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;
143: PetscScalar Efd,RF,VR,Vr,Vi,Vm;
146: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
147: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
149: VecGetArrayRead(Xgen,&xgen);
150: VecGetArrayRead(Xnet,&xnet);
152: /* Event for fault-on time */
153: fvalue[0] = t - user->tfaulton;
154: /* Event for fault-off time */
155: fvalue[1] = t - user->tfaultoff;
157: for (i=0; i < ngen; i++) {
158: Efd = xgen[idx+6];
159: RF = xgen[idx+7];
160: VR = xgen[idx+8];
162: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
163: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
164: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi);
166: if (!VRatmax[i]) {
167: fvalue[2+2*i] = VRMAX[i] - VR;
168: } else {
169: fvalue[2+2*i] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
170: }
171: if (!VRatmin[i]) {
172: fvalue[2+2*i+1] = VRMIN[i] - VR;
173: } else {
174: fvalue[2+2*i+1] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
175: }
176: idx = idx+9;
177: }
178: VecRestoreArrayRead(Xgen,&xgen);
179: VecRestoreArrayRead(Xnet,&xnet);
181: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
183: return 0;
184: }
186: PetscErrorCode PostEventFunction(TS ts,PetscInt nevents,PetscInt event_list[],PetscReal t,Vec X,PetscBool forwardsolve,void* ctx)
187: {
188: Userctx *user=(Userctx*)ctx;
189: Vec Xgen,Xnet;
190: PetscScalar *xgen,*xnet;
191: PetscInt row_loc,col_loc;
192: PetscScalar val;
193: PetscInt i,idx=0,event_num;
194: PetscScalar fvalue;
195: PetscScalar Efd, RF, VR;
196: PetscScalar Vr,Vi,Vm;
199: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
200: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
202: VecGetArray(Xgen,&xgen);
203: VecGetArray(Xnet,&xnet);
205: for (i=0; i < nevents; i++) {
206: if (event_list[i] == 0) {
207: /* Apply disturbance - resistive fault at user->faultbus */
208: /* This is done by adding shunt conductance to the diagonal location
209: in the Ybus matrix */
210: row_loc = 2*user->faultbus; col_loc = 2*user->faultbus+1; /* Location for G */
211: val = 1/user->Rfault;
212: MatSetValues(user->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
213: row_loc = 2*user->faultbus+1; col_loc = 2*user->faultbus; /* Location for G */
214: val = 1/user->Rfault;
215: MatSetValues(user->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
217: MatAssemblyBegin(user->Ybus,MAT_FINAL_ASSEMBLY);
218: MatAssemblyEnd(user->Ybus,MAT_FINAL_ASSEMBLY);
220: /* Solve the algebraic equations */
221: SNESSolve(user->snes_alg,NULL,X);
222: } else if (event_list[i] == 1) {
223: /* Remove the fault */
224: row_loc = 2*user->faultbus; col_loc = 2*user->faultbus+1;
225: val = -1/user->Rfault;
226: MatSetValues(user->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
227: row_loc = 2*user->faultbus+1; col_loc = 2*user->faultbus;
228: val = -1/user->Rfault;
229: MatSetValues(user->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
231: MatAssemblyBegin(user->Ybus,MAT_FINAL_ASSEMBLY);
232: MatAssemblyEnd(user->Ybus,MAT_FINAL_ASSEMBLY);
234: /* Solve the algebraic equations */
235: SNESSolve(user->snes_alg,NULL,X);
237: /* Check the VR derivatives and reset flags if needed */
238: for (i=0; i < ngen; i++) {
239: Efd = xgen[idx+6];
240: RF = xgen[idx+7];
241: VR = xgen[idx+8];
243: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
244: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
245: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi);
247: if (VRatmax[i]) {
248: fvalue = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
249: if (fvalue < 0) {
250: VRatmax[i] = 0;
251: PetscPrintf(PETSC_COMM_SELF,"VR[%d]: dVR_dt went negative on fault clearing at time %g\n",i,t);
252: }
253: }
254: if (VRatmin[i]) {
255: fvalue = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
257: if (fvalue > 0) {
258: VRatmin[i] = 0;
259: PetscPrintf(PETSC_COMM_SELF,"VR[%d]: dVR_dt went positive on fault clearing at time %g\n",i,t);
260: }
261: }
262: idx = idx+9;
263: }
264: } else {
265: idx = (event_list[i]-2)/2;
266: event_num = (event_list[i]-2)%2;
267: if (event_num == 0) { /* Max VR */
268: if (!VRatmax[idx]) {
269: VRatmax[idx] = 1;
270: PetscPrintf(PETSC_COMM_SELF,"VR[%d]: hit upper limit at time %g\n",idx,t);
271: }
272: else {
273: VRatmax[idx] = 0;
