Actual source code: ex9busoptfd.c
petsc-3.12.0 2019-09-29
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 */
100: PetscErrorCode dq2ri(PetscScalar Fd,PetscScalar Fq,PetscScalar delta,PetscScalar *Fr, PetscScalar *Fi)
101: {
103: *Fr = Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
104: *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
105: return(0);
106: }
108: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
109: PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd, PetscScalar *Fq)
110: {
112: *Fd = Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
113: *Fq = Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
114: return(0);
115: }
117: PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
118: {
120: Vec Xgen,Xnet;
121: PetscScalar *xgen,*xnet;
122: PetscInt i,idx=0;
123: PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
124: PetscScalar Eqp,Edp,delta;
125: PetscScalar Efd,RF,VR; /* Exciter variables */
126: PetscScalar Id,Iq; /* Generator dq axis currents */
127: PetscScalar theta,Vd,Vq,SE;
130: M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
131: D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
133: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
135: /* Network subsystem initialization */
136: VecCopy(user->V0,Xnet);
138: /* Generator subsystem initialization */
139: VecGetArray(Xgen,&xgen);
140: VecGetArray(Xnet,&xnet);
142: for (i=0; i < ngen; i++) {
143: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
144: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
145: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
146: IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
147: IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;
149: delta = PetscAtan2Real(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
151: theta = PETSC_PI/2.0 - delta;
153: Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
154: Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
156: Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
157: Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
159: Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
160: Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
162: TM[i] = PG[i];
164: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
165: xgen[idx] = Eqp;
166: xgen[idx+1] = Edp;
167: xgen[idx+2] = delta;
168: xgen[idx+3] = w_s;
170: idx = idx + 4;
172: xgen[idx] = Id;
173: xgen[idx+1] = Iq;
175: idx = idx + 2;
177: /* Exciter */
178: Efd = Eqp + (Xd[i] - Xdp[i])*Id;
179: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
180: VR = KE[i]*Efd + SE;
181: RF = KF[i]*Efd/TF[i];
183: xgen[idx] = Efd;
184: xgen[idx+1] = RF;
185: xgen[idx+2] = VR;
187: Vref[i] = Vm + (VR/KA[i]);
189: idx = idx + 3;
190: }
192: VecRestoreArray(Xgen,&xgen);
193: VecRestoreArray(Xnet,&xnet);
195: /* VecView(Xgen,0); */
196: DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet);
197: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
198: return(0);
199: }
201: /* Computes F = [-f(x,y);g(x,y)] */
202: PetscErrorCode ResidualFunction(SNES snes,Vec X, Vec F, Userctx *user)
203: {
205: Vec Xgen,Xnet,Fgen,Fnet;
206: PetscScalar *xgen,*xnet,*fgen,*fnet;
207: PetscInt i,idx=0;
208: PetscScalar Vr,Vi,Vm,Vm2;
209: PetscScalar Eqp,Edp,delta,w; /* Generator variables */
210: PetscScalar Efd,RF,VR; /* Exciter variables */
211: PetscScalar Id,Iq; /* Generator dq axis currents */
212: PetscScalar Vd,Vq,SE;
213: PetscScalar IGr,IGi,IDr,IDi;
214: PetscScalar Zdq_inv[4],det;
215: PetscScalar PD,QD,Vm0,*v0;
216: PetscInt k;
219: VecZeroEntries(F);
220: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
221: DMCompositeGetLocalVectors(user->dmpgrid,&Fgen,&Fnet);
222: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
223: DMCompositeScatter(user->dmpgrid,F,Fgen,Fnet);
225: /* Network current balance residual IG + Y*V + IL = 0. Only YV is added here.
226: The generator current injection, IG, and load current injection, ID are added later
227: */
228: /* Note that the values in Ybus are stored assuming the imaginary current balance
229: equation is ordered first followed by real current balance equation for each bus.
