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: {
102: *Fr = Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
103: *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
104: return(0);
105: }
107: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
108: PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd, PetscScalar *Fq)
109: {
111: *Fd = Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
112: *Fq = Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
113: return(0);
114: }
116: PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
117: {
119: Vec Xgen,Xnet;
120: PetscScalar *xgen,*xnet;
121: PetscInt i,idx=0;
122: PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
123: PetscScalar Eqp,Edp,delta;
124: PetscScalar Efd,RF,VR; /* Exciter variables */
125: PetscScalar Id,Iq; /* Generator dq axis currents */
126: PetscScalar theta,Vd,Vq,SE;
129: M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
130: D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
132: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
134: /* Network subsystem initialization */
135: VecCopy(user->V0,Xnet);
137: /* Generator subsystem initialization */
138: VecGetArray(Xgen,&xgen);
139: VecGetArray(Xnet,&xnet);
141: for (i=0; i < ngen; i++) {
142: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
143: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
144: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
145: IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
146: IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;
148: delta = PetscAtan2Real(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
150: theta = PETSC_PI/2.0 - delta;
152: Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
153: Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
155: Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
156: Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
158: Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
159: Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
161: TM[i] = PG[i];
163: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
164: xgen[idx] = Eqp;
165: xgen[idx+1] = Edp;
166: xgen[idx+2] = delta;
167: xgen[idx+3] = w_s;
169: idx = idx + 4;
171: xgen[idx] = Id;
172: xgen[idx+1] = Iq;
174: idx = idx + 2;
176: /* Exciter */
177: Efd = Eqp + (Xd[i] - Xdp[i])*Id;
178: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
179: VR = KE[i]*Efd + SE;
180: RF = KF[i]*Efd/TF[i];
182: xgen[idx] = Efd;
183: xgen[idx+1] = RF;
184: xgen[idx+2] = VR;
186: Vref[i] = Vm + (VR/KA[i]);
188: idx = idx + 3;
189: }
191: VecRestoreArray(Xgen,&xgen);
192: VecRestoreArray(Xnet,&xnet);
194: /* VecView(Xgen,0); */
195: DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet);
196: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
197: return(0);
198: }
200: /* Computes F = [-f(x,y);g(x,y)] */
201: PetscErrorCode ResidualFunction(SNES snes,Vec X, Vec F, Userctx *user)
202: {
204: Vec Xgen,Xnet,Fgen,Fnet;
205: PetscScalar *xgen,*xnet,*fgen,*fnet;
206: PetscInt i,idx=0;
207: PetscScalar Vr,Vi,Vm,Vm2;
208: PetscScalar Eqp,Edp,delta,w; /* Generator variables */
209: PetscScalar Efd,RF,VR; /* Exciter variables */
210: PetscScalar Id,Iq; /* Generator dq axis currents */
211: PetscScalar Vd,Vq,SE;
212: PetscScalar IGr,IGi,IDr,IDi;
213: PetscScalar Zdq_inv[4],det;
214: PetscScalar PD,QD,Vm0,*v0;
215: PetscInt k;
218: VecZeroEntries(F);
219: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
220: DMCompositeGetLocalVectors(user->dmpgrid,&Fgen,&Fnet);
221: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
222: DMCompositeScatter(user->dmpgrid,F,Fgen,Fnet);
224: /* Network current balance residual IG + Y*V + IL = 0. Only YV is added here.
225: The generator current injection, IG, and load current injection, ID are added later
226: */
227: /* Note that the values in Ybus are stored assuming the imaginary current balance
228: equation is ordered first followed by real current balance equation for each bus.
