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

Actual source code: ex3opt_fd.c

      2: static char help[] = "Finds optimal parameter P_m for the generator system while maintaining generator stability.\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}

     13: /*
     14:   Solve the same optimization problem as in ex3opt.c.
     15:   Use finite difference to approximate the gradients.
     16: */
     17: #include <petsctao.h>
     18: #include <petscts.h>
     19: #include "ex3.h"

     21: PetscErrorCode FormFunction(Tao,Vec,PetscReal*,void*);

     23: PetscErrorCode monitor(Tao tao,AppCtx *ctx)
     24: {
     25:   FILE               *fp;
     26:   PetscInt           iterate;
     27:   PetscReal          f,gnorm,cnorm,xdiff;
     28:   Vec                X,G;
     29:   const PetscScalar  *x,*g;
     30:   TaoConvergedReason reason;

     33:   TaoGetSolutionStatus(tao,&iterate,&f,&gnorm,&cnorm,&xdiff,&reason);
     34:   TaoGetSolution(tao,&X);
     35:   TaoGetGradient(tao,&G,NULL,NULL);
     36:   VecGetArrayRead(X,&x);
     37:   VecGetArrayRead(G,&g);
     38:   fp = fopen("ex3opt_fd_conv.out","a");
     39:   PetscFPrintf(PETSC_COMM_WORLD,fp,"%d %g %.12lf %.12lf\n",iterate,gnorm,x[0],g[0]);
     40:   VecRestoreArrayRead(X,&x);
     41:   VecRestoreArrayRead(G,&g);
     42:   fclose(fp);
     43:   return 0;
     44: }

     46: int main(int argc,char **argv)
     47: {
     48:   Vec                p;
     49:   PetscScalar        *x_ptr;
     50:   PetscErrorCode     ierr;
     51:   PetscMPIInt        size;
     52:   AppCtx             ctx;
     53:   Vec                lowerb,upperb;
     54:   Tao                tao;
     55:   KSP                ksp;
     56:   PC                 pc;
     57:   PetscBool          printtofile;
     58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     59:      Initialize program
     60:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     61:   PetscInitialize(&argc,&argv,NULL,help);
     63:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

     66:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     67:     Set runtime options
     68:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     69:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
     70:   {
     71:     ctx.beta    = 2;
     72:     ctx.c       = 10000.0;
     73:     ctx.u_s     = 1.0;
     74:     ctx.omega_s = 1.0;
     75:     ctx.omega_b = 120.0*PETSC_PI;
     76:     ctx.H       = 5.0;
     77:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
     78:     ctx.D       = 5.0;
     79:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
     80:     ctx.E       = 1.1378;
     81:     ctx.V       = 1.0;
     82:     ctx.X       = 0.545;
     83:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
     84:     ctx.Pmax_ini = ctx.Pmax;
     85:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
     86:     ctx.Pm      = 1.06;
     87:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
     88:     ctx.tf      = 0.1;
     89:     ctx.tcl     = 0.2;
     90:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
     91:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
     92:     printtofile = PETSC_FALSE;
     93:     PetscOptionsBool("-printtofile","Print convergence results to file","",printtofile,&printtofile,NULL);
     94:   }
     95:   PetscOptionsEnd();

     97:   /* Create TAO solver and set desired solution method */
     98:   TaoCreate(PETSC_COMM_WORLD,&tao);
     99:   TaoSetType(tao,TAOBLMVM);
    100:   if (printtofile) {
    101:     TaoSetMonitor(tao,(PetscErrorCode (*)(Tao, void*))monitor,(void *)&ctx,PETSC_NULL);
    102:   }
    103:   TaoSetMaximumIterations(tao,30);
    104:   /*
    105:      Optimization starts
    106:   */
    107:   /* Set initial solution guess */
    108:   VecCreateSeq(PETSC_COMM_WORLD,1,&p);
    109:   VecGetArray(p,&x_ptr);
    110:   x_ptr[0]   = ctx.Pm;
    111:   VecRestoreArray(p,&x_ptr);

    113:   TaoSetSolution(tao,p);
    114:   /* Set routine for function and gradient evaluation */
    115:   TaoSetObjective(tao,FormFunction,(void *)&ctx);
    116:   TaoSetGradient(tao,NULL,TaoDefaultComputeGradient,(void *)&ctx);

