Actual source code: ex9bus.c

petsc-3.12.2 2019-11-22
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  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: */

 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;
200: 

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);
220: 
221:       MatAssemblyBegin(user->Ybus,MAT_FINAL_ASSEMBLY);
222:       MatAssemblyEnd(user->Ybus,MAT_FINAL_ASSEMBLY);
223: 
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);
234: 
235:       MatAssemblyBegin(user->Ybus,MAT_FINAL_ASSEMBLY);
236:       MatAssemblyEnd(user->Ybus,MAT_FINAL_ASSEMBLY);
237: 
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: {
348:   Vec            Xgen,Xnet;
349:   PetscScalar    *xgen,*xnet;
350:   PetscInt       i,idx=0;
351:   PetscScalar    Vr,Vi,IGr,IGi,Vm,Vm2;
352:   PetscScalar    Eqp,Edp,delta;
353:   PetscScalar    Efd,RF,VR; /* Exciter variables */
354:   PetscScalar    Id,Iq;  /* Generator dq axis currents */
355:   PetscScalar    theta,Vd,Vq,SE;

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

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

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

366:   /* Generator subsystem initialization */
367:   VecGetArray(Xgen,&xgen);
368:   VecGetArray(Xnet,&xnet);

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

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

379:     theta = PETSC_PI/2.0 - delta;

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

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

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

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

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

398:     idx = idx + 4;

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

403:     idx = idx + 2;

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

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

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

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

419:     idx = idx + 3;
420:   }

422:   VecRestoreArray(Xgen,&xgen);
423:   VecRestoreArray(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: {
435:   Vec            Xgen,Xnet,Fgen,Fnet;
436:   PetscScalar    *xgen,*xnet,*fgen,*fnet;
437:   PetscInt       i,idx=0;
438:   PetscScalar    Vr,Vi,Vm,Vm2;
439:   PetscScalar    Eqp,Edp,delta,w; /* Generator variables */
440:   PetscScalar    Efd,RF,VR; /* Exciter variables */
441:   PetscScalar    Id,Iq;  /* Generator dq axis currents */
442:   PetscScalar    Vd,Vq,SE;
443:   PetscScalar    IGr,IGi,IDr,IDi;
444:   PetscScalar    Zdq_inv[4],det;
445:   PetscScalar    PD,QD,Vm0,*v0;
446:   PetscInt       k;

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

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

465:   VecGetArray(Xgen,&xgen);
466:   VecGetArray(Xnet,&xnet);
467:   VecGetArray(Fgen,&fgen);
468:   VecGetArray(Fnet,&fnet);

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

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

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

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

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

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

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

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

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

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

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

520:     idx = idx + 9;
521:   }

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

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

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

542:   VecRestoreArray(Xgen,&xgen);
543:   VecRestoreArray(Xnet,&xnet);
544:   VecRestoreArray(Fgen,&fgen);
545:   VecRestoreArray(Fnet,&fnet);

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

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

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

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


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

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

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

623: PetscErrorCode PostStage(TS ts, PetscReal t, PetscInt i, Vec *X)
624: {
626:   Userctx        *user;

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

634: PetscErrorCode PostEvaluate(TS ts)
635: {
637:   Userctx        *user;
638:   Vec            X;

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


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

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

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

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

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

675:     idx = idx + 9;
676:   }

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:   }

687:   MatSeqAIJSetPreallocation(J,0,d_nnz);

689:   PetscFree(d_nnz);
690:   return(0);
691: }

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


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

731:   VecGetArray(Xgen,&xgen);
732:   VecGetArray(Xnet,&xnet);

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

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

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

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

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

762:     /*    fgen[idx+3] = (TM[i] - Edp*Id - Eqp*Iq - (Xqp[i] - Xdp[i])*Id*Iq - D[i]*(w - w_s))/M[i]; */
763:     row[0] = idx + 3;
764:     col[0] = idx; col[1] = idx + 1; col[2] = idx + 3;       col[3] = idx + 4;                  col[4] = idx + 5;
765:     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];
766:     MatSetValues(J,1,row,5,col,val,INSERT_VALUES);