229: Thus imaginary current contribution goes in location 2*i, and
230: real current contribution in 2*i+1
231: */
232: MatMult(user->Ybus,Xnet,Fnet);
234: VecGetArray(Xgen,&xgen);
235: VecGetArray(Xnet,&xnet);
236: VecGetArray(Fgen,&fgen);
237: VecGetArray(Fnet,&fnet);
239: /* Generator subsystem */
240: for (i=0; i < ngen; i++) {
241: Eqp = xgen[idx];
242: Edp = xgen[idx+1];
243: delta = xgen[idx+2];
244: w = xgen[idx+3];
245: Id = xgen[idx+4];
246: Iq = xgen[idx+5];
247: Efd = xgen[idx+6];
248: RF = xgen[idx+7];
249: VR = xgen[idx+8];
251: /* Generator differential equations */
252: fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i];
253: fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i];
254: fgen[idx+2] = -w + w_s;
255: fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i];
257: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
258: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
260: ri2dq(Vr,Vi,delta,&Vd,&Vq);
261: /* Algebraic equations for stator currents */
262: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
264: Zdq_inv[0] = Rs[i]/det;
265: Zdq_inv[1] = Xqp[i]/det;
266: Zdq_inv[2] = -Xdp[i]/det;
267: Zdq_inv[3] = Rs[i]/det;
269: fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id;
270: fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq;
272: /* Add generator current injection to network */
273: dq2ri(Id,Iq,delta,&IGr,&IGi);
275: fnet[2*gbus[i]] -= IGi;
276: fnet[2*gbus[i]+1] -= IGr;
278: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
280: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
282: /* Exciter differential equations */
283: fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i];
284: fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i];
285: fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
287: idx = idx + 9;
288: }
290: VecGetArray(user->V0,&v0);
291: for (i=0; i < nload; i++) {
292: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
293: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
294: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
295: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
296: PD = QD = 0.0;
297: for (k=0; k < ld_nsegsp[i]; k++) PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
298: for (k=0; k < ld_nsegsq[i]; k++) QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
300: /* Load currents */
301: IDr = (PD*Vr + QD*Vi)/Vm2;
302: IDi = (-QD*Vr + PD*Vi)/Vm2;
304: fnet[2*lbus[i]] += IDi;
305: fnet[2*lbus[i]+1] += IDr;
306: }
307: VecRestoreArray(user->V0,&v0);
309: VecRestoreArray(Xgen,&xgen);
310: VecRestoreArray(Xnet,&xnet);
311: VecRestoreArray(Fgen,&fgen);
312: VecRestoreArray(Fnet,&fnet);
314: DMCompositeGather(user->dmpgrid,INSERT_VALUES,F,Fgen,Fnet);
315: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
316: DMCompositeRestoreLocalVectors(user->dmpgrid,&Fgen,&Fnet);
317: return(0);
318: }
320: /* \dot{x} - f(x,y)
321: g(x,y) = 0
322: */
323: PetscErrorCode IFunction(TS ts,PetscReal t, Vec X, Vec Xdot, Vec F, Userctx *user)
324: {
325: PetscErrorCode ierr;
326: SNES snes;
327: PetscScalar *f;
328: const PetscScalar *xdot;
329: PetscInt i;
332: user->t = t;
334: TSGetSNES(ts,&snes);
335: ResidualFunction(snes,X,F,user);
336: VecGetArray(F,&f);
337: VecGetArrayRead(Xdot,&xdot);
338: for (i=0;i < ngen;i++) {
339: f[9*i] += xdot[9*i];
340: f[9*i+1] += xdot[9*i+1];
341: f[9*i+2] += xdot[9*i+2];
342: f[9*i+3] += xdot[9*i+3];
343: f[9*i+6] += xdot[9*i+6];
344: f[9*i+7] += xdot[9*i+7];
345: f[9*i+8] += xdot[9*i+8];
346: }
347: VecRestoreArray(F,&f);
348: VecRestoreArrayRead(Xdot,&xdot);
349: return(0);
350: }
352: /* This function is used for solving the algebraic system only during fault on and
353: off times. It computes the entire F and then zeros out the part corresponding to
354: differential equations
355: F = [0;g(y)];
