1 static char help[] = "Basic equation for generator stability analysis.\n"; 2 3 /*F 4 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} 9 10 Ensemble of initial conditions 11 ./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 12 13 Fault at .1 seconds 14 ./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 15 16 Initial conditions same as when fault is ended 17 ./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 18 19 F*/ 20 21 /* 22 Include "petscts.h" so that we can use TS solvers. Note that this 23 file automatically includes: 24 petscsys.h - base PETSc routines petscvec.h - vectors 25 petscmat.h - matrices 26 petscis.h - index sets petscksp.h - Krylov subspace methods 27 petscviewer.h - viewers petscpc.h - preconditioners 28 petscksp.h - linear solvers 29 */ 30 31 #include <petscts.h> 32 33 typedef struct { 34 PetscScalar H, D, omega_b, omega_s, Pmax, Pm, E, V, X, u_s, c; 35 PetscInt beta; 36 PetscReal tf, tcl; 37 } AppCtx; 38 39 PetscErrorCode PostStepFunction(TS ts) 40 { 41 Vec U; 42 PetscReal t; 43 const PetscScalar *u; 44 45 PetscFunctionBegin; 46 PetscCall(TSGetTime(ts, &t)); 47 PetscCall(TSGetSolution(ts, &U)); 48 PetscCall(VecGetArrayRead(U, &u)); 49 PetscCall(PetscPrintf(PETSC_COMM_SELF, "delta(%3.2f) = %8.7f\n", (double)t, (double)u[0])); 50 PetscCall(VecRestoreArrayRead(U, &u)); 51 PetscFunctionReturn(PETSC_SUCCESS); 52 } 53 54 /* 55 Defines the ODE passed to the ODE solver 56 */ 57 static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec U, Vec F, AppCtx *ctx) 58 { 59 PetscScalar *f, Pmax; 60 const PetscScalar *u; 61 62 PetscFunctionBegin; 63 /* The next three lines allow us to access the entries of the vectors directly */ 64 PetscCall(VecGetArrayRead(U, &u)); 65 PetscCall(VecGetArray(F, &f)); 66 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 */ 67 else Pmax = ctx->Pmax; 68 69 f[0] = ctx->omega_b * (u[1] - ctx->omega_s); 70 f[1] = (-Pmax * PetscSinScalar(u[0]) - ctx->D * (u[1] - ctx->omega_s) + ctx->Pm) * ctx->omega_s / (2.0 * ctx->H); 71 72 PetscCall(VecRestoreArrayRead(U, &u)); 73 PetscCall(VecRestoreArray(F, &f)); 74 PetscFunctionReturn(PETSC_SUCCESS); 75 } 76 77 /* 78 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 79 */ 80 static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat A, Mat B, AppCtx *ctx) 81 { 82 PetscInt rowcol[] = {0, 1}; 83 PetscScalar J[2][2], Pmax; 84 const PetscScalar *u; 85 86 PetscFunctionBegin; 87 PetscCall(VecGetArrayRead(U, &u)); 88 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 */ 89 else Pmax = ctx->Pmax; 90 91 J[0][0] = 0; 92 J[0][1] = ctx->omega_b; 93 J[1][1] = -ctx->D * ctx->omega_s / (2.0 * ctx->H); 94 J[1][0] = -Pmax * PetscCosScalar(u[0]) * ctx->omega_s / (2.0 * ctx->H); 95 96 PetscCall(MatSetValues(A, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 97 PetscCall(VecRestoreArrayRead(U, &u)); 98 99 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 100 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 101 if (A != B) { 102 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 103 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 104 } 105 PetscFunctionReturn(PETSC_SUCCESS); 106 } 107 108 static PetscErrorCode RHSJacobianP(TS ts, PetscReal t, Vec X, Mat A, void *ctx0) 109 { 110 PetscInt row[] = {0, 1}, col[] = {0}; 111 PetscScalar J[2][1]; 112 AppCtx *ctx = (AppCtx *)ctx0; 113 114 PetscFunctionBeginUser; 