xref: /petsc/src/ts/tutorials/power_grid/ex5.c (revision 3ba1676111f5c958fe6c2729b46ca4d523958bb3)

static char help[] = "Basic equation for an induction generator driven by a wind turbine.\n";

/*F
\begin{eqnarray}
          T_w\frac{dv_w}{dt} & = & v_w - v_we \\
          2(H_t+H_m)\frac{ds}{dt} & = & P_w - P_e
\end{eqnarray}
F*/
/*
 - Pw is the power extracted from the wind turbine given by
           Pw = 0.5*\rho*cp*Ar*vw^3

 - The wind speed time series is modeled using a Weibull distribution and then
   passed through a low pass filter (with time constant T_w).
 - v_we is the wind speed data calculated using Weibull distribution while v_w is
   the output of the filter.
 - P_e is assumed as constant electrical torque

 - This example does not work with adaptive time stepping!

Reference:
Power System Modeling and Scripting - F. Milano
*/

#include <petscts.h>

#define freq    50
#define ws      (2 * PETSC_PI * freq)
#define MVAbase 100

typedef struct {
  /* Parameters for wind speed model */
  PetscInt  nsamples;  /* Number of wind samples */
  PetscReal cw;        /* Scale factor for Weibull distribution */
  PetscReal kw;        /* Shape factor for Weibull distribution */
  Vec       wind_data; /* Vector to hold wind speeds */
  Vec       t_wind;    /* Vector to hold wind speed times */
  PetscReal Tw;        /* Filter time constant */

  /* Wind turbine parameters */
  PetscScalar Rt;  /* Rotor radius */
  PetscScalar Ar;  /* Area swept by rotor (pi*R*R) */
  PetscReal   nGB; /* Gear box ratio */
  PetscReal   Ht;  /* Turbine inertia constant */
  PetscReal   rho; /* Atmospheric pressure */

  /* Induction generator parameters */
  PetscInt    np; /* Number of poles */
  PetscReal   Xm; /* Magnetizing reactance */
  PetscReal   Xs; /* Stator Reactance */
  PetscReal   Xr; /* Rotor reactance */
  PetscReal   Rs; /* Stator resistance */
  PetscReal   Rr; /* Rotor resistance */
  PetscReal   Hm; /* Motor inertia constant */
  PetscReal   Xp; /* Xs + Xm*Xr/(Xm + Xr) */
  PetscScalar Te; /* Electrical Torque */

  Mat      Sol;     /* Solution matrix */
  PetscInt stepnum; /* Column number of solution matrix */
} AppCtx;

/* Initial values computed by Power flow and initialization */
PetscScalar s = -0.00011577790353;
/*Pw = 0.011064344110238; %Te*wm */
PetscScalar vwa  = 22.317142184449754;
PetscReal   tmax = 20.0;

/* Saves the solution at each time to a matrix */
PetscErrorCode SaveSolution(TS ts)
{
  AppCtx            *user;
  Vec                X;
  PetscScalar       *mat;
  const PetscScalar *x;
  PetscInt           idx;
  PetscReal          t;

  PetscFunctionBegin;
  PetscCall(TSGetApplicationContext(ts, &user));
  PetscCall(TSGetTime(ts, &t));
  PetscCall(TSGetSolution(ts, &X));
  idx = 3 * user->stepnum;
  PetscCall(MatDenseGetArray(user->Sol, &mat));
  PetscCall(VecGetArrayRead(X, &x));
  mat[idx] = t;
  PetscCall(PetscArraycpy(mat + idx + 1, x, 2));
  PetscCall(MatDenseRestoreArray(user->Sol, &mat));
  PetscCall(VecRestoreArrayRead(X, &x));
  user->stepnum++;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Computes the wind speed using Weibull distribution */
PetscErrorCode WindSpeeds(AppCtx *user)
{
  PetscScalar *x, *t, avg_dev, sum;
  PetscInt     i;

