Actual source code: ex5.c
petsc-3.8.4 2018-03-24
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: #include <petscts.h>
27: #define freq 50
28: #define ws (2*PETSC_PI*freq)
29: #define MVAbase 100
31: typedef struct {
32: /* Parameters for wind speed model */
33: PetscInt nsamples; /* Number of wind samples */
34: PetscReal cw; /* Scale factor for Weibull distribution */
35: PetscReal kw; /* Shape factor for Weibull distribution */
36: Vec wind_data; /* Vector to hold wind speeds */
37: Vec t_wind; /* Vector to hold wind speed times */
38: PetscReal Tw; /* Filter time constant */
40: /* Wind turbine parameters */
41: PetscScalar Rt; /* Rotor radius */
42: PetscScalar Ar; /* Area swept by rotor (pi*R*R) */
43: PetscReal nGB; /* Gear box ratio */
44: PetscReal Ht; /* Turbine inertia constant */
45: PetscReal rho; /* Atmospheric pressure */
47: /* Induction generator parameters */
48: PetscInt np; /* Number of poles */
49: PetscReal Xm; /* Magnetizing reactance */
50: PetscReal Xs; /* Stator Reactance */
51: PetscReal Xr; /* Rotor reactance */
52: PetscReal Rs; /* Stator resistance */
53: PetscReal Rr; /* Rotor resistance */
54: PetscReal Hm; /* Motor inertia constant */
55: PetscReal Xp; /* Xs + Xm*Xr/(Xm + Xr) */
56: PetscScalar Te; /* Electrical Torque */
58: Mat Sol; /* Solution matrix */
59: PetscInt stepnum; /* Column number of solution matrix */
60: } AppCtx;
62: /* Initial values computed by Power flow and initialization */
63: PetscScalar s = -0.00011577790353;
64: /*Pw = 0.011064344110238; %Te*wm */
65: PetscScalar vwa = 22.317142184449754;
66: PetscReal tmax = 20.0;
68: /* Saves the solution at each time to a matrix */
69: PetscErrorCode SaveSolution(TS ts)
70: {
71: PetscErrorCode ierr;
72: AppCtx *user;
73: Vec X;
74: PetscScalar *mat;
75: const PetscScalar *x;
76: PetscInt idx;
77: PetscReal t;
80: TSGetApplicationContext(ts,&user);
81: TSGetTime(ts,&t);
82: TSGetSolution(ts,&X);
83: idx = 3*user->stepnum;
84: MatDenseGetArray(user->Sol,&mat);
85: VecGetArrayRead(X,&x);
86: mat[idx] = t;
87: PetscMemcpy(mat+idx+1,x,2*sizeof(PetscScalar));
88: MatDenseRestoreArray(user->Sol,&mat);
89: VecRestoreArrayRead(X,&x);
90: user->stepnum++;
91: return(0);
92: }
95: /* Computes the wind speed using Weibull distribution */
96: PetscErrorCode WindSpeeds(AppCtx *user)
97: {
99: PetscScalar *x,*t,avg_dev,sum;
100: 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: {
143: user->Rt = 35;
144: user->Ar = PETSC_PI*user->Rt*user->Rt;
145: user->nGB = 1.0/89.0;
146: user->rho = 1.225;
147: user->Ht = 1.5;
148: return(0);
149: }
151: /* Sets the parameters for induction generator */
152: PetscErrorCode SetInductionGeneratorParams(AppCtx *user)
153: {
155: user->np = 4;
156: user->Xm = 3.0;
157: user->Xs = 0.1;
158: user->Xr = 0.08;
159: user->Rs = 0.01;
160: user->Rr = 0.01;
161: user->Xp = user->Xs + user->Xm*user->Xr/(user->Xm + user->Xr);
162: user->Hm = 1.0;
163: user->Te = 0.011063063063251968;
164: return(0);
165: }
167: /* Computes the power extracted from wind */
168: PetscErrorCode GetWindPower(PetscScalar wm,PetscScalar vw,PetscScalar *Pw,AppCtx *user)
169: {
170: PetscScalar temp,lambda,lambda_i,cp;
173: temp = user->nGB*2*user->Rt*ws/user->np;
174: lambda = temp*wm/vw;
175: lambda_i = 1/(1/lambda + 0.002);
176: cp = 0.44*(125/lambda_i - 6.94)*PetscExpScalar(-16.5/lambda_i);
177: *Pw = 0.5*user->rho*cp*user->Ar*vw*vw*vw/(MVAbase*1e6);
178: return(0);
179: }
181: /*
182: Defines the ODE passed to the ODE solver
183: */
184: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *user)
185: {
186: PetscErrorCode ierr;
187: PetscScalar *f,wm,Pw,*wd;
188: const PetscScalar *u,*udot;
189: PetscInt stepnum;
192: TSGetStepNumber(ts,&stepnum);
193: /* The next three lines allow us to access the entries of the vectors directly */
194: VecGetArrayRead(U,&u);
195: VecGetArrayRead(Udot,&udot);
196: VecGetArray(F,&f);
197: VecGetArray(user->wind_data,&wd);
199: f[0] = user->Tw*udot[0] - wd[stepnum] + u[0];
200: wm = 1-u[1];
201: GetWindPower(wm,u[0],&Pw,user);
