Actual source code: ex3.c
petsc-3.7.2 2016-06-05
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,Pmax_ini,Pm,E,V,X;
38: PetscReal tf,tcl;
39: } AppCtx;
41: /* Event check */
44: PetscErrorCode EventFunction(TS ts,PetscReal t,Vec X,PetscScalar *fvalue,void *ctx)
45: {
46: AppCtx *user=(AppCtx*)ctx;
49: /* Event for fault-on time */
50: fvalue[0] = t - user->tf;
51: /* Event for fault-off time */
52: fvalue[1] = t - user->tcl;
54: return (0);
55: }
59: PetscErrorCode PostEventFunction(TS ts,PetscInt nevents,PetscInt event_list[],PetscReal t,Vec X,PetscBool forwardsolve,void* ctx)
60: {
61: AppCtx *user=(AppCtx*)ctx;
62:
65: if (event_list[0] == 0) user->Pmax = 0.0; /* Apply disturbance - this is done by setting Pmax = 0 */
66: else if (event_list[0] == 1) user->Pmax = user->Pmax_ini; /* Remove the fault - this is done by setting Pmax = Pmax_ini */
67: return (0);
68: }
72: /*
73: Defines the ODE passed to the ODE solver
74: */
75: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
76: {
77: PetscErrorCode ierr;
78: const PetscScalar *u,*udot;
79: PetscScalar *f,Pmax;
82: /* The next three lines allow us to access the entries of the vectors directly */
83: VecGetArrayRead (U,&u);
84: VecGetArrayRead (Udot,&udot);
85: VecGetArray (F,&f);
86: Pmax = ctx->Pmax;
88: f[0] = udot[0] - ctx->omega_b*(u[1] - ctx->omega_s);
89: f[1] = 2.0*ctx->H/ctx->omega_s*udot[1] + Pmax*PetscSinScalar(u[0]) + ctx->D*(u[1] - ctx->omega_s)- ctx->Pm;
91: VecRestoreArrayRead (U,&u);
92: VecRestoreArrayRead (Udot,&udot);
93: VecRestoreArray (F,&f);
94: return (0);
95: }
99: /*
100: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian () for the meaning of a and the Jacobian.
101: */
102: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
103: {
104: PetscErrorCode ierr;
105: PetscInt rowcol[] = {0,1};
106: PetscScalar J[2][2],Pmax;
107: const PetscScalar *u,*udot;
110: VecGetArrayRead (U,&u);
111: VecGetArrayRead (Udot,&udot);
112: Pmax = ctx->Pmax;
114: J[0][0] = a; J[0][1] = -ctx->omega_b;
115: J[1][1] = 2.0*ctx->H/ctx->omega_s*a + ctx->D; J[1][0] = Pmax*PetscCosScalar(u[0]);
117: MatSetValues (B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES );
118: VecRestoreArrayRead (U,&u);
119: VecRestoreArrayRead (Udot,&udot);
121: MatAssemblyBegin (A,MAT_FINAL_ASSEMBLY);
122: MatAssemblyEnd (A,MAT_FINAL_ASSEMBLY);
123: if (A != B) {
124: MatAssemblyBegin (B,MAT_FINAL_ASSEMBLY);
125: MatAssemblyEnd (B,MAT_FINAL_ASSEMBLY);
126: }
127: return (0);
128: }
132: int main(int argc,char **argv)
133: {
134: TS ts; /* ODE integrator */
135: Vec U; /* solution will be stored here */
136: Mat A; /* Jacobian matrix */
138: PetscMPIInt size;
139: PetscInt n = 2;
140: AppCtx ctx;
141: PetscScalar *u;
142: PetscReal du[2] = {0.0,0.0};
143: PetscBool ensemble = PETSC_FALSE ,flg1,flg2;
144: PetscInt direction[2];
145: PetscBool terminate[2];
147: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: Initialize program
149: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150: PetscInitialize (&argc,&argv,(char*)0,help);
151: MPI_Comm_size (PETSC_COMM_WORLD ,&size);
152: if (size > 1) SETERRQ (PETSC_COMM_WORLD ,PETSC_ERR_SUP,"Only for sequential runs" );
154: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
155: Create necessary matrix and vectors
156: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
157: MatCreate (PETSC_COMM_WORLD ,&A);
158: MatSetSizes (A,n,n,PETSC_DETERMINE ,PETSC_DETERMINE );
159: MatSetType (A,MATDENSE );
160: MatSetFromOptions (A);
161: MatSetUp (A);
163: MatCreateVecs (A,&U,NULL);
165: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
