GCC Code Coverage Report

Directory: ./
File: src/eps/tutorials/ex31.c
Date: 2026-02-22 03:58:10
Exec Total Coverage
Lines: 341 358 95.3%
Functions: 5 6 83.3%
Branches: 526 880 59.8%
Line Branch Exec Source
1 /*
2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 SLEPc - Scalable Library for Eigenvalue Problem Computations
4 Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5
6 This file is part of SLEPc.
7 SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9 */
10
11 static char help[] = "Power grid small signal stability analysis of WECC 9 bus system.\n\n\
12 This example is based on the 9-bus (node) example given in the book Power\n\
13 Systems Dynamics and Stability (Chapter 8) by P. Sauer and M. A. Pai.\n\
14 The power grid in this example consists of 9 buses (nodes), 3 generators,\n\
15 3 loads, and 9 transmission lines. The network equations are written\n\
16 in current balance form using rectangular coordinates. It uses the SLEPc\n\
17 package to calculate the eigenvalues for small signal stability analysis\n\n";
18
19 /*
20 This example is based on PETSc's ex9bus example (under TS).
21
22 The equations for the stability analysis are described by the DAE
23
24 \dot{x} = f(x,y,t)
25 0 = g(x,y,t)
26
27 where the generators are described by differential equations, while the algebraic
28 constraints define the network equations.
29
30 The generators are modeled with a 4th order differential equation describing the electrical
31 and mechanical dynamics. Each generator also has an exciter system modeled by 3rd order
32 diff. eqns. describing the exciter, voltage regulator, and the feedback stabilizer
33 mechanism.
34
35 The network equations are described by nodal current balance equations.
36 I(x,y) - Y*V = 0
37
38 where:
39 I(x,y) is the current injected from generators and loads.
40 Y is the admittance matrix, and
41 V is the voltage vector
42
43 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
44
45 The linearized equations for the eigenvalue analysis are
46
47 \dot{\delta{x}} = f_x*\delta{x} + f_y*\delta{y}
48 0 = g_x*\delta{x} + g_y*\delta{y}
49
50 This gives the linearized sensitivity matrix
51 A = | f_x f_y |
52 | g_x g_y |
53
54 We are interested in the eigenvalues of the Schur complement of A
55 \hat{A} = f_x - g_x*inv(g_y)*f_y
56
57 Example contributed by: Shrirang Abhyankar
58 */
59
60 #include <petscdm.h>
61 #include <petscdmda.h>
62 #include <petscdmcomposite.h>
63 #include <slepceps.h>
64
65 #define freq 60
66 #define w_s (2*PETSC_PI*freq)
67
68 /* Sizes and indices */
69 const PetscInt nbus = 9; /* Number of network buses */
70 const PetscInt ngen = 3; /* Number of generators */
71 const PetscInt nload = 3; /* Number of loads */
72 const PetscInt gbus[3] = {0,1,2}; /* Buses at which generators are incident */
73 const PetscInt lbus[3] = {4,5,7}; /* Buses at which loads are incident */
74
75 /* Generator real and reactive powers (found via loadflow) */
76 const PetscScalar PG[3] = {0.716786142395021,1.630000000000000,0.850000000000000};
77 const PetscScalar QG[3] = {0.270702180178785,0.066120127797275,-0.108402221791588};
78 /* Generator constants */
79 const PetscScalar H[3] = {23.64,6.4,3.01}; /* Inertia constant */
80 const PetscScalar Rs[3] = {0.0,0.0,0.0}; /* Stator Resistance */
81 const PetscScalar Xd[3] = {0.146,0.8958,1.3125}; /* d-axis reactance */
82 const PetscScalar Xdp[3] = {0.0608,0.1198,0.1813}; /* d-axis transient reactance */
83 const PetscScalar Xq[3] = {0.0969,0.8645,1.2578}; /* q-axis reactance Xq(1) set to 0.4360, value given in text 0.0969 */
84 const PetscScalar Xqp[3] = {0.0969,0.1969,0.25}; /* q-axis transient reactance */
85 const PetscScalar Td0p[3] = {8.96,6.0,5.89}; /* d-axis open circuit time constant */
86 const PetscScalar Tq0p[3] = {0.31,0.535,0.6}; /* q-axis open circuit time constant */
87 PetscScalar M[3]; /* M = 2*H/w_s */
88 PetscScalar D[3]; /* D = 0.1*M */
89
90 PetscScalar TM[3]; /* Mechanical Torque */
91 /* Exciter system constants */
92 const PetscScalar KA[3] = {20.0,20.0,20.0}; /* Voltage regulartor gain constant */
93 const PetscScalar TA[3] = {0.2,0.2,0.2}; /* Voltage regulator time constant */
94 const PetscScalar KE[3] = {1.0,1.0,1.0}; /* Exciter gain constant */
95 const PetscScalar TE[3] = {0.314,0.314,0.314}; /* Exciter time constant */
96 const PetscScalar KF[3] = {0.063,0.063,0.063}; /* Feedback stabilizer gain constant */
