Actual source code: ex9busopt_fd.c
petsc-3.7.4 2016-10-02
1: static char help[] = "Using finite difference for the problem in ex9busopt.c \n\n";
3: /*
4: Use finite difference approximations to solve the same optimization problem as in ex9busopt.c.
5: */
7: #include <petsctao.h>
8: #include <petscts.h>
9: #include <petscdm.h>
10: #include <petscdmda.h>
11: #include <petscdmcomposite.h>
13: PetscErrorCode FormFunction(Tao,Vec,PetscReal*,void*);
15: #define freq 60
16: #define w_s (2*PETSC_PI*freq)
18: /* Sizes and indices */
19: const PetscInt nbus = 9; /* Number of network buses */
20: const PetscInt ngen = 3; /* Number of generators */
21: const PetscInt nload = 3; /* Number of loads */
22: const PetscInt gbus[3] = {0,1,2}; /* Buses at which generators are incident */
23: const PetscInt lbus[3] = {4,5,7}; /* Buses at which loads are incident */
25: /* Generator real and reactive powers (found via loadflow) */
26: PetscScalar PG[3] = { 0.69,1.59,0.69};
27: /* PetscScalar PG[3] = {0.716786142395021,1.630000000000000,0.850000000000000};*/
28: const PetscScalar QG[3] = {0.270702180178785,0.066120127797275,-0.108402221791588};
29: /* Generator constants */
30: const PetscScalar H[3] = {23.64,6.4,3.01}; /* Inertia constant */
31: const PetscScalar Rs[3] = {0.0,0.0,0.0}; /* Stator Resistance */
32: const PetscScalar Xd[3] = {0.146,0.8958,1.3125}; /* d-axis reactance */
33: const PetscScalar Xdp[3] = {0.0608,0.1198,0.1813}; /* d-axis transient reactance */
34: const PetscScalar Xq[3] = {0.4360,0.8645,1.2578}; /* q-axis reactance Xq(1) set to 0.4360, value given in text 0.0969 */
35: const PetscScalar Xqp[3] = {0.0969,0.1969,0.25}; /* q-axis transient reactance */
36: const PetscScalar Td0p[3] = {8.96,6.0,5.89}; /* d-axis open circuit time constant */
37: const PetscScalar Tq0p[3] = {0.31,0.535,0.6}; /* q-axis open circuit time constant */
38: PetscScalar M[3]; /* M = 2*H/w_s */
39: PetscScalar D[3]; /* D = 0.1*M */
41: PetscScalar TM[3]; /* Mechanical Torque */
42: /* Exciter system constants */
43: const PetscScalar KA[3] = {20.0,20.0,20.0}; /* Voltage regulartor gain constant */
44: const PetscScalar TA[3] = {0.2,0.2,0.2}; /* Voltage regulator time constant */
45: const PetscScalar KE[3] = {1.0,1.0,1.0}; /* Exciter gain constant */
46: const PetscScalar TE[3] = {0.314,0.314,0.314}; /* Exciter time constant */
47: const PetscScalar KF[3] = {0.063,0.063,0.063}; /* Feedback stabilizer gain constant */
48: const PetscScalar TF[3] = {0.35,0.35,0.35}; /* Feedback stabilizer time constant */
49: const PetscScalar k1[3] = {0.0039,0.0039,0.0039};
50: const PetscScalar k2[3] = {1.555,1.555,1.555}; /* k1 and k2 for calculating the saturation function SE = k1*exp(k2*Efd) */
52: PetscScalar Vref[3];
53: /* Load constants
54: We use a composite load model that describes the load and reactive powers at each time instant as follows
55: P(t) = \sum\limits_{i=0}^ld_nsegsp \ld_alphap_i*P_D0(\frac{V_m(t)}{V_m0})^\ld_betap_i
56: Q(t) = \sum\limits_{i=0}^ld_nsegsq \ld_alphaq_i*Q_D0(\frac{V_m(t)}{V_m0})^\ld_betaq_i
57: where
58: ld_nsegsp,ld_nsegsq - Number of individual load models for real and reactive power loads
59: ld_alphap,ld_alphap - Percentage contribution (weights) or loads
60: P_D0 - Real power load
61: Q_D0 - Reactive power load
62: V_m(t) - Voltage magnitude at time t
63: V_m0 - Voltage magnitude at t = 0
64: ld_betap, ld_betaq - exponents describing the load model for real and reactive part
66: Note: All loads have the same characteristic currently.
