Actual source code: ex2.c
petsc-3.7.1 2016-05-15
2: static char help[] = "Basic equation for generator stability analysis.\n" ;
\begin{eqnarray}
\frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - \frac{EV}{X} \sin(\theta) -D(\omega - \omega_s)\\
\frac{d \theta}{dt} = \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_s,Pmax,Pm,E,V,X;
38: PetscReal tf,tcl;
39: } AppCtx;
43: /*
44: Defines the ODE passed to the ODE solver
45: */
46: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
47: {
48: PetscErrorCode ierr;
49: PetscScalar *f,Pmax;
50: const PetscScalar *u,*udot;
53: /* The next three lines allow us to access the entries of the vectors directly */
54: VecGetArrayRead (U,&u);
55: VecGetArrayRead (Udot,&udot);
56: VecGetArray (F,&f);
57: 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 */
58: else if (t >= ctx->tcl) Pmax = ctx->E/0.745;
59: else Pmax = ctx->Pmax;
60: f[0] = udot[0] - ctx->omega_s*(u[1] - 1.0);
61: f[1] = 2.0*ctx->H*udot[1] + Pmax*PetscSinScalar(u[0]) + ctx->D*(u[1] - 1.0)- ctx->Pm;
63: VecRestoreArrayRead (U,&u);
64: VecRestoreArrayRead (Udot,&udot);
65: VecRestoreArray (F,&f);
66: return (0);
67: }
71: /*
72: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian () for the meaning of a and the Jacobian.
73: */
74: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
75: {
76: PetscErrorCode ierr;
77: PetscInt rowcol[] = {0,1};
78: PetscScalar J[2][2],Pmax;
79: const PetscScalar *u,*udot;
82: VecGetArrayRead (U,&u);
83: VecGetArrayRead (Udot,&udot);
84: 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 */
85: else if (t >= ctx->tcl) Pmax = ctx->E/0.745;
86: else Pmax = ctx->Pmax;
88: J[0][0] = a; J[0][1] = -ctx->omega_s;
89: J[1][1] = 2.0*ctx->H*a + ctx->D; J[1][0] = Pmax*PetscCosScalar(u[0]);
91: MatSetValues (B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES );
92: VecRestoreArrayRead (U,&u);
93: VecRestoreArrayRead (Udot,&udot);
95: MatAssemblyBegin (A,MAT_FINAL_ASSEMBLY);
96: MatAssemblyEnd (A,MAT_FINAL_ASSEMBLY);
97: if (A != B) {
98: MatAssemblyBegin (B,MAT_FINAL_ASSEMBLY);
99: MatAssemblyEnd (B,MAT_FINAL_ASSEMBLY);
100: }
101: return (0);
102: }
107: PetscErrorCode PostStep(TS ts)
108: {
110: Vec X;
111: PetscReal t;
114: TSGetTime (ts,&t);
115: if (t >= .2) {
116: TSGetSolution (ts,&X);
117: VecView (X,PETSC_VIEWER_STDOUT_WORLD );
118: exit(0);
119: /* results in initial conditions after fault of -u 0.496792,1.00932 */
120: }
121: return (0);
122: }
127: int main(int argc,char **argv)
128: {
129: TS ts; /* ODE integrator */
130: Vec U; /* solution will be stored here */
131: Mat A; /* Jacobian matrix */
133: PetscMPIInt size;
134: PetscInt n = 2;
135: AppCtx ctx;
136: PetscScalar *u;
137: PetscReal du[2] = {0.0,0.0};
138: PetscBool ensemble = PETSC_FALSE ,flg1,flg2;
140: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
141: Initialize program
142: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
143: PetscInitialize (&argc,&argv,(char*)0,help);
144: MPI_Comm_size (PETSC_COMM_WORLD ,&size);
145: if (size > 1) SETERRQ (PETSC_COMM_WORLD ,PETSC_ERR_SUP,"Only for sequential runs" );
147: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: Create necessary matrix and vectors
149: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150: MatCreate (PETSC_COMM_WORLD ,&A);
151: MatSetSizes (A,n,n,PETSC_DETERMINE ,PETSC_DETERMINE );
