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

     25: /*
     26:    Include "petscts.h" so that we can use TS solvers.  Note that this
     27:    file automatically includes:
     28:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     29:      petscmat.h - matrices
     30:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     31:      petscviewer.h - viewers               petscpc.h  - preconditioners
     32:      petscksp.h   - linear solvers
     33: */

     35: #include <petscts.h>

     37: typedef struct {
     38:   PetscScalar H,D,omega_b,omega_s,Pmax,Pm,E,V,X;
     39:   PetscReal   tf,tcl;
     40: } AppCtx;

     42: /*
     43:      Defines the ODE passed to the ODE solver
     44: */
     45: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
     46: {
     47:   PetscErrorCode    ierr;
     48:   const PetscScalar *u;
     49:   PetscScalar       *f,Pmax;

     52:   /*  The next three lines allow us to access the entries of the vectors directly */
     53:   VecGetArrayRead(U,&u);
     54:   VecGetArray(F,&f);
     55:   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 */
     56:   else Pmax = ctx->Pmax;

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

     61:   VecRestoreArrayRead(U,&u);
     62:   VecRestoreArray(F,&f);
     63:   return(0);
     64: }

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

     77:   VecGetArrayRead(U,&u);
     78:   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 */
     79:   else Pmax = ctx->Pmax;

     81:   J[0][0] = 0;                                    J[0][1] = ctx->omega_b;
     82:   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);

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

     87:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     88:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     89:   if (A != B) {
     90:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     91:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
     92:   }
     93:   return(0);
     94: }

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

    109:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    110:      Initialize program
    111:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    112:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
    113:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
    114:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

    116:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    117:     Create necessary matrix and vectors
    118:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    119:   MatCreate(PETSC_COMM_WORLD,&A);
    120:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
    121:   MatSetType(A,MATDENSE);
    122:   MatSetFromOptions(A);
    123:   MatSetUp(A);

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

    127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    128:     Set runtime options
    129:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    130:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
    131:   {
    132:     ctx.omega_b = 1.0;
    133:     ctx.omega_s = 2.0*PETSC_PI*60.0;
    134:     ctx.H       = 5.0;
    135:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
    136:     ctx.D       = 5.0;
    137:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
    138:     ctx.E       = 1.1378;
    139:     ctx.V       = 1.0;
    140:     ctx.X       = 0.545;
    141:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
    142:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
    143:     ctx.Pm      = 0.9;
    144:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
    145:     ctx.tf      = 1.0;
    146:     ctx.tcl     = 1.05;
    147:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
    148:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
    149:     PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
    150:     if (ensemble) {
    151:       ctx.tf      = -1;
    152:       ctx.tcl     = -1;
    153:     }

    155:     VecGetArray(U,&u);
    156:     u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
    157:     u[1] = 1.0;
    158:     PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);
    159:     n    = 2;
    160:     PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);
    161:     u[0] += du[0];
    162:     u[1] += du[1];
    163:     VecRestoreArray(U,&u);
    164:     if (flg1 || flg2) {
    165:       ctx.tf      = -1;
    166:       ctx.tcl     = -1;
    167:     }
    168:   }
    169:   PetscOptionsEnd();

    171:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    172:      Create timestepping solver context
    173:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    174:   TSCreate(PETSC_COMM_WORLD,&ts);
    175:   TSSetProblemType(ts,TS_NONLINEAR);
    176:   TSSetType(ts,TSTHETA);
    177:   TSSetRHSFunction(ts,NULL,(TSRHSFunction)RHSFunction,&ctx);
    178:   TSSetRHSJacobian(ts,A,A,(TSRHSJacobian)RHSJacobian,&ctx);

    180:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    181:      Set initial conditions
    182:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    183:   TSSetSolution(ts,U);

    185:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    186:      Set solver options
    187:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    188:   TSSetMaxTime(ts,35.0);
    189:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
    190:   TSSetTimeStep(ts,.01);
    191:   TSSetFromOptions(ts);

    193:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    194:      Solve nonlinear system
    195:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    196:   if (ensemble) {
    197:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
    198:       VecGetArray(U,&u);
    199:       u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
    200:       u[1] = ctx.omega_s;
    201:       u[0] += du[0];
    202:       u[1] += du[1];
    203:       VecRestoreArray(U,&u);
    204:       TSSetTimeStep(ts,.01);
    205:       TSSolve(ts,U);
    206:     }
    207:   } else {
    208:     TSSolve(ts,U);
    209:   }
    210:   VecView(U,PETSC_VIEWER_STDOUT_WORLD);
    211:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    212:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    213:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    214:   MatDestroy(&A);
    215:   VecDestroy(&U);
    216:   TSDestroy(&ts);
    217:   PetscFinalize();
    218:   return ierr;
    219: }

    222: /*TEST

    224:    build:
    225:      requires: !complex

    227:    test:

    229: TEST*/