97 const PetscScalar TF[3] = {0.35,0.35,0.35}; /* Feedback stabilizer time constant */
98 const PetscScalar k1[3] = {0.0039,0.0039,0.0039};
99 const PetscScalar k2[3] = {1.555,1.555,1.555}; /* k1 and k2 for calculating the saturation function SE = k1*exp(k2*Efd) */
100
101 PetscScalar Vref[3];
102 /* Load constants
103 We use a composite load model that describes the load and reactive powers at each time instant as follows
104 P(t) = \sum\limits_{i=0}^ld_nsegsp \ld_alphap_i*P_D0(\frac{V_m(t)}{V_m0})^\ld_betap_i
105 Q(t) = \sum\limits_{i=0}^ld_nsegsq \ld_alphaq_i*Q_D0(\frac{V_m(t)}{V_m0})^\ld_betaq_i
106 where
107 ld_nsegsp,ld_nsegsq - Number of individual load models for real and reactive power loads
108 ld_alphap,ld_alphap - Percentage contribution (weights) or loads
109 P_D0 - Real power load
110 Q_D0 - Reactive power load
111 V_m(t) - Voltage magnitude at time t
112 V_m0 - Voltage magnitude at t = 0
113 ld_betap, ld_betaq - exponents describing the load model for real and reactive part
114
115 Note: All loads have the same characteristic currently.
116 */
117 const PetscScalar PD0[3] = {1.25,0.9,1.0};
118 const PetscScalar QD0[3] = {0.5,0.3,0.35};
119 const PetscInt ld_nsegsp[3] = {3,3,3};
120 const PetscScalar ld_alphap[3] = {0.0,0.0,1.0};
121 const PetscScalar ld_betap[3] = {2.0,1.0,0.0};
122 const PetscInt ld_nsegsq[3] = {3,3,3};
123 const PetscScalar ld_alphaq[3] = {0.0,0.0,1.0};
124 const PetscScalar ld_betaq[3] = {2.0,1.0,0.0};
125
126 typedef struct {
127 DM dmgen, dmnet; /* DMs to manage generator and network subsystem */
128 DM dmpgrid; /* Composite DM to manage the entire power grid */
129 Mat Ybus; /* Network admittance matrix */
130 Vec V0; /* Initial voltage vector (Power flow solution) */
131 PetscInt neqs_gen,neqs_net,neqs_pgrid;
132 IS is_diff; /* indices for differential equations */
133 IS is_alg; /* indices for algebraic equations */
134 } Userctx;
135
136 /* Converts from machine frame (dq) to network (phase a real,imag) reference frame */
137 ✗ PetscErrorCode dq2ri(PetscScalar Fd,PetscScalar Fq,PetscScalar delta,PetscScalar *Fr,PetscScalar *Fi)
138 {
139 ✗ PetscFunctionBegin;
140 ✗ *Fr = Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
141 ✗ *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
142 ✗ PetscFunctionReturn(PETSC_SUCCESS);
143 }
144
145 /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
146 12 PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd,PetscScalar *Fq)
147 {
148
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 12 PetscFunctionBegin;
149 12 *Fd = Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
150 12 *Fq = Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
151
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 12 PetscFunctionReturn(PETSC_SUCCESS);
152 }
153
154 4 PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
155 {
156 4 Vec Xgen,Xnet;
157 4 PetscScalar *xgen,*xnet;
158 4 PetscInt i,idx=0;
159 4 PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
160 4 PetscScalar Eqp,Edp,delta;
161 4 PetscScalar Efd,RF,VR; /* Exciter variables */
162 4 PetscScalar Id,Iq; /* Generator dq axis currents */
163 4 PetscScalar theta,Vd,Vq,SE;
164
165
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 4 PetscFunctionBegin;
166 4 M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
167 /* D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
168 */
169 4 D[0] = D[1] = D[2] = 0.0;
170
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 4 PetscCall(DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet));
171
172 /* Network subsystem initialization */
173
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 4 PetscCall(VecCopy(user->V0,Xnet));
174
175 /* Generator subsystem initialization */
176
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 4 PetscCall(VecGetArray(Xgen,&xgen));
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 4 PetscCall(VecGetArray(Xnet,&xnet));
178
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 16 for (i=0; i < ngen; i++) {
180 12 Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
181 12 Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
182 12 Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
183 12 IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
184 12 IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;
185
186 12 delta = atan2(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
187
