Actual source code: ex9.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 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_b, 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 RHSFunction(TS ts, PetscReal t, Vec U, Vec F, AppCtx *ctx)
     42: {
     43:   const PetscScalar *u;
     44:   PetscScalar       *f, Pmax;

     46:   PetscFunctionBegin;
     47:   /*  The next three lines allow us to access the entries of the vectors directly */
     48:   PetscCall(VecGetArrayRead(U, &u));
     49:   PetscCall(VecGetArray(F, &f));
     50:   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 */
     51:   else Pmax = ctx->Pmax;

     53:   f[0] = ctx->omega_b * (u[1] - ctx->omega_s);
     54:   f[1] = (-Pmax * PetscSinScalar(u[0]) - ctx->D * (u[1] - ctx->omega_s) + ctx->Pm) * ctx->omega_s / (2.0 * ctx->H);

     56:   PetscCall(VecRestoreArrayRead(U, &u));
     57:   PetscCall(VecRestoreArray(F, &f));
     58:   PetscFunctionReturn(PETSC_SUCCESS);
     59: }

     61: /*
     62:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
     63: */
     64: static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat A, Mat B, AppCtx *ctx)
     65: {
     66:   PetscInt           rowcol[] = {0, 1};
     67:   PetscScalar        J[2][2], Pmax;
     68:   const PetscScalar *u;

     70:   PetscFunctionBegin;
     71:   PetscCall(VecGetArrayRead(U, &u));
     72:   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 */
     73:   else Pmax = ctx->Pmax;

     75:   J[0][0] = 0;
     76:   J[0][1] = ctx->omega_b;
     77:   J[1][1] = -ctx->D * ctx->omega_s / (2.0 * ctx->H);
     78:   J[1][0] = -Pmax * PetscCosScalar(u[0]) * ctx->omega_s / (2.0 * ctx->H);

     80:   PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
     81:   PetscCall(VecRestoreArrayRead(U, &u));

     83:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
     84:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
     85:   if (A != B) {
     86:     PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
     87:     PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
     88:   }
     89:   PetscFunctionReturn(PETSC_SUCCESS);
     90: }

     92: int main(int argc, char **argv)
     93: {
     94:   TS           ts; /* ODE integrator */
     95:   Vec          U;  /* solution will be stored here */
     96:   Mat          A;  /* Jacobian matrix */
     97:   PetscMPIInt  size;
     98:   PetscInt     n = 2;
     99:   AppCtx       ctx;
    100:   PetscScalar *u;
    101:   PetscReal    du[2]    = {0.0, 0.0};
    102:   PetscBool    ensemble = PETSC_FALSE, flg1, flg2;

    104:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    105:      Initialize program
    106:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    107:   PetscFunctionBeginUser;
    108:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
    109:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
    110:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");

    112:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    113:     Create necessary matrix and vectors
    114:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    115:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
    116:   PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
    117:   PetscCall(MatSetType(A, MATDENSE));
    118:   PetscCall(MatSetFromOptions(A));
    119:   PetscCall(MatSetUp(A));

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

    123:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    124:     Set runtime options
    125:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    126:   PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", "");
    127:   {
    128:     ctx.omega_b = 1.0;
    129:     ctx.omega_s = 2.0 * PETSC_PI * 60.0;
    130:     ctx.H       = 5.0;
    131:     PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL));
    132:     ctx.D = 5.0;
    133:     PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL));
    134:     ctx.E    = 1.1378;
    135:     ctx.V    = 1.0;
    136:     ctx.X    = 0.545;
    137:     ctx.Pmax = ctx.E * ctx.V / ctx.X;
    138:     PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL));
    139:     ctx.Pm = 0.9;
    140:     PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL));
    141:     ctx.tf  = 1.0;
    142:     ctx.tcl = 1.05;
    143:     PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL));
    144:     PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL));
    145:     PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL));
    146:     if (ensemble) {
    147:       ctx.tf  = -1;
    148:       ctx.tcl = -1;
    149:     }

    151:     PetscCall(VecGetArray(U, &u));
    152:     u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
    153:     u[1] = 1.0;
    154:     PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1));
    155:     n = 2;
    156:     PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2));
    157:     u[0] += du[0];
    158:     u[1] += du[1];
    159:     PetscCall(VecRestoreArray(U, &u));
    160:     if (flg1 || flg2) {
    161:       ctx.tf  = -1;
    162:       ctx.tcl = -1;
    163:     }
    164:   }
    165:   PetscOptionsEnd();

    167:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    168:      Create timestepping solver context
    169:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    170:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
    171:   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
    172:   PetscCall(TSSetType(ts, TSTHETA));
    173:   PetscCall(TSSetRHSFunction(ts, NULL, (TSRHSFunctionFn *)RHSFunction, &ctx));
    174:   PetscCall(TSSetRHSJacobian(ts, A, A, (TSRHSJacobianFn *)RHSJacobian, &ctx));

    176:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    177:      Set initial conditions
    178:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    179:   PetscCall(TSSetSolution(ts, U));

    181:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    182:      Set solver options
    183:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    184:   PetscCall(TSSetMaxTime(ts, 35.0));
    185:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
    186:   PetscCall(TSSetTimeStep(ts, .01));
    187:   PetscCall(TSSetFromOptions(ts));

    189:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    190:      Solve nonlinear system
    191:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    192:   if (ensemble) {
    193:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
    194:       PetscCall(VecGetArray(U, &u));
    195:       u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
    196:       u[1] = ctx.omega_s;
    197:       u[0] += du[0];
    198:       u[1] += du[1];
    199:       PetscCall(VecRestoreArray(U, &u));
    200:       PetscCall(TSSetTimeStep(ts, .01));
    201:       PetscCall(TSSolve(ts, U));
    202:     }
    203:   } else {
    204:     PetscCall(TSSolve(ts, U));
    205:   }
    206:   PetscCall(VecView(U, PETSC_VIEWER_STDOUT_WORLD));
    207:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    208:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    209:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    210:   PetscCall(MatDestroy(&A));
    211:   PetscCall(VecDestroy(&U));
    212:   PetscCall(TSDestroy(&ts));
    213:   PetscCall(PetscFinalize());
    214:   return 0;
    215: }

    217: /*TEST

    219:    build:
    220:      requires: !complex

    222:    test:

    224: TEST*/