Actual source code: ex9bus.c
petsc-3.7.3 2016-07-24
2: static char help[] = "Power grid stability analysis of WECC 9 bus system.\n\
3: This example is based on the 9-bus (node) example given in the book Power\n\
4: Systems Dynamics and Stability (Chapter 7) by P. Sauer and M. A. Pai.\n\
5: The power grid in this example consists of 9 buses (nodes), 3 generators,\n\
6: 3 loads, and 9 transmission lines. The network equations are written\n\
7: in current balance form using rectangular coordiantes.\n\n";
9: /*
10: The equations for the stability analysis are described by the DAE
12: \dot{x} = f(x,y,t)
13: 0 = g(x,y,t)
15: where the generators are described by differential equations, while the algebraic
16: constraints define the network equations.
18: The generators are modeled with a 4th order differential equation describing the electrical
19: and mechanical dynamics. Each generator also has an exciter system modeled by 3rd order
20: diff. eqns. describing the exciter, voltage regulator, and the feedback stabilizer
21: mechanism.
23: The network equations are described by nodal current balance equations.
24: I(x,y) - Y*V = 0
26: where:
27: I(x,y) is the current injected from generators and loads.
28: Y is the admittance matrix, and
29: V is the voltage vector
30: */
32: /*
33: Include "petscts.h" so that we can use TS solvers. Note that this
34: file automatically includes:
35: petscsys.h - base PETSc routines petscvec.h - vectors
36: petscmat.h - matrices
37: petscis.h - index sets petscksp.h - Krylov subspace methods
38: petscviewer.h - viewers petscpc.h - preconditioners
39: petscksp.h - linear solvers
40: */
41: #include <petscts.h>
42: #include <petscdm.h>
43: #include <petscdmda.h>
44: #include <petscdmcomposite.h>
46: #define freq 60
47: #define w_s (2*PETSC_PI*freq)
49: /* Sizes and indices */
50: const PetscInt nbus = 9; /* Number of network buses */
51: const PetscInt ngen = 3; /* Number of generators */
52: const PetscInt nload = 3; /* Number of loads */
53: const PetscInt gbus[3] = {0,1,2}; /* Buses at which generators are incident */
54: const PetscInt lbus[3] = {4,5,7}; /* Buses at which loads are incident */
56: /* Generator real and reactive powers (found via loadflow) */
57: const PetscScalar PG[3] = {0.716786142395021,1.630000000000000,0.850000000000000};
58: const PetscScalar QG[3] = {0.270702180178785,0.066120127797275,-0.108402221791588};
59: /* Generator constants */
60: const PetscScalar H[3] = {23.64,6.4,3.01}; /* Inertia constant */
61: const PetscScalar Rs[3] = {0.0,0.0,0.0}; /* Stator Resistance */
62: const PetscScalar Xd[3] = {0.146,0.8958,1.3125}; /* d-axis reactance */
63: const PetscScalar Xdp[3] = {0.0608,0.1198,0.1813}; /* d-axis transient reactance */
64: 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 */
65: const PetscScalar Xqp[3] = {0.0969,0.1969,0.25}; /* q-axis transient reactance */
66: const PetscScalar Td0p[3] = {8.96,6.0,5.89}; /* d-axis open circuit time constant */
67: const PetscScalar Tq0p[3] = {0.31,0.535,0.6}; /* q-axis open circuit time constant */
68: PetscScalar M[3]; /* M = 2*H/w_s */
69: PetscScalar D[3]; /* D = 0.1*M */
71: PetscScalar TM[3]; /* Mechanical Torque */
72: /* Exciter system constants */
73: const PetscScalar KA[3] = {20.0,20.0,20.0}; /* Voltage regulartor gain constant */
74: const PetscScalar TA[3] = {0.2,0.2,0.2}; /* Voltage regulator time constant */
75: const PetscScalar KE[3] = {1.0,1.0,1.0}; /* Exciter gain constant */
76: const PetscScalar TE[3] = {0.314,0.314,0.314}; /* Exciter time constant */
77: const PetscScalar KF[3] = {0.063,0.063,0.063}; /* Feedback stabilizer gain constant */
78: const PetscScalar TF[3] = {0.35,0.35,0.35}; /* Feedback stabilizer time constant */
79: const PetscScalar k1[3] = {0.0039,0.0039,0.0039};
80: const PetscScalar k2[3] = {1.555,1.555,1.555}; /* k1 and k2 for calculating the saturation function SE = k1*exp(k2*Efd) */
82: PetscScalar Vref[3];
83: /* Load constants
84: We use a composite load model that describes the load and reactive powers at each time instant as follows
85: P(t) = \sum\limits_{i=0}^ld_nsegsp \ld_alphap_i*P_D0(\frac{V_m(t)}{V_m0})^\ld_betap_i
86: Q(t) = \sum\limits_{i=0}^ld_nsegsq \ld_alphaq_i*Q_D0(\frac{V_m(t)}{V_m0})^\ld_betaq_i
87: where
88: ld_nsegsp,ld_nsegsq - Number of individual load models for real and reactive power loads
89: ld_alphap,ld_alphap - Percentage contribution (weights) or loads
90: P_D0 - Real power load
91: Q_D0 - Reactive power load
92: V_m(t) - Voltage magnitude at time t
93: V_m0 - Voltage magnitude at t = 0
94: ld_betap, ld_betaq - exponents describing the load model for real and reactive part
96: Note: All loads have the same characteristic currently.
