Actual source code: ex9busoptfd.c
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;
98: /* Converts from machine frame (dq) to network (phase a real,imag) reference frame */
99: PetscErrorCode dq2ri(PetscScalar Fd,PetscScalar Fq,PetscScalar delta,PetscScalar *Fr, PetscScalar *Fi)
100: {
101: *Fr = Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
102: *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
103: return 0;
104: }
106: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
107: PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd, PetscScalar *Fq)
108: {
109: *Fd = Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
110: *Fq = Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
111: return 0;
112: }
114: PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
115: {
116: Vec Xgen,Xnet;
117: PetscScalar *xgen,*xnet;
118: PetscInt i,idx=0;
119: PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
120: PetscScalar Eqp,Edp,delta;
121: PetscScalar Efd,RF,VR; /* Exciter variables */
122: PetscScalar Id,Iq; /* Generator dq axis currents */
123: PetscScalar theta,Vd,Vq,SE;
125: M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
126: D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
128: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
130: /* Network subsystem initialization */
131: VecCopy(user->V0,Xnet);
133: /* Generator subsystem initialization */
134: VecGetArray(Xgen,&xgen);
135: VecGetArray(Xnet,&xnet);
137: for (i=0; i < ngen; i++) {
138: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
139: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
140: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
141: IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
142: IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;
144: delta = PetscAtan2Real(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
146: theta = PETSC_PI/2.0 - delta;
148: Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
149: Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
151: Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
152: Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
154: Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
155: Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
157: TM[i] = PG[i];
159: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
160: xgen[idx] = Eqp;
161: xgen[idx+1] = Edp;
162: xgen[idx+2] = delta;
163: xgen[idx+3] = w_s;
165: idx = idx + 4;
167: xgen[idx] = Id;
168: xgen[idx+1] = Iq;
170: idx = idx + 2;
172: /* Exciter */
173: Efd = Eqp + (Xd[i] - Xdp[i])*Id;
174: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
175: VR = KE[i]*Efd + SE;
176: RF = KF[i]*Efd/TF[i];
178: xgen[idx] = Efd;
179: xgen[idx+1] = RF;
180: xgen[idx+2] = VR;
182: Vref[i] = Vm + (VR/KA[i]);
184: idx = idx + 3;
185: }
187: VecRestoreArray(Xgen,&xgen);
188: VecRestoreArray(Xnet,&xnet);
190: /* VecView(Xgen,0); */
191: DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet);
192: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
193: return 0;
194: }
196: /* Computes F = [-f(x,y);g(x,y)] */
197: PetscErrorCode ResidualFunction(SNES snes,Vec X, Vec F, Userctx *user)
198: {
199: Vec Xgen,Xnet,Fgen,Fnet;
200: PetscScalar *xgen,*xnet,*fgen,*fnet;
201: PetscInt i,idx=0;
202: PetscScalar Vr,Vi,Vm,Vm2;
203: PetscScalar Eqp,Edp,delta,w; /* Generator variables */
204: PetscScalar Efd,RF,VR; /* Exciter variables */
205: PetscScalar Id,Iq; /* Generator dq axis currents */
206: PetscScalar Vd,Vq,SE;
207: PetscScalar IGr,IGi,IDr,IDi;
208: PetscScalar Zdq_inv[4],det;
209: PetscScalar PD,QD,Vm0,*v0;
210: PetscInt k;
212: VecZeroEntries(F);
213: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
214: DMCompositeGetLocalVectors(user->dmpgrid,&Fgen,&Fnet);
215: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
216: DMCompositeScatter(user->dmpgrid,F,Fgen,Fnet);
218: /* Network current balance residual IG + Y*V + IL = 0. Only YV is added here.
219: The generator current injection, IG, and load current injection, ID are added later
220: */
221: /* Note that the values in Ybus are stored assuming the imaginary current balance
222: equation is ordered first followed by real current balance equation for each bus.
