1 2 static char help[] = "Basic equation for an induction generator driven by a wind turbine.\n"; 3 4 /*F 5 \begin{eqnarray} 6 T_w\frac{dv_w}{dt} & = & v_w - v_we \\ 7 2(H_t+H_m)\frac{ds}{dt} & = & P_w - P_e 8 \end{eqnarray} 9 F*/ 10 /* 11 - Pw is the power extracted from the wind turbine given by 12 Pw = 0.5*\rho*cp*Ar*vw^3 13 14 - The wind speed time series is modeled using a Weibull distribution and then 15 passed through a low pass filter (with time constant T_w). 16 - v_we is the wind speed data calculated using Weibull distribution while v_w is 17 the output of the filter. 18 - P_e is assumed as constant electrical torque 19 20 - This example does not work with adaptive time stepping! 21 22 Reference: 23 Power System Modeling and Scripting - F. Milano 24 */ 25 26 #include <petscts.h> 27 28 #define freq 50 29 #define ws (2 * PETSC_PI * freq) 30 #define MVAbase 100 31 32 typedef struct { 33 /* Parameters for wind speed model */ 34 PetscInt nsamples; /* Number of wind samples */ 35 PetscReal cw; /* Scale factor for Weibull distribution */ 36 PetscReal kw; /* Shape factor for Weibull distribution */ 37 Vec wind_data; /* Vector to hold wind speeds */ 38 Vec t_wind; /* Vector to hold wind speed times */ 39 PetscReal Tw; /* Filter time constant */ 40 41 /* Wind turbine parameters */ 42 PetscScalar Rt; /* Rotor radius */ 43 PetscScalar Ar; /* Area swept by rotor (pi*R*R) */ 44 PetscReal nGB; /* Gear box ratio */ 45 PetscReal Ht; /* Turbine inertia constant */ 46 PetscReal rho; /* Atmospheric pressure */ 47 48 /* Induction generator parameters */ 49 PetscInt np; /* Number of poles */ 50 PetscReal Xm; /* Magnetizing reactance */ 51 PetscReal Xs; /* Stator Reactance */ 52 PetscReal Xr; /* Rotor reactance */ 53 PetscReal Rs; /* Stator resistance */ 54 PetscReal Rr; /* Rotor resistance */ 55 PetscReal Hm; /* Motor inertia constant */ 56 PetscReal Xp; /* Xs + Xm*Xr/(Xm + Xr) */ 57 PetscScalar Te; /* Electrical Torque */ 58 59 Mat Sol; /* Solution matrix */ 60 PetscInt stepnum; /* Column number of solution matrix */ 61 } AppCtx; 62 63 /* Initial values computed by Power flow and initialization */ 64 PetscScalar s = -0.00011577790353; 65 /*Pw = 0.011064344110238; %Te*wm */ 66 PetscScalar vwa = 22.317142184449754; 67 PetscReal tmax = 20.0; 68 69 /* Saves the solution at each time to a matrix */ 70 PetscErrorCode SaveSolution(TS ts) 71 { 72 AppCtx *user; 73 Vec X; 74 PetscScalar *mat; 75 const PetscScalar *x; 76 PetscInt idx; 77 PetscReal t; 78 79 PetscFunctionBegin; 80 PetscCall(TSGetApplicationContext(ts, &user)); 81 PetscCall(TSGetTime(ts, &t)); 82 PetscCall(TSGetSolution(ts, &X)); 83 idx = 3 * user->stepnum; 84 PetscCall(MatDenseGetArray(user->Sol, &mat)); 85 PetscCall(VecGetArrayRead(X, &x)); 86 mat[idx] = t; 87 PetscCall(PetscArraycpy(mat + idx + 1, x, 2)); 88 PetscCall(MatDenseRestoreArray(user->Sol, &mat)); 89 PetscCall(VecRestoreArrayRead(X, &x)); 90 user->stepnum++; 91 PetscFunctionReturn(PETSC_SUCCESS); 92 } 93 94 /* Computes the wind speed using Weibull distribution */ 95 PetscErrorCode WindSpeeds(AppCtx *user) 96 { 97 PetscScalar *x, *t, avg_dev, sum; 98 PetscInt i; 99 100 PetscFunctionBegin; 101 user->cw = 5; 102 user->kw = 2; /* Rayleigh distribution */ 103 user->nsamples = 2000; 104 user->Tw = 0.2; 105 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Wind Speed Options", ""); 106 { 107 PetscCall(PetscOptionsReal("-cw", "", "", user->cw, &user->cw, NULL)); 108 PetscCall(PetscOptionsReal("-kw", "", "", user->kw, &user->kw, NULL)); 109 PetscCall(PetscOptionsInt("-nsamples", "", "", user->nsamples, &user->nsamples, NULL)); 110 PetscCall(PetscOptionsReal("-Tw", "", "", user->Tw, &user->Tw, NULL)); 111 } 112 PetscOptionsEnd(); 113 PetscCall(VecCreate(PETSC_COMM_WORLD, &user->wind_data)); 114 PetscCall(VecSetSizes(user->wind_data, PETSC_DECIDE, user->nsamples)); 115 PetscCall(VecSetFromOptions(user->wind_data)); 