Actual source code: ex9bus.c


  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 coordinates.\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: */

 42: #include <petscts.h>
 43: #include <petscdm.h>
 44: #include <petscdmda.h>
 45: #include <petscdmcomposite.h>

 47: #define freq 60
 48: #define w_s (2*PETSC_PI*freq)

 50: /* Sizes and indices */
 51: const PetscInt nbus    = 9; /* Number of network buses */
 52: const PetscInt ngen    = 3; /* Number of generators */
 53: const PetscInt nload   = 3; /* Number of loads */
 54: const PetscInt gbus[3] = {0,1,2}; /* Buses at which generators are incident */
 55: const PetscInt lbus[3] = {4,5,7}; /* Buses at which loads are incident */

 57: /* Generator real and reactive powers (found via loadflow) */
 58: const PetscScalar PG[3] = {0.716786142395021,1.630000000000000,0.850000000000000};
 59: const PetscScalar QG[3] = {0.270702180178785,0.066120127797275,-0.108402221791588};
 60: /* Generator constants */
 61: const PetscScalar H[3]    = {23.64,6.4,3.01};   /* Inertia constant */
 62: const PetscScalar Rs[3]   = {0.0,0.0,0.0}; /* Stator Resistance */
 63: const PetscScalar Xd[3]   = {0.146,0.8958,1.3125};  /* d-axis reactance */
 64: const PetscScalar Xdp[3]  = {0.0608,0.1198,0.1813}; /* d-axis transient reactance */
 65: 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 */
 66: const PetscScalar Xqp[3]  = {0.0969,0.1969,0.25}; /* q-axis transient reactance */
 67: const PetscScalar Td0p[3] = {8.96,6.0,5.89}; /* d-axis open circuit time constant */
 68: const PetscScalar Tq0p[3] = {0.31,0.535,0.6}; /* q-axis open circuit time constant */
 69: PetscScalar M[3]; /* M = 2*H/w_s */
 70: PetscScalar D[3]; /* D = 0.1*M */

 72: PetscScalar TM[3]; /* Mechanical Torque */
 73: /* Exciter system constants */
 74: const PetscScalar KA[3] = {20.0,20.0,20.0};  /* Voltage regulartor gain constant */
 75: const PetscScalar TA[3] = {0.2,0.2,0.2};     /* Voltage regulator time constant */
 76: const PetscScalar KE[3] = {1.0,1.0,1.0};     /* Exciter gain constant */
 77: const PetscScalar TE[3] = {0.314,0.314,0.314}; /* Exciter time constant */
 78: const PetscScalar KF[3] = {0.063,0.063,0.063};  /* Feedback stabilizer gain constant */
 79: const PetscScalar TF[3] = {0.35,0.35,0.35};    /* Feedback stabilizer time constant */
 80: const PetscScalar k1[3] = {0.0039,0.0039,0.0039};
 81: const PetscScalar k2[3] = {1.555,1.555,1.555};  /* k1 and k2 for calculating the saturation function SE = k1*exp(k2*Efd) */
 82: const PetscScalar VRMIN[3] = {-4.0,-4.0,-4.0};
 83: const PetscScalar VRMAX[3] = {7.0,7.0,7.0};
 84: PetscInt VRatmin[3];
 85: PetscInt VRatmax[3];

 87: PetscScalar Vref[3];
 88: /* Load constants
 89:   We use a composite load model that describes the load and reactive powers at each time instant as follows
 90:   P(t) = \sum\limits_{i=0}^ld_nsegsp \ld_alphap_i*P_D0(\frac{V_m(t)}{V_m0})^\ld_betap_i
 91:   Q(t) = \sum\limits_{i=0}^ld_nsegsq \ld_alphaq_i*Q_D0(\frac{V_m(t)}{V_m0})^\ld_betaq_i
 92:   where
 93:     ld_nsegsp,ld_nsegsq - Number of individual load models for real and reactive power loads
 94:     ld_alphap,ld_alphap - Percentage contribution (weights) or loads
 95:     P_D0                - Real power load
 96:     Q_D0                - Reactive power load
 97:     V_m(t)              - Voltage magnitude at time t
 98:     V_m0                - Voltage magnitude at t = 0
 99:     ld_betap, ld_betaq  - exponents describing the load model for real and reactive part

101:     Note: All loads have the same characteristic currently.
102: */
103: const PetscScalar PD0[3] = {1.25,0.9,1.0};
104: const PetscScalar QD0[3] = {0.5,0.3,0.35};
105: const PetscInt    ld_nsegsp[3] = {3,3,3};
106: const PetscScalar ld_alphap[3] = {1.0,0.0,0.0};
107: const PetscScalar ld_betap[3]  = {2.0,1.0,0.0};
108: const PetscInt    ld_nsegsq[3] = {3,3,3};
109: const PetscScalar ld_alphaq[3] = {1.0,0.0,0.0};
110: const PetscScalar ld_betaq[3]  = {2.0,1.0,0.0};

112: typedef struct {
113:   DM          dmgen, dmnet; /* DMs to manage generator and network subsystem */
114:   DM          dmpgrid; /* Composite DM to manage the entire power grid */
115:   Mat         Ybus; /* Network admittance matrix */
116:   Vec         V0;  /* Initial voltage vector (Power flow solution) */
117:   PetscReal   tfaulton,tfaultoff; /* Fault on and off times */
118:   PetscInt    faultbus; /* Fault bus */
119:   PetscScalar Rfault;
120:   PetscReal   t0,tmax;
121:   PetscInt    neqs_gen,neqs_net,neqs_pgrid;
122:   Mat         Sol; /* Matrix to save solution at each time step */
123:   PetscInt    stepnum;
124:   PetscReal   t;
125:   SNES        snes_alg;
126:   IS          is_diff; /* indices for differential equations */
127:   IS          is_alg; /* indices for algebraic equations */
128:   PetscBool   setisdiff; /* TS computes truncation error based only on the differential variables */
129:   PetscBool   semiexplicit; /* If the flag is set then a semi-explicit method is used using TSRK */
130: } Userctx;