97: */
98: const PetscScalar PD0[3] = {1.25,0.9,1.0};
99: const PetscScalar QD0[3] = {0.5,0.3,0.35};
100: const PetscInt ld_nsegsp[3] = {3,3,3};
101: const PetscScalar ld_alphap[3] = {1.0,0.0,0.0};
102: const PetscScalar ld_betap[3] = {2.0,1.0,0.0};
103: const PetscInt ld_nsegsq[3] = {3,3,3};
104: const PetscScalar ld_alphaq[3] = {1.0,0.0,0.0};
105: const PetscScalar ld_betaq[3] = {2.0,1.0,0.0};
107: typedef struct {
108: DM dmgen, dmnet; /* DMs to manage generator and network subsystem */
109: DM dmpgrid; /* Composite DM to manage the entire power grid */
110: Mat Ybus; /* Network admittance matrix */
111: Vec V0; /* Initial voltage vector (Power flow solution) */
112: PetscReal tfaulton,tfaultoff; /* Fault on and off times */
113: PetscInt faultbus; /* Fault bus */
114: PetscScalar Rfault;
115: PetscReal t0,tmax;
116: PetscInt neqs_gen,neqs_net,neqs_pgrid;
117: Mat Sol; /* Matrix to save solution at each time step */
118: PetscInt stepnum;
119: PetscBool alg_flg;
120: PetscReal t;
121: IS is_diff; /* indices for differential equations */
122: IS is_alg; /* indices for algebraic equations */
123: PetscBool setisdiff; /* TS computes truncation error based only on the differential variables */
124: } Userctx;
127: /* Converts from machine frame (dq) to network (phase a real,imag) reference frame */
130: PetscErrorCode dq2ri(PetscScalar Fd,PetscScalar Fq,PetscScalar delta,PetscScalar *Fr, PetscScalar *Fi)
131: {
133: *Fr = Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
134: *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
135: return(0);
136: }
138: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
141: PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd, PetscScalar *Fq)
142: {
144: *Fd = Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
145: *Fq = Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
146: return(0);
147: }
149: /* Saves the solution at each time to a matrix */
152: PetscErrorCode SaveSolution(TS ts)
153: {
155: Userctx *user;
156: Vec X;
157: PetscScalar *x,*mat;
158: PetscInt idx;
159: PetscReal t;
162: TSGetApplicationContext(ts,&user);
163: TSGetTime(ts,&t);
164: TSGetSolution(ts,&X);
165: idx = user->stepnum*(user->neqs_pgrid+1);
166: MatDenseGetArray(user->Sol,&mat);
167: VecGetArray(X,&x);
168: mat[idx] = t;
169: PetscMemcpy(mat+idx+1,x,user->neqs_pgrid*sizeof(PetscScalar));
170: MatDenseRestoreArray(user->Sol,&mat);
171: VecRestoreArray(X,&x);
172: user->stepnum++;
173: return(0);
174: }
178: PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
179: {
181: Vec Xgen,Xnet;
182: PetscScalar *xgen,*xnet;
183: PetscInt i,idx=0;
184: PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
185: PetscScalar Eqp,Edp,delta;
186: PetscScalar Efd,RF,VR; /* Exciter variables */
187: PetscScalar Id,Iq; /* Generator dq axis currents */
188: PetscScalar theta,Vd,Vq,SE;
191: M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
192: D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
194: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
196: /* Network subsystem initialization */
197: VecCopy(user->V0,Xnet);
199: /* Generator subsystem initialization */
200: VecGetArray(Xgen,&xgen);
201: VecGetArray(Xnet,&xnet);
203: for (i=0; i < ngen; i++) {
204: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
205: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
206: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
207: IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
208: IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;
210: delta = atan2(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
212: theta = PETSC_PI/2.0 - delta;
214: Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
215: Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
217: Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
218: Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
220: Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
221: Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
223: TM[i] = PG[i];
225: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
226: xgen[idx] = Eqp;
227: xgen[idx+1] = Edp;
228: xgen[idx+2] = delta;
229: xgen[idx+3] = w_s;
231: idx = idx + 4;
233: xgen[idx] = Id;
234: xgen[idx+1] = Iq;
236: idx = idx + 2;
238: /* Exciter */
239: Efd = Eqp + (Xd[i] - Xdp[i])*Id;
240: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
241: VR = KE[i]*Efd + SE;