356: */
357: PetscErrorCode AlgFunction(SNES snes, Vec X, Vec F, void *ctx)
358: {
360: Userctx *user=(Userctx*)ctx;
361: PetscScalar *f;
362: PetscInt i;
365: ResidualFunction(snes,X,F,user);
366: VecGetArray(F,&f);
367: for (i=0; i < ngen; i++) {
368: f[9*i] = 0;
369: f[9*i+1] = 0;
370: f[9*i+2] = 0;
371: f[9*i+3] = 0;
372: f[9*i+6] = 0;
373: f[9*i+7] = 0;
374: f[9*i+8] = 0;
375: }
376: VecRestoreArray(F,&f);
377: return(0);
378: }
380: PetscErrorCode PreallocateJacobian(Mat J, Userctx *user)
381: {
383: PetscInt *d_nnz;
384: PetscInt i,idx=0,start=0;
385: PetscInt ncols;
388: PetscMalloc1(user->neqs_pgrid,&d_nnz);
389: for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
390: /* Generator subsystem */
391: for (i=0; i < ngen; i++) {
393: d_nnz[idx] += 3;
394: d_nnz[idx+1] += 2;
395: d_nnz[idx+2] += 2;
396: d_nnz[idx+3] += 5;
397: d_nnz[idx+4] += 6;
398: d_nnz[idx+5] += 6;
400: d_nnz[user->neqs_gen+2*gbus[i]] += 3;
401: d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;
403: d_nnz[idx+6] += 2;
404: d_nnz[idx+7] += 2;
405: d_nnz[idx+8] += 5;
407: idx = idx + 9;
408: }
410: start = user->neqs_gen;
412: for (i=0; i < nbus; i++) {
413: MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL);
414: d_nnz[start+2*i] += ncols;
415: d_nnz[start+2*i+1] += ncols;
416: MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL);
417: }
419: MatSeqAIJSetPreallocation(J,0,d_nnz);
421: PetscFree(d_nnz);
422: return(0);
423: }
425: /*
426: J = [-df_dx, -df_dy
427: dg_dx, dg_dy]
428: */
429: PetscErrorCode ResidualJacobian(SNES snes,Vec X,Mat J,Mat B,void *ctx)
430: {
431: PetscErrorCode ierr;
432: Userctx *user=(Userctx*)ctx;
433: Vec Xgen,Xnet;
434: PetscScalar *xgen,*xnet;
435: PetscInt i,idx=0;
436: PetscScalar Vr,Vi,Vm,Vm2;
437: PetscScalar Eqp,Edp,delta; /* Generator variables */
438: PetscScalar Efd; /* Exciter variables */
439: PetscScalar Id,Iq; /* Generator dq axis currents */
440: PetscScalar Vd,Vq;
441: PetscScalar val[10];
442: PetscInt row[2],col[10];
443: PetscInt net_start=user->neqs_gen;
444: PetscScalar Zdq_inv[4],det;
445: PetscScalar dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
446: PetscScalar dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
447: PetscScalar dSE_dEfd;
448: PetscScalar dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
449: PetscInt ncols;
450: const PetscInt *cols;
451: const PetscScalar *yvals;
452: PetscInt k;
453: PetscScalar PD,QD,Vm0,*v0,Vm4;
454: PetscScalar dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
455: PetscScalar dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;
458: MatZeroEntries(B);
459: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
460: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
462: VecGetArray(Xgen,&xgen);
463: VecGetArray(Xnet,&xnet);
465: /* Generator subsystem */
466: for (i=0; i < ngen; i++) {
467: Eqp = xgen[idx];
468: Edp = xgen[idx+1];
469: delta = xgen[idx+2];
470: Id = xgen[idx+4];
471: Iq = xgen[idx+5];
472: Efd = xgen[idx+6];
474: /* fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i]; */
475: row[0] = idx;
476: col[0] = idx; col[1] = idx+4; col[2] = idx+6;
477: val[0] = 1/ Td0p[i]; val[1] = (Xd[i] - Xdp[i])/ Td0p[i]; val[2] = -1/Td0p[i];
479: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
481: /* fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
482: row[0] = idx + 1;
483: col[0] = idx + 1; col[1] = idx+5;
484: val[0] = 1/Tq0p[i]; val[1] = -(Xq[i] - Xqp[i])/Tq0p[i];
485: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
487: /* fgen[idx+2] = - w + w_s; */
488: row[0] = idx + 2;
489: col[0] = idx + 2; col[1] = idx + 3;
490: val[0] = 0; val[1] = -1;
491: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
493: /* fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i]; */
494: row[0] = idx + 3;
