Actual source code: ex9opt.c
1: static char help[] = "Basic equation for generator stability analysis.\n";
3: /*F
5: \begin{eqnarray}
6: \frac{d \theta}{dt} = \omega_b (\omega - \omega_s)
7: \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - P_max \sin(\theta) -D(\omega - \omega_s)\\
8: \end{eqnarray}
10: Ensemble of initial conditions
11: ./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
13: Fault at .1 seconds
14: ./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
16: Initial conditions same as when fault is ended
17: ./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
19: F*/
21: /*
22: Include "petscts.h" so that we can use the TS ODE integrators. Note that this
23: file automatically includes:
24: petscsys.h - base PETSc routines
25: petscis.h - index sets
26: petscvec.h - vectors
27: petscmat.h - matrices
28: 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, PetscCtx 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: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
191: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
193: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194: Set runtime options
195: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
196: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", "");
197: {
198: ctx.beta = 2;
199: ctx.c = PetscRealConstant(10000.0);
200: ctx.u_s = PetscRealConstant(1.0);
201: ctx.omega_s = PetscRealConstant(1.0);
202: ctx.omega_b = PetscRealConstant(120.0) * PETSC_PI;
203: ctx.H = PetscRealConstant(5.0);
204: PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL));
205: ctx.D = PetscRealConstant(5.0);
206: PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL));
207: ctx.E = PetscRealConstant(1.1378);
208: ctx.V = PetscRealConstant(1.0);
209: ctx.X = PetscRealConstant(0.545);
210: ctx.Pmax = ctx.E * ctx.V / ctx.X;
211: PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL));
212: ctx.Pm = PetscRealConstant(1.0194);
213: PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL));
214: ctx.tf = PetscRealConstant(0.1);
215: ctx.tcl = PetscRealConstant(0.2);
216: PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL));
217: PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL));
218: }
219: PetscOptionsEnd();
221: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
222: Create necessary matrix and vectors
223: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
224: PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
225: PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
226: PetscCall(MatSetType(A, MATDENSE));
227: PetscCall(MatSetFromOptions(A));
228: PetscCall(MatSetUp(A));
230: PetscCall(MatCreateVecs(A, &U, NULL));
232: PetscCall(MatCreate(PETSC_COMM_WORLD, &Jacp));
233: PetscCall(MatSetSizes(Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1));
234: PetscCall(MatSetFromOptions(Jacp));
235: PetscCall(MatSetUp(Jacp));
236: PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &DRDP));
237: PetscCall(MatSetUp(DRDP));
238: PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 2, NULL, &DRDU));
239: PetscCall(MatSetUp(DRDU));
241: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
242: Create timestepping solver context
243: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
244: PetscCall(TSCreate(PETSC_COMM_WORLD, &ctx.ts));
245: PetscCall(TSSetProblemType(ctx.ts, TS_NONLINEAR));
246: PetscCall(TSSetEquationType(ctx.ts, TS_EQ_ODE_EXPLICIT)); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
247: PetscCall(TSSetType(ctx.ts, TSRK));
248: PetscCall(TSSetRHSFunction(ctx.ts, NULL, (TSRHSFunctionFn *)RHSFunction, &ctx));
249: PetscCall(TSSetRHSJacobian(ctx.ts, A, A, (TSRHSJacobianFn *)RHSJacobian, &ctx));
250: PetscCall(TSSetExactFinalTime(ctx.ts, TS_EXACTFINALTIME_MATCHSTEP));
252: PetscCall(MatCreateVecs(A, &lambda[0], NULL));