115 J[0][0] = 0; 116 J[1][0] = ctx->omega_s / (2.0 * ctx->H); 117 PetscCall(MatSetValues(A, 2, row, 1, col, &J[0][0], INSERT_VALUES)); 118 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 119 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 120 PetscFunctionReturn(PETSC_SUCCESS); 121 } 122 123 static PetscErrorCode CostIntegrand(TS ts, PetscReal t, Vec U, Vec R, AppCtx *ctx) 124 { 125 PetscScalar *r; 126 const PetscScalar *u; 127 128 PetscFunctionBegin; 129 PetscCall(VecGetArrayRead(U, &u)); 130 PetscCall(VecGetArray(R, &r)); 131 r[0] = ctx->c * PetscPowScalarInt(PetscMax(0., u[0] - ctx->u_s), ctx->beta); 132 PetscCall(VecRestoreArray(R, &r)); 133 PetscCall(VecRestoreArrayRead(U, &u)); 134 PetscFunctionReturn(PETSC_SUCCESS); 135 } 136 137 static PetscErrorCode DRDUJacobianTranspose(TS ts, PetscReal t, Vec U, Mat DRDU, Mat B, AppCtx *ctx) 138 { 139 PetscScalar ru[1]; 140 const PetscScalar *u; 141 PetscInt row[] = {0}, col[] = {0}; 142 143 PetscFunctionBegin; 144 PetscCall(VecGetArrayRead(U, &u)); 145 ru[0] = ctx->c * ctx->beta * PetscPowScalarInt(PetscMax(0., u[0] - ctx->u_s), ctx->beta - 1); 146 PetscCall(VecRestoreArrayRead(U, &u)); 147 PetscCall(MatSetValues(DRDU, 1, row, 1, col, ru, INSERT_VALUES)); 148 PetscCall(MatAssemblyBegin(DRDU, MAT_FINAL_ASSEMBLY)); 149 PetscCall(MatAssemblyEnd(DRDU, MAT_FINAL_ASSEMBLY)); 150 PetscFunctionReturn(PETSC_SUCCESS); 151 } 152 153 static PetscErrorCode DRDPJacobianTranspose(TS ts, PetscReal t, Vec U, Mat DRDP, AppCtx *ctx) 154 { 155 PetscFunctionBegin; 156 PetscCall(MatZeroEntries(DRDP)); 157 PetscCall(MatAssemblyBegin(DRDP, MAT_FINAL_ASSEMBLY)); 158 PetscCall(MatAssemblyEnd(DRDP, MAT_FINAL_ASSEMBLY)); 159 PetscFunctionReturn(PETSC_SUCCESS); 160 } 161 162 PetscErrorCode ComputeSensiP(Vec lambda, Vec mu, AppCtx *ctx) 163 { 164 PetscScalar sensip; 165 const PetscScalar *x, *y; 166 167 PetscFunctionBegin; 168 PetscCall(VecGetArrayRead(lambda, &x)); 169 PetscCall(VecGetArrayRead(mu, &y)); 170 sensip = 1. / PetscSqrtScalar(1. - (ctx->Pm / ctx->Pmax) * (ctx->Pm / ctx->Pmax)) / ctx->Pmax * x[0] + y[0]; 171 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n sensitivity wrt parameter pm: %.7f \n", (double)sensip)); 172 PetscCall(VecRestoreArrayRead(lambda, &x)); 173 PetscCall(VecRestoreArrayRead(mu, &y)); 174 PetscFunctionReturn(PETSC_SUCCESS); 175 } 176 177 int main(int argc, char **argv) 178 { 179 TS ts, quadts; /* ODE integrator */ 180 Vec U; /* solution will be stored here */ 181 Mat A; /* Jacobian matrix */ 182 Mat Jacp; /* Jacobian matrix */ 183 Mat DRDU, DRDP; 184 PetscMPIInt size; 185 PetscInt n = 2; 186 AppCtx ctx; 187 PetscScalar *u; 188 PetscReal du[2] = {0.0, 0.0}; 189 PetscBool ensemble = PETSC_FALSE, flg1, flg2; 190 PetscReal ftime; 191 PetscInt steps; 192 PetscScalar *x_ptr, *y_ptr; 193 Vec lambda[1], q, mu[1]; 194 195 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 196 Initialize program 197 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 198 PetscFunctionBeginUser; 199 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 200 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 201 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 202 203 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 204 Create necessary matrix and vectors 205 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 206 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 