Actual source code: ex2.c
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
22: /*
23: Include "petscts.h" so that we can use TS solvers. Note that this
24: file automatically includes:
25: petscsys.h - base PETSc routines petscvec.h - vectors
26: petscmat.h - matrices
27: petscis.h - index sets petscksp.h - Krylov subspace methods
28: petscviewer.h - viewers petscpc.h - preconditioners
29: petscksp.h - linear solvers
30: */
32: #include <petscts.h>
34: typedef struct {
35: PetscScalar H,D,omega_s,Pmax,Pm,E,V,X;
36: PetscReal tf,tcl;
37: } AppCtx;
39: /*
40: Defines the ODE passed to the ODE solver
41: */
42: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
43: {
44: PetscScalar *f,Pmax;
45: const PetscScalar *u,*udot;
47: /* The next three lines allow us to access the entries of the vectors directly */
48: VecGetArrayRead(U,&u);
49: VecGetArrayRead(Udot,&udot);
50: VecGetArray(F,&f);
51: 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 */
52: else if (t >= ctx->tcl) Pmax = ctx->E/0.745;
53: else Pmax = ctx->Pmax;
54: f[0] = udot[0] - ctx->omega_s*(u[1] - 1.0);
55: f[1] = 2.0*ctx->H*udot[1] + Pmax*PetscSinScalar(u[0]) + ctx->D*(u[1] - 1.0)- ctx->Pm;
57: VecRestoreArrayRead(U,&u);
58: VecRestoreArrayRead(Udot,&udot);
59: VecRestoreArray(F,&f);
60: return 0;
61: }
63: /*
64: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
65: */
66: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
67: {
68: PetscInt rowcol[] = {0,1};
69: PetscScalar J[2][2],Pmax;
70: const PetscScalar *u,*udot;
72: VecGetArrayRead(U,&u);
73: VecGetArrayRead(Udot,&udot);
74: 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 */
75: else if (t >= ctx->tcl) Pmax = ctx->E/0.745;
76: else Pmax = ctx->Pmax;
78: J[0][0] = a; J[0][1] = -ctx->omega_s;
79: J[1][1] = 2.0*ctx->H*a + ctx->D; J[1][0] = Pmax*PetscCosScalar(u[0]);
81: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
82: VecRestoreArrayRead(U,&u);
83: VecRestoreArrayRead(Udot,&udot);
85: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
86: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
87: if (A != B) {
88: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
89: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
90: }
91: return 0;
92: }
94: PetscErrorCode PostStep(TS ts)
95: {
96: Vec X;
97: PetscReal t;
99: TSGetTime(ts,&t);
100: if (t >= .2) {
101: TSGetSolution(ts,&X);
102: VecView(X,PETSC_VIEWER_STDOUT_WORLD);
103: exit(0);
104: /* results in initial conditions after fault of -u 0.496792,1.00932 */
105: }
106: return 0;
107: }
109: int main(int argc,char **argv)
110: {
111: TS ts; /* ODE integrator */
112: Vec U; /* solution will be stored here */
113: Mat A; /* Jacobian matrix */
115: PetscMPIInt size;
116: PetscInt n = 2;
117: AppCtx ctx;
118: PetscScalar *u;
119: PetscReal du[2] = {0.0,0.0};
120: PetscBool ensemble = PETSC_FALSE,flg1,flg2;
122: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
123: Initialize program
124: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
125: PetscInitialize(&argc,&argv,(char*)0,help);
126: MPI_Comm_size(PETSC_COMM_WORLD,&size);
129: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130: Create necessary matrix and vectors
131: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
132: MatCreate(PETSC_COMM_WORLD,&A);
133: MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
134: MatSetType(A,MATDENSE);
135: MatSetFromOptions(A);
136: MatSetUp(A);
138: MatCreateVecs(A,&U,NULL);
140: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
141: Set runtime options
142: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
143: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
144: {
145: ctx.omega_s = 2.0*PETSC_PI*60.0;
146: ctx.H = 5.0;
147: PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
148: ctx.D = 5.0;
149: PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
150: ctx.E = 1.1378;
151: ctx.V = 1.0;
152: ctx.X = 0.545;
153: ctx.Pmax = ctx.E*ctx.V/ctx.X;
154: PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
155: ctx.Pm = 0.9;
156: PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
157: ctx.tf = 1.0;
158: ctx.tcl = 1.05;
159: PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
160: PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
161: PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
162: if (ensemble) {
163: ctx.tf = -1;
164: ctx.tcl = -1;
165: }
167: VecGetArray(U,&u);
168: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
169: u[1] = 1.0;
170: PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);
171: n = 2;
172: PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);
173: u[0] += du[0];
174: u[1] += du[1];
175: VecRestoreArray(U,&u);
176: if (flg1 || flg2) {
177: ctx.tf = -1;
178: ctx.tcl = -1;
179: }
180: }
181: PetscOptionsEnd();
183: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
184: Create timestepping solver context
185: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
186: TSCreate(PETSC_COMM_WORLD,&ts);
187: TSSetProblemType(ts,TS_NONLINEAR);
188: TSSetType(ts,TSROSW);
189: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);
190: TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);
192: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193: Set initial conditions
194: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
195: TSSetSolution(ts,U);
197: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198: Set solver options
199: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
200: TSSetMaxTime(ts,35.0);
201: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
202: TSSetTimeStep(ts,.01);
203: TSSetFromOptions(ts);
204: /* TSSetPostStep(ts,PostStep); */
206: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
207: Solve nonlinear system
208: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
209: if (ensemble) {
210: for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
211: VecGetArray(U,&u);
212: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
213: u[1] = ctx.omega_s;
214: u[0] += du[0];
215: u[1] += du[1];
216: VecRestoreArray(U,&u);
217: TSSetTimeStep(ts,.01);
218: TSSolve(ts,U);
219: }
220: } else {
221: TSSolve(ts,U);
222: }
223: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
224: Free work space. All PETSc objects should be destroyed when they are no longer needed.
225: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
226: MatDestroy(&A);
227: VecDestroy(&U);
228: TSDestroy(&ts);
229: PetscFinalize();
230: return 0;
231: }
233: /*TEST
235: build:
236: requires: !complex
238: test:
239: args: -nox -ts_dt 10
241: TEST*/