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

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

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

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

784:     /*    fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
785:     row[0] = idx+4;
786:     col[0] = idx;         col[1] = idx+1;        col[2] = idx + 2;
787:     val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0];  val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
788:     col[3] = idx + 4; col[4] = net_start+2*gbus[i];                     col[5] = net_start + 2*gbus[i]+1;
789:     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;
790:     MatSetValues(J,1,row,6,col,val,INSERT_VALUES);

792:     /*  fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
793:     row[0] = idx+5;
794:     col[0] = idx;         col[1] = idx+1;        col[2] = idx + 2;
795:     val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2];  val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
796:     col[3] = idx + 5; col[4] = net_start+2*gbus[i];                     col[5] = net_start + 2*gbus[i]+1;
797:     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;
798:     MatSetValues(J,1,row,6,col,val,INSERT_VALUES);

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

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

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

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

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

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

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

829:     /* Exciter differential equations */

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

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

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

859:     idx        = idx + 9;
860:   }

862:   for (i=0; i<nbus; i++) {
863:     MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
864:     row[0] = net_start + 2*i;
865:     for (k=0; k<ncols; k++) {
866:       col[k] = net_start + cols[k];
867:       val[k] = yvals[k];
868:     }
869:     MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
870:     MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);

872:     MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
873:     row[0] = net_start + 2*i+1;
874:     for (k=0; k<ncols; k++) {
875:       col[k] = net_start + cols[k];
876:       val[k] = yvals[k];
877:     }
878:     MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
879:     MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
880:   }

882:   MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
883:   MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);

885:   VecGetArray(user->V0,&v0);
886:   for (i=0; i < nload; i++) {
887:     Vr      = xnet[2*lbus[i]]; /* Real part of load bus voltage */
888:     Vi      = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
889:     Vm      = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm; Vm4 = Vm2*Vm2;
890:     Vm0     = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
891:     PD      = QD = 0.0;
892:     dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
893:     for (k=0; k < ld_nsegsp[i]; k++) {
894:       PD      += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
895:       dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
896:       dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
897:     }
898:     for (k=0; k < ld_nsegsq[i]; k++) {
899:       QD      += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
900:       dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
901:       dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
902:     }

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

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

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


914:     /*    fnet[2*lbus[i]]   += IDi; */
915:     row[0] = net_start + 2*lbus[i];
916:     col[0] = net_start + 2*lbus[i];  col[1] = net_start + 2*lbus[i]+1;
917:     val[0] = dIDi_dVr;               val[1] = dIDi_dVi;
918:     MatSetValues(J,1,row,2,col,val,ADD_VALUES);
919:     /*    fnet[2*lbus[i]+1] += IDr; */
920:     row[0] = net_start + 2*lbus[i]+1;
921:     col[0] = net_start + 2*lbus[i];  col[1] = net_start + 2*lbus[i]+1;
922:     val[0] = dIDr_dVr;               val[1] = dIDr_dVi;
923:     MatSetValues(J,1,row,2,col,val,ADD_VALUES);
924:   }
925:   VecRestoreArray(user->V0,&v0);

927:   VecRestoreArray(Xgen,&xgen);
928:   VecRestoreArray(Xnet,&xnet);

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

932:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
933:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
934:   return(0);
935: }

937: /*
938:    J = [I, 0
939:         dg_dx, dg_dy]
940: */
941: PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
942: {
944:   Userctx        *user=(Userctx*)ctx;

947:   ResidualJacobian(X,A,B,ctx);
948:   MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
949:   MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);
950:   return(0);
951: }

953: /*
954:    J = [-df_dx, -df_dy
955:         dg_dx, dg_dy]
956: */

958: PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec X,Mat A,Mat B,void *ctx)
959: {
961:   Userctx        *user=(Userctx*)ctx;

964:   user->t = t;

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

968:   return(0);
969: }

971: /*
972:    J = [df_dx-aI, df_dy
973:         dg_dx, dg_dy]
974: */

976: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
977: {
979:   PetscScalar    atmp = (PetscScalar) a;
980:   PetscInt       i,row;

983:   user->t = t;
984:   atmp *= -1;