223: Thus imaginary current contribution goes in location 2*i, and
224: real current contribution in 2*i+1
225: */
226: MatMult(user->Ybus,Xnet,Fnet);
228: VecGetArray(Xgen,&xgen);
229: VecGetArray(Xnet,&xnet);
230: VecGetArray(Fgen,&fgen);
231: VecGetArray(Fnet,&fnet);
233: /* Generator subsystem */
234: for (i=0; i < ngen; i++) {
235: Eqp = xgen[idx];
236: Edp = xgen[idx+1];
237: delta = xgen[idx+2];
238: w = xgen[idx+3];
239: Id = xgen[idx+4];
240: Iq = xgen[idx+5];
241: Efd = xgen[idx+6];
242: RF = xgen[idx+7];
243: VR = xgen[idx+8];
245: /* Generator differential equations */
246: fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i];
247: fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i];
248: fgen[idx+2] = -w + w_s;
249: fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i];
251: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
252: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
254: ri2dq(Vr,Vi,delta,&Vd,&Vq);
255: /* Algebraic equations for stator currents */
256: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
258: Zdq_inv[0] = Rs[i]/det;
259: Zdq_inv[1] = Xqp[i]/det;
260: Zdq_inv[2] = -Xdp[i]/det;
261: Zdq_inv[3] = Rs[i]/det;
263: fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id;
264: fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq;
266: /* Add generator current injection to network */
267: dq2ri(Id,Iq,delta,&IGr,&IGi);
269: fnet[2*gbus[i]] -= IGi;
270: fnet[2*gbus[i]+1] -= IGr;
272: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
274: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
276: /* Exciter differential equations */
277: fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i];
278: fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i];
279: fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
281: idx = idx + 9;
282: }
284: VecGetArray(user->V0,&v0);
285: for (i=0; i < nload; i++) {
286: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
287: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
288: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
289: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
290: PD = QD = 0.0;
291: for (k=0; k < ld_nsegsp[i]; k++) PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
292: for (k=0; k < ld_nsegsq[i]; k++) QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
294: /* Load currents */
295: IDr = (PD*Vr + QD*Vi)/Vm2;
296: IDi = (-QD*Vr + PD*Vi)/Vm2;
298: fnet[2*lbus[i]] += IDi;
299: fnet[2*lbus[i]+1] += IDr;
300: }
301: VecRestoreArray(user->V0,&v0);
303: VecRestoreArray(Xgen,&xgen);
304: VecRestoreArray(Xnet,&xnet);
305: VecRestoreArray(Fgen,&fgen);
306: VecRestoreArray(Fnet,&fnet);
308: DMCompositeGather(user->dmpgrid,INSERT_VALUES,F,Fgen,Fnet);
309: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
310: DMCompositeRestoreLocalVectors(user->dmpgrid,&Fgen,&Fnet);
311: return 0;
312: }
314: /* \dot{x} - f(x,y)
315: g(x,y) = 0
316: */
317: PetscErrorCode IFunction(TS ts,PetscReal t, Vec X, Vec Xdot, Vec F, Userctx *user)
318: {
319: SNES snes;
320: PetscScalar *f;
321: const PetscScalar *xdot;
322: PetscInt i;
324: user->t = t;
326: TSGetSNES(ts,&snes);
327: ResidualFunction(snes,X,F,user);
328: VecGetArray(F,&f);
329: VecGetArrayRead(Xdot,&xdot);
330: for (i=0;i < ngen;i++) {
331: f[9*i] += xdot[9*i];
332: f[9*i+1] += xdot[9*i+1];
333: f[9*i+2] += xdot[9*i+2];
334: f[9*i+3] += xdot[9*i+3];
335: f[9*i+6] += xdot[9*i+6];
336: f[9*i+7] += xdot[9*i+7];
337: f[9*i+8] += xdot[9*i+8];
338: }
339: VecRestoreArray(F,&f);
340: VecRestoreArrayRead(Xdot,&xdot);
341: return 0;
342: }
344: /* This function is used for solving the algebraic system only during fault on and
345: off times. It computes the entire F and then zeros out the part corresponding to
346: differential equations
347: F = [0;g(y)];
348: */