116 PetscCall(VecDuplicate(user->wind_data, &user->t_wind)); 117 118 PetscCall(VecGetArray(user->t_wind, &t)); 119 for (i = 0; i < user->nsamples; i++) t[i] = (i + 1) * tmax / user->nsamples; 120 PetscCall(VecRestoreArray(user->t_wind, &t)); 121 122 /* Wind speed deviation = (-log(rand)/cw)^(1/kw) */ 123 PetscCall(VecSetRandom(user->wind_data, NULL)); 124 PetscCall(VecLog(user->wind_data)); 125 PetscCall(VecScale(user->wind_data, -1 / user->cw)); 126 PetscCall(VecGetArray(user->wind_data, &x)); 127 for (i = 0; i < user->nsamples; i++) x[i] = PetscPowScalar(x[i], (1 / user->kw)); 128 PetscCall(VecRestoreArray(user->wind_data, &x)); 129 PetscCall(VecSum(user->wind_data, &sum)); 130 avg_dev = sum / user->nsamples; 131 /* Wind speed (t) = (1 + wind speed deviation(t) - avg_dev)*average wind speed */ 132 PetscCall(VecShift(user->wind_data, (1 - avg_dev))); 133 PetscCall(VecScale(user->wind_data, vwa)); 134 PetscFunctionReturn(PETSC_SUCCESS); 135 } 136 137 /* Sets the parameters for wind turbine */ 138 PetscErrorCode SetWindTurbineParams(AppCtx *user) 139 { 140 PetscFunctionBegin; 141 user->Rt = 35; 142 user->Ar = PETSC_PI * user->Rt * user->Rt; 143 user->nGB = 1.0 / 89.0; 144 user->rho = 1.225; 145 user->Ht = 1.5; 146 PetscFunctionReturn(PETSC_SUCCESS); 147 } 148 149 /* Sets the parameters for induction generator */ 150 PetscErrorCode SetInductionGeneratorParams(AppCtx *user) 151 { 152 PetscFunctionBegin; 153 user->np = 4; 154 user->Xm = 3.0; 155 user->Xs = 0.1; 156 user->Xr = 0.08; 157 user->Rs = 0.01; 158 user->Rr = 0.01; 159 user->Xp = user->Xs + user->Xm * user->Xr / (user->Xm + user->Xr); 160 user->Hm = 1.0; 161 user->Te = 0.011063063063251968; 162 PetscFunctionReturn(PETSC_SUCCESS); 163 } 164 165 /* Computes the power extracted from wind */ 166 PetscErrorCode GetWindPower(PetscScalar wm, PetscScalar vw, PetscScalar *Pw, AppCtx *user) 167 { 168 PetscScalar temp, lambda, lambda_i, cp; 169 170 PetscFunctionBegin; 171 temp = user->nGB * 2 * user->Rt * ws / user->np; 172 lambda = temp * wm / vw; 173 lambda_i = 1 / (1 / lambda + 0.002); 174 cp = 0.44 * (125 / lambda_i - 6.94) * PetscExpScalar(-16.5 / lambda_i); 175 *Pw = 0.5 * user->rho * cp * user->Ar * vw * vw * vw / (MVAbase * 1e6); 176 PetscFunctionReturn(PETSC_SUCCESS); 177 } 178 179 /* 180 Defines the ODE passed to the ODE solver 181 */ 182 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, AppCtx *user) 183 { 184 PetscScalar *f, wm, Pw, *wd; 185 const PetscScalar *u, *udot; 186 PetscInt stepnum; 187 188 PetscFunctionBegin; 189 PetscCall(TSGetStepNumber(ts, &stepnum)); 190 /* The next three lines allow us to access the entries of the vectors directly */ 191 PetscCall(VecGetArrayRead(U, &u)); 192 PetscCall(VecGetArrayRead(Udot, &udot)); 193 PetscCall(VecGetArray(F, &f)); 194 PetscCall(VecGetArray(user->wind_data, &wd)); 195 196 f[0] = user->Tw * udot[0] - wd[stepnum] + u[0]; 197 wm = 1 - u[1]; 198 PetscCall(GetWindPower(wm, u[0], &Pw, user)); 199 f[1] = 2.0 * (user->Ht + user->Hm) * udot[1] - Pw / wm + user->Te; 200 201 PetscCall(VecRestoreArray(user->wind_data, &wd)); 202 PetscCall(VecRestoreArrayRead(U, &u)); 203 PetscCall(VecRestoreArrayRead(Udot, &udot)); 204 PetscCall(VecRestoreArray(F, &f)); 205 PetscFunctionReturn(PETSC_SUCCESS); 206 } 207 208 int main(int argc, char **argv) 209 { 210 TS ts; /* ODE integrator */ 211 Vec U; /* solution will be stored here */ 212 Mat A; /* Jacobian matrix */ 213 PetscMPIInt size; 214 PetscInt n = 2, idx; 215 AppCtx user; 216 PetscScalar *u; 217 SNES snes; 218 PetscScalar *mat; 219 const PetscScalar *x, *rmat; 220 Mat B; 221 PetscScalar *amat; 222 PetscViewer viewer; 223 224 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 225 Initialize program 226 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 227 PetscFunctionBeginUser; 228 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 229 