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 AppCtx *user; 72 Vec X; 73 PetscScalar *mat; 74 const PetscScalar *x; 75 PetscInt idx; 76 PetscReal t; 77 78 PetscFunctionBegin; 79 PetscCall(TSGetApplicationContext(ts, &user)); 80 PetscCall(TSGetTime(ts, &t)); 81 PetscCall(TSGetSolution(ts, &X)); 82 idx = 3 * user->stepnum; 83 PetscCall(MatDenseGetArray(user->Sol, &mat)); 84 PetscCall(VecGetArrayRead(X, &x)); 85 mat[idx] = t; 86 PetscCall(PetscArraycpy(mat + idx + 1, x, 2)); 87 PetscCall(MatDenseRestoreArray(user->Sol, &mat)); 88 PetscCall(VecRestoreArrayRead(X, &x)); 89 user->stepnum++; 90 PetscFunctionReturn(0); 91 } 92 93 /* Computes the wind speed using Weibull distribution */ 94 PetscErrorCode WindSpeeds(AppCtx *user) { 95 PetscScalar *x, *t, avg_dev, sum; 96 PetscInt i; 97 98 PetscFunctionBegin; 99 user->cw = 5; 100 user->kw = 2; /* Rayleigh distribution */ 101 user->nsamples = 2000; 102 user->Tw = 0.2; 103 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Wind Speed Options", ""); 104 { 105 PetscCall(PetscOptionsReal("-cw", "", "", user->cw, &user->cw, NULL)); 106 PetscCall(PetscOptionsReal("-kw", "", "", user->kw, &user->kw, NULL)); 107 PetscCall(PetscOptionsInt("-nsamples", "", "", user->nsamples, &user->nsamples, NULL)); 108 PetscCall(PetscOptionsReal("-Tw", "", "", user->Tw, &user->Tw, NULL)); 109 } 110 PetscOptionsEnd(); 111 PetscCall(VecCreate(PETSC_COMM_WORLD, &user->wind_data)); 112 PetscCall(VecSetSizes(user->wind_data, PETSC_DECIDE, user->nsamples)); 113 PetscCall(VecSetFromOptions(user->wind_data)); 114 PetscCall(VecDuplicate(user->wind_data, &user->t_wind)); 115 116 PetscCall(VecGetArray(user->t_wind, &t)); 117 for (i = 0; i < user->nsamples; i++) t[i] = (i + 1) * tmax / user->nsamples; 118 PetscCall(VecRestoreArray(user->t_wind, &t)); 119 120 /* Wind speed deviation = (-log(rand)/cw)^(1/kw) */ 121 PetscCall(VecSetRandom(user->wind_data, NULL)); 122 PetscCall(VecLog(user->wind_data)); 123 PetscCall(VecScale(user->wind_data, -1 / user->cw)); 124 PetscCall(VecGetArray(user->wind_data, &x)); 125 for (i = 0; i < user->nsamples; i++) x[i] = PetscPowScalar(x[i], (1 / user->kw)); 126 PetscCall(VecRestoreArray(user->wind_data, &x)); 127 PetscCall(VecSum(user->wind_data, &sum)); 128 avg_dev = sum / user->nsamples; 129 /* Wind speed (t) = (1 + wind speed deviation(t) - avg_dev)*average wind speed */ 130 PetscCall(VecShift(user->wind_data, (1 - avg_dev))); 131 PetscCall(VecScale(user->wind_data, vwa)); 132 PetscFunctionReturn(0); 133 } 134 135 /* Sets the parameters for wind turbine */ 136 PetscErrorCode SetWindTurbineParams(AppCtx *user) { 137 PetscFunctionBegin; 138 user->Rt = 35; 139 user->Ar = PETSC_PI * user->Rt * user->Rt; 140 user->nGB = 1.0 / 89.0; 141 user->rho = 1.225; 142 user->Ht = 1.5; 143 PetscFunctionReturn(0); 144 } 145 146 /* Sets the parameters for induction generator */ 147 PetscErrorCode SetInductionGeneratorParams(AppCtx *user) { 148 PetscFunctionBegin; 149 user->np = 4; 150 user->Xm = 3.0; 151 user->Xs = 0.1; 152 user->Xr = 0.08; 153 user->Rs = 0.01; 154 user->Rr = 0.01; 155 user->Xp = user->Xs + user->Xm * user->Xr / (user->Xm + user->Xr); 156 user->Hm = 1.0; 157 user->Te = 0.011063063063251968; 158 PetscFunctionReturn(0); 159 } 160 161 /* Computes the power extracted from wind */ 162 PetscErrorCode GetWindPower(PetscScalar wm, PetscScalar vw, PetscScalar *Pw, AppCtx *user) { 163 PetscScalar temp, lambda, lambda_i, cp; 164 165 PetscFunctionBegin; 166 temp = user->nGB * 2 * user->Rt * ws / user->np; 167 lambda = temp * wm / vw; 168 lambda_i = 1 / (1 / lambda + 0.002); 169 cp = 0.44 * (125 / lambda_i - 6.94) * PetscExpScalar(-16.5 / lambda_i); 170 *Pw = 0.5 * user->rho * cp * user->Ar * vw * vw * vw / (MVAbase * 1e6); 171 PetscFunctionReturn(0); 172 } 173 174 /* 175 Defines the ODE passed to the ODE solver 176 */ 177 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, AppCtx *user) { 178 PetscScalar *f, wm, Pw, *wd; 179 const PetscScalar *u, *udot; 180 PetscInt stepnum; 181 182 PetscFunctionBegin; 183 PetscCall(TSGetStepNumber(ts, &stepnum)); 184 /* The next three lines allow us to access the entries of the vectors directly */ 185 PetscCall(VecGetArrayRead(U, &u)); 186 PetscCall(VecGetArrayRead(Udot, &udot)); 187 PetscCall(VecGetArray(F, &f)); 188 PetscCall(VecGetArray(user->wind_data, &wd)); 189 190 f[0] = user->Tw * udot[0] - wd[stepnum] + u[0]; 191 wm = 1 - u[1]; 192 PetscCall(GetWindPower(wm, u[0], &Pw, user)); 193 f[1] = 2.0 * (user->Ht + user->Hm) * udot[1] - Pw / wm + user->Te; 194 195 PetscCall(VecRestoreArray(user->wind_data, &wd)); 196 PetscCall(VecRestoreArrayRead(U, &u)); 