Actual source code: ex9.c

petsc-3.12.0 2019-09-29
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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: */

 35: #include <petscts.h>

 37: typedef struct {
 38:   PetscScalar H,D,omega_b,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 RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
 46: {
 47:   PetscErrorCode    ierr;
 48:   const PetscScalar *u;
 49:   PetscScalar       *f,Pmax;

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

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

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

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

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

 81:   J[0][0] = 0;                                    J[0][1] = ctx->omega_b;
 82:   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);

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

 87:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 88:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 89:   if (A != B) {
 90:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 91:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
 92:   }
 93:   return(0);
 94: }

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

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

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

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

127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128:     Set runtime options
129:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
130:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
131:   {
132:     ctx.omega_b = 1.0;
133:     ctx.omega_s = 2.0*PETSC_PI*60.0;
134:     ctx.H       = 5.0;
135:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
136:     ctx.D       = 5.0;
137:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
138:     ctx.E       = 1.1378;
139:     ctx.V       = 1.0;
140:     ctx.X       = 0.545;
141:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;;
142:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
143:     ctx.Pm      = 0.9;
144:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
145:     ctx.tf      = 1.0;
146:     ctx.tcl     = 1.05;
147:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
148:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
149:     PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
150:     if (ensemble) {
151:       ctx.tf      = -1;
152:       ctx.tcl     = -1;
153:     }

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

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

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

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

193:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194:      Solve nonlinear system
195:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
196:   if (ensemble) {
197:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
198:       VecGetArray(U,&u);
199:       u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
200:       u[1] = ctx.omega_s;
201:       u[0] += du[0];
202:       u[1] += du[1];
203:       VecRestoreArray(U,&u);
204:       TSSetTimeStep(ts,.01);
205:       TSSolve(ts,U);
206:     }
207:   } else {
208:     TSSolve(ts,U);
209:   }
210:   VecView(U,PETSC_VIEWER_STDOUT_WORLD);
211:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
212:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
213:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
214:   MatDestroy(&A);
215:   VecDestroy(&U);
216:   TSDestroy(&ts);
217:   PetscFinalize();
218:   return ierr;
219: }


222: /*TEST

224:    build:
225:      requires: !complex

227:    test:

229: TEST*/