1 2 static char help[] = "Basic equation for generator stability analysis.\n"; 3 4 /*F 5 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} 10 11 Ensemble of initial conditions 12 ./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 13 14 Fault at .1 seconds 15 ./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 16 17 Initial conditions same as when fault is ended 18 ./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 19 20 F*/ 21 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 */ 31 32 #include <petscts.h> 33 34 typedef struct { 35 PetscScalar H, D, omega_b, omega_s, Pmax, Pm, E, V, X, u_s, c; 36 PetscInt beta; 37 PetscReal tf, tcl; 38 } AppCtx; 39 40 PetscErrorCode PostStepFunction(TS ts) 41 { 42 Vec U; 43 PetscReal t; 44 const PetscScalar *u; 45 46 PetscFunctionBegin; 47 PetscCall(TSGetTime(ts, &t)); 48 PetscCall(TSGetSolution(ts, &U)); 49 PetscCall(VecGetArrayRead(U, &u)); 50 PetscCall(PetscPrintf(PETSC_COMM_SELF, "delta(%3.2f) = %8.7f\n", (double)t, (double)u[0])); 51 PetscCall(VecRestoreArrayRead(U, &u)); 52 PetscFunctionReturn(0); 53 } 54 55 /* 56 Defines the ODE passed to the ODE solver 57 */ 58 static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec U, Vec F, AppCtx *ctx) 59 { 60 PetscScalar *f, Pmax; 61 const PetscScalar *u; 62 63 PetscFunctionBegin; 64 /* The next three lines allow us to access the entries of the vectors directly */ 65 PetscCall(VecGetArrayRead(U, &u)); 66 PetscCall(VecGetArray(F, &f)); 67 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 */ 68 else Pmax = ctx->Pmax; 69 70 f[0] = ctx->omega_b * (u[1] - ctx->omega_s); 71 f[1] = (-Pmax * PetscSinScalar(u[0]) - ctx->D * (u[1] - ctx->omega_s) + ctx->Pm) * ctx->omega_s / (2.0 * ctx->H); 72 73 PetscCall(VecRestoreArrayRead(U, &u)); 74 PetscCall(VecRestoreArray(F, &f)); 75 PetscFunctionReturn(0); 76 } 77 78 /* 79 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 80 */ 81 static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat A, Mat B, AppCtx *ctx) 82 { 83 PetscInt rowcol[] = {0, 1}; 84 PetscScalar J[2][2], Pmax; 85 const PetscScalar *u; 86 87 PetscFunctionBegin; 88 PetscCall(VecGetArrayRead(U, &u)); 89 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 */ 90 else Pmax = ctx->Pmax; 91 92 J[0][0] = 0; 93 J[0][1] = ctx->omega_b; 94 J[1][1] = -ctx->D * ctx->omega_s / (2.0 * ctx->H); 95 J[1][0] = -Pmax * PetscCosScalar(u[0]) * ctx->omega_s / (2.0 * ctx->H); 96 97 PetscCall(MatSetValues(A, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 98 PetscCall(VecRestoreArrayRead(U, &u)); 99 100 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 101 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 102 if (A != B) { 103 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 104 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 105 } 106 PetscFunctionReturn(0); 107 } 108 109 static PetscErrorCode RHSJacobianP(TS ts, PetscReal t, Vec X, Mat A, void *ctx0) 110 { 111 PetscInt row[] = {0, 1}, col[] = {0}; 112 PetscScalar J[2][1]; 113 AppCtx *ctx = (AppCtx *)ctx0; 114 115 PetscFunctionBeginUser; 116 J[0][0] = 0; 117 J[1][0] = ctx->omega_s / (2.0 * ctx->H); 118 PetscCall(MatSetValues(A, 2, row, 1, col, &J[0][0], INSERT_VALUES)); 119 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 120 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 121 PetscFunctionReturn(0); 122 } 123 124 static PetscErrorCode CostIntegrand(TS ts, PetscReal t, Vec U, Vec R, AppCtx *ctx) 125 { 126 PetscScalar *r; 127 const PetscScalar *u; 128 129 PetscFunctionBegin; 130 PetscCall(VecGetArrayRead(U, &u)); 131 PetscCall(VecGetArray(R, &r)); 132 r[0] = ctx->c * PetscPowScalarInt(PetscMax(0., u[0] - ctx->u_s), ctx->beta); 133 PetscCall(VecRestoreArray(R, &r)); 134 PetscCall(VecRestoreArrayRead(U, &u)); 135 PetscFunctionReturn(0); 136 } 137 138 static PetscErrorCode DRDUJacobianTranspose(TS ts, PetscReal t, Vec U, Mat DRDU, Mat B, AppCtx *ctx) 139 { 140 