Actual source code: ex5.c

petsc-3.13.4 2020-08-01
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  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:   PetscErrorCode    ierr;
 76:   AppCtx            *user;
 77:   Vec               X;
 78:   PetscScalar       *mat;
 79:   const PetscScalar *x;
 80:   PetscInt          idx;
 81:   PetscReal         t;

 84:   TSGetApplicationContext(ts,&user);
 85:   TSGetTime(ts,&t);
 86:   TSGetSolution(ts,&X);
 87:   idx      =  3*user->stepnum;
 88:   MatDenseGetArray(user->Sol,&mat);
 89:   VecGetArrayRead(X,&x);
 90:   mat[idx] = t;
 91:   PetscArraycpy(mat+idx+1,x,2);
 92:   MatDenseRestoreArray(user->Sol,&mat);
 93:   VecRestoreArrayRead(X,&x);
 94:   user->stepnum++;
 95:   return(0);
 96: }


 99: /* Computes the wind speed using Weibull distribution */
100: PetscErrorCode WindSpeeds(AppCtx *user)
101: {
103:   PetscScalar    *x,*t,avg_dev,sum;
104:   PetscInt       i;

107:   user->cw       = 5;
108:   user->kw       = 2; /* Rayleigh distribution */
109:   user->nsamples = 2000;
110:   user->Tw       = 0.2;
111:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Wind Speed Options","");
112:   {
113:     PetscOptionsReal("-cw","","",user->cw,&user->cw,NULL);
114:     PetscOptionsReal("-kw","","",user->kw,&user->kw,NULL);
115:     PetscOptionsInt("-nsamples","","",user->nsamples,&user->nsamples,NULL);
116:     PetscOptionsReal("-Tw","","",user->Tw,&user->Tw,NULL);
117:   }
118:   PetscOptionsEnd();
119:   VecCreate(PETSC_COMM_WORLD,&user->wind_data);
120:   VecSetSizes(user->wind_data,PETSC_DECIDE,user->nsamples);
121:   VecSetFromOptions(user->wind_data);
122:   VecDuplicate(user->wind_data,&user->t_wind);

124:   VecGetArray(user->t_wind,&t);
125:   for (i=0; i < user->nsamples; i++) t[i] = (i+1)*tmax/user->nsamples;
126:   VecRestoreArray(user->t_wind,&t);

128:   /* Wind speed deviation = (-log(rand)/cw)^(1/kw) */
129:   VecSetRandom(user->wind_data,NULL);
130:   VecLog(user->wind_data);
131:   VecScale(user->wind_data,-1/user->cw);
132:   VecGetArray(user->wind_data,&x);
133:   for (i=0;i < user->nsamples;i++) x[i] = PetscPowScalar(x[i],(1/user->kw));
134:   VecRestoreArray(user->wind_data,&x);
135:   VecSum(user->wind_data,&sum);
136:   avg_dev = sum/user->nsamples;
137:   /* Wind speed (t) = (1 + wind speed deviation(t) - avg_dev)*average wind speed */
138:   VecShift(user->wind_data,(1-avg_dev));
139:   VecScale(user->wind_data,vwa);
140:   return(0);
141: }

143: /* Sets the parameters for wind turbine */
144: PetscErrorCode SetWindTurbineParams(AppCtx *user)
145: {
147:   user->Rt  = 35;
148:   user->Ar  = PETSC_PI*user->Rt*user->Rt;
149:   user->nGB = 1.0/89.0;
150:   user->rho = 1.225;
151:   user->Ht  = 1.5;
152:   return(0);
153: }

155: /* Sets the parameters for induction generator */
156: PetscErrorCode SetInductionGeneratorParams(AppCtx *user)
157: {
159:   user->np = 4;
160:   user->Xm = 3.0;
161:   user->Xs = 0.1;
162:   user->Xr = 0.08;
163:   user->Rs = 0.01;
164:   user->Rr = 0.01;
165:   user->Xp = user->Xs + user->Xm*user->Xr/(user->Xm + user->Xr);
166:   user->Hm = 1.0;
167:   user->Te = 0.011063063063251968;
168:   return(0);
169: }

171: /* Computes the power extracted from wind */
172: PetscErrorCode GetWindPower(PetscScalar wm,PetscScalar vw,PetscScalar *Pw,AppCtx *user)
173: {
174:   PetscScalar temp,lambda,lambda_i,cp;

177:   temp     = user->nGB*2*user->Rt*ws/user->np;
178:   lambda   = temp*wm/vw;
179:   lambda_i = 1/(1/lambda + 0.002);
180:   cp       = 0.44*(125/lambda_i - 6.94)*PetscExpScalar(-16.5/lambda_i);
181:   *Pw      = 0.5*user->rho*cp*user->Ar*vw*vw*vw/(MVAbase*1e6);
182:   return(0);
183: }

185: /*
186:      Defines the ODE passed to the ODE solver
187: */
188: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *user)
189: {
190:   PetscErrorCode    ierr;
191:   PetscScalar       *f,wm,Pw,*wd;
192:   const PetscScalar *u,*udot;
193:   PetscInt          stepnum;

