Actual source code: ex9.c


  2: static char help[] = "Basic equation for generator stability analysis.\n";

  4: /*F

  6: \begin{eqnarray}
  7:                  \frac{d \theta}{dt} = \omega_b (\omega - \omega_s)
  8:                  \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - P_max \sin(\theta) -D(\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_b, 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 RHSFunction(TS ts, PetscReal t, Vec U, Vec F, AppCtx *ctx)
 43: {
 44:   const PetscScalar *u;
 45:   PetscScalar       *f, Pmax;

 47:   PetscFunctionBegin;
 48:   /*  The next three lines allow us to access the entries of the vectors directly */
 49:   PetscCall(VecGetArrayRead(U, &u));
 50:   PetscCall(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 Pmax = ctx->Pmax;

 54:   f[0] = ctx->omega_b * (u[1] - ctx->omega_s);
 55:   f[1] = (-Pmax * PetscSinScalar(u[0]) - ctx->D * (u[1] - ctx->omega_s) + ctx->Pm) * ctx->omega_s / (2.0 * ctx->H);

 57:   PetscCall(VecRestoreArrayRead(U, &u));
 58:   PetscCall(VecRestoreArray(F, &f));
 59:   PetscFunctionReturn(PETSC_SUCCESS);
 60: }

 62: /*
 63:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
 64: */
 65: static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat A, Mat B, AppCtx *ctx)
 66: {
 67:   PetscInt           rowcol[] = {0, 1};
 68:   PetscScalar        J[2][2], Pmax;
 69:   const PetscScalar *u;

 71:   PetscFunctionBegin;
 72:   PetscCall(VecGetArrayRead(U, &u));
 73:   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 */
 74:   else Pmax = ctx->Pmax;

 76:   J[0][0] = 0;
 77:   J[0][1] = ctx->omega_b;
 78:   J[1][1] = -ctx->D * ctx->omega_s / (2.0 * ctx->H);
 79:   J[1][0] = -Pmax * PetscCosScalar(u[0]) * ctx->omega_s / (2.0 * ctx->H);

 81:   PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
 82:   PetscCall(VecRestoreArrayRead(U, &u));

 84:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
 85:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
 86:   if (A != B) {
 87:     PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
 88:     PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
 89:   }
 90:   PetscFunctionReturn(PETSC_SUCCESS);
 91: }

 93: int main(int argc, char **argv)
 94: {
 95:   TS           ts; /* ODE integrator */
 96:   Vec          U;  /* solution will be stored here */
 97:   Mat          A;  /* Jacobian matrix */
 98:   PetscMPIInt  size;
 99:   PetscInt     n = 2;
100:   AppCtx       ctx;
101:   PetscScalar *u;
102:   PetscReal    du[2]    = {0.0, 0.0};
103:   PetscBool    ensemble = PETSC_FALSE, flg1, flg2;

105:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
106:      Initialize program
107:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
108:   PetscFunctionBeginUser;
109:   PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
110:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
111:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");

113:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114:     Create necessary matrix and vectors
115:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
116:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
117:   PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
118:   PetscCall(MatSetType(A, MATDENSE));
119:   PetscCall(MatSetFromOptions(A));
120:   PetscCall(MatSetUp(A));

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

124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125:     Set runtime options
126:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
127:   PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", "");
128:   {
129:     ctx.omega_b = 1.0;
130:     ctx.omega_s = 2.0 * PETSC_PI * 60.0;
131:     ctx.H       = 5.0;
132:     PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL));
133:     ctx.D = 5.0;
134:     PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL));
135:     ctx.E    = 1.1378;
136:     ctx.V    = 1.0;
137:     ctx.X    = 0.545;
138:     ctx.Pmax = ctx.E * ctx.V / ctx.X;
139:     PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL));
140:     ctx.Pm = 0.9;
141:     PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL));
142:     ctx.tf  = 1.0;
143:     ctx.tcl = 1.05;
144:     PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL));
145:     PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL));
146:     PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL));
147:     if (ensemble) {
148:       ctx.tf  = -1;
149:       ctx.tcl = -1;
150:     }

152:     PetscCall(VecGetArray(U, &u));
153:     u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
154:     u[1] = 1.0;
155:     PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1));
156:     n = 2;
157:     PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2));
158:     u[0] += du[0];
159:     u[1] += du[1];
160:     PetscCall(VecRestoreArray(U, &u));
161:     if (flg1 || flg2) {
162:       ctx.tf  = -1;
163:       ctx.tcl = -1;
164:     }
165:   }
166:   PetscOptionsEnd();

168:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
169:      Create timestepping solver context
170:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
171:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
172:   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
173:   PetscCall(TSSetType(ts, TSTHETA));
174:   PetscCall(TSSetRHSFunction(ts, NULL, (TSRHSFunction)RHSFunction, &ctx));
175:   PetscCall(TSSetRHSJacobian(ts, A, A, (TSRHSJacobian)RHSJacobian, &ctx));

177:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178:      Set initial conditions
179:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
180:   PetscCall(TSSetSolution(ts, U));

182:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
183:      Set solver options
184:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
185:   PetscCall(TSSetMaxTime(ts, 35.0));
186:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
187:   PetscCall(TSSetTimeStep(ts, .01));
188:   PetscCall(TSSetFromOptions(ts));

190:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
191:      Solve nonlinear system
192:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
193:   if (ensemble) {
194:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
195:       PetscCall(VecGetArray(U, &u));
196:       u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
197:       u[1] = ctx.omega_s;
198:       u[0] += du[0];
199:       u[1] += du[1];
200:       PetscCall(VecRestoreArray(U, &u));
201:       PetscCall(TSSetTimeStep(ts, .01));
202:       PetscCall(TSSolve(ts, U));
203:     }
204:   } else {
205:     PetscCall(TSSolve(ts, U));
206:   }
207:   PetscCall(VecView(U, PETSC_VIEWER_STDOUT_WORLD));
208:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
210:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
211:   PetscCall(MatDestroy(&A));
212:   PetscCall(VecDestroy(&U));
213:   PetscCall(TSDestroy(&ts));
214:   PetscCall(PetscFinalize());
215:   return 0;
216: }

218: /*TEST

220:    build:
221:      requires: !complex

223:    test:

225: TEST*/