242: RF = KF[i]*Efd/TF[i];
244: xgen[idx] = Efd;
245: xgen[idx+1] = RF;
246: xgen[idx+2] = VR;
248: Vref[i] = Vm + (VR/KA[i]);
250: idx = idx + 3;
251: }
253: VecRestoreArray(Xgen,&xgen);
254: VecRestoreArray(Xnet,&xnet);
256: /* VecView(Xgen,0); */
257: DMCompositeGather(user->dmpgrid,X,INSERT_VALUES,Xgen,Xnet);
258: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
259: return(0);
260: }
262: /* Computes F = [f(x,y);g(x,y)] */
265: PetscErrorCode ResidualFunction(SNES snes,Vec X, Vec F, Userctx *user)
266: {
268: Vec Xgen,Xnet,Fgen,Fnet;
269: PetscScalar *xgen,*xnet,*fgen,*fnet;
270: PetscInt i,idx=0;
271: PetscScalar Vr,Vi,Vm,Vm2;
272: PetscScalar Eqp,Edp,delta,w; /* Generator variables */
273: PetscScalar Efd,RF,VR; /* Exciter variables */
274: PetscScalar Id,Iq; /* Generator dq axis currents */
275: PetscScalar Vd,Vq,SE;
276: PetscScalar IGr,IGi,IDr,IDi;
277: PetscScalar Zdq_inv[4],det;
278: PetscScalar PD,QD,Vm0,*v0;
279: PetscInt k;
282: VecZeroEntries(F);
283: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
284: DMCompositeGetLocalVectors(user->dmpgrid,&Fgen,&Fnet);
285: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
286: DMCompositeScatter(user->dmpgrid,F,Fgen,Fnet);
288: /* Network current balance residual IG + Y*V + IL = 0. Only YV is added here.
289: The generator current injection, IG, and load current injection, ID are added later
290: */
291: /* Note that the values in Ybus are stored assuming the imaginary current balance
292: equation is ordered first followed by real current balance equation for each bus.
293: Thus imaginary current contribution goes in location 2*i, and
294: real current contribution in 2*i+1
295: */
296: MatMult(user->Ybus,Xnet,Fnet);
298: VecGetArray(Xgen,&xgen);
299: VecGetArray(Xnet,&xnet);
300: VecGetArray(Fgen,&fgen);
301: VecGetArray(Fnet,&fnet);
303: /* Generator subsystem */
304: for (i=0; i < ngen; i++) {
305: Eqp = xgen[idx];
306: Edp = xgen[idx+1];
307: delta = xgen[idx+2];
308: w = xgen[idx+3];
309: Id = xgen[idx+4];
310: Iq = xgen[idx+5];
311: Efd = xgen[idx+6];
312: RF = xgen[idx+7];
313: VR = xgen[idx+8];
315: /* Generator differential equations */
316: fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i];
317: fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i];
318: fgen[idx+2] = -w + w_s;
319: fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i];
321: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
322: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
324: ri2dq(Vr,Vi,delta,&Vd,&Vq);
325: /* Algebraic equations for stator currents */
326: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
328: Zdq_inv[0] = Rs[i]/det;
329: Zdq_inv[1] = Xqp[i]/det;
330: Zdq_inv[2] = -Xdp[i]/det;
331: Zdq_inv[3] = Rs[i]/det;
333: fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id;
334: fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq;
336: /* Add generator current injection to network */
337: dq2ri(Id,Iq,delta,&IGr,&IGi);
339: fnet[2*gbus[i]] -= IGi;
340: fnet[2*gbus[i]+1] -= IGr;
342: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
344: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
346: /* Exciter differential equations */
347: fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i];
348: fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i];
349: fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
351: idx = idx + 9;
352: }
354: VecGetArray(user->V0,&v0);
355: for (i=0; i < nload; i++) {
356: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
357: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
358: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
359: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
360: PD = QD = 0.0;
361: for (k=0; k < ld_nsegsp[i]; k++) PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
362: for (k=0; k < ld_nsegsq[i]; k++) QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
364: /* Load currents */
365: IDr = (PD*Vr + QD*Vi)/Vm2;
366: IDi = (-QD*Vr + PD*Vi)/Vm2;
368: fnet[2*lbus[i]] += IDi;
369: fnet[2*lbus[i]+1] += IDr;
370: }
371: VecRestoreArray(user->V0,&v0);
373: VecRestoreArray(Xgen,&xgen);
374: VecRestoreArray(Xnet,&xnet);
375: VecRestoreArray(Fgen,&fgen);
376: VecRestoreArray(Fnet,&fnet);
378: DMCompositeGather(user->dmpgrid,F,INSERT_VALUES,Fgen,Fnet);
379: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
380: DMCompositeRestoreLocalVectors(user->dmpgrid,&Fgen,&Fnet);