986:   RHSJacobian(ts,t,X,A,B,user);
987:   for (i=0;i < ngen;i++) {
988:     row = 9*i;
989:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
990:     row  = 9*i+1;
991:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
992:     row  = 9*i+2;
993:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
994:     row  = 9*i+3;
995:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
996:     row  = 9*i+6;
997:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
998:     row  = 9*i+7;
999:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
1000:     row  = 9*i+8;
1001:     MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
1002:   }
1003:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
1004:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
1005:   return(0);
1006: }

1008: int main(int argc,char **argv)
1009: {
1010:   TS               ts;
1011:   SNES              snes_alg;
1012:   PetscErrorCode    ierr;
1013:   PetscMPIInt       size;
1014:   Userctx           user;
1015:   PetscViewer       Xview,Ybusview,viewer;
1016:   Vec               X,F_alg;
1017:   Mat               J,A;
1018:   PetscInt          i,idx,*idx2;
1019:   Vec               Xdot;
1020:   PetscScalar       *x,*mat,*amat;
1021:   const PetscScalar *rmat;
1022:   Vec               vatol;
1023:   PetscInt          *direction;
1024:   PetscBool         *terminate;
1025:   const PetscInt    *idx3;
1026:   PetscScalar       *vatoli;
1027:   PetscInt          k;


1030:   PetscInitialize(&argc,&argv,"petscoptions",help);if (ierr) return ierr;
1031:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
1032:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

1034:   user.neqs_gen   = 9*ngen; /* # eqs. for generator subsystem */
1035:   user.neqs_net   = 2*nbus; /* # eqs. for network subsystem   */
1036:   user.neqs_pgrid = user.neqs_gen + user.neqs_net;

1038:   /* Create indices for differential and algebraic equations */

1040:   PetscMalloc1(7*ngen,&idx2);
1041:   for (i=0; i<ngen; i++) {
1042:     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;
1043:     idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
1044:   }
1045:   ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
1046:   ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
1047:   PetscFree(idx2);

1049:   /* Read initial voltage vector and Ybus */
1050:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
1051:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);

1053:   VecCreate(PETSC_COMM_WORLD,&user.V0);
1054:   VecSetSizes(user.V0,PETSC_DECIDE,user.neqs_net);
1055:   VecLoad(user.V0,Xview);

1057:   MatCreate(PETSC_COMM_WORLD,&user.Ybus);
1058:   MatSetSizes(user.Ybus,PETSC_DECIDE,PETSC_DECIDE,user.neqs_net,user.neqs_net);
1059:   MatSetType(user.Ybus,MATBAIJ);
1060:   /*  MatSetBlockSize(user.Ybus,2); */
1061:   MatLoad(user.Ybus,Ybusview);

1063:   /* Set run time options */
1064:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Transient stability fault options","");
1065:   {
1066:     user.tfaulton  = 1.0;
1067:     user.tfaultoff = 1.2;
1068:     user.Rfault    = 0.0001;
1069:     user.setisdiff = PETSC_FALSE;
1070:     user.semiexplicit = PETSC_FALSE;
1071:     user.faultbus  = 8;
1072:     PetscOptionsReal("-tfaulton","","",user.tfaulton,&user.tfaulton,NULL);
1073:     PetscOptionsReal("-tfaultoff","","",user.tfaultoff,&user.tfaultoff,NULL);
1074:     PetscOptionsInt("-faultbus","","",user.faultbus,&user.faultbus,NULL);
1075:     user.t0        = 0.0;
1076:     user.tmax      = 5.0;
1077:     PetscOptionsReal("-t0","","",user.t0,&user.t0,NULL);
1078:     PetscOptionsReal("-tmax","","",user.tmax,&user.tmax,NULL);
1079:     PetscOptionsBool("-setisdiff","","",user.setisdiff,&user.setisdiff,NULL);
1080:     PetscOptionsBool("-dae_semiexplicit","","",user.semiexplicit,&user.semiexplicit,NULL);
1081:   }
1082:   PetscOptionsEnd();

1084:   PetscViewerDestroy(&Xview);
1085:   PetscViewerDestroy(&Ybusview);