196:   TSGetStepNumber(ts,&stepnum);
197:   /*  The next three lines allow us to access the entries of the vectors directly */
198:   VecGetArrayRead(U,&u);
199:   VecGetArrayRead(Udot,&udot);
200:   VecGetArray(F,&f);
201:   VecGetArray(user->wind_data,&wd);

203:   f[0] = user->Tw*udot[0] - wd[stepnum] + u[0];
204:   wm   = 1-u[1];
205:   GetWindPower(wm,u[0],&Pw,user);
206:   f[1] = 2.0*(user->Ht+user->Hm)*udot[1] - Pw/wm + user->Te;

208:   VecRestoreArray(user->wind_data,&wd);
209:   VecRestoreArrayRead(U,&u);
210:   VecRestoreArrayRead(Udot,&udot);
211:   VecRestoreArray(F,&f);
212:   return(0);
213: }

215: int main(int argc,char **argv)
216: {
217:   TS                ts;            /* ODE integrator */
218:   Vec               U;             /* solution will be stored here */
219:   Mat               A;             /* Jacobian matrix */
220:   PetscErrorCode    ierr;
221:   PetscMPIInt       size;
222:   PetscInt          n = 2,idx;
223:   AppCtx            user;
224:   PetscScalar       *u;
225:   SNES              snes;
226:   PetscScalar       *mat;
227:   const PetscScalar *x,*rmat;
228:   Mat               B;
229:   PetscScalar       *amat;
230:   PetscViewer       viewer;



234:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
235:      Initialize program
236:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
237:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
238:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
239:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

241:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
242:     Create necessary matrix and vectors
243:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
244:   MatCreate(PETSC_COMM_WORLD,&A);
245:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
246:   MatSetFromOptions(A);
247:   MatSetUp(A);

249:   MatCreateVecs(A,&U,NULL);

251:   /* Create wind speed data using Weibull distribution */
252:   WindSpeeds(&user);
253:   /* Set parameters for wind turbine and induction generator */
254:   SetWindTurbineParams(&user);
255:   SetInductionGeneratorParams(&user);

257:   VecGetArray(U,&u);
258:   u[0] = vwa;
259:   u[1] = s;
260:   VecRestoreArray(U,&u);

262:   /* Create matrix to save solutions at each time step */
263:   user.stepnum = 0;

265:   MatCreateSeqDense(PETSC_COMM_SELF,3,2010,NULL,&user.Sol);

267:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
268:      Create timestepping solver context
269:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
270:   TSCreate(PETSC_COMM_WORLD,&ts);
271:   TSSetProblemType(ts,TS_NONLINEAR);
272:   TSSetType(ts,TSBEULER);
273:   TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&user);

275:   TSGetSNES(ts,&snes);
276:   SNESSetJacobian(snes,A,A,SNESComputeJacobianDefault,NULL);
277:   /*  TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&user); */
278:   TSSetApplicationContext(ts,&user);

280:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
281:      Set initial conditions
282:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
283:   TSSetSolution(ts,U);

285:   /* Save initial solution */
286:   idx=3*user.stepnum;

288:   MatDenseGetArray(user.Sol,&mat);
289:   VecGetArrayRead(U,&x);

291:   mat[idx] = 0.0;

293:   PetscArraycpy(mat+idx+1,x,2);
294:   MatDenseRestoreArray(user.Sol,&mat);
295:   VecRestoreArrayRead(U,&x);
296:   user.stepnum++;


299:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
300:      Set solver options
301:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
302:   TSSetMaxTime(ts,20.0);
303:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
304:   TSSetTimeStep(ts,.01);
305:   TSSetFromOptions(ts);
306:   TSSetPostStep(ts,SaveSolution);
307:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
308:      Solve nonlinear system
309:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
310:   TSSolve(ts,U);

312:   MatCreateSeqDense(PETSC_COMM_SELF,3,user.stepnum,NULL,&B);
313:   MatDenseGetArrayRead(user.Sol,&rmat);
314:   MatDenseGetArray(B,&amat);
315:   PetscArraycpy(amat,rmat,user.stepnum*3);
316:   MatDenseRestoreArray(B,&amat);
317:   MatDenseRestoreArrayRead(user.Sol,&rmat);

319:   PetscViewerBinaryOpen(PETSC_COMM_SELF,"out.bin",FILE_MODE_WRITE,&viewer);
320:   MatView(B,viewer);
321:   PetscViewerDestroy(&viewer);
322:   MatDestroy(&user.Sol);
323:   MatDestroy(&B);
324:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
325:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
326:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
327:   VecDestroy(&user.wind_data);
328:   VecDestroy(&user.t_wind);
329:   MatDestroy(&A);
330:   VecDestroy(&U);
331:   TSDestroy(&ts);

333:   PetscFinalize();
334:   return ierr;
335: }


338: /*TEST

340:    build:
341:       requires: !complex

343:    test:


346: TEST*/