495: col[0] = idx; col[1] = idx + 1; col[2] = idx + 3; col[3] = idx + 4; col[4] = idx + 5;
496: 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];
497: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
499: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
500: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
501: ri2dq(Vr,Vi,delta,&Vd,&Vq);
503: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
505: Zdq_inv[0] = Rs[i]/det;
506: Zdq_inv[1] = Xqp[i]/det;
507: Zdq_inv[2] = -Xdp[i]/det;
508: Zdq_inv[3] = Rs[i]/det;
510: dVd_dVr = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
511: dVq_dVr = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
512: dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
513: dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);
515: /* fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
516: row[0] = idx+4;
517: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
518: val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0]; val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
519: col[3] = idx + 4; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
520: 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;
521: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
523: /* fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
524: row[0] = idx+5;
525: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
526: val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2]; val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
527: col[3] = idx + 5; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
528: 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;
529: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
531: dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
532: dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
533: dIGr_dId = PetscSinScalar(delta); dIGr_dIq = PetscCosScalar(delta);
534: dIGi_dId = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);
536: /* fnet[2*gbus[i]] -= IGi; */
537: row[0] = net_start + 2*gbus[i];
538: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
539: val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
540: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
542: /* fnet[2*gbus[i]+1] -= IGr; */
543: row[0] = net_start + 2*gbus[i]+1;
544: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
545: val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
546: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
548: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
550: /* fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i]; */
551: /* SE = k1[i]*PetscExpScalar(k2[i]*Efd); */
553: dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);
555: row[0] = idx + 6;
556: col[0] = idx + 6; col[1] = idx + 8;
557: val[0] = (KE[i] + dSE_dEfd)/TE[i]; val[1] = -1/TE[i];
558: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
560: /* Exciter differential equations */
562: /* fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i]; */
563: row[0] = idx + 7;
564: col[0] = idx + 6; col[1] = idx + 7;
565: val[0] = (-KF[i]/TF[i])/TF[i]; val[1] = 1/TF[i];
566: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
568: /* fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i]; */
569: /* Vm = (Vd^2 + Vq^2)^0.5; */
570: dVm_dVd = Vd/Vm; dVm_dVq = Vq/Vm;
571: dVm_dVr = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
572: dVm_dVi = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
573: row[0] = idx + 8;
574: col[0] = idx + 6; col[1] = idx + 7; col[2] = idx + 8;
575: val[0] = (KA[i]*KF[i]/TF[i])/TA[i]; val[1] = -KA[i]/TA[i]; val[2] = 1/TA[i];
576: col[3] = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
577: val[3] = KA[i]*dVm_dVr/TA[i]; val[4] = KA[i]*dVm_dVi/TA[i];
578: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