207 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 208 PetscCall(MatSetType(A, MATDENSE)); 209 PetscCall(MatSetFromOptions(A)); 210 PetscCall(MatSetUp(A)); 211 212 PetscCall(MatCreateVecs(A, &U, NULL)); 213 214 PetscCall(MatCreate(PETSC_COMM_WORLD, &Jacp)); 215 PetscCall(MatSetSizes(Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1)); 216 PetscCall(MatSetFromOptions(Jacp)); 217 PetscCall(MatSetUp(Jacp)); 218 219 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &DRDP)); 220 PetscCall(MatSetUp(DRDP)); 221 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 2, NULL, &DRDU)); 222 PetscCall(MatSetUp(DRDU)); 223 224 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 225 Set runtime options 226 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 227 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", ""); 228 { 229 ctx.beta = 2; 230 ctx.c = 10000.0; 231 ctx.u_s = 1.0; 232 ctx.omega_s = 1.0; 233 ctx.omega_b = 120.0 * PETSC_PI; 234 ctx.H = 5.0; 235 PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL)); 236 ctx.D = 5.0; 237 PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL)); 238 ctx.E = 1.1378; 239 ctx.V = 1.0; 240 ctx.X = 0.545; 241 ctx.Pmax = ctx.E * ctx.V / ctx.X; 242 PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL)); 243 ctx.Pm = 1.1; 244 PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL)); 245 ctx.tf = 0.1; 246 ctx.tcl = 0.2; 247 PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL)); 248 PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL)); 249 PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL)); 250 if (ensemble) { 251 ctx.tf = -1; 252 ctx.tcl = -1; 253 } 254 255 PetscCall(VecGetArray(U, &u)); 256 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); 257 u[1] = 1.0; 258 PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1)); 259 n = 2; 260 PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2)); 261 u[0] += du[0]; 262 u[1] += du[1]; 263 PetscCall(VecRestoreArray(U, &u)); 264 if (flg1 || flg2) { 265 ctx.tf = -1; 266 ctx.tcl = -1; 267 } 268 } 269 PetscOptionsEnd(); 270 271 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 272 Create timestepping solver context 273 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 274 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 275 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 276 PetscCall(TSSetEquationType(ts, TS_EQ_ODE_EXPLICIT)); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */ 277 PetscCall(TSSetType(ts, TSRK)); 278 PetscCall(TSSetRHSFunction(ts, NULL, (TSRHSFunctionFn *)RHSFunction, &ctx)); 279 PetscCall(TSSetRHSJacobian(ts, A, A, (TSRHSJacobianFn *)RHSJacobian, &ctx)); 280 PetscCall(TSCreateQuadratureTS(ts, PETSC_TRUE, &quadts)); 281 PetscCall(TSSetRHSFunction(quadts, NULL, (TSRHSFunctionFn *)CostIntegrand, &ctx)); 282 PetscCall(TSSetRHSJacobian(quadts, DRDU, DRDU, (TSRHSJacobianFn *)DRDUJacobianTranspose, &ctx)); 283 PetscCall(TSSetRHSJacobianP(quadts, DRDP, (TSRHSJacobianPFn *)DRDPJacobianTranspose, &ctx)); 284 PetscCall(TSSetCostGradients(ts, 1, lambda, mu)); 285 PetscCall(TSSetRHSJacobianP(ts, Jacp, RHSJacobianP, &ctx)); 286 287 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 288 Set initial conditions 289 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 290 PetscCall(TSSetSolution(ts, U)); 291 292 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 