67: */
68: const PetscScalar PD0[3] = {1.25,0.9,1.0};
69: const PetscScalar QD0[3] = {0.5,0.3,0.35};
70: const PetscInt ld_nsegsp[3] = {3,3,3};
71: const PetscScalar ld_alphap[3] = {1.0,0.0,0.0};
72: const PetscScalar ld_betap[3] = {2.0,1.0,0.0};
73: const PetscInt ld_nsegsq[3] = {3,3,3};
74: const PetscScalar ld_alphaq[3] = {1.0,0.0,0.0};
75: const PetscScalar ld_betaq[3] = {2.0,1.0,0.0};
77: typedef struct {
78: DM dmgen, dmnet; /* DMs to manage generator and network subsystem */
79: DM dmpgrid; /* Composite DM to manage the entire power grid */
80: Mat Ybus; /* Network admittance matrix */
81: Vec V0; /* Initial voltage vector (Power flow solution) */
82: PetscReal tfaulton,tfaultoff; /* Fault on and off times */
83: PetscInt faultbus; /* Fault bus */
84: PetscScalar Rfault;
85: PetscReal t0,tmax;
86: PetscInt neqs_gen,neqs_net,neqs_pgrid;
87: Mat Sol; /* Matrix to save solution at each time step */
88: PetscInt stepnum;
89: PetscBool alg_flg;
90: PetscReal t;
91: IS is_diff; /* indices for differential equations */
92: IS is_alg; /* indices for algebraic equations */
93: PetscReal freq_u,freq_l; /* upper and lower frequency limit */
94: PetscInt pow; /* power coefficient used in the cost function */
95: Vec vec_q;
96: } Userctx;
99: /* Converts from machine frame (dq) to network (phase a real,imag) reference frame */
102: PetscErrorCode dq2ri(PetscScalar Fd,PetscScalar Fq,PetscScalar delta,PetscScalar *Fr, PetscScalar *Fi)
103: {
105: *Fr = Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
106: *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
107: return(0);
108: }
110: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
113: PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd, PetscScalar *Fq)
114: {
116: *Fd = Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
117: *Fq = Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
118: return(0);
119: }
123: PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
124: {
126: Vec Xgen,Xnet;
127: PetscScalar *xgen,*xnet;
128: PetscInt i,idx=0;
129: PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
130: PetscScalar Eqp,Edp,delta;
131: PetscScalar Efd,RF,VR; /* Exciter variables */
132: PetscScalar Id,Iq; /* Generator dq axis currents */
133: PetscScalar theta,Vd,Vq,SE;
136: M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
137: D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
139: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
141: /* Network subsystem initialization */
142: VecCopy(user->V0,Xnet);
144: /* Generator subsystem initialization */
145: VecGetArray(Xgen,&xgen);
146: VecGetArray(Xnet,&xnet);
148: for (i=0; i < ngen; i++) {
149: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
150: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
151: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
152: IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
153: IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;
155: delta = atan2(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
157: theta = PETSC_PI/2.0 - delta;
159: Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
160: Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
162: Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
163: Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
165: Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
166: Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
168: TM[i] = PG[i];
170: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
171: xgen[idx] = Eqp;
172: xgen[idx+1] = Edp;
173: xgen[idx+2] = delta;
174: xgen[idx+3] = w_s;
176: idx = idx + 4;
178: xgen[idx] = Id;
179: xgen[idx+1] = Iq;
181: idx = idx + 2;
183: /* Exciter */
184: Efd = Eqp + (Xd[i] - Xdp[i])*Id;
185: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
186: VR = KE[i]*Efd + SE;
187: RF = KF[i]*Efd/TF[i];
189: xgen[idx] = Efd;
190: xgen[idx+1] = RF;
191: xgen[idx+2] = VR;
193: Vref[i] = Vm + (VR/KA[i]);
195: idx = idx + 3;
196: }
198: VecRestoreArray(Xgen,&xgen);
199: VecRestoreArray(Xnet,&xnet);
201: /* VecView(Xgen,0); */
202: DMCompositeGather(user->dmpgrid,X,INSERT_VALUES,Xgen,Xnet);
203: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
204: return(0);
205: }
207: /* Computes F = [-f(x,y);g(x,y)] */
210: PetscErrorCode ResidualFunction(SNES snes,Vec X, Vec F, Userctx *user)
211: {
213: Vec Xgen,Xnet,Fgen,Fnet;
214: PetscScalar *xgen,*xnet,*fgen,*fnet;
215: PetscInt i,idx=0;
216: PetscScalar Vr,Vi,Vm,Vm2;
217: PetscScalar Eqp,Edp,delta,w; /* Generator variables */
218: PetscScalar Efd,RF,VR; /* Exciter variables */
219: PetscScalar Id,Iq; /* Generator dq axis currents */
220: PetscScalar Vd,Vq,SE;
221: PetscScalar IGr,IGi,IDr,IDi;
222: PetscScalar Zdq_inv[4],det;
223: PetscScalar PD,QD,Vm0,*v0;
224: PetscInt k;
227: VecZeroEntries(F);
228: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
229: DMCompositeGetLocalVectors(user->dmpgrid,&Fgen,&Fnet);
230: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
231: DMCompositeScatter(user->dmpgrid,F,Fgen,Fnet);
233: /* Network current balance residual IG + Y*V + IL = 0. Only YV is added here.