1087:   /* Create DMs for generator and network subsystems */
1088:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
1089:   DMSetOptionsPrefix(user.dmgen,"dmgen_");
1090:   DMSetFromOptions(user.dmgen);
1091:   DMSetUp(user.dmgen);
1092:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
1093:   DMSetOptionsPrefix(user.dmnet,"dmnet_");
1094:   DMSetFromOptions(user.dmnet);
1095:   DMSetUp(user.dmnet);
1096:   /* Create a composite DM packer and add the two DMs */
1097:   DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
1098:   DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
1099:   DMCompositeAddDM(user.dmpgrid,user.dmgen);
1100:   DMCompositeAddDM(user.dmpgrid,user.dmnet);

1102:   DMCreateGlobalVector(user.dmpgrid,&X);

1104:   MatCreate(PETSC_COMM_WORLD,&J);
1105:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,user.neqs_pgrid);
1106:   MatSetFromOptions(J);
1107:   PreallocateJacobian(J,&user);

1109:   /* Create matrix to save solutions at each time step */
1110:   user.stepnum = 0;

1112:   MatCreateSeqDense(PETSC_COMM_SELF,user.neqs_pgrid+1,1002,NULL,&user.Sol);
1113:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1114:      Create timestepping solver context
1115:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1116:   TSCreate(PETSC_COMM_WORLD,&ts);
1117:   TSSetProblemType(ts,TS_NONLINEAR);
1118:   if(user.semiexplicit) {
1119:     TSSetType(ts,TSRK);
1120:     TSSetRHSFunction(ts,NULL,RHSFunction,&user);
1121:     TSSetRHSJacobian(ts,J,J,RHSJacobian,&user);
1122:   } else {
1123:     TSSetType(ts,TSCN);
1124:     TSSetEquationType(ts,TS_EQ_DAE_IMPLICIT_INDEX1);
1125:     TSARKIMEXSetFullyImplicit(ts,PETSC_TRUE);
1126:     TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&user);
1127:     TSSetIJacobian(ts,J,J,(TSIJacobian)IJacobian,&user);
1128:   }
1129:   TSSetApplicationContext(ts,&user);

1131:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1132:      Set initial conditions
1133:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1134:   SetInitialGuess(X,&user);
1135:   /* Just to set up the Jacobian structure */

1137:   VecDuplicate(X,&Xdot);
1138:   IJacobian(ts,0.0,X,Xdot,0.0,J,J,&user);
1139:   VecDestroy(&Xdot);

1141:   /* Save initial solution */

1143:   idx=user.stepnum*(user.neqs_pgrid+1);
1144:   MatDenseGetArray(user.Sol,&mat);
1145:   VecGetArray(X,&x);

1147:   mat[idx] = 0.0;

1149:   PetscArraycpy(mat+idx+1,x,user.neqs_pgrid);
1150:   MatDenseRestoreArray(user.Sol,&mat);
1151:   VecRestoreArray(X,&x);
1152:   user.stepnum++;

1154:   TSSetMaxTime(ts,user.tmax);
1155:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
1156:   TSSetTimeStep(ts,0.01);
1157:   TSSetFromOptions(ts);
1158:   TSSetPostStep(ts,SaveSolution);
1159:   TSSetSolution(ts,X);

1161:   PetscMalloc1((2*ngen+2),&direction);
1162:   PetscMalloc1((2*ngen+2),&terminate);
1163:   direction[0] = direction[1] = 1;
1164:   terminate[0] = terminate[1] = PETSC_FALSE;
1165:   for (i=0; i < ngen;i++) {
1166:     direction[2+2*i] = -1; direction[2+2*i+1] = 1;
1167:     terminate[2+2*i] = terminate[2+2*i+1] = PETSC_FALSE;
1168:   }

1170:   TSSetEventHandler(ts,2*ngen+2,direction,terminate,EventFunction,PostEventFunction,(void*)&user);

1172:   if(user.semiexplicit) {
1173:     /* Use a semi-explicit approach with the time-stepping done by an explicit method and the
1174:        algrebraic part solved via PostStage and PostEvaluate callbacks 
1175:     */
1176:     TSSetType(ts,TSRK);
1177:     TSSetPostStage(ts,PostStage);
1178:     TSSetPostEvaluate(ts,PostEvaluate);
1179:   }


