Actual source code: ex3.c

petsc-3.9.1 2018-04-29
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  2: static char help[] = "Basic equation for generator stability analysis.\n";


\begin{eqnarray}
\frac{d \theta}{dt} = \omega_b (\omega - \omega_s)
\frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - P_max \sin(\theta) -D(\omega - \omega_s)\\
\end{eqnarray}



Ensemble of initial conditions
./ex2 -ensemble -ts_monitor_draw_solution_phase -1,-3,3,3 -ts_adapt_dt_max .01 -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly

Fault at .1 seconds
./ex2 -ts_monitor_draw_solution_phase .42,.95,.6,1.05 -ts_adapt_dt_max .01 -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly

Initial conditions same as when fault is ended
./ex2 -u 0.496792,1.00932 -ts_monitor_draw_solution_phase .42,.95,.6,1.05 -ts_adapt_dt_max .01 -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly


 25: /*
 26:    Include "petscts.h" so that we can use TS solvers.  Note that this
 27:    file automatically includes:
 28:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 29:      petscmat.h - matrices
 30:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 31:      petscviewer.h - viewers               petscpc.h  - preconditioners
 32:      petscksp.h   - linear solvers
 33: */
 34: /*T

 36: T*/

 38: #include <petscts.h>

 40: typedef struct {
 41:   PetscScalar H,D,omega_b,omega_s,Pmax,Pmax_ini,Pm,E,V,X;
 42:   PetscReal   tf,tcl;
 43: } AppCtx;

 45: /* Event check */
 46: PetscErrorCode EventFunction(TS ts,PetscReal t,Vec X,PetscScalar *fvalue,void *ctx)
 47: {
 48:   AppCtx        *user=(AppCtx*)ctx;

 51:   /* Event for fault-on time */
 52:   fvalue[0] = t - user->tf;
 53:   /* Event for fault-off time */
 54:   fvalue[1] = t - user->tcl;

 56:   return(0);
 57: }

 59: PetscErrorCode PostEventFunction(TS ts,PetscInt nevents,PetscInt event_list[],PetscReal t,Vec X,PetscBool forwardsolve,void* ctx)
 60: {
 61:   AppCtx *user=(AppCtx*)ctx;
 62: 

 65:   if (event_list[0] == 0) user->Pmax = 0.0; /* Apply disturbance - this is done by setting Pmax = 0 */
 66:   else if(event_list[0] == 1) user->Pmax = user->Pmax_ini; /* Remove the fault  - this is done by setting Pmax = Pmax_ini */
 67:   return(0);
 68: }

 70: /*
 71:      Defines the ODE passed to the ODE solver
 72: */
 73: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
 74: {
 75:   PetscErrorCode    ierr;
 76:   const PetscScalar *u,*udot;
 77:   PetscScalar       *f,Pmax;

 80:   /*  The next three lines allow us to access the entries of the vectors directly */
 81:   VecGetArrayRead(U,&u);
 82:   VecGetArrayRead(Udot,&udot);
 83:   VecGetArray(F,&f);
 84:   Pmax = ctx->Pmax;

 86:   f[0] = udot[0] - ctx->omega_b*(u[1] - ctx->omega_s);
 87:   f[1] = 2.0*ctx->H/ctx->omega_s*udot[1] +  Pmax*PetscSinScalar(u[0]) + ctx->D*(u[1] - ctx->omega_s)- ctx->Pm;

 89:   VecRestoreArrayRead(U,&u);
 90:   VecRestoreArrayRead(Udot,&udot);
 91:   VecRestoreArray(F,&f);
 92:   return(0);
 93: }

 95: /*
 96:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
 97: */
 98: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
 99: {
100:   PetscErrorCode    ierr;
101:   PetscInt          rowcol[] = {0,1};
102:   PetscScalar       J[2][2],Pmax;
103:   const PetscScalar *u,*udot;

106:   VecGetArrayRead(U,&u);
107:   VecGetArrayRead(Udot,&udot);
108:   Pmax = ctx->Pmax;

110:   J[0][0] = a;                                    J[0][1] = -ctx->omega_b;
111:   J[1][1] = 2.0*ctx->H/ctx->omega_s*a + ctx->D;   J[1][0] = Pmax*PetscCosScalar(u[0]);

