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: PetscErrorCode ierr;
45: PetscScalar *f,Pmax;
46: const PetscScalar *u,*udot;
49: /* The next three lines allow us to access the entries of the vectors directly */
50: VecGetArrayRead(U,&u);
51: VecGetArrayRead(Udot,&udot);
52: VecGetArray(F,&f);
53: 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 */
54: else if (t >= ctx->tcl) Pmax = ctx->E/0.745;
55: else Pmax = ctx->Pmax;
56: f[0] = udot[0] - ctx->omega_s*(u[1] - 1.0);
57: f[1] = 2.0*ctx->H*udot[1] + Pmax*PetscSinScalar(u[0]) + ctx->D*(u[1] - 1.0)- ctx->Pm;
59: VecRestoreArrayRead(U,&u);
60: VecRestoreArrayRead(Udot,&udot);
61: VecRestoreArray(F,&f);
62: return(0);
63: }
65: /*
66: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
67: */
68: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
69: {
70: PetscErrorCode ierr;
71: PetscInt rowcol[] = {0,1};
72: PetscScalar J[2][2],Pmax;
73: const PetscScalar *u,*udot;
76: VecGetArrayRead(U,&u);
77: VecGetArrayRead(Udot,&udot);
78: 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 */
79: else if (t >= ctx->tcl) Pmax = ctx->E/0.745;
80: else Pmax = ctx->Pmax;
82: J[0][0] = a; J[0][1] = -ctx->omega_s;
83: J[1][1] = 2.0*ctx->H*a + ctx->D; J[1][0] = Pmax*PetscCosScalar(u[0]);
85: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
86: VecRestoreArrayRead(U,&u);
87: VecRestoreArrayRead(Udot,&udot);
89: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
90: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
91: if (A != B) {
92: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
93: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
94: }
95: return(0);
96: }
98: PetscErrorCode PostStep(TS ts)
99: {
101: Vec X;
102: PetscReal t;
105: TSGetTime(ts,&t);
106: if (t >= .2) {
107: TSGetSolution(ts,&X);
108: VecView(X,PETSC_VIEWER_STDOUT_WORLD);
109: exit(0);
110: /* results in initial conditions after fault of -u 0.496792,1.00932 */
111: }
112: return(0);
113: }
115: int main(int argc,char **argv)
116: {
117: TS ts; /* ODE integrator */
118: Vec U; /* solution will be stored here */
119: Mat A; /* Jacobian matrix */
121: PetscMPIInt size;
122: PetscInt n = 2;
123: AppCtx ctx;
124: PetscScalar *u;
125: PetscReal du[2] = {0.0,0.0};
126: PetscBool ensemble = PETSC_FALSE,flg1,flg2;
128: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129: Initialize program
130: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
131: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
132: MPI_Comm_size(PETSC_COMM_WORLD,&size);
133: if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
135: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136: Create necessary matrix and vectors
137: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138: MatCreate(PETSC_COMM_WORLD,&A);
139: MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
140: MatSetType(A,MATDENSE);
141: MatSetFromOptions(A);
142: MatSetUp(A);
144: MatCreateVecs(A,&U,NULL);
146: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147: Set runtime options
148: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
150: {
151: ctx.omega_s = 2.0*PETSC_PI*60.0;
152: ctx.H = 5.0;
153: PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
154: ctx.D = 5.0;
155: PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
156: ctx.E = 1.1378;
157: ctx.V = 1.0;
158: ctx.X = 0.545;
159: ctx.Pmax = ctx.E*ctx.V/ctx.X;
160: PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
161: ctx.Pm = 0.9;
162: PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
163: ctx.tf = 1.0;
164: ctx.tcl = 1.05;
165: PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
166: PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
167: PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
168: if (ensemble) {
169: ctx.tf = -1;
170: ctx.tcl = -1;
171: }
173: VecGetArray(U,&u);
174: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
175: u[1] = 1.0;
176: PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);
177: n = 2;
178: PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);
179: u[0] += du[0];
180: u[1] += du[1];
181: VecRestoreArray(U,&u);
182: if (flg1 || flg2) {
183: ctx.tf = -1;
184: ctx.tcl = -1;
185: }
186: }
187: PetscOptionsEnd();
189: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: Create timestepping solver context
191: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
192: TSCreate(PETSC_COMM_WORLD,&ts);
193: TSSetProblemType(ts,TS_NONLINEAR);
194: TSSetType(ts,TSROSW);
195: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);
196: TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);
198: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: Set initial conditions
200: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
201: TSSetSolution(ts,U);
203: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204: Set solver options
205: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
206: TSSetMaxTime(ts,35.0);
207: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
208: TSSetTimeStep(ts,.01);
209: TSSetFromOptions(ts);
210: /* TSSetPostStep(ts,PostStep); */
212: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
213: Solve nonlinear system
214: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
215: if (ensemble) {
216: for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
217: VecGetArray(U,&u);
218: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
219: u[1] = ctx.omega_s;
220: u[0] += du[0];
221: u[1] += du[1];
222: VecRestoreArray(U,&u);
223: TSSetTimeStep(ts,.01);
224: TSSolve(ts,U);
225: }
226: } else {
227: TSSolve(ts,U);
228: }
229: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
230: Free work space. All PETSc objects should be destroyed when they are no longer needed.
231: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
232: MatDestroy(&A);
233: VecDestroy(&U);
234: TSDestroy(&ts);
235: PetscFinalize();
236: return ierr;
237: }
239: /*TEST
241: build:
242: requires: !complex
244: test:
245: args: -nox -ts_dt 10
247: TEST*/