Actual source code: ex5.c
2: static char help[] = "Basic equation for an induction generator driven by a wind turbine.\n";
\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}
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: */
25: /*T
27: T*/
29: #include <petscts.h>
31: #define freq 50
32: #define ws (2*PETSC_PI*freq)
33: #define MVAbase 100
35: typedef struct {
36: /* Parameters for wind speed model */
37: PetscInt nsamples; /* Number of wind samples */
38: PetscReal cw; /* Scale factor for Weibull distribution */
39: PetscReal kw; /* Shape factor for Weibull distribution */
40: Vec wind_data; /* Vector to hold wind speeds */
41: Vec t_wind; /* Vector to hold wind speed times */
42: PetscReal Tw; /* Filter time constant */
44: /* Wind turbine parameters */
45: PetscScalar Rt; /* Rotor radius */
46: PetscScalar Ar; /* Area swept by rotor (pi*R*R) */
47: PetscReal nGB; /* Gear box ratio */
48: PetscReal Ht; /* Turbine inertia constant */
49: PetscReal rho; /* Atmospheric pressure */
51: /* Induction generator parameters */
52: PetscInt np; /* Number of poles */
53: PetscReal Xm; /* Magnetizing reactance */
54: PetscReal Xs; /* Stator Reactance */
55: PetscReal Xr; /* Rotor reactance */
56: PetscReal Rs; /* Stator resistance */
57: PetscReal Rr; /* Rotor resistance */
58: PetscReal Hm; /* Motor inertia constant */
59: PetscReal Xp; /* Xs + Xm*Xr/(Xm + Xr) */
60: PetscScalar Te; /* Electrical Torque */
62: Mat Sol; /* Solution matrix */
63: PetscInt stepnum; /* Column number of solution matrix */
64: } AppCtx;
66: /* Initial values computed by Power flow and initialization */
67: PetscScalar s = -0.00011577790353;
68: /*Pw = 0.011064344110238; %Te*wm */
69: PetscScalar vwa = 22.317142184449754;
70: PetscReal tmax = 20.0;
72: /* Saves the solution at each time to a matrix */
73: PetscErrorCode SaveSolution(TS ts)
74: {
75: AppCtx *user;
76: Vec X;
77: PetscScalar *mat;
78: const PetscScalar *x;
79: PetscInt idx;
80: PetscReal t;
82: TSGetApplicationContext(ts,&user);
83: TSGetTime(ts,&t);
84: TSGetSolution(ts,&X);
85: idx = 3*user->stepnum;
86: MatDenseGetArray(user->Sol,&mat);
87: VecGetArrayRead(X,&x);
88: mat[idx] = t;
89: PetscArraycpy(mat+idx+1,x,2);
90: MatDenseRestoreArray(user->Sol,&mat);
91: VecRestoreArrayRead(X,&x);
92: user->stepnum++;
93: return 0;
94: }
96: /* Computes the wind speed using Weibull distribution */
97: PetscErrorCode WindSpeeds(AppCtx *user)
98: {
100: PetscScalar *x,*t,avg_dev,sum;
101: PetscInt i;
103: user->cw = 5;
104: user->kw = 2; /* Rayleigh distribution */
105: user->nsamples = 2000;
106: user->Tw = 0.2;
107: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Wind Speed Options","");
108: {
109: PetscOptionsReal("-cw","","",user->cw,&user->cw,NULL);
110: PetscOptionsReal("-kw","","",user->kw,&user->kw,NULL);
111: PetscOptionsInt("-nsamples","","",user->nsamples,&user->nsamples,NULL);
112: PetscOptionsReal("-Tw","","",user->Tw,&user->Tw,NULL);
113: }
114: PetscOptionsEnd();
115: VecCreate(PETSC_COMM_WORLD,&user->wind_data);
116: VecSetSizes(user->wind_data,PETSC_DECIDE,user->nsamples);
117: VecSetFromOptions(user->wind_data);
118: VecDuplicate(user->wind_data,&user->t_wind);
120: VecGetArray(user->t_wind,&t);
121: for (i=0; i < user->nsamples; i++) t[i] = (i+1)*tmax/user->nsamples;
122: VecRestoreArray(user->t_wind,&t);
124: /* Wind speed deviation = (-log(rand)/cw)^(1/kw) */
125: VecSetRandom(user->wind_data,NULL);
126: VecLog(user->wind_data);
127: VecScale(user->wind_data,-1/user->cw);
128: VecGetArray(user->wind_data,&x);
129: for (i=0;i < user->nsamples;i++) x[i] = PetscPowScalar(x[i],(1/user->kw));
130: VecRestoreArray(user->wind_data,&x);
131: VecSum(user->wind_data,&sum);
132: avg_dev = sum/user->nsamples;
133: /* Wind speed (t) = (1 + wind speed deviation(t) - avg_dev)*average wind speed */
134: VecShift(user->wind_data,(1-avg_dev));
135: VecScale(user->wind_data,vwa);
136: return 0;
137: }
139: /* Sets the parameters for wind turbine */
140: PetscErrorCode SetWindTurbineParams(AppCtx *user)
141: {
142: user->Rt = 35;
143: user->Ar = PETSC_PI*user->Rt*user->Rt;
144: user->nGB = 1.0/89.0;
145: user->rho = 1.225;
146: user->Ht = 1.5;
147: return 0;
148: }
150: /* Sets the parameters for induction generator */
151: PetscErrorCode SetInductionGeneratorParams(AppCtx *user)
152: {
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: return 0;
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: temp = user->nGB*2*user->Rt*ws/user->np;
171: lambda = temp*wm/vw;
172: lambda_i = 1/(1/lambda + 0.002);
173: cp = 0.44*(125/lambda_i - 6.94)*PetscExpScalar(-16.5/lambda_i);
