Actual source code: ex9.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
./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
Fault at .1 seconds
./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
Initial conditions same as when fault is ended
./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

     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>

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

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

     47:   /*  The next three lines allow us to access the entries of the vectors directly */
     48:   VecGetArrayRead(U,&u);
     49:   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:   VecRestoreArrayRead(U,&u);
     57:   VecRestoreArray(F,&f);
     58:   return 0;
     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:   VecGetArrayRead(U,&u);
     71:   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 */
     72:   else Pmax = ctx->Pmax;

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

     77:   MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
     78:   VecRestoreArrayRead(U,&u);

     80:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     81:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     82:   if (A != B) {
     83:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     84:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
     85:   }
     86:   return 0;
     87: }

     89: int main(int argc,char **argv)
     90: {
     91:   TS             ts;            /* ODE integrator */
     92:   Vec            U;             /* solution will be stored here */
     93:   Mat            A;             /* Jacobian matrix */
     95:   PetscMPIInt    size;
     96:   PetscInt       n = 2;
     97:   AppCtx         ctx;
     98:   PetscScalar    *u;
     99:   PetscReal      du[2] = {0.0,0.0};
    100:   PetscBool      ensemble = PETSC_FALSE,flg1,flg2;

    102:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    103:      Initialize program
    104:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    105:   PetscInitialize(&argc,&argv,(char*)0,help);
    106:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

    109:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    110:     Create necessary matrix and vectors
    111:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    112:   MatCreate(PETSC_COMM_WORLD,&A);
    113:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
    114:   MatSetType(A,MATDENSE);
    115:   MatSetFromOptions(A);
    116:   MatSetUp(A);

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

    120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    121:     Set runtime options
    122:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    123:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
    124:   {
    125:     ctx.omega_b = 1.0;
    126:     ctx.omega_s = 2.0*PETSC_PI*60.0;
    127:     ctx.H       = 5.0;
    128:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
    129:     ctx.D       = 5.0;
    130:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
    131:     ctx.E       = 1.1378;
    132:     ctx.V       = 1.0;
    133:     ctx.X       = 0.545;
    134:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
    135:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
    136:     ctx.Pm      = 0.9;
    137:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
    138:     ctx.tf      = 1.0;
    139:     ctx.tcl     = 1.05;
    140:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
    141:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
    142:     PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
    143:     if (ensemble) {
    144:       ctx.tf      = -1;
    145:       ctx.tcl     = -1;
    146:     }

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

    164:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    165:      Create timestepping solver context
    166:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    167:   TSCreate(PETSC_COMM_WORLD,&ts);
    168:   TSSetProblemType(ts,TS_NONLINEAR);
    169:   TSSetType(ts,TSTHETA);
    170:   TSSetRHSFunction(ts,NULL,(TSRHSFunction)RHSFunction,&ctx);
    171:   TSSetRHSJacobian(ts,A,A,(TSRHSJacobian)RHSJacobian,&ctx);

    173:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    174:      Set initial conditions
    175:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    176:   TSSetSolution(ts,U);

    178:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    179:      Set solver options
    180:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    181:   TSSetMaxTime(ts,35.0);
    182:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
    183:   TSSetTimeStep(ts,.01);
    184:   TSSetFromOptions(ts);

    186:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    187:      Solve nonlinear system
    188:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    189:   if (ensemble) {
    190:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
    191:       VecGetArray(U,&u);
    192:       u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
    193:       u[1] = ctx.omega_s;
    194:       u[0] += du[0];
    195:       u[1] += du[1];
    196:       VecRestoreArray(U,&u);
    197:       TSSetTimeStep(ts,.01);
    198:       TSSolve(ts,U);
    199:     }
    200:   } else {
    201:     TSSolve(ts,U);
    202:   }
    203:   VecView(U,PETSC_VIEWER_STDOUT_WORLD);
    204:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    205:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    206:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    207:   MatDestroy(&A);
    208:   VecDestroy(&U);
    209:   TSDestroy(&ts);
    210:   PetscFinalize();
    211:   return 0;
    212: }

    214: /*TEST

    216:    build:
    217:      requires: !complex

    219:    test:

    221: TEST*/