static char help[] = "Basic equation for generator stability analysis.\n"; /*F \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 F*/ /* Include "petscts.h" so that we can use TS solvers. Note that this file automatically includes: petscsys.h - base PETSc routines petscvec.h - vectors petscmat.h - matrices petscis.h - index sets petscksp.h - Krylov subspace methods petscviewer.h - viewers petscpc.h - preconditioners petscksp.h - linear solvers */ #include typedef struct { PetscScalar H, D, omega_s, Pmax, Pm, E, V, X; PetscReal tf, tcl; } AppCtx; /* Defines the ODE passed to the ODE solver */ static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, AppCtx *ctx) { PetscScalar *f, Pmax; const PetscScalar *u, *udot; PetscFunctionBegin; /* The next three lines allow us to access the entries of the vectors directly */ PetscCall(VecGetArrayRead(U, &u)); PetscCall(VecGetArrayRead(Udot, &udot)); PetscCall(VecGetArray(F, &f)); 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 */ else if (t >= ctx->tcl) Pmax = ctx->E / 0.745; else Pmax = ctx->Pmax; f[0] = udot[0] - ctx->omega_s * (u[1] - 1.0); f[1] = 2.0 * ctx->H * udot[1] + Pmax * PetscSinScalar(u[0]) + ctx->D * (u[1] - 1.0) - ctx->Pm; PetscCall(VecRestoreArrayRead(U, &u)); PetscCall(VecRestoreArrayRead(Udot, &udot)); PetscCall(VecRestoreArray(F, &f)); PetscFunctionReturn(PETSC_SUCCESS); } /* Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. */ static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, AppCtx *ctx) { PetscInt rowcol[] = {0, 1}; PetscScalar J[2][2], Pmax; const PetscScalar *u, *udot; PetscFunctionBegin; PetscCall(VecGetArrayRead(U, &u)); PetscCall(VecGetArrayRead(Udot, &udot)); 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 */ else if (t >= ctx->tcl) Pmax = ctx->E / 0.745; else Pmax = ctx->Pmax; J[0][0] = a; J[0][1] = -ctx->omega_s; J[1][1] = 2.0 * ctx->H * a + ctx->D; J[1][0] = Pmax * PetscCosScalar(u[0]); PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); PetscCall(VecRestoreArrayRead(U, &u)); PetscCall(VecRestoreArrayRead(Udot, &udot)); PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); if (A != B) { PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); } PetscFunctionReturn(PETSC_SUCCESS); } PetscErrorCode PostStep(TS ts) { Vec X; PetscReal t; PetscFunctionBegin; PetscCall(TSGetTime(ts, &t)); if (t >= .2) { PetscCall(TSGetSolution(ts, &X)); PetscCall(VecView(X, PETSC_VIEWER_STDOUT_WORLD)); exit(0); /* results in initial conditions after fault of -u 0.496792,1.00932 */ } PetscFunctionReturn(PETSC_SUCCESS); } int main(int argc, char **argv) { TS ts; /* ODE integrator */ Vec U; /* solution will be stored here */ Mat A; /* Jacobian matrix */ PetscMPIInt size; PetscInt n = 2; AppCtx ctx; PetscScalar *u; PetscReal du[2] = {0.0, 0.0}; PetscBool ensemble = PETSC_FALSE, flg1, flg2; /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Initialize program - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscFunctionBeginUser; PetscCall(PetscInitialize(&argc, &argv, NULL, help)); PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create necessary matrix and vectors - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); PetscCall(MatSetType(A, MATDENSE)); PetscCall(MatSetFromOptions(A)); PetscCall(MatSetUp(A)); PetscCall(MatCreateVecs(A, &U, NULL)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set runtime options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", ""); { ctx.omega_s = 2.0 * PETSC_PI * 60.0; ctx.H = 5.0; PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL)); ctx.D = 5.0; PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL)); ctx.E = 1.1378; ctx.V = 1.0; ctx.X = 0.545; ctx.Pmax = ctx.E * ctx.V / ctx.X; PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL)); ctx.Pm = 0.9; PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL)); ctx.tf = 1.0; ctx.tcl = 1.05; PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL)); PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL)); PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL)); if (ensemble) { ctx.tf = -1; ctx.tcl = -1; } PetscCall(VecGetArray(U, &u)); u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); u[1] = 1.0; PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1)); n = 2; PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2)); u[0] += du[0]; u[1] += du[1]; PetscCall(VecRestoreArray(U, &u)); if (flg1 || flg2) { ctx.tf = -1; ctx.tcl = -1; } } PetscOptionsEnd(); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create timestepping solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); PetscCall(TSSetType(ts, TSROSW)); PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, &ctx)); PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, &ctx)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set initial conditions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSetSolution(ts, U)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set solver options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSetMaxTime(ts, 35.0)); PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); PetscCall(TSSetTimeStep(ts, .01)); PetscCall(TSSetFromOptions(ts)); /* PetscCall(TSSetPostStep(ts,PostStep)); */ /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Solve nonlinear system - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ if (ensemble) { for (du[1] = -2.5; du[1] <= .01; du[1] += .1) { PetscCall(VecGetArray(U, &u)); u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); u[1] = ctx.omega_s; u[0] += du[0]; u[1] += du[1]; PetscCall(VecRestoreArray(U, &u)); PetscCall(TSSetTimeStep(ts, .01)); PetscCall(TSSolve(ts, U)); } } else { PetscCall(TSSolve(ts, U)); } /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. All PETSc objects should be destroyed when they are no longer needed. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(MatDestroy(&A)); PetscCall(VecDestroy(&U)); PetscCall(TSDestroy(&ts)); PetscCall(PetscFinalize()); return 0; } /*TEST build: requires: !complex test: args: -nox -ts_time_step 10 output_file: output/empty.out TEST*/