Actual source code: ex3.c

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

\begin{eqnarray}
\frac{d \theta}{dt} = \omega_b (\omega - \omega_s)
\frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - P_max \sin(\theta) -D(\omega - \omega_s)\\
\end{eqnarray}
Ensemble of initial conditions
./ex3 -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
Fault at .1 seconds
./ex3 -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
Initial conditions same as when fault is ended
./ex3 -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

     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: */

     32: #include <petscts.h>
     33: #include "ex3.h"

     35: int main(int argc,char **argv)
     36: {
     37:   TS             ts;            /* ODE integrator */
     38:   Vec            U;             /* solution will be stored here */
     39:   Mat            A;             /* Jacobian matrix */
     41:   PetscMPIInt    size;
     42:   PetscInt       n = 2;
     43:   AppCtx         ctx;
     44:   PetscScalar    *u;
     45:   PetscReal      du[2] = {0.0,0.0};
     46:   PetscBool      ensemble = PETSC_FALSE,flg1,flg2;
     47:   PetscInt       direction[2];
     48:   PetscBool      terminate[2];

     50:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     51:      Initialize program
     52:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     53:   PetscInitialize(&argc,&argv,(char*)0,help);
     54:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

     57:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     58:     Create necessary matrix and vectors
     59:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     60:   MatCreate(PETSC_COMM_WORLD,&A);
     61:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
     62:   MatSetType(A,MATDENSE);
     63:   MatSetFromOptions(A);
     64:   MatSetUp(A);

     66:   MatCreateVecs(A,&U,NULL);

     68:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     69:     Set runtime options
     70:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     71:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
     72:   {
     73:     ctx.omega_b = 1.0;
     74:     ctx.omega_s = 2.0*PETSC_PI*60.0;
     75:     ctx.H       = 5.0;
     76:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
     77:     ctx.D       = 5.0;
     78:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
     79:     ctx.E       = 1.1378;
     80:     ctx.V       = 1.0;
     81:     ctx.X       = 0.545;
     82:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
     83:     ctx.Pmax_ini = ctx.Pmax;
     84:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
     85:     ctx.Pm      = 0.9;
     86:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
     87:     ctx.tf      = 1.0;
     88:     ctx.tcl     = 1.05;
     89:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
     90:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
     91:     PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
     92:     if (ensemble) {
     93:       ctx.tf      = -1;
     94:       ctx.tcl     = -1;
     95:     }

     97:     VecGetArray(U,&u);
     98:     u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
     99:     u[1] = 1.0;
    100:     PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);
    101:     n    = 2;
    102:     PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);
    103:     u[0] += du[0];
    104:     u[1] += du[1];
    105:     VecRestoreArray(U,&u);
    106:     if (flg1 || flg2) {
    107:       ctx.tf      = -1;
    108:       ctx.tcl     = -1;
    109:     }
    110:   }
    111:   PetscOptionsEnd();

    113:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    114:      Create timestepping solver context
    115:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    116:   TSCreate(PETSC_COMM_WORLD,&ts);
    117:   TSSetProblemType(ts,TS_NONLINEAR);
    118:   TSSetType(ts,TSTHETA);
    119:   TSSetEquationType(ts,TS_EQ_IMPLICIT);
    120:   TSARKIMEXSetFullyImplicit(ts,PETSC_TRUE);
    121:   TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);
    122:   TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);

    124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    125:      Set initial conditions
    126:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    127:   TSSetSolution(ts,U);

    129:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    130:      Set solver options
    131:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    132:   TSSetMaxTime(ts,35.0);
    133:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
    134:   TSSetTimeStep(ts,.1);
    135:   TSSetFromOptions(ts);

    137:   direction[0] = direction[1] = 1;
    138:   terminate[0] = terminate[1] = PETSC_FALSE;

    140:   TSSetEventHandler(ts,2,direction,terminate,EventFunction,PostEventFunction,(void*)&ctx);

    142:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    143:      Solve nonlinear system
    144:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    145:   if (ensemble) {
    146:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
    147:       VecGetArray(U,&u);
    148:       u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
    149:       u[1] = ctx.omega_s;
    150:       u[0] += du[0];
    151:       u[1] += du[1];
    152:       VecRestoreArray(U,&u);
    153:       TSSetTimeStep(ts,.01);
    154:       TSSolve(ts,U);
    155:     }
    156:   } else {
    157:     TSSolve(ts,U);
    158:   }
    159:   VecView(U,PETSC_VIEWER_STDOUT_WORLD);
    160:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    161:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    162:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    163:   MatDestroy(&A);
    164:   VecDestroy(&U);
    165:   TSDestroy(&ts);
    166:   PetscFinalize();
    167:   return 0;
    168: }

    170: /*TEST

    172:    build:
    173:      requires: !complex !single

    175:    test:
    176:       args: -nox

    178: TEST*/