230: Thus imaginary current contribution goes in location 2*i, and
231: real current contribution in 2*i+1
232: */
233: MatMult(user->Ybus,Xnet,Fnet);
235: VecGetArray(Xgen,&xgen);
236: VecGetArray(Xnet,&xnet);
237: VecGetArray(Fgen,&fgen);
238: VecGetArray(Fnet,&fnet);
240: /* Generator subsystem */
241: for (i=0; i < ngen; i++) {
242: Eqp = xgen[idx];
243: Edp = xgen[idx+1];
244: delta = xgen[idx+2];
245: w = xgen[idx+3];
246: Id = xgen[idx+4];
247: Iq = xgen[idx+5];
248: Efd = xgen[idx+6];
249: RF = xgen[idx+7];
250: VR = xgen[idx+8];
252: /* Generator differential equations */
253: fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i];
254: fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i];
255: fgen[idx+2] = -w + w_s;
256: fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i];
258: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
259: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
261: ri2dq(Vr,Vi,delta,&Vd,&Vq);
262: /* Algebraic equations for stator currents */
263: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
265: Zdq_inv[0] = Rs[i]/det;
266: Zdq_inv[1] = Xqp[i]/det;
267: Zdq_inv[2] = -Xdp[i]/det;
268: Zdq_inv[3] = Rs[i]/det;
270: fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id;
271: fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq;
273: /* Add generator current injection to network */
274: dq2ri(Id,Iq,delta,&IGr,&IGi);
276: fnet[2*gbus[i]] -= IGi;
277: fnet[2*gbus[i]+1] -= IGr;
279: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
281: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
283: /* Exciter differential equations */
284: fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i];
285: fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i];
286: fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
288: idx = idx + 9;
289: }
291: VecGetArray(user->V0,&v0);
292: for (i=0; i < nload; i++) {
293: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
294: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
295: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
296: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
297: PD = QD = 0.0;
298: for (k=0; k < ld_nsegsp[i]; k++) PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
299: for (k=0; k < ld_nsegsq[i]; k++) QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
301: /* Load currents */
302: IDr = (PD*Vr + QD*Vi)/Vm2;
303: IDi = (-QD*Vr + PD*Vi)/Vm2;
305: fnet[2*lbus[i]] += IDi;
306: fnet[2*lbus[i]+1] += IDr;
307: }
308: VecRestoreArray(user->V0,&v0);
310: VecRestoreArray(Xgen,&xgen);
311: VecRestoreArray(Xnet,&xnet);
312: VecRestoreArray(Fgen,&fgen);
313: VecRestoreArray(Fnet,&fnet);
315: DMCompositeGather(user->dmpgrid,INSERT_VALUES,F,Fgen,Fnet);
316: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
317: DMCompositeRestoreLocalVectors(user->dmpgrid,&Fgen,&Fnet);
318: return(0);
319: }
321: /* \dot{x} - f(x,y)
322: g(x,y) = 0
323: */
324: PetscErrorCode IFunction(TS ts,PetscReal t, Vec X, Vec Xdot, Vec F, Userctx *user)
325: {
326: PetscErrorCode ierr;
327: SNES snes;
328: PetscScalar *f;
329: const PetscScalar *xdot;
330: PetscInt i;
333: user->t = t;
335: TSGetSNES(ts,&snes);
336: ResidualFunction(snes,X,F,user);
337: VecGetArray(F,&f);
338: VecGetArrayRead(Xdot,&xdot);
339: for (i=0;i < ngen;i++) {
340: f[9*i] += xdot[9*i];
341: f[9*i+1] += xdot[9*i+1];
342: f[9*i+2] += xdot[9*i+2];
343: f[9*i+3] += xdot[9*i+3];
344: f[9*i+6] += xdot[9*i+6];
345: f[9*i+7] += xdot[9*i+7];
346: f[9*i+8] += xdot[9*i+8];
347: }
348: VecRestoreArray(F,&f);
349: VecRestoreArrayRead(Xdot,&xdot);
350: return(0);
351: }
353: /* This function is used for solving the algebraic system only during fault on and
354: off times. It computes the entire F and then zeros out the part corresponding to
355: differential equations
