Actual source code: ex9.c
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: */
35: #include <petscts.h>
37: typedef struct {
38: PetscScalar H,D,omega_b,omega_s,Pmax,Pm,E,V,X;
39: PetscReal tf,tcl;
40: } AppCtx;
42: /*
43: Defines the ODE passed to the ODE solver
44: */
45: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
46: {
47: PetscErrorCode ierr;
48: const PetscScalar *u;
49: PetscScalar *f,Pmax;
52: /* The next three lines allow us to access the entries of the vectors directly */
53: VecGetArrayRead(U,&u);
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 Pmax = ctx->Pmax;
58: f[0] = ctx->omega_b*(u[1] - ctx->omega_s);
59: f[1] = (-Pmax*PetscSinScalar(u[0]) - ctx->D*(u[1] - ctx->omega_s) + ctx->Pm)*ctx->omega_s/(2.0*ctx->H);
61: VecRestoreArrayRead(U,&u);
62: VecRestoreArray(F,&f);
63: return(0);
64: }
66: /*
67: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
68: */
69: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,AppCtx *ctx)
70: {
71: PetscErrorCode ierr;
72: PetscInt rowcol[] = {0,1};
73: PetscScalar J[2][2],Pmax;
74: const PetscScalar *u;
77: VecGetArrayRead(U,&u);
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 Pmax = ctx->Pmax;
81: J[0][0] = 0; J[0][1] = ctx->omega_b;
82: J[1][1] = -ctx->D*ctx->omega_s/(2.0*ctx->H); J[1][0] = -Pmax*PetscCosScalar(u[0])*ctx->omega_s/(2.0*ctx->H);
84: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
85: VecRestoreArrayRead(U,&u);
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: int main(int argc,char **argv)
97: {
98: TS ts; /* ODE integrator */
99: Vec U; /* solution will be stored here */
100: Mat A; /* Jacobian matrix */
102: PetscMPIInt size;
103: PetscInt n = 2;
104: AppCtx ctx;
105: PetscScalar *u;
106: PetscReal du[2] = {0.0,0.0};
107: PetscBool ensemble = PETSC_FALSE,flg1,flg2;
109: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
110: Initialize program
111: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
112: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
113: MPI_Comm_size(PETSC_COMM_WORLD,&size);
114: if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
116: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
117: Create necessary matrix and vectors
118: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
119: MatCreate(PETSC_COMM_WORLD,&A);
120: MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
121: MatSetType(A,MATDENSE);
122: MatSetFromOptions(A);
123: MatSetUp(A);
125: MatCreateVecs(A,&U,NULL);
127: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128: Set runtime options
129: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
130: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
131: {
132: ctx.omega_b = 1.0;
133: ctx.omega_s = 2.0*PETSC_PI*60.0;
134: ctx.H = 5.0;
135: PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
136: ctx.D = 5.0;
137: PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
138: ctx.E = 1.1378;
139: ctx.V = 1.0;
140: ctx.X = 0.545;
141: ctx.Pmax = ctx.E*ctx.V/ctx.X;
142: PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
143: ctx.Pm = 0.9;
144: PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
145: ctx.tf = 1.0;
146: ctx.tcl = 1.05;
147: PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
148: PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
149: PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
150: if (ensemble) {
151: ctx.tf = -1;
152: ctx.tcl = -1;
153: }
155: VecGetArray(U,&u);
156: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
157: u[1] = 1.0;
158: PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);
159: n = 2;
160: PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);
161: u[0] += du[0];
162: u[1] += du[1];
163: VecRestoreArray(U,&u);
164: if (flg1 || flg2) {
165: ctx.tf = -1;
166: ctx.tcl = -1;
167: }
168: }
169: PetscOptionsEnd();
171: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
172: Create timestepping solver context
173: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
174: TSCreate(PETSC_COMM_WORLD,&ts);
175: TSSetProblemType(ts,TS_NONLINEAR);
176: TSSetType(ts,TSTHETA);
177: TSSetRHSFunction(ts,NULL,(TSRHSFunction)RHSFunction,&ctx);
178: TSSetRHSJacobian(ts,A,A,(TSRHSJacobian)RHSJacobian,&ctx);
180: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181: Set initial conditions
182: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
183: TSSetSolution(ts,U);
185: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
186: Set solver options
187: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
188: TSSetMaxTime(ts,35.0);
189: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
190: TSSetTimeStep(ts,.01);
191: TSSetFromOptions(ts);
193: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194: Solve nonlinear system
195: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
196: if (ensemble) {
197: for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
198: VecGetArray(U,&u);
199: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
200: u[1] = ctx.omega_s;
201: u[0] += du[0];
202: u[1] += du[1];
203: VecRestoreArray(U,&u);
204: TSSetTimeStep(ts,.01);
205: TSSolve(ts,U);
206: }
207: } else {
208: TSSolve(ts,U);
209: }
210: VecView(U,PETSC_VIEWER_STDOUT_WORLD);
211: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
212: Free work space. All PETSc objects should be destroyed when they are no longer needed.
213: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
214: MatDestroy(&A);
215: VecDestroy(&U);
216: TSDestroy(&ts);
217: PetscFinalize();
218: return ierr;
219: }
222: /*TEST
224: build:
225: requires: !complex
227: test:
229: TEST*/