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:   PetscFunctionBegin;
 48:   /*  The next three lines allow us to access the entries of the vectors directly */
 49:   PetscCall(VecGetArrayRead(U, &u));
 50:   PetscCall(VecGetArrayRead(Udot, &udot));
 51:   PetscCall(VecGetArray(F, &f));
 52:   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 */
 53:   else if (t >= ctx->tcl) Pmax = ctx->E / 0.745;
 54:   else Pmax = ctx->Pmax;
 55:   f[0] = udot[0] - ctx->omega_s * (u[1] - 1.0);
 56:   f[1] = 2.0 * ctx->H * udot[1] + Pmax * PetscSinScalar(u[0]) + ctx->D * (u[1] - 1.0) - ctx->Pm;

 58:   PetscCall(VecRestoreArrayRead(U, &u));
 59:   PetscCall(VecRestoreArrayRead(Udot, &udot));
 60:   PetscCall(VecRestoreArray(F, &f));
 61:   PetscFunctionReturn(PETSC_SUCCESS);
 62: }

 64: /*
 65:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
 66: */
 67: static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, AppCtx *ctx)
 68: {
 69:   PetscInt           rowcol[] = {0, 1};
 70:   PetscScalar        J[2][2], Pmax;
 71:   const PetscScalar *u, *udot;

 73:   PetscFunctionBegin;
 74:   PetscCall(VecGetArrayRead(U, &u));
 75:   PetscCall(VecGetArrayRead(Udot, &udot));
 76:   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 */
 77:   else if (t >= ctx->tcl) Pmax = ctx->E / 0.745;
 78:   else Pmax = ctx->Pmax;

 80:   J[0][0] = a;
 81:   J[0][1] = -ctx->omega_s;
 82:   J[1][1] = 2.0 * ctx->H * a + ctx->D;
 83:   J[1][0] = Pmax * PetscCosScalar(u[0]);

 85:   PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
 86:   PetscCall(VecRestoreArrayRead(U, &u));
 87:   PetscCall(VecRestoreArrayRead(Udot, &udot));

 89:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
 90:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
 91:   if (A != B) {
 92:     PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
 93:     PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
 94:   }
 95:   PetscFunctionReturn(PETSC_SUCCESS);
 96: }

 98: PetscErrorCode PostStep(TS ts)
 99: {
100:   Vec       X;
101:   PetscReal t;

103:   PetscFunctionBegin;
104:   PetscCall(TSGetTime(ts, &t));
105:   if (t >= .2) {
106:     PetscCall(TSGetSolution(ts, &X));
107:     PetscCall(VecView(X, PETSC_VIEWER_STDOUT_WORLD));
108:     exit(0);
109:     /* results in initial conditions after fault of -u 0.496792,1.00932 */
110:   }
111:   PetscFunctionReturn(PETSC_SUCCESS);
112: }

114: int main(int argc, char **argv)
115: {
116:   TS           ts; /* ODE integrator */
117:   Vec          U;  /* solution will be stored here */
118:   Mat          A;  /* Jacobian matrix */
119:   PetscMPIInt  size;
120:   PetscInt     n = 2;
121:   AppCtx       ctx;
122:   PetscScalar *u;
123:   PetscReal    du[2]    = {0.0, 0.0};
124:   PetscBool    ensemble = PETSC_FALSE, flg1, flg2;

126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127:      Initialize program
128:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
129:   PetscFunctionBeginUser;
130:   PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
131:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
132:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");

134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135:     Create necessary matrix and vectors
136:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
137:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
138:   PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
139:   PetscCall(MatSetType(A, MATDENSE));
140:   PetscCall(MatSetFromOptions(A));
141:   PetscCall(MatSetUp(A));

143:   PetscCall(MatCreateVecs(A, &U, NULL));

145:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146:     Set runtime options
147:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
148:   PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", "");
149:   {
150:     ctx.omega_s = 2.0 * PETSC_PI * 60.0;
151:     ctx.H       = 5.0;
152:     PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL));
153:     ctx.D = 5.0;
154:     PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL));
155:     ctx.E    = 1.1378;
156:     ctx.V    = 1.0;
157:     ctx.X    = 0.545;
158:     ctx.Pmax = ctx.E * ctx.V / ctx.X;
159:     PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL));
160:     ctx.Pm = 0.9;
161:     PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL));
162:     ctx.tf  = 1.0;
163:     ctx.tcl = 1.05;
164:     PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL));
165:     PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL));
166:     PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL));
167:     if (ensemble) {
168:       ctx.tf  = -1;
169:       ctx.tcl = -1;
170:     }

172:     PetscCall(VecGetArray(U, &u));
173:     u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
174:     u[1] = 1.0;
175:     PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1));
176:     n = 2;
177:     PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2));
178:     u[0] += du[0];
179:     u[1] += du[1];
180:     PetscCall(VecRestoreArray(U, &u));
181:     if (flg1 || flg2) {
182:       ctx.tf  = -1;
183:       ctx.tcl = -1;
184:     }
185:   }
186:   PetscOptionsEnd();

188:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
189:      Create timestepping solver context
190:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
191:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
192:   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
193:   PetscCall(TSSetType(ts, TSROSW));
194:   PetscCall(TSSetIFunction(ts, NULL, (TSIFunction)IFunction, &ctx));
195:   PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobian)IJacobian, &ctx));

197:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198:      Set initial conditions
199:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
200:   PetscCall(TSSetSolution(ts, U));

202:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
203:      Set solver options
204:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
205:   PetscCall(TSSetMaxTime(ts, 35.0));
206:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
207:   PetscCall(TSSetTimeStep(ts, .01));
208:   PetscCall(TSSetFromOptions(ts));
209:   /* PetscCall(TSSetPostStep(ts,PostStep));  */

211:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
212:      Solve nonlinear system
213:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
214:   if (ensemble) {
215:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
216:       PetscCall(VecGetArray(U, &u));
217:       u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
218:       u[1] = ctx.omega_s;
219:       u[0] += du[0];
220:       u[1] += du[1];
221:       PetscCall(VecRestoreArray(U, &u));
222:       PetscCall(TSSetTimeStep(ts, .01));
223:       PetscCall(TSSolve(ts, U));
224:     }
225:   } else {
226:     PetscCall(TSSolve(ts, U));
227:   }
228:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
229:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
230:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
231:   PetscCall(MatDestroy(&A));
232:   PetscCall(VecDestroy(&U));
233:   PetscCall(TSDestroy(&ts));
234:   PetscCall(PetscFinalize());
235:   return 0;
236: }

238: /*TEST

240:    build:
241:       requires: !complex

243:    test:
244:       args: -nox -ts_dt 10

246: TEST*/