Actual source code: ex31.c
slepc-3.18.2 2023-01-26
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
11: static char help[] = "Power grid small signal stability analysis of WECC 9 bus system.\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";
19: /*
20: This example is based on PETSc's ex9bus example (under TS).
22: The equations for the stability analysis are described by the DAE
24: \dot{x} = f(x,y,t)
25: 0 = g(x,y,t)
27: where the generators are described by differential equations, while the algebraic
28: constraints define the network equations.
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.
35: The network equations are described by nodal current balance equations.
36: I(x,y) - Y*V = 0
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
43: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
45: The linearized equations for the eigenvalue analysis are
47: \dot{\delta{x}} = f_x*\delta{x} + f_y*\delta{y}
48: 0 = g_x*\delta{x} + g_y*\delta{y}
50: This gives the linearized sensitivity matrix
51: A = | f_x f_y |
52: | g_x g_y |
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
57: Example contributed by: Shrirang Abhyankar
58: */
60: #include <petscdm.h>
61: #include <petscdmda.h>
62: #include <petscdmcomposite.h>
63: #include <slepceps.h>
65: #define freq 60
66: #define w_s (2*PETSC_PI*freq)
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 */
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 */
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) */
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
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};
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;
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: *Fr = Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
140: *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
141: return 0;
142: }
144: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
145: PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd,PetscScalar *Fq)
146: {
147: *Fd = Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
148: *Fq = Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
149: return 0;
150: }
152: PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
153: {
154: Vec Xgen,Xnet;
155: PetscScalar *xgen,*xnet;
156: PetscInt i,idx=0;
157: PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
158: PetscScalar Eqp,Edp,delta;
159: PetscScalar Efd,RF,VR; /* Exciter variables */
160: PetscScalar Id,Iq; /* Generator dq axis currents */
161: PetscScalar theta,Vd,Vq,SE;
163: M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
164: /* D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
165: */
166: D[0] = D[1] = D[2] = 0.0;
167: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
169: /* Network subsystem initialization */
170: VecCopy(user->V0,Xnet);
172: /* Generator subsystem initialization */
173: VecGetArray(Xgen,&xgen);
174: VecGetArray(Xnet,&xnet);
176: for (i=0; i < ngen; i++) {
177: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
178: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
179: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
180: IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
181: IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;
183: delta = atan2(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
185: theta = PETSC_PI/2.0 - delta;
187: Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
188: Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
190: Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
191: Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
193: Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
194: Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
196: TM[i] = PG[i];
198: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
199: xgen[idx] = Eqp;
200: xgen[idx+1] = Edp;
201: xgen[idx+2] = delta;
202: xgen[idx+3] = w_s;
204: idx = idx + 4;
206: xgen[idx] = Id;
207: xgen[idx+1] = Iq;
209: idx = idx + 2;
211: /* Exciter */
212: Efd = Eqp + (Xd[i] - Xdp[i])*Id;
213: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
214: VR = KE[i]*Efd + SE;
215: RF = KF[i]*Efd/TF[i];
217: xgen[idx] = Efd;
218: xgen[idx+1] = RF;
219: xgen[idx+2] = VR;
221: Vref[i] = Vm + (VR/KA[i]);
223: idx = idx + 3;
224: }
226: VecRestoreArray(Xgen,&xgen);
227: VecRestoreArray(Xnet,&xnet);
229: /* VecView(Xgen,0); */
230: DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet);
231: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
232: return 0;
233: }
235: PetscErrorCode PreallocateJacobian(Mat J,Userctx *user)
236: {
237: PetscInt *d_nnz;
238: PetscInt i,idx=0,start=0;
239: PetscInt ncols;
241: PetscMalloc1(user->neqs_pgrid,&d_nnz);
242: for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
243: /* Generator subsystem */
244: for (i=0; i < ngen; i++) {
246: d_nnz[idx] += 3;
247: d_nnz[idx+1] += 2;
248: d_nnz[idx+2] += 2;
249: d_nnz[idx+3] += 5;
250: d_nnz[idx+4] += 6;
251: d_nnz[idx+5] += 6;
253: d_nnz[user->neqs_gen+2*gbus[i]] += 3;
254: d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;