356: F = [0;g(y)];
357: */
358: PetscErrorCode AlgFunction(SNES snes, Vec X, Vec F, void *ctx)
359: {
361: Userctx *user=(Userctx*)ctx;
362: PetscScalar *f;
363: PetscInt i;
366: ResidualFunction(snes,X,F,user);
367: VecGetArray(F,&f);
368: for (i=0; i < ngen; i++) {
369: f[9*i] = 0;
370: f[9*i+1] = 0;
371: f[9*i+2] = 0;
372: f[9*i+3] = 0;
373: f[9*i+6] = 0;
374: f[9*i+7] = 0;
375: f[9*i+8] = 0;
376: }
377: VecRestoreArray(F,&f);
378: return(0);
379: }
381: PetscErrorCode PreallocateJacobian(Mat J, Userctx *user)
382: {
384: PetscInt *d_nnz;
385: PetscInt i,idx=0,start=0;
386: PetscInt ncols;
389: PetscMalloc1(user->neqs_pgrid,&d_nnz);
390: for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
391: /* Generator subsystem */
392: for (i=0; i < ngen; i++) {
394: d_nnz[idx] += 3;
395: d_nnz[idx+1] += 2;
396: d_nnz[idx+2] += 2;
397: d_nnz[idx+3] += 5;
398: d_nnz[idx+4] += 6;
399: d_nnz[idx+5] += 6;
401: d_nnz[user->neqs_gen+2*gbus[i]] += 3;
402: d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;
404: d_nnz[idx+6] += 2;
405: d_nnz[idx+7] += 2;
406: d_nnz[idx+8] += 5;
408: idx = idx + 9;
409: }
411: start = user->neqs_gen;
413: for (i=0; i < nbus; i++) {
414: MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL);
415: d_nnz[start+2*i] += ncols;
416: d_nnz[start+2*i+1] += ncols;
417: MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL);
418: }
420: MatSeqAIJSetPreallocation(J,0,d_nnz);
422: PetscFree(d_nnz);
423: return(0);
424: }
426: /*
427: J = [-df_dx, -df_dy
428: dg_dx, dg_dy]
429: */
430: PetscErrorCode ResidualJacobian(SNES snes,Vec X,Mat J,Mat B,void *ctx)
431: {
432: PetscErrorCode ierr;
433: Userctx *user=(Userctx*)ctx;
434: Vec Xgen,Xnet;
435: PetscScalar *xgen,*xnet;
436: PetscInt i,idx=0;
437: PetscScalar Vr,Vi,Vm,Vm2;
438: PetscScalar Eqp,Edp,delta; /* Generator variables */
439: PetscScalar Efd; /* Exciter variables */
440: PetscScalar Id,Iq; /* Generator dq axis currents */
441: PetscScalar Vd,Vq;
442: PetscScalar val[10];
443: PetscInt row[2],col[10];
444: PetscInt net_start=user->neqs_gen;
445: PetscScalar Zdq_inv[4],det;
446: PetscScalar dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
447: PetscScalar dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
448: PetscScalar dSE_dEfd;
449: PetscScalar dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
450: PetscInt ncols;
451: const PetscInt *cols;
452: const PetscScalar *yvals;
453: PetscInt k;
454: PetscScalar PD,QD,Vm0,*v0,Vm4;
455: PetscScalar dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
456: PetscScalar dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;
459: MatZeroEntries(B);
460: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
461: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
463: VecGetArray(Xgen,&xgen);
464: VecGetArray(Xnet,&xnet);
466: /* Generator subsystem */
467: for (i=0; i < ngen; i++) {
468: Eqp = xgen[idx];
469: Edp = xgen[idx+1];
470: delta = xgen[idx+2];
471: Id = xgen[idx+4];
472: Iq = xgen[idx+5];
473: Efd = xgen[idx+6];
475: /* fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i]; */
476: row[0] = idx;
477: col[0] = idx; col[1] = idx+4; col[2] = idx+6;
478: val[0] = 1/ Td0p[i]; val[1] = (Xd[i] - Xdp[i])/ Td0p[i]; val[2] = -1/Td0p[i];
480: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
482: /* fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
483: row[0] = idx + 1;
484: col[0] = idx + 1; col[1] = idx+5;
485: val[0] = 1/Tq0p[i]; val[1] = -(Xq[i] - Xqp[i])/Tq0p[i];
486: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
488: /* fgen[idx+2] = - w + w_s; */
489: row[0] = idx + 2;
490: col[0] = idx + 2; col[1] = idx + 3;
491: val[0] = 0; val[1] = -1;
492: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
494: /* fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i]; */
495: row[0] = idx + 3;