188 12 theta = PETSC_PI/2.0 - delta;
189
190 12 Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
191 12 Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
192
193 12 Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
194 12 Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
195
196 12 Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
197 12 Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
198
199 12 TM[i] = PG[i];
200
201 /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
202 12 xgen[idx] = Eqp;
203 12 xgen[idx+1] = Edp;
204 12 xgen[idx+2] = delta;
205 12 xgen[idx+3] = w_s;
206
207 12 idx = idx + 4;
208
209 12 xgen[idx] = Id;
210 12 xgen[idx+1] = Iq;
211
212 12 idx = idx + 2;
213
214 /* Exciter */
215 12 Efd = Eqp + (Xd[i] - Xdp[i])*Id;
216 12 SE = k1[i]*PetscExpScalar(k2[i]*Efd);
217 12 VR = KE[i]*Efd + SE;
218 12 RF = KF[i]*Efd/TF[i];
219
220 12 xgen[idx] = Efd;
221 12 xgen[idx+1] = RF;
222 12 xgen[idx+2] = VR;
223
224 12 Vref[i] = Vm + (VR/KA[i]);
225
226 12 idx = idx + 3;
227 }
228
229
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 4 PetscCall(VecRestoreArray(Xgen,&xgen));
230
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 4 PetscCall(VecRestoreArray(Xnet,&xnet));
231
232 /* PetscCall(VecView(Xgen,0)); */
233
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 4 PetscCall(DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet));
234
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 4 PetscCall(DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet));
235
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 1 PetscFunctionReturn(PETSC_SUCCESS);
236 }
237
238 4 PetscErrorCode PreallocateJacobian(Mat J,Userctx *user)
239 {
240 4 PetscInt *d_nnz;
241 4 PetscInt i,idx=0,start=0;
242 4 PetscInt ncols;
243
244
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 4 PetscFunctionBegin;
245
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 4 PetscCall(PetscMalloc1(user->neqs_pgrid,&d_nnz));
246
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 184 for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
247 /* Generator subsystem */
248
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 16 for (i=0; i < ngen; i++) {
249
250 12 d_nnz[idx] += 3;
251 12 d_nnz[idx+1] += 2;
252 12 d_nnz[idx+2] += 2;
253 12 d_nnz[idx+3] += 5;
254 12 d_nnz[idx+4] += 6;
255 12 d_nnz[idx+5] += 6;
256
257 12 d_nnz[user->neqs_gen+2*gbus[i]] += 3;
258 12 d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;
259
260 12 d_nnz[idx+6] += 2;
261 12 d_nnz[idx+7] += 2;
262 12 d_nnz[idx+8] += 5;
263
264 12 idx = idx + 9;
265 }
266
267 4 start = user->neqs_gen;
268
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 40 for (i=0; i < nbus; i++) {
270
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 36 PetscCall(MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL));
271 36 d_nnz[start+2*i] += ncols;
272 36 d_nnz[start+2*i+1] += ncols;
273
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 36 PetscCall(MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL));
274 }
275
276
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 4 PetscCall(MatSeqAIJSetPreallocation(J,0,d_nnz));
277
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 4 PetscCall(PetscFree(d_nnz));
279
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 1 PetscFunctionReturn(PETSC_SUCCESS);
280 }
281
282 /*
283 J = [-df_dx, -df_dy
284 dg_dx, dg_dy]
285 */
286 4 PetscErrorCode ResidualJacobian(Vec X,Mat J,void *ctx)
287 {
288 4 Userctx *user=(Userctx*)ctx;
289 4 Vec Xgen,Xnet;
290 4 PetscScalar *xgen,*xnet;
291 4 PetscInt i,idx=0;
292 4 PetscScalar Vr,Vi,Vm,Vm2;
293 4 PetscScalar Eqp,Edp,delta; /* Generator variables */
294 4 PetscScalar Efd;
295 4 PetscScalar Id,Iq; /* Generator dq axis currents */
296 4 PetscScalar Vd,Vq;
297 4 PetscScalar val[10];
298 4 PetscInt row[2],col[10];
299 4 PetscInt net_start=user->neqs_gen;
300 4 PetscScalar Zdq_inv[4],det;
301 4 PetscScalar dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
302 4 PetscScalar dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
303 4 PetscScalar dSE_dEfd;
304 4 PetscScalar dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
305 4 PetscInt ncols;
306 4 const PetscInt *cols;
307 4 const PetscScalar *yvals;
308 4 PetscInt k;
309 4 PetscScalar PD,QD,Vm0,*v0,Vm4;
310 4 PetscScalar dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