  PetscFunctionBegin;
  user->cw       = 5;
  user->kw       = 2; /* Rayleigh distribution */
  user->nsamples = 2000;
  user->Tw       = 0.2;
  PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Wind Speed Options", "");
  {
    PetscCall(PetscOptionsReal("-cw", "", "", user->cw, &user->cw, NULL));
    PetscCall(PetscOptionsReal("-kw", "", "", user->kw, &user->kw, NULL));
    PetscCall(PetscOptionsInt("-nsamples", "", "", user->nsamples, &user->nsamples, NULL));
    PetscCall(PetscOptionsReal("-Tw", "", "", user->Tw, &user->Tw, NULL));
  }
  PetscOptionsEnd();
  PetscCall(VecCreate(PETSC_COMM_WORLD, &user->wind_data));
  PetscCall(VecSetSizes(user->wind_data, PETSC_DECIDE, user->nsamples));
  PetscCall(VecSetFromOptions(user->wind_data));
  PetscCall(VecDuplicate(user->wind_data, &user->t_wind));

  PetscCall(VecGetArray(user->t_wind, &t));
  for (i = 0; i < user->nsamples; i++) t[i] = (i + 1) * tmax / user->nsamples;
  PetscCall(VecRestoreArray(user->t_wind, &t));

  /* Wind speed deviation = (-log(rand)/cw)^(1/kw) */
  PetscCall(VecSetRandom(user->wind_data, NULL));
  PetscCall(VecLog(user->wind_data));
  PetscCall(VecScale(user->wind_data, -1 / user->cw));
  PetscCall(VecGetArray(user->wind_data, &x));
  for (i = 0; i < user->nsamples; i++) x[i] = PetscPowScalar(x[i], (1 / user->kw));
  PetscCall(VecRestoreArray(user->wind_data, &x));
  PetscCall(VecSum(user->wind_data, &sum));
  avg_dev = sum / user->nsamples;
  /* Wind speed (t) = (1 + wind speed deviation(t) - avg_dev)*average wind speed */
  PetscCall(VecShift(user->wind_data, (1 - avg_dev)));
  PetscCall(VecScale(user->wind_data, vwa));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Sets the parameters for wind turbine */
PetscErrorCode SetWindTurbineParams(AppCtx *user)
{
  PetscFunctionBegin;
  user->Rt  = 35;
  user->Ar  = PETSC_PI * user->Rt * user->Rt;
  user->nGB = 1.0 / 89.0;
  user->rho = 1.225;
  user->Ht  = 1.5;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Sets the parameters for induction generator */
PetscErrorCode SetInductionGeneratorParams(AppCtx *user)
{
  PetscFunctionBegin;
  user->np = 4;
  user->Xm = 3.0;
  user->Xs = 0.1;
  user->Xr = 0.08;
  user->Rs = 0.01;
  user->Rr = 0.01;
  user->Xp = user->Xs + user->Xm * user->Xr / (user->Xm + user->Xr);
  user->Hm = 1.0;
  user->Te = 0.011063063063251968;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Computes the power extracted from wind */
PetscErrorCode GetWindPower(PetscScalar wm, PetscScalar vw, PetscScalar *Pw, AppCtx *user)
{
  PetscScalar temp, lambda, lambda_i, cp;

  PetscFunctionBegin;
  temp     = user->nGB * 2 * user->Rt * ws / user->np;
  lambda   = temp * wm / vw;
  lambda_i = 1 / (1 / lambda + 0.002);
  cp       = 0.44 * (125 / lambda_i - 6.94) * PetscExpScalar(-16.5 / lambda_i);
  *Pw      = 0.5 * user->rho * cp * user->Ar * vw * vw * vw / (MVAbase * 1e6);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
     Defines the ODE passed to the ODE solver
*/
static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, AppCtx *user)
{
  PetscScalar       *f, wm, Pw, *wd;
  const PetscScalar *u, *udot;
  PetscInt           stepnum;

  PetscFunctionBegin;
  PetscCall(TSGetStepNumber(ts, &stepnum));
  /*  The next three lines allow us to access the entries of the vectors directly */
  PetscCall(VecGetArrayRead(U, &u));
  PetscCall(VecGetArrayRead(Udot, &udot));
  PetscCall(VecGetArray(F, &f));
  PetscCall(VecGetArray(user->wind_data, &wd));

  f[0] = user->Tw * udot[0] - wd[stepnum] + u[0];
  wm   = 1 - u[1];
  PetscCall(GetWindPower(wm, u[0], &Pw, user));
  f[1] = 2.0 * (user->Ht + user->Hm) * udot[1] - Pw / wm + user->Te;

