GCC Code Coverage Report

Directory: ./
File: src/eps/tutorials/ex31.c
Date: 2025-10-03 04:28:47
Exec Total Coverage
Lines: 341 358 95.3%
Functions: 5 6 83.3%
Branches: 527 880 59.9%
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 15 PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd,PetscScalar *Fq)
147 {
148
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 15 PetscFunctionBegin;
149 15 *Fd = Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
150 15 *Fq = Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
151
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 15 PetscFunctionReturn(PETSC_SUCCESS);
152 }
153
154 5 PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
155 {
156 5 Vec Xgen,Xnet;
157 5 PetscScalar *xgen,*xnet;
158 5 PetscInt i,idx=0;
159 5 PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
160 5 PetscScalar Eqp,Edp,delta;
161 5 PetscScalar Efd,RF,VR; /* Exciter variables */
162 5 PetscScalar Id,Iq; /* Generator dq axis currents */
163 5 PetscScalar theta,Vd,Vq,SE;
164
165
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 5 PetscFunctionBegin;
166 5 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 5 D[0] = D[1] = D[2] = 0.0;
170
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 5 PetscCall(DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet));
171
172 /* Network subsystem initialization */
173
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 5 PetscCall(VecCopy(user->V0,Xnet));
174
175 /* Generator subsystem initialization */
176
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 5 PetscCall(VecGetArray(Xgen,&xgen));
177
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 5 PetscCall(VecGetArray(Xnet,&xnet));
178
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 20 for (i=0; i < ngen; i++) {
180 15 Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
181 15 Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
182 15 Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
183 15 IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
184 15 IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;
185
186 15 delta = atan2(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
187
188 15 theta = PETSC_PI/2.0 - delta;
189
190 15 Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
191 15 Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
192
193 15 Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
194 15 Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
195
196 15 Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
197 15 Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
198
199 15 TM[i] = PG[i];
200
201 /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
202 15 xgen[idx] = Eqp;
203 15 xgen[idx+1] = Edp;
204 15 xgen[idx+2] = delta;
205 15 xgen[idx+3] = w_s;
206
207 15 idx = idx + 4;
208
209 15 xgen[idx] = Id;
210 15 xgen[idx+1] = Iq;
211
212 15 idx = idx + 2;
213
214 /* Exciter */
215 15 Efd = Eqp + (Xd[i] - Xdp[i])*Id;
216 15 SE = k1[i]*PetscExpScalar(k2[i]*Efd);
217 15 VR = KE[i]*Efd + SE;
218 15 RF = KF[i]*Efd/TF[i];
219
220 15 xgen[idx] = Efd;
221 15 xgen[idx+1] = RF;
222 15 xgen[idx+2] = VR;
223
224 15 Vref[i] = Vm + (VR/KA[i]);
225
226 15 idx = idx + 3;
227 }
228
229
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 5 PetscCall(VecRestoreArray(Xgen,&xgen));
230
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 5 PetscCall(VecRestoreArray(Xnet,&xnet));
231
232 /* PetscCall(VecView(Xgen,0)); */
233
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 5 PetscCall(DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet));
234
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 5 PetscCall(DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet));
235
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 1 PetscFunctionReturn(PETSC_SUCCESS);
236 }
237
238 5 PetscErrorCode PreallocateJacobian(Mat J,Userctx *user)
239 {
240 5 PetscInt *d_nnz;
241 5 PetscInt i,idx=0,start=0;
242 5 PetscInt ncols;
243
244
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 5 PetscFunctionBegin;
245
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 5 PetscCall(PetscMalloc1(user->neqs_pgrid,&d_nnz));
246
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 230 for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
247 /* Generator subsystem */
248
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 20 for (i=0; i < ngen; i++) {
249
250 15 d_nnz[idx] += 3;
251 15 d_nnz[idx+1] += 2;
252 15 d_nnz[idx+2] += 2;
253 15 d_nnz[idx+3] += 5;
254 15 d_nnz[idx+4] += 6;
255 15 d_nnz[idx+5] += 6;
256
257 15 d_nnz[user->neqs_gen+2*gbus[i]] += 3;
258 15 d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;
259
260 15 d_nnz[idx+6] += 2;
261 15 d_nnz[idx+7] += 2;
262 15 d_nnz[idx+8] += 5;
263
264 15 idx = idx + 9;
265 }
266
267 5 start = user->neqs_gen;
268
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 50 for (i=0; i < nbus; i++) {
270
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 45 PetscCall(MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL));
271 45 d_nnz[start+2*i] += ncols;
272 45 d_nnz[start+2*i+1] += ncols;
