Date: 2022-03-31T04:48:51+00:00

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: */
     31: /*T

     33: T*/

     35: #include <petscts.h>
     36: #include "ex3.h"

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

     53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     54:      Initialize program
     55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     56:   PetscInitialize(&argc,&argv,(char*)0,help);
     57:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

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

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

     71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     72:     Set runtime options
     73:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     74:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
     75:   {
     76:     ctx.omega_b = 1.0;
     77:     ctx.omega_s = 2.0*PETSC_PI*60.0;
     78:     ctx.H       = 5.0;
     79:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
     80:     ctx.D       = 5.0;
     81:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
     82:     ctx.E       = 1.1378;
     83:     ctx.V       = 1.0;
     84:     ctx.X       = 0.545;
     85:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
     86:     ctx.Pmax_ini = ctx.Pmax;
     87:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
     88:     ctx.Pm      = 0.9;
     89:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
     90:     ctx.tf      = 1.0;
     91:     ctx.tcl     = 1.05;
     92:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
     93:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
     94:     PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
     95:     if (ensemble) {
     96:       ctx.tf      = -1;
     97:       ctx.tcl     = -1;
     98:     }

    100:     VecGetArray(U,&u);
    101:     u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
    102:     u[1] = 1.0;
    103:     PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);
    104:     n    = 2;
    105:     PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);
    106:     u[0] += du[0];
    107:     u[1] += du[1];
    108:     VecRestoreArray(U,&u);
    109:     if (flg1 || flg2) {
    110:       ctx.tf      = -1;
    111:       ctx.tcl     = -1;
    112:     }
    113:   }
    114:   PetscOptionsEnd();

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

    127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    128:      Set initial conditions
    129:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    130:   TSSetSolution(ts,U);

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

    140:   direction[0] = direction[1] = 1;
    141:   terminate[0] = terminate[1] = PETSC_FALSE;

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

    145:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    146:      Solve nonlinear system
    147:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    148:   if (ensemble) {
    149:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
    150:       VecGetArray(U,&u);
    151:       u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
    152:       u[1] = ctx.omega_s;
    153:       u[0] += du[0];
    154:       u[1] += du[1];
    155:       VecRestoreArray(U,&u);
    156:       TSSetTimeStep(ts,.01);
    157:       TSSolve(ts,U);
    158:     }
    159:   } else {
    160:     TSSolve(ts,U);
    161:   }
    162:   VecView(U,PETSC_VIEWER_STDOUT_WORLD);
    163:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    164:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    165:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    166:   MatDestroy(&A);
    167:   VecDestroy(&U);
    168:   TSDestroy(&ts);
    169:   PetscFinalize();
    170:   return 0;
    171: }

    173: /*TEST

    175:    build:
    176:      requires: !complex !single

    178:    test:
    179:       args: -nox

    181: TEST*/