1 2 static char help[] = "Basic equation for generator stability analysis.\n"; 3 4 /*F 5 6 \begin{eqnarray} 7 \frac{d \theta}{dt} = \omega_b (\omega - \omega_s) 8 \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - P_max \sin(\theta) -D(\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_b, 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 RHSFunction(TS ts, PetscReal t, Vec U, Vec F, AppCtx *ctx) 43 { 44 const PetscScalar *u; 45 PetscScalar *f, Pmax; 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(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 Pmax = ctx->Pmax; 53 54 f[0] = ctx->omega_b * (u[1] - ctx->omega_s); 55 f[1] = (-Pmax * PetscSinScalar(u[0]) - ctx->D * (u[1] - ctx->omega_s) + ctx->Pm) * ctx->omega_s / (2.0 * ctx->H); 56 57 PetscCall(VecRestoreArrayRead(U, &u)); 58 PetscCall(VecRestoreArray(F, &f)); 59 PetscFunctionReturn(PETSC_SUCCESS); 60 } 61 62 /* 63 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 64 */ 65 static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat A, Mat B, AppCtx *ctx) 66 { 67 PetscInt rowcol[] = {0, 1}; 68 PetscScalar J[2][2], Pmax; 69 const PetscScalar *u; 70 71 PetscFunctionBegin; 72 PetscCall(VecGetArrayRead(U, &u)); 73 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 */ 74 else Pmax = ctx->Pmax; 75 76 J[0][0] = 0; 77 J[0][1] = ctx->omega_b; 78 J[1][1] = -ctx->D * ctx->omega_s / (2.0 * ctx->H); 79 J[1][0] = -Pmax * PetscCosScalar(u[0]) * ctx->omega_s / (2.0 * ctx->H); 80 81 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 82 PetscCall(VecRestoreArrayRead(U, &u)); 83 84 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 85 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 86 if (A != B) { 87 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 88 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 89 } 90 PetscFunctionReturn(PETSC_SUCCESS); 91 } 92 93 int main(int argc, char **argv) 94 { 95 TS ts; /* ODE integrator */ 96 Vec U; /* solution will be stored here */ 97 Mat A; /* Jacobian matrix */ 98 PetscMPIInt size; 99 PetscInt n = 2; 100 AppCtx ctx; 101 PetscScalar *u; 102 PetscReal du[2] = {0.0, 0.0}; 103 PetscBool ensemble = PETSC_FALSE, flg1, flg2; 104 105 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 106 Initialize program 107 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 108 PetscFunctionBeginUser; 109 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 110 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 111 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 112 113 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 114 Create necessary matrix and vectors 115 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 116 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 117 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 118 PetscCall(MatSetType(A, MATDENSE)); 119 PetscCall(MatSetFromOptions(A)); 120 PetscCall(MatSetUp(A)); 121 122 PetscCall(MatCreateVecs(A, &U, NULL)); 123 124 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 125 Set runtime options 126 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 127 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", ""); 128 { 129 ctx.omega_b = 1.0; 130 ctx.omega_s = 2.0 * PETSC_PI * 60.0; 131 ctx.H = 5.0; 132 PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL)); 133 ctx.D = 5.0; 134 PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL)); 135 ctx.E = 1.1378; 136 ctx.V = 1.0; 137 ctx.X = 0.545; 138 ctx.Pmax = ctx.E * ctx.V / ctx.X; 139 PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL)); 140 ctx.Pm = 0.9; 141 PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL)); 142 ctx.tf = 1.0; 143 ctx.tcl = 1.05; 144 PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL)); 145 PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL)); 146 PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL)); 147 if (ensemble) { 148 ctx.tf = -1; 149 ctx.tcl = -1; 150 } 151 152 PetscCall(VecGetArray(U, &u)); 153 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); 154 u[1] = 1.0; 155 PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1)); 156 n = 2; 157 PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2)); 158 u[0] += du[0]; 159 u[1] += du[1]; 160 PetscCall(VecRestoreArray(U, &u)); 161 if (flg1 || flg2) { 162 ctx.tf = -1; 163 ctx.tcl = -1; 164 } 165 } 166 PetscOptionsEnd(); 167 168 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 169 Create timestepping solver context 170 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 171 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 172 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 173 PetscCall(TSSetType(ts, TSTHETA)); 174 PetscCall(TSSetRHSFunction(ts, NULL, (TSRHSFunction)RHSFunction, &ctx)); 175 PetscCall(TSSetRHSJacobian(ts, A, A, (TSRHSJacobian)RHSJacobian, &ctx)); 176 177 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 178 Set initial conditions 179 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 180 PetscCall(TSSetSolution(ts, U)); 181 182 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 183 Set solver options 184 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 185 PetscCall(TSSetMaxTime(ts, 35.0)); 186 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 187 PetscCall(TSSetTimeStep(ts, .01)); 188 PetscCall(TSSetFromOptions(ts)); 189 190 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 191 Solve nonlinear system 192 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 193 if (ensemble) { 194 for (du[1] = -2.5; du[1] <= .01; du[1] += .1) { 195 PetscCall(VecGetArray(U, &u)); 196 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); 197 u[1] = ctx.omega_s; 198 u[0] += du[0]; 199 u[1] += du[1]; 200 PetscCall(VecRestoreArray(U, &u)); 201 PetscCall(TSSetTimeStep(ts, .01)); 202 PetscCall(TSSolve(ts, U)); 203 } 204 } else { 205 PetscCall(TSSolve(ts, U)); 206 } 207 PetscCall(VecView(U, PETSC_VIEWER_STDOUT_WORLD)); 208 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 209 Free work space. All PETSc objects should be destroyed when they are no longer needed. 210 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 211 PetscCall(MatDestroy(&A)); 212 PetscCall(VecDestroy(&U)); 213 PetscCall(TSDestroy(&ts)); 214 PetscCall(PetscFinalize()); 215 return 0; 216 } 217 218 /*TEST 219 220 build: 221 requires: !complex 222 223 test: 224 225 TEST*/ 226