Actual source code: ex2.c
2: static char help[] = "Basic equation for generator stability analysis.\n";
4: /*F
6: \begin{eqnarray}
7: \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - \frac{EV}{X} \sin(\theta) -D(\omega - \omega_s)\\
8: \frac{d \theta}{dt} = \omega - \omega_s
9: \end{eqnarray}
11: Ensemble of initial conditions
12: ./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
14: Fault at .1 seconds
15: ./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
17: Initial conditions same as when fault is ended
18: ./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
20: F*/
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;
79: J[0][1] = -ctx->omega_s;
80: J[1][1] = 2.0 * ctx->H * a + ctx->D;
81: J[1][0] = Pmax * PetscCosScalar(u[0]);
83: MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES);
84: VecRestoreArrayRead(U, &u);
85: VecRestoreArrayRead(Udot, &udot);
87: MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
88: MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
89: if (A != B) {
90: MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY);
91: MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY);
92: }
93: return 0;
94: }
96: PetscErrorCode PostStep(TS ts)
97: {
98: Vec X;
99: PetscReal t;
101: TSGetTime(ts, &t);
102: if (t >= .2) {
103: TSGetSolution(ts, &X);
104: VecView(X, PETSC_VIEWER_STDOUT_WORLD);
105: exit(0);
106: /* results in initial conditions after fault of -u 0.496792,1.00932 */
107: }
108: return 0;
109: }
111: int main(int argc, char **argv)
112: {
113: TS ts; /* ODE integrator */
114: Vec U; /* solution will be stored here */
115: Mat A; /* Jacobian matrix */
116: PetscMPIInt size;
117: PetscInt n = 2;
118: AppCtx ctx;
119: PetscScalar *u;
120: PetscReal du[2] = {0.0, 0.0};
121: PetscBool ensemble = PETSC_FALSE, flg1, flg2;
123: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
124: Initialize program
125: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
127: PetscInitialize(&argc, &argv, (char *)0, help);
128: MPI_Comm_size(PETSC_COMM_WORLD, &size);
131: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
132: Create necessary matrix and vectors
133: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
134: MatCreate(PETSC_COMM_WORLD, &A);
135: MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE);
136: MatSetType(A, MATDENSE);
137: MatSetFromOptions(A);
138: MatSetUp(A);
140: MatCreateVecs(A, &U, NULL);
142: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
143: Set runtime options
144: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
145: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", "");
146: {
147: ctx.omega_s = 2.0 * PETSC_PI * 60.0;
148: ctx.H = 5.0;
149: PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL);
150: ctx.D = 5.0;
151: PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL);
152: ctx.E = 1.1378;
153: ctx.V = 1.0;
154: ctx.X = 0.545;
155: ctx.Pmax = ctx.E * ctx.V / ctx.X;
156: PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL);
157: ctx.Pm = 0.9;
158: PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL);
159: ctx.tf = 1.0;
160: ctx.tcl = 1.05;
161: PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL);
162: PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL);
163: PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL);
164: if (ensemble) {
165: ctx.tf = -1;
166: ctx.tcl = -1;
167: }
169: VecGetArray(U, &u);
170: u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
171: u[1] = 1.0;
172: PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1);
173: n = 2;
174: PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2);
175: u[0] += du[0];
176: u[1] += du[1];
177: VecRestoreArray(U, &u);
178: if (flg1 || flg2) {
179: ctx.tf = -1;
180: ctx.tcl = -1;
181: }
182: }
183: PetscOptionsEnd();
185: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
186: Create timestepping solver context
187: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
188: TSCreate(PETSC_COMM_WORLD, &ts);
189: TSSetProblemType(ts, TS_NONLINEAR);
190: TSSetType(ts, TSROSW);
191: TSSetIFunction(ts, NULL, (TSIFunction)IFunction, &ctx);
192: TSSetIJacobian(ts, A, A, (TSIJacobian)IJacobian, &ctx);
194: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195: Set initial conditions
196: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
197: TSSetSolution(ts, U);
199: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
200: Set solver options
201: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
202: TSSetMaxTime(ts, 35.0);
203: TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP);
204: TSSetTimeStep(ts, .01);
205: TSSetFromOptions(ts);
206: /* TSSetPostStep(ts,PostStep); */
208: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209: Solve nonlinear system
210: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
211: if (ensemble) {
212: for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
213: VecGetArray(U, &u);
214: u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
215: u[1] = ctx.omega_s;
216: u[0] += du[0];
217: u[1] += du[1];
218: VecRestoreArray(U, &u);
219: TSSetTimeStep(ts, .01);
220: TSSolve(ts, U);
221: }
222: } else {
223: TSSolve(ts, U);
224: }
225: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
226: Free work space. All PETSc objects should be destroyed when they are no longer needed.
227: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
228: MatDestroy(&A);
229: VecDestroy(&U);
230: TSDestroy(&ts);
231: PetscFinalize();
232: return 0;
233: }
235: /*TEST
237: build:
238: requires: !complex
240: test:
241: args: -nox -ts_dt 10
243: TEST*/