197 PetscCall(VecRestoreArrayRead(Udot, &udot)); 198 PetscCall(VecRestoreArray(F, &f)); 199 PetscFunctionReturn(0); 200 } 201 202 int main(int argc, char **argv) { 203 TS ts; /* ODE integrator */ 204 Vec U; /* solution will be stored here */ 205 Mat A; /* Jacobian matrix */ 206 PetscMPIInt size; 207 PetscInt n = 2, idx; 208 AppCtx user; 209 PetscScalar *u; 210 SNES snes; 211 PetscScalar *mat; 212 const PetscScalar *x, *rmat; 213 Mat B; 214 PetscScalar *amat; 215 PetscViewer viewer; 216 217 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 218 Initialize program 219 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 220 PetscFunctionBeginUser; 221 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 222 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 223 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 224 225 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 226 Create necessary matrix and vectors 227 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 228 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 229 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 230 PetscCall(MatSetFromOptions(A)); 231 PetscCall(MatSetUp(A)); 232 233 PetscCall(MatCreateVecs(A, &U, NULL)); 234 235 /* Create wind speed data using Weibull distribution */ 236 PetscCall(WindSpeeds(&user)); 237 /* Set parameters for wind turbine and induction generator */ 238 PetscCall(SetWindTurbineParams(&user)); 239 PetscCall(SetInductionGeneratorParams(&user)); 240 241 PetscCall(VecGetArray(U, &u)); 242 u[0] = vwa; 243 u[1] = s; 244 PetscCall(VecRestoreArray(U, &u)); 245 246 /* Create matrix to save solutions at each time step */ 247 user.stepnum = 0; 248 249 PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, 3, 2010, NULL, &user.Sol)); 250 251 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 252 Create timestepping solver context 253 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 254 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 255 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 256 PetscCall(TSSetType(ts, TSBEULER)); 257 PetscCall(TSSetIFunction(ts, NULL, (TSIFunction)IFunction, &user)); 258 259 PetscCall(TSGetSNES(ts, &snes)); 260 PetscCall(SNESSetJacobian(snes, A, A, SNESComputeJacobianDefault, NULL)); 261 /* PetscCall(TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&user)); */ 262 PetscCall(TSSetApplicationContext(ts, &user)); 263 264 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 265 Set initial conditions 266 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 267 PetscCall(TSSetSolution(ts, U)); 268 269 /* Save initial solution */ 270 idx = 3 * user.stepnum; 271 272 PetscCall(MatDenseGetArray(user.Sol, &mat)); 273 PetscCall(VecGetArrayRead(U, &x)); 274 275 mat[idx] = 0.0; 276 277 PetscCall(PetscArraycpy(mat + idx + 1, x, 2)); 278 PetscCall(MatDenseRestoreArray(user.Sol, &mat)); 279 PetscCall(VecRestoreArrayRead(U, &x)); 280 user.stepnum++; 281 282 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 283 Set solver options 284 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 285 PetscCall(TSSetMaxTime(ts, 20.0)); 286 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 287 PetscCall(TSSetTimeStep(ts, .01)); 288 PetscCall(TSSetFromOptions(ts)); 289 PetscCall(TSSetPostStep(ts, SaveSolution)); 290 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 291 Solve nonlinear system 292 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 293 PetscCall(TSSolve(ts, U)); 294 295 PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, 3, user.stepnum, NULL, &B)); 296 PetscCall(MatDenseGetArrayRead(user.Sol, &rmat)); 297 PetscCall(MatDenseGetArray(B, &amat)); 298 PetscCall(PetscArraycpy(amat, rmat, user.stepnum * 3)); 299 PetscCall(MatDenseRestoreArray(B, &amat)); 300 PetscCall(MatDenseRestoreArrayRead(user.Sol, &rmat)); 301 302 PetscCall(PetscViewerBinaryOpen(PETSC_COMM_SELF, "out.bin", FILE_MODE_WRITE, &viewer)); 303 PetscCall(MatView(B, viewer)); 304 PetscCall(PetscViewerDestroy(&viewer)); 305 PetscCall(MatDestroy(&user.Sol)); 306 PetscCall(MatDestroy(&B)); 307 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 308 Free work space. All PETSc objects should be destroyed when they are no longer needed. 309 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 310 PetscCall(VecDestroy(&user.wind_data)); 311 PetscCall(VecDestroy(&user.t_wind)); 312 PetscCall(MatDestroy(&A)); 313 PetscCall(VecDestroy(&U)); 314 PetscCall(TSDestroy(&ts)); 315 316 PetscCall(PetscFinalize()); 317 return 0; 318 } 319 320 /*TEST 321 322 build: 323 requires: !complex 324 325 test: 326 327 TEST*/ 328