273
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 45 PetscCall(MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL));
274 }
275
276
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 5 PetscCall(MatSeqAIJSetPreallocation(J,0,d_nnz));
277
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 5 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 5 PetscErrorCode ResidualJacobian(Vec X,Mat J,void *ctx)
287 {
288 5 Userctx *user=(Userctx*)ctx;
289 5 Vec Xgen,Xnet;
290 5 PetscScalar *xgen,*xnet;
291 5 PetscInt i,idx=0;
292 5 PetscScalar Vr,Vi,Vm,Vm2;
293 5 PetscScalar Eqp,Edp,delta; /* Generator variables */
294 5 PetscScalar Efd;
295 5 PetscScalar Id,Iq; /* Generator dq axis currents */
296 5 PetscScalar Vd,Vq;
297 5 PetscScalar val[10];
298 5 PetscInt row[2],col[10];
299 5 PetscInt net_start=user->neqs_gen;
300 5 PetscScalar Zdq_inv[4],det;
301 5 PetscScalar dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
302 5 PetscScalar dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
303 5 PetscScalar dSE_dEfd;
304 5 PetscScalar dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
305 5 PetscInt ncols;
306 5 const PetscInt *cols;
307 5 const PetscScalar *yvals;
308 5 PetscInt k;
309 5 PetscScalar PD,QD,Vm0,*v0,Vm4;
310 5 PetscScalar dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
311 5 PetscScalar dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;
312
313
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 5 PetscFunctionBegin;
314
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 5 PetscCall(MatZeroEntries(J));
315
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 5 PetscCall(DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet));
316
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 5 PetscCall(DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet));
317
318
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 5 PetscCall(VecGetArray(Xgen,&xgen));
319
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 5 PetscCall(VecGetArray(Xnet,&xnet));
320
321 /* Generator subsystem */
322
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 20 for (i=0; i < ngen; i++) {
323 15 Eqp = xgen[idx];
324 15 Edp = xgen[idx+1];
325 15 delta = xgen[idx+2];
326 15 Id = xgen[idx+4];
327 15 Iq = xgen[idx+5];
328 15 Efd = xgen[idx+6];
329
330 /* fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i]; */
331 15 row[0] = idx;
332 15 col[0] = idx; col[1] = idx+4; col[2] = idx+6;
333 15 val[0] = 1/ Td0p[i]; val[1] = (Xd[i] - Xdp[i])/ Td0p[i]; val[2] = -1/Td0p[i];
334
335
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 15 PetscCall(MatSetValues(J,1,row,3,col,val,INSERT_VALUES));
336
337 /* fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
338 15 row[0] = idx + 1;
339 15 col[0] = idx + 1; col[1] = idx+5;
340 15 val[0] = 1/Tq0p[i]; val[1] = -(Xq[i] - Xqp[i])/Tq0p[i];
341
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 15 PetscCall(MatSetValues(J,1,row,2,col,val,INSERT_VALUES));
342
343 /* fgen[idx+2] = - w + w_s; */
344 15 row[0] = idx + 2;
345 15 col[0] = idx + 2; col[1] = idx + 3;
346 15 val[0] = 0; val[1] = -1;
347
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 15 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 15 row[0] = idx + 3;
351 15 col[0] = idx; col[1] = idx + 1; col[2] = idx + 3; col[3] = idx + 4; col[4] = idx + 5;
352 15 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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 15 PetscCall(MatSetValues(J,1,row,5,col,val,INSERT_VALUES));
354
355 15 Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
356 15 Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
357
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 15 PetscCall(ri2dq(Vr,Vi,delta,&Vd,&Vq));
358
359 15 det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
360
361 15 Zdq_inv[0] = Rs[i]/det;
362 15 Zdq_inv[1] = Xqp[i]/det;
363 15 Zdq_inv[2] = -Xdp[i]/det;
364 15 Zdq_inv[3] = Rs[i]/det;
365
366 15 dVd_dVr = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
367 15 dVq_dVr = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
368 15 dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
369 15 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 15 row[0] = idx+4;
373 15 col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
374 15 val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0]; val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
375 15 col[3] = idx + 4; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
376 15 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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 15 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 15 row[0] = idx+5;
381 15 col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
382 15 val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2]; val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
383 15 col[3] = idx + 5; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
384 15 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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 15 PetscCall(MatSetValues(J,1,row,6,col,val,INSERT_VALUES));
