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:   PetscErrorCode    ierr;
 45:   const PetscScalar *u;
 46:   PetscScalar       *f,Pmax;

 49:   /*  The next three lines allow us to access the entries of the vectors directly */
 50:   VecGetArrayRead(U,&u);
 51:   VecGetArray(F,&f);
 52:   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 */
 53:   else Pmax = ctx->Pmax;

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

 58:   VecRestoreArrayRead(U,&u);
 59:   VecRestoreArray(F,&f);
 60:   return(0);
 61: }

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

 74:   VecGetArrayRead(U,&u);
 75:   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 */
 76:   else Pmax = ctx->Pmax;

 78:   J[0][0] = 0;                                    J[0][1] = ctx->omega_b;
 79:   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);

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

 84:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 85:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 86:   if (A != B) {
 87:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 88:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
 89:   }
 90:   return(0);
 91: }

 93: int main(int argc,char **argv)
 94: {
 95:   TS             ts;            /* ODE integrator */
 96:   Vec            U;             /* solution will be stored here */
 97:   Mat            A;             /* Jacobian matrix */
 99:   PetscMPIInt    size;
100:   PetscInt       n = 2;
101:   AppCtx         ctx;
102:   PetscScalar    *u;
103:   PetscReal      du[2] = {0.0,0.0};
104:   PetscBool      ensemble = PETSC_FALSE,flg1,flg2;

106:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
107:      Initialize program
108:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
109:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
110:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
111:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

113:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114:     Create necessary matrix and vectors
115:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
116:   MatCreate(PETSC_COMM_WORLD,&A);
117:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
118:   MatSetType(A,MATDENSE);
119:   MatSetFromOptions(A);
120:   MatSetUp(A);

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

124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125:     Set runtime options
126:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
127:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
128:   {
129:     ctx.omega_b = 1.0;
130:     ctx.omega_s = 2.0*PETSC_PI*60.0;
131:     ctx.H       = 5.0;
132:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
133:     ctx.D       = 5.0;
134:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
135:     ctx.E       = 1.1378;
136:     ctx.V       = 1.0;
137:     ctx.X       = 0.545;
138:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
139:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
140:     ctx.Pm      = 0.9;
141:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
142:     ctx.tf      = 1.0;
143:     ctx.tcl     = 1.05;
144:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
145:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
146:     PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
147:     if (ensemble) {
148:       ctx.tf      = -1;
149:       ctx.tcl     = -1;
150:     }

152:     VecGetArray(U,&u);
153:     u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
154:     u[1] = 1.0;
155:     PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);
156:     n    = 2;
157:     PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);
158:     u[0] += du[0];
159:     u[1] += du[1];
160:     VecRestoreArray(U,&u);
161:     if (flg1 || flg2) {
162:       ctx.tf      = -1;
163:       ctx.tcl     = -1;
164:     }
165:   }
166:   PetscOptionsEnd();

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

177:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178:      Set initial conditions
179:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
180:   TSSetSolution(ts,U);

182:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
183:      Set solver options
184:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
185:   TSSetMaxTime(ts,35.0);
186:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
187:   TSSetTimeStep(ts,.01);
188:   TSSetFromOptions(ts);

190:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
191:      Solve nonlinear system
192:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
193:   if (ensemble) {
194:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
195:       VecGetArray(U,&u);
196:       u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
197:       u[1] = ctx.omega_s;
198:       u[0] += du[0];
199:       u[1] += du[1];
200:       VecRestoreArray(U,&u);
201:       TSSetTimeStep(ts,.01);
202:       TSSolve(ts,U);
203:     }
204:   } else {
205:     TSSolve(ts,U);
206:   }
207:   VecView(U,PETSC_VIEWER_STDOUT_WORLD);
208:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
210:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
211:   MatDestroy(&A);
212:   VecDestroy(&U);
213:   TSDestroy(&ts);
214:   PetscFinalize();
215:   return ierr;
216: }

218: /*TEST

220:    build:
221:      requires: !complex

223:    test:

225: TEST*/