234: The generator current injection, IG, and load current injection, ID are added later
235: */
236: /* Note that the values in Ybus are stored assuming the imaginary current balance
237: equation is ordered first followed by real current balance equation for each bus.
238: Thus imaginary current contribution goes in location 2*i, and
239: real current contribution in 2*i+1
240: */
241: MatMult(user->Ybus,Xnet,Fnet);
243: VecGetArray(Xgen,&xgen);
244: VecGetArray(Xnet,&xnet);
245: VecGetArray(Fgen,&fgen);
246: VecGetArray(Fnet,&fnet);
248: /* Generator subsystem */
249: for (i=0; i < ngen; i++) {
250: Eqp = xgen[idx];
251: Edp = xgen[idx+1];
252: delta = xgen[idx+2];
253: w = xgen[idx+3];
254: Id = xgen[idx+4];
255: Iq = xgen[idx+5];
256: Efd = xgen[idx+6];
257: RF = xgen[idx+7];
258: VR = xgen[idx+8];
260: /* Generator differential equations */
261: fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i];
262: fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i];
263: fgen[idx+2] = -w + w_s;
264: fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i];
266: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
267: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
269: ri2dq(Vr,Vi,delta,&Vd,&Vq);
270: /* Algebraic equations for stator currents */
271: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
273: Zdq_inv[0] = Rs[i]/det;
274: Zdq_inv[1] = Xqp[i]/det;
275: Zdq_inv[2] = -Xdp[i]/det;
276: Zdq_inv[3] = Rs[i]/det;
278: fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id;
279: fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq;
281: /* Add generator current injection to network */
282: dq2ri(Id,Iq,delta,&IGr,&IGi);
284: fnet[2*gbus[i]] -= IGi;
285: fnet[2*gbus[i]+1] -= IGr;
287: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq); Vm2 = Vm*Vm;
289: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
291: /* Exciter differential equations */
292: fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i];
293: fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i];
294: fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
296: idx = idx + 9;
297: }
299: VecGetArray(user->V0,&v0);
300: for (i=0; i < nload; i++) {
301: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
302: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
303: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
304: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
305: PD = QD = 0.0;
306: for (k=0; k < ld_nsegsp[i]; k++) PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
307: for (k=0; k < ld_nsegsq[i]; k++) QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
309: /* Load currents */
310: IDr = (PD*Vr + QD*Vi)/Vm2;
311: IDi = (-QD*Vr + PD*Vi)/Vm2;
313: fnet[2*lbus[i]] += IDi;
314: fnet[2*lbus[i]+1] += IDr;
315: }
316: VecRestoreArray(user->V0,&v0);
318: VecRestoreArray(Xgen,&xgen);
319: VecRestoreArray(Xnet,&xnet);
320: VecRestoreArray(Fgen,&fgen);
321: VecRestoreArray(Fnet,&fnet);
323: DMCompositeGather(user->dmpgrid,F,INSERT_VALUES,Fgen,Fnet);
324: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
325: DMCompositeRestoreLocalVectors(user->dmpgrid,&Fgen,&Fnet);
326: return(0);
327: }
329: /* \dot{x} - f(x,y)
330: g(x,y) = 0
331: */
334: PetscErrorCode IFunction(TS ts,PetscReal t, Vec X, Vec Xdot, Vec F, Userctx *user)
335: {
336: PetscErrorCode ierr;
337: SNES snes;
338: PetscScalar *f;
339: const PetscScalar *xdot;
340: PetscInt i;
343: user->t = t;
345: TSGetSNES(ts,&snes);
346: ResidualFunction(snes,X,F,user);
347: VecGetArray(F,&f);
348: VecGetArrayRead(Xdot,&xdot);
349: for (i=0;i < ngen;i++) {
350: f[9*i] += xdot[9*i];
351: f[9*i+1] += xdot[9*i+1];
352: f[9*i+2] += xdot[9*i+2];
353: f[9*i+3] += xdot[9*i+3];
354: f[9*i+6] += xdot[9*i+6];
355: f[9*i+7] += xdot[9*i+7];
356: f[9*i+8] += xdot[9*i+8];
357: }
358: VecRestoreArray(F,&f);
359: VecRestoreArrayRead(Xdot,&xdot);
360: return(0);
361: }
363: /* This function is used for solving the algebraic system only during fault on and
364: off times. It computes the entire F and then zeros out the part corresponding to
365: differential equations
366: F = [0;g(y)];
367: */
370: PetscErrorCode AlgFunction(SNES snes, Vec X, Vec F, void *ctx)
371: {
373: Userctx *user=(Userctx*)ctx;
374: PetscScalar *f;
375: PetscInt i;
378: ResidualFunction(snes,X,F,user);
379: VecGetArray(F,&f);
380: for (i=0; i < ngen; i++) {
381: f[9*i] = 0;
382: f[9*i+1] = 0;
383: f[9*i+2] = 0;
384: f[9*i+3] = 0;
385: f[9*i+6] = 0;
386: f[9*i+7] = 0;
387: f[9*i+8] = 0;
388: }
