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 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(0); 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 PetscInt rowcol[] = {0, 1}; 68 PetscScalar J[2][2], Pmax; 69 const PetscScalar *u, *udot; 70 71 PetscFunctionBegin; 72 PetscCall(VecGetArrayRead(U, &u)); 73 PetscCall(VecGetArrayRead(Udot, &udot)); 74 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 */ 75 else if (t >= ctx->tcl) Pmax = ctx->E / 0.745; 76 else Pmax = ctx->Pmax; 77 78 J[0][0] = a; 79 J[0][1] = -ctx->omega_s; 80 J[1][1] = 2.0 * ctx->H * a + ctx->D; 81 J[1][0] = Pmax * PetscCosScalar(u[0]); 82 83 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 84 PetscCall(VecRestoreArrayRead(U, &u)); 85 PetscCall(VecRestoreArrayRead(Udot, &udot)); 86 87 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 88 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 89 if (A != B) { 90 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 91 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 92 } 93 PetscFunctionReturn(0); 94 } 95 96 PetscErrorCode PostStep(TS ts) { 97 Vec X; 98 PetscReal t; 99 100 PetscFunctionBegin; 101 PetscCall(TSGetTime(ts, &t)); 102 if (t >= .2) { 103 PetscCall(TSGetSolution(ts, &X)); 104 PetscCall(VecView(X, PETSC_VIEWER_STDOUT_WORLD)); 105 exit(0); 106 /* results in initial conditions after fault of -u 0.496792,1.00932 */ 107 } 108 PetscFunctionReturn(0); 109 } 110 111 int main(int argc, char **argv) { 112 TS ts; /* ODE integrator */ 113 Vec U; /* solution will be stored here */ 114 Mat A; /* Jacobian matrix */ 115 PetscMPIInt size; 116 PetscInt n = 2; 117 AppCtx ctx; 118 PetscScalar *u; 119 PetscReal du[2] = {0.0, 0.0}; 120 PetscBool ensemble = PETSC_FALSE, flg1, flg2; 121 122 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 123 Initialize program 124 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 125 PetscFunctionBeginUser; 126 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 127 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 128 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 129 130 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 131 Create necessary matrix and vectors 132 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 133 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 134 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 135 PetscCall(MatSetType(A, MATDENSE)); 136 PetscCall(MatSetFromOptions(A)); 137 PetscCall(MatSetUp(A)); 138 139 PetscCall(MatCreateVecs(A, &U, NULL)); 140 141 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 142 Set runtime options 143 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 144 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", ""); 145 { 146 ctx.omega_s = 2.0 * PETSC_PI * 60.0; 147 ctx.H = 5.0; 148 PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL)); 149 ctx.D = 5.0; 150 PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL)); 151 ctx.E = 1.1378; 152 ctx.V = 1.0; 153 ctx.X = 0.545; 154 ctx.Pmax = ctx.E * ctx.V / ctx.X; 155 PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL)); 156 ctx.Pm = 0.9; 157 PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL)); 158 ctx.tf = 1.0; 159 ctx.tcl = 1.05; 160 PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL)); 161 PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL)); 162 PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL)); 163 if (ensemble) { 164 ctx.tf = -1; 165 ctx.tcl = -1; 166 } 167 168 PetscCall(VecGetArray(U, &u)); 169 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); 170 u[1] = 1.0; 171 PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1)); 172 n = 2; 173 PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2)); 174 u[0] += du[0]; 175 u[1] += du[1]; 176 PetscCall(VecRestoreArray(U, &u)); 177 if (flg1 || flg2) { 178 ctx.tf = -1; 179 ctx.tcl = -1; 180 } 181 } 182 PetscOptionsEnd(); 183 184 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 185 Create timestepping solver context 186 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 187 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 188 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 189 PetscCall(TSSetType(ts, TSROSW)); 190 PetscCall(TSSetIFunction(ts, NULL, (TSIFunction)IFunction, &ctx)); 191 PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobian)IJacobian, &ctx)); 192 193 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 194 Set initial conditions 195 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 196 PetscCall(TSSetSolution(ts, U)); 197 198 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 199 Set solver options 200 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 201 PetscCall(TSSetMaxTime(ts, 35.0)); 202 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 203 PetscCall(TSSetTimeStep(ts, .01)); 204 PetscCall(TSSetFromOptions(ts)); 205 /* PetscCall(TSSetPostStep(ts,PostStep)); */ 206 207 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 208 Solve nonlinear system 209 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 210 if (ensemble) { 211 for (du[1] = -2.5; du[1] <= .01; du[1] += .1) { 212 PetscCall(VecGetArray(U, &u)); 213 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); 214 u[1] = ctx.omega_s; 215 u[0] += du[0]; 216 u[1] += du[1]; 217 PetscCall(VecRestoreArray(U, &u)); 218 PetscCall(TSSetTimeStep(ts, .01)); 219 PetscCall(TSSolve(ts, U)); 220 } 221 } else { 222 PetscCall(TSSolve(ts, U)); 223 } 224 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 225 Free work space. All PETSc objects should be destroyed when they are no longer needed. 226 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 227 PetscCall(MatDestroy(&A)); 228 PetscCall(VecDestroy(&U)); 229 PetscCall(TSDestroy(&ts)); 230 PetscCall(PetscFinalize()); 231 return 0; 232 } 233 234 /*TEST 235 236 build: 237 requires: !complex 238 239 test: 240 args: -nox -ts_dt 10 241 242 TEST*/ 243