496: col[0] = idx; col[1] = idx + 1; col[2] = idx + 3; col[3] = idx + 4; col[4] = idx + 5;
497: 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];
498: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
500: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
501: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
502: ri2dq(Vr,Vi,delta,&Vd,&Vq);
504: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
506: Zdq_inv[0] = Rs[i]/det;
507: Zdq_inv[1] = Xqp[i]/det;
508: Zdq_inv[2] = -Xdp[i]/det;
509: Zdq_inv[3] = Rs[i]/det;
511: dVd_dVr = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
512: dVq_dVr = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
513: dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
514: dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);
516: /* fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
517: row[0] = idx+4;
518: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
519: val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0]; val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
520: col[3] = idx + 4; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
521: 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;
522: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
524: /* fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
525: row[0] = idx+5;
526: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
527: val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2]; val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
528: col[3] = idx + 5; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
529: 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;
530: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
532: dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
533: dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
534: dIGr_dId = PetscSinScalar(delta); dIGr_dIq = PetscCosScalar(delta);
535: dIGi_dId = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);
537: /* fnet[2*gbus[i]] -= IGi; */
538: row[0] = net_start + 2*gbus[i];
539: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
540: val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
541: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
543: /* fnet[2*gbus[i]+1] -= IGr; */
544: row[0] = net_start + 2*gbus[i]+1;
545: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
546: val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
547: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
549: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
551: /* fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i]; */
552: /* SE = k1[i]*PetscExpScalar(k2[i]*Efd); */
554: dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);
556: row[0] = idx + 6;
557: col[0] = idx + 6; col[1] = idx + 8;
558: val[0] = (KE[i] + dSE_dEfd)/TE[i]; val[1] = -1/TE[i];
559: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
561: /* Exciter differential equations */
563: /* fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i]; */
564: row[0] = idx + 7;
565: col[0] = idx + 6; col[1] = idx + 7;
566: val[0] = (-KF[i]/TF[i])/TF[i]; val[1] = 1/TF[i];
567: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
569: /* fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i]; */
570: /* Vm = (Vd^2 + Vq^2)^0.5; */
571: dVm_dVd = Vd/Vm; dVm_dVq = Vq/Vm;
572: dVm_dVr = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
573: dVm_dVi = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
574: row[0] = idx + 8;
575: col[0] = idx + 6; col[1] = idx + 7; col[2] = idx + 8;
576: val[0] = (KA[i]*KF[i]/TF[i])/TA[i]; val[1] = -KA[i]/TA[i]; val[2] = 1/TA[i];
577: col[3] = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
578: val[3] = KA[i]*dVm_dVr/TA[i]; val[4] = KA[i]*dVm_dVi/TA[i];
579: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