256: d_nnz[idx+6] += 2;
257: d_nnz[idx+7] += 2;
258: d_nnz[idx+8] += 5;
260: idx = idx + 9;
261: }
263: start = user->neqs_gen;
265: for (i=0; i < nbus; i++) {
266: MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL);
267: d_nnz[start+2*i] += ncols;
268: d_nnz[start+2*i+1] += ncols;
269: MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL);
270: }
272: MatSeqAIJSetPreallocation(J,0,d_nnz);
274: PetscFree(d_nnz);
275: return 0;
276: }
278: /*
279: J = [-df_dx, -df_dy
280: dg_dx, dg_dy]
281: */
282: PetscErrorCode ResidualJacobian(Vec X,Mat J,void *ctx)
283: {
284: Userctx *user=(Userctx*)ctx;
285: Vec Xgen,Xnet;
286: PetscScalar *xgen,*xnet;
287: PetscInt i,idx=0;
288: PetscScalar Vr,Vi,Vm,Vm2;
289: PetscScalar Eqp,Edp,delta; /* Generator variables */
290: PetscScalar Efd;
291: PetscScalar Id,Iq; /* Generator dq axis currents */
292: PetscScalar Vd,Vq;
293: PetscScalar val[10];
294: PetscInt row[2],col[10];
295: PetscInt net_start=user->neqs_gen;
296: PetscScalar Zdq_inv[4],det;
297: PetscScalar dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
298: PetscScalar dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
299: PetscScalar dSE_dEfd;
300: PetscScalar dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
301: PetscInt ncols;
302: const PetscInt *cols;
303: const PetscScalar *yvals;
304: PetscInt k;
305: PetscScalar PD,QD,Vm0,*v0,Vm4;
306: PetscScalar dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
307: PetscScalar dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;
309: MatZeroEntries(J);
310: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
311: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
313: VecGetArray(Xgen,&xgen);
314: VecGetArray(Xnet,&xnet);
316: /* Generator subsystem */
317: for (i=0; i < ngen; i++) {
318: Eqp = xgen[idx];
319: Edp = xgen[idx+1];
320: delta = xgen[idx+2];
321: Id = xgen[idx+4];
322: Iq = xgen[idx+5];
323: Efd = xgen[idx+6];
325: /* fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i]; */
326: row[0] = idx;
327: col[0] = idx; col[1] = idx+4; col[2] = idx+6;
328: val[0] = 1/ Td0p[i]; val[1] = (Xd[i] - Xdp[i])/ Td0p[i]; val[2] = -1/Td0p[i];
330: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
332: /* fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
333: row[0] = idx + 1;
334: col[0] = idx + 1; col[1] = idx+5;
335: val[0] = 1/Tq0p[i]; val[1] = -(Xq[i] - Xqp[i])/Tq0p[i];
336: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
338: /* fgen[idx+2] = - w + w_s; */
339: row[0] = idx + 2;
340: col[0] = idx + 2; col[1] = idx + 3;
341: val[0] = 0; val[1] = -1;
342: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
344: /* fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i]; */
345: row[0] = idx + 3;
346: col[0] = idx; col[1] = idx + 1; col[2] = idx + 3; col[3] = idx + 4; col[4] = idx + 5;
347: 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];
348: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
350: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
351: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
352: ri2dq(Vr,Vi,delta,&Vd,&Vq);
354: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
356: Zdq_inv[0] = Rs[i]/det;
357: Zdq_inv[1] = Xqp[i]/det;
358: Zdq_inv[2] = -Xdp[i]/det;
359: Zdq_inv[3] = Rs[i]/det;
361: dVd_dVr = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
362: dVq_dVr = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
363: dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
364: dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);
366: /* fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
367: row[0] = idx+4;
368: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
369: val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0]; val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
370: col[3] = idx + 4; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
371: 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;
372: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
374: /* fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
375: row[0] = idx+5;
376: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
377: val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2]; val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
378: col[3] = idx + 5; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
379: 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;
380: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
382: dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
383: dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
384: dIGr_dId = PetscSinScalar(delta); dIGr_dIq = PetscCosScalar(delta);
385: dIGi_dId = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);
387: /* fnet[2*gbus[i]] -= IGi; */
388: row[0] = net_start + 2*gbus[i];
389: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
390: val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
391: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
393: /* fnet[2*gbus[i]+1] -= IGr; */
394: row[0] = net_start + 2*gbus[i]+1;
