Actual source code: ex5.c
2: static char help[] = "Basic equation for an induction generator driven by a wind turbine.\n";
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
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
20: - This example does not work with adaptive time stepping!
22: Reference:
23: Power System Modeling and Scripting - F. Milano
24: */
26: #include <petscts.h>
28: #define freq 50
29: #define ws (2 * PETSC_PI * freq)
30: #define MVAbase 100
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 */
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 */
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 */
59: Mat Sol; /* Solution matrix */
60: PetscInt stepnum; /* Column number of solution matrix */
61: } AppCtx;
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;
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;
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: }
94: /* Computes the wind speed using Weibull distribution */
95: PetscErrorCode WindSpeeds(AppCtx *user)
96: {
97: PetscScalar *x, *t, avg_dev, sum;
98: PetscInt i;
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));
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));
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: }
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: }
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: }
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;
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: }
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;
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));
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;
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: }
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;
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");
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));
240: PetscCall(MatCreateVecs(A, &U, NULL));
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));
248: PetscCall(VecGetArray(U, &u));
249: u[0] = vwa;
250: u[1] = s;
251: PetscCall(VecRestoreArray(U, &u));
253: /* Create matrix to save solutions at each time step */
254: user.stepnum = 0;
256: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, 3, 2010, NULL, &user.Sol));
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));
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));
271: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
272: Set initial conditions
273: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
274: PetscCall(TSSetSolution(ts, U));
276: /* Save initial solution */
277: idx = 3 * user.stepnum;
279: PetscCall(MatDenseGetArray(user.Sol, &mat));
280: PetscCall(VecGetArrayRead(U, &x));
282: mat[idx] = 0.0;
284: PetscCall(PetscArraycpy(mat + idx + 1, x, 2));
285: PetscCall(MatDenseRestoreArray(user.Sol, &mat));
286: PetscCall(VecRestoreArrayRead(U, &x));
287: user.stepnum++;
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));
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));
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));
323: PetscCall(PetscFinalize());
324: return 0;
325: }
327: /*TEST
329: build:
330: requires: !complex
332: test:
334: TEST*/