Actual source code: ex3.c
petsc-3.8.3 2017-12-09
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 */
42: PetscErrorCode EventFunction(TS ts,PetscReal t,Vec X,PetscScalar *fvalue,void *ctx)
43: {
44: AppCtx *user=(AppCtx*)ctx;
47: /* Event for fault-on time */
48: fvalue[0] = t - user->tf;
49: /* Event for fault-off time */
50: fvalue[1] = t - user->tcl;
52: return (0);
53: }
55: PetscErrorCode PostEventFunction(TS ts,PetscInt nevents,PetscInt event_list[],PetscReal t,Vec X,PetscBool forwardsolve,void* ctx)
56: {
57: AppCtx *user=(AppCtx*)ctx;
58:
61: if (event_list[0] == 0) user->Pmax = 0.0; /* Apply disturbance - this is done by setting Pmax = 0 */
62: else if (event_list[0] == 1) user->Pmax = user->Pmax_ini; /* Remove the fault - this is done by setting Pmax = Pmax_ini */
63: return (0);
64: }
66: /*
67: Defines the ODE passed to the ODE solver
68: */
69: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
70: {
71: PetscErrorCode ierr;
72: const PetscScalar *u,*udot;
73: PetscScalar *f,Pmax;
76: /* The next three lines allow us to access the entries of the vectors directly */
77: VecGetArrayRead (U,&u);
78: VecGetArrayRead (Udot,&udot);
79: VecGetArray (F,&f);
80: Pmax = ctx->Pmax;
82: f[0] = udot[0] - ctx->omega_b*(u[1] - ctx->omega_s);
83: f[1] = 2.0*ctx->H/ctx->omega_s*udot[1] + Pmax*PetscSinScalar(u[0]) + ctx->D*(u[1] - ctx->omega_s)- ctx->Pm;
85: VecRestoreArrayRead (U,&u);
86: VecRestoreArrayRead (Udot,&udot);
87: VecRestoreArray (F,&f);
88: return (0);
89: }
91: /*
92: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian () for the meaning of a and the Jacobian.
93: */
94: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
95: {
96: PetscErrorCode ierr;
97: PetscInt rowcol[] = {0,1};
98: PetscScalar J[2][2],Pmax;
99: const PetscScalar *u,*udot;
102: VecGetArrayRead (U,&u);
103: VecGetArrayRead (Udot,&udot);
104: Pmax = ctx->Pmax;
106: J[0][0] = a; J[0][1] = -ctx->omega_b;
107: J[1][1] = 2.0*ctx->H/ctx->omega_s*a + ctx->D; J[1][0] = Pmax*PetscCosScalar(u[0]);
109: MatSetValues (B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES );
110: VecRestoreArrayRead (U,&u);
111: VecRestoreArrayRead (Udot,&udot);
113: MatAssemblyBegin (A,MAT_FINAL_ASSEMBLY );
114: MatAssemblyEnd (A,MAT_FINAL_ASSEMBLY );
115: if (A != B) {
116: MatAssemblyBegin (B,MAT_FINAL_ASSEMBLY );
117: MatAssemblyEnd (B,MAT_FINAL_ASSEMBLY );
118: }
119: return (0);
120: }
122: int main(int argc,char **argv)
123: {
124: TS ts; /* ODE integrator */
125: Vec U; /* solution will be stored here */
126: Mat A; /* Jacobian matrix */
128: PetscMPIInt size;
129: PetscInt n = 2;
130: AppCtx ctx;
131: PetscScalar *u;
132: PetscReal du[2] = {0.0,0.0};
133: PetscBool ensemble = PETSC_FALSE ,flg1,flg2;
134: PetscInt direction[2];
135: PetscBool terminate[2];
137: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
138: Initialize program
139: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
140: PetscInitialize (&argc,&argv,(char*)0,help);if (ierr) return ierr;
141: MPI_Comm_size (PETSC_COMM_WORLD ,&size);
142: if (size > 1) SETERRQ (PETSC_COMM_WORLD ,PETSC_ERR_SUP,"Only for sequential runs" );
144: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145: Create necessary matrix and vectors
146: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147: MatCreate (PETSC_COMM_WORLD ,&A);
148: MatSetSizes (A,n,n,PETSC_DETERMINE ,PETSC_DETERMINE );
149: MatSetType (A,MATDENSE );
150: MatSetFromOptions (A);
151: MatSetUp (A);
153: MatCreateVecs (A,&U,NULL);