132: /*
133:   The first two events are for fault on and off, respectively. The following events are
134:   to check the min/max limits on the state variable VR. A non windup limiter is used for
135:   the VR limits.
136: */
137: PetscErrorCode EventFunction(TS ts,PetscReal t,Vec X,PetscScalar *fvalue,void *ctx)
138: {
139:   Userctx        *user=(Userctx*)ctx;
140:   Vec            Xgen,Xnet;
141:   PetscInt       i,idx=0;
142:   const PetscScalar *xgen,*xnet;
144:   PetscScalar    Efd,RF,VR,Vr,Vi,Vm;


148:   DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
149:   DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);

151:   VecGetArrayRead(Xgen,&xgen);
152:   VecGetArrayRead(Xnet,&xnet);

154:   /* Event for fault-on time */
155:   fvalue[0] = t - user->tfaulton;
156:   /* Event for fault-off time */
157:   fvalue[1] = t - user->tfaultoff;

159:   for (i=0; i < ngen; i++) {
160:     Efd   = xgen[idx+6];
161:     RF    = xgen[idx+7];
162:     VR    = xgen[idx+8];

164:     Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
165:     Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
166:     Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi);

168:     if (!VRatmax[i]) {
169:       fvalue[2+2*i] = VRMAX[i] - VR;
170:     } else {
171:       fvalue[2+2*i] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
172:     }
173:     if (!VRatmin[i]) {
174:       fvalue[2+2*i+1] = VRMIN[i] - VR;
175:     } else {
176:       fvalue[2+2*i+1] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
177:     }
178:     idx = idx+9;
179:   }
180:   VecRestoreArrayRead(Xgen,&xgen);
181:   VecRestoreArrayRead(Xnet,&xnet);

183:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);

185:   return(0);
186: }

188: PetscErrorCode PostEventFunction(TS ts,PetscInt nevents,PetscInt event_list[],PetscReal t,Vec X,PetscBool forwardsolve,void* ctx)
189: {
190:   Userctx *user=(Userctx*)ctx;
191:   Vec      Xgen,Xnet;
192:   PetscScalar *xgen,*xnet;
193:   PetscInt row_loc,col_loc;
194:   PetscScalar val;
196:   PetscInt i,idx=0,event_num;
197:   PetscScalar fvalue;
198:   PetscScalar Efd, RF, VR;
199:   PetscScalar Vr,Vi,Vm;


203:   DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
204:   DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);

206:   VecGetArray(Xgen,&xgen);
207:   VecGetArray(Xnet,&xnet);

209:   for (i=0; i < nevents; i++) {
210:     if (event_list[i] == 0) {
211:       /* Apply disturbance - resistive fault at user->faultbus */
212:       /* This is done by adding shunt conductance to the diagonal location
213:          in the Ybus matrix */
214:       row_loc = 2*user->faultbus; col_loc = 2*user->faultbus+1; /* Location for G */
215:       val     = 1/user->Rfault;
216:       MatSetValues(user->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
217:       row_loc = 2*user->faultbus+1; col_loc = 2*user->faultbus; /* Location for G */
218:       val     = 1/user->Rfault;
219:       MatSetValues(user->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);

221:       MatAssemblyBegin(user->Ybus,MAT_FINAL_ASSEMBLY);
222:       MatAssemblyEnd(user->Ybus,MAT_FINAL_ASSEMBLY);

224:       /* Solve the algebraic equations */
225:       SNESSolve(user->snes_alg,NULL,X);
226:     } else if (event_list[i] == 1) {
227:       /* Remove the fault */
228:       row_loc = 2*user->faultbus; col_loc = 2*user->faultbus+1;
229:       val     = -1/user->Rfault;
230:       MatSetValues(user->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
231:       row_loc = 2*user->faultbus+1; col_loc = 2*user->faultbus;
232:       val     = -1/user->Rfault;
233:       MatSetValues(user->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);

235:       MatAssemblyBegin(user->Ybus,MAT_FINAL_ASSEMBLY);
236:       MatAssemblyEnd(user->Ybus,MAT_FINAL_ASSEMBLY);

238:       /* Solve the algebraic equations */
239:       SNESSolve(user->snes_alg,NULL,X);

241:       /* Check the VR derivatives and reset flags if needed */
242:       for (i=0; i < ngen; i++) {
243:         Efd   = xgen[idx+6];
244:         RF    = xgen[idx+7];
245:         VR    = xgen[idx+8];

247:         Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
248:         Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
249:         Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi);

251:         if (VRatmax[i]) {
252:           fvalue = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
253:           if (fvalue < 0) {
254:             VRatmax[i] = 0;
255:             PetscPrintf(PETSC_COMM_SELF,"VR[%d]: dVR_dt went negative on fault clearing at time %g\n",i,t);
256:           }
257:         }
258:         if (VRatmin[i]) {
259:           fvalue =  (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];

261:           if (fvalue > 0) {
262:             VRatmin[i] = 0;
263:             PetscPrintf(PETSC_COMM_SELF,"VR[%d]: dVR_dt went positive on fault clearing at time %g\n",i,t);
264:           }
265:         }
266:         idx = idx+9;
267:       }
268:     } else {
269:       idx = (event_list[i]-2)/2;
270:       event_num = (event_list[i]-2)%2;
271:       if (event_num == 0) { /* Max VR */
272:         if (!VRatmax[idx]) {
273:           VRatmax[idx] = 1;
274:           PetscPrintf(PETSC_COMM_SELF,"VR[%d]: hit upper limit at time %g\n",idx,t);
275:         }
276:         else {
277:           VRatmax[idx] = 0;
278:           PetscPrintf(PETSC_COMM_SELF,"VR[%d]: freeing variable as dVR_dt is negative at time %g\n",idx,t);
279:         }
280:       } else {
281:         if (!VRatmin[idx]) {
282:           VRatmin[idx] = 1;
283:           PetscPrintf(PETSC_COMM_SELF,"VR[%d]: hit lower limit at time %g\n",idx,t);
284:         }
285:         else {
286:           VRatmin[idx] = 0;
287:           PetscPrintf(PETSC_COMM_SELF,"VR[%d]: freeing variable as dVR_dt is positive at time %g\n",idx,t);
288:         }
289:       }
290:     }
291:   }

293:   VecRestoreArray(Xgen,&xgen);
294:   VecRestoreArray(Xnet,&xnet);

296:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);

298:   return(0);
299: }

301: /* Converts from machine frame (dq) to network (phase a real,imag) reference frame */
302: PetscErrorCode dq2ri(PetscScalar Fd,PetscScalar Fq,PetscScalar delta,PetscScalar *Fr, PetscScalar *Fi)
303: {
305:   *Fr =  Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
306:   *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
307:   return(0);
308: }

