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(0); 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; J[0][1] = -ctx->omega_s; 81 J[1][1] = 2.0*ctx->H*a + ctx->D; 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 { 98 Vec X; 99 PetscReal t; 100 101 PetscFunctionBegin; 102 PetscCall(TSGetTime(ts,&t)); 103 if (t >= .2) { 104 PetscCall(TSGetSolution(ts,&X)); 105 PetscCall(VecView(X,PETSC_VIEWER_STDOUT_WORLD)); 106 exit(0); 107 /* results in initial conditions after fault of -u 0.496792,1.00932 */ 108 } 109 PetscFunctionReturn(0); 110 } 111 112 int main(int argc,char **argv) 113 { 114 TS ts; /* ODE integrator */ 115 Vec U; /* solution will be stored here */ 116 Mat A; /* Jacobian matrix */ 117 PetscMPIInt size; 118 PetscInt n = 2; 119 AppCtx ctx; 120 PetscScalar *u; 121 PetscReal du[2] = {0.0,0.0}; 122 PetscBool ensemble = PETSC_FALSE,flg1,flg2; 123 124 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 125 Initialize program 126 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 127 PetscCall(PetscInitialize(&argc,&argv,(char*)0,help)); 128 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); 129 PetscCheck(size == 1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"Only for sequential runs"); 130 131 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 132 Create necessary matrix and vectors 133 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 134 PetscCall(MatCreate(PETSC_COMM_WORLD,&A)); 135 PetscCall(MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE)); 136 PetscCall(MatSetType(A,MATDENSE)); 137 PetscCall(MatSetFromOptions(A)); 138 PetscCall(MatSetUp(A)); 139 140 PetscCall(MatCreateVecs(A,&U,NULL)); 141 142 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 143 Set runtime options 144 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 145 PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options",""); 146 { 147 ctx.omega_s = 2.0*PETSC_PI*60.0; 148 ctx.H = 5.0; 149 PetscCall(PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL)); 150 ctx.D = 5.0; 151 PetscCall(PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL)); 152 ctx.E = 1.1378; 153 ctx.V = 1.0; 154 ctx.X = 0.545; 155 ctx.Pmax = ctx.E*ctx.V/ctx.X; 156 PetscCall(PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL)); 157 ctx.Pm = 0.9; 158 PetscCall(PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL)); 159 ctx.tf = 1.0; 160 ctx.tcl = 1.05; 161 PetscCall(PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL)); 162 PetscCall(PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL)); 163 PetscCall(PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL)); 164 if (ensemble) { 165 ctx.tf = -1; 166 ctx.tcl = -1; 167 } 168 169 PetscCall(VecGetArray(U,&u)); 170 u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax); 171 u[1] = 1.0; 172 PetscCall(PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1)); 173 n = 2; 174 PetscCall(PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2)); 175 u[0] += du[0]; 176 u[1] += du[1]; 177 PetscCall(VecRestoreArray(U,&u)); 178 if (flg1 || flg2) { 179 ctx.tf = -1; 180 ctx.tcl = -1; 181 } 182 } 183 PetscOptionsEnd(); 184 185 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 186 Create timestepping solver context 187 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 188 PetscCall(TSCreate(PETSC_COMM_WORLD,&ts)); 189 PetscCall(TSSetProblemType(ts,TS_NONLINEAR)); 190 PetscCall(TSSetType(ts,TSROSW)); 191 PetscCall(TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx)); 192 PetscCall(TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx)); 193 194 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 195 Set initial conditions 196 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 197 PetscCall(TSSetSolution(ts,U)); 198 199 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 200 Set solver options 201 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 202 PetscCall(TSSetMaxTime(ts,35.0)); 203 PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP)); 204 PetscCall(TSSetTimeStep(ts,.01)); 205 PetscCall(TSSetFromOptions(ts)); 206 /* PetscCall(TSSetPostStep(ts,PostStep)); */ 207 208 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 209 Solve nonlinear system 210 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 211 if (ensemble) { 212 for (du[1] = -2.5; du[1] <= .01; du[1] += .1) { 213 PetscCall(VecGetArray(U,&u)); 214 u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax); 215 u[1] = ctx.omega_s; 216 u[0] += du[0]; 217 u[1] += du[1]; 218 PetscCall(VecRestoreArray(U,&u)); 219 PetscCall(TSSetTimeStep(ts,.01)); 220 PetscCall(TSSolve(ts,U)); 221 } 222 } else { 223 PetscCall(TSSolve(ts,U)); 224 } 225 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 226 Free work space. All PETSc objects should be destroyed when they are no longer needed. 227 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 228 PetscCall(MatDestroy(&A)); 229 PetscCall(VecDestroy(&U)); 230 PetscCall(TSDestroy(&ts)); 231 PetscCall(PetscFinalize()); 232 return 0; 233 } 234 235 /*TEST 236 237 build: 238 requires: !complex 239 240 test: 241 args: -nox -ts_dt 10 242 243 TEST*/ 244