155: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156: Set runtime options
157: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158: PetscOptionsBegin (PETSC_COMM_WORLD ,NULL,"Swing equation options" ,"" );
159: {
160: ctx.omega_b = 1.0;
161: ctx.omega_s = 2.0*PETSC_PI*60.0;
162: ctx.H = 5.0;
163: PetscOptionsScalar ("-Inertia" ,"" ,"" ,ctx.H,&ctx.H,NULL);
164: ctx.D = 5.0;
165: PetscOptionsScalar ("-D" ,"" ,"" ,ctx.D,&ctx.D,NULL);
166: ctx.E = 1.1378;
167: ctx.V = 1.0;
168: ctx.X = 0.545;
169: ctx.Pmax = ctx.E*ctx.V/ctx.X;
170: ctx.Pmax_ini = ctx.Pmax;
171: PetscOptionsScalar ("-Pmax" ,"" ,"" ,ctx.Pmax,&ctx.Pmax,NULL);
172: ctx.Pm = 0.9;
173: PetscOptionsScalar ("-Pm" ,"" ,"" ,ctx.Pm,&ctx.Pm,NULL);
174: ctx.tf = 1.0;
175: ctx.tcl = 1.05;
176: PetscOptionsReal ("-tf" ,"Time to start fault" ,"" ,ctx.tf,&ctx.tf,NULL);
177: PetscOptionsReal ("-tcl" ,"Time to end fault" ,"" ,ctx.tcl,&ctx.tcl,NULL);
178: PetscOptionsBool ("-ensemble" ,"Run ensemble of different initial conditions" ,"" ,ensemble,&ensemble,NULL);
179: if (ensemble) {
180: ctx.tf = -1;
181: ctx.tcl = -1;
182: }
184: VecGetArray (U,&u);
185: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
186: u[1] = 1.0;
187: PetscOptionsRealArray ("-u" ,"Initial solution" ,"" ,u,&n,&flg1);
188: n = 2;
189: PetscOptionsRealArray ("-du" ,"Perturbation in initial solution" ,"" ,du,&n,&flg2);
190: u[0] += du[0];
191: u[1] += du[1];
192: VecRestoreArray (U,&u);
193: if (flg1 || flg2) {
194: ctx.tf = -1;
195: ctx.tcl = -1;
196: }
197: }
198: PetscOptionsEnd ();
200: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
201: Create timestepping solver context
202: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
203: TSCreate (PETSC_COMM_WORLD ,&ts);
204: TSSetProblemType (ts,TS_NONLINEAR );
205: TSSetType (ts,TSTHETA );
206: TSSetEquationType (ts,TS_EQ_IMPLICIT );
207: TSARKIMEXSetFullyImplicit (ts,PETSC_TRUE );
208: TSSetIFunction (ts,NULL,(TSIFunction) IFunction,&ctx);
209: TSSetIJacobian (ts,A,A,(TSIJacobian)IJacobian,&ctx);
211: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
212: Set initial conditions
213: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
214: TSSetSolution (ts,U);
216: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
217: Set solver options
218: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
219: TSSetMaxTime (ts,35.0);
220: TSSetExactFinalTime (ts,TS_EXACTFINALTIME_MATCHSTEP );
221: TSSetTimeStep (ts,.1);
222: TSSetFromOptions (ts);
224: direction[0] = direction[1] = 1;
225: terminate[0] = terminate[1] = PETSC_FALSE ;
227: TSSetEventHandler (ts,2,direction,terminate,EventFunction,PostEventFunction,(void*)&ctx);
229: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
230: Solve nonlinear system
231: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
232: if (ensemble) {
233: for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
234: VecGetArray (U,&u);
235: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
236: u[1] = ctx.omega_s;
237: u[0] += du[0];
238: u[1] += du[1];
239: VecRestoreArray (U,&u);
240: TSSetTimeStep (ts,.01);
241: TSSolve (ts,U);
242: }
243: } else {
244: TSSolve (ts,U);
245: }
246: VecView (U,PETSC_VIEWER_STDOUT_WORLD );
247: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
248: Free work space. All PETSc objects should be destroyed when they are no longer needed.
249: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
250: MatDestroy (&A);
251: VecDestroy (&U);
252: TSDestroy (&ts);
253: PetscFinalize ();
254: return ierr;
255: }