381: return(0);
382: }
384: /* \dot{x} - f(x,y)
385: g(x,y) = 0
386: */
389: PetscErrorCode IFunction(TS ts,PetscReal t, Vec X, Vec Xdot, Vec F, Userctx *user)
390: {
392: SNES snes;
393: PetscScalar *f,*xdot;
394: PetscInt i;
397: user->t = t;
399: TSGetSNES(ts,&snes);
400: ResidualFunction(snes,X,F,user);
401: VecGetArray(F,&f);
402: VecGetArray(Xdot,&xdot);
403: for (i=0;i < ngen;i++) {
404: f[9*i] += xdot[9*i];
405: f[9*i+1] += xdot[9*i+1];
406: f[9*i+2] += xdot[9*i+2];
407: f[9*i+3] += xdot[9*i+3];
408: f[9*i+6] += xdot[9*i+6];
409: f[9*i+7] += xdot[9*i+7];
410: f[9*i+8] += xdot[9*i+8];
411: }
412: VecRestoreArray(F,&f);
413: VecRestoreArray(Xdot,&xdot);
414: return(0);
415: }
417: /* This function is used for solving the algebraic system only during fault on and
418: off times. It computes the entire F and then zeros out the part corresponding to
419: differential equations
420: F = [0;g(y)];
421: */
424: PetscErrorCode AlgFunction(SNES snes, Vec X, Vec F, void *ctx)
425: {
427: Userctx *user=(Userctx*)ctx;
428: PetscScalar *f;
429: PetscInt i;
432: ResidualFunction(snes,X,F,user);
433: VecGetArray(F,&f);
434: for (i=0; i < ngen; i++) {
435: f[9*i] = 0;
436: f[9*i+1] = 0;
437: f[9*i+2] = 0;
438: f[9*i+3] = 0;
439: f[9*i+6] = 0;
440: f[9*i+7] = 0;
441: f[9*i+8] = 0;
442: }
443: VecRestoreArray(F,&f);
444: return(0);
445: }
449: PetscErrorCode PreallocateJacobian(Mat J, Userctx *user)
450: {
452: PetscInt *d_nnz;
453: PetscInt i,idx=0,start=0;
454: PetscInt ncols;
457: PetscMalloc1(user->neqs_pgrid,&d_nnz);
458: for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
459: /* Generator subsystem */
460: for (i=0; i < ngen; i++) {
462: d_nnz[idx] += 3;
463: d_nnz[idx+1] += 2;
464: d_nnz[idx+2] += 2;
465: d_nnz[idx+3] += 5;
466: d_nnz[idx+4] += 6;
467: d_nnz[idx+5] += 6;
469: d_nnz[user->neqs_gen+2*gbus[i]] += 3;
470: d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;
472: d_nnz[idx+6] += 2;
473: d_nnz[idx+7] += 2;
474: d_nnz[idx+8] += 5;
476: idx = idx + 9;
477: }
479: start = user->neqs_gen;
481: for (i=0; i < nbus; i++) {
482: MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL);
483: d_nnz[start+2*i] += ncols;
484: d_nnz[start+2*i+1] += ncols;
485: MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL);
486: }
488: MatSeqAIJSetPreallocation(J,0,d_nnz);
490: PetscFree(d_nnz);
491: return(0);
492: }
494: /*
495: J = [-df_dx, -df_dy
496: dg_dx, dg_dy]
497: */
500: PetscErrorCode ResidualJacobian(SNES snes,Vec X,Mat J,Mat B,void *ctx)
501: {
503: Userctx *user=(Userctx*)ctx;
504: Vec Xgen,Xnet;
505: PetscScalar *xgen,*xnet;
506: PetscInt i,idx=0;
507: PetscScalar Vr,Vi,Vm,Vm2;
508: PetscScalar Eqp,Edp,delta; /* Generator variables */
509: PetscScalar Efd;
510: PetscScalar Id,Iq; /* Generator dq axis currents */
511: PetscScalar Vd,Vq;
512: PetscScalar val[10];
513: PetscInt row[2],col[10];
514: PetscInt net_start=user->neqs_gen;
515: PetscScalar Zdq_inv[4],det;
516: PetscScalar dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
517: PetscScalar dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
518: PetscScalar dSE_dEfd;
519: PetscScalar dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
520: PetscInt ncols;
521: const PetscInt *cols;
522: const PetscScalar *yvals;
523: PetscInt k;
524: PetscScalar PD,QD,Vm0,*v0,Vm4;
525: PetscScalar dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
526: PetscScalar dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;
530: MatZeroEntries(B);
531: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
532: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
534: VecGetArray(Xgen,&xgen);
535: VecGetArray(Xnet,&xnet);
537: /* Generator subsystem */
538: for (i=0; i < ngen; i++) {
539: Eqp = xgen[idx];
540: Edp = xgen[idx+1];
541: delta = xgen[idx+2];
542: Id = xgen[idx+4];
543: Iq = xgen[idx+5];
544: Efd = xgen[idx+6];
546: /* fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i]; */
547: row[0] = idx;
548: col[0] = idx; col[1] = idx+4; col[2] = idx+6;
549: val[0] = 1/ Td0p[i]; val[1] = (Xd[i] - Xdp[i])/ Td0p[i]; val[2] = -1/Td0p[i];
551: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
553: /* fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
554: row[0] = idx + 1;
555: col[0] = idx + 1; col[1] = idx+5;
556: val[0] = 1/Tq0p[i]; val[1] = -(Xq[i] - Xqp[i])/Tq0p[i];
557: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
