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 PetscErrorCode ierr; 45 const PetscScalar *u; 46 PetscScalar *f,Pmax; 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 = VecGetArray(F,&f);CHKERRQ(ierr); 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 Pmax = ctx->Pmax; 54 55 f[0] = ctx->omega_b*(u[1] - ctx->omega_s); 56 f[1] = (-Pmax*PetscSinScalar(u[0]) - ctx->D*(u[1] - ctx->omega_s) + ctx->Pm)*ctx->omega_s/(2.0*ctx->H); 57 58 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 59 ierr = VecRestoreArray(F,&f);CHKERRQ(ierr); 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 RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,AppCtx *ctx) 67 { 68 PetscErrorCode ierr; 69 PetscInt rowcol[] = {0,1}; 70 PetscScalar J[2][2],Pmax; 71 const PetscScalar *u; 72 73 PetscFunctionBegin; 74 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); 75 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 */ 76 else Pmax = ctx->Pmax; 77 78 J[0][0] = 0; J[0][1] = ctx->omega_b; 79 J[1][1] = -ctx->D*ctx->omega_s/(2.0*ctx->H); J[1][0] = -Pmax*PetscCosScalar(u[0])*ctx->omega_s/(2.0*ctx->H); 80 81 ierr = MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr); 82 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 83 84 ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 85 ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 86 if (A != B) { 87 ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 88 ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 89 } 90 PetscFunctionReturn(0); 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 PetscErrorCode ierr; 99 PetscMPIInt size; 100 PetscInt n = 2; 101 AppCtx ctx; 102 PetscScalar *u; 103 PetscReal du[2] = {0.0,0.0}; 104 PetscBool ensemble = PETSC_FALSE,flg1,flg2; 105 106 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 107 Initialize program 108 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 109 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 110 ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRMPI(ierr); 111 if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs"); 112 113 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 114 Create necessary matrix and vectors 115 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 116 ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); 117 ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 118 ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr); 119 ierr = MatSetFromOptions(A);CHKERRQ(ierr); 120 ierr = MatSetUp(A);CHKERRQ(ierr); 121 122 ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr); 123 124 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 125 Set runtime options 126 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 127 ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");CHKERRQ(ierr); 128 { 129 ctx.omega_b = 1.0; 130 ctx.omega_s = 2.0*PETSC_PI*60.0; 131 ctx.H = 5.0; 132 ierr = PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);CHKERRQ(ierr); 133 ctx.D = 5.0; 134 ierr = PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);CHKERRQ(ierr); 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 ierr = PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);CHKERRQ(ierr); 140 ctx.Pm = 0.9; 141 ierr = PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);CHKERRQ(ierr); 142 ctx.tf = 1.0; 143 ctx.tcl = 1.05; 144 ierr = PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);CHKERRQ(ierr); 145 ierr = PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);CHKERRQ(ierr); 146 ierr = PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);CHKERRQ(ierr); 147 if (ensemble) { 148 ctx.tf = -1; 149 ctx.tcl = -1; 150 } 151 152 ierr = VecGetArray(U,&u);CHKERRQ(ierr); 153 u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax); 154 u[1] = 1.0; 155 ierr = PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);CHKERRQ(ierr); 156 n = 2; 157 ierr = PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);CHKERRQ(ierr); 158 u[0] += du[0]; 159 u[1] += du[1]; 160 ierr = VecRestoreArray(U,&u);CHKERRQ(ierr); 161 if (flg1 || flg2) { 162 ctx.tf = -1; 163 ctx.tcl = -1; 164 } 165 } 166 ierr = PetscOptionsEnd();CHKERRQ(ierr); 167 168 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 169 Create timestepping solver context 170 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 171 ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); 172 ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr); 173 ierr = TSSetType(ts,TSTHETA);CHKERRQ(ierr); 174 ierr = TSSetRHSFunction(ts,NULL,(TSRHSFunction)RHSFunction,&ctx);CHKERRQ(ierr); 175 ierr = TSSetRHSJacobian(ts,A,A,(TSRHSJacobian)RHSJacobian,&ctx);CHKERRQ(ierr); 176 177 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 178 Set initial conditions 179 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 180 ierr = TSSetSolution(ts,U);CHKERRQ(ierr); 181 182 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 183 Set solver options 184 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 185 ierr = TSSetMaxTime(ts,35.0);CHKERRQ(ierr); 186 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr); 187 ierr = TSSetTimeStep(ts,.01);CHKERRQ(ierr); 188 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 189 190 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 191 Solve nonlinear system 192 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 193 if (ensemble) { 194 for (du[1] = -2.5; du[1] <= .01; du[1] += .1) { 195 ierr = VecGetArray(U,&u);CHKERRQ(ierr); 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 ierr = VecRestoreArray(U,&u);CHKERRQ(ierr); 201 ierr = TSSetTimeStep(ts,.01);CHKERRQ(ierr); 202 ierr = TSSolve(ts,U);CHKERRQ(ierr); 203 } 204 } else { 205 ierr = TSSolve(ts,U);CHKERRQ(ierr); 206 } 207 ierr = VecView(U,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); 208 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 209 Free work space. All PETSc objects should be destroyed when they are no longer needed. 210 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 211 ierr = MatDestroy(&A);CHKERRQ(ierr); 212 ierr = VecDestroy(&U);CHKERRQ(ierr); 213 ierr = TSDestroy(&ts);CHKERRQ(ierr); 214 ierr = PetscFinalize(); 215 return ierr; 216 } 217 218 /*TEST 219 220 build: 221 requires: !complex 222 223 test: 224 225 TEST*/ 226