Actual source code: ex9.c


  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

 22: /*
 23:    Include "petscts.h" so that we can use TS solvers.  Note that this
 24:    file automatically includes:
 25:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 26:      petscmat.h - matrices
 27:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 28:      petscviewer.h - viewers               petscpc.h  - preconditioners
 29:      petscksp.h   - linear solvers
 30: */

 32: #include <petscts.h>

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

 39: /*
 40:      Defines the ODE passed to the ODE solver
 41: */
 42: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
 43: {
 44:   const PetscScalar *u;
 45:   PetscScalar       *f,Pmax;

 47:   /*  The next three lines allow us to access the entries of the vectors directly */
 48:   VecGetArrayRead(U,&u);
 49:   VecGetArray(F,&f);
 50:   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 */
 51:   else Pmax = ctx->Pmax;

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

 56:   VecRestoreArrayRead(U,&u);
 57:   VecRestoreArray(F,&f);
 58:   return 0;
 59: }

 61: /*
 62:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
 63: */
 64: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,AppCtx *ctx)
 65: {
 66:   PetscInt          rowcol[] = {0,1};
 67:   PetscScalar       J[2][2],Pmax;
 68:   const PetscScalar *u;

 70:   VecGetArrayRead(U,&u);
 71:   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 */
 72:   else Pmax = ctx->Pmax;

 74:   J[0][0] = 0;                                    J[0][1] = ctx->omega_b;
 75:   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);

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

 80:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 81:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 82:   if (A != B) {
 83:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 84:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
 85:   }
 86:   return 0;
 87: }

 89: int main(int argc,char **argv)
 90: {
 91:   TS             ts;            /* ODE integrator */
 92:   Vec            U;             /* solution will be stored here */
 93:   Mat            A;             /* Jacobian matrix */
 95:   PetscMPIInt    size;
 96:   PetscInt       n = 2;
 97:   AppCtx         ctx;
 98:   PetscScalar    *u;
 99:   PetscReal      du[2] = {0.0,0.0};
100:   PetscBool      ensemble = PETSC_FALSE,flg1,flg2;

102:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103:      Initialize program
104:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
105:   PetscInitialize(&argc,&argv,(char*)0,help);
106:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

109:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
110:     Create necessary matrix and vectors
111:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
112:   MatCreate(PETSC_COMM_WORLD,&A);
113:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
114:   MatSetType(A,MATDENSE);
115:   MatSetFromOptions(A);
116:   MatSetUp(A);

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

120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
121:     Set runtime options
122:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
123:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
124:   {
125:     ctx.omega_b = 1.0;
126:     ctx.omega_s = 2.0*PETSC_PI*60.0;
127:     ctx.H       = 5.0;
128:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
129:     ctx.D       = 5.0;
130:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
131:     ctx.E       = 1.1378;
132:     ctx.V       = 1.0;
133:     ctx.X       = 0.545;
134:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
135:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
136:     ctx.Pm      = 0.9;
137:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
138:     ctx.tf      = 1.0;
139:     ctx.tcl     = 1.05;
140:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
141:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
142:     PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
143:     if (ensemble) {
144:       ctx.tf      = -1;
145:       ctx.tcl     = -1;
146:     }

148:     VecGetArray(U,&u);
149:     u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
150:     u[1] = 1.0;
151:     PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);
152:     n    = 2;
153:     PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);
154:     u[0] += du[0];
155:     u[1] += du[1];
156:     VecRestoreArray(U,&u);
157:     if (flg1 || flg2) {
158:       ctx.tf      = -1;
159:       ctx.tcl     = -1;
160:     }
161:   }
162:   PetscOptionsEnd();

164:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
165:      Create timestepping solver context
166:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
167:   TSCreate(PETSC_COMM_WORLD,&ts);
168:   TSSetProblemType(ts,TS_NONLINEAR);
169:   TSSetType(ts,TSTHETA);
170:   TSSetRHSFunction(ts,NULL,(TSRHSFunction)RHSFunction,&ctx);
171:   TSSetRHSJacobian(ts,A,A,(TSRHSJacobian)RHSJacobian,&ctx);

173:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
174:      Set initial conditions
175:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
176:   TSSetSolution(ts,U);

178:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
179:      Set solver options
180:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
181:   TSSetMaxTime(ts,35.0);
182:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
183:   TSSetTimeStep(ts,.01);
184:   TSSetFromOptions(ts);

186:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187:      Solve nonlinear system
188:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
189:   if (ensemble) {
190:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
191:       VecGetArray(U,&u);
192:       u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
193:       u[1] = ctx.omega_s;
194:       u[0] += du[0];
195:       u[1] += du[1];
196:       VecRestoreArray(U,&u);
197:       TSSetTimeStep(ts,.01);
198:       TSSolve(ts,U);
199:     }
200:   } else {
201:     TSSolve(ts,U);
202:   }
203:   VecView(U,PETSC_VIEWER_STDOUT_WORLD);
204:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
205:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
206:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
207:   MatDestroy(&A);
208:   VecDestroy(&U);
209:   TSDestroy(&ts);
210:   PetscFinalize();
211:   return 0;
212: }

214: /*TEST

216:    build:
217:      requires: !complex

219:    test:

221: TEST*/