Actual source code: ex2.c
petsc-3.8.3 2017-12-09
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;
41: /*
42: Defines the ODE passed to the ODE solver
43: */
44: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
45: {
46: PetscErrorCode ierr;
47: PetscScalar *f,Pmax;
48: const PetscScalar *u,*udot;
51: /* The next three lines allow us to access the entries of the vectors directly */
52: VecGetArrayRead (U,&u);
53: VecGetArrayRead (Udot,&udot);
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 if (t >= ctx->tcl) Pmax = ctx->E/0.745;
57: else Pmax = ctx->Pmax;
58: f[0] = udot[0] - ctx->omega_s*(u[1] - 1.0);
59: f[1] = 2.0*ctx->H*udot[1] + Pmax*PetscSinScalar(u[0]) + ctx->D*(u[1] - 1.0)- ctx->Pm;
61: VecRestoreArrayRead (U,&u);
62: VecRestoreArrayRead (Udot,&udot);
63: VecRestoreArray (F,&f);
64: return (0);
65: }
67: /*
68: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian () for the meaning of a and the Jacobian.
69: */
70: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
71: {
72: PetscErrorCode ierr;
73: PetscInt rowcol[] = {0,1};
74: PetscScalar J[2][2],Pmax;
75: const PetscScalar *u,*udot;
78: VecGetArrayRead (U,&u);
79: VecGetArrayRead (Udot,&udot);
80: 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 */
81: else if (t >= ctx->tcl) Pmax = ctx->E/0.745;
82: else Pmax = ctx->Pmax;
84: J[0][0] = a; J[0][1] = -ctx->omega_s;
85: J[1][1] = 2.0*ctx->H*a + ctx->D; J[1][0] = Pmax*PetscCosScalar(u[0]);
87: MatSetValues (B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES );
88: VecRestoreArrayRead (U,&u);
89: VecRestoreArrayRead (Udot,&udot);
91: MatAssemblyBegin (A,MAT_FINAL_ASSEMBLY );
92: MatAssemblyEnd (A,MAT_FINAL_ASSEMBLY );
93: if (A != B) {
94: MatAssemblyBegin (B,MAT_FINAL_ASSEMBLY );
95: MatAssemblyEnd (B,MAT_FINAL_ASSEMBLY );
96: }
97: return (0);
98: }
101: PetscErrorCode PostStep(TS ts)
102: {
104: Vec X;
105: PetscReal t;
108: TSGetTime (ts,&t);
109: if (t >= .2) {
110: TSGetSolution (ts,&X);
111: VecView (X,PETSC_VIEWER_STDOUT_WORLD );
112: exit(0);
113: /* results in initial conditions after fault of -u 0.496792,1.00932 */
114: }
115: return (0);
116: }
119: int main(int argc,char **argv)
120: {
121: TS ts; /* ODE integrator */
122: Vec U; /* solution will be stored here */
123: Mat A; /* Jacobian matrix */
125: PetscMPIInt size;
126: PetscInt n = 2;
127: AppCtx ctx;
128: PetscScalar *u;
129: PetscReal du[2] = {0.0,0.0};
130: PetscBool ensemble = PETSC_FALSE ,flg1,flg2;
132: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133: Initialize program
134: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
135: PetscInitialize (&argc,&argv,(char*)0,help);if (ierr) return ierr;
136: MPI_Comm_size (PETSC_COMM_WORLD ,&size);
137: if (size > 1) SETERRQ (PETSC_COMM_WORLD ,PETSC_ERR_SUP,"Only for sequential runs" );
139: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140: Create necessary matrix and vectors
141: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
142: MatCreate (PETSC_COMM_WORLD ,&A);
143: MatSetSizes (A,n,n,PETSC_DETERMINE ,PETSC_DETERMINE );
144: MatSetType (A,MATDENSE );
145: MatSetFromOptions (A);
146: MatSetUp (A);
148: MatCreateVecs (A,&U,NULL);
150: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151: Set runtime options
152: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153: PetscOptionsBegin (PETSC_COMM_WORLD ,NULL,"Swing equation options" ,"" );
154: {
155: ctx.omega_s = 2.0*PETSC_PI*60.0;
156: ctx.H = 5.0;
157: PetscOptionsScalar ("-Inertia" ,"" ,"" ,ctx.H,&ctx.H,NULL);
158: ctx.D = 5.0;
159: PetscOptionsScalar ("-D" ,"" ,"" ,ctx.D,&ctx.D,NULL);
160: ctx.E = 1.1378;
161: ctx.V = 1.0;
162: ctx.X = 0.545;
163: ctx.Pmax = ctx.E*ctx.V/ctx.X;;
164: PetscOptionsScalar ("-Pmax" ,"" ,"" ,ctx.Pmax,&ctx.Pmax,NULL);
165: ctx.Pm = 0.9;
166: PetscOptionsScalar ("-Pm" ,"" ,"" ,ctx.Pm,&ctx.Pm,NULL);
167: ctx.tf = 1.0;
168: ctx.tcl = 1.05;
169: PetscOptionsReal ("-tf" ,"Time to start fault" ,"" ,ctx.tf,&ctx.tf,NULL);
170: PetscOptionsReal ("-tcl" ,"Time to end fault" ,"" ,ctx.tcl,&ctx.tcl,NULL);
171: PetscOptionsBool ("-ensemble" ,"Run ensemble of different initial conditions" ,"" ,ensemble,&ensemble,NULL);
172: if (ensemble) {
173: ctx.tf = -1;
174: ctx.tcl = -1;
175: }
177: VecGetArray (U,&u);
178: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
179: u[1] = 1.0;
180: PetscOptionsRealArray ("-u" ,"Initial solution" ,"" ,u,&n,&flg1);
181: n = 2;
182: PetscOptionsRealArray ("-du" ,"Perturbation in initial solution" ,"" ,du,&n,&flg2);
183: u[0] += du[0];
184: u[1] += du[1];
185: VecRestoreArray (U,&u);
186: if (flg1 || flg2) {
187: ctx.tf = -1;
188: ctx.tcl = -1;
189: }
190: }
191: PetscOptionsEnd ();
193: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194: Create timestepping solver context
195: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
196: TSCreate (PETSC_COMM_WORLD ,&ts);
197: TSSetProblemType (ts,TS_NONLINEAR );
198: TSSetType (ts,TSROSW );
199: TSSetIFunction (ts,NULL,(TSIFunction) IFunction,&ctx);
200: TSSetIJacobian (ts,A,A,(TSIJacobian)IJacobian,&ctx);
202: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
203: Set initial conditions
204: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
205: TSSetSolution (ts,U);
207: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
208: Set solver options
209: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
210: TSSetMaxTime (ts,35.0);
211: TSSetExactFinalTime (ts,TS_EXACTFINALTIME_MATCHSTEP );
212: TSSetTimeStep (ts,.01);
213: TSSetFromOptions (ts);
214: /* TSSetPostStep (ts,PostStep); */
217: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
218: Solve nonlinear system
219: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
220: if (ensemble) {
221: for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
222: VecGetArray (U,&u);
223: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
224: u[1] = ctx.omega_s;
225: u[0] += du[0];
226: u[1] += du[1];
227: VecRestoreArray (U,&u);
228: TSSetTimeStep (ts,.01);
229: TSSolve (ts,U);
230: }
231: } else {
232: TSSolve (ts,U);
233: }
234: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
235: Free work space. All PETSc objects should be destroyed when they are no longer needed.
236: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
237: MatDestroy (&A);
238: VecDestroy (&U);
239: TSDestroy (&ts);
240: PetscFinalize ();
241: return ierr;
242: }