253: PetscCall(MatCreateVecs(Jacp, &mu[0], NULL));
254: PetscCall(TSSetCostGradients(ctx.ts, 1, lambda, mu));
255: PetscCall(TSSetRHSJacobianP(ctx.ts, Jacp, RHSJacobianP, &ctx));
257: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
258: Set solver options
259: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
260: PetscCall(TSSetMaxTime(ctx.ts, PetscRealConstant(1.0)));
261: PetscCall(TSSetTimeStep(ctx.ts, PetscRealConstant(0.01)));
262: PetscCall(TSSetFromOptions(ctx.ts));
264: PetscCall(TSGetTimeStep(ctx.ts, &ctx.dt)); /* save the stepsize */
266: PetscCall(TSCreateQuadratureTS(ctx.ts, PETSC_TRUE, &quadts));
267: PetscCall(TSSetRHSFunction(quadts, NULL, (TSRHSFunctionFn *)CostIntegrand, &ctx));
268: PetscCall(TSSetRHSJacobian(quadts, DRDU, DRDU, (TSRHSJacobianFn *)DRDUJacobianTranspose, &ctx));
269: PetscCall(TSSetRHSJacobianP(quadts, DRDP, (TSRHSJacobianPFn *)DRDPJacobianTranspose, &ctx));
270: PetscCall(TSSetSolution(ctx.ts, U));
272: /* Create TAO solver and set desired solution method */
273: PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
274: PetscCall(TaoSetType(tao, TAOBLMVM));
276: /*
277: Optimization starts
278: */
279: /* Set initial solution guess */
280: PetscCall(VecCreateSeq(PETSC_COMM_WORLD, 1, &p));
281: PetscCall(VecGetArray(p, &x_ptr));
282: x_ptr[0] = ctx.Pm;
283: PetscCall(VecRestoreArray(p, &x_ptr));
285: PetscCall(TaoSetSolution(tao, p));
286: /* Set routine for function and gradient evaluation */
287: PetscCall(TaoSetObjective(tao, FormFunction, (void *)&ctx));
288: PetscCall(TaoSetGradient(tao, NULL, FormGradient, (void *)&ctx));
290: /* Set bounds for the optimization */
291: PetscCall(VecDuplicate(p, &lowerb));
292: PetscCall(VecDuplicate(p, &upperb));
293: PetscCall(VecGetArray(lowerb, &x_ptr));
294: x_ptr[0] = 0.;
295: PetscCall(VecRestoreArray(lowerb, &x_ptr));
296: PetscCall(VecGetArray(upperb, &x_ptr));
297: x_ptr[0] = PetscRealConstant(1.1);
298: PetscCall(VecRestoreArray(upperb, &x_ptr));
299: PetscCall(TaoSetVariableBounds(tao, lowerb, upperb));
301: /* Check for any TAO command line options */
302: PetscCall(TaoSetFromOptions(tao));
303: PetscCall(TaoGetKSP(tao, &ksp));
304: if (ksp) {
305: PetscCall(KSPGetPC(ksp, &pc));
306: PetscCall(PCSetType(pc, PCNONE));
307: }
309: /* SOLVE THE APPLICATION */
310: PetscCall(TaoSolve(tao));
312: PetscCall(VecView(p, PETSC_VIEWER_STDOUT_WORLD));
313: /* Free TAO data structures */
314: PetscCall(TaoDestroy(&tao));
315: PetscCall(VecDestroy(&p));
316: PetscCall(VecDestroy(&lowerb));
317: PetscCall(VecDestroy(&upperb));
319: PetscCall(TSDestroy(&ctx.ts));
320: PetscCall(VecDestroy(&U));
321: PetscCall(MatDestroy(&A));
322: PetscCall(MatDestroy(&Jacp));
323: PetscCall(MatDestroy(&DRDU));
324: PetscCall(MatDestroy(&DRDP));
325: PetscCall(VecDestroy(&lambda[0]));
326: PetscCall(VecDestroy(&mu[0]));
327: PetscCall(PetscFinalize());
328: return 0;
329: }
331: /* ------------------------------------------------------------------ */
332: /*
333: FormFunction - Evaluates the function
335: Input Parameters:
336: tao - the Tao context
337: X - the input vector
338: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient()
340: Output Parameters:
341: f - the newly evaluated function
342: */
343: PetscErrorCode FormFunction(Tao tao, Vec P, PetscReal *f, PetscCtx ctx0)
344: {
345: AppCtx *ctx = (AppCtx *)ctx0;
346: TS ts = ctx->ts;
347: Vec U; /* solution will be stored here */
348: PetscScalar *u;
349: PetscScalar *x_ptr;
350: Vec q;
352: PetscFunctionBeginUser;
353: PetscCall(VecGetArrayRead(P, (const PetscScalar **)&x_ptr));
354: ctx->Pm = x_ptr[0];
355: PetscCall(VecRestoreArrayRead(P, (const PetscScalar **)&x_ptr));
357: /* reset time */
358: PetscCall(TSSetTime(ts, 0.0));
359: /* reset step counter, this is critical for adjoint solver */