389: VecRestoreArray(F,&f);
390: return(0);
391: }
395: PetscErrorCode PreallocateJacobian(Mat J, Userctx *user)
396: {
398: PetscInt *d_nnz;
399: PetscInt i,idx=0,start=0;
400: PetscInt ncols;
403: PetscMalloc1(user->neqs_pgrid,&d_nnz);
404: for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
405: /* Generator subsystem */
406: for (i=0; i < ngen; i++) {
408: d_nnz[idx] += 3;
409: d_nnz[idx+1] += 2;
410: d_nnz[idx+2] += 2;
411: d_nnz[idx+3] += 5;
412: d_nnz[idx+4] += 6;
413: d_nnz[idx+5] += 6;
415: d_nnz[user->neqs_gen+2*gbus[i]] += 3;
416: d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;
418: d_nnz[idx+6] += 2;
419: d_nnz[idx+7] += 2;
420: d_nnz[idx+8] += 5;
422: idx = idx + 9;
423: }
425: start = user->neqs_gen;
427: for (i=0; i < nbus; i++) {
428: MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL);
429: d_nnz[start+2*i] += ncols;
430: d_nnz[start+2*i+1] += ncols;
431: MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL);
432: }
434: MatSeqAIJSetPreallocation(J,0,d_nnz);
436: PetscFree(d_nnz);
437: return(0);
438: }
440: /*
441: J = [-df_dx, -df_dy
442: dg_dx, dg_dy]
443: */
446: PetscErrorCode ResidualJacobian(SNES snes,Vec X,Mat J,Mat B,void *ctx)
447: {
448: PetscErrorCode ierr;
449: Userctx *user=(Userctx*)ctx;
450: Vec Xgen,Xnet;
451: PetscScalar *xgen,*xnet;
452: PetscInt i,idx=0;
453: PetscScalar Vr,Vi,Vm,Vm2;
454: PetscScalar Eqp,Edp,delta; /* Generator variables */
455: PetscScalar Efd; /* Exciter variables */
456: PetscScalar Id,Iq; /* Generator dq axis currents */
457: PetscScalar Vd,Vq;
458: PetscScalar val[10];
459: PetscInt row[2],col[10];
460: PetscInt net_start=user->neqs_gen;
461: PetscScalar Zdq_inv[4],det;
462: PetscScalar dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
463: PetscScalar dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
464: PetscScalar dSE_dEfd;
465: PetscScalar dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
466: PetscInt ncols;
467: const PetscInt *cols;
468: const PetscScalar *yvals;
469: PetscInt k;
470: PetscScalar PD,QD,Vm0,*v0,Vm4;
471: PetscScalar dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
472: PetscScalar dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;
475: MatZeroEntries(B);
476: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
477: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
479: VecGetArray(Xgen,&xgen);
480: VecGetArray(Xnet,&xnet);
482: /* Generator subsystem */
483: for (i=0; i < ngen; i++) {
484: Eqp = xgen[idx];
485: Edp = xgen[idx+1];
486: delta = xgen[idx+2];
487: Id = xgen[idx+4];
488: Iq = xgen[idx+5];
489: Efd = xgen[idx+6];
491: /* fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i]; */
492: row[0] = idx;
493: col[0] = idx; col[1] = idx+4; col[2] = idx+6;
494: val[0] = 1/ Td0p[i]; val[1] = (Xd[i] - Xdp[i])/ Td0p[i]; val[2] = -1/Td0p[i];
496: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
498: /* fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
499: row[0] = idx + 1;
500: col[0] = idx + 1; col[1] = idx+5;
501: val[0] = 1/Tq0p[i]; val[1] = -(Xq[i] - Xqp[i])/Tq0p[i];
502: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
504: /* fgen[idx+2] = - w + w_s; */
505: row[0] = idx + 2;
506: col[0] = idx + 2; col[1] = idx + 3;
507: val[0] = 0; val[1] = -1;
508: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
510: /* fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i]; */
511: row[0] = idx + 3;
512: col[0] = idx; col[1] = idx + 1; col[2] = idx + 3; col[3] = idx + 4; col[4] = idx + 5;
513: 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];
514: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
516: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
517: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
518: ri2dq(Vr,Vi,delta,&Vd,&Vq);
520: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
522: Zdq_inv[0] = Rs[i]/det;
523: Zdq_inv[1] = Xqp[i]/det;
524: Zdq_inv[2] = -Xdp[i]/det;
525: Zdq_inv[3] = Rs[i]/det;
527: dVd_dVr = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
528: dVq_dVr = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
529: dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
530: dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);
532: /* fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
533: row[0] = idx+4;
534: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
535: val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0]; val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
536: col[3] = idx + 4; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
