NONLINEAR);
241: TSSetEquationType(ctx.ts, TS_EQ_ODE_EXPLICIT); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
242: TSSetType(ctx.ts, TSRK);
243: TSSetRHSFunction(ctx.ts, NULL, (TSRHSFunction)RHSFunction, &ctx);
244: TSSetRHSJacobian(ctx.ts, A, A, (TSRHSJacobian)RHSJacobian, &ctx);
245: TSSetExactFinalTime(ctx.ts, TS_EXACTFINALTIME_MATCHSTEP);
247: MatCreateVecs(A, &lambda[0], NULL);
248: MatCreateVecs(Jacp, &mu[0], NULL);
249: TSSetCostGradients(ctx.ts, 1, lambda, mu);
250: TSSetRHSJacobianP(ctx.ts, Jacp, RHSJacobianP, &ctx);
252: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
253: Set solver options
254: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
255: TSSetMaxTime(ctx.ts, PetscRealConstant(1.0));
256: TSSetTimeStep(ctx.ts, PetscRealConstant(0.01));
257: TSSetFromOptions(ctx.ts);
259: TSGetTimeStep(ctx.ts, &ctx.dt); /* save the stepsize */
261: TSCreateQuadratureTS(ctx.ts, PETSC_TRUE, &quadts);
262: TSSetRHSFunction(quadts, NULL, (TSRHSFunction)CostIntegrand, &ctx);
263: TSSetRHSJacobian(quadts, DRDU, DRDU, (TSRHSJacobian)DRDUJacobianTranspose, &ctx);
264: TSSetRHSJacobianP(quadts, DRDP, (TSRHSJacobianP)DRDPJacobianTranspose, &ctx);
265: TSSetSolution(ctx.ts, U);
267: /* Create TAO solver and set desired solution method */
268: TaoCreate(PETSC_COMM_WORLD, &tao);
269: TaoSetType(tao, TAOBLMVM);
271: /*
272: Optimization starts
273: */
274: /* Set initial solution guess */
275: VecCreateSeq(PETSC_COMM_WORLD, 1, &p);
276: VecGetArray(p, &x_ptr);
277: x_ptr[0] = ctx.Pm;
278: VecRestoreArray(p, &x_ptr);
280: TaoSetSolution(tao, p);
281: /* Set routine for function and gradient evaluation */
282: TaoSetObjective(tao, FormFunction, (void *)&ctx);
283: TaoSetGradient(tao, NULL, FormGradient, (void *)&ctx);
285: /* Set bounds for the optimization */
286: VecDuplicate(p, &lowerb);
287: VecDuplicate(p, &upperb);
288: VecGetArray(lowerb, &x_ptr);
289: x_ptr[0] = 0.;
290: VecRestoreArray(lowerb, &x_ptr);
291: VecGetArray(upperb, &x_ptr);
292: x_ptr[0] = PetscRealConstant(1.1);
293: VecRestoreArray(upperb, &x_ptr);
294: TaoSetVariableBounds(tao, lowerb, upperb);
296: /* Check for any TAO command line options */
297: TaoSetFromOptions(tao);
298: TaoGetKSP(tao, &ksp);
299: if (ksp) {
300: KSPGetPC(ksp, &pc);
301: PCSetType(pc, PCNONE);
302: }
304: /* SOLVE THE APPLICATION */
305: TaoSolve(tao);
307: VecView(p, PETSC_VIEWER_STDOUT_WORLD);
308: /* Free TAO data structures */
309: TaoDestroy(&tao);
310: VecDestroy(&p);
311: VecDestroy(&lowerb);
312: VecDestroy(&upperb);
314: TSDestroy(&ctx.ts);
315: VecDestroy(&U);
316: MatDestroy(&A);
317: MatDestroy(&Jacp);
318: MatDestroy(&DRDU);
319: MatDestroy(&DRDP);
320: VecDestroy(&lambda[0]);
321: VecDestroy(&mu[0]);
322: PetscFinalize();
323: return 0;
324: }
326: /* ------------------------------------------------------------------ */
327: /*
328: FormFunction - Evaluates the function
330: Input Parameters:
331: tao - the Tao context
332: X - the input vector
333: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient()
335: Output Parameters:
336: f - the newly evaluated function
337: */
338: PetscErrorCode FormFunction(Tao tao, Vec P, PetscReal *f, void *ctx0)
339: {
340: AppCtx *ctx = (AppCtx *)ctx0;
341: TS ts = ctx->ts;
342: Vec U; /* solution will be stored here */
343: PetscScalar *u;
344: PetscScalar *x_ptr;
345: Vec q;
347: VecGetArrayRead(P, (const PetscScalar **)&x_ptr);
348: ctx->Pm = x_ptr[0];