395: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
396: val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
397: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
399: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq); Vm2 = Vm*Vm;
401: /* fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i]; */
402: /* SE = k1[i]*PetscExpScalar(k2[i]*Efd); */
404: dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);
406: row[0] = idx + 6;
407: col[0] = idx + 6; col[1] = idx + 8;
408: val[0] = (KE[i] + dSE_dEfd)/TE[i]; val[1] = -1/TE[i];
409: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
411: /* Exciter differential equations */
413: /* fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i]; */
414: row[0] = idx + 7;
415: col[0] = idx + 6; col[1] = idx + 7;
416: val[0] = (-KF[i]/TF[i])/TF[i]; val[1] = 1/TF[i];
417: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
419: /* fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i]; */
420: /* Vm = (Vd^2 + Vq^2)^0.5; */
422: dVm_dVd = Vd/Vm; dVm_dVq = Vq/Vm;
423: dVm_dVr = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
424: dVm_dVi = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
425: row[0] = idx + 8;
426: col[0] = idx + 6; col[1] = idx + 7; col[2] = idx + 8;
427: val[0] = (KA[i]*KF[i]/TF[i])/TA[i]; val[1] = -KA[i]/TA[i]; val[2] = 1/TA[i];
428: col[3] = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
429: val[3] = KA[i]*dVm_dVr/TA[i]; val[4] = KA[i]*dVm_dVi/TA[i];
430: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
431: idx = idx + 9;
432: }
434: for (i=0; i<nbus; i++) {
435: MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
436: row[0] = net_start + 2*i;
437: for (k=0; k<ncols; k++) {
438: col[k] = net_start + cols[k];
439: val[k] = yvals[k];
440: }
441: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
442: MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);
444: MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
445: row[0] = net_start + 2*i+1;
446: for (k=0; k<ncols; k++) {
447: col[k] = net_start + cols[k];
448: val[k] = yvals[k];
449: }
450: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
451: MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
452: }
454: MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
455: MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);
457: VecGetArray(user->V0,&v0);
458: for (i=0; i < nload; i++) {
459: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
460: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
461: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm; Vm4 = Vm2*Vm2;
462: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
463: PD = QD = 0.0;
464: dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
465: for (k=0; k < ld_nsegsp[i]; k++) {
466: PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
467: dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
468: dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
469: }
470: for (k=0; k < ld_nsegsq[i]; k++) {
471: QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
472: dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
473: dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
474: }
476: /* IDr = (PD*Vr + QD*Vi)/Vm2; */
477: /* IDi = (-QD*Vr + PD*Vi)/Vm2; */
479: dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
480: dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;
482: dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
483: dIDi_dVi = (-dQD_dVi*Vr + dPD_dVi*Vi + PD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vi)/Vm4;
485: /* fnet[2*lbus[i]] += IDi; */
486: row[0] = net_start + 2*lbus[i];
487: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
488: val[0] = dIDi_dVr; val[1] = dIDi_dVi;
489: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
490: /* fnet[2*lbus[i]+1] += IDr; */
491: row[0] = net_start + 2*lbus[i]+1;
492: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
493: val[0] = dIDr_dVr; val[1] = dIDr_dVi;
494: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
495: }
496: VecRestoreArray(user->V0,&v0);
498: VecRestoreArray(Xgen,&xgen);
499: VecRestoreArray(Xnet,&xnet);
501: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
503: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
504: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
505: return 0;
506: }
508: int main(int argc,char **argv)
509: {
510: EPS eps;
511: EPSType type;
512: PetscMPIInt size;
513: Userctx user;
514: PetscViewer Xview,Ybusview;
515: Vec X,Xr,Xi;
516: Mat J,Jred=NULL;
517: IS is0,is1;
518: PetscInt i,*idx2,its,nev,nconv;
519: PetscReal error,re,im;
520: PetscScalar kr,ki;
521: PetscBool terse;
524: SlepcInitialize(&argc,&argv,(char*)0,help);
525: MPI_Comm_size(PETSC_COMM_WORLD,&size);
527: /* show detailed info unless -terse option is given by user */
528: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
530: user.neqs_gen = 9*ngen; /* # eqs. for generator subsystem */
531: user.neqs_net = 2*nbus; /* # eqs. for network subsystem */
532: user.neqs_pgrid = user.neqs_gen + user.neqs_net;
