1 2 static char help[] = "Basic equation for generator stability analysis.\n"; 3 4 /*F 5 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} 10 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 13 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 16 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 19 20 F*/ 21 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 */ 31 32 #include <petscts.h> 33 34 typedef struct { 35 PetscScalar H, D, omega_s, Pmax, Pm, E, V, X; 36 PetscReal tf, tcl; 37 } AppCtx; 38 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; 46 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; 57 58 PetscCall(VecRestoreArrayRead(U, &u)); 59 PetscCall(VecRestoreArrayRead(Udot, &udot)); 60 PetscCall(VecRestoreArray(F, &f)); 61 PetscFunctionReturn(PETSC_SUCCESS); 62 } 63 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; 72 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; 79 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]); 84 85 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 86 PetscCall(VecRestoreArrayRead(U, &u)); 87 PetscCall(VecRestoreArrayRead(Udot, &udot)); 88 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 } 97 98 PetscErrorCode PostStep(TS ts) 99 { 100 Vec X; 101 PetscReal t; 102 103 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 } 113 114 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; 125 126 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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"); 133 134 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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)); 142 143 PetscCall(MatCreateVecs(A, &U, NULL)); 144 145 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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 } 171 172 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(); 187 188 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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)); 196 197 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 198 Set initial conditions 199 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 200 PetscCall(TSSetSolution(ts, U)); 201 202 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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)); */ 210 211 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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 } 237 238 /*TEST 239 240 build: 241 requires: !complex 242 243 test: 244 args: -nox -ts_dt 10 245 246 TEST*/ 247