580: idx = idx + 9;
581: }
584: for (i=0; i<nbus; i++) {
585: MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
586: row[0] = net_start + 2*i;
587: for (k=0; k<ncols; k++) {
588: col[k] = net_start + cols[k];
589: val[k] = yvals[k];
590: }
591: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
592: MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);
594: MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
595: row[0] = net_start + 2*i+1;
596: for (k=0; k<ncols; k++) {
597: col[k] = net_start + cols[k];
598: val[k] = yvals[k];
599: }
600: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
601: MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
602: }
604: MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
605: MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);
607: VecGetArray(user->V0,&v0);
608: for (i=0; i < nload; i++) {
609: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
610: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
611: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm; Vm4 = Vm2*Vm2;
612: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
613: PD = QD = 0.0;
614: dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
615: for (k=0; k < ld_nsegsp[i]; k++) {
616: PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
617: dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
618: dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
619: }
620: for (k=0; k < ld_nsegsq[i]; k++) {
621: QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
622: dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
623: dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
624: }
626: /* IDr = (PD*Vr + QD*Vi)/Vm2; */
627: /* IDi = (-QD*Vr + PD*Vi)/Vm2; */
629: dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
630: dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;
632: dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
633: dIDi_dVi = (-dQD_dVi*Vr + dPD_dVi*Vi + PD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vi)/Vm4;
636: /* fnet[2*lbus[i]] += IDi; */
637: row[0] = net_start + 2*lbus[i];
638: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
639: val[0] = dIDi_dVr; val[1] = dIDi_dVi;
640: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
641: /* fnet[2*lbus[i]+1] += IDr; */
642: row[0] = net_start + 2*lbus[i]+1;
643: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
644: val[0] = dIDr_dVr; val[1] = dIDr_dVi;
645: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
646: }
647: VecRestoreArray(user->V0,&v0);
649: VecRestoreArray(Xgen,&xgen);
650: VecRestoreArray(Xnet,&xnet);
652: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
654: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
655: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
656: return(0);
657: }
659: /*
660: J = [I, 0
661: dg_dx, dg_dy]
662: */
663: PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
664: {
666: Userctx *user=(Userctx*)ctx;
669: ResidualJacobian(snes,X,A,B,ctx);
670: MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
671: MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);
672: return(0);
673: }
675: /*
676: J = [a*I-df_dx, -df_dy
677: dg_dx, dg_dy]
678: */
680: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
681: {
683: SNES snes;
684: PetscScalar atmp = (PetscScalar) a;
685: PetscInt i,row;
688: user->t = t;
690: TSGetSNES(ts,&snes);
691: ResidualJacobian(snes,X,A,B,user);
692: for (i=0;i < ngen;i++) {
693: row = 9*i;
694: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
695: row = 9*i+1;
696: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
697: row = 9*i+2;
698: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
699: row = 9*i+3;
700: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
701: row = 9*i+6;
702: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