152: MatSetType (A,MATDENSE );
153: MatSetFromOptions (A);
154: MatSetUp (A);
156: MatCreateVecs (A,&U,NULL);
158: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
159: Set runtime options
160: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
161: PetscOptionsBegin (PETSC_COMM_WORLD ,NULL,"Swing equation options" ,"" );
162: {
163: ctx.omega_s = 2.0*PETSC_PI*60.0;
164: ctx.H = 5.0;
165: PetscOptionsScalar ("-Inertia" ,"" ,"" ,ctx.H,&ctx.H,NULL);
166: ctx.D = 5.0;
167: PetscOptionsScalar ("-D" ,"" ,"" ,ctx.D,&ctx.D,NULL);
168: ctx.E = 1.1378;
169: ctx.V = 1.0;
170: ctx.X = 0.545;
171: ctx.Pmax = ctx.E*ctx.V/ctx.X;;
172: PetscOptionsScalar ("-Pmax" ,"" ,"" ,ctx.Pmax,&ctx.Pmax,NULL);
173: ctx.Pm = 0.9;
174: PetscOptionsScalar ("-Pm" ,"" ,"" ,ctx.Pm,&ctx.Pm,NULL);
175: ctx.tf = 1.0;
176: ctx.tcl = 1.05;
177: PetscOptionsReal ("-tf" ,"Time to start fault" ,"" ,ctx.tf,&ctx.tf,NULL);
178: PetscOptionsReal ("-tcl" ,"Time to end fault" ,"" ,ctx.tcl,&ctx.tcl,NULL);
179: PetscOptionsBool ("-ensemble" ,"Run ensemble of different initial conditions" ,"" ,ensemble,&ensemble,NULL);
180: if (ensemble) {
181: ctx.tf = -1;
182: ctx.tcl = -1;
183: }
185: VecGetArray (U,&u);
186: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
187: u[1] = 1.0;
188: PetscOptionsRealArray ("-u" ,"Initial solution" ,"" ,u,&n,&flg1);
189: n = 2;
190: PetscOptionsRealArray ("-du" ,"Perturbation in initial solution" ,"" ,du,&n,&flg2);
191: u[0] += du[0];
192: u[1] += du[1];
193: VecRestoreArray (U,&u);
194: if (flg1 || flg2) {
195: ctx.tf = -1;
196: ctx.tcl = -1;
197: }
198: }
199: PetscOptionsEnd ();
201: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
202: Create timestepping solver context
203: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
204: TSCreate (PETSC_COMM_WORLD ,&ts);
205: TSSetProblemType (ts,TS_NONLINEAR);
206: TSSetType (ts,TSROSW );
207: TSSetIFunction (ts,NULL,(TSIFunction) IFunction,&ctx);
208: TSSetIJacobian (ts,A,A,(TSIJacobian)IJacobian,&ctx);
210: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
211: Set initial conditions
212: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
213: TSSetSolution (ts,U);
215: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
216: Set solver options
217: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
218: TSSetDuration (ts,100000,35.0);
219: TSSetExactFinalTime (ts,TS_EXACTFINALTIME_STEPOVER);
220: TSSetInitialTimeStep (ts,0.0,.01);
221: TSSetFromOptions (ts);
222: /* TSSetPostStep (ts,PostStep); */
225: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
226: Solve nonlinear system
227: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
228: if (ensemble) {
229: for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
230: VecGetArray (U,&u);
231: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
232: u[1] = ctx.omega_s;
233: u[0] += du[0];
234: u[1] += du[1];
235: VecRestoreArray (U,&u);
236: TSSetInitialTimeStep (ts,0.0,.01);
237: TSSolve (ts,U);
238: }
239: } else {
240: TSSolve (ts,U);
241: }
242: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
243: Free work space. All PETSc objects should be destroyed when they are no longer needed.
244: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
245: MatDestroy (&A);
246: VecDestroy (&U);
247: TSDestroy (&ts);
249: PetscFinalize ();
250: return (0);
251: }