559: /* fgen[idx+2] = - w + w_s; */
560: row[0] = idx + 2;
561: col[0] = idx + 2; col[1] = idx + 3;
562: val[0] = 0; val[1] = -1;
563: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
565: /* fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i]; */
566: row[0] = idx + 3;
567: col[0] = idx; col[1] = idx + 1; col[2] = idx + 3; col[3] = idx + 4; col[4] = idx + 5;
568: 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];
569: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
571: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
572: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
573: ri2dq(Vr,Vi,delta,&Vd,&Vq);
575: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
577: Zdq_inv[0] = Rs[i]/det;
578: Zdq_inv[1] = Xqp[i]/det;
579: Zdq_inv[2] = -Xdp[i]/det;
580: Zdq_inv[3] = Rs[i]/det;
582: dVd_dVr = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
583: dVq_dVr = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
584: dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
585: dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);
587: /* fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
588: row[0] = idx+4;
589: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
590: val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0]; val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
591: col[3] = idx + 4; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
592: 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;
593: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
595: /* fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
596: row[0] = idx+5;
597: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
598: val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2]; val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
599: col[3] = idx + 5; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
600: 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;
601: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
603: dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
604: dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
605: dIGr_dId = PetscSinScalar(delta); dIGr_dIq = PetscCosScalar(delta);
606: dIGi_dId = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);
608: /* fnet[2*gbus[i]] -= IGi; */
609: row[0] = net_start + 2*gbus[i];
610: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
611: val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
612: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
614: /* fnet[2*gbus[i]+1] -= IGr; */
615: row[0] = net_start + 2*gbus[i]+1;
616: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
617: val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
618: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
620: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
622: /* fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i]; */
623: /* SE = k1[i]*PetscExpScalar(k2[i]*Efd); */
625: dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);
627: row[0] = idx + 6;
628: col[0] = idx + 6; col[1] = idx + 8;
629: val[0] = (KE[i] + dSE_dEfd)/TE[i]; val[1] = -1/TE[i];
630: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
632: /* Exciter differential equations */
634: /* fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i]; */
635: row[0] = idx + 7;
636: col[0] = idx + 6; col[1] = idx + 7;
637: val[0] = (-KF[i]/TF[i])/TF[i]; val[1] = 1/TF[i];
638: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
640: /* fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i]; */
641: /* Vm = (Vd^2 + Vq^2)^0.5; */
643: dVm_dVd = Vd/Vm; dVm_dVq = Vq/Vm;
644: dVm_dVr = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
645: dVm_dVi = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
646: row[0] = idx + 8;
647: col[0] = idx + 6; col[1] = idx + 7; col[2] = idx + 8;
648: val[0] = (KA[i]*KF[i]/TF[i])/TA[i]; val[1] = -KA[i]/TA[i]; val[2] = 1/TA[i];
649: col[3] = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
650: val[3] = KA[i]*dVm_dVr/TA[i]; val[4] = KA[i]*dVm_dVi/TA[i];
651: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
652: idx = idx + 9;
653: }
655: for (i=0; i<nbus; i++) {
656: MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
657: row[0] = net_start + 2*i;
658: for (k=0; k<ncols; k++) {
659: col[k] = net_start + cols[k];
660: val[k] = yvals[k];
661: }
662: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