202: f[1] = 2.0*(user->Ht+user->Hm)*udot[1] - Pw/wm + user->Te;
204: VecRestoreArray(user->wind_data,&wd);
205: VecRestoreArrayRead(U,&u);
206: VecRestoreArrayRead(Udot,&udot);
207: VecRestoreArray(F,&f);
208: return(0);
209: }
211: int main(int argc,char **argv)
212: {
213: TS ts; /* ODE integrator */
214: Vec U; /* solution will be stored here */
215: Mat A; /* Jacobian matrix */
217: PetscMPIInt size;
218: PetscInt n = 2,idx;
219: AppCtx user;
220: PetscScalar *u;
221: SNES snes;
222: PetscScalar *mat;
223: const PetscScalar *x;
224: Mat B;
225: PetscScalar *amat;
226: PetscViewer viewer;
230: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
231: Initialize program
232: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
233: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
234: MPI_Comm_size(PETSC_COMM_WORLD,&size);
235: if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
237: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
238: Create necessary matrix and vectors
239: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
240: MatCreate(PETSC_COMM_WORLD,&A);
241: MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
242: MatSetFromOptions(A);
243: MatSetUp(A);
245: MatCreateVecs(A,&U,NULL);
247: /* Create wind speed data using Weibull distribution */
248: WindSpeeds(&user);
249: /* Set parameters for wind turbine and induction generator */
250: SetWindTurbineParams(&user);
251: SetInductionGeneratorParams(&user);
253: VecGetArray(U,&u);
254: u[0] = vwa;
255: u[1] = s;
256: VecRestoreArray(U,&u);
258: /* Create matrix to save solutions at each time step */
259: user.stepnum = 0;
261: MatCreateSeqDense(PETSC_COMM_SELF,3,2010,NULL,&user.Sol);
263: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
264: Create timestepping solver context
265: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
266: TSCreate(PETSC_COMM_WORLD,&ts);
267: TSSetProblemType(ts,TS_NONLINEAR);
268: TSSetType(ts,TSBEULER);
269: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&user);
271: TSGetSNES(ts,&snes);
272: SNESSetJacobian(snes,A,A,SNESComputeJacobianDefault,NULL);
273: /* TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&user); */
274: TSSetApplicationContext(ts,&user);
276: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
277: Set initial conditions
278: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
279: TSSetSolution(ts,U);
281: /* Save initial solution */
282: idx=3*user.stepnum;
284: MatDenseGetArray(user.Sol,&mat);
285: VecGetArrayRead(U,&x);
287: mat[idx] = 0.0;
289: PetscMemcpy(mat+idx+1,x,2*sizeof(PetscScalar));
290: MatDenseRestoreArray(user.Sol,&mat);
291: VecRestoreArrayRead(U,&x);
292: user.stepnum++;
295: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
296: Set solver options
297: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
298: TSSetMaxTime(ts,20.0);
299: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
300: TSSetTimeStep(ts,.01);
301: TSSetFromOptions(ts);
302: TSSetPostStep(ts,SaveSolution);
303: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
304: Solve nonlinear system
305: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
306: TSSolve(ts,U);
308: MatCreateSeqDense(PETSC_COMM_SELF,3,user.stepnum,NULL,&B);
309: MatDenseGetArray(user.Sol,&mat);
310: MatDenseGetArray(B,&amat);
311: PetscMemcpy(amat,mat,user.stepnum*3*sizeof(PetscScalar));
312: MatDenseRestoreArray(B,&amat);
313: MatDenseRestoreArray(user.Sol,&mat);
315: PetscViewerBinaryOpen(PETSC_COMM_SELF,"out.bin",FILE_MODE_WRITE,&viewer);
316: MatView(B,viewer);
317: PetscViewerDestroy(&viewer);
318: MatDestroy(&user.Sol);
319: MatDestroy(&B);
320: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
321: Free work space. All PETSc objects should be destroyed when they are no longer needed.
322: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
323: VecDestroy(&user.wind_data);
324: VecDestroy(&user.t_wind);
325: MatDestroy(&A);
326: VecDestroy(&U);
327: TSDestroy(&ts);
329: PetscFinalize();
330: return ierr;
331: }