293 Save trajectory of solution so that TSAdjointSolve() may be used 294 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 295 PetscCall(TSSetSaveTrajectory(ts)); 296 297 PetscCall(MatCreateVecs(A, &lambda[0], NULL)); 298 /* Set initial conditions for the adjoint integration */ 299 PetscCall(VecGetArray(lambda[0], &y_ptr)); 300 y_ptr[0] = 0.0; 301 y_ptr[1] = 0.0; 302 PetscCall(VecRestoreArray(lambda[0], &y_ptr)); 303 304 PetscCall(MatCreateVecs(Jacp, &mu[0], NULL)); 305 PetscCall(VecGetArray(mu[0], &x_ptr)); 306 x_ptr[0] = -1.0; 307 PetscCall(VecRestoreArray(mu[0], &x_ptr)); 308 309 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 310 Set solver options 311 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 312 PetscCall(TSSetMaxTime(ts, 10.0)); 313 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 314 PetscCall(TSSetTimeStep(ts, .01)); 315 PetscCall(TSSetFromOptions(ts)); 316 317 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 318 Solve nonlinear system 319 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 320 if (ensemble) { 321 for (du[1] = -2.5; du[1] <= .01; du[1] += .1) { 322 PetscCall(VecGetArray(U, &u)); 323 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); 324 u[1] = ctx.omega_s; 325 u[0] += du[0]; 326 u[1] += du[1]; 327 PetscCall(VecRestoreArray(U, &u)); 328 PetscCall(TSSetTimeStep(ts, .01)); 329 PetscCall(TSSolve(ts, U)); 330 } 331 } else { 332 PetscCall(TSSolve(ts, U)); 333 } 334 PetscCall(VecView(U, PETSC_VIEWER_STDOUT_WORLD)); 335 PetscCall(TSGetSolveTime(ts, &ftime)); 336 PetscCall(TSGetStepNumber(ts, &steps)); 337 338 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 339 Adjoint model starts here 340 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 341 /* Set initial conditions for the adjoint integration */ 342 PetscCall(VecGetArray(lambda[0], &y_ptr)); 343 y_ptr[0] = 0.0; 344 y_ptr[1] = 0.0; 345 PetscCall(VecRestoreArray(lambda[0], &y_ptr)); 346 347 PetscCall(VecGetArray(mu[0], &x_ptr)); 348 x_ptr[0] = -1.0; 349 PetscCall(VecRestoreArray(mu[0], &x_ptr)); 350 351 PetscCall(TSAdjointSolve(ts)); 352 353 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n sensitivity wrt initial conditions: d[Psi(tf)]/d[phi0] d[Psi(tf)]/d[omega0]\n")); 354 PetscCall(VecView(lambda[0], PETSC_VIEWER_STDOUT_WORLD)); 355 PetscCall(VecView(mu[0], PETSC_VIEWER_STDOUT_WORLD)); 356 PetscCall(TSGetCostIntegral(ts, &q)); 357 PetscCall(VecView(q, PETSC_VIEWER_STDOUT_WORLD)); 358 PetscCall(VecGetArray(q, &x_ptr)); 359 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n cost function=%g\n", (double)(x_ptr[0] - ctx.Pm))); 360 PetscCall(VecRestoreArray(q, &x_ptr)); 361 362 PetscCall(ComputeSensiP(lambda[0], mu[0], &ctx)); 363 364 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 365 Free work space. All PETSc objects should be destroyed when they are no longer needed. 366 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 367 PetscCall(MatDestroy(&A)); 368 PetscCall(MatDestroy(&Jacp)); 369 PetscCall(MatDestroy(&DRDU)); 370 PetscCall(MatDestroy(&DRDP)); 371 PetscCall(VecDestroy(&U)); 372 PetscCall(VecDestroy(&lambda[0])); 373 PetscCall(VecDestroy(&mu[0])); 374 PetscCall(TSDestroy(&ts)); 375 PetscCall(PetscFinalize()); 376 return 0; 377 } 378 379 /*TEST 380 381 build: 382 requires: !complex 383 384 test: 385 args: -viewer_binary_skip_info -ts_adapt_type none 386 387 TEST*/ 388