Date: 2022-03-04T17:39:43+00:00

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:   PetscErrorCode    ierr;
     45:   const PetscScalar *u;
     46:   PetscScalar       *f,Pmax;

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

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

     58:   VecRestoreArrayRead(U,&u);
     59:   VecRestoreArray(F,&f);
     60:   return(0);
     61: }

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

     74:   VecGetArrayRead(U,&u);
     75:   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 */
     76:   else Pmax = ctx->Pmax;

     78:   J[0][0] = 0;                                    J[0][1] = ctx->omega_b;
     79:   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);

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

     84:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     85:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     86:   if (A != B) {
     87:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     88:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
     89:   }
     90:   return(0);
     91: }

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

    106:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    107:      Initialize program
    108:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    109:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
    110:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
    111:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

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

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

    124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    125:     Set runtime options
    126:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    127:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
    128:   {
    129:     ctx.omega_b = 1.0;
    130:     ctx.omega_s = 2.0*PETSC_PI*60.0;
    131:     ctx.H       = 5.0;
    132:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
    133:     ctx.D       = 5.0;
    134:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
    135:     ctx.E       = 1.1378;
    136:     ctx.V       = 1.0;
    137:     ctx.X       = 0.545;
    138:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
    139:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
    140:     ctx.Pm      = 0.9;
    141:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
    142:     ctx.tf      = 1.0;
    143:     ctx.tcl     = 1.05;
    144:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
    145:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
    146:     PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
    147:     if (ensemble) {
    148:       ctx.tf      = -1;
    149:       ctx.tcl     = -1;
    150:     }

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

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

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

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

    190:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    191:      Solve nonlinear system
    192:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    193:   if (ensemble) {
    194:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
    195:       VecGetArray(U,&u);
    196:       u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
    197:       u[1] = ctx.omega_s;
    198:       u[0] += du[0];
    199:       u[1] += du[1];
    200:       VecRestoreArray(U,&u);
    201:       TSSetTimeStep(ts,.01);
    202:       TSSolve(ts,U);
    203:     }
    204:   } else {
    205:     TSSolve(ts,U);
    206:   }
    207:   VecView(U,PETSC_VIEWER_STDOUT_WORLD);
    208:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    209:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    210:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    211:   MatDestroy(&A);
    212:   VecDestroy(&U);
    213:   TSDestroy(&ts);
    214:   PetscFinalize();
    215:   return ierr;
    216: }

    218: /*TEST

    220:    build:
    221:      requires: !complex

    223:    test:

    225: TEST*/