310: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
311: PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd, PetscScalar *Fq)
312: {
314:   *Fd =  Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
315:   *Fq =  Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
316:   return(0);
317: }

319: /* Saves the solution at each time to a matrix */
320: PetscErrorCode SaveSolution(TS ts)
321: {
322:   PetscErrorCode    ierr;
323:   Userctx           *user;
324:   Vec               X;
325:   const PetscScalar *x;
326:   PetscScalar       *mat;
327:   PetscInt          idx;
328:   PetscReal         t;

331:   TSGetApplicationContext(ts,&user);
332:   TSGetTime(ts,&t);
333:   TSGetSolution(ts,&X);
334:   idx      = user->stepnum*(user->neqs_pgrid+1);
335:   MatDenseGetArray(user->Sol,&mat);
336:   VecGetArrayRead(X,&x);
337:   mat[idx] = t;
338:   PetscArraycpy(mat+idx+1,x,user->neqs_pgrid);
339:   MatDenseRestoreArray(user->Sol,&mat);
340:   VecRestoreArrayRead(X,&x);
341:   user->stepnum++;
342:   return(0);
343: }

345: PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
346: {
347:   PetscErrorCode    ierr;
348:   Vec               Xgen,Xnet;
349:   PetscScalar       *xgen;
350:   const PetscScalar *xnet;
351:   PetscInt          i,idx=0;
352:   PetscScalar       Vr,Vi,IGr,IGi,Vm,Vm2;
353:   PetscScalar       Eqp,Edp,delta;
354:   PetscScalar       Efd,RF,VR; /* Exciter variables */
355:   PetscScalar       Id,Iq;  /* Generator dq axis currents */
356:   PetscScalar       theta,Vd,Vq,SE;

359:   M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
360:   D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];

362:   DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);

364:   /* Network subsystem initialization */
365:   VecCopy(user->V0,Xnet);

367:   /* Generator subsystem initialization */
368:   VecGetArrayWrite(Xgen,&xgen);
369:   VecGetArrayRead(Xnet,&xnet);

371:   for (i=0; i < ngen; i++) {
372:     Vr  = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
373:     Vi  = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
374:     Vm  = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
375:     IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
376:     IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;

378:     delta = PetscAtan2Real(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */

380:     theta = PETSC_PI/2.0 - delta;

382:     Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
383:     Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */

385:     Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
386:     Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);

388:     Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
389:     Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */

391:     TM[i] = PG[i];

393:     /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
394:     xgen[idx]   = Eqp;
395:     xgen[idx+1] = Edp;
396:     xgen[idx+2] = delta;
397:     xgen[idx+3] = w_s;

399:     idx = idx + 4;

401:     xgen[idx]   = Id;
402:     xgen[idx+1] = Iq;

404:     idx = idx + 2;

406:     /* Exciter */
407:     Efd = Eqp + (Xd[i] - Xdp[i])*Id;
408:     SE  = k1[i]*PetscExpScalar(k2[i]*Efd);
409:     VR  =  KE[i]*Efd + SE;
410:     RF  =  KF[i]*Efd/TF[i];

412:     xgen[idx]   = Efd;
413:     xgen[idx+1] = RF;
414:     xgen[idx+2] = VR;

416:     Vref[i] = Vm + (VR/KA[i]);

418:     VRatmin[i] = VRatmax[i] = 0;

420:     idx = idx + 3;
421:   }
422:   VecRestoreArrayWrite(Xgen,&xgen);
423:   VecRestoreArrayRead(Xnet,&xnet);

425:   /* VecView(Xgen,0); */
426:   DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet);
427:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
428:   return(0);
429: }

431: /* Computes F = [f(x,y);g(x,y)] */
432: PetscErrorCode ResidualFunction(Vec X, Vec F, Userctx *user)
433: {
434:   PetscErrorCode    ierr;
435:   Vec               Xgen,Xnet,Fgen,Fnet;
436:   const PetscScalar *xgen,*xnet;
437:   PetscScalar       *fgen,*fnet;
438:   PetscInt          i,idx=0;
439:   PetscScalar       Vr,Vi,Vm,Vm2;
440:   PetscScalar       Eqp,Edp,delta,w; /* Generator variables */
441:   PetscScalar       Efd,RF,VR; /* Exciter variables */
442:   PetscScalar       Id,Iq;  /* Generator dq axis currents */
443:   PetscScalar       Vd,Vq,SE;
444:   PetscScalar       IGr,IGi,IDr,IDi;
445:   PetscScalar       Zdq_inv[4],det;
446:   PetscScalar       PD,QD,Vm0,*v0;
447:   PetscInt          k;

450:   VecZeroEntries(F);
451:   DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
452:   DMCompositeGetLocalVectors(user->dmpgrid,&Fgen,&Fnet);
453:   DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
454:   DMCompositeScatter(user->dmpgrid,F,Fgen,Fnet);

456:   /* Network current balance residual IG + Y*V + IL = 0. Only YV is added here.
457:      The generator current injection, IG, and load current injection, ID are added later
458:   */
459:   /* Note that the values in Ybus are stored assuming the imaginary current balance
460:      equation is ordered first followed by real current balance equation for each bus.
461:      Thus imaginary current contribution goes in location 2*i, and
462:      real current contribution in 2*i+1
463:   */
464:   MatMult(user->Ybus,Xnet,Fnet);

466:   VecGetArrayRead(Xgen,&xgen);
467:   VecGetArrayRead(Xnet,&xnet);
468:   VecGetArrayWrite(Fgen,&fgen);
469:   VecGetArrayWrite(Fnet,&fnet);

471:   /* Generator subsystem */
472:   for (i=0; i < ngen; i++) {
473:     Eqp   = xgen[idx];
474:     Edp   = xgen[idx+1];
475:     delta = xgen[idx+2];
476:     w     = xgen[idx+3];
477:     Id    = xgen[idx+4];
478:     Iq    = xgen[idx+5];
479:     Efd   = xgen[idx+6];
480:     RF    = xgen[idx+7];
481:     VR    = xgen[idx+8];