663: MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);
665: MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
666: row[0] = net_start + 2*i+1;
667: for (k=0; k<ncols; k++) {
668: col[k] = net_start + cols[k];
669: val[k] = yvals[k];
670: }
671: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
672: MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
673: }
675: MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
676: MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);
678: VecGetArray(user->V0,&v0);
679: for (i=0; i < nload; i++) {
680: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
681: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
682: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm; Vm4 = Vm2*Vm2;
683: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
684: PD = QD = 0.0;
685: dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
686: for (k=0; k < ld_nsegsp[i]; k++) {
687: PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
688: dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
689: dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
690: }
691: for (k=0; k < ld_nsegsq[i]; k++) {
692: QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
693: dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
694: dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
695: }
697: /* IDr = (PD*Vr + QD*Vi)/Vm2; */
698: /* IDi = (-QD*Vr + PD*Vi)/Vm2; */
700: dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
701: dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;
703: dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
704: dIDi_dVi = (-dQD_dVi*Vr + dPD_dVi*Vi + PD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vi)/Vm4;
707: /* fnet[2*lbus[i]] += IDi; */
708: row[0] = net_start + 2*lbus[i];
709: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
710: val[0] = dIDi_dVr; val[1] = dIDi_dVi;
711: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
712: /* fnet[2*lbus[i]+1] += IDr; */
713: row[0] = net_start + 2*lbus[i]+1;
714: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
715: val[0] = dIDr_dVr; val[1] = dIDr_dVi;
716: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
717: }
718: VecRestoreArray(user->V0,&v0);
720: VecRestoreArray(Xgen,&xgen);
721: VecRestoreArray(Xnet,&xnet);
723: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
725: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
726: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
727: return(0);
728: }
730: /*
731: J = [I, 0
732: dg_dx, dg_dy]
733: */
736: PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
737: {
739: Userctx *user=(Userctx*)ctx;
742: ResidualJacobian(snes,X,A,B,ctx);
743: MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
744: MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);
745: return(0);
746: }
748: /*
749: J = [a*I-df_dx, -df_dy
750: dg_dx, dg_dy]
751: */
755: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
756: {
758: SNES snes;
759: PetscScalar atmp = (PetscScalar) a;
760: PetscInt i,row;
763: user->t = t;
765: TSGetSNES(ts,&snes);
766: ResidualJacobian(snes,X,A,B,user);
767: for (i=0;i < ngen;i++) {
768: row = 9*i;
769: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
770: row = 9*i+1;
771: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
772: row = 9*i+2;
773: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
774: row = 9*i+3;
775: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
776: row = 9*i+6;
777: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
778: row = 9*i+7;
779: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
780: row = 9*i+8;
781: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
782: }
783: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
784: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
785: return(0);
786: }
790: int main(int argc,char **argv)
791: {
792: TS ts;
793: SNES snes_alg;
795: PetscMPIInt size;
796: Userctx user;
797: PetscViewer Xview,Ybusview,viewer;
798: Vec X,F_alg;
799: Mat J,A;
800: PetscInt i,idx,*idx2,row_loc,col_loc;
801: Vec Xdot;
802: PetscScalar *x,*mat,val,*amat;
803: Vec vatol;
805: PetscInitialize(&argc,&argv,"petscoptions",help);
806: MPI_Comm_size(PETSC_COMM_WORLD,&size);
807: if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
809: user.neqs_gen = 9*ngen; /* # eqs. for generator subsystem */
810: user.neqs_net = 2*nbus; /* # eqs. for network subsystem */