311 4 PetscScalar dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;
312
313
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 4 PetscFunctionBegin;
314
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 4 PetscCall(MatZeroEntries(J));
315
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 4 PetscCall(DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet));
316
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 4 PetscCall(DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet));
317
318
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 4 PetscCall(VecGetArray(Xgen,&xgen));
319
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 4 PetscCall(VecGetArray(Xnet,&xnet));
320
321 /* Generator subsystem */
322
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 16 for (i=0; i < ngen; i++) {
323 12 Eqp = xgen[idx];
324 12 Edp = xgen[idx+1];
325 12 delta = xgen[idx+2];
326 12 Id = xgen[idx+4];
327 12 Iq = xgen[idx+5];
328 12 Efd = xgen[idx+6];
329
330 /* fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i]; */
331 12 row[0] = idx;
332 12 col[0] = idx; col[1] = idx+4; col[2] = idx+6;
333 12 val[0] = 1/ Td0p[i]; val[1] = (Xd[i] - Xdp[i])/ Td0p[i]; val[2] = -1/Td0p[i];
334
335
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 12 PetscCall(MatSetValues(J,1,row,3,col,val,INSERT_VALUES));
336
337 /* fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
338 12 row[0] = idx + 1;
339 12 col[0] = idx + 1; col[1] = idx+5;
340 12 val[0] = 1/Tq0p[i]; val[1] = -(Xq[i] - Xqp[i])/Tq0p[i];
341
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 12 PetscCall(MatSetValues(J,1,row,2,col,val,INSERT_VALUES));
342
343 /* fgen[idx+2] = - w + w_s; */
344 12 row[0] = idx + 2;
345 12 col[0] = idx + 2; col[1] = idx + 3;
346 12 val[0] = 0; val[1] = -1;
347
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 12 PetscCall(MatSetValues(J,1,row,2,col,val,INSERT_VALUES));
348
349 /* fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i]; */
350 12 row[0] = idx + 3;
351 12 col[0] = idx; col[1] = idx + 1; col[2] = idx + 3; col[3] = idx + 4; col[4] = idx + 5;
352 12 val[0] = Iq/M[i]; val[1] = Id/M[i]; val[2] = D[i]/M[i]; val[3] = (Edp + (Xqp[i]-Xdp[i])*Iq)/M[i]; val[4] = (Eqp + (Xqp[i] - Xdp[i])*Id)/M[i];
353
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 12 PetscCall(MatSetValues(J,1,row,5,col,val,INSERT_VALUES));
354
355 12 Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
356 12 Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
357
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 12 PetscCall(ri2dq(Vr,Vi,delta,&Vd,&Vq));
358
359 12 det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
360
361 12 Zdq_inv[0] = Rs[i]/det;
362 12 Zdq_inv[1] = Xqp[i]/det;
363 12 Zdq_inv[2] = -Xdp[i]/det;
364 12 Zdq_inv[3] = Rs[i]/det;
365
366 12 dVd_dVr = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
367 12 dVq_dVr = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
368 12 dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
369 12 dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);
370
371 /* fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
372 12 row[0] = idx+4;
373 12 col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
374 12 val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0]; val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
375 12 col[3] = idx + 4; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
376 12 val[3] = 1; val[4] = Zdq_inv[0]*dVd_dVr + Zdq_inv[1]*dVq_dVr; val[5] = Zdq_inv[0]*dVd_dVi + Zdq_inv[1]*dVq_dVi;
377
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 12 PetscCall(MatSetValues(J,1,row,6,col,val,INSERT_VALUES));
378
379 /* fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
380 12 row[0] = idx+5;
381 12 col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
382 12 val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2]; val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
383 12 col[3] = idx + 5; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
384 12 val[3] = 1; val[4] = Zdq_inv[2]*dVd_dVr + Zdq_inv[3]*dVq_dVr; val[5] = Zdq_inv[2]*dVd_dVi + Zdq_inv[3]*dVq_dVi;
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 12 PetscCall(MatSetValues(J,1,row,6,col,val,INSERT_VALUES));
386
387 12 dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
388 12 dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
389 12 dIGr_dId = PetscSinScalar(delta); dIGr_dIq = PetscCosScalar(delta);