386
387 15 dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
388 15 dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
389 15 dIGr_dId = PetscSinScalar(delta); dIGr_dIq = PetscCosScalar(delta);
390 15 dIGi_dId = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);
391
392 /* fnet[2*gbus[i]] -= IGi; */
393 15 row[0] = net_start + 2*gbus[i];
394 15 col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
395 15 val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
396
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 15 PetscCall(MatSetValues(J,1,row,3,col,val,INSERT_VALUES));
397
398 /* fnet[2*gbus[i]+1] -= IGr; */
399 15 row[0] = net_start + 2*gbus[i]+1;
400 15 col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
401 15 val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
402
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 15 PetscCall(MatSetValues(J,1,row,3,col,val,INSERT_VALUES));
403
404 15 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 15 dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);
410
411 15 row[0] = idx + 6;
412 15 col[0] = idx + 6; col[1] = idx + 8;
413 15 val[0] = (KE[i] + dSE_dEfd)/TE[i]; val[1] = -1/TE[i];
414
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 15 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 15 row[0] = idx + 7;
420 15 col[0] = idx + 6; col[1] = idx + 7;
421 15 val[0] = (-KF[i]/TF[i])/TF[i]; val[1] = 1/TF[i];
422
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 15 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 15 dVm_dVd = Vd/Vm; dVm_dVq = Vq/Vm;
428 15 dVm_dVr = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
429 15 dVm_dVi = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
430 15 row[0] = idx + 8;
431 15 col[0] = idx + 6; col[1] = idx + 7; col[2] = idx + 8;
432 15 val[0] = (KA[i]*KF[i]/TF[i])/TA[i]; val[1] = -KA[i]/TA[i]; val[2] = 1/TA[i];
433 15 col[3] = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
434 15 val[3] = KA[i]*dVm_dVr/TA[i]; val[4] = KA[i]*dVm_dVi/TA[i];
435
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 15 PetscCall(MatSetValues(J,1,row,5,col,val,INSERT_VALUES));
436 15 idx = idx + 9;
437 }
438
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 50 for (i=0; i<nbus; i++) {
440
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 45 PetscCall(MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals));
441 45 row[0] = net_start + 2*i;
442
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 315 for (k=0; k<ncols; k++) {
443 270 col[k] = net_start + cols[k];
444 270 val[k] = yvals[k];
445 }
446
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 45 PetscCall(MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES));
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 45 PetscCall(MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals));
448
449
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 45 PetscCall(MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals));
450 45 row[0] = net_start + 2*i+1;
451
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 315 for (k=0; k<ncols; k++) {
452 270 col[k] = net_start + cols[k];
453 270 val[k] = yvals[k];
454 }
455
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 45 PetscCall(MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES));
456
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 45 PetscCall(MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals));
457 }
458
459
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 5 PetscCall(MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY));
460
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 5 PetscCall(MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY));
461
462
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 5 PetscCall(VecGetArray(user->V0,&v0));
463
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 20 for (i=0; i < nload; i++) {
464 15 Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
465 15 Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
466 15 Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm; Vm4 = Vm2*Vm2;
467 15 Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
468 15 PD = QD = 0.0;
469 15 dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
470
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 60 for (k=0; k < ld_nsegsp[i]; k++) {
471 45 PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
472 45 dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
473 45 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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 60 for (k=0; k < ld_nsegsq[i]; k++) {
476 45 QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
477 45 dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
478 45 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 15 dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
485 15 dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;
486
487 15 dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
488 15 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 15 row[0] = net_start + 2*lbus[i];