579: idx = idx + 9;
580: }
582: for (i=0; i<nbus; i++) {
583: MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
584: row[0] = net_start + 2*i;
585: for (k=0; k<ncols; k++) {
586: col[k] = net_start + cols[k];
587: val[k] = yvals[k];
588: }
589: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
590: MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);
592: MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
593: row[0] = net_start + 2*i+1;
594: for (k=0; k<ncols; k++) {
595: col[k] = net_start + cols[k];
596: val[k] = yvals[k];
597: }
598: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
599: MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
600: }
602: MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
603: MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);
605: VecGetArray(user->V0,&v0);
606: for (i=0; i < nload; i++) {
607: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
608: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
609: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm; Vm4 = Vm2*Vm2;
610: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
611: PD = QD = 0.0;
612: dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
613: for (k=0; k < ld_nsegsp[i]; k++) {
614: PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
615: dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
616: dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
617: }
618: for (k=0; k < ld_nsegsq[i]; k++) {
619: QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
620: dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
621: dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
622: }
624: /* IDr = (PD*Vr + QD*Vi)/Vm2; */
625: /* IDi = (-QD*Vr + PD*Vi)/Vm2; */
627: dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
628: dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;
630: dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
631: dIDi_dVi = (-dQD_dVi*Vr + dPD_dVi*Vi + PD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vi)/Vm4;
633: /* fnet[2*lbus[i]] += IDi; */
634: row[0] = net_start + 2*lbus[i];
635: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
636: val[0] = dIDi_dVr; val[1] = dIDi_dVi;
637: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
638: /* fnet[2*lbus[i]+1] += IDr; */
639: row[0] = net_start + 2*lbus[i]+1;
640: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
641: val[0] = dIDr_dVr; val[1] = dIDr_dVi;
642: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
643: }
644: VecRestoreArray(user->V0,&v0);
646: VecRestoreArray(Xgen,&xgen);
647: VecRestoreArray(Xnet,&xnet);
649: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
651: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
652: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
653: return(0);
654: }
656: /*
657: J = [I, 0
658: dg_dx, dg_dy]
659: */
660: PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
661: {
663: Userctx *user=(Userctx*)ctx;
666: ResidualJacobian(snes,X,A,B,ctx);
667: MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
668: MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);
669: return(0);
670: }
672: /*
673: J = [a*I-df_dx, -df_dy
674: dg_dx, dg_dy]
675: */
677: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
678: {
680: SNES snes;
681: PetscScalar atmp = (PetscScalar) a;
682: PetscInt i,row;
685: user->t = t;
687: TSGetSNES(ts,&snes);
688: ResidualJacobian(snes,X,A,B,user);
689: for (i=0;i < ngen;i++) {
690: row = 9*i;
691: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
692: row = 9*i+1;
693: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
694: row = 9*i+2;
695: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
696: row = 9*i+3;
697: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
698: row = 9*i+6;
699: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
