Actual source code: ex9.c

petsc-3.7.2 2016-06-05
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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: #include <petscts.h>

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

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

 53:   /*  The next three lines allow us to access the entries of the vectors directly */
 54:   VecGetArrayRead(U,&u);
 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 Pmax = ctx->Pmax;

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

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

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

 80:   VecGetArrayRead(U,&u);
 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 Pmax = ctx->Pmax;

 84:   J[0][0] = 0;                                    J[0][1] = ctx->omega_b;
 85:   J[1][1] = -ctx->D*ctx->omega_s/(2.0*ctx->H);    J[1][0] = -Pmax*PetscCosScalar(u[0])*ctx->omega_s/(2.0*ctx->H);

 87:   MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
 88:   VecRestoreArrayRead(U,&u);

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

101: int main(int argc,char **argv)
102: {
103:   TS             ts;            /* ODE integrator */
104:   Vec            U;             /* solution will be stored here */
105:   Mat            A;             /* Jacobian matrix */
107:   PetscMPIInt    size;
108:   PetscInt       n = 2;
109:   AppCtx         ctx;
110:   PetscScalar    *u;
111:   PetscReal      du[2] = {0.0,0.0};
112:   PetscBool      ensemble = PETSC_FALSE,flg1,flg2;

114:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
115:      Initialize program
116:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
117:   PetscInitialize(&argc,&argv,(char*)0,help);
118:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
119:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

121:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
122:     Create necessary matrix and vectors
123:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
124:   MatCreate(PETSC_COMM_WORLD,&A);
125:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
126:   MatSetType(A,MATDENSE);
127:   MatSetFromOptions(A);
128:   MatSetUp(A);

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

132:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133:     Set runtime options
134:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
135:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
136:   {
137:     ctx.omega_b = 1.0;
138:     ctx.omega_s = 2.0*PETSC_PI*60.0;
139:     ctx.H       = 5.0;
140:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
141:     ctx.D       = 5.0;
142:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
143:     ctx.E       = 1.1378;
144:     ctx.V       = 1.0;
145:     ctx.X       = 0.545;
146:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;;
147:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
148:     ctx.Pm      = 0.9;
149:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
150:     ctx.tf      = 1.0;
151:     ctx.tcl     = 1.05;
152:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
153:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
154:     PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
155:     if (ensemble) {
156:       ctx.tf      = -1;
157:       ctx.tcl     = -1;
158:     }

160:     VecGetArray(U,&u);
161:     u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
162:     u[1] = 1.0;
163:     PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);
164:     n    = 2;
165:     PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);
166:     u[0] += du[0];
167:     u[1] += du[1];
168:     VecRestoreArray(U,&u);
169:     if (flg1 || flg2) {
170:       ctx.tf      = -1;
171:       ctx.tcl     = -1;
172:     }
173:   }
174:   PetscOptionsEnd();

176:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177:      Create timestepping solver context
178:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
179:   TSCreate(PETSC_COMM_WORLD,&ts);
180:   TSSetProblemType(ts,TS_NONLINEAR);
181:   TSSetType(ts,TSTHETA);
182:   TSSetRHSFunction(ts,NULL,(TSRHSFunction)RHSFunction,&ctx);
183:   TSSetRHSJacobian(ts,A,A,(TSRHSJacobian)RHSJacobian,&ctx);
184:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);

186:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187:      Set initial conditions
188:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
189:   TSSetSolution(ts,U);

191:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
192:      Set solver options
193:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
194:   TSSetDuration(ts,100000,35.0);
195:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
196:   TSSetInitialTimeStep(ts,0.0,.01);
197:   TSSetFromOptions(ts);

199:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
200:      Solve nonlinear system
201:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
202:   if (ensemble) {
203:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
204:       VecGetArray(U,&u);
205:       u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
206:       u[1] = ctx.omega_s;
207:       u[0] += du[0];
208:       u[1] += du[1];
209:       VecRestoreArray(U,&u);
210:       TSSetInitialTimeStep(ts,0.0,.01);
211:       TSSolve(ts,U);
212:     }
213:   } else {
214:     TSSolve(ts,U);
215:   }
216:   VecView(U,PETSC_VIEWER_STDOUT_WORLD);
217:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
218:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
219:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
220:   MatDestroy(&A);
221:   VecDestroy(&U);
222:   TSDestroy(&ts);

224:   PetscFinalize();
225:   return(0);
226: }