Actual source code: ex2.c

petsc-3.12.1 2019-10-22
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  2: static char help[] = "Basic equation for generator stability analysis.\n";


\begin{eqnarray}
\frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - \frac{EV}{X} \sin(\theta) -D(\omega - \omega_s)\\
\frac{d \theta}{dt} = \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: */

 35: #include <petscts.h>

 37: typedef struct {
 38:   PetscScalar H,D,omega_s,Pmax,Pm,E,V,X;
 39:   PetscReal   tf,tcl;
 40: } AppCtx;

 42: /*
 43:      Defines the ODE passed to the ODE solver
 44: */
 45: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
 46: {
 47:   PetscErrorCode    ierr;
 48:   PetscScalar       *f,Pmax;
 49:   const PetscScalar *u,*udot;

 52:   /*  The next three lines allow us to access the entries of the vectors directly */
 53:   VecGetArrayRead(U,&u);
 54:   VecGetArrayRead(Udot,&udot);
 55:   VecGetArray(F,&f);
 56:   if ((t > ctx->tf) && (t < ctx->tcl)) Pmax = 0.0; /* A short-circuit on the generator terminal that drives the electrical power output (Pmax*sin(delta)) to 0 */
 57:   else if (t >= ctx->tcl) Pmax = ctx->E/0.745;
 58:   else Pmax = ctx->Pmax;
 59:   f[0] = udot[0] - ctx->omega_s*(u[1] - 1.0);
 60:   f[1] = 2.0*ctx->H*udot[1] +  Pmax*PetscSinScalar(u[0]) + ctx->D*(u[1] - 1.0)- ctx->Pm;

 62:   VecRestoreArrayRead(U,&u);
 63:   VecRestoreArrayRead(Udot,&udot);
 64:   VecRestoreArray(F,&f);
 65:   return(0);
 66: }

 68: /*
 69:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
 70: */
 71: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
 72: {
 73:   PetscErrorCode    ierr;
 74:   PetscInt          rowcol[] = {0,1};
 75:   PetscScalar       J[2][2],Pmax;
 76:   const PetscScalar *u,*udot;

 79:   VecGetArrayRead(U,&u);
 80:   VecGetArrayRead(Udot,&udot);
 81:   if ((t > ctx->tf) && (t < ctx->tcl)) Pmax = 0.0; /* A short-circuit on the generator terminal that drives the electrical power output (Pmax*sin(delta)) to 0 */
 82:   else if (t >= ctx->tcl) Pmax = ctx->E/0.745;
 83:   else Pmax = ctx->Pmax;

 85:   J[0][0] = a;                       J[0][1] = -ctx->omega_s;
 86:   J[1][1] = 2.0*ctx->H*a + ctx->D;   J[1][0] = Pmax*PetscCosScalar(u[0]);

 88:   MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
 89:   VecRestoreArrayRead(U,&u);
 90:   VecRestoreArrayRead(Udot,&udot);

 92:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 93:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 94:   if (A != B) {
 95:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 96:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
 97:   }
 98:   return(0);
 99: }


102: PetscErrorCode PostStep(TS ts)
103: {
105:   Vec            X;
106:   PetscReal      t;

109:   TSGetTime(ts,&t);
110:   if (t >= .2) {
111:     TSGetSolution(ts,&X);
112:     VecView(X,PETSC_VIEWER_STDOUT_WORLD);
113:     exit(0);
114:     /* results in initial conditions after fault of -u 0.496792,1.00932 */
115:   }
116:   return(0);
117: }


120: int main(int argc,char **argv)
121: {
122:   TS             ts;            /* ODE integrator */
123:   Vec            U;             /* solution will be stored here */
124:   Mat            A;             /* Jacobian matrix */
126:   PetscMPIInt    size;
127:   PetscInt       n = 2;
128:   AppCtx         ctx;
129:   PetscScalar    *u;
130:   PetscReal      du[2] = {0.0,0.0};
131:   PetscBool      ensemble = PETSC_FALSE,flg1,flg2;

133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134:      Initialize program
135:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
136:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
137:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
138:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

140:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
141:     Create necessary matrix and vectors
142:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
143:   MatCreate(PETSC_COMM_WORLD,&A);
144:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
145:   MatSetType(A,MATDENSE);
146:   MatSetFromOptions(A);
147:   MatSetUp(A);

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

151:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
152:     Set runtime options
153:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
154:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
155:   {
156:     ctx.omega_s = 2.0*PETSC_PI*60.0;
157:     ctx.H       = 5.0;
158:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
159:     ctx.D       = 5.0;
160:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
161:     ctx.E       = 1.1378;
162:     ctx.V       = 1.0;
163:     ctx.X       = 0.545;
164:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
165:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
166:     ctx.Pm      = 0.9;
167:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
168:     ctx.tf      = 1.0;
169:     ctx.tcl     = 1.05;
170:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
171:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
172:     PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
173:     if (ensemble) {
174:       ctx.tf      = -1;
175:       ctx.tcl     = -1;
176:     }

178:     VecGetArray(U,&u);
179:     u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
180:     u[1] = 1.0;
181:     PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);
182:     n    = 2;
183:     PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);
184:     u[0] += du[0];
185:     u[1] += du[1];
186:     VecRestoreArray(U,&u);
187:     if (flg1 || flg2) {
188:       ctx.tf      = -1;
189:       ctx.tcl     = -1;
190:     }
191:   }
192:   PetscOptionsEnd();

194:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195:      Create timestepping solver context
196:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
197:   TSCreate(PETSC_COMM_WORLD,&ts);
198:   TSSetProblemType(ts,TS_NONLINEAR);
199:   TSSetType(ts,TSROSW);
200:   TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);
201:   TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);

203:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204:      Set initial conditions
205:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
206:   TSSetSolution(ts,U);

208:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209:      Set solver options
210:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
211:   TSSetMaxTime(ts,35.0);
212:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
213:   TSSetTimeStep(ts,.01);
214:   TSSetFromOptions(ts);
215:   /* TSSetPostStep(ts,PostStep);  */


218:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
219:      Solve nonlinear system
220:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
221:   if (ensemble) {
222:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
223:       VecGetArray(U,&u);
224:       u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
225:       u[1] = ctx.omega_s;
226:       u[0] += du[0];
227:       u[1] += du[1];
228:       VecRestoreArray(U,&u);
229:       TSSetTimeStep(ts,.01);
230:       TSSolve(ts,U);
231:     }
232:   } else {
233:     TSSolve(ts,U);
234:   }
235:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
236:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
237:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
238:   MatDestroy(&A);
239:   VecDestroy(&U);
240:   TSDestroy(&ts);
241:   PetscFinalize();
242:   return ierr;
243: }


246: /*TEST

248:    build:
249:       requires: !complex

251:    test:
252:       args: -nox -ts_dt 10

254: TEST*/