700: row = 9*i+7;
701: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
702: row = 9*i+8;
703: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
704: }
705: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
706: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
707: return(0);
708: }
710: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,Userctx *user)
711: {
712: PetscErrorCode ierr;
713: PetscScalar *r;
714: const PetscScalar *u;
715: PetscInt idx;
716: Vec Xgen,Xnet;
717: PetscScalar *xgen;
718: PetscInt i;
721: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
722: DMCompositeScatter(user->dmpgrid,U,Xgen,Xnet);
724: VecGetArray(Xgen,&xgen);
726: VecGetArrayRead(U,&u);
727: VecGetArray(R,&r);
728: r[0] = 0.;
730: idx = 0;
731: for (i=0;i<ngen;i++) {
732: 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);
733: idx += 9;
734: }
735: VecRestoreArray(R,&r);
736: VecRestoreArrayRead(U,&u);
737: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
738: return(0);
739: }
741: static PetscErrorCode MonitorUpdateQ(TS ts,PetscInt stepnum,PetscReal time,Vec X,void *ctx0)
742: {
744: Vec C,*Y;
745: PetscInt Nr;
746: PetscReal h,theta;
747: Userctx *ctx=(Userctx*)ctx0;
750: theta = 0.5;
751: TSGetStages(ts,&Nr,&Y);
752: TSGetTimeStep(ts,&h);
753: VecDuplicate(ctx->vec_q,&C);
754: /* compute integrals */
755: if (stepnum>0) {
756: CostIntegrand(ts,time,X,C,ctx);
757: VecAXPY(ctx->vec_q,h*theta,C);
758: CostIntegrand(ts,time+h*theta,Y[0],C,ctx);
759: VecAXPY(ctx->vec_q,h*(1-theta),C);
760: }
761: VecDestroy(&C);
762: return(0);
763: }
765: int main(int argc,char **argv)
766: {
767: Userctx user;
768: Vec p;
769: PetscScalar *x_ptr;
770: PetscErrorCode ierr;
771: PetscMPIInt size;
772: PetscInt i;
773: KSP ksp;
774: PC pc;
775: PetscInt *idx2;
776: Tao tao;
777: Vec lowerb,upperb;
780: PetscInitialize(&argc,&argv,"petscoptions",help);if (ierr) return ierr;
781: MPI_Comm_size(PETSC_COMM_WORLD,&size);
782: if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
784: VecCreateSeq(PETSC_COMM_WORLD,1,&user.vec_q);
786: user.neqs_gen = 9*ngen; /* # eqs. for generator subsystem */
787: user.neqs_net = 2*nbus; /* # eqs. for network subsystem */
788: user.neqs_pgrid = user.neqs_gen + user.neqs_net;
790: /* Create indices for differential and algebraic equations */
791: PetscMalloc1(7*ngen,&idx2);
792: for (i=0; i<ngen; i++) {
793: 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;
794: idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
795: }
796: ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
797: ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
798: PetscFree(idx2);
800: /* Set run time options */
801: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Transient stability fault options","");
802: {
803: user.tfaulton = 1.0;
804: user.tfaultoff = 1.2;
805: user.Rfault = 0.0001;
806: user.faultbus = 8;
807: PetscOptionsReal("-tfaulton","","",user.tfaulton,&user.tfaulton,NULL);
808: PetscOptionsReal("-tfaultoff","","",user.tfaultoff,&user.tfaultoff,NULL);
809: PetscOptionsInt("-faultbus","","",user.faultbus,&user.faultbus,NULL);
810: user.t0 = 0.0;
811: user.tmax = 1.5;
812: PetscOptionsReal("-t0","","",user.t0,&user.t0,NULL);
813: PetscOptionsReal("-tmax","","",user.tmax,&user.tmax,NULL);
814: user.freq_u = 61.0;
815: user.freq_l = 59.0;
816: user.pow = 2;
817: PetscOptionsReal("-frequ","","",user.freq_u,&user.freq_u,NULL);
818: PetscOptionsReal("-freql","","",user.freq_l,&user.freq_l,NULL);
819: PetscOptionsInt("-pow","","",user.pow,&user.pow,NULL);
821: }
822: PetscOptionsEnd();
824: /* Create DMs for generator and network subsystems */
825: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
826: DMSetOptionsPrefix(user.dmgen,"dmgen_");
827: DMSetFromOptions(user.dmgen);
828: DMSetUp(user.dmgen);