  PetscCall(VecRestoreArray(user->wind_data, &wd));
  PetscCall(VecRestoreArrayRead(U, &u));
  PetscCall(VecRestoreArrayRead(Udot, &udot));
  PetscCall(VecRestoreArray(F, &f));
  PetscFunctionReturn(PETSC_SUCCESS);
}

int main(int argc, char **argv)
{
  TS                 ts; /* ODE integrator */
  Vec                U;  /* solution will be stored here */
  Mat                A;  /* Jacobian matrix */
  PetscMPIInt        size;
  PetscInt           n = 2, idx;
  AppCtx             user;
  PetscScalar       *u;
  SNES               snes;
  PetscScalar       *mat;
  const PetscScalar *x, *rmat;
  Mat                B;
  PetscScalar       *amat;
  PetscViewer        viewer;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize program
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
  PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
  PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Create necessary matrix and vectors
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
  PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
  PetscCall(MatSetFromOptions(A));
  PetscCall(MatSetUp(A));

  PetscCall(MatCreateVecs(A, &U, NULL));

  /* Create wind speed data using Weibull distribution */
  PetscCall(WindSpeeds(&user));
  /* Set parameters for wind turbine and induction generator */
  PetscCall(SetWindTurbineParams(&user));
  PetscCall(SetInductionGeneratorParams(&user));

  PetscCall(VecGetArray(U, &u));
  u[0] = vwa;
  u[1] = s;
  PetscCall(VecRestoreArray(U, &u));

  /* Create matrix to save solutions at each time step */
  user.stepnum = 0;

  PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, 3, 2010, NULL, &user.Sol));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
  PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
  PetscCall(TSSetType(ts, TSBEULER));
  PetscCall(TSSetIFunction(ts, NULL, (TSIFunction)IFunction, &user));

  PetscCall(TSGetSNES(ts, &snes));
  PetscCall(SNESSetJacobian(snes, A, A, SNESComputeJacobianDefault, NULL));
  /*  PetscCall(TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&user)); */
  PetscCall(TSSetApplicationContext(ts, &user));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetSolution(ts, U));

  /* Save initial solution */
  idx = 3 * user.stepnum;

  PetscCall(MatDenseGetArray(user.Sol, &mat));
  PetscCall(VecGetArrayRead(U, &x));

  mat[idx] = 0.0;

  PetscCall(PetscArraycpy(mat + idx + 1, x, 2));
  PetscCall(MatDenseRestoreArray(user.Sol, &mat));
  PetscCall(VecRestoreArrayRead(U, &x));
  user.stepnum++;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set solver options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetMaxTime(ts, 20.0));
  PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
  PetscCall(TSSetTimeStep(ts, .01));
  PetscCall(TSSetFromOptions(ts));
  PetscCall(TSSetPostStep(ts, SaveSolution));
  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Solve nonlinear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSolve(ts, U));

  PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, 3, user.stepnum, NULL, &B));
  PetscCall(MatDenseGetArrayRead(user.Sol, &rmat));
  PetscCall(MatDenseGetArray(B, &amat));
  PetscCall(PetscArraycpy(amat, rmat, user.stepnum * 3));
  PetscCall(MatDenseRestoreArray(B, &amat));
  PetscCall(MatDenseRestoreArrayRead(user.Sol, &rmat));

  PetscCall(PetscViewerBinaryOpen(PETSC_COMM_SELF, "out.bin", FILE_MODE_WRITE, &viewer));
  PetscCall(MatView(B, viewer));
  PetscCall(PetscViewerDestroy(&viewer));
  PetscCall(MatDestroy(&user.Sol));
  PetscCall(MatDestroy(&B));
  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Free work space.  All PETSc objects should be destroyed when they are no longer needed.
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(VecDestroy(&user.wind_data));
  PetscCall(VecDestroy(&user.t_wind));
  PetscCall(MatDestroy(&A));
  PetscCall(VecDestroy(&U));
  PetscCall(TSDestroy(&ts));

  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   build:
      requires: !complex

   test:

TEST*/