811: user.neqs_pgrid = user.neqs_gen + user.neqs_net;
813: /* Create indices for differential and algebraic equations */
815: PetscMalloc1(7*ngen,&idx2);
816: for (i=0; i<ngen; i++) {
817: 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;
818: idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
819: }
820: ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
821: ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
822: PetscFree(idx2);
824: /* Read initial voltage vector and Ybus */
825: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
826: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);
828: VecCreate(PETSC_COMM_WORLD,&user.V0);
829: VecSetSizes(user.V0,PETSC_DECIDE,user.neqs_net);
830: VecLoad(user.V0,Xview);
832: MatCreate(PETSC_COMM_WORLD,&user.Ybus);
833: MatSetSizes(user.Ybus,PETSC_DECIDE,PETSC_DECIDE,user.neqs_net,user.neqs_net);
834: MatSetType(user.Ybus,MATBAIJ);
835: /* MatSetBlockSize(user.Ybus,2); */
836: MatLoad(user.Ybus,Ybusview);
838: /* Set run time options */
839: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Transient stability fault options","");
840: {
841: user.tfaulton = 1.0;
842: user.tfaultoff = 1.2;
843: user.Rfault = 0.0001;
844: user.setisdiff = PETSC_FALSE;
845: user.faultbus = 8;
846: PetscOptionsReal("-tfaulton","","",user.tfaulton,&user.tfaulton,NULL);
847: PetscOptionsReal("-tfaultoff","","",user.tfaultoff,&user.tfaultoff,NULL);
848: PetscOptionsInt("-faultbus","","",user.faultbus,&user.faultbus,NULL);
849: user.t0 = 0.0;
850: user.tmax = 5.0;
851: PetscOptionsReal("-t0","","",user.t0,&user.t0,NULL);
852: PetscOptionsReal("-tmax","","",user.tmax,&user.tmax,NULL);
853: PetscOptionsBool("-setisdiff","","",user.setisdiff,&user.setisdiff,NULL);
854: }
855: PetscOptionsEnd();
857: PetscViewerDestroy(&Xview);
858: PetscViewerDestroy(&Ybusview);
860: /* Create DMs for generator and network subsystems */
861: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
862: DMSetOptionsPrefix(user.dmgen,"dmgen_");
863: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
864: DMSetOptionsPrefix(user.dmnet,"dmnet_");
865: /* Create a composite DM packer and add the two DMs */
866: DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
867: DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
868: DMCompositeAddDM(user.dmpgrid,user.dmgen);
869: DMCompositeAddDM(user.dmpgrid,user.dmnet);
871: DMCreateGlobalVector(user.dmpgrid,&X);
873: MatCreate(PETSC_COMM_WORLD,&J);
874: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,user.neqs_pgrid);
875: MatSetFromOptions(J);
876: PreallocateJacobian(J,&user);
878: /* Create matrix to save solutions at each time step */
879: user.stepnum = 0;
881: MatCreateSeqDense(PETSC_COMM_SELF,user.neqs_pgrid+1,1002,NULL,&user.Sol);
882: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
883: Create timestepping solver context
884: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
885: TSCreate(PETSC_COMM_WORLD,&ts);
886: TSSetProblemType(ts,TS_NONLINEAR);
887: TSSetEquationType(ts,TS_EQ_DAE_IMPLICIT_INDEX1);
888: TSARKIMEXSetFullyImplicit(ts,PETSC_TRUE);
889: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&user);
890: TSSetIJacobian(ts,J,J,(TSIJacobian)IJacobian,&user);
891: TSSetApplicationContext(ts,&user);
893: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
894: Set initial conditions
895: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
896: SetInitialGuess(X,&user);
897: /* Just to set up the Jacobian structure */
899: VecDuplicate(X,&Xdot);
900: IJacobian(ts,0.0,X,Xdot,0.0,J,J,&user);
901: VecDestroy(&Xdot);
903: /* Save initial solution */
905: idx=user.stepnum*(user.neqs_pgrid+1);
906: MatDenseGetArray(user.Sol,&mat);
907: VecGetArray(X,&x);
909: mat[idx] = 0.0;
911: PetscMemcpy(mat+idx+1,x,user.neqs_pgrid*sizeof(PetscScalar));
912: MatDenseRestoreArray(user.Sol,&mat);
913: VecRestoreArray(X,&x);
914: user.stepnum++;
916: TSSetDuration(ts,1000,user.tfaulton);
917: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
918: TSSetInitialTimeStep(ts,0.0,0.01);
919: TSSetFromOptions(ts);
920: TSSetPostStep(ts,SaveSolution);
922: if(user.setisdiff) {
923: const PetscInt *idx;
924: PetscScalar *vatoli;
925: PetscInt k;
926: /* Create vector of absolute tolerances and set the algebraic part to infinity */
927: VecDuplicate(X,&vatol);
928: VecSet(X,100000.0);
929: VecGetArray(vatol,&vatoli);