349: PetscErrorCode AlgFunction(SNES snes, Vec X, Vec F, void *ctx)
350: {
351: Userctx *user=(Userctx*)ctx;
352: PetscScalar *f;
353: PetscInt i;
355: ResidualFunction(snes,X,F,user);
356: VecGetArray(F,&f);
357: for (i=0; i < ngen; i++) {
358: f[9*i] = 0;
359: f[9*i+1] = 0;
360: f[9*i+2] = 0;
361: f[9*i+3] = 0;
362: f[9*i+6] = 0;
363: f[9*i+7] = 0;
364: f[9*i+8] = 0;
365: }
366: VecRestoreArray(F,&f);
367: return 0;
368: }
370: PetscErrorCode PreallocateJacobian(Mat J, Userctx *user)
371: {
372: PetscInt *d_nnz;
373: PetscInt i,idx=0,start=0;
374: PetscInt ncols;
376: PetscMalloc1(user->neqs_pgrid,&d_nnz);
377: for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
378: /* Generator subsystem */
379: for (i=0; i < ngen; i++) {
381: d_nnz[idx] += 3;
382: d_nnz[idx+1] += 2;
383: d_nnz[idx+2] += 2;
384: d_nnz[idx+3] += 5;
385: d_nnz[idx+4] += 6;
386: d_nnz[idx+5] += 6;
388: d_nnz[user->neqs_gen+2*gbus[i]] += 3;
389: d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;
391: d_nnz[idx+6] += 2;
392: d_nnz[idx+7] += 2;
393: d_nnz[idx+8] += 5;
395: idx = idx + 9;
396: }
398: start = user->neqs_gen;
400: for (i=0; i < nbus; i++) {
401: MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL);
402: d_nnz[start+2*i] += ncols;
403: d_nnz[start+2*i+1] += ncols;
404: MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL);
405: }
407: MatSeqAIJSetPreallocation(J,0,d_nnz);
409: PetscFree(d_nnz);
410: return 0;
411: }
413: /*
414: J = [-df_dx, -df_dy
415: dg_dx, dg_dy]
416: */
417: PetscErrorCode ResidualJacobian(SNES snes,Vec X,Mat J,Mat B,void *ctx)
418: {
419: Userctx *user=(Userctx*)ctx;
420: Vec Xgen,Xnet;
421: PetscScalar *xgen,*xnet;
422: PetscInt i,idx=0;
423: PetscScalar Vr,Vi,Vm,Vm2;
424: PetscScalar Eqp,Edp,delta; /* Generator variables */
425: PetscScalar Efd; /* Exciter variables */
426: PetscScalar Id,Iq; /* Generator dq axis currents */
427: PetscScalar Vd,Vq;
428: PetscScalar val[10];
429: PetscInt row[2],col[10];
430: PetscInt net_start=user->neqs_gen;
431: PetscScalar Zdq_inv[4],det;
432: PetscScalar dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
433: PetscScalar dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
434: PetscScalar dSE_dEfd;
435: PetscScalar dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
436: PetscInt ncols;
437: const PetscInt *cols;
438: const PetscScalar *yvals;
439: PetscInt k;
440: PetscScalar PD,QD,Vm0,*v0,Vm4;
441: PetscScalar dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
442: PetscScalar dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;
444: MatZeroEntries(B);
445: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
446: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
448: VecGetArray(Xgen,&xgen);
449: VecGetArray(Xnet,&xnet);
451: /* Generator subsystem */
452: for (i=0; i < ngen; i++) {
453: Eqp = xgen[idx];
454: Edp = xgen[idx+1];
455: delta = xgen[idx+2];
456: Id = xgen[idx+4];
457: Iq = xgen[idx+5];
458: Efd = xgen[idx+6];
460: /* fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i]; */
461: row[0] = idx;
462: col[0] = idx; col[1] = idx+4; col[2] = idx+6;
463: val[0] = 1/ Td0p[i]; val[1] = (Xd[i] - Xdp[i])/ Td0p[i]; val[2] = -1/Td0p[i];
465: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
467: /* fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
468: row[0] = idx + 1;
469: col[0] = idx + 1; col[1] = idx+5;
470: val[0] = 1/Tq0p[i]; val[1] = -(Xq[i] - Xqp[i])/Tq0p[i];
471: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
473: /* fgen[idx+2] = - w + w_s; */
474: row[0] = idx + 2;
475: col[0] = idx + 2; col[1] = idx + 3;
476: val[0] = 0; val[1] = -1;
477: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
479: /* fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i]; */
480: row[0] = idx + 3;
481: col[0] = idx; col[1] = idx + 1; col[2] = idx + 3; col[3] = idx + 4; col[4] = idx + 5;