492 15 col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
493 15 val[0] = dIDi_dVr; val[1] = dIDi_dVi;
494
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 15 PetscCall(MatSetValues(J,1,row,2,col,val,ADD_VALUES));
495 /* fnet[2*lbus[i]+1] += IDr; */
496 15 row[0] = net_start + 2*lbus[i]+1;
497 15 col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
498 15 val[0] = dIDr_dVr; val[1] = dIDr_dVi;
499
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 15 PetscCall(MatSetValues(J,1,row,2,col,val,ADD_VALUES));
500 }
501
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 5 PetscCall(VecRestoreArray(user->V0,&v0));
502
503
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 5 PetscCall(VecRestoreArray(Xgen,&xgen));
504
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 5 PetscCall(VecRestoreArray(Xnet,&xnet));
505
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 5 PetscCall(DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet));
507
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 5 PetscCall(MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY));
509
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 5 PetscCall(MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY));
510
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 1 PetscFunctionReturn(PETSC_SUCCESS);
511 }
512
513 5 int main(int argc,char **argv)
514 {
515 5 EPS eps;
516 5 EPSType type;
517 5 PetscMPIInt size;
518 5 Userctx user;
519 5 PetscViewer Xview,Ybusview;
520 5 Vec X,Xr,Xi;
521 5 Mat J,Jred=NULL;
522 5 IS is0,is1;
523 5 PetscInt i,*idx2,its,nev,nconv;
524 5 PetscReal error,re,im;
525 5 PetscScalar kr,ki;
526 5 PetscBool terse;
527
528
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 5 PetscFunctionBeginUser;
529
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 5 PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
530
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 5 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size));
531
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 5 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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 5 PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
534
535 5 user.neqs_gen = 9*ngen; /* # eqs. for generator subsystem */
536 5 user.neqs_net = 2*nbus; /* # eqs. for network subsystem */
537 5 user.neqs_pgrid = user.neqs_gen + user.neqs_net;
538
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 5 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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 5 PetscCall(PetscMalloc1(7*ngen,&idx2));
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 20 for (i=0; i<ngen; i++) {
543 15 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 15 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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 5 PetscCall(ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff));
547
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 5 PetscCall(ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg));
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 5 PetscCall(PetscFree(idx2));
549
550 /* Read initial voltage vector and Ybus */
551
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 5 PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview));
552
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 5 PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview));
553
554
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 5 PetscCall(VecCreate(PETSC_COMM_WORLD,&user.V0));
555
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 5 PetscCall(VecSetSizes(user.V0,PETSC_DECIDE,user.neqs_net));
556
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 5 PetscCall(VecLoad(user.V0,Xview));
557
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 5 PetscCall(MatCreate(PETSC_COMM_WORLD,&user.Ybus));
559
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 5 PetscCall(MatSetSizes(user.Ybus,PETSC_DECIDE,PETSC_DECIDE,user.neqs_net,user.neqs_net));
560
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 5 PetscCall(MatSetType(user.Ybus,MATBAIJ));
561 /* PetscCall(MatSetBlockSize(user.Ybus,2)); */
562
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 5 PetscCall(MatLoad(user.Ybus,Ybusview));
563
564
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 5 PetscCall(PetscViewerDestroy(&Xview));
565
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 5 PetscCall(PetscViewerDestroy(&Ybusview));
566
567 /* Create DMs for generator and network subsystems */
568
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 5 PetscCall(DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen));
569
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 5 PetscCall(DMSetOptionsPrefix(user.dmgen,"dmgen_"));
570
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 5 PetscCall(DMSetFromOptions(user.dmgen));
571
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 5 PetscCall(DMSetUp(user.dmgen));
572
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 5 PetscCall(DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet));