360: PetscCall(TSSetStepNumber(ts, 0));
361: /* reset step size, the step size becomes negative after TSAdjointSolve */
362: PetscCall(TSSetTimeStep(ts, ctx->dt));
363: /* reinitialize the integral value */
364: PetscCall(TSGetCostIntegral(ts, &q));
365: PetscCall(VecSet(q, 0.0));
367: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
368: Set initial conditions
369: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
370: PetscCall(TSGetSolution(ts, &U));
371: PetscCall(VecGetArray(U, &u));
372: u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax);
373: u[1] = PetscRealConstant(1.0);
374: PetscCall(VecRestoreArray(U, &u));
376: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
377: Solve nonlinear system
378: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
379: PetscCall(TSSolve(ts, U));
380: PetscCall(TSGetCostIntegral(ts, &q));
381: PetscCall(VecGetArray(q, &x_ptr));
382: *f = -ctx->Pm + x_ptr[0];
383: PetscCall(VecRestoreArray(q, &x_ptr));
384: PetscFunctionReturn(PETSC_SUCCESS);
385: }
387: PetscErrorCode FormGradient(Tao tao, Vec P, Vec G, PetscCtx ctx0)
388: {
389: AppCtx *ctx = (AppCtx *)ctx0;
390: TS ts = ctx->ts;
391: Vec U; /* solution will be stored here */
392: PetscReal ftime;
393: PetscInt steps;
394: PetscScalar *u;
395: PetscScalar *x_ptr, *y_ptr;
396: Vec *lambda, q, *mu;
398: PetscFunctionBeginUser;
399: PetscCall(VecGetArrayRead(P, (const PetscScalar **)&x_ptr));
400: ctx->Pm = x_ptr[0];
401: PetscCall(VecRestoreArrayRead(P, (const PetscScalar **)&x_ptr));
403: /* reset time */
404: PetscCall(TSSetTime(ts, 0.0));
405: /* reset step counter, this is critical for adjoint solver */
406: PetscCall(TSSetStepNumber(ts, 0));
407: /* reset step size, the step size becomes negative after TSAdjointSolve */
408: PetscCall(TSSetTimeStep(ts, ctx->dt));
409: /* reinitialize the integral value */
410: PetscCall(TSGetCostIntegral(ts, &q));
411: PetscCall(VecSet(q, 0.0));
413: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
414: Set initial conditions
415: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
416: PetscCall(TSGetSolution(ts, &U));
417: PetscCall(VecGetArray(U, &u));
418: u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax);
419: u[1] = PetscRealConstant(1.0);
420: PetscCall(VecRestoreArray(U, &u));
422: /* Set up to save trajectory before TSSetFromOptions() so that TSTrajectory options can be captured */
423: PetscCall(TSSetSaveTrajectory(ts));
424: PetscCall(TSSetFromOptions(ts));
426: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
427: Solve nonlinear system
428: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
429: PetscCall(TSSolve(ts, U));
431: PetscCall(TSGetSolveTime(ts, &ftime));
432: PetscCall(TSGetStepNumber(ts, &steps));
434: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
435: Adjoint model starts here
436: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
437: PetscCall(TSGetCostGradients(ts, NULL, &lambda, &mu));
438: /* Set initial conditions for the adjoint integration */
439: PetscCall(VecGetArray(lambda[0], &y_ptr));
440: y_ptr[0] = 0.0;
441: y_ptr[1] = 0.0;
442: PetscCall(VecRestoreArray(lambda[0], &y_ptr));
443: PetscCall(VecGetArray(mu[0], &x_ptr));
444: x_ptr[0] = PetscRealConstant(-1.0);
445: PetscCall(VecRestoreArray(mu[0], &x_ptr));
447: PetscCall(TSAdjointSolve(ts));
448: PetscCall(TSGetCostIntegral(ts, &q));
449: PetscCall(ComputeSensiP(lambda[0], mu[0], ctx));
450: PetscCall(VecCopy(mu[0], G));
451: PetscFunctionReturn(PETSC_SUCCESS);
452: }
454: /*TEST
456: build:
457: requires: !complex !single
459: test:
460: args: -viewer_binary_skip_info -ts_adapt_type none -tao_monitor -tao_gatol 0.0 -tao_grtol 1.e-3 -tao_converged_reason
462: test:
463: suffix: 2
464: 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
466: TEST*/