1 static char help[] = "Basic equation for generator stability analysis.\n";
2
3 /*F
4
5 \begin{eqnarray}
6 \frac{d \theta}{dt} = \omega_b (\omega - \omega_s)
7 \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - P_max \sin(\theta) -D(\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_b, 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 */
RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx * ctx)41 static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec U, Vec F, AppCtx *ctx)
42 {
43 const PetscScalar *u;
44 PetscScalar *f, Pmax;
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(VecGetArray(F, &f));
50 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 */
51 else Pmax = ctx->Pmax;
52
53 f[0] = ctx->omega_b * (u[1] - ctx->omega_s);
54 f[1] = (-Pmax * PetscSinScalar(u[0]) - ctx->D * (u[1] - ctx->omega_s) + ctx->Pm) * ctx->omega_s / (2.0 * ctx->H);
55
56 PetscCall(VecRestoreArrayRead(U, &u));
57 PetscCall(VecRestoreArray(F, &f));
58 PetscFunctionReturn(PETSC_SUCCESS);
59 }
60
61 /*
62 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
63 */
RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,AppCtx * ctx)64 static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat A, Mat B, AppCtx *ctx)
65 {
66 PetscInt rowcol[] = {0, 1};
67 PetscScalar J[2][2], Pmax;
68 const PetscScalar *u;
69
70 PetscFunctionBegin;
71 PetscCall(VecGetArrayRead(U, &u));
72 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 */
73 else Pmax = ctx->Pmax;
74
75 J[0][0] = 0;
76 J[0][1] = ctx->omega_b;
77 J[1][1] = -ctx->D * ctx->omega_s / (2.0 * ctx->H);
78 J[1][0] = -Pmax * PetscCosScalar(u[0]) * ctx->omega_s / (2.0 * ctx->H);
79
80 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
81 PetscCall(VecRestoreArrayRead(U, &u));
82
83 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
84 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
85 if (A != B) {
86 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
87 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
88 }
89 PetscFunctionReturn(PETSC_SUCCESS);
90 }
91
main(int argc,char ** argv)92 int main(int argc, char **argv)
93 {
94 TS ts; /* ODE integrator */
95 Vec U; /* solution will be stored here */
96 Mat A; /* Jacobian matrix */
97 PetscMPIInt size;
98 PetscInt n = 2;
99 AppCtx ctx;
100 PetscScalar *u;
101 PetscReal du[2] = {0.0, 0.0};
102 PetscBool ensemble = PETSC_FALSE, flg1, flg2;
103
104 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
105 Initialize program
106 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
107 PetscFunctionBeginUser;
108 PetscCall(PetscInitialize(&argc, &argv, NULL, help));
109 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
110 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");
111
112 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
113 Create necessary matrix and vectors
114 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
115 PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
116 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
117 PetscCall(MatSetType(A, MATDENSE));
118 PetscCall(MatSetFromOptions(A));
119 PetscCall(MatSetUp(A));
120
121 PetscCall(MatCreateVecs(A, &U, NULL));
122
123 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
124 Set runtime options
125 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
126 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", "");
127 {
128 ctx.omega_b = 1.0;
129 ctx.omega_s = 2.0 * PETSC_PI * 60.0;
130 ctx.H = 5.0;
131 PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL));
132 ctx.D = 5.0;
133 PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL));
134 ctx.E = 1.1378;
135 ctx.V = 1.0;
136 ctx.X = 0.545;
137 ctx.Pmax = ctx.E * ctx.V / ctx.X;
138 PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL));
139 ctx.Pm = 0.9;
140 PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL));
141 ctx.tf = 1.0;
142 ctx.tcl = 1.05;
143 PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL));
144 PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL));
145 PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL));
146 if (ensemble) {
147 ctx.tf = -1;
148 ctx.tcl = -1;
149 }
150
151 PetscCall(VecGetArray(U, &u));
152 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
153 u[1] = 1.0;
154 PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1));
155 n = 2;
156 PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2));
157 u[0] += du[0];
158 u[1] += du[1];
159 PetscCall(VecRestoreArray(U, &u));
160 if (flg1 || flg2) {
161 ctx.tf = -1;
162 ctx.tcl = -1;
163 }
164 }
165 PetscOptionsEnd();
166
167 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
168 Create timestepping solver context
169 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
170 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
171 PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
172 PetscCall(TSSetType(ts, TSTHETA));
173 PetscCall(TSSetRHSFunction(ts, NULL, (TSRHSFunctionFn *)RHSFunction, &ctx));
174 PetscCall(TSSetRHSJacobian(ts, A, A, (TSRHSJacobianFn *)RHSJacobian, &ctx));
175
176 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177 Set initial conditions
178 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
179 PetscCall(TSSetSolution(ts, U));
180
181 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
182 Set solver options
183 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
184 PetscCall(TSSetMaxTime(ts, 35.0));
185 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
186 PetscCall(TSSetTimeStep(ts, .01));
187 PetscCall(TSSetFromOptions(ts));
188
189 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190 Solve nonlinear system
191 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
192 if (ensemble) {
193 for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
194 PetscCall(VecGetArray(U, &u));
195 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
196 u[1] = ctx.omega_s;
197 u[0] += du[0];
198 u[1] += du[1];
199 PetscCall(VecRestoreArray(U, &u));
200 PetscCall(TSSetTimeStep(ts, .01));
201 PetscCall(TSSolve(ts, U));
202 }
203 } else {
204 PetscCall(TSSolve(ts, U));
205 }
206 PetscCall(VecView(U, PETSC_VIEWER_STDOUT_WORLD));
207 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
208 Free work space. All PETSc objects should be destroyed when they are no longer needed.
209 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
210 PetscCall(MatDestroy(&A));
211 PetscCall(VecDestroy(&U));
212 PetscCall(TSDestroy(&ts));
213 PetscCall(PetscFinalize());
214 return 0;
215 }
216
217 /*TEST
218
219 build:
220 requires: !complex
221
222 test:
223
224 TEST*/
225