390 12 dIGi_dId = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);
391
392 /* fnet[2*gbus[i]] -= IGi; */
393 12 row[0] = net_start + 2*gbus[i];
394 12 col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
395 12 val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
396
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 12 PetscCall(MatSetValues(J,1,row,3,col,val,INSERT_VALUES));
397
398 /* fnet[2*gbus[i]+1] -= IGr; */
399 12 row[0] = net_start + 2*gbus[i]+1;
400 12 col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
401 12 val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
402
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 12 PetscCall(MatSetValues(J,1,row,3,col,val,INSERT_VALUES));
403
404 12 Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq); Vm2 = Vm*Vm;
405
406 /* fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i]; */
407 /* SE = k1[i]*PetscExpScalar(k2[i]*Efd); */
408
409 12 dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);
410
411 12 row[0] = idx + 6;
412 12 col[0] = idx + 6; col[1] = idx + 8;
413 12 val[0] = (KE[i] + dSE_dEfd)/TE[i]; val[1] = -1/TE[i];
414
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 12 PetscCall(MatSetValues(J,1,row,2,col,val,INSERT_VALUES));
415
416 /* Exciter differential equations */
417
418 /* fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i]; */
419 12 row[0] = idx + 7;
420 12 col[0] = idx + 6; col[1] = idx + 7;
421 12 val[0] = (-KF[i]/TF[i])/TF[i]; val[1] = 1/TF[i];
422
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 12 PetscCall(MatSetValues(J,1,row,2,col,val,INSERT_VALUES));
423
424 /* fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i]; */
425 /* Vm = (Vd^2 + Vq^2)^0.5; */
426
427 12 dVm_dVd = Vd/Vm; dVm_dVq = Vq/Vm;
428 12 dVm_dVr = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
429 12 dVm_dVi = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
430 12 row[0] = idx + 8;
431 12 col[0] = idx + 6; col[1] = idx + 7; col[2] = idx + 8;
432 12 val[0] = (KA[i]*KF[i]/TF[i])/TA[i]; val[1] = -KA[i]/TA[i]; val[2] = 1/TA[i];
433 12 col[3] = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
434 12 val[3] = KA[i]*dVm_dVr/TA[i]; val[4] = KA[i]*dVm_dVi/TA[i];
435
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 12 PetscCall(MatSetValues(J,1,row,5,col,val,INSERT_VALUES));
436 12 idx = idx + 9;
437 }
438
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 40 for (i=0; i<nbus; i++) {
440
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 36 PetscCall(MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals));
441 36 row[0] = net_start + 2*i;
442
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 252 for (k=0; k<ncols; k++) {
443 216 col[k] = net_start + cols[k];
444 216 val[k] = yvals[k];
445 }
446
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 36 PetscCall(MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES));
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 36 PetscCall(MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals));
448
449
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 36 PetscCall(MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals));
450 36 row[0] = net_start + 2*i+1;
451
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 252 for (k=0; k<ncols; k++) {
452 216 col[k] = net_start + cols[k];
453 216 val[k] = yvals[k];
454 }
455
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 36 PetscCall(MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES));
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 36 PetscCall(MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals));
457 }
458
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 4 PetscCall(MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY));
460
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 4 PetscCall(MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY));
461
462
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 4 PetscCall(VecGetArray(user->V0,&v0));
463
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 16 for (i=0; i < nload; i++) {
464 12 Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
465 12 Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
466 12 Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm; Vm4 = Vm2*Vm2;
467 12 Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
468 12 PD = QD = 0.0;
469 12 dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