482: 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];
483: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
485: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
486: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
487: ri2dq(Vr,Vi,delta,&Vd,&Vq);
489: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
491: Zdq_inv[0] = Rs[i]/det;
492: Zdq_inv[1] = Xqp[i]/det;
493: Zdq_inv[2] = -Xdp[i]/det;
494: Zdq_inv[3] = Rs[i]/det;
496: dVd_dVr = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
497: dVq_dVr = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
498: dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
499: dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);
501: /* fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
502: row[0] = idx+4;
503: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
504: val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0]; val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
505: col[3] = idx + 4; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
506: 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;
507: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
509: /* fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
510: row[0] = idx+5;
511: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
512: val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2]; val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
513: col[3] = idx + 5; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
514: 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;
515: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
517: dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
518: dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
519: dIGr_dId = PetscSinScalar(delta); dIGr_dIq = PetscCosScalar(delta);
520: dIGi_dId = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);
522: /* fnet[2*gbus[i]] -= IGi; */
523: row[0] = net_start + 2*gbus[i];
524: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
525: val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
526: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
528: /* fnet[2*gbus[i]+1] -= IGr; */
529: row[0] = net_start + 2*gbus[i]+1;
530: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
531: val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
532: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
534: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
536: /* fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i]; */
537: /* SE = k1[i]*PetscExpScalar(k2[i]*Efd); */
539: dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);
541: row[0] = idx + 6;
542: col[0] = idx + 6; col[1] = idx + 8;
543: val[0] = (KE[i] + dSE_dEfd)/TE[i]; val[1] = -1/TE[i];
544: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
546: /* Exciter differential equations */
548: /* fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i]; */
549: row[0] = idx + 7;
550: col[0] = idx + 6; col[1] = idx + 7;
551: val[0] = (-KF[i]/TF[i])/TF[i]; val[1] = 1/TF[i];
552: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
554: /* fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i]; */
555: /* Vm = (Vd^2 + Vq^2)^0.5; */
556: dVm_dVd = Vd/Vm; dVm_dVq = Vq/Vm;
557: dVm_dVr = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
558: dVm_dVi = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
559: row[0] = idx + 8;
560: col[0] = idx + 6; col[1] = idx + 7; col[2] = idx + 8;
561: val[0] = (KA[i]*KF[i]/TF[i])/TA[i]; val[1] = -KA[i]/TA[i]; val[2] = 1/TA[i];
562: col[3] = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
563: val[3] = KA[i]*dVm_dVr/TA[i]; val[4] = KA[i]*dVm_dVi/TA[i];
564: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
565: idx = idx + 9;
566: }
568: for (i=0; i<nbus; i++) {