166: Set runtime options
167: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
168: PetscOptionsBegin (PETSC_COMM_WORLD ,NULL,"Swing equation options" ,"" );
169: {
170: ctx.omega_b = 1.0;
171: ctx.omega_s = 2.0*PETSC_PI*60.0;
172: ctx.H = 5.0;
173: PetscOptionsScalar ("-Inertia" ,"" ,"" ,ctx.H,&ctx.H,NULL);
174: ctx.D = 5.0;
175: PetscOptionsScalar ("-D" ,"" ,"" ,ctx.D,&ctx.D,NULL);
176: ctx.E = 1.1378;
177: ctx.V = 1.0;
178: ctx.X = 0.545;
179: ctx.Pmax = ctx.E*ctx.V/ctx.X;
180: ctx.Pmax_ini = ctx.Pmax;
181: PetscOptionsScalar ("-Pmax" ,"" ,"" ,ctx.Pmax,&ctx.Pmax,NULL);
182: ctx.Pm = 0.9;
183: PetscOptionsScalar ("-Pm" ,"" ,"" ,ctx.Pm,&ctx.Pm,NULL);
184: ctx.tf = 1.0;
185: ctx.tcl = 1.05;
186: PetscOptionsReal ("-tf" ,"Time to start fault" ,"" ,ctx.tf,&ctx.tf,NULL);
187: PetscOptionsReal ("-tcl" ,"Time to end fault" ,"" ,ctx.tcl,&ctx.tcl,NULL);
188: PetscOptionsBool ("-ensemble" ,"Run ensemble of different initial conditions" ,"" ,ensemble,&ensemble,NULL);
189: if (ensemble) {
190: ctx.tf = -1;
191: ctx.tcl = -1;
192: }
194: VecGetArray (U,&u);
195: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
196: u[1] = 1.0;
197: PetscOptionsRealArray ("-u" ,"Initial solution" ,"" ,u,&n,&flg1);
198: n = 2;
199: PetscOptionsRealArray ("-du" ,"Perturbation in initial solution" ,"" ,du,&n,&flg2);
200: u[0] += du[0];
201: u[1] += du[1];
202: VecRestoreArray (U,&u);
203: if (flg1 || flg2) {
204: ctx.tf = -1;
205: ctx.tcl = -1;
206: }
207: }
208: PetscOptionsEnd ();
210: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
211: Create timestepping solver context
212: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
213: TSCreate (PETSC_COMM_WORLD ,&ts);
214: TSSetProblemType (ts,TS_NONLINEAR);
215: TSSetType (ts,TSTHETA );
216: TSSetEquationType (ts,TS_EQ_IMPLICIT);
217: TSARKIMEXSetFullyImplicit (ts,PETSC_TRUE );
218: TSSetIFunction (ts,NULL,(TSIFunction) IFunction,&ctx);
219: TSSetIJacobian (ts,A,A,(TSIJacobian)IJacobian,&ctx);
220: TSSetExactFinalTime (ts,TS_EXACTFINALTIME_MATCHSTEP);
222: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
223: Set initial conditions
224: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
225: TSSetSolution (ts,U);
227: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
228: Set solver options
229: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
230: TSSetDuration (ts,100000,35.0);
231: TSSetExactFinalTime (ts,TS_EXACTFINALTIME_STEPOVER);
232: TSSetInitialTimeStep (ts,0.0,.01);
233: TSSetFromOptions (ts);
235: direction[0] = direction[1] = 1;
236: terminate[0] = terminate[1] = PETSC_FALSE ;
238: TSSetEventHandler (ts,2,direction,terminate,EventFunction,PostEventFunction,(void*)&ctx);
240: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
241: Solve nonlinear system
242: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
243: if (ensemble) {
244: for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
245: VecGetArray (U,&u);
246: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
247: u[1] = ctx.omega_s;
248: u[0] += du[0];
249: u[1] += du[1];
250: VecRestoreArray (U,&u);
251: TSSetInitialTimeStep (ts,0.0,.01);
252: TSSolve (ts,U);
253: }
254: } else {
255: TSSolve (ts,U);
256: }
257: VecView (U,PETSC_VIEWER_STDOUT_WORLD );
258: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
259: Free work space. All PETSc objects should be destroyed when they are no longer needed.
260: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
261: MatDestroy (&A);
262: VecDestroy (&U);
263: TSDestroy (&ts);
265: PetscFinalize ();
266: return (0);
267: }