Actual source code: ex2.c

      1: static char help[] = "Basic equation for generator stability analysis.\n";

      3: /*F

      5: \begin{eqnarray}
      6:                  \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - \frac{EV}{X} \sin(\theta) -D(\omega - \omega_s)\\
      7:                  \frac{d \theta}{dt} = \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 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: */

     31: #include <petscts.h>

     33: typedef struct {
     34:   PetscScalar H, D, omega_s, Pmax, Pm, E, V, X;
     35:   PetscReal   tf, tcl;
     36: } AppCtx;

     38: /*
     39:      Defines the ODE passed to the ODE solver
     40: */
     41: static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, AppCtx *ctx)
     42: {
     43:   PetscScalar       *f, Pmax;
     44:   const PetscScalar *u, *udot;

     46:   PetscFunctionBegin;
     47:   /*  The next three lines allow us to access the entries of the vectors directly */
     48:   PetscCall(VecGetArrayRead(U, &u));
     49:   PetscCall(VecGetArrayRead(Udot, &udot));
     50:   PetscCall(VecGetArray(F, &f));
     51:   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 */
     52:   else if (t >= ctx->tcl) Pmax = ctx->E / 0.745;
     53:   else Pmax = ctx->Pmax;
     54:   f[0] = udot[0] - ctx->omega_s * (u[1] - 1.0);
     55:   f[1] = 2.0 * ctx->H * udot[1] + Pmax * PetscSinScalar(u[0]) + ctx->D * (u[1] - 1.0) - ctx->Pm;

     57:   PetscCall(VecRestoreArrayRead(U, &u));
     58:   PetscCall(VecRestoreArrayRead(Udot, &udot));
     59:   PetscCall(VecRestoreArray(F, &f));
     60:   PetscFunctionReturn(PETSC_SUCCESS);
     61: }

     63: /*
     64:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
     65: */
     66: static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, AppCtx *ctx)
     67: {
     68:   PetscInt           rowcol[] = {0, 1};
     69:   PetscScalar        J[2][2], Pmax;
     70:   const PetscScalar *u, *udot;

     72:   PetscFunctionBegin;
     73:   PetscCall(VecGetArrayRead(U, &u));
     74:   PetscCall(VecGetArrayRead(Udot, &udot));
     75:   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 */
     76:   else if (t >= ctx->tcl) Pmax = ctx->E / 0.745;
     77:   else Pmax = ctx->Pmax;

     79:   J[0][0] = a;
     80:   J[0][1] = -ctx->omega_s;
     81:   J[1][1] = 2.0 * ctx->H * a + ctx->D;
     82:   J[1][0] = Pmax * PetscCosScalar(u[0]);

     84:   PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
     85:   PetscCall(VecRestoreArrayRead(U, &u));
     86:   PetscCall(VecRestoreArrayRead(Udot, &udot));

     88:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
     89:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
     90:   if (A != B) {
     91:     PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
     92:     PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
     93:   }
     94:   PetscFunctionReturn(PETSC_SUCCESS);
     95: }

     97: PetscErrorCode PostStep(TS ts)
     98: {
     99:   Vec       X;
    100:   PetscReal t;

    102:   PetscFunctionBegin;
    103:   PetscCall(TSGetTime(ts, &t));
    104:   if (t >= .2) {
    105:     PetscCall(TSGetSolution(ts, &X));
    106:     PetscCall(VecView(X, PETSC_VIEWER_STDOUT_WORLD));
    107:     exit(0);
    108:     /* results in initial conditions after fault of -u 0.496792,1.00932 */
    109:   }
    110:   PetscFunctionReturn(PETSC_SUCCESS);
    111: }