1182:   if(user.setisdiff) {
1183:     /* Create vector of absolute tolerances and set the algebraic part to infinity */
1184:     VecDuplicate(X,&vatol);
1185:     VecSet(vatol,100000.0);
1186:     VecGetArray(vatol,&vatoli);
1187:     ISGetIndices(user.is_diff,&idx3);
1188:     for(k=0; k < 7*ngen; k++) vatoli[idx3[k]] = 1e-2;
1189:     VecRestoreArray(vatol,&vatoli);
1190:   }

1192:   /* Create the nonlinear solver for solving the algebraic system */
1193:   /* Note that although the algebraic system needs to be solved only for
1194:      Idq and V, we reuse the entire system including xgen. The xgen
1195:      variables are held constant by setting their residuals to 0 and
1196:      putting a 1 on the Jacobian diagonal for xgen rows
1197:   */

1199:   VecDuplicate(X,&F_alg);
1200:   SNESCreate(PETSC_COMM_WORLD,&snes_alg);
1201:   SNESSetFunction(snes_alg,F_alg,AlgFunction,&user);
1202:   SNESSetJacobian(snes_alg,J,J,AlgJacobian,&user);
1203:   SNESSetFromOptions(snes_alg);

1205:   user.snes_alg=snes_alg;

1207:   /* Solve */
1208:   TSSolve(ts,X);

1210:   MatAssemblyBegin(user.Sol,MAT_FINAL_ASSEMBLY);
1211:   MatAssemblyEnd(user.Sol,MAT_FINAL_ASSEMBLY);

1213:   MatCreateSeqDense(PETSC_COMM_SELF,user.neqs_pgrid+1,user.stepnum,NULL,&A);
1214:   MatDenseGetArrayRead(user.Sol,&rmat);
1215:   MatDenseGetArray(A,&amat);
1216:   PetscArraycpy(amat,rmat,user.stepnum*(user.neqs_pgrid+1));
1217:   MatDenseRestoreArray(A,&amat);
1218:   MatDenseRestoreArrayRead(user.Sol,&rmat);
1219:   PetscViewerBinaryOpen(PETSC_COMM_SELF,"out.bin",FILE_MODE_WRITE,&viewer);
1220:   MatView(A,viewer);
1221:   PetscViewerDestroy(&viewer);
1222:   MatDestroy(&A);

1224:   PetscFree(direction);
1225:   PetscFree(terminate);
1226:   SNESDestroy(&snes_alg);
1227:   VecDestroy(&F_alg);
1228:   MatDestroy(&J);
1229:   MatDestroy(&user.Ybus);
1230:   MatDestroy(&user.Sol);
1231:   VecDestroy(&X);
1232:   VecDestroy(&user.V0);
1233:   DMDestroy(&user.dmgen);
1234:   DMDestroy(&user.dmnet);
1235:   DMDestroy(&user.dmpgrid);
1236:   ISDestroy(&user.is_diff);
1237:   ISDestroy(&user.is_alg);
1238:   TSDestroy(&ts);
1239:   if(user.setisdiff) {
1240:     VecDestroy(&vatol);
1241:   }
1242:   PetscFinalize();
1243:   return ierr;
1244: }

1246: /*TEST

1248:    build:
1249:       requires: double !complex !define(PETSC_USE_64BIT_INDICES)

1251:    test:
1252:       suffix: implicit
1253:       args: -ts_monitor -snes_monitor_short
1254:       localrunfiles: petscoptions X.bin Ybus.bin

1256:    test:
1257:       suffix: semiexplicit
1258:       args: -ts_monitor -snes_monitor_short -dae_semiexplicit -ts_rk_type 2a
1259:       localrunfiles: petscoptions X.bin Ybus.bin

1261:    test:
1262:       suffix: steprestart
1263:       args: -ts_monitor -snes_monitor_short -ts_type arkimex
1264:       localrunfiles: petscoptions X.bin Ybus.bin

1266: TEST*/