PetscScalar ru[1]; 141 const PetscScalar *u; 142 PetscInt row[] = {0}, col[] = {0}; 143 144 PetscFunctionBegin; 145 PetscCall(VecGetArrayRead(U, &u)); 146 ru[0] = ctx->c * ctx->beta * PetscPowScalarInt(PetscMax(0., u[0] - ctx->u_s), ctx->beta - 1); 147 PetscCall(VecRestoreArrayRead(U, &u)); 148 PetscCall(MatSetValues(DRDU, 1, row, 1, col, ru, INSERT_VALUES)); 149 PetscCall(MatAssemblyBegin(DRDU, MAT_FINAL_ASSEMBLY)); 150 PetscCall(MatAssemblyEnd(DRDU, MAT_FINAL_ASSEMBLY)); 151 PetscFunctionReturn(0); 152 } 153 154 static PetscErrorCode DRDPJacobianTranspose(TS ts, PetscReal t, Vec U, Mat DRDP, AppCtx *ctx) 155 { 156 PetscFunctionBegin; 157 PetscCall(MatZeroEntries(DRDP)); 158 PetscCall(MatAssemblyBegin(DRDP, MAT_FINAL_ASSEMBLY)); 159 PetscCall(MatAssemblyEnd(DRDP, MAT_FINAL_ASSEMBLY)); 160 PetscFunctionReturn(0); 161 } 162 163 PetscErrorCode ComputeSensiP(Vec lambda, Vec mu, AppCtx *ctx) 164 { 165 PetscScalar sensip; 166 const PetscScalar *x, *y; 167 168 PetscFunctionBegin; 169 PetscCall(VecGetArrayRead(lambda, &x)); 170 PetscCall(VecGetArrayRead(mu, &y)); 171 sensip = 1. / PetscSqrtScalar(1. - (ctx->Pm / ctx->Pmax) * (ctx->Pm / ctx->Pmax)) / ctx->Pmax * x[0] + y[0]; 172 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n sensitivity wrt parameter pm: %.7f \n", (double)sensip)); 173 PetscCall(VecRestoreArrayRead(lambda, &x)); 174 PetscCall(VecRestoreArrayRead(mu, &y)); 175 PetscFunctionReturn(0); 176 } 177 178 int main(int argc, char **argv) 179 { 180 TS ts, quadts; /* ODE integrator */ 181 Vec U; /* solution will be stored here */ 182 Mat A; /* Jacobian matrix */ 183 Mat Jacp; /* Jacobian matrix */ 184 Mat DRDU, DRDP; 185 PetscMPIInt size; 186 PetscInt n = 2; 187 AppCtx ctx; 188 PetscScalar *u; 189 PetscReal du[2] = {0.0, 0.0}; 190 PetscBool ensemble = PETSC_FALSE, flg1, flg2; 191 PetscReal ftime; 192 PetscInt steps; 193 PetscScalar *x_ptr, *y_ptr; 194 Vec lambda[1], q, mu[1]; 195 196 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 197 Initialize program 198 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 199 PetscFunctionBeginUser; 200 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 201 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 202 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 203 204 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 205 Create necessary matrix and vectors 206 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 207 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 208 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 209 PetscCall(MatSetType(A, MATDENSE)); 210 PetscCall(MatSetFromOptions(A)); 211 PetscCall(MatSetUp(A)); 212 213 PetscCall(MatCreateVecs(A, &U, NULL)); 214 215 PetscCall(MatCreate(PETSC_COMM_WORLD, &Jacp)); 216 PetscCall(MatSetSizes(Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1)); 217 PetscCall(MatSetFromOptions(Jacp)); 218 PetscCall(MatSetUp(Jacp)); 219 220 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &DRDP)); 221 PetscCall(MatSetUp(DRDP)); 222 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 2, NULL, &DRDU)); 223 PetscCall(MatSetUp(DRDU)); 224 225 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 226 Set runtime options 227 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 228 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", ""); 229 { 230 ctx.beta = 2; 231 ctx.c = 10000.0; 232 ctx.u_s = 1.0; 233 ctx.omega_s = 1.0; 234 ctx.omega_b = 120.0 * PETSC_PI; 235 ctx.H = 5.0; 236 PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL)); 237 ctx.D = 5.0; 238 PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL)); 239 ctx.E = 1.1378; 240 ctx.V = 1.0; 241 ctx.X = 0.545; 242 ctx.Pmax = ctx.E * ctx.V / ctx.X; 243 PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL)); 244 ctx.Pm = 1.1; 245 PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL)); 246 ctx.tf = 0.1; 247 ctx.tcl = 0.2; 248 PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL)); 249 PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL)); 250 PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL)); 251 if (ensemble) { 252 ctx.tf = -1; 253 ctx.tcl = -1; 254 } 255 256 PetscCall(VecGetArray(U, &u)); 257 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); 258 u[1] = 1.0; 259 PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1)); 260 n = 2; 261 PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2)); 262 u[0] += du[0]; 263 u[1] += du[1]; 264 PetscCall(VecRestoreArray(U, &u)); 265 if (flg1 || flg2) { 266 ctx.tf = -1; 267 ctx.tcl = -1; 268 } 269 } 270 PetscOptionsEnd(); 271 272 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 273 Create timestepping solver context 274 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 275 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 276 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 277 PetscCall(TSSetEquationType(ts, TS_EQ_ODE_EXPLICIT)); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */ 278 PetscCall(TSSetType(ts, TSRK)); 279 PetscCall(TSSetRHSFunction(ts, NULL, (TSRHSFunction)RHSFunction, &ctx)); 280 PetscCall(TSSetRHSJacobian(ts, A, A, (TSRHSJacobian)RHSJacobian, &ctx)); 281 PetscCall(TSCreateQuadratureTS(ts, PETSC_TRUE, &quadts)); 282 PetscCall(TSSetRHSFunction(quadts, NULL, (TSRHSFunction)CostIntegrand, &ctx)); 283 PetscCall(TSSetRHSJacobian(quadts, DRDU, DRDU, (TSRHSJacobian)DRDUJacobianTranspose, &ctx)); 284 PetscCall(TSSetRHSJacobianP(quadts, DRDP, (TSRHSJacobianP)DRDPJacobianTranspose, &ctx)); 285 286 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 287 Set initial conditions 288 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 289 PetscCall(TSSetSolution(ts, U)); 290 291 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 292 Save trajectory of solution so that TSAdjointSolve() may be used 293 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 294 PetscCall(TSSetSaveTrajectory(ts)); 295 296 PetscCall(MatCreateVecs(A, &lambda[0], NULL)); 297 /* Set initial conditions for the adjoint integration */ 298 PetscCall(VecGetArray(lambda[0], &y_ptr)); 299 y_ptr[0] = 0.0; 300 y_ptr[1] = 0.0; 301 PetscCall(VecRestoreArray(lambda[0], &y_ptr)); 302 303 PetscCall(MatCreateVecs(Jacp, &mu[0], NULL)); 304 PetscCall(VecGetArray(mu[0], &x_ptr)); 305 x_ptr[0] = -1.0; 306 PetscCall(VecRestoreArray(mu[0], &x_ptr)); 307 PetscCall(TSSetCostGradients(ts, 1, lambda, mu)); 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 /* Set RHS JacobianP */ 352 PetscCall(TSSetRHSJacobianP(ts, Jacp, RHSJacobianP, &ctx)); 353 354 PetscCall(TSAdjointSolve(ts)); 355 356 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n sensitivity wrt initial conditions: d[Psi(tf)]/d[phi0] d[Psi(tf)]/d[omega0]\n")); 357 PetscCall(VecView(lambda[0], PETSC_VIEWER_STDOUT_WORLD)); 358 PetscCall(VecView(mu[0], PETSC_VIEWER_STDOUT_WORLD)); 359 PetscCall(TSGetCostIntegral(ts, &q)); 360 PetscCall(VecView(q, PETSC_VIEWER_STDOUT_WORLD)); 361 PetscCall(VecGetArray(q, &x_ptr)); 362 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n cost function=%g\n", (double)(x_ptr[0] - ctx.Pm))); 363 PetscCall(VecRestoreArray(q, &x_ptr)); 364 365 PetscCall(ComputeSensiP(lambda[0], mu[0], &ctx)); 366 367 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 368 Free work space. All PETSc objects should be destroyed when they are no longer needed. 369 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 370 PetscCall(MatDestroy(&A)); 371 PetscCall(MatDestroy(&Jacp)); 372 PetscCall(MatDestroy(&DRDU)); 373 PetscCall(MatDestroy(&DRDP)); 374 PetscCall(VecDestroy(&U)); 375 PetscCall(VecDestroy(&lambda[0])); 376 PetscCall(VecDestroy(&mu[0])); 377 PetscCall(TSDestroy(&ts)); 378 PetscCall(PetscFinalize()); 379 return 0; 380 } 381 382 /*TEST 383 384 build: 385 requires: !complex 386 387 test: 388 args: -viewer_binary_skip_info -ts_adapt_type none 389 390 TEST*/ 391