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 PetscErrorCode ierr; 45 PetscScalar *f,Pmax; 46 const PetscScalar *u,*udot; 47 48 PetscFunctionBegin; 49 /* The next three lines allow us to access the entries of the vectors directly */ 50 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); 51 ierr = VecGetArrayRead(Udot,&udot);CHKERRQ(ierr); 52 ierr = VecGetArray(F,&f);CHKERRQ(ierr); 53 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 */ 54 else if (t >= ctx->tcl) Pmax = ctx->E/0.745; 55 else Pmax = ctx->Pmax; 56 f[0] = udot[0] - ctx->omega_s*(u[1] - 1.0); 57 f[1] = 2.0*ctx->H*udot[1] + Pmax*PetscSinScalar(u[0]) + ctx->D*(u[1] - 1.0)- ctx->Pm; 58 59 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 60 ierr = VecRestoreArrayRead(Udot,&udot);CHKERRQ(ierr); 61 ierr = VecRestoreArray(F,&f);CHKERRQ(ierr); 62 PetscFunctionReturn(0); 63 } 64 65 /* 66 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 67 */ 68 static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx) 69 { 70 PetscErrorCode ierr; 71 PetscInt rowcol[] = {0,1}; 72 PetscScalar J[2][2],Pmax; 73 const PetscScalar *u,*udot; 74 75 PetscFunctionBegin; 76 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); 77 ierr = VecGetArrayRead(Udot,&udot);CHKERRQ(ierr); 78 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 */ 79 else if (t >= ctx->tcl) Pmax = ctx->E/0.745; 80 else Pmax = ctx->Pmax; 81 82 J[0][0] = a; J[0][1] = -ctx->omega_s; 83 J[1][1] = 2.0*ctx->H*a + ctx->D; J[1][0] = Pmax*PetscCosScalar(u[0]); 84 85 ierr = MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr); 86 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 87 ierr = VecRestoreArrayRead(Udot,&udot);CHKERRQ(ierr); 88 89 ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 90 ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 91 if (A != B) { 92 ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 93 ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 94 } 95 PetscFunctionReturn(0); 96 } 97 98 PetscErrorCode PostStep(TS ts) 99 { 100 PetscErrorCode ierr; 101 Vec X; 102 PetscReal t; 103 104 PetscFunctionBegin; 105 ierr = TSGetTime(ts,&t);CHKERRQ(ierr); 106 if (t >= .2) { 107 ierr = TSGetSolution(ts,&X);CHKERRQ(ierr); 108 ierr = VecView(X,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); 109 exit(0); 110 /* results in initial conditions after fault of -u 0.496792,1.00932 */ 111 } 112 PetscFunctionReturn(0); 113 } 114 115 int main(int argc,char **argv) 116 { 117 TS ts; /* ODE integrator */ 118 Vec U; /* solution will be stored here */ 119 Mat A; /* Jacobian matrix */ 120 PetscErrorCode ierr; 121 PetscMPIInt size; 122 PetscInt n = 2; 123 AppCtx ctx; 124 PetscScalar *u; 125 PetscReal du[2] = {0.0,0.0}; 126 PetscBool ensemble = PETSC_FALSE,flg1,flg2; 127 128 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 129 Initialize program 130 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 131 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 132 ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRMPI(ierr); 133 if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs"); 134 135 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 136 Create necessary matrix and vectors 137 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 138 ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); 139 ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 140 ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr); 141 ierr = MatSetFromOptions(A);CHKERRQ(ierr); 142 ierr = MatSetUp(A);CHKERRQ(ierr); 143 144 ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr); 145 146 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 147 Set runtime options 148 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 149 ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");CHKERRQ(ierr); 150 { 151 ctx.omega_s = 2.0*PETSC_PI*60.0; 152 ctx.H = 5.0; 153 ierr = PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);CHKERRQ(ierr); 154 ctx.D = 5.0; 155 ierr = PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);CHKERRQ(ierr); 156 ctx.E = 1.1378; 157 ctx.V = 1.0; 158 ctx.X = 0.545; 159 ctx.Pmax = ctx.E*ctx.V/ctx.X; 160 ierr = PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);CHKERRQ(ierr); 161 ctx.Pm = 0.9; 162 ierr = PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);CHKERRQ(ierr); 163 ctx.tf = 1.0; 164 ctx.tcl = 1.05; 165 ierr = PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);CHKERRQ(ierr); 166 ierr = PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);CHKERRQ(ierr); 167 ierr = PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);CHKERRQ(ierr); 168 if (ensemble) { 169 ctx.tf = -1; 170 ctx.tcl = -1; 171 } 172 173 ierr = VecGetArray(U,&u);CHKERRQ(ierr); 174 u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax); 175 u[1] = 1.0; 176 ierr = PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);CHKERRQ(ierr); 177 n = 2; 178 ierr = PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);CHKERRQ(ierr); 179 u[0] += du[0]; 180 u[1] += du[1]; 181 ierr = VecRestoreArray(U,&u);CHKERRQ(ierr); 182 if (flg1 || flg2) { 183 ctx.tf = -1; 184 ctx.tcl = -1; 185 } 186 } 187 ierr = PetscOptionsEnd();CHKERRQ(ierr); 188 189 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 190 Create timestepping solver context 191 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 192 ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); 193 ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr); 194 ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr); 195 ierr = TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);CHKERRQ(ierr); 196 ierr = TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);CHKERRQ(ierr); 197 198 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 199 Set initial conditions 200 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 201 ierr = TSSetSolution(ts,U);CHKERRQ(ierr); 202 203 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 204 Set solver options 205 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 206 ierr = TSSetMaxTime(ts,35.0);CHKERRQ(ierr); 207 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr); 208 ierr = TSSetTimeStep(ts,.01);CHKERRQ(ierr); 209 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 210 /* ierr = TSSetPostStep(ts,PostStep);CHKERRQ(ierr); */ 211 212 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 213 Solve nonlinear system 214 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 215 if (ensemble) { 216 for (du[1] = -2.5; du[1] <= .01; du[1] += .1) { 217 ierr = VecGetArray(U,&u);CHKERRQ(ierr); 218 u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax); 219 u[1] = ctx.omega_s; 220 u[0] += du[0]; 221 u[1] += du[1]; 222 ierr = VecRestoreArray(U,&u);CHKERRQ(ierr); 223 ierr = TSSetTimeStep(ts,.01);CHKERRQ(ierr); 224 ierr = TSSolve(ts,U);CHKERRQ(ierr); 225 } 226 } else { 227 ierr = TSSolve(ts,U);CHKERRQ(ierr); 228 } 229 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 230 Free work space. All PETSc objects should be destroyed when they are no longer needed. 231 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 232 ierr = MatDestroy(&A);CHKERRQ(ierr); 233 ierr = VecDestroy(&U);CHKERRQ(ierr); 234 ierr = TSDestroy(&ts);CHKERRQ(ierr); 235 ierr = PetscFinalize(); 236 return ierr; 237 } 238 239 /*TEST 240 241 build: 242 requires: !complex 243 244 test: 245 args: -nox -ts_dt 10 246 247 TEST*/ 248