483:     /* Generator differential equations */
484:     fgen[idx]   = (-Eqp - (Xd[i] - Xdp[i])*Id + Efd)/Td0p[i];
485:     fgen[idx+1] = (-Edp + (Xq[i] - Xqp[i])*Iq)/Tq0p[i];
486:     fgen[idx+2] = w - w_s;
487:     fgen[idx+3] = (TM[i] - Edp*Id - Eqp*Iq - (Xqp[i] - Xdp[i])*Id*Iq - D[i]*(w - w_s))/M[i];

489:     Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
490:     Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */

492:     ri2dq(Vr,Vi,delta,&Vd,&Vq);
493:     /* Algebraic equations for stator currents */
494:     det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];

496:     Zdq_inv[0] = Rs[i]/det;
497:     Zdq_inv[1] = Xqp[i]/det;
498:     Zdq_inv[2] = -Xdp[i]/det;
499:     Zdq_inv[3] = Rs[i]/det;

501:     fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id;
502:     fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq;

504:     /* Add generator current injection to network */
505:     dq2ri(Id,Iq,delta,&IGr,&IGi);

507:     fnet[2*gbus[i]]   -= IGi;
508:     fnet[2*gbus[i]+1] -= IGr;

510:     Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);

512:     SE = k1[i]*PetscExpScalar(k2[i]*Efd);

514:     /* Exciter differential equations */
515:     fgen[idx+6] = (-KE[i]*Efd - SE + VR)/TE[i];
516:     fgen[idx+7] = (-RF + KF[i]*Efd/TF[i])/TF[i];
517:     if (VRatmax[i]) fgen[idx+8] = VR - VRMAX[i];
518:     else if (VRatmin[i]) fgen[idx+8] = VRMIN[i] - VR;
519:     else fgen[idx+8] = (-VR + KA[i]*RF - KA[i]*KF[i]*Efd/TF[i] + KA[i]*(Vref[i] - Vm))/TA[i];

521:     idx = idx + 9;
522:   }

524:   VecGetArray(user->V0,&v0);
525:   for (i=0; i < nload; i++) {
526:     Vr  = xnet[2*lbus[i]]; /* Real part of load bus voltage */
527:     Vi  = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
528:     Vm  = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
529:     Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
530:     PD  = QD = 0.0;
531:     for (k=0; k < ld_nsegsp[i]; k++) PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
532:     for (k=0; k < ld_nsegsq[i]; k++) QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);

534:     /* Load currents */
535:     IDr = (PD*Vr + QD*Vi)/Vm2;
536:     IDi = (-QD*Vr + PD*Vi)/Vm2;

538:     fnet[2*lbus[i]]   += IDi;
539:     fnet[2*lbus[i]+1] += IDr;
540:   }
541:   VecRestoreArray(user->V0,&v0);

543:   VecRestoreArrayRead(Xgen,&xgen);
544:   VecRestoreArrayRead(Xnet,&xnet);
545:   VecRestoreArrayWrite(Fgen,&fgen);
546:   VecRestoreArrayWrite(Fnet,&fnet);

548:   DMCompositeGather(user->dmpgrid,INSERT_VALUES,F,Fgen,Fnet);
549:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
550:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Fgen,&Fnet);
551:   return(0);
552: }

554: /*   f(x,y)
555:      g(x,y)
556:  */
557: PetscErrorCode RHSFunction(TS ts,PetscReal t, Vec X, Vec F, void *ctx)
558: {
560:   Userctx        *user=(Userctx*)ctx;

563:   user->t = t;
564:   ResidualFunction(X,F,user);
565:   return(0);
566: }

568: /* f(x,y) - \dot{x}
569:      g(x,y) = 0
570:  */
571: PetscErrorCode IFunction(TS ts,PetscReal t, Vec X, Vec Xdot, Vec F, void *ctx)
572: {
573:   PetscErrorCode    ierr;
574:   PetscScalar       *f;
575:   const PetscScalar *xdot;
576:   PetscInt          i;

579:   RHSFunction(ts,t,X,F,ctx);
580:   VecScale(F,-1.0);
581:   VecGetArray(F,&f);
582:   VecGetArrayRead(Xdot,&xdot);
583:   for (i=0;i < ngen;i++) {
584:     f[9*i]   += xdot[9*i];
585:     f[9*i+1] += xdot[9*i+1];
586:     f[9*i+2] += xdot[9*i+2];
587:     f[9*i+3] += xdot[9*i+3];
588:     f[9*i+6] += xdot[9*i+6];
589:     f[9*i+7] += xdot[9*i+7];
590:     f[9*i+8] += xdot[9*i+8];
591:   }
592:   VecRestoreArray(F,&f);
593:   VecRestoreArrayRead(Xdot,&xdot);
594:   return(0);
595: }

597: /* This function is used for solving the algebraic system only during fault on and
598:    off times. It computes the entire F and then zeros out the part corresponding to
599:    differential equations
600:  F = [0;g(y)];
601: */
602: PetscErrorCode AlgFunction(SNES snes, Vec X, Vec F, void *ctx)
603: {
605:   Userctx        *user=(Userctx*)ctx;
606:   PetscScalar    *f;
607:   PetscInt       i;

610:   ResidualFunction(X,F,user);
611:   VecGetArray(F,&f);
612:   for (i=0; i < ngen; i++) {
613:     f[9*i]   = 0;
614:     f[9*i+1] = 0;
615:     f[9*i+2] = 0;
616:     f[9*i+3] = 0;
617:     f[9*i+6] = 0;
618:     f[9*i+7] = 0;
619:     f[9*i+8] = 0;
620:   }
621:   VecRestoreArray(F,&f);
622:   return(0);
623: }

625: PetscErrorCode PostStage(TS ts, PetscReal t, PetscInt i, Vec *X)
626: {
628:   Userctx        *user;

631:   TSGetApplicationContext(ts,&user);
632:   SNESSolve(user->snes_alg,NULL,X[i]);
633:   return(0);
634: }

636: PetscErrorCode PostEvaluate(TS ts)
637: {
639:   Userctx        *user;
640:   Vec            X;

643:   TSGetApplicationContext(ts,&user);
644:   TSGetSolution(ts,&X);
645:   SNESSolve(user->snes_alg,NULL,X);
646:   return(0);
647: }

649: PetscErrorCode PreallocateJacobian(Mat J, Userctx *user)
650: {
652:   PetscInt       *d_nnz;
653:   PetscInt       i,idx=0,start=0;
654:   PetscInt       ncols;