829: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
830: DMSetOptionsPrefix(user.dmnet,"dmnet_");
831: DMSetFromOptions(user.dmnet);
832: DMSetUp(user.dmnet);
833: /* Create a composite DM packer and add the two DMs */
834: DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
835: DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
836: DMCompositeAddDM(user.dmpgrid,user.dmgen);
837: DMCompositeAddDM(user.dmpgrid,user.dmnet);
839: /* Create TAO solver and set desired solution method */
840: TaoCreate(PETSC_COMM_WORLD,&tao);
841: TaoSetType(tao,TAOBLMVM);
842: /*
843: Optimization starts
844: */
845: /* Set initial solution guess */
846: VecCreateSeq(PETSC_COMM_WORLD,3,&p);
847: VecGetArray(p,&x_ptr);
848: x_ptr[0] = PG[0]; x_ptr[1] = PG[1]; x_ptr[2] = PG[2];
849: VecRestoreArray(p,&x_ptr);
851: TaoSetInitialVector(tao,p);
852: /* Set routine for function and gradient evaluation */
853: TaoSetObjectiveRoutine(tao,FormFunction,(void *)&user);
854: TaoSetGradientRoutine(tao,TaoDefaultComputeGradient,(void *)&user);
856: /* Set bounds for the optimization */
857: VecDuplicate(p,&lowerb);
858: VecDuplicate(p,&upperb);
859: VecGetArray(lowerb,&x_ptr);
860: x_ptr[0] = 0.5; x_ptr[1] = 0.5; x_ptr[2] = 0.5;
861: VecRestoreArray(lowerb,&x_ptr);
862: VecGetArray(upperb,&x_ptr);
863: x_ptr[0] = 2.0; x_ptr[1] = 2.0; x_ptr[2] = 2.0;
864: VecRestoreArray(upperb,&x_ptr);
865: TaoSetVariableBounds(tao,lowerb,upperb);
867: /* Check for any TAO command line options */
868: TaoSetFromOptions(tao);
869: TaoGetKSP(tao,&ksp);
870: if (ksp) {
871: KSPGetPC(ksp,&pc);
872: PCSetType(pc,PCNONE);
873: }
875: /* SOLVE THE APPLICATION */
876: TaoSolve(tao);
878: VecView(p,PETSC_VIEWER_STDOUT_WORLD);
879: /* Free TAO data structures */
880: TaoDestroy(&tao);
881: VecDestroy(&user.vec_q);
882: VecDestroy(&lowerb);
883: VecDestroy(&upperb);
884: VecDestroy(&p);
885: DMDestroy(&user.dmgen);
886: DMDestroy(&user.dmnet);
887: DMDestroy(&user.dmpgrid);
888: ISDestroy(&user.is_diff);
889: ISDestroy(&user.is_alg);
890: PetscFinalize();
891: return ierr;
892: }
894: /* ------------------------------------------------------------------ */
895: /*
896: FormFunction - Evaluates the function and corresponding gradient.
898: Input Parameters:
899: tao - the Tao context
900: X - the input vector
901: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
903: Output Parameters:
904: f - the newly evaluated function
905: */
906: PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
907: {
908: TS ts;
909: SNES snes_alg;
911: Userctx *ctx = (Userctx*)ctx0;
912: Vec X;
913: Mat J;
914: /* sensitivity context */
915: PetscScalar *x_ptr;
916: PetscViewer Xview,Ybusview;
917: Vec F_alg;
918: Vec Xdot;
919: PetscInt row_loc,col_loc;
920: PetscScalar val;
922: VecGetArrayRead(P,(const PetscScalar**)&x_ptr);
923: PG[0] = x_ptr[0];
924: PG[1] = x_ptr[1];
925: PG[2] = x_ptr[2];
926: VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);
928: ctx->stepnum = 0;
930: VecZeroEntries(ctx->vec_q);
932: /* Read initial voltage vector and Ybus */
933: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
934: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);
936: VecCreate(PETSC_COMM_WORLD,&ctx->V0);
937: VecSetSizes(ctx->V0,PETSC_DECIDE,ctx->neqs_net);
938: VecLoad(ctx->V0,Xview);
940: MatCreate(PETSC_COMM_WORLD,&ctx->Ybus);
941: MatSetSizes(ctx->Ybus,PETSC_DECIDE,PETSC_DECIDE,ctx->neqs_net,ctx->neqs_net);
942: MatSetType(ctx->Ybus,MATBAIJ);
943: /* MatSetBlockSize(ctx->Ybus,2); */
944: MatLoad(ctx->Ybus,Ybusview);
946: PetscViewerDestroy(&Xview);
947: PetscViewerDestroy(&Ybusview);
949: DMCreateGlobalVector(ctx->dmpgrid,&X);
951: MatCreate(PETSC_COMM_WORLD,&J);
952: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,ctx->neqs_pgrid,ctx->neqs_pgrid);
953: MatSetFromOptions(J);
