1 static char help[] = "Basic equation for generator stability analysis.\n"; 2 3 /*F 4 5 \begin{eqnarray} 6 \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - \frac{EV}{X} \sin(\theta) -D(\omega - \omega_s)\\ 7 \frac{d \theta}{dt} = \omega - \omega_s 8 \end{eqnarray} 9 10 Ensemble of initial conditions 11 ./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 12 13 Fault at .1 seconds 14 ./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 15 16 Initial conditions same as when fault is ended 17 ./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 18 19 F*/ 20 21 /* 22 Include "petscts.h" so that we can use TS solvers. Note that this 23 file automatically includes: 24 petscsys.h - base PETSc routines petscvec.h - vectors 25 petscmat.h - matrices 26 petscis.h - index sets petscksp.h - Krylov subspace methods 27 petscviewer.h - viewers petscpc.h - preconditioners 28 petscksp.h - linear solvers 29 */ 30 31 #include <petscts.h> 32 33 typedef struct { 34 PetscScalar H, D, omega_s, Pmax, Pm, E, V, X; 35 PetscReal tf, tcl; 36 } AppCtx; 37 38 /* 39 Defines the ODE passed to the ODE solver 40 */ 41 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, AppCtx *ctx) 42 { 43 PetscScalar *f, Pmax; 44 const PetscScalar *u, *udot; 45 46 PetscFunctionBegin; 47 /* The next three lines allow us to access the entries of the vectors directly */ 48 PetscCall(VecGetArrayRead(U, &u)); 49 PetscCall(VecGetArrayRead(Udot, &udot)); 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 if (t >= ctx->tcl) Pmax = ctx->E / 0.745; 53 else Pmax = ctx->Pmax; 54 f[0] = udot[0] - ctx->omega_s * (u[1] - 1.0); 55 f[1] = 2.0 * ctx->H * udot[1] + Pmax * PetscSinScalar(u[0]) + ctx->D * (u[1] - 1.0) - ctx->Pm; 56 57 PetscCall(VecRestoreArrayRead(U, &u)); 58 PetscCall(VecRestoreArrayRead(Udot, &udot)); 59 PetscCall(VecRestoreArray(F, &f)); 60 PetscFunctionReturn(PETSC_SUCCESS); 61 } 62 63 /* 64 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 65 */ 66 static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, AppCtx *ctx) 67 { 68 PetscInt rowcol[] = {0, 1}; 69 PetscScalar J[2][2], Pmax; 70 const PetscScalar *u, *udot; 71 72 PetscFunctionBegin; 73 PetscCall(VecGetArrayRead(U, &u)); 74 PetscCall(VecGetArrayRead(Udot, &udot)); 75 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 */ 76 else if (t >= ctx->tcl) Pmax = ctx->E / 0.745; 77 else Pmax = ctx->Pmax; 78 79 J[0][0] = a; 80 J[0][1] = -ctx->omega_s; 81 J[1][1] = 2.0 * ctx->H * a + ctx->D; 82 J[1][0] = Pmax * PetscCosScalar(u[0]); 83 84 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 85 PetscCall(VecRestoreArrayRead(U, &u)); 86 PetscCall(VecRestoreArrayRead(Udot, &udot)); 87 88 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 89 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 90 if (A != B) { 91 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 92 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 93 } 94 PetscFunctionReturn(PETSC_SUCCESS); 95 } 96 97 PetscErrorCode PostStep(TS ts) 98 { 99 Vec X; 100 PetscReal t; 101 102 PetscFunctionBegin; 103 PetscCall(TSGetTime(ts, &t)); 104 if (t >= .2) { 105 PetscCall(TSGetSolution(ts, &X)); 106 PetscCall(VecView(X, PETSC_VIEWER_STDOUT_WORLD)); 107 exit(0); 108 /* results in initial conditions after fault of -u 0.496792,1.00932 */ 109 } 110 PetscFunctionReturn(PETSC_SUCCESS); 111 } 112 113 int main(int argc, char **argv) 114 { 115 TS ts; /* ODE integrator */ 116 Vec U; /* solution will be stored here */ 117 Mat A; /* Jacobian matrix */ 118 PetscMPIInt size; 119 PetscInt n = 2; 120 AppCtx ctx; 121 PetscScalar *u; 122 PetscReal du[2] = {0.0, 0.0}; 123 PetscBool ensemble = PETSC_FALSE, flg1, flg2; 124 125 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 126 Initialize program 127 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 128 PetscFunctionBeginUser; 129 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 130 