657:   PetscMalloc1(user->neqs_pgrid,&d_nnz);
658:   for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
659:   /* Generator subsystem */
660:   for (i=0; i < ngen; i++) {

662:     d_nnz[idx]   += 3;
663:     d_nnz[idx+1] += 2;
664:     d_nnz[idx+2] += 2;
665:     d_nnz[idx+3] += 5;
666:     d_nnz[idx+4] += 6;
667:     d_nnz[idx+5] += 6;

669:     d_nnz[user->neqs_gen+2*gbus[i]]   += 3;
670:     d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;

672:     d_nnz[idx+6] += 2;
673:     d_nnz[idx+7] += 2;
674:     d_nnz[idx+8] += 5;

676:     idx = idx + 9;
677:   }
678:   start = user->neqs_gen;

680:   for (i=0; i < nbus; i++) {
681:     MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL);
682:     d_nnz[start+2*i]   += ncols;
683:     d_nnz[start+2*i+1] += ncols;
684:     MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL);
685:   }
686:   MatSeqAIJSetPreallocation(J,0,d_nnz);
687:   PetscFree(d_nnz);
688:   return(0);
689: }

691: /*
692:    J = [df_dx, df_dy
693:         dg_dx, dg_dy]
694: */
695: PetscErrorCode ResidualJacobian(Vec X,Mat J,Mat B,void *ctx)
696: {
697:   PetscErrorCode    ierr;
698:   Userctx           *user = (Userctx*)ctx;
699:   Vec               Xgen,Xnet;
700:   const PetscScalar *xgen,*xnet;
701:   PetscInt          i,idx=0;
702:   PetscScalar       Vr,Vi,Vm,Vm2;
703:   PetscScalar       Eqp,Edp,delta; /* Generator variables */
704:   PetscScalar       Efd;
705:   PetscScalar       Id,Iq;  /* Generator dq axis currents */
706:   PetscScalar       Vd,Vq;
707:   PetscScalar       val[10];
708:   PetscInt          row[2],col[10];
709:   PetscInt          net_start = user->neqs_gen;
710:   PetscScalar       Zdq_inv[4],det;
711:   PetscScalar       dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
712:   PetscScalar       dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
713:   PetscScalar       dSE_dEfd;
714:   PetscScalar       dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
715:   PetscInt          ncols;
716:   const PetscInt    *cols;
717:   const PetscScalar *yvals;
718:   PetscInt          k;
719:   PetscScalar       PD,QD,Vm0,Vm4;
720:   const PetscScalar *v0;
721:   PetscScalar       dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
722:   PetscScalar       dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;

725:   MatZeroEntries(B);
726:   DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
727:   DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);

729:   VecGetArrayRead(Xgen,&xgen);
730:   VecGetArrayRead(Xnet,&xnet);

732:   /* Generator subsystem */
733:   for (i=0; i < ngen; i++) {
734:     Eqp   = xgen[idx];
735:     Edp   = xgen[idx+1];
736:     delta = xgen[idx+2];
737:     Id    = xgen[idx+4];
738:     Iq    = xgen[idx+5];
739:     Efd   = xgen[idx+6];

741:     /*    fgen[idx]   = (-Eqp - (Xd[i] - Xdp[i])*Id + Efd)/Td0p[i]; */
742:     row[0] = idx;
743:     col[0] = idx;           col[1] = idx+4;          col[2] = idx+6;
744:     val[0] = -1/ Td0p[i]; val[1] = -(Xd[i] - Xdp[i])/ Td0p[i]; val[2] = 1/Td0p[i];

746:     MatSetValues(J,1,row,3,col,val,INSERT_VALUES);

748:     /*    fgen[idx+1] = (-Edp + (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
749:     row[0] = idx + 1;
750:     col[0] = idx + 1;       col[1] = idx+5;
751:     val[0] = -1/Tq0p[i]; val[1] = (Xq[i] - Xqp[i])/Tq0p[i];
752:     MatSetValues(J,1,row,2,col,val,INSERT_VALUES);

754:     /*    fgen[idx+2] = w - w_s; */
755:     row[0] = idx + 2;
756:     col[0] = idx + 2; col[1] = idx + 3;
757:     val[0] = 0;       val[1] = 1;
758:     MatSetValues(J,1,row,2,col,val,INSERT_VALUES);

760:     /*    fgen[idx+3] = (TM[i] - Edp*Id - Eqp*Iq - (Xqp[i] - Xdp[i])*Id*Iq - D[i]*(w - w_s))/M[i]; */
761:     row[0] = idx + 3;
762:     col[0] = idx; col[1] = idx + 1; col[2] = idx + 3;       col[3] = idx + 4;                  col[4] = idx + 5;
763:     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];
764:     MatSetValues(J,1,row,5,col,val,INSERT_VALUES);

766:     Vr   = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
767:     Vi   = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
768:     ri2dq(Vr,Vi,delta,&Vd,&Vq);

770:     det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];

772:     Zdq_inv[0] = Rs[i]/det;
773:     Zdq_inv[1] = Xqp[i]/det;
774:     Zdq_inv[2] = -Xdp[i]/det;
775:     Zdq_inv[3] = Rs[i]/det;

777:     dVd_dVr    = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
778:     dVq_dVr    = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
779:     dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
780:     dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);

782:     /*    fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
783:     row[0] = idx+4;
784:     col[0] = idx;         col[1] = idx+1;        col[2] = idx + 2;
785:     val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0];  val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
786:     col[3] = idx + 4; col[4] = net_start+2*gbus[i];                     col[5] = net_start + 2*gbus[i]+1;
787:     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;
788:     MatSetValues(J,1,row,6,col,val,INSERT_VALUES);

790:     /*  fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
791:     row[0] = idx+5;
792:     col[0] = idx;         col[1] = idx+1;        col[2] = idx + 2;
793:     val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2];  val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
794:     col[3] = idx + 5; col[4] = net_start+2*gbus[i];                     col[5] = net_start + 2*gbus[i]+1;
795:     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;
796:     MatSetValues(J,1,row,6,col,val,INSERT_VALUES);

798:     dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
799:     dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
800:     dIGr_dId    = PetscSinScalar(delta);  dIGr_dIq = PetscCosScalar(delta);
801:     dIGi_dId    = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);