537: 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;
538: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
540: /* fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
541: row[0] = idx+5;
542: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
543: val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2]; val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
544: col[3] = idx + 5; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
545: 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;
546: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
548: dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
549: dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
550: dIGr_dId = PetscSinScalar(delta); dIGr_dIq = PetscCosScalar(delta);
551: dIGi_dId = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);
553: /* fnet[2*gbus[i]] -= IGi; */
554: row[0] = net_start + 2*gbus[i];
555: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
556: val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
557: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
559: /* fnet[2*gbus[i]+1] -= IGr; */
560: row[0] = net_start + 2*gbus[i]+1;
561: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
562: val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
563: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
565: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq); Vm2 = Vm*Vm;
567: /* fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i]; */
568: /* SE = k1[i]*PetscExpScalar(k2[i]*Efd); */
570: dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);
572: row[0] = idx + 6;
573: col[0] = idx + 6; col[1] = idx + 8;
574: val[0] = (KE[i] + dSE_dEfd)/TE[i]; val[1] = -1/TE[i];
575: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
577: /* Exciter differential equations */
579: /* fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i]; */
580: row[0] = idx + 7;
581: col[0] = idx + 6; col[1] = idx + 7;
582: val[0] = (-KF[i]/TF[i])/TF[i]; val[1] = 1/TF[i];
583: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
585: /* fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i]; */
586: /* Vm = (Vd^2 + Vq^2)^0.5; */
587: dVm_dVd = Vd/Vm; dVm_dVq = Vq/Vm;
588: dVm_dVr = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
589: dVm_dVi = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
590: row[0] = idx + 8;
591: col[0] = idx + 6; col[1] = idx + 7; col[2] = idx + 8;
592: val[0] = (KA[i]*KF[i]/TF[i])/TA[i]; val[1] = -KA[i]/TA[i]; val[2] = 1/TA[i];
593: col[3] = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
594: val[3] = KA[i]*dVm_dVr/TA[i]; val[4] = KA[i]*dVm_dVi/TA[i];
595: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
596: idx = idx + 9;
597: }
600: for (i=0; i<nbus; i++) {
601: MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
602: row[0] = net_start + 2*i;
603: for (k=0; k<ncols; k++) {
604: col[k] = net_start + cols[k];
605: val[k] = yvals[k];
606: }
607: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
608: MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);
610: MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
611: row[0] = net_start + 2*i+1;
612: for (k=0; k<ncols; k++) {
613: col[k] = net_start + cols[k];
614: val[k] = yvals[k];
615: }
616: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
617: MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
618: }
620: MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
621: MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);
623: VecGetArray(user->V0,&v0);
624: for (i=0; i < nload; i++) {
625: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
626: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
627: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm; Vm4 = Vm2*Vm2;
628: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
629: PD = QD = 0.0;
630: dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
631: for (k=0; k < ld_nsegsp[i]; k++) {
632: PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
633: dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
634: dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
635: }
636: for (k=0; k < ld_nsegsq[i]; k++) {
637: QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
638: dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
639: dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
640: }
642: /* IDr = (PD*Vr + QD*Vi)/Vm2; */
643: /* IDi = (-QD*Vr + PD*Vi)/Vm2; */
645: dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