703: row = 9*i+7;
704: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
705: row = 9*i+8;
706: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
707: }
708: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
709: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
710: return(0);
711: }
713: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,Userctx *user)
714: {
715: PetscErrorCode ierr;
716: PetscScalar *r;
717: const PetscScalar *u;
718: PetscInt idx;
719: Vec Xgen,Xnet;
720: PetscScalar *xgen;
721: PetscInt i;
724: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
725: DMCompositeScatter(user->dmpgrid,U,Xgen,Xnet);
727: VecGetArray(Xgen,&xgen);
729: VecGetArrayRead(U,&u);
730: VecGetArray(R,&r);
731: r[0] = 0.;
733: idx = 0;
734: for (i=0;i<ngen;i++) {
735: 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);
736: idx += 9;
737: }
738: VecRestoreArray(R,&r);
739: VecRestoreArrayRead(U,&u);
740: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
741: return(0);
742: }
744: static PetscErrorCode MonitorUpdateQ(TS ts,PetscInt stepnum,PetscReal time,Vec X,void *ctx0)
745: {
747: Vec C,*Y;
748: PetscInt Nr;
749: PetscReal h,theta;
750: Userctx *ctx=(Userctx*)ctx0;
753: theta = 0.5;
754: TSGetStages(ts,&Nr,&Y);
755: TSGetTimeStep(ts,&h);
756: VecDuplicate(ctx->vec_q,&C);
757: /* compute integrals */
758: if (stepnum>0) {
759: CostIntegrand(ts,time,X,C,ctx);
760: VecAXPY(ctx->vec_q,h*theta,C);
761: CostIntegrand(ts,time+h*theta,Y[0],C,ctx);
762: VecAXPY(ctx->vec_q,h*(1-theta),C);
763: }
764: VecDestroy(&C);
765: return(0);
766: }
768: int main(int argc,char **argv)
769: {
770: Userctx user;
771: Vec p;
772: PetscScalar *x_ptr;
773: PetscErrorCode ierr;
774: PetscMPIInt size;
775: PetscInt i;
776: KSP ksp;
777: PC pc;
778: PetscInt *idx2;
779: Tao tao;
780: Vec lowerb,upperb;
783: PetscInitialize(&argc,&argv,"petscoptions",help);if (ierr) return ierr;
784: MPI_Comm_size(PETSC_COMM_WORLD,&size);
785: if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
787: VecCreateSeq(PETSC_COMM_WORLD,1,&user.vec_q);
789: user.neqs_gen = 9*ngen; /* # eqs. for generator subsystem */
790: user.neqs_net = 2*nbus; /* # eqs. for network subsystem */
791: user.neqs_pgrid = user.neqs_gen + user.neqs_net;
793: /* Create indices for differential and algebraic equations */
794: PetscMalloc1(7*ngen,&idx2);
795: for (i=0; i<ngen; i++) {
796: 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;
797: idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
798: }
799: ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
800: ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
801: PetscFree(idx2);
803: /* Set run time options */
804: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Transient stability fault options","");
805: {
806: user.tfaulton = 1.0;
807: user.tfaultoff = 1.2;
808: user.Rfault = 0.0001;
809: user.faultbus = 8;
810: PetscOptionsReal("-tfaulton","","",user.tfaulton,&user.tfaulton,NULL);
811: PetscOptionsReal("-tfaultoff","","",user.tfaultoff,&user.tfaultoff,NULL);
812: PetscOptionsInt("-faultbus","","",user.faultbus,&user.faultbus,NULL);
813: user.t0 = 0.0;
814: user.tmax = 1.5;
815: PetscOptionsReal("-t0","","",user.t0,&user.t0,NULL);
816: PetscOptionsReal("-tmax","","",user.tmax,&user.tmax,NULL);
817: user.freq_u = 61.0;
818: user.freq_l = 59.0;
819: user.pow = 2;
820: PetscOptionsReal("-frequ","","",user.freq_u,&user.freq_u,NULL);
821: PetscOptionsReal("-freql","","",user.freq_l,&user.freq_l,NULL);
822: PetscOptionsInt("-pow","","",user.pow,&user.pow,NULL);
824: }
825: PetscOptionsEnd();
827: /* Create DMs for generator and network subsystems */
828: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
829: DMSetOptionsPrefix(user.dmgen,"dmgen_");
830: DMSetFromOptions(user.dmgen);