470
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 48 for (k=0; k < ld_nsegsp[i]; k++) {
471 36 PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
472 36 dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
473 36 dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
474 }
475
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 48 for (k=0; k < ld_nsegsq[i]; k++) {
476 36 QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
477 36 dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
478 36 dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
479 }
480
481 /* IDr = (PD*Vr + QD*Vi)/Vm2; */
482 /* IDi = (-QD*Vr + PD*Vi)/Vm2; */
483
484 12 dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
485 12 dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;
486
487 12 dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
488 12 dIDi_dVi = (-dQD_dVi*Vr + dPD_dVi*Vi + PD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vi)/Vm4;
489
490 /* fnet[2*lbus[i]] += IDi; */
491 12 row[0] = net_start + 2*lbus[i];
492 12 col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
493 12 val[0] = dIDi_dVr; val[1] = dIDi_dVi;
494
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 12 PetscCall(MatSetValues(J,1,row,2,col,val,ADD_VALUES));
495 /* fnet[2*lbus[i]+1] += IDr; */
496 12 row[0] = net_start + 2*lbus[i]+1;
497 12 col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
498 12 val[0] = dIDr_dVr; val[1] = dIDr_dVi;
499
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 12 PetscCall(MatSetValues(J,1,row,2,col,val,ADD_VALUES));
500 }
501
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 4 PetscCall(VecRestoreArray(user->V0,&v0));
502
503
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 4 PetscCall(VecRestoreArray(Xgen,&xgen));
504
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 4 PetscCall(VecRestoreArray(Xnet,&xnet));
505
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 4 PetscCall(DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet));
507
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 4 PetscCall(MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY));
509
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 4 PetscCall(MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY));
510
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 1 PetscFunctionReturn(PETSC_SUCCESS);
511 }
512
513 4 int main(int argc,char **argv)
514 {
515 4 EPS eps;
516 4 EPSType type;
517 4 PetscMPIInt size;
518 4 Userctx user;
519 4 PetscViewer Xview,Ybusview;
520 4 Vec X,Xr,Xi;
521 4 Mat J,Jred=NULL;
522 4 IS is0,is1;
523 4 PetscInt i,*idx2,its,nev,nconv;
524 4 PetscReal error,re,im;
525 4 PetscScalar kr,ki;
526 4 PetscBool terse;
527
528
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 4 PetscFunctionBeginUser;
529
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 4 PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
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 4 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size));
531
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 4 PetscCheck(size==1,PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
532 /* show detailed info unless -terse option is given by user */
533
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 4 PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
534
535 4 user.neqs_gen = 9*ngen; /* # eqs. for generator subsystem */
536 4 user.neqs_net = 2*nbus; /* # eqs. for network subsystem */
537 4 user.neqs_pgrid = user.neqs_gen + user.neqs_net;
538
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 4 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nStability analysis in a network with %" PetscInt_FMT " buses and %" PetscInt_FMT " generators\n\n",nbus,ngen));
539
540 /* Create indices for differential and algebraic equations */
541
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 4 PetscCall(PetscMalloc1(7*ngen,&idx2));
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 16 for (i=0; i<ngen; i++) {
543 12 idx2[7*i] = 9*i; idx2[7*i+1] = 9*i+1; idx2[7*i+2] = 9*i+2; idx2[7*i+3] = 9*i+3;
544 12 idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
545 }
546
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 4 PetscCall(ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff));
547
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 4 PetscCall(ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg));
