1 static char help[] = "Basic equation for generator stability analysis.\n";
2
3 /*F
4
5 \begin{eqnarray}
6 \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - \frac{EV}{X} \sin(\theta) -D(\omega - \omega_s)\\
7 \frac{d \theta}{dt} = \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_s, Pmax, Pm, E, V, X;
35 PetscReal tf, tcl;
36 } AppCtx;
37
38 /*
39 Defines the ODE passed to the ODE solver
40 */
IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx * ctx)41 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, AppCtx *ctx)
42 {
43 PetscScalar *f, Pmax;
44 const PetscScalar *u, *udot;
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(VecGetArrayRead(Udot, &udot));
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 if (t >= ctx->tcl) Pmax = ctx->E / 0.745;
53 else Pmax = ctx->Pmax;
54 f[0] = udot[0] - ctx->omega_s * (u[1] - 1.0);
55 f[1] = 2.0 * ctx->H * udot[1] + Pmax * PetscSinScalar(u[0]) + ctx->D * (u[1] - 1.0) - ctx->Pm;
56
57 PetscCall(VecRestoreArrayRead(U, &u));
58 PetscCall(VecRestoreArrayRead(Udot, &udot));
59 PetscCall(VecRestoreArray(F, &f));
60 PetscFunctionReturn(PETSC_SUCCESS);
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 */
IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx * ctx)66 static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, AppCtx *ctx)
67 {
68 PetscInt rowcol[] = {0, 1};
69 PetscScalar J[2][2], Pmax;
70 const PetscScalar *u, *udot;
71
72 PetscFunctionBegin;
73 PetscCall(VecGetArrayRead(U, &u));
74 PetscCall(VecGetArrayRead(Udot, &udot));
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 if (t >= ctx->tcl) Pmax = ctx->E / 0.745;
77 else Pmax = ctx->Pmax;
78
79 J[0][0] = a;
80 J[0][1] = -ctx->omega_s;
81 J[1][1] = 2.0 * ctx->H * a + ctx->D;
82 J[1][0] = Pmax * PetscCosScalar(u[0]);
83
84 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
85 PetscCall(VecRestoreArrayRead(U, &u));
86 PetscCall(VecRestoreArrayRead(Udot, &udot));
87
88 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
89 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
90 if (A != B) {
91 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
92 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
93 }
94 PetscFunctionReturn(PETSC_SUCCESS);
95 }
96
PostStep(TS ts)97 PetscErrorCode PostStep(TS ts)
98 {
99 Vec X;
100 PetscReal t;
101
102 PetscFunctionBegin;
103 PetscCall(TSGetTime(ts, &t));
104 if (t >= .2) {
105 PetscCall(TSGetSolution(ts, &X));
106 PetscCall(VecView(X, PETSC_VIEWER_STDOUT_WORLD));
107 exit(0);
108 /* results in initial conditions after fault of -u 0.496792,1.00932 */
109 }
110 PetscFunctionReturn(PETSC_SUCCESS);
111 }
112
main(int argc,char ** argv)113 int main(int argc, char **argv)
114 {
115 TS ts; /* ODE integrator */
116 Vec U; /* solution will be stored here */
117 Mat A; /* Jacobian matrix */
118 PetscMPIInt size;
119 PetscInt n = 2;
120 AppCtx ctx;
121 PetscScalar *u;
122 PetscReal du[2] = {0.0, 0.0};
123 PetscBool ensemble = PETSC_FALSE, flg1, flg2;
124
125 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
126 Initialize program
127 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
128 PetscFunctionBeginUser;
129 PetscCall(PetscInitialize(&argc, &argv, NULL, help));
130 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
131 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");
132
133 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134 Create necessary matrix and vectors
135 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
136 PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
137 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
138 PetscCall(MatSetType(A, MATDENSE));
139 PetscCall(MatSetFromOptions(A));
140 PetscCall(MatSetUp(A));
141
142 PetscCall(MatCreateVecs(A, &U, NULL));
143
144 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145 Set runtime options
146 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", "");
148 {
149 ctx.omega_s = 2.0 * PETSC_PI * 60.0;
150 ctx.H = 5.0;
151 PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL));
152 ctx.D = 5.0;
153 PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL));
154 ctx.E = 1.1378;
155 ctx.V = 1.0;
156 ctx.X = 0.545;
157 ctx.Pmax = ctx.E * ctx.V / ctx.X;
158 PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL));
159 ctx.Pm = 0.9;
160 PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL));
161 ctx.tf = 1.0;
162 ctx.tcl = 1.05;
163 PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL));
164 PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL));
165 PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL));
166 if (ensemble) {
167 ctx.tf = -1;
168 ctx.tcl = -1;
169 }
170
171 PetscCall(VecGetArray(U, &u));
172 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
173 u[1] = 1.0;
174 PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1));
175 n = 2;
176 PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2));
177 u[0] += du[0];
178 u[1] += du[1];
179 PetscCall(VecRestoreArray(U, &u));
180 if (flg1 || flg2) {
181 ctx.tf = -1;
182 ctx.tcl = -1;
183 }
184 }
185 PetscOptionsEnd();
186
187 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
188 Create timestepping solver context
189 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
190 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
191 PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
192 PetscCall(TSSetType(ts, TSROSW));
193 PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, &ctx));
194 PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, &ctx));
195
196 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
197 Set initial conditions
198 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
199 PetscCall(TSSetSolution(ts, U));
200
201 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
202 Set solver options
203 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
204 PetscCall(TSSetMaxTime(ts, 35.0));
205 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
206 PetscCall(TSSetTimeStep(ts, .01));
207 PetscCall(TSSetFromOptions(ts));
208 /* PetscCall(TSSetPostStep(ts,PostStep)); */
209
210 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
211 Solve nonlinear system
212 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
213 if (ensemble) {
214 for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
215 PetscCall(VecGetArray(U, &u));
216 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
217 u[1] = ctx.omega_s;
218 u[0] += du[0];
219 u[1] += du[1];
220 PetscCall(VecRestoreArray(U, &u));
221 PetscCall(TSSetTimeStep(ts, .01));
222 PetscCall(TSSolve(ts, U));
223 }
224 } else {
225 PetscCall(TSSolve(ts, U));
226 }
227 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
228 Free work space. All PETSc objects should be destroyed when they are no longer needed.
229 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
230 PetscCall(MatDestroy(&A));
231 PetscCall(VecDestroy(&U));
232 PetscCall(TSDestroy(&ts));
233 PetscCall(PetscFinalize());
234 return 0;
235 }
236
237 /*TEST
238
239 build:
240 requires: !complex
241
242 test:
243 args: -nox -ts_time_step 10
244 output_file: output/empty.out
245
246 TEST*/
247