569: MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
570: row[0] = net_start + 2*i;
571: for (k=0; k<ncols; k++) {
572: col[k] = net_start + cols[k];
573: val[k] = yvals[k];
574: }
575: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
576: MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);
578: MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
579: row[0] = net_start + 2*i+1;
580: for (k=0; k<ncols; k++) {
581: col[k] = net_start + cols[k];
582: val[k] = yvals[k];
583: }
584: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
585: MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
586: }
588: MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
589: MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);
591: VecGetArray(user->V0,&v0);
592: for (i=0; i < nload; i++) {
593: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
594: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
595: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm; Vm4 = Vm2*Vm2;
596: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
597: PD = QD = 0.0;
598: dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
599: for (k=0; k < ld_nsegsp[i]; k++) {
600: PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
601: dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
602: dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
603: }
604: for (k=0; k < ld_nsegsq[i]; k++) {
605: QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
606: dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
607: dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
608: }
610: /* IDr = (PD*Vr + QD*Vi)/Vm2; */
611: /* IDi = (-QD*Vr + PD*Vi)/Vm2; */
613: dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
614: dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;
616: dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
617: dIDi_dVi = (-dQD_dVi*Vr + dPD_dVi*Vi + PD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vi)/Vm4;
619: /* fnet[2*lbus[i]] += IDi; */
620: row[0] = net_start + 2*lbus[i];
621: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
622: val[0] = dIDi_dVr; val[1] = dIDi_dVi;
623: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
624: /* fnet[2*lbus[i]+1] += IDr; */
625: row[0] = net_start + 2*lbus[i]+1;
626: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
627: val[0] = dIDr_dVr; val[1] = dIDr_dVi;
628: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
629: }
630: VecRestoreArray(user->V0,&v0);
632: VecRestoreArray(Xgen,&xgen);
633: VecRestoreArray(Xnet,&xnet);
635: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
637: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
638: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
639: return 0;
640: }
642: /*
643: J = [I, 0
644: dg_dx, dg_dy]
645: */
646: PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
647: {
648: Userctx *user=(Userctx*)ctx;
650: ResidualJacobian(snes,X,A,B,ctx);
651: MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
652: MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);
653: return 0;
654: }
656: /*
657: J = [a*I-df_dx, -df_dy
658: dg_dx, dg_dy]
659: */
661: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
662: {
663: SNES snes;
664: PetscScalar atmp = (PetscScalar) a;
665: PetscInt i,row;
667: user->t = t;
669: TSGetSNES(ts,&snes);
670: ResidualJacobian(snes,X,A,B,user);
671: for (i=0;i < ngen;i++) {
672: row = 9*i;
673: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
674: row = 9*i+1;
675: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
676: row = 9*i+2;
677: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
678: row = 9*i+3;
679: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
680: row = 9*i+6;
681: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
682: row = 9*i+7;
683: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
