1 static char help[] = "Basic equation for generator stability analysis.\n"; 2 3 /*F 4 5 \begin{eqnarray} 6 \frac{d \theta}{dt} = \omega_b (\omega - \omega_s) 7 \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - P_max \sin(\theta) -D(\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_b, 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 RHSFunction(TS ts, PetscReal t, Vec U, Vec F, AppCtx *ctx) 42 { 43 const PetscScalar *u; 44 PetscScalar *f, Pmax; 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(VecGetArray(F, &f)); 50 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 */ 51 else Pmax = ctx->Pmax; 52 53 f[0] = ctx->omega_b * (u[1] - ctx->omega_s); 54 f[1] = (-Pmax * PetscSinScalar(u[0]) - ctx->D * (u[1] - ctx->omega_s) + ctx->Pm) * ctx->omega_s / (2.0 * ctx->H); 55 56 PetscCall(VecRestoreArrayRead(U, &u)); 57 PetscCall(VecRestoreArray(F, &f)); 58 PetscFunctionReturn(PETSC_SUCCESS); 59 } 60 61 /* 62 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 63 */ 64 static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat A, Mat B, AppCtx *ctx) 65 { 66 PetscInt rowcol[] = {0, 1}; 67 PetscScalar J[2][2], Pmax; 68 const PetscScalar *u; 69 70 PetscFunctionBegin; 71 PetscCall(VecGetArrayRead(U, &u)); 72 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 */ 73 else Pmax = ctx->Pmax; 74 75 J[0][0] = 0; 76 J[0][1] = ctx->omega_b; 77 J[1][1] = -ctx->D * ctx->omega_s / (2.0 * ctx->H); 78 J[1][0] = -Pmax * PetscCosScalar(u[0]) * ctx->omega_s / (2.0 * ctx->H); 79 80 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 81 PetscCall(VecRestoreArrayRead(U, &u)); 82 83 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 84 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 85 if (A != B) { 86 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 87 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 88 } 89 PetscFunctionReturn(PETSC_SUCCESS); 90 } 91 92 int main(int argc, char **argv) 93 { 94 TS ts; /* ODE integrator */ 95 Vec U; /* solution will be stored here */ 96 Mat A; /* Jacobian matrix */ 97 PetscMPIInt size; 98 PetscInt n = 2; 99 AppCtx ctx; 100 PetscScalar *u; 101 PetscReal du[2] = {0.0, 0.0}; 102 PetscBool ensemble = PETSC_FALSE, flg1, flg2; 103 104 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 105 Initialize program 106 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 107 PetscFunctionBeginUser; 108 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 109 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 110 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 111 112 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 113 Create necessary matrix and vectors 114 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 115 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 116 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 117 PetscCall(MatSetType(A, MATDENSE)); 118 PetscCall(MatSetFromOptions(A)); 119 PetscCall(MatSetUp(A)); 120 121 PetscCall(MatCreateVecs(A, &U, NULL)); 122 123 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 124 Set runtime options 125 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 126 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", ""); 127 { 128 ctx.omega_b = 1.0; 129 ctx.omega_s = 2.0 * PETSC_PI * 60.0; 130 ctx.H = 5.0; 131 PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL)); 132 ctx.D = 5.0; 133 PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL)); 134 ctx.E = 1.1378; 135 ctx.V = 1.0; 136 ctx.X = 0.545; 137 ctx.Pmax = ctx.E * ctx.V / ctx.X; 138 PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL)); 139 ctx.Pm = 0.9; 140 PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL)); 141 ctx.tf = 1.0; 142 ctx.tcl = 1.05; 143 PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL)); 144 PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL)); 145 PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL)); 146 if (ensemble) { 147 ctx.tf = -1; 148 ctx.tcl = -1; 149 } 150 151 PetscCall(VecGetArray(U, &u)); 152 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); 153 u[1] = 1.0; 154 PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1)); 155 n = 2; 156 PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2)); 157 u[0] += du[0]; 158 u[1] += du[1]; 159 PetscCall(VecRestoreArray(U, &u)); 160 if (flg1 || flg2) { 161 ctx.tf = -1; 162 ctx.tcl = -1; 163 } 164 } 165 PetscOptionsEnd(); 166 167 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 168 Create timestepping solver context 169 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 170 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 171 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 172 PetscCall(TSSetType(ts, TSTHETA)); 173 PetscCall(TSSetRHSFunction(ts, NULL, (TSRHSFunctionFn *)RHSFunction, &ctx)); 174 PetscCall(TSSetRHSJacobian(ts, A, A, (TSRHSJacobianFn *)RHSJacobian, &ctx)); 175 176 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 177 Set initial conditions 178 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 179 PetscCall(TSSetSolution(ts, U)); 180 181 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 182 Set solver options 183 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 184 PetscCall(TSSetMaxTime(ts, 35.0)); 185 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 186 PetscCall(TSSetTimeStep(ts, .01)); 187 PetscCall(TSSetFromOptions(ts)); 188 189 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 190 Solve nonlinear system 191 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 192 if (ensemble) { 193 for (du[1] = -2.5; du[1] <= .01; du[1] += .1) { 194 PetscCall(VecGetArray(U, &u)); 195 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); 196 u[1] = ctx.omega_s; 197 u[0] += du[0]; 198 u[1] += du[1]; 199 PetscCall(VecRestoreArray(U, &u)); 200 PetscCall(TSSetTimeStep(ts, .01)); 201 PetscCall(TSSolve(ts, U)); 202 } 203 } else { 204 PetscCall(TSSolve(ts, U)); 205 } 206 PetscCall(VecView(U, PETSC_VIEWER_STDOUT_WORLD)); 207 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 208 Free work space. All PETSc objects should be destroyed when they are no longer needed. 209 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 210 PetscCall(MatDestroy(&A)); 211 PetscCall(VecDestroy(&U)); 212 PetscCall(TSDestroy(&ts)); 213 PetscCall(PetscFinalize()); 214 return 0; 215 } 216 217 /*TEST 218 219 build: 220 requires: !complex 221 222 test: 223 224 TEST*/ 225