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 131 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 132 133 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 134 Create necessary matrix and vectors 135 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 136 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 137 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 138 PetscCall(MatSetType(A, MATDENSE)); 139 PetscCall(MatSetFromOptions(A)); 140 PetscCall(MatSetUp(A)); 141 142 PetscCall(MatCreateVecs(A, &U, NULL)); 143 144 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 145 Set runtime options 146 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 147 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", ""); 148 { 149 ctx.omega_s = 2.0 * PETSC_PI * 60.0; 150 ctx.H = 5.0; 151 PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL)); 152 ctx.D = 5.0; 153 PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL)); 154 ctx.E = 1.1378; 155 ctx.V = 1.0; 156 ctx.X = 0.545; 157 ctx.Pmax = ctx.E * ctx.V / ctx.X; 158 PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL)); 159 ctx.Pm = 0.9; 160 PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL)); 161 ctx.tf = 1.0; 162 ctx.tcl = 1.05; 163 PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL)); 164 PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL)); 165 PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL)); 166 if (ensemble) { 167 ctx.tf = -1; 168 ctx.tcl = -1; 169 } 170 171 PetscCall(VecGetArray(U, &u)); 172 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); 173 u[1] = 1.0; 174 PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1)); 175 n = 2; 176 PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2)); 177 u[0] += du[0]; 178 u[1] += du[1]; 179 PetscCall(VecRestoreArray(U, &u)); 180 if (flg1 || flg2) { 181 ctx.tf = -1; 182 ctx.tcl = -1; 183 } 184 } 185 PetscOptionsEnd(); 186 187 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 188 Create timestepping solver context 189 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 190 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 191 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 192 PetscCall(TSSetType(ts, TSROSW)); 193 PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, &ctx)); 194 PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, &ctx)); 195 196 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 197 Set initial conditions 198 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 199 PetscCall(TSSetSolution(ts, U)); 200 201 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 202 Set solver options 203 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 204 PetscCall(TSSetMaxTime(ts, 35.0)); 205 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 206 PetscCall(TSSetTimeStep(ts, .01)); 207 PetscCall(TSSetFromOptions(ts)); 208 /* PetscCall(TSSetPostStep(ts,PostStep)); */ 209 210 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 211 Solve nonlinear system 212 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 213 if (ensemble) { 214 for (du[1] = -2.5; du[1] <= .01; du[1] += .1) { 215 PetscCall(VecGetArray(U, &u)); 216 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); 217 u[1] = ctx.omega_s; 218 u[0] += du[0]; 219 u[1] += du[1]; 220 PetscCall(VecRestoreArray(U, &u)); 221 PetscCall(TSSetTimeStep(ts, .01)); 222 PetscCall(TSSolve(ts, U)); 223 } 224 } else { 225 PetscCall(TSSolve(ts, U)); 226 } 227 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 228 Free work space. All PETSc objects should be destroyed when they are no longer needed. 229 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 230 PetscCall(MatDestroy(&A)); 231 PetscCall(VecDestroy(&U)); 232 PetscCall(TSDestroy(&ts)); 233 PetscCall(PetscFinalize()); 234 return 0; 235 } 236 237 /*TEST 238 239 build: 240 requires: !complex 241 242 test: 243 args: -nox -ts_dt 10 244 245 TEST*/ 246