684: row = 9*i+8;
685: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
686: }
687: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
688: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
689: return 0;
690: }
692: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,Userctx *user)
693: {
694: PetscScalar *r;
695: const PetscScalar *u;
696: PetscInt idx;
697: Vec Xgen,Xnet;
698: PetscScalar *xgen;
699: PetscInt i;
701: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
702: DMCompositeScatter(user->dmpgrid,U,Xgen,Xnet);
704: VecGetArray(Xgen,&xgen);
706: VecGetArrayRead(U,&u);
707: VecGetArray(R,&r);
708: r[0] = 0.;
710: idx = 0;
711: for (i=0;i<ngen;i++) {
712: 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);
713: idx += 9;
714: }
715: VecRestoreArray(R,&r);
716: VecRestoreArrayRead(U,&u);
717: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
718: return 0;
719: }
721: static PetscErrorCode MonitorUpdateQ(TS ts,PetscInt stepnum,PetscReal time,Vec X,void *ctx0)
722: {
723: Vec C,*Y;
724: PetscInt Nr;
725: PetscReal h,theta;
726: Userctx *ctx=(Userctx*)ctx0;
728: theta = 0.5;
729: TSGetStages(ts,&Nr,&Y);
730: TSGetTimeStep(ts,&h);
731: VecDuplicate(ctx->vec_q,&C);
732: /* compute integrals */
733: if (stepnum>0) {
734: CostIntegrand(ts,time,X,C,ctx);
735: VecAXPY(ctx->vec_q,h*theta,C);
736: CostIntegrand(ts,time+h*theta,Y[0],C,ctx);
737: VecAXPY(ctx->vec_q,h*(1-theta),C);
738: }
739: VecDestroy(&C);
740: return 0;
741: }
743: int main(int argc,char **argv)
744: {
745: Userctx user;
746: Vec p;
747: PetscScalar *x_ptr;
748: PetscErrorCode ierr;
749: PetscMPIInt size;
750: PetscInt i;
751: KSP ksp;
752: PC pc;
753: PetscInt *idx2;
754: Tao tao;
755: Vec lowerb,upperb;
758: PetscInitialize(&argc,&argv,"petscoptions",help);
759: MPI_Comm_size(PETSC_COMM_WORLD,&size);
762: VecCreateSeq(PETSC_COMM_WORLD,1,&user.vec_q);
764: user.neqs_gen = 9*ngen; /* # eqs. for generator subsystem */
765: user.neqs_net = 2*nbus; /* # eqs. for network subsystem */
766: user.neqs_pgrid = user.neqs_gen + user.neqs_net;
768: /* Create indices for differential and algebraic equations */
769: PetscMalloc1(7*ngen,&idx2);
770: for (i=0; i<ngen; i++) {
771: 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;
772: idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
773: }
774: ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
775: ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
776: PetscFree(idx2);
778: /* Set run time options */
779: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Transient stability fault options","");
780: {
781: user.tfaulton = 1.0;
782: user.tfaultoff = 1.2;
783: user.Rfault = 0.0001;
784: user.faultbus = 8;
785: PetscOptionsReal("-tfaulton","","",user.tfaulton,&user.tfaulton,NULL);
786: PetscOptionsReal("-tfaultoff","","",user.tfaultoff,&user.tfaultoff,NULL);
787: PetscOptionsInt("-faultbus","","",user.faultbus,&user.faultbus,NULL);
788: user.t0 = 0.0;
789: user.tmax = 1.5;
790: PetscOptionsReal("-t0","","",user.t0,&user.t0,NULL);
791: PetscOptionsReal("-tmax","","",user.tmax,&user.tmax,NULL);
792: user.freq_u = 61.0;
793: user.freq_l = 59.0;
794: user.pow = 2;
795: PetscOptionsReal("-frequ","","",user.freq_u,&user.freq_u,NULL);
796: PetscOptionsReal("-freql","","",user.freq_l,&user.freq_l,NULL);
797: PetscOptionsInt("-pow","","",user.pow,&user.pow,NULL);
799: }
800: PetscOptionsEnd();
802: /* Create DMs for generator and network subsystems */
803: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
804: DMSetOptionsPrefix(user.dmgen,"dmgen_");
805: DMSetFromOptions(user.dmgen);
806: DMSetUp(user.dmgen);
807: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
808: DMSetOptionsPrefix(user.dmnet,"dmnet_");
809: DMSetFromOptions(user.dmnet);
810: DMSetUp(user.dmnet);