646: dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;
648: dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
649: dIDi_dVi = (-dQD_dVi*Vr + dPD_dVi*Vi + PD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vi)/Vm4;
652: /* fnet[2*lbus[i]] += IDi; */
653: row[0] = net_start + 2*lbus[i];
654: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
655: val[0] = dIDi_dVr; val[1] = dIDi_dVi;
656: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
657: /* fnet[2*lbus[i]+1] += IDr; */
658: row[0] = net_start + 2*lbus[i]+1;
659: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
660: val[0] = dIDr_dVr; val[1] = dIDr_dVi;
661: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
662: }
663: VecRestoreArray(user->V0,&v0);
665: VecRestoreArray(Xgen,&xgen);
666: VecRestoreArray(Xnet,&xnet);
668: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
670: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
671: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
672: return(0);
673: }
675: /*
676: J = [I, 0
677: dg_dx, dg_dy]
678: */
681: PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
682: {
684: Userctx *user=(Userctx*)ctx;
687: ResidualJacobian(snes,X,A,B,ctx);
688: MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
689: MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);
690: return(0);
691: }
693: /*
694: J = [a*I-df_dx, -df_dy
695: dg_dx, dg_dy]
696: */
700: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
701: {
703: SNES snes;
704: PetscScalar atmp = (PetscScalar) a;
705: PetscInt i,row;
708: user->t = t;
710: TSGetSNES(ts,&snes);
711: ResidualJacobian(snes,X,A,B,user);
712: for (i=0;i < ngen;i++) {
713: row = 9*i;
714: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
715: row = 9*i+1;
716: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
717: row = 9*i+2;
718: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
719: row = 9*i+3;
720: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
721: row = 9*i+6;
722: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
723: row = 9*i+7;
724: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
725: row = 9*i+8;
726: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
727: }
728: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
729: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
730: return(0);
731: }
735: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,Userctx *user)
736: {
737: PetscErrorCode ierr;
738: PetscScalar *r;
739: const PetscScalar *u;
740: PetscInt idx;
741: Vec Xgen,Xnet;
742: PetscScalar *xgen;
743: PetscInt i;
746: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
747: DMCompositeScatter(user->dmpgrid,U,Xgen,Xnet);
749: VecGetArray(Xgen,&xgen);
751: VecGetArrayRead(U,&u);
752: VecGetArray(R,&r);
753: r[0] = 0.;
755: idx = 0;
756: for (i=0;i<ngen;i++) {
757: r[0] += PetscPowScalarInt(PetscMax(0.,PetscMax(xgen[idx+3]/(2.*PETSC_PI)-user->freq_u,user->freq_l-xgen[idx+3]/(2.*PETSC_PI))),user->pow);
758: idx += 9;
759: }
760: VecRestoreArray(R,&r);
761: VecRestoreArrayRead(U,&u);
762: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
763: return(0);
764: }
768: static PetscErrorCode MonitorUpdateQ(TS ts,PetscInt stepnum,PetscReal time,Vec X,void *ctx0)
769: {
771: Vec C,*Y;
772: PetscInt Nr;
773: PetscReal h,theta;
774: Userctx *ctx=(Userctx*)ctx0;
777: theta = 0.5;
778: TSGetStages(ts,&Nr,&Y);
779: TSGetTimeStep(ts,&h);
780: VecDuplicate(ctx->vec_q,&C);
781: /* compute integrals */
782: if (stepnum>0) {
783: CostIntegrand(ts,time,X,C,ctx);
784: VecAXPY(ctx->vec_q,h*theta,C);
785: CostIntegrand(ts,time+h*theta,Y[0],C,ctx);
786: VecAXPY(ctx->vec_q,h*(1-theta),C);
787: }
788: VecDestroy(&C);
789: return(0);
790: }
794: int main(int argc,char **argv)
795: {
796: Userctx user;
797: Vec p;
798: PetscScalar *x_ptr;
799: PetscErrorCode ierr;
800: PetscMPIInt size;
801: PetscInt i;
802: KSP ksp;
803: PC pc;
804: PetscInt *idx2;
805: Tao tao;
806: Vec lowerb,upperb;
809: PetscInitialize(&argc,&argv,"petscoptions",help);
810: MPI_Comm_size(PETSC_COMM_WORLD,&size);
811: if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
813: VecCreateSeq(PETSC_COMM_WORLD,1,&user.vec_q);
815: user.neqs_gen = 9*ngen; /* # eqs. for generator subsystem */
816: user.neqs_net = 2*nbus; /* # eqs. for network subsystem */
817: user.neqs_pgrid = user.neqs_gen + user.neqs_net;
819: /* Create indices for differential and algebraic equations */
820: PetscMalloc1(7*ngen,&idx2);
821: for (i=0; i<ngen; i++) {
822: 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;
