Actual source code: ex9.c

petsc-3.8.4 2018-03-24
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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;

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

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

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

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

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

 76:   VecGetArrayRead(U,&u);
 77:   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 */
 78:   else Pmax = ctx->Pmax;

 80:   J[0][0] = 0;                                    J[0][1] = ctx->omega_b;
 81:   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);

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

 86:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 87:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 88:   if (A != B) {
 89:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 90:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
 91:   }
 92:   return(0);
 93: }

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

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

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

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

126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127:     Set runtime options
128:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
129:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
130:   {
131:     ctx.omega_b = 1.0;
132:     ctx.omega_s = 2.0*PETSC_PI*60.0;
133:     ctx.H       = 5.0;
134:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
135:     ctx.D       = 5.0;
136:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
137:     ctx.E       = 1.1378;
138:     ctx.V       = 1.0;
139:     ctx.X       = 0.545;
140:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;;
141:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
142:     ctx.Pm      = 0.9;
143:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
144:     ctx.tf      = 1.0;
145:     ctx.tcl     = 1.05;
146:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
147:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
148:     PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
149:     if (ensemble) {
150:       ctx.tf      = -1;
151:       ctx.tcl     = -1;
152:     }

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

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

179:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
180:      Set initial conditions
181:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
182:   TSSetSolution(ts,U);

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

192:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193:      Solve nonlinear system
194:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
195:   if (ensemble) {
196:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
197:       VecGetArray(U,&u);
198:       u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
199:       u[1] = ctx.omega_s;
200:       u[0] += du[0];
201:       u[1] += du[1];
202:       VecRestoreArray(U,&u);
203:       TSSetTimeStep(ts,.01);
204:       TSSolve(ts,U);
205:     }
206:   } else {
207:     TSSolve(ts,U);
208:   }
209:   VecView(U,PETSC_VIEWER_STDOUT_WORLD);
210:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
211:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
212:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
213:   MatDestroy(&A);
214:   VecDestroy(&U);
215:   TSDestroy(&ts);
216:   PetscFinalize();
217:   return ierr;
218: }