174: *Pw = 0.5*user->rho*cp*user->Ar*vw*vw*vw/(MVAbase*1e6);
175: return 0;
176: }
178: /*
179: Defines the ODE passed to the ODE solver
180: */
181: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *user)
182: {
183: PetscScalar *f,wm,Pw,*wd;
184: const PetscScalar *u,*udot;
185: PetscInt stepnum;
187: TSGetStepNumber(ts,&stepnum);
188: /* The next three lines allow us to access the entries of the vectors directly */
189: VecGetArrayRead(U,&u);
190: VecGetArrayRead(Udot,&udot);
191: VecGetArray(F,&f);
192: VecGetArray(user->wind_data,&wd);
194: f[0] = user->Tw*udot[0] - wd[stepnum] + u[0];
195: wm = 1-u[1];
196: GetWindPower(wm,u[0],&Pw,user);
197: f[1] = 2.0*(user->Ht+user->Hm)*udot[1] - Pw/wm + user->Te;
199: VecRestoreArray(user->wind_data,&wd);
200: VecRestoreArrayRead(U,&u);
201: VecRestoreArrayRead(Udot,&udot);
202: VecRestoreArray(F,&f);
203: return 0;
204: }
206: int main(int argc,char **argv)
207: {
208: TS ts; /* ODE integrator */
209: Vec U; /* solution will be stored here */
210: Mat A; /* Jacobian matrix */
211: PetscMPIInt size;
212: PetscInt n = 2,idx;
213: AppCtx user;
214: PetscScalar *u;
215: SNES snes;
216: PetscScalar *mat;
217: const PetscScalar *x,*rmat;
218: Mat B;
219: PetscScalar *amat;
220: PetscViewer viewer;
222: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
223: Initialize program
224: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
225: PetscInitialize(&argc,&argv,(char*)0,help);
226: MPI_Comm_size(PETSC_COMM_WORLD,&size);
229: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
230: Create necessary matrix and vectors
231: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
232: MatCreate(PETSC_COMM_WORLD,&A);
233: MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
234: MatSetFromOptions(A);
235: MatSetUp(A);
237: MatCreateVecs(A,&U,NULL);
239: /* Create wind speed data using Weibull distribution */
240: WindSpeeds(&user);
241: /* Set parameters for wind turbine and induction generator */
242: SetWindTurbineParams(&user);
243: SetInductionGeneratorParams(&user);
245: VecGetArray(U,&u);
246: u[0] = vwa;
247: u[1] = s;
248: VecRestoreArray(U,&u);
250: /* Create matrix to save solutions at each time step */
251: user.stepnum = 0;
253: MatCreateSeqDense(PETSC_COMM_SELF,3,2010,NULL,&user.Sol);
255: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
256: Create timestepping solver context
257: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
258: TSCreate(PETSC_COMM_WORLD,&ts);
259: TSSetProblemType(ts,TS_NONLINEAR);
260: TSSetType(ts,TSBEULER);
261: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&user);
263: TSGetSNES(ts,&snes);
264: SNESSetJacobian(snes,A,A,SNESComputeJacobianDefault,NULL);
265: /* TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&user); */
266: TSSetApplicationContext(ts,&user);
268: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
269: Set initial conditions
270: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
271: TSSetSolution(ts,U);
273: /* Save initial solution */
274: idx=3*user.stepnum;
276: MatDenseGetArray(user.Sol,&mat);
277: VecGetArrayRead(U,&x);
279: mat[idx] = 0.0;
281: PetscArraycpy(mat+idx+1,x,2);
282: MatDenseRestoreArray(user.Sol,&mat);
283: VecRestoreArrayRead(U,&x);
284: user.stepnum++;
286: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
287: Set solver options
288: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
289: TSSetMaxTime(ts,20.0);
290: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
291: TSSetTimeStep(ts,.01);
292: TSSetFromOptions(ts);
293: TSSetPostStep(ts,SaveSolution);
294: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
295: Solve nonlinear system
296: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
297: TSSolve(ts,U);
299: MatCreateSeqDense(PETSC_COMM_SELF,3,user.stepnum,NULL,&B);
300: MatDenseGetArrayRead(user.Sol,&rmat);
301: MatDenseGetArray(B,&amat);
302: PetscArraycpy(amat,rmat,user.stepnum*3);
303: MatDenseRestoreArray(B,&amat);
304: MatDenseRestoreArrayRead(user.Sol,&rmat);
306: PetscViewerBinaryOpen(PETSC_COMM_SELF,"out.bin",FILE_MODE_WRITE,&viewer);
307: MatView(B,viewer);
308: PetscViewerDestroy(&viewer);
309: MatDestroy(&user.Sol);
310: MatDestroy(&B);
311: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
312: Free work space. All PETSc objects should be destroyed when they are no longer needed.
313: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
314: VecDestroy(&user.wind_data);
315: VecDestroy(&user.t_wind);
316: MatDestroy(&A);
317: VecDestroy(&U);
318: TSDestroy(&ts);
320: PetscFinalize();
321: return 0;
322: }
324: /*TEST
326: build:
327: requires: !complex
329: test:
331: TEST*/