823: idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
824: }
825: ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
826: ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
827: PetscFree(idx2);
829: /* Set run time options */
830: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Transient stability fault options","");
831: {
832: user.tfaulton = 1.0;
833: user.tfaultoff = 1.2;
834: user.Rfault = 0.0001;
835: user.faultbus = 8;
836: PetscOptionsReal("-tfaulton","","",user.tfaulton,&user.tfaulton,NULL);
837: PetscOptionsReal("-tfaultoff","","",user.tfaultoff,&user.tfaultoff,NULL);
838: PetscOptionsInt("-faultbus","","",user.faultbus,&user.faultbus,NULL);
839: user.t0 = 0.0;
840: user.tmax = 1.5;
841: PetscOptionsReal("-t0","","",user.t0,&user.t0,NULL);
842: PetscOptionsReal("-tmax","","",user.tmax,&user.tmax,NULL);
843: user.freq_u = 61.0;
844: user.freq_l = 59.0;
845: user.pow = 2;
846: PetscOptionsReal("-frequ","","",user.freq_u,&user.freq_u,NULL);
847: PetscOptionsReal("-freql","","",user.freq_l,&user.freq_l,NULL);
848: PetscOptionsInt("-pow","","",user.pow,&user.pow,NULL);
850: }
851: PetscOptionsEnd();
853: /* Create DMs for generator and network subsystems */
854: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
855: DMSetOptionsPrefix(user.dmgen,"dmgen_");
856: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
857: DMSetOptionsPrefix(user.dmnet,"dmnet_");
858: /* Create a composite DM packer and add the two DMs */
859: DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
860: DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
861: DMCompositeAddDM(user.dmpgrid,user.dmgen);
862: DMCompositeAddDM(user.dmpgrid,user.dmnet);
864: /* Create TAO solver and set desired solution method */
865: TaoCreate(PETSC_COMM_WORLD,&tao);
866: TaoSetType(tao,TAOBLMVM);
867: /*
868: Optimization starts
869: */
870: /* Set initial solution guess */
871: VecCreateSeq(PETSC_COMM_WORLD,3,&p);
872: VecGetArray(p,&x_ptr);
873: x_ptr[0] = PG[0]; x_ptr[1] = PG[1]; x_ptr[2] = PG[2];
874: VecRestoreArray(p,&x_ptr);
876: TaoSetInitialVector(tao,p);
877: /* Set routine for function and gradient evaluation */
878: TaoSetObjectiveRoutine(tao,FormFunction,(void *)&user);
879: TaoSetGradientRoutine(tao,TaoDefaultComputeGradient,(void *)&user);
881: /* Set bounds for the optimization */
882: VecDuplicate(p,&lowerb);
883: VecDuplicate(p,&upperb);
884: VecGetArray(lowerb,&x_ptr);
885: x_ptr[0] = 0.5; x_ptr[1] = 0.5; x_ptr[2] = 0.5;
886: VecRestoreArray(lowerb,&x_ptr);
887: VecGetArray(upperb,&x_ptr);
888: x_ptr[0] = 2.0; x_ptr[1] = 2.0; x_ptr[2] = 2.0;
889: VecRestoreArray(upperb,&x_ptr);
890: TaoSetVariableBounds(tao,lowerb,upperb);
892: /* Check for any TAO command line options */
893: TaoSetFromOptions(tao);
894: TaoGetKSP(tao,&ksp);
895: if (ksp) {
896: KSPGetPC(ksp,&pc);
897: PCSetType(pc,PCNONE);
898: }
900: /* SOLVE THE APPLICATION */
901: TaoSolve(tao);
903: VecView(p,PETSC_VIEWER_STDOUT_WORLD);
904: /* Free TAO data structures */
905: TaoDestroy(&tao);
906: VecDestroy(&user.vec_q);
907: VecDestroy(&lowerb);
908: VecDestroy(&upperb);
909: VecDestroy(&p);
910: DMDestroy(&user.dmgen);
911: DMDestroy(&user.dmnet);
912: DMDestroy(&user.dmpgrid);
913: ISDestroy(&user.is_diff);
914: ISDestroy(&user.is_alg);
915: PetscFinalize();
916: return(0);
917: }
919: /* ------------------------------------------------------------------ */
922: /*
923: FormFunction - Evaluates the function and corresponding gradient.
925: Input Parameters:
926: tao - the Tao context
927: X - the input vector
928: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
930: Output Parameters:
931: f - the newly evaluated function
932: */
933: PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
934: {
935: TS ts;
936: SNES snes_alg;
938: Userctx *ctx = (Userctx*)ctx0;
939: Vec X;
940: Mat J;
941: /* sensitivity context */
942: PetscScalar *x_ptr;
943: PetscViewer Xview,Ybusview;
944: Vec F_alg;
945: Vec Xdot;
946: PetscInt row_loc,col_loc;
947: PetscScalar val;
949: VecGetArray(P,&x_ptr);
950: PG[0] = x_ptr[0];
951: PG[1] = x_ptr[1];
952: PG[2] = x_ptr[2];
953: VecRestoreArray(P,&x_ptr);
955: ctx->stepnum = 0;
957: VecZeroEntries(ctx->vec_q);
959: /* Read initial voltage vector and Ybus */
960: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
961: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);
963: VecCreate(PETSC_COMM_WORLD,&ctx->V0);
964: VecSetSizes(ctx->V0,PETSC_DECIDE,ctx->neqs_net);
965: VecLoad(ctx->V0,Xview);