533: PetscPrintf(PETSC_COMM_WORLD,"\nStability analysis in a network with %" PetscInt_FMT " buses and %" PetscInt_FMT " generators\n\n",nbus,ngen);
535: /* Create indices for differential and algebraic equations */
536: PetscMalloc1(7*ngen,&idx2);
537: for (i=0; i<ngen; i++) {
538: 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;
539: idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
540: }
541: ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
542: ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
543: PetscFree(idx2);
545: /* Read initial voltage vector and Ybus */
546: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
547: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);
549: VecCreate(PETSC_COMM_WORLD,&user.V0);
550: VecSetSizes(user.V0,PETSC_DECIDE,user.neqs_net);
551: VecLoad(user.V0,Xview);
553: MatCreate(PETSC_COMM_WORLD,&user.Ybus);
554: MatSetSizes(user.Ybus,PETSC_DECIDE,PETSC_DECIDE,user.neqs_net,user.neqs_net);
555: MatSetType(user.Ybus,MATBAIJ);
556: /* MatSetBlockSize(user.Ybus,2); */
557: MatLoad(user.Ybus,Ybusview);
559: PetscViewerDestroy(&Xview);
560: PetscViewerDestroy(&Ybusview);
562: /* Create DMs for generator and network subsystems */
563: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
564: DMSetOptionsPrefix(user.dmgen,"dmgen_");
565: DMSetFromOptions(user.dmgen);
566: DMSetUp(user.dmgen);
567: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
568: DMSetOptionsPrefix(user.dmnet,"dmnet_");
569: DMSetFromOptions(user.dmnet);
570: DMSetUp(user.dmnet);
572: /* Create a composite DM packer and add the two DMs */
573: DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
574: DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
575: DMCompositeAddDM(user.dmpgrid,user.dmgen);
576: DMCompositeAddDM(user.dmpgrid,user.dmnet);
578: DMCreateGlobalVector(user.dmpgrid,&X);
580: MatCreate(PETSC_COMM_WORLD,&J);
581: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,user.neqs_pgrid);
582: MatSetFromOptions(J);
583: PreallocateJacobian(J,&user);
585: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
586: Set initial conditions
587: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
588: SetInitialGuess(X,&user);
590: /* Form Jacobian */
591: ResidualJacobian(X,J,(void*)&user);
592: MatScale(J,-1);
593: is0 = user.is_diff;
594: is1 = user.is_alg;
596: MatGetSchurComplement(J,is1,is1,is0,is0,MAT_IGNORE_MATRIX,NULL,MAT_SCHUR_COMPLEMENT_AINV_DIAG,MAT_INITIAL_MATRIX,&Jred);
598: if (!terse) MatView(Jred,NULL);
600: MatCreateVecs(Jred,NULL,&Xr);
601: MatCreateVecs(Jred,NULL,&Xi);
603: /* Create the eigensolver and set the various options */
604: EPSCreate(PETSC_COMM_WORLD,&eps);
605: EPSSetOperators(eps,Jred,NULL);
606: EPSSetProblemType(eps,EPS_NHEP);
607: EPSSetFromOptions(eps);
609: /* Solve the eigenvalue problem */
610: EPSSolve(eps);
612: EPSGetIterationNumber(eps,&its);
613: PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the eigensolver: %" PetscInt_FMT "\n",its);
614: EPSGetType(eps,&type);
615: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n", type);
616: EPSGetDimensions(eps,&nev,NULL,NULL);
617: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);
619: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
620: Display solution and clean up
621: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
622: if (terse) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
623: else {
624: /* Get number of converged approximate eigenpairs */
625: EPSGetConverged(eps,&nconv);
626: PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %" PetscInt_FMT "\n\n",nconv);
628: if (nconv>0) {
629: /* Display eigenvalues and relative errors */
630: PetscCall(PetscPrintf(PETSC_COMM_WORLD,
631: " k ||Ax-kx||/||kx||\n"
632: " ----------------- ------------------\n"));
634: for (i=0;i<nconv;i++) {
635: /* Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
636: ki (imaginary part) */
637: EPSGetEigenpair(eps,i,&kr,&ki,Xr,Xi);
638: /* Compute the relative error associated to each eigenpair */
639: EPSComputeError(eps,i,EPS_ERROR_RELATIVE,&error);
641: #if defined(PETSC_USE_COMPLEX)
642: re = PetscRealPart(kr);
643: im = PetscImaginaryPart(kr);
644: #else
645: re = kr;
646: im = ki;
647: #endif
648: if (im!=0.0) PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi %12g\n",(double)re,(double)im,(double)error);
649: else PetscPrintf(PETSC_COMM_WORLD," %12f %12g\n",(double)re,(double)error);
650: }
651: PetscPrintf(PETSC_COMM_WORLD,"\n");
652: }
653: }
655: /* Free work space */
656: EPSDestroy(&eps);
657: MatDestroy(&J);
658: MatDestroy(&Jred);
659: MatDestroy(&user.Ybus);
660: VecDestroy(&X);
661: VecDestroy(&Xr);
662: VecDestroy(&Xi);
663: VecDestroy(&user.V0);
664: DMDestroy(&user.dmgen);
665: DMDestroy(&user.dmnet);
666: DMDestroy(&user.dmpgrid);
667: ISDestroy(&user.is_diff);
668: ISDestroy(&user.is_alg);
669: SlepcFinalize();
670: return 0;
671: }
673: /*TEST
675: build:
676: requires: !complex
678: test:
679: suffix: 1
680: args: -terse
681: requires: double !complex !defined(PETSC_USE_64BIT_INDICES)
682: localrunfiles: X.bin Ybus.bin
684: TEST*/