573
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 5 PetscCall(DMSetOptionsPrefix(user.dmnet,"dmnet_"));
574
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 5 PetscCall(DMSetFromOptions(user.dmnet));
575
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 5 PetscCall(DMSetUp(user.dmnet));
576
577 /* Create a composite DM packer and add the two DMs */
578
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 5 PetscCall(DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid));
579
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 5 PetscCall(DMSetOptionsPrefix(user.dmpgrid,"pgrid_"));
580
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 5 PetscCall(DMCompositeAddDM(user.dmpgrid,user.dmgen));
581
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 5 PetscCall(DMCompositeAddDM(user.dmpgrid,user.dmnet));
582
583
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 5 PetscCall(DMCreateGlobalVector(user.dmpgrid,&X));
584
585
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 5 PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
586
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 5 PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,user.neqs_pgrid));
587
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 5 PetscCall(MatSetFromOptions(J));
588
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 5 PetscCall(PreallocateJacobian(J,&user));
589
590 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
591 Set initial conditions
592 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
593
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 5 PetscCall(SetInitialGuess(X,&user));
594
595 /* Form Jacobian */
596
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 5 PetscCall(ResidualJacobian(X,J,(void*)&user));
597
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 5 PetscCall(MatScale(J,-1));
598 5 is0 = user.is_diff;
599 5 is1 = user.is_alg;
600
601
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 5 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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 5 if (!terse) PetscCall(MatView(Jred,NULL));
604
605
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 5 PetscCall(MatCreateVecs(Jred,NULL,&Xr));
606
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 5 PetscCall(MatCreateVecs(Jred,NULL,&Xi));
607
608 /* Create the eigensolver and set the various options */
609
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 5 PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
610
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 5 PetscCall(EPSSetOperators(eps,Jred,NULL));
611
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 5 PetscCall(EPSSetProblemType(eps,EPS_NHEP));
612
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 5 PetscCall(EPSSetFromOptions(eps));
613
614 /* Solve the eigenvalue problem */
615
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 5 PetscCall(EPSSolve(eps));
616
617
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 5 PetscCall(EPSGetIterationNumber(eps,&its));
618
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 5 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the eigensolver: %" PetscInt_FMT "\n",its));
619
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 5 PetscCall(EPSGetType(eps,&type));
620
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 5 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n", type));
621
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 5 PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
622
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 5 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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 5 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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 5 PetscCall(EPSDestroy(&eps));
662
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 5 PetscCall(MatDestroy(&J));
663
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 5 PetscCall(MatDestroy(&Jred));
664
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 5 PetscCall(MatDestroy(&user.Ybus));
665
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 5 PetscCall(VecDestroy(&X));
666
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 5 PetscCall(VecDestroy(&Xr));
667
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 5 PetscCall(VecDestroy(&Xi));
668
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 5 PetscCall(VecDestroy(&user.V0));
669
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 5 PetscCall(DMDestroy(&user.dmgen));
670
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 5 PetscCall(DMDestroy(&user.dmnet));
671
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 5 PetscCall(DMDestroy(&user.dmpgrid));
672
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 5 PetscCall(ISDestroy(&user.is_diff));
673
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 5 PetscCall(ISDestroy(&user.is_alg));
674
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 5 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