967: MatCreate(PETSC_COMM_WORLD,&ctx->Ybus);
968: MatSetSizes(ctx->Ybus,PETSC_DECIDE,PETSC_DECIDE,ctx->neqs_net,ctx->neqs_net);
969: MatSetType(ctx->Ybus,MATBAIJ);
970: /* MatSetBlockSize(ctx->Ybus,2); */
971: MatLoad(ctx->Ybus,Ybusview);
973: PetscViewerDestroy(&Xview);
974: PetscViewerDestroy(&Ybusview);
976: DMCreateGlobalVector(ctx->dmpgrid,&X);
978: MatCreate(PETSC_COMM_WORLD,&J);
979: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,ctx->neqs_pgrid,ctx->neqs_pgrid);
980: MatSetFromOptions(J);
981: PreallocateJacobian(J,ctx);
983: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
984: Create timestepping solver context
985: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
986: TSCreate(PETSC_COMM_WORLD,&ts);
987: TSSetProblemType(ts,TS_NONLINEAR);
988: TSSetType(ts,TSCN);
989: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,ctx);
990: TSSetIJacobian(ts,J,J,(TSIJacobian)IJacobian,ctx);
991: TSSetApplicationContext(ts,ctx);
993: TSMonitorSet(ts,MonitorUpdateQ,ctx,NULL);
994: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
995: Set initial conditions
996: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
997: SetInitialGuess(X,ctx);
999: VecDuplicate(X,&F_alg);
1000: SNESCreate(PETSC_COMM_WORLD,&snes_alg);
1001: SNESSetFunction(snes_alg,F_alg,AlgFunction,ctx);
1002: MatZeroEntries(J);
1003: SNESSetJacobian(snes_alg,J,J,AlgJacobian,ctx);
1004: SNESSetOptionsPrefix(snes_alg,"alg_");
1005: SNESSetFromOptions(snes_alg);
1006: ctx->alg_flg = PETSC_TRUE;
1007: /* Solve the algebraic equations */
1008: SNESSolve(snes_alg,NULL,X);
1010: /* Just to set up the Jacobian structure */
1011: VecDuplicate(X,&Xdot);
1012: IJacobian(ts,0.0,X,Xdot,0.0,J,J,ctx);
1013: VecDestroy(&Xdot);
1015: ctx->stepnum++;
1017: TSSetDuration(ts,1000,ctx->tfaulton);
1018: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
1019: TSSetInitialTimeStep(ts,0.0,0.01);
1020: TSSetFromOptions(ts);
1021: /* TSSetPostStep(ts,SaveSolution); */
1023: ctx->alg_flg = PETSC_FALSE;
1024: /* Prefault period */
1025: TSSolve(ts,X);
1027: /* Create the nonlinear solver for solving the algebraic system */
1028: /* Note that although the algebraic system needs to be solved only for
1029: Idq and V, we reuse the entire system including xgen. The xgen
1030: variables are held constant by setting their residuals to 0 and
1031: putting a 1 on the Jacobian diagonal for xgen rows
1032: */
1033: MatZeroEntries(J);
1035: /* Apply disturbance - resistive fault at ctx->faultbus */
1036: /* This is done by adding shunt conductance to the diagonal location
1037: in the Ybus matrix */
1038: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
1039: val = 1/ctx->Rfault;
1040: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1041: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
1042: val = 1/ctx->Rfault;
1043: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1045: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1046: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1048: ctx->alg_flg = PETSC_TRUE;
1049: /* Solve the algebraic equations */
1050: SNESSolve(snes_alg,NULL,X);
1052: ctx->stepnum++;
1054: /* Disturbance period */
1055: TSSetDuration(ts,1000,ctx->tfaultoff);
1056: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
1057: TSSetInitialTimeStep(ts,ctx->tfaulton,.01);
1059: ctx->alg_flg = PETSC_FALSE;
1061: TSSolve(ts,X);
1063: /* Remove the fault */
1064: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1;
1065: val = -1/ctx->Rfault;
1066: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1067: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus;
1068: val = -1/ctx->Rfault;
1069: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1071: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1072: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1074: MatZeroEntries(J);
1076: ctx->alg_flg = PETSC_TRUE;
1078: /* Solve the algebraic equations */
1079: SNESSolve(snes_alg,NULL,X);
1081: ctx->stepnum++;
1083: /* Post-disturbance period */
1084: TSSetDuration(ts,1000,ctx->tmax);
1085: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
1086: TSSetInitialTimeStep(ts,ctx->tfaultoff,.01);
1088: ctx->alg_flg = PETSC_TRUE;
1090: TSSolve(ts,X);
1091: VecGetArray(ctx->vec_q,&x_ptr);
1092: *f = x_ptr[0];
1093: VecRestoreArray(ctx->vec_q,&x_ptr);
1095: MatDestroy(&ctx->Ybus);
1096: VecDestroy(&ctx->V0);
1097: SNESDestroy(&snes_alg);
1098: VecDestroy(&F_alg);
1099: MatDestroy(&J);
1100: VecDestroy(&X);
1101: TSDestroy(&ts);
1103: return 0;
1104: }