811: /* Create a composite DM packer and add the two DMs */
812: DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
813: DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
814: DMCompositeAddDM(user.dmpgrid,user.dmgen);
815: DMCompositeAddDM(user.dmpgrid,user.dmnet);
817: /* Create TAO solver and set desired solution method */
818: TaoCreate(PETSC_COMM_WORLD,&tao);
819: TaoSetType(tao,TAOBLMVM);
820: /*
821: Optimization starts
822: */
823: /* Set initial solution guess */
824: VecCreateSeq(PETSC_COMM_WORLD,3,&p);
825: VecGetArray(p,&x_ptr);
826: x_ptr[0] = PG[0]; x_ptr[1] = PG[1]; x_ptr[2] = PG[2];
827: VecRestoreArray(p,&x_ptr);
829: TaoSetSolution(tao,p);
830: /* Set routine for function and gradient evaluation */
831: TaoSetObjective(tao,FormFunction,(void *)&user);
832: TaoSetGradient(tao,NULL,TaoDefaultComputeGradient,(void *)&user);
834: /* Set bounds for the optimization */
835: VecDuplicate(p,&lowerb);
836: VecDuplicate(p,&upperb);
837: VecGetArray(lowerb,&x_ptr);
838: x_ptr[0] = 0.5; x_ptr[1] = 0.5; x_ptr[2] = 0.5;
839: VecRestoreArray(lowerb,&x_ptr);
840: VecGetArray(upperb,&x_ptr);
841: x_ptr[0] = 2.0; x_ptr[1] = 2.0; x_ptr[2] = 2.0;
842: VecRestoreArray(upperb,&x_ptr);
843: TaoSetVariableBounds(tao,lowerb,upperb);
845: /* Check for any TAO command line options */
846: TaoSetFromOptions(tao);
847: TaoGetKSP(tao,&ksp);
848: if (ksp) {
849: KSPGetPC(ksp,&pc);
850: PCSetType(pc,PCNONE);
851: }
853: /* SOLVE THE APPLICATION */
854: TaoSolve(tao);
856: VecView(p,PETSC_VIEWER_STDOUT_WORLD);
857: /* Free TAO data structures */
858: TaoDestroy(&tao);
859: VecDestroy(&user.vec_q);
860: VecDestroy(&lowerb);
861: VecDestroy(&upperb);
862: VecDestroy(&p);
863: DMDestroy(&user.dmgen);
864: DMDestroy(&user.dmnet);
865: DMDestroy(&user.dmpgrid);
866: ISDestroy(&user.is_diff);
867: ISDestroy(&user.is_alg);
868: PetscFinalize();
869: return 0;
870: }
872: /* ------------------------------------------------------------------ */
873: /*
874: FormFunction - Evaluates the function and corresponding gradient.
876: Input Parameters:
877: tao - the Tao context
878: X - the input vector
879: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient()
881: Output Parameters:
882: f - the newly evaluated function
883: */
884: PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
885: {
886: TS ts;
887: SNES snes_alg;
888: Userctx *ctx = (Userctx*)ctx0;
889: Vec X;
890: Mat J;
891: /* sensitivity context */
892: PetscScalar *x_ptr;
893: PetscViewer Xview,Ybusview;
894: Vec F_alg;
895: Vec Xdot;
896: PetscInt row_loc,col_loc;
897: PetscScalar val;
899: VecGetArrayRead(P,(const PetscScalar**)&x_ptr);
900: PG[0] = x_ptr[0];
901: PG[1] = x_ptr[1];
902: PG[2] = x_ptr[2];
903: VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);
905: ctx->stepnum = 0;
907: VecZeroEntries(ctx->vec_q);
909: /* Read initial voltage vector and Ybus */
910: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
911: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);
913: VecCreate(PETSC_COMM_WORLD,&ctx->V0);
914: VecSetSizes(ctx->V0,PETSC_DECIDE,ctx->neqs_net);
915: VecLoad(ctx->V0,Xview);
917: MatCreate(PETSC_COMM_WORLD,&ctx->Ybus);
918: MatSetSizes(ctx->Ybus,PETSC_DECIDE,PETSC_DECIDE,ctx->neqs_net,ctx->neqs_net);
919: MatSetType(ctx->Ybus,MATBAIJ);
920: /* MatSetBlockSize(ctx->Ybus,2); */
921: MatLoad(ctx->Ybus,Ybusview);
923: PetscViewerDestroy(&Xview);
924: PetscViewerDestroy(&Ybusview);
926: DMCreateGlobalVector(ctx->dmpgrid,&X);
928: MatCreate(PETSC_COMM_WORLD,&J);
929: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,ctx->neqs_pgrid,ctx->neqs_pgrid);
930: MatSetFromOptions(J);
931: PreallocateJacobian(J,ctx);
933: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
934: Create timestepping solver context
935: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
936: TSCreate(PETSC_COMM_WORLD,&ts);