    118:   /* Set bounds for the optimization */
    119:   VecDuplicate(p,&lowerb);
    120:   VecDuplicate(p,&upperb);
    121:   VecGetArray(lowerb,&x_ptr);
    122:   x_ptr[0] = 0.;
    123:   VecRestoreArray(lowerb,&x_ptr);
    124:   VecGetArray(upperb,&x_ptr);
    125:   x_ptr[0] = 1.1;
    126:   VecRestoreArray(upperb,&x_ptr);
    127:   TaoSetVariableBounds(tao,lowerb,upperb);

    129:   /* Check for any TAO command line options */
    130:   TaoSetFromOptions(tao);
    131:   TaoGetKSP(tao,&ksp);
    132:   if (ksp) {
    133:     KSPGetPC(ksp,&pc);
    134:     PCSetType(pc,PCNONE);
    135:   }

    137:   /* SOLVE THE APPLICATION */
    138:   TaoSolve(tao);

    140:   VecView(p,PETSC_VIEWER_STDOUT_WORLD);

    142:   /* Free TAO data structures */
    143:   TaoDestroy(&tao);
    144:   VecDestroy(&p);
    145:   VecDestroy(&lowerb);
    146:   VecDestroy(&upperb);
    147:   PetscFinalize();
    148:   return 0;
    149: }

    151: /* ------------------------------------------------------------------ */
    152: /*
    153:    FormFunction - Evaluates the function and corresponding gradient.

    155:    Input Parameters:
    156:    tao - the Tao context
    157:    X   - the input vector
    158:    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient()

    160:    Output Parameters:
    161:    f   - the newly evaluated function
    162: */
    163: PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
    164: {
    165:   AppCtx            *ctx = (AppCtx*)ctx0;
    166:   TS                ts,quadts;
    167:   Vec               U;             /* solution will be stored here */
    168:   Mat               A;             /* Jacobian matrix */
    169:   PetscInt          n = 2;
    170:   PetscReal         ftime;
    171:   PetscInt          steps;
    172:   PetscScalar       *u;
    173:   const PetscScalar *x_ptr,*qx_ptr;
    174:   Vec               q;
    175:   PetscInt          direction[2];
    176:   PetscBool         terminate[2];

    178:   VecGetArrayRead(P,&x_ptr);
    179:   ctx->Pm = x_ptr[0];
    180:   VecRestoreArrayRead(P,&x_ptr);
    181:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    182:     Create necessary matrix and vectors
    183:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    184:   MatCreate(PETSC_COMM_WORLD,&A);
    185:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
    186:   MatSetType(A,MATDENSE);
    187:   MatSetFromOptions(A);
    188:   MatSetUp(A);

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

    192:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    193:      Create timestepping solver context
    194:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    195:   TSCreate(PETSC_COMM_WORLD,&ts);
    196:   TSSetProblemType(ts,TS_NONLINEAR);
    197:   TSSetType(ts,TSCN);
    198:   TSSetIFunction(ts,NULL,(TSIFunction) IFunction,ctx);
    199:   TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,ctx);

    201:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    202:      Set initial conditions
    203:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    204:   VecGetArray(U,&u);
    205:   u[0] = PetscAsinScalar(ctx->Pm/ctx->Pmax);
    206:   u[1] = 1.0;
    207:   VecRestoreArray(U,&u);
    208:   TSSetSolution(ts,U);

    210:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    211:      Set solver options
    212:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    213:   TSSetMaxTime(ts,1.0);
    214:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
    215:   TSSetTimeStep(ts,0.03125);
    216:   TSCreateQuadratureTS(ts,PETSC_TRUE,&quadts);
    217:   TSGetSolution(quadts,&q);
    218:   VecSet(q,0.0);
    219:   TSSetRHSFunction(quadts,NULL,(TSRHSFunction)CostIntegrand,ctx);
    220:   TSSetFromOptions(ts);

    222:   direction[0] = direction[1] = 1;
    223:   terminate[0] = terminate[1] = PETSC_FALSE;

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

    227:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    228:      Solve nonlinear system
    229:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    230:   TSSolve(ts,U);

    232:   TSGetSolveTime(ts,&ftime);
    233:   TSGetStepNumber(ts,&steps);
    234:   VecGetArrayRead(q,&qx_ptr);
    235:   *f   = -ctx->Pm + qx_ptr[0];
    236:   VecRestoreArrayRead(q,&qx_ptr);

    238:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    239:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    240:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    241:   MatDestroy(&A);
    242:   VecDestroy(&U);
    243:   TSDestroy(&ts);
    244:   return 0;
    245: }

    247: /*TEST

    249:    build:
    250:       requires: !complex !single

    252:    test:
    253:       args: -ts_type cn -pc_type lu -tao_monitor -tao_gatol 1e-3

    255: TEST*/