803:     /* fnet[2*gbus[i]]   -= IGi; */
804:     row[0] = net_start + 2*gbus[i];
805:     col[0] = idx+2;        col[1] = idx + 4;   col[2] = idx + 5;
806:     val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
807:     MatSetValues(J,1,row,3,col,val,INSERT_VALUES);

809:     /* fnet[2*gbus[i]+1]   -= IGr; */
810:     row[0] = net_start + 2*gbus[i]+1;
811:     col[0] = idx+2;        col[1] = idx + 4;   col[2] = idx + 5;
812:     val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
813:     MatSetValues(J,1,row,3,col,val,INSERT_VALUES);

815:     Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);

817:     /*    fgen[idx+6] = (-KE[i]*Efd - SE + VR)/TE[i]; */
818:     /*    SE  = k1[i]*PetscExpScalar(k2[i]*Efd); */

820:     dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);

822:     row[0] = idx + 6;
823:     col[0] = idx + 6;                     col[1] = idx + 8;
824:     val[0] = (-KE[i] - dSE_dEfd)/TE[i];  val[1] = 1/TE[i];
825:     MatSetValues(J,1,row,2,col,val,INSERT_VALUES);

827:     /* Exciter differential equations */

829:     /*    fgen[idx+7] = (-RF + KF[i]*Efd/TF[i])/TF[i]; */
830:     row[0] = idx + 7;
831:     col[0] = idx + 6;       col[1] = idx + 7;
832:     val[0] = (KF[i]/TF[i])/TF[i];  val[1] = -1/TF[i];
833:     MatSetValues(J,1,row,2,col,val,INSERT_VALUES);

835:     /*    fgen[idx+8] = (-VR + KA[i]*RF - KA[i]*KF[i]*Efd/TF[i] + KA[i]*(Vref[i] - Vm))/TA[i]; */
836:     /* Vm = (Vd^2 + Vq^2)^0.5; */

838:     row[0] = idx + 8;
839:     if (VRatmax[i]) {
840:       col[0] = idx + 8; val[0] = 1.0;
841:       MatSetValues(J,1,row,1,col,val,INSERT_VALUES);
842:     } else if (VRatmin[i]) {
843:       col[0] = idx + 8; val[0] = -1.0;
844:       MatSetValues(J,1,row,1,col,val,INSERT_VALUES);
845:     } else {
846:       dVm_dVd    = Vd/Vm; dVm_dVq = Vq/Vm;
847:       dVm_dVr    = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
848:       dVm_dVi    = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
849:       row[0]     = idx + 8;
850:       col[0]     = idx + 6;           col[1] = idx + 7; col[2] = idx + 8;
851:       val[0]     = -(KA[i]*KF[i]/TF[i])/TA[i]; val[1] = KA[i]/TA[i];  val[2] = -1/TA[i];
852:       col[3]     = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
853:       val[3]     = -KA[i]*dVm_dVr/TA[i];         val[4] = -KA[i]*dVm_dVi/TA[i];
854:       MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
855:     }
856:     idx        = idx + 9;
857:   }

859:   for (i=0; i<nbus; i++) {
860:     MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
861:     row[0] = net_start + 2*i;
862:     for (k=0; k<ncols; k++) {
863:       col[k] = net_start + cols[k];
864:       val[k] = yvals[k];
865:     }
866:     MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
867:     MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);

869:     MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
870:     row[0] = net_start + 2*i+1;
871:     for (k=0; k<ncols; k++) {
872:       col[k] = net_start + cols[k];
873:       val[k] = yvals[k];
874:     }
875:     MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
876:     MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
877:   }

879:   MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
880:   MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);

882:   VecGetArrayRead(user->V0,&v0);
883:   for (i=0; i < nload; i++) {
884:     Vr      = xnet[2*lbus[i]]; /* Real part of load bus voltage */
885:     Vi      = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
886:     Vm      = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm; Vm4 = Vm2*Vm2;
887:     Vm0     = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
888:     PD      = QD = 0.0;
889:     dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
890:     for (k=0; k < ld_nsegsp[i]; k++) {
891:       PD      += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
892:       dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
893:       dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
894:     }
895:     for (k=0; k < ld_nsegsq[i]; k++) {
896:       QD      += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
897:       dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
898:       dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
899:     }

901:     /*    IDr = (PD*Vr + QD*Vi)/Vm2; */
902:     /*    IDi = (-QD*Vr + PD*Vi)/Vm2; */

904:     dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
905:     dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;

907:     dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
908:     dIDi_dVi = (-dQD_dVi*Vr + dPD_dVi*Vi + PD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vi)/Vm4;

910:     /*    fnet[2*lbus[i]]   += IDi; */
911:     row[0] = net_start + 2*lbus[i];
912:     col[0] = net_start + 2*lbus[i];  col[1] = net_start + 2*lbus[i]+1;
913:     val[0] = dIDi_dVr;               val[1] = dIDi_dVi;
914:     MatSetValues(J,1,row,2,col,val,ADD_VALUES);
915:     /*    fnet[2*lbus[i]+1] += IDr; */
916:     row[0] = net_start + 2*lbus[i]+1;
917:     col[0] = net_start + 2*lbus[i];  col[1] = net_start + 2*lbus[i]+1;
918:     val[0] = dIDr_dVr;               val[1] = dIDr_dVi;
919:     MatSetValues(J,1,row,2,col,val,ADD_VALUES);
920:   }
921:   VecRestoreArrayRead(user->V0,&v0);

923:   VecRestoreArrayRead(Xgen,&xgen);
924:   VecRestoreArrayRead(Xnet,&xnet);

926:   DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);

928:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
929:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
930:   return(0);
931: }

933: /*
934:    J = [I, 0
935:         dg_dx, dg_dy]
936: */
937: PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
938: {
940:   Userctx        *user=(Userctx*)ctx;

943:   ResidualJacobian(X,A,B,ctx);
944:   MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
945:   MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);
946:   return(0);
947: }

949: /*
950:    J = [-df_dx, -df_dy
951:         dg_dx, dg_dy]
952: */

954: PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec X,Mat A,Mat B,void *ctx)
955: {
957:   Userctx        *user=(Userctx*)ctx;

960:   user->t = t;

962:   ResidualJacobian(X,A,B,user);