831: DMSetUp(user.dmgen);
832: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
833: DMSetOptionsPrefix(user.dmnet,"dmnet_");
834: DMSetFromOptions(user.dmnet);
835: DMSetUp(user.dmnet);
836: /* Create a composite DM packer and add the two DMs */
837: DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
838: DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
839: DMCompositeAddDM(user.dmpgrid,user.dmgen);
840: DMCompositeAddDM(user.dmpgrid,user.dmnet);
842: /* Create TAO solver and set desired solution method */
843: TaoCreate(PETSC_COMM_WORLD,&tao);
844: TaoSetType(tao,TAOBLMVM);
845: /*
846: Optimization starts
847: */
848: /* Set initial solution guess */
849: VecCreateSeq(PETSC_COMM_WORLD,3,&p);
850: VecGetArray(p,&x_ptr);
851: x_ptr[0] = PG[0]; x_ptr[1] = PG[1]; x_ptr[2] = PG[2];
852: VecRestoreArray(p,&x_ptr);
854: TaoSetInitialVector(tao,p);
855: /* Set routine for function and gradient evaluation */
856: TaoSetObjectiveRoutine(tao,FormFunction,(void *)&user);
857: TaoSetGradientRoutine(tao,TaoDefaultComputeGradient,(void *)&user);
859: /* Set bounds for the optimization */
860: VecDuplicate(p,&lowerb);
861: VecDuplicate(p,&upperb);
862: VecGetArray(lowerb,&x_ptr);
863: x_ptr[0] = 0.5; x_ptr[1] = 0.5; x_ptr[2] = 0.5;
864: VecRestoreArray(lowerb,&x_ptr);
865: VecGetArray(upperb,&x_ptr);
866: x_ptr[0] = 2.0; x_ptr[1] = 2.0; x_ptr[2] = 2.0;
867: VecRestoreArray(upperb,&x_ptr);
868: TaoSetVariableBounds(tao,lowerb,upperb);
870: /* Check for any TAO command line options */
871: TaoSetFromOptions(tao);
872: TaoGetKSP(tao,&ksp);
873: if (ksp) {
874: KSPGetPC(ksp,&pc);
875: PCSetType(pc,PCNONE);
876: }
878: /* SOLVE THE APPLICATION */
879: TaoSolve(tao);
881: VecView(p,PETSC_VIEWER_STDOUT_WORLD);
882: /* Free TAO data structures */
883: TaoDestroy(&tao);
884: VecDestroy(&user.vec_q);
885: VecDestroy(&lowerb);
886: VecDestroy(&upperb);
887: VecDestroy(&p);
888: DMDestroy(&user.dmgen);
889: DMDestroy(&user.dmnet);
890: DMDestroy(&user.dmpgrid);
891: ISDestroy(&user.is_diff);
892: ISDestroy(&user.is_alg);
893: PetscFinalize();
894: return ierr;
895: }
897: /* ------------------------------------------------------------------ */
898: /*
899: FormFunction - Evaluates the function and corresponding gradient.
901: Input Parameters:
902: tao - the Tao context
903: X - the input vector
904: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
906: Output Parameters:
907: f - the newly evaluated function
908: */
909: PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
910: {
911: TS ts;
912: SNES snes_alg;
914: Userctx *ctx = (Userctx*)ctx0;
915: Vec X;
916: Mat J;
917: /* sensitivity context */
918: PetscScalar *x_ptr;
919: PetscViewer Xview,Ybusview;
920: Vec F_alg;
921: Vec Xdot;
922: PetscInt row_loc,col_loc;
923: PetscScalar val;
925: VecGetArrayRead(P,(const PetscScalar**)&x_ptr);
926: PG[0] = x_ptr[0];
927: PG[1] = x_ptr[1];
928: PG[2] = x_ptr[2];
929: VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);
931: ctx->stepnum = 0;
933: VecZeroEntries(ctx->vec_q);
935: /* Read initial voltage vector and Ybus */
936: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
937: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);
939: VecCreate(PETSC_COMM_WORLD,&ctx->V0);
940: VecSetSizes(ctx->V0,PETSC_DECIDE,ctx->neqs_net);
941: VecLoad(ctx->V0,Xview);
943: MatCreate(PETSC_COMM_WORLD,&ctx->Ybus);
944: MatSetSizes(ctx->Ybus,PETSC_DECIDE,PETSC_DECIDE,ctx->neqs_net,ctx->neqs_net);
945: MatSetType(ctx->Ybus,MATBAIJ);
946: /* MatSetBlockSize(ctx->Ybus,2); */
947: MatLoad(ctx->Ybus,Ybusview);
949: PetscViewerDestroy(&Xview);
950: PetscViewerDestroy(&Ybusview);
952: DMCreateGlobalVector(ctx->dmpgrid,&X);
954: MatCreate(PETSC_COMM_WORLD,&J);
955: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,ctx->neqs_pgrid,ctx->neqs_pgrid);
956: MatSetFromOptions(J);
