Actual source code: ex3.c
petsc-3.6.4 2016-04-12
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,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: const PetscScalar *u,*udot;
50: PetscScalar *f,Pmax;
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 Pmax = ctx->Pmax;
60: f[0] = udot[0] - ctx->omega_b*(u[1] - ctx->omega_s);
61: f[1] = 2.0*ctx->H/ctx->omega_s*udot[1] + Pmax*PetscSinScalar(u[0]) + ctx->D*(u[1] - ctx->omega_s)- 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 Pmax = ctx->Pmax;
87: J[0][0] = a; J[0][1] = -ctx->omega_b;
88: J[1][1] = 2.0*ctx->H/ctx->omega_s*a + ctx->D; J[1][0] = Pmax*PetscCosScalar(u[0]);
90: MatSetValues (B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES );
91: VecRestoreArrayRead (U,&u);
92: VecRestoreArrayRead (Udot,&udot);
94: MatAssemblyBegin (A,MAT_FINAL_ASSEMBLY);
95: MatAssemblyEnd (A,MAT_FINAL_ASSEMBLY);
96: if (A != B) {
97: MatAssemblyBegin (B,MAT_FINAL_ASSEMBLY);
98: MatAssemblyEnd (B,MAT_FINAL_ASSEMBLY);
99: }
100: return (0);
101: }
105: int main(int argc,char **argv)
106: {
107: TS ts; /* ODE integrator */
108: Vec U; /* solution will be stored here */
109: Mat A; /* Jacobian matrix */
111: PetscMPIInt size;
112: PetscInt n = 2;
113: AppCtx ctx;
114: PetscScalar *u;
115: PetscReal du[2] = {0.0,0.0};
116: PetscBool ensemble = PETSC_FALSE ,flg1,flg2;
118: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
119: Initialize program
120: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
121: PetscInitialize (&argc,&argv,(char*)0,help);
122: MPI_Comm_size (PETSC_COMM_WORLD ,&size);
123: if (size > 1) SETERRQ (PETSC_COMM_WORLD ,PETSC_ERR_SUP,"Only for sequential runs" );
125: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
126: Create necessary matrix and vectors
127: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
128: MatCreate (PETSC_COMM_WORLD ,&A);
129: MatSetSizes (A,n,n,PETSC_DETERMINE ,PETSC_DETERMINE );
130: MatSetType (A,MATDENSE );
131: MatSetFromOptions (A);
132: MatSetUp (A);
134: MatCreateVecs (A,&U,NULL);
136: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137: Set runtime options
138: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
139: PetscOptionsBegin (PETSC_COMM_WORLD ,NULL,"Swing equation options" ,"" );
140: {
141: ctx.omega_b = 1.0;
142: ctx.omega_s = 2.0*PETSC_PI*60.0;
143: ctx.H = 5.0;
144: PetscOptionsScalar ("-Inertia" ,"" ,"" ,ctx.H,&ctx.H,NULL);
145: ctx.D = 5.0;
146: PetscOptionsScalar ("-D" ,"" ,"" ,ctx.D,&ctx.D,NULL);
147: ctx.E = 1.1378;
148: ctx.V = 1.0;
149: ctx.X = 0.545;
150: ctx.Pmax = ctx.E*ctx.V/ctx.X;;
151: PetscOptionsScalar ("-Pmax" ,"" ,"" ,ctx.Pmax,&ctx.Pmax,NULL);
152: ctx.Pm = 0.9;
153: PetscOptionsScalar ("-Pm" ,"" ,"" ,ctx.Pm,&ctx.Pm,NULL);
154: ctx.tf = 1.0;
155: ctx.tcl = 1.05;
156: PetscOptionsReal ("-tf" ,"Time to start fault" ,"" ,ctx.tf,&ctx.tf,NULL);
157: PetscOptionsReal ("-tcl" ,"Time to end fault" ,"" ,ctx.tcl,&ctx.tcl,NULL);
158: PetscOptionsBool ("-ensemble" ,"Run ensemble of different initial conditions" ,"" ,ensemble,&ensemble,NULL);
159: if (ensemble) {
160: ctx.tf = -1;
161: ctx.tcl = -1;
162: }
164: VecGetArray (U,&u);
165: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
166: u[1] = 1.0;
167: PetscOptionsRealArray ("-u" ,"Initial solution" ,"" ,u,&n,&flg1);
168: n = 2;
169: PetscOptionsRealArray ("-du" ,"Perturbation in initial solution" ,"" ,du,&n,&flg2);
170: u[0] += du[0];
171: u[1] += du[1];
172: VecRestoreArray (U,&u);
173: if (flg1 || flg2) {
174: ctx.tf = -1;
175: ctx.tcl = -1;
176: }
177: }
178: PetscOptionsEnd ();
180: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181: Create timestepping solver context
182: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
183: TSCreate (PETSC_COMM_WORLD ,&ts);
184: TSSetProblemType (ts,TS_NONLINEAR);
185: TSSetType (ts,TSTHETA );
186: TSSetIFunction (ts,NULL,(TSIFunction) IFunction,&ctx);
187: TSSetIJacobian (ts,A,A,(TSIJacobian)IJacobian,&ctx);
188: TSSetExactFinalTime (ts,TS_EXACTFINALTIME_MATCHSTEP);
190: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
191: Set initial conditions
192: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
193: TSSetSolution (ts,U);
195: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196: Set solver options
197: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
198: TSSetDuration (ts,100000,35.0);
199: TSSetInitialTimeStep (ts,0.0,.01);
200: TSSetFromOptions (ts);
203: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204: Solve nonlinear system
205: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
206: if (ensemble) {
207: for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
208: VecGetArray (U,&u);
209: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
210: u[1] = ctx.omega_s;
211: u[0] += du[0];
212: u[1] += du[1];
213: VecRestoreArray (U,&u);
214: TSSetInitialTimeStep (ts,0.0,.01);
215: TSSolve (ts,U);
216: }
217: } else {
218: TSSolve (ts,U);
219: }
220: VecView (U,PETSC_VIEWER_STDOUT_WORLD );
221: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
222: Free work space. All PETSc objects should be destroyed when they are no longer needed.
223: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
224: MatDestroy (&A);
225: VecDestroy (&U);
226: TSDestroy (&ts);
228: PetscFinalize ();
229: return (0);
230: }