954: PreallocateJacobian(J,ctx);
956: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
957: Create timestepping solver context
958: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
959: TSCreate(PETSC_COMM_WORLD,&ts);
960: TSSetProblemType(ts,TS_NONLINEAR);
961: TSSetType(ts,TSCN);
962: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,ctx);
963: TSSetIJacobian(ts,J,J,(TSIJacobian)IJacobian,ctx);
964: TSSetApplicationContext(ts,ctx);
966: TSMonitorSet(ts,MonitorUpdateQ,ctx,NULL);
967: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
968: Set initial conditions
969: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
970: SetInitialGuess(X,ctx);
972: VecDuplicate(X,&F_alg);
973: SNESCreate(PETSC_COMM_WORLD,&snes_alg);
974: SNESSetFunction(snes_alg,F_alg,AlgFunction,ctx);
975: MatZeroEntries(J);
976: SNESSetJacobian(snes_alg,J,J,AlgJacobian,ctx);
977: SNESSetOptionsPrefix(snes_alg,"alg_");
978: SNESSetFromOptions(snes_alg);
979: ctx->alg_flg = PETSC_TRUE;
980: /* Solve the algebraic equations */
981: SNESSolve(snes_alg,NULL,X);
983: /* Just to set up the Jacobian structure */
984: VecDuplicate(X,&Xdot);
985: IJacobian(ts,0.0,X,Xdot,0.0,J,J,ctx);
986: VecDestroy(&Xdot);
988: ctx->stepnum++;
990: TSSetTimeStep(ts,0.01);
991: TSSetMaxTime(ts,ctx->tmax);
992: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
993: TSSetFromOptions(ts);
995: /* Prefault period */
996: ctx->alg_flg = PETSC_FALSE;
997: TSSetTime(ts,0.0);
998: TSSetMaxTime(ts,ctx->tfaulton);
999: TSSolve(ts,X);
1001: /* Create the nonlinear solver for solving the algebraic system */
1002: /* Note that although the algebraic system needs to be solved only for
1003: Idq and V, we reuse the entire system including xgen. The xgen
1004: variables are held constant by setting their residuals to 0 and
1005: putting a 1 on the Jacobian diagonal for xgen rows
1006: */
1007: MatZeroEntries(J);
1009: /* Apply disturbance - resistive fault at ctx->faultbus */
1010: /* This is done by adding shunt conductance to the diagonal location
1011: in the Ybus matrix */
1012: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
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; /* Location for G */
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: ctx->alg_flg = PETSC_TRUE;
1023: /* Solve the algebraic equations */
1024: SNESSolve(snes_alg,NULL,X);
1026: ctx->stepnum++;
1028: /* Disturbance period */
1029: ctx->alg_flg = PETSC_FALSE;
1030: TSSetTime(ts,ctx->tfaulton);
1031: TSSetMaxTime(ts,ctx->tfaultoff);
1032: TSSolve(ts,X);
1034: /* Remove the fault */
1035: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1;
1036: val = -1/ctx->Rfault;
1037: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1038: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus;
1039: val = -1/ctx->Rfault;
1040: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1042: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1043: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1045: MatZeroEntries(J);
1047: ctx->alg_flg = PETSC_TRUE;
1049: /* Solve the algebraic equations */
1050: SNESSolve(snes_alg,NULL,X);
1052: ctx->stepnum++;
1054: /* Post-disturbance period */
1055: ctx->alg_flg = PETSC_TRUE;
1056: TSSetTime(ts,ctx->tfaultoff);
1057: TSSetMaxTime(ts,ctx->tmax);
1058: TSSolve(ts,X);
1060: VecGetArray(ctx->vec_q,&x_ptr);
1061: *f = x_ptr[0];
1062: VecRestoreArray(ctx->vec_q,&x_ptr);
1064: MatDestroy(&ctx->Ybus);
1065: VecDestroy(&ctx->V0);
1066: SNESDestroy(&snes_alg);
1067: VecDestroy(&F_alg);
1068: MatDestroy(&J);
1069: VecDestroy(&X);
1070: TSDestroy(&ts);
1072: return 0;
1073: }
1075: /*TEST
1077: build:
1078: requires: double !complex !defined(USE_64BIT_INDICES)
1080: test:
1081: args: -viewer_binary_skip_info -tao_monitor -tao_gttol .2
1082: localrunfiles: petscoptions X.bin Ybus.bin
1084: TEST*/