349: VecRestoreArrayRead(P, (const PetscScalar **)&x_ptr);
351: /* reset time */
352: TSSetTime(ts, 0.0);
353: /* reset step counter, this is critical for adjoint solver */
354: TSSetStepNumber(ts, 0);
355: /* reset step size, the step size becomes negative after TSAdjointSolve */
356: TSSetTimeStep(ts, ctx->dt);
357: /* reinitialize the integral value */
358: TSGetCostIntegral(ts, &q);
359: VecSet(q, 0.0);
361: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
362: Set initial conditions
363: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
364: TSGetSolution(ts, &U);
365: VecGetArray(U, &u);
366: u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax);
367: u[1] = PetscRealConstant(1.0);
368: VecRestoreArray(U, &u);
370: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
371: Solve nonlinear system
372: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
373: TSSolve(ts, U);
374: TSGetCostIntegral(ts, &q);
375: VecGetArray(q, &x_ptr);
376: *f = -ctx->Pm + x_ptr[0];
377: VecRestoreArray(q, &x_ptr);
378: return 0;
379: }
381: PetscErrorCode FormGradient(Tao tao, Vec P, Vec G, void *ctx0)
382: {
383: AppCtx *ctx = (AppCtx *)ctx0;
384: TS ts = ctx->ts;
385: Vec U; /* solution will be stored here */
386: PetscReal ftime;
387: PetscInt steps;
388: PetscScalar *u;
389: PetscScalar *x_ptr, *y_ptr;
390: Vec *lambda, q, *mu;
392: VecGetArrayRead(P, (const PetscScalar **)&x_ptr);
393: ctx->Pm = x_ptr[0];
394: VecRestoreArrayRead(P, (const PetscScalar **)&x_ptr);
396: /* reset time */
397: TSSetTime(ts, 0.0);
398: /* reset step counter, this is critical for adjoint solver */
399: TSSetStepNumber(ts, 0);
400: /* reset step size, the step size becomes negative after TSAdjointSolve */
401: TSSetTimeStep(ts, ctx->dt);
402: /* reinitialize the integral value */
403: TSGetCostIntegral(ts, &q);
404: VecSet(q, 0.0);
406: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
407: Set initial conditions
408: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
409: TSGetSolution(ts, &U);
410: VecGetArray(U, &u);
411: u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax);
412: u[1] = PetscRealConstant(1.0);
413: VecRestoreArray(U, &u);
415: /* Set up to save trajectory before TSSetFromOptions() so that TSTrajectory options can be captured */
416: TSSetSaveTrajectory(ts);
417: TSSetFromOptions(ts);
419: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
420: Solve nonlinear system
421: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
422: TSSolve(ts, U);
424: TSGetSolveTime(ts, &ftime);
425: TSGetStepNumber(ts, &steps);
427: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
428: Adjoint model starts here
429: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
430: TSGetCostGradients(ts, NULL, &lambda, &mu);
431: /* Set initial conditions for the adjoint integration */
432: VecGetArray(lambda[0], &y_ptr);
433: y_ptr[0] = 0.0;
434: y_ptr[1] = 0.0;
435: VecRestoreArray(lambda[0], &y_ptr);
436: VecGetArray(mu[0], &x_ptr);
437: x_ptr[0] = PetscRealConstant(-1.0);
438: VecRestoreArray(mu[0], &x_ptr);
440: TSAdjointSolve(ts);
441: TSGetCostIntegral(ts, &q);
442: ComputeSensiP(lambda[0], mu[0], ctx);
443: VecCopy(mu[0], G);
444: return 0;
445: }
447: /*TEST
449: build:
450: requires: !complex
452: test:
453: args: -viewer_binary_skip_info -ts_adapt_type none -tao_monitor -tao_gatol 0.0 -tao_grtol 1.e-3 -tao_converged_reason
455: test:
456: suffix: 2
457: 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
459: TEST*/