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 230 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 231 232 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 233 Create necessary matrix and vectors 234 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 235 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 236 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 237 PetscCall(MatSetFromOptions(A)); 238 PetscCall(MatSetUp(A)); 239 240 PetscCall(MatCreateVecs(A, &U, NULL)); 241 242 /* Create wind speed data using Weibull distribution */ 243 PetscCall(WindSpeeds(&user)); 244 /* Set parameters for wind turbine and induction generator */ 245 PetscCall(SetWindTurbineParams(&user)); 246 PetscCall(SetInductionGeneratorParams(&user)); 247 248 PetscCall(VecGetArray(U, &u)); 249 u[0] = vwa; 250 u[1] = s; 251 PetscCall(VecRestoreArray(U, &u)); 252 253 /* Create matrix to save solutions at each time step */ 254 user.stepnum = 0; 255 256 PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, 3, 2010, NULL, &user.Sol)); 257 258 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 259 Create timestepping solver context 260 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 261 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 262 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 263 PetscCall(TSSetType(ts, TSBEULER)); 264 PetscCall(TSSetIFunction(ts, NULL, (TSIFunction)IFunction, &user)); 265 266 PetscCall(TSGetSNES(ts, &snes)); 267 PetscCall(SNESSetJacobian(snes, A, A, SNESComputeJacobianDefault, NULL)); 268 /* PetscCall(TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&user)); */ 269 PetscCall(TSSetApplicationContext(ts, &user)); 270 271 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 272 Set initial conditions 273 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 274 PetscCall(TSSetSolution(ts, U)); 275 276 /* Save initial solution */ 277 idx = 3 * user.stepnum; 278 279 PetscCall(MatDenseGetArray(user.Sol, &mat)); 280 PetscCall(VecGetArrayRead(U, &x)); 281 282 mat[idx] = 0.0; 283 284 PetscCall(PetscArraycpy(mat + idx + 1, x, 2)); 285 PetscCall(MatDenseRestoreArray(user.Sol, &mat)); 286 PetscCall(VecRestoreArrayRead(U, &x)); 287 user.stepnum++; 288 289 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 290 Set solver options 291 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 292 PetscCall(TSSetMaxTime(ts, 20.0)); 293 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 294 PetscCall(TSSetTimeStep(ts, .01)); 295 PetscCall(TSSetFromOptions(ts)); 296 PetscCall(TSSetPostStep(ts, SaveSolution)); 297 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 298 Solve nonlinear system 299 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 300 PetscCall(TSSolve(ts, U)); 301 302 PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, 3, user.stepnum, NULL, &B)); 303 PetscCall(MatDenseGetArrayRead(user.Sol, &rmat)); 304 PetscCall(MatDenseGetArray(B, &amat)); 305 PetscCall(PetscArraycpy(amat, rmat, user.stepnum * 3)); 306 PetscCall(MatDenseRestoreArray(B, &amat)); 307 PetscCall(MatDenseRestoreArrayRead(user.Sol, &rmat)); 308 309 PetscCall(PetscViewerBinaryOpen(PETSC_COMM_SELF, "out.bin", FILE_MODE_WRITE, &viewer)); 310 PetscCall(MatView(B, viewer)); 311 PetscCall(PetscViewerDestroy(&viewer)); 312 PetscCall(MatDestroy(&user.Sol)); 313 PetscCall(MatDestroy(&B)); 314 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 315 Free work space. All PETSc objects should be destroyed when they are no longer needed. 316 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 317 PetscCall(VecDestroy(&user.wind_data)); 318 PetscCall(VecDestroy(&user.t_wind)); 319 PetscCall(MatDestroy(&A)); 320 PetscCall(VecDestroy(&U)); 321 PetscCall(TSDestroy(&ts)); 322 323 PetscCall(PetscFinalize()); 324 return 0; 325 } 326 327 /*TEST 328 329 build: 330 requires: !complex 331 332 test: 333 334 TEST*/ 335