113:   MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
114:   VecRestoreArrayRead(U,&u);
115:   VecRestoreArrayRead(Udot,&udot);

117:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
118:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
119:   if (A != B) {
120:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
121:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
122:   }
123:   return(0);
124: }

126: int main(int argc,char **argv)
127: {
128:   TS             ts;            /* ODE integrator */
129:   Vec            U;             /* solution will be stored here */
130:   Mat            A;             /* Jacobian matrix */
132:   PetscMPIInt    size;
133:   PetscInt       n = 2;
134:   AppCtx         ctx;
135:   PetscScalar    *u;
136:   PetscReal      du[2] = {0.0,0.0};
137:   PetscBool      ensemble = PETSC_FALSE,flg1,flg2;
138:   PetscInt       direction[2];
139:   PetscBool      terminate[2];

141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142:      Initialize program
143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
144:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
145:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
146:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

148:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149:     Create necessary matrix and vectors
150:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
151:   MatCreate(PETSC_COMM_WORLD,&A);
152:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
153:   MatSetType(A,MATDENSE);
154:   MatSetFromOptions(A);
155:   MatSetUp(A);

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

159:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160:     Set runtime options
161:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
162:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
163:   {
164:     ctx.omega_b = 1.0;
165:     ctx.omega_s = 2.0*PETSC_PI*60.0;
166:     ctx.H       = 5.0;
167:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
168:     ctx.D       = 5.0;
169:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
170:     ctx.E       = 1.1378;
171:     ctx.V       = 1.0;
172:     ctx.X       = 0.545;
173:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
174:     ctx.Pmax_ini = ctx.Pmax;
175:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
176:     ctx.Pm      = 0.9;
177:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
178:     ctx.tf      = 1.0;
179:     ctx.tcl     = 1.05;
180:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
181:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
182:     PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
183:     if (ensemble) {
184:       ctx.tf      = -1;
185:       ctx.tcl     = -1;
186:     }

188:     VecGetArray(U,&u);
189:     u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
190:     u[1] = 1.0;
191:     PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);
192:     n    = 2;
193:     PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);
194:     u[0] += du[0];
195:     u[1] += du[1];
196:     VecRestoreArray(U,&u);
197:     if (flg1 || flg2) {
198:       ctx.tf      = -1;
199:       ctx.tcl     = -1;
200:     }
201:   }
202:   PetscOptionsEnd();

204:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
205:      Create timestepping solver context
206:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
207:   TSCreate(PETSC_COMM_WORLD,&ts);
208:   TSSetProblemType(ts,TS_NONLINEAR);
209:   TSSetType(ts,TSTHETA);
210:   TSSetEquationType(ts,TS_EQ_IMPLICIT);
211:   TSARKIMEXSetFullyImplicit(ts,PETSC_TRUE);
212:   TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);
213:   TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);

215:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
216:      Set initial conditions
217:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
218:   TSSetSolution(ts,U);

220:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
221:      Set solver options
222:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
223:   TSSetMaxTime(ts,35.0);
224:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
225:   TSSetTimeStep(ts,.1);
226:   TSSetFromOptions(ts);

228:   direction[0] = direction[1] = 1;
229:   terminate[0] = terminate[1] = PETSC_FALSE;

231:   TSSetEventHandler(ts,2,direction,terminate,EventFunction,PostEventFunction,(void*)&ctx);

233:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
234:      Solve nonlinear system
235:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
236:   if (ensemble) {
237:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
238:       VecGetArray(U,&u);
239:       u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
240:       u[1] = ctx.omega_s;
241:       u[0] += du[0];
242:       u[1] += du[1];
243:       VecRestoreArray(U,&u);
244:       TSSetTimeStep(ts,.01);
245:       TSSolve(ts,U);
246:     }
247:   } else {
248:     TSSolve(ts,U);
249:   }
250:   VecView(U,PETSC_VIEWER_STDOUT_WORLD);
251:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
252:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
253:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
254:   MatDestroy(&A);
255:   VecDestroy(&U);
256:   TSDestroy(&ts);
257:   PetscFinalize();
258:   return ierr;
259: }


262: /*TEST

264:    build:
265:      requires: !complex !single

267:    test:
268:       args: -nox

270: TEST*/