930: ISGetIndices(user.is_diff,&idx);
931: for(k=0; k < 7*ngen; k++) vatoli[idx[k]] = 1e-2;
932: VecRestoreArray(vatol,&vatoli);
933: }
934:
935: user.alg_flg = PETSC_FALSE;
936: /* Prefault period */
937: TSSolve(ts,X);
939: /* Create the nonlinear solver for solving the algebraic system */
940: /* Note that although the algebraic system needs to be solved only for
941: Idq and V, we reuse the entire system including xgen. The xgen
942: variables are held constant by setting their residuals to 0 and
943: putting a 1 on the Jacobian diagonal for xgen rows
944: */
946: VecDuplicate(X,&F_alg);
947: SNESCreate(PETSC_COMM_WORLD,&snes_alg);
948: SNESSetFunction(snes_alg,F_alg,AlgFunction,&user);
949: MatZeroEntries(J);
950: SNESSetJacobian(snes_alg,J,J,AlgJacobian,&user);
951: SNESSetOptionsPrefix(snes_alg,"alg_");
952: SNESSetFromOptions(snes_alg);
954: /* Apply disturbance - resistive fault at user.faultbus */
955: /* This is done by adding shunt conductance to the diagonal location
956: in the Ybus matrix */
957: row_loc = 2*user.faultbus; col_loc = 2*user.faultbus+1; /* Location for G */
958: val = 1/user.Rfault;
959: MatSetValues(user.Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
960: row_loc = 2*user.faultbus+1; col_loc = 2*user.faultbus; /* Location for G */
961: val = 1/user.Rfault;
962: MatSetValues(user.Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
964: MatAssemblyBegin(user.Ybus,MAT_FINAL_ASSEMBLY);
965: MatAssemblyEnd(user.Ybus,MAT_FINAL_ASSEMBLY);
967: user.alg_flg = PETSC_TRUE;
968: /* Solve the algebraic equations */
969: SNESSolve(snes_alg,NULL,X);
971: /* Save fault-on solution */
972: idx = user.stepnum*(user.neqs_pgrid+1);
973: MatDenseGetArray(user.Sol,&mat);
974: VecGetArray(X,&x);
975: mat[idx] = user.tfaulton;
976: PetscMemcpy(mat+idx+1,x,user.neqs_pgrid*sizeof(PetscScalar));
977: MatDenseRestoreArray(user.Sol,&mat);
978: VecRestoreArray(X,&x);
979: user.stepnum++;
981: /* Disturbance period */
982: TSSetDuration(ts,1000,user.tfaultoff);
983: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
984: TSSetInitialTimeStep(ts,user.tfaulton,.01);
986: user.alg_flg = PETSC_FALSE;
988: TSSolve(ts,X);
990: /* Remove the fault */
991: row_loc = 2*user.faultbus; col_loc = 2*user.faultbus+1;
992: val = -1/user.Rfault;
993: MatSetValues(user.Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
994: row_loc = 2*user.faultbus+1; col_loc = 2*user.faultbus;
995: val = -1/user.Rfault;
996: MatSetValues(user.Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
998: MatAssemblyBegin(user.Ybus,MAT_FINAL_ASSEMBLY);
999: MatAssemblyEnd(user.Ybus,MAT_FINAL_ASSEMBLY);
1001: MatZeroEntries(J);
1003: user.alg_flg = PETSC_TRUE;
1005: /* Solve the algebraic equations */
1006: SNESSolve(snes_alg,NULL,X);
1008: /* Save tfault off solution */
1009: idx = user.stepnum*(user.neqs_pgrid+1);
1010: MatDenseGetArray(user.Sol,&mat);
1011: VecGetArray(X,&x);
1012: mat[idx] = user.tfaultoff;
1013: PetscMemcpy(mat+idx+1,x,user.neqs_pgrid*sizeof(PetscScalar));
1014: MatDenseRestoreArray(user.Sol,&mat);
1015: VecRestoreArray(X,&x);
1016: user.stepnum++;
1018: /* Post-disturbance period */
1019: TSSetDuration(ts,1000,user.tmax);
1020: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
1021: TSSetInitialTimeStep(ts,user.tfaultoff,.01);
1023: user.alg_flg = PETSC_TRUE;
1025: TSSolve(ts,X);
1027: MatAssemblyBegin(user.Sol,MAT_FINAL_ASSEMBLY);
1028: MatAssemblyEnd(user.Sol,MAT_FINAL_ASSEMBLY);
1030: MatCreateSeqDense(PETSC_COMM_SELF,user.neqs_pgrid+1,user.stepnum,NULL,&A);
1031: MatDenseGetArray(user.Sol,&mat);
1032: MatDenseGetArray(A,&amat);
1033: PetscMemcpy(amat,mat,(user.stepnum*(user.neqs_pgrid+1))*sizeof(PetscScalar));
1034: MatDenseRestoreArray(A,&amat);
1035: MatDenseRestoreArray(user.Sol,&mat);
1036: PetscViewerBinaryOpen(PETSC_COMM_SELF,"out.bin",FILE_MODE_WRITE,&viewer);
1037: MatView(A,viewer);
1038: PetscViewerDestroy(&viewer);
1039: MatDestroy(&A);
1040: SNESDestroy(&snes_alg);
1041: VecDestroy(&F_alg);
1042: MatDestroy(&J);
1043: MatDestroy(&user.Ybus);
1044: MatDestroy(&user.Sol);
1045: VecDestroy(&X);
1046: VecDestroy(&user.V0);
1047: DMDestroy(&user.dmgen);
1048: DMDestroy(&user.dmnet);
1049: DMDestroy(&user.dmpgrid);
1050: ISDestroy(&user.is_diff);
1051: ISDestroy(&user.is_alg);
1052: TSDestroy(&ts);
1053: if(user.setisdiff) {
1054: VecDestroy(&vatol);
1055: }
1056: PetscFinalize();
1057: return(0);
1058: }