964:   return(0);
965: }

967: /*
968:    J = [df_dx-aI, df_dy
969:         dg_dx, dg_dy]
970: */

972: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
973: {
975:   PetscScalar    atmp = (PetscScalar) a;
976:   PetscInt       i,row;

979:   user->t = t;

981:   RHSJacobian(ts,t,X,A,B,user);
982:   MatScale(B,-1.0);
983:   for (i=0;i < ngen;i++) {
984:     row = 9*i;
985:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
986:     row  = 9*i+1;
987:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
988:     row  = 9*i+2;
989:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
990:     row  = 9*i+3;
991:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
992:     row  = 9*i+6;
993:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
994:     row  = 9*i+7;
995:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
996:     row  = 9*i+8;
997:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
998:   }
999:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
1000:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
1001:   return(0);
1002: }

1004: int main(int argc,char **argv)
1005: {
1006:   TS               ts;
1007:   SNES              snes_alg;
1008:   PetscErrorCode    ierr;
1009:   PetscMPIInt       size;
1010:   Userctx           user;
1011:   PetscViewer       Xview,Ybusview,viewer;
1012:   Vec               X,F_alg;
1013:   Mat               J,A;
1014:   PetscInt          i,idx,*idx2;
1015:   Vec               Xdot;
1016:   PetscScalar       *x,*mat,*amat;
1017:   const PetscScalar *rmat;
1018:   Vec               vatol;
1019:   PetscInt          *direction;
1020:   PetscBool         *terminate;
1021:   const PetscInt    *idx3;
1022:   PetscScalar       *vatoli;
1023:   PetscInt          k;

1025:   PetscInitialize(&argc,&argv,"petscoptions",help);if (ierr) return ierr;
1026:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
1027:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

1029:   user.neqs_gen   = 9*ngen; /* # eqs. for generator subsystem */
1030:   user.neqs_net   = 2*nbus; /* # eqs. for network subsystem   */
1031:   user.neqs_pgrid = user.neqs_gen + user.neqs_net;

1033:   /* Create indices for differential and algebraic equations */

1035:   PetscMalloc1(7*ngen,&idx2);
1036:   for (i=0; i<ngen; i++) {
1037:     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;
1038:     idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
1039:   }
1040:   ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
1041:   ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
1042:   PetscFree(idx2);

1044:   /* Read initial voltage vector and Ybus */
1045:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
1046:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);

1048:   VecCreate(PETSC_COMM_WORLD,&user.V0);
1049:   VecSetSizes(user.V0,PETSC_DECIDE,user.neqs_net);
1050:   VecLoad(user.V0,Xview);

1052:   MatCreate(PETSC_COMM_WORLD,&user.Ybus);
1053:   MatSetSizes(user.Ybus,PETSC_DECIDE,PETSC_DECIDE,user.neqs_net,user.neqs_net);
1054:   MatSetType(user.Ybus,MATBAIJ);
1055:   /*  MatSetBlockSize(user.Ybus,2); */
1056:   MatLoad(user.Ybus,Ybusview);

1058:   /* Set run time options */
1059:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Transient stability fault options","");
1060:   {
1061:     user.tfaulton  = 1.0;
1062:     user.tfaultoff = 1.2;
1063:     user.Rfault    = 0.0001;
1064:     user.setisdiff = PETSC_FALSE;
1065:     user.semiexplicit = PETSC_FALSE;
1066:     user.faultbus  = 8;
1067:     PetscOptionsReal("-tfaulton","","",user.tfaulton,&user.tfaulton,NULL);
1068:     PetscOptionsReal("-tfaultoff","","",user.tfaultoff,&user.tfaultoff,NULL);
1069:     PetscOptionsInt("-faultbus","","",user.faultbus,&user.faultbus,NULL);
1070:     user.t0        = 0.0;
1071:     user.tmax      = 5.0;
1072:     PetscOptionsReal("-t0","","",user.t0,&user.t0,NULL);
1073:     PetscOptionsReal("-tmax","","",user.tmax,&user.tmax,NULL);
1074:     PetscOptionsBool("-setisdiff","","",user.setisdiff,&user.setisdiff,NULL);
1075:     PetscOptionsBool("-dae_semiexplicit","","",user.semiexplicit,&user.semiexplicit,NULL);
1076:   }
1077:   PetscOptionsEnd();

1079:   PetscViewerDestroy(&Xview);
1080:   PetscViewerDestroy(&Ybusview);

1082:   /* Create DMs for generator and network subsystems */
1083:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
1084:   DMSetOptionsPrefix(user.dmgen,"dmgen_");
1085:   DMSetFromOptions(user.dmgen);
1086:   DMSetUp(user.dmgen);
1087:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
1088:   DMSetOptionsPrefix(user.dmnet,"dmnet_");
1089:   DMSetFromOptions(user.dmnet);
1090:   DMSetUp(user.dmnet);
1091:   /* Create a composite DM packer and add the two DMs */
1092:   DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
1093:   DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
1094:   DMCompositeAddDM(user.dmpgrid,user.dmgen);
1095:   DMCompositeAddDM(user.dmpgrid,user.dmnet);

1097:   DMCreateGlobalVector(user.dmpgrid,&X);

1099:   MatCreate(PETSC_COMM_WORLD,&J);
1100:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,user.neqs_pgrid);
1101:   MatSetFromOptions(J);
1102:   PreallocateJacobian(J,&user);

1104:   /* Create matrix to save solutions at each time step */
1105:   user.stepnum = 0;

1107:   MatCreateSeqDense(PETSC_COMM_SELF,user.neqs_pgrid+1,1002,NULL,&user.Sol);
1108:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1109:      Create timestepping solver context
1110:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1111:   TSCreate(PETSC_COMM_WORLD,&ts);
1112:   TSSetProblemType(ts,TS_NONLINEAR);
1113:   if (user.semiexplicit) {
1114:     TSSetType(ts,TSRK);
1115:     TSSetRHSFunction(ts,NULL,RHSFunction,&user);
1116:     TSSetRHSJacobian(ts,J,J,RHSJacobian,&user);
1117:   } else {
1118:     TSSetType(ts,TSCN);
1119:     TSSetEquationType(ts,TS_EQ_DAE_IMPLICIT_INDEX1);
1120:     TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&user);
1121:     TSSetIJacobian(ts,J,J,(TSIJacobian)IJacobian,&user);
1122:   }
1123:   TSSetApplicationContext(ts,&user);