    113: int main(int argc, char **argv)
    114: {
    115:   TS           ts; /* ODE integrator */
    116:   Vec          U;  /* solution will be stored here */
    117:   Mat          A;  /* Jacobian matrix */
    118:   PetscMPIInt  size;
    119:   PetscInt     n = 2;
    120:   AppCtx       ctx;
    121:   PetscScalar *u;
    122:   PetscReal    du[2]    = {0.0, 0.0};
    123:   PetscBool    ensemble = PETSC_FALSE, flg1, flg2;

    125:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    126:      Initialize program
    127:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    128:   PetscFunctionBeginUser;
    129:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
    130:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
    131:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");

    133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    134:     Create necessary matrix and vectors
    135:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    136:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
    137:   PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
    138:   PetscCall(MatSetType(A, MATDENSE));
    139:   PetscCall(MatSetFromOptions(A));
    140:   PetscCall(MatSetUp(A));

    142:   PetscCall(MatCreateVecs(A, &U, NULL));

    144:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    145:     Set runtime options
    146:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    147:   PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", "");
    148:   {
    149:     ctx.omega_s = 2.0 * PETSC_PI * 60.0;
    150:     ctx.H       = 5.0;
    151:     PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL));
    152:     ctx.D = 5.0;
    153:     PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL));
    154:     ctx.E    = 1.1378;
    155:     ctx.V    = 1.0;
    156:     ctx.X    = 0.545;
    157:     ctx.Pmax = ctx.E * ctx.V / ctx.X;
    158:     PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL));
    159:     ctx.Pm = 0.9;
    160:     PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL));
    161:     ctx.tf  = 1.0;
    162:     ctx.tcl = 1.05;
    163:     PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL));
    164:     PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL));
    165:     PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL));
    166:     if (ensemble) {
    167:       ctx.tf  = -1;
    168:       ctx.tcl = -1;
    169:     }

    171:     PetscCall(VecGetArray(U, &u));
    172:     u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
    173:     u[1] = 1.0;
    174:     PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1));
    175:     n = 2;
    176:     PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2));
    177:     u[0] += du[0];
    178:     u[1] += du[1];
    179:     PetscCall(VecRestoreArray(U, &u));
    180:     if (flg1 || flg2) {
    181:       ctx.tf  = -1;
    182:       ctx.tcl = -1;
    183:     }
    184:   }
    185:   PetscOptionsEnd();

    187:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    188:      Create timestepping solver context
    189:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    190:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
    191:   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
    192:   PetscCall(TSSetType(ts, TSROSW));
    193:   PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, &ctx));
    194:   PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, &ctx));

    196:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    197:      Set initial conditions
    198:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    199:   PetscCall(TSSetSolution(ts, U));

    201:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    202:      Set solver options
    203:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    204:   PetscCall(TSSetMaxTime(ts, 35.0));
    205:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
    206:   PetscCall(TSSetTimeStep(ts, .01));
    207:   PetscCall(TSSetFromOptions(ts));
    208:   /* PetscCall(TSSetPostStep(ts,PostStep));  */

    210:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    211:      Solve nonlinear system
    212:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    213:   if (ensemble) {
    214:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
    215:       PetscCall(VecGetArray(U, &u));
    216:       u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
    217:       u[1] = ctx.omega_s;
    218:       u[0] += du[0];
    219:       u[1] += du[1];
    220:       PetscCall(VecRestoreArray(U, &u));
    221:       PetscCall(TSSetTimeStep(ts, .01));
    222:       PetscCall(TSSolve(ts, U));
    223:     }
    224:   } else {
    225:     PetscCall(TSSolve(ts, U));
    226:   }
    227:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    228:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    229:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    230:   PetscCall(MatDestroy(&A));
    231:   PetscCall(VecDestroy(&U));
    232:   PetscCall(TSDestroy(&ts));
    233:   PetscCall(PetscFinalize());
    234:   return 0;
    235: }

    237: /*TEST

    239:    build:
    240:       requires: !complex

    242:    test:
    243:       args: -nox -ts_dt 10
    244:       output_file: output/empty.out

    246: TEST*/