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 4 PetscCall(PetscFree(idx2));
549
550 /* Read initial voltage vector and Ybus */
551
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 4 PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview));
552
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 4 PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview));
553
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 4 PetscCall(VecCreate(PETSC_COMM_WORLD,&user.V0));
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 4 PetscCall(VecSetSizes(user.V0,PETSC_DECIDE,user.neqs_net));
556
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 4 PetscCall(VecLoad(user.V0,Xview));
557
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 4 PetscCall(MatCreate(PETSC_COMM_WORLD,&user.Ybus));
559
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 4 PetscCall(MatSetSizes(user.Ybus,PETSC_DECIDE,PETSC_DECIDE,user.neqs_net,user.neqs_net));
560
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 4 PetscCall(MatSetType(user.Ybus,MATBAIJ));
561 /* PetscCall(MatSetBlockSize(user.Ybus,2)); */
562
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 4 PetscCall(MatLoad(user.Ybus,Ybusview));
563
564
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 4 PetscCall(PetscViewerDestroy(&Xview));
565
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 4 PetscCall(PetscViewerDestroy(&Ybusview));
566
567 /* Create DMs for generator and network subsystems */
568
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 4 PetscCall(DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen));
569
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 4 PetscCall(DMSetOptionsPrefix(user.dmgen,"dmgen_"));
570
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 4 PetscCall(DMSetFromOptions(user.dmgen));
571
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 4 PetscCall(DMSetUp(user.dmgen));
572
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 4 PetscCall(DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet));
573
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 4 PetscCall(DMSetOptionsPrefix(user.dmnet,"dmnet_"));
574
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 4 PetscCall(DMSetFromOptions(user.dmnet));
575
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 4 PetscCall(DMSetUp(user.dmnet));
576
577 /* Create a composite DM packer and add the two DMs */
578
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 4 PetscCall(DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid));
579
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 4 PetscCall(DMSetOptionsPrefix(user.dmpgrid,"pgrid_"));
580
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 4 PetscCall(DMCompositeAddDM(user.dmpgrid,user.dmgen));
581
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 4 PetscCall(DMCompositeAddDM(user.dmpgrid,user.dmnet));
582
583
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 4 PetscCall(DMCreateGlobalVector(user.dmpgrid,&X));
584
585
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 4 PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
586
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 4 PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,user.neqs_pgrid));
587
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 4 PetscCall(MatSetFromOptions(J));
588
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 4 PetscCall(PreallocateJacobian(J,&user));
589
590 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
591 Set initial conditions
592 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
593
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 4 PetscCall(SetInitialGuess(X,&user));
594
595 /* Form Jacobian */
596
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 4 PetscCall(ResidualJacobian(X,J,(void*)&user));
597
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 4 PetscCall(MatScale(J,-1));
598 4 is0 = user.is_diff;
599 4 is1 = user.is_alg;
600
601
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 4 PetscCall(MatGetSchurComplement(J,is1,is1,is0,is0,MAT_IGNORE_MATRIX,NULL,MAT_SCHUR_COMPLEMENT_AINV_DIAG,MAT_INITIAL_MATRIX,&Jred));
602
603
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 4 if (!terse) PetscCall(MatView(Jred,NULL));
604
605
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 4 PetscCall(MatCreateVecs(Jred,NULL,&Xr));