1125:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1126:      Set initial conditions
1127:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1128:   SetInitialGuess(X,&user);
1129:   /* Just to set up the Jacobian structure */

1131:   VecDuplicate(X,&Xdot);
1132:   IJacobian(ts,0.0,X,Xdot,0.0,J,J,&user);
1133:   VecDestroy(&Xdot);

1135:   /* Save initial solution */

1137:   idx=user.stepnum*(user.neqs_pgrid+1);
1138:   MatDenseGetArray(user.Sol,&mat);
1139:   VecGetArray(X,&x);

1141:   mat[idx] = 0.0;

1143:   PetscArraycpy(mat+idx+1,x,user.neqs_pgrid);
1144:   MatDenseRestoreArray(user.Sol,&mat);
1145:   VecRestoreArray(X,&x);
1146:   user.stepnum++;

1148:   TSSetMaxTime(ts,user.tmax);
1149:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
1150:   TSSetTimeStep(ts,0.01);
1151:   TSSetFromOptions(ts);
1152:   TSSetPostStep(ts,SaveSolution);
1153:   TSSetSolution(ts,X);

1155:   PetscMalloc1((2*ngen+2),&direction);
1156:   PetscMalloc1((2*ngen+2),&terminate);
1157:   direction[0] = direction[1] = 1;
1158:   terminate[0] = terminate[1] = PETSC_FALSE;
1159:   for (i=0; i < ngen;i++) {
1160:     direction[2+2*i] = -1; direction[2+2*i+1] = 1;
1161:     terminate[2+2*i] = terminate[2+2*i+1] = PETSC_FALSE;
1162:   }

1164:   TSSetEventHandler(ts,2*ngen+2,direction,terminate,EventFunction,PostEventFunction,(void*)&user);

1166:   if (user.semiexplicit) {
1167:     /* Use a semi-explicit approach with the time-stepping done by an explicit method and the
1168:        algrebraic part solved via PostStage and PostEvaluate callbacks
1169:     */
1170:     TSSetType(ts,TSRK);
1171:     TSSetPostStage(ts,PostStage);
1172:     TSSetPostEvaluate(ts,PostEvaluate);
1173:   }

1175:   if (user.setisdiff) {
1176:     /* Create vector of absolute tolerances and set the algebraic part to infinity */
1177:     VecDuplicate(X,&vatol);
1178:     VecSet(vatol,100000.0);
1179:     VecGetArray(vatol,&vatoli);
1180:     ISGetIndices(user.is_diff,&idx3);
1181:     for (k=0; k < 7*ngen; k++) vatoli[idx3[k]] = 1e-2;
1182:     VecRestoreArray(vatol,&vatoli);
1183:   }

1185:   /* Create the nonlinear solver for solving the algebraic system */
1186:   /* Note that although the algebraic system needs to be solved only for
1187:      Idq and V, we reuse the entire system including xgen. The xgen
1188:      variables are held constant by setting their residuals to 0 and
1189:      putting a 1 on the Jacobian diagonal for xgen rows
1190:   */

1192:   VecDuplicate(X,&F_alg);
1193:   SNESCreate(PETSC_COMM_WORLD,&snes_alg);
1194:   SNESSetFunction(snes_alg,F_alg,AlgFunction,&user);
1195:   SNESSetJacobian(snes_alg,J,J,AlgJacobian,&user);
1196:   SNESSetFromOptions(snes_alg);

1198:   user.snes_alg=snes_alg;

1200:   /* Solve */
1201:   TSSolve(ts,X);

1203:   MatAssemblyBegin(user.Sol,MAT_FINAL_ASSEMBLY);
1204:   MatAssemblyEnd(user.Sol,MAT_FINAL_ASSEMBLY);

1206:   MatCreateSeqDense(PETSC_COMM_SELF,user.neqs_pgrid+1,user.stepnum,NULL,&A);
1207:   MatDenseGetArrayRead(user.Sol,&rmat);
1208:   MatDenseGetArray(A,&amat);
1209:   PetscArraycpy(amat,rmat,user.stepnum*(user.neqs_pgrid+1));
1210:   MatDenseRestoreArray(A,&amat);
1211:   MatDenseRestoreArrayRead(user.Sol,&rmat);
1212:   PetscViewerBinaryOpen(PETSC_COMM_SELF,"out.bin",FILE_MODE_WRITE,&viewer);
1213:   MatView(A,viewer);
1214:   PetscViewerDestroy(&viewer);
1215:   MatDestroy(&A);

1217:   PetscFree(direction);
1218:   PetscFree(terminate);
1219:   SNESDestroy(&snes_alg);
1220:   VecDestroy(&F_alg);
1221:   MatDestroy(&J);
1222:   MatDestroy(&user.Ybus);
1223:   MatDestroy(&user.Sol);
1224:   VecDestroy(&X);
1225:   VecDestroy(&user.V0);
1226:   DMDestroy(&user.dmgen);
1227:   DMDestroy(&user.dmnet);
1228:   DMDestroy(&user.dmpgrid);
1229:   ISDestroy(&user.is_diff);
1230:   ISDestroy(&user.is_alg);
1231:   TSDestroy(&ts);
1232:   if (user.setisdiff) {
1233:     VecDestroy(&vatol);
1234:   }
1235:   PetscFinalize();
1236:   return ierr;
1237: }

1239: /*TEST

1241:    build:
1242:       requires: double !complex !defined(PETSC_USE_64BIT_INDICES)

1244:    test:
1245:       suffix: implicit
1246:       args: -ts_monitor -snes_monitor_short
1247:       localrunfiles: petscoptions X.bin Ybus.bin

1249:    test:
1250:       suffix: semiexplicit
1251:       args: -ts_monitor -snes_monitor_short -dae_semiexplicit -ts_rk_type 2a
1252:       localrunfiles: petscoptions X.bin Ybus.bin

1254:    test:
1255:       suffix: steprestart
1256:       # needs ARKIMEX methods with all implicit stages since the mass matrix is not the identity
1257:       args: -ts_monitor -snes_monitor_short -ts_type arkimex -ts_arkimex_type prssp2
1258:       localrunfiles: petscoptions X.bin Ybus.bin

1260: TEST*/