937: TSSetProblemType(ts,TS_NONLINEAR);
938: TSSetType(ts,TSCN);
939: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,ctx);
940: TSSetIJacobian(ts,J,J,(TSIJacobian)IJacobian,ctx);
941: TSSetApplicationContext(ts,ctx);
943: TSMonitorSet(ts,MonitorUpdateQ,ctx,NULL);
944: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
945: Set initial conditions
946: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
947: SetInitialGuess(X,ctx);
949: VecDuplicate(X,&F_alg);
950: SNESCreate(PETSC_COMM_WORLD,&snes_alg);
951: SNESSetFunction(snes_alg,F_alg,AlgFunction,ctx);
952: MatZeroEntries(J);
953: SNESSetJacobian(snes_alg,J,J,AlgJacobian,ctx);
954: SNESSetOptionsPrefix(snes_alg,"alg_");
955: SNESSetFromOptions(snes_alg);
956: ctx->alg_flg = PETSC_TRUE;
957: /* Solve the algebraic equations */
958: SNESSolve(snes_alg,NULL,X);
960: /* Just to set up the Jacobian structure */
961: VecDuplicate(X,&Xdot);
962: IJacobian(ts,0.0,X,Xdot,0.0,J,J,ctx);
963: VecDestroy(&Xdot);
965: ctx->stepnum++;
967: TSSetTimeStep(ts,0.01);
968: TSSetMaxTime(ts,ctx->tmax);
969: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
970: TSSetFromOptions(ts);
972: /* Prefault period */
973: ctx->alg_flg = PETSC_FALSE;
974: TSSetTime(ts,0.0);
975: TSSetMaxTime(ts,ctx->tfaulton);
976: TSSolve(ts,X);
978: /* Create the nonlinear solver for solving the algebraic system */
979: /* Note that although the algebraic system needs to be solved only for
980: Idq and V, we reuse the entire system including xgen. The xgen
981: variables are held constant by setting their residuals to 0 and
982: putting a 1 on the Jacobian diagonal for xgen rows
983: */
984: MatZeroEntries(J);
986: /* Apply disturbance - resistive fault at ctx->faultbus */
987: /* This is done by adding shunt conductance to the diagonal location
988: in the Ybus matrix */
989: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
990: val = 1/ctx->Rfault;
991: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
992: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
993: val = 1/ctx->Rfault;
994: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
996: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
997: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
999: ctx->alg_flg = PETSC_TRUE;
1000: /* Solve the algebraic equations */
1001: SNESSolve(snes_alg,NULL,X);
1003: ctx->stepnum++;
1005: /* Disturbance period */
1006: ctx->alg_flg = PETSC_FALSE;
1007: TSSetTime(ts,ctx->tfaulton);
1008: TSSetMaxTime(ts,ctx->tfaultoff);
1009: TSSolve(ts,X);
1011: /* Remove the fault */
1012: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1;
1013: val = -1/ctx->Rfault;
1014: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1015: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus;
1016: val = -1/ctx->Rfault;
1017: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1019: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1020: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1022: MatZeroEntries(J);
1024: ctx->alg_flg = PETSC_TRUE;
1026: /* Solve the algebraic equations */
1027: SNESSolve(snes_alg,NULL,X);
1029: ctx->stepnum++;
1031: /* Post-disturbance period */
1032: ctx->alg_flg = PETSC_TRUE;
1033: TSSetTime(ts,ctx->tfaultoff);
1034: TSSetMaxTime(ts,ctx->tmax);
1035: TSSolve(ts,X);
1037: VecGetArray(ctx->vec_q,&x_ptr);
1038: *f = x_ptr[0];
1039: VecRestoreArray(ctx->vec_q,&x_ptr);
1041: MatDestroy(&ctx->Ybus);
1042: VecDestroy(&ctx->V0);
1043: SNESDestroy(&snes_alg);
1044: VecDestroy(&F_alg);
1045: MatDestroy(&J);
1046: VecDestroy(&X);
1047: TSDestroy(&ts);
1049: return 0;
1050: }
1052: /*TEST
1054: build:
1055: requires: double !complex !defined(USE_64BIT_INDICES)
1057: test:
1058: args: -viewer_binary_skip_info -tao_monitor -tao_gttol .2
1059: localrunfiles: petscoptions X.bin Ybus.bin
1061: TEST*/