957: PreallocateJacobian(J,ctx);
959: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
960: Create timestepping solver context
961: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
962: TSCreate(PETSC_COMM_WORLD,&ts);
963: TSSetProblemType(ts,TS_NONLINEAR);
964: TSSetType(ts,TSCN);
965: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,ctx);
966: TSSetIJacobian(ts,J,J,(TSIJacobian)IJacobian,ctx);
967: TSSetApplicationContext(ts,ctx);
969: TSMonitorSet(ts,MonitorUpdateQ,ctx,NULL);
970: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
971: Set initial conditions
972: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
973: SetInitialGuess(X,ctx);
975: VecDuplicate(X,&F_alg);
976: SNESCreate(PETSC_COMM_WORLD,&snes_alg);
977: SNESSetFunction(snes_alg,F_alg,AlgFunction,ctx);
978: MatZeroEntries(J);
979: SNESSetJacobian(snes_alg,J,J,AlgJacobian,ctx);
980: SNESSetOptionsPrefix(snes_alg,"alg_");
981: SNESSetFromOptions(snes_alg);
982: ctx->alg_flg = PETSC_TRUE;
983: /* Solve the algebraic equations */
984: SNESSolve(snes_alg,NULL,X);
986: /* Just to set up the Jacobian structure */
987: VecDuplicate(X,&Xdot);
988: IJacobian(ts,0.0,X,Xdot,0.0,J,J,ctx);
989: VecDestroy(&Xdot);
991: ctx->stepnum++;
993: TSSetTimeStep(ts,0.01);
994: TSSetMaxTime(ts,ctx->tmax);
995: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
996: TSSetFromOptions(ts);
998: /* Prefault period */
999: ctx->alg_flg = PETSC_FALSE;
1000: TSSetTime(ts,0.0);
1001: TSSetMaxTime(ts,ctx->tfaulton);
1002: TSSolve(ts,X);
1004: /* Create the nonlinear solver for solving the algebraic system */
1005: /* Note that although the algebraic system needs to be solved only for
1006: Idq and V, we reuse the entire system including xgen. The xgen
1007: variables are held constant by setting their residuals to 0 and
1008: putting a 1 on the Jacobian diagonal for xgen rows
1009: */
1010: MatZeroEntries(J);
1012: /* Apply disturbance - resistive fault at ctx->faultbus */
1013: /* This is done by adding shunt conductance to the diagonal location
1014: in the Ybus matrix */
1015: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
1016: val = 1/ctx->Rfault;
1017: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1018: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
1019: val = 1/ctx->Rfault;
1020: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1022: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1023: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1025: ctx->alg_flg = PETSC_TRUE;
1026: /* Solve the algebraic equations */
1027: SNESSolve(snes_alg,NULL,X);
1029: ctx->stepnum++;
1031: /* Disturbance period */
1032: ctx->alg_flg = PETSC_FALSE;
1033: TSSetTime(ts,ctx->tfaulton);
1034: TSSetMaxTime(ts,ctx->tfaultoff);
1035: TSSolve(ts,X);
1037: /* Remove the fault */
1038: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1;
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;
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: MatZeroEntries(J);
1050: ctx->alg_flg = PETSC_TRUE;
1052: /* Solve the algebraic equations */
1053: SNESSolve(snes_alg,NULL,X);
1055: ctx->stepnum++;
1057: /* Post-disturbance period */
1058: ctx->alg_flg = PETSC_TRUE;
1059: TSSetTime(ts,ctx->tfaultoff);
1060: TSSetMaxTime(ts,ctx->tmax);
1061: TSSolve(ts,X);
1063: VecGetArray(ctx->vec_q,&x_ptr);
1064: *f = x_ptr[0];
1065: VecRestoreArray(ctx->vec_q,&x_ptr);
1067: MatDestroy(&ctx->Ybus);
1068: VecDestroy(&ctx->V0);
1069: SNESDestroy(&snes_alg);
1070: VecDestroy(&F_alg);
1071: MatDestroy(&J);
1072: VecDestroy(&X);
1073: TSDestroy(&ts);
1075: return 0;
1076: }
1078: /*TEST
1080: build:
1081: requires: double !complex !define(USE_64BIT_INDICES)
1083: test:
1084: args: -viewer_binary_skip_info -tao_monitor -tao_gttol .2
1085: localrunfiles: petscoptions X.bin Ybus.bin
1087: TEST*/