606
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 4 PetscCall(MatCreateVecs(Jred,NULL,&Xi));
607
608 /* Create the eigensolver and set the various options */
609
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 4 PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
610
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 4 PetscCall(EPSSetOperators(eps,Jred,NULL));
611
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 4 PetscCall(EPSSetProblemType(eps,EPS_NHEP));
612
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 4 PetscCall(EPSSetFromOptions(eps));
613
614 /* Solve the eigenvalue problem */
615
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 4 PetscCall(EPSSolve(eps));
616
617
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 4 PetscCall(EPSGetIterationNumber(eps,&its));
618
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 4 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the eigensolver: %" PetscInt_FMT "\n",its));
619
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 4 PetscCall(EPSGetType(eps,&type));
620
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 4 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n", type));
621
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 4 PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
622
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 4 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
623
624 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
625 Display solution and clean up
626 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
627
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 4 if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
628 else {
629 /* Get number of converged approximate eigenpairs */
630 ✗ PetscCall(EPSGetConverged(eps,&nconv));
631 ✗ PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %" PetscInt_FMT "\n\n",nconv));
632
633 ✗ if (nconv>0) {
634 /* Display eigenvalues and relative errors */
635 ✗ PetscCall(PetscPrintf(PETSC_COMM_WORLD,
636 " k ||Ax-kx||/||kx||\n"
637 " ----------------- ------------------\n"));
638
639 ✗ for (i=0;i<nconv;i++) {
640 /* Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
641 ki (imaginary part) */
642 ✗ PetscCall(EPSGetEigenpair(eps,i,&kr,&ki,Xr,Xi));
643 /* Compute the relative error associated to each eigenpair */
644 ✗ PetscCall(EPSComputeError(eps,i,EPS_ERROR_RELATIVE,&error));
645
646 #if defined(PETSC_USE_COMPLEX)
647 re = PetscRealPart(kr);
648 im = PetscImaginaryPart(kr);
649 #else
650 ✗ re = kr;
651 ✗ im = ki;
652 #endif
653 ✗ if (im!=0.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi %12g\n",(double)re,(double)im,(double)error));
654 ✗ else PetscCall(PetscPrintf(PETSC_COMM_WORLD," %12f %12g\n",(double)re,(double)error));
655 }
656 ✗ PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
657 }
658 }
659
660 /* Free work space */
661
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 4 PetscCall(EPSDestroy(&eps));
662
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 4 PetscCall(MatDestroy(&J));
663
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 4 PetscCall(MatDestroy(&Jred));
664
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 4 PetscCall(MatDestroy(&user.Ybus));
665
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 4 PetscCall(VecDestroy(&X));
666
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 4 PetscCall(VecDestroy(&Xr));
667
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 4 PetscCall(VecDestroy(&Xi));
668
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 4 PetscCall(VecDestroy(&user.V0));
669
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 4 PetscCall(DMDestroy(&user.dmgen));
670
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 4 PetscCall(DMDestroy(&user.dmnet));
671
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 4 PetscCall(DMDestroy(&user.dmpgrid));
672
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 4 PetscCall(ISDestroy(&user.is_diff));
673
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 4 PetscCall(ISDestroy(&user.is_alg));
674
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 4 PetscCall(SlepcFinalize());
675 return 0;
676 }
677
678 /*TEST
679
680 build:
681 requires: !complex
682
683 test:
684 suffix: 1
685 args: -terse
686 requires: double !complex !defined(PETSC_USE_64BIT_INDICES)
687 localrunfiles: X.bin Ybus.bin
688
689 TEST*/
690