274: PetscPrintf(PETSC_COMM_SELF,"VR[%d]: freeing variable as dVR_dt is negative at time %g\n",idx,t);
275: }
276: } else {
277: if (!VRatmin[idx]) {
278: VRatmin[idx] = 1;
279: PetscPrintf(PETSC_COMM_SELF,"VR[%d]: hit lower limit at time %g\n",idx,t);
280: }
281: else {
282: VRatmin[idx] = 0;
283: PetscPrintf(PETSC_COMM_SELF,"VR[%d]: freeing variable as dVR_dt is positive at time %g\n",idx,t);
284: }
285: }
286: }
287: }
289: VecRestoreArray(Xgen,&xgen);
290: VecRestoreArray(Xnet,&xnet);
292: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
294: return 0;
295: }
297: /* Converts from machine frame (dq) to network (phase a real,imag) reference frame */
298: PetscErrorCode dq2ri(PetscScalar Fd,PetscScalar Fq,PetscScalar delta,PetscScalar *Fr, PetscScalar *Fi)
299: {
300: *Fr = Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
301: *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
302: return 0;
303: }
305: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
306: PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd, PetscScalar *Fq)
307: {
308: *Fd = Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
309: *Fq = Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
310: return 0;
311: }
313: /* Saves the solution at each time to a matrix */
314: PetscErrorCode SaveSolution(TS ts)
315: {
316: Userctx *user;
317: Vec X;
318: const PetscScalar *x;
319: PetscScalar *mat;
320: PetscInt idx;
321: PetscReal t;
323: TSGetApplicationContext(ts,&user);
324: TSGetTime(ts,&t);
325: TSGetSolution(ts,&X);
326: idx = user->stepnum*(user->neqs_pgrid+1);
327: MatDenseGetArray(user->Sol,&mat);
328: VecGetArrayRead(X,&x);
329: mat[idx] = t;
330: PetscArraycpy(mat+idx+1,x,user->neqs_pgrid);
331: MatDenseRestoreArray(user->Sol,&mat);
332: VecRestoreArrayRead(X,&x);
333: user->stepnum++;
334: return 0;
335: }
337: PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
338: {
339: Vec Xgen,Xnet;
340: PetscScalar *xgen;
341: const PetscScalar *xnet;
342: PetscInt i,idx=0;
343: PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
344: PetscScalar Eqp,Edp,delta;
345: PetscScalar Efd,RF,VR; /* Exciter variables */
346: PetscScalar Id,Iq; /* Generator dq axis currents */
347: PetscScalar theta,Vd,Vq,SE;
349: M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
350: D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
352: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
354: /* Network subsystem initialization */
355: VecCopy(user->V0,Xnet);
357: /* Generator subsystem initialization */
358: VecGetArrayWrite(Xgen,&xgen);
359: VecGetArrayRead(Xnet,&xnet);
361: for (i=0; i < ngen; i++) {
362: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
363: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
364: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
365: IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
366: IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;
368: delta = PetscAtan2Real(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
370: theta = PETSC_PI/2.0 - delta;
372: Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
373: Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
375: Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
376: Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
378: Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
379: Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
381: TM[i] = PG[i];
383: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
384: xgen[idx] = Eqp;
385: xgen[idx+1] = Edp;
386: xgen[idx+2] = delta;
387: xgen[idx+3] = w_s;
389: idx = idx + 4;
391: xgen[idx] = Id;
392: xgen[idx+1] = Iq;
394: idx = idx + 2;
396: /* Exciter */
397: Efd = Eqp + (Xd[i] - Xdp[i])*Id;
398: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
399: VR = KE[i]*Efd + SE;
400: RF = KF[i]*Efd/TF[i];
402: xgen[idx] = Efd;
403: xgen[idx+1] = RF;
404: xgen[idx+2] = VR;
406: Vref[i] = Vm + (VR/KA[i]);
408: VRatmin[i] = VRatmax[i] = 0;
410: idx = idx + 3;
411: }
412: VecRestoreArrayWrite(Xgen,&xgen);
413: VecRestoreArrayRead(Xnet,&xnet);
415: /* VecView(Xgen,0); */
416: DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet);
417: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
418: return 0;
419: }
421: /* Computes F = [f(x,y);g(x,y)] */
422: PetscErrorCode ResidualFunction(Vec X, Vec F, Userctx *user)
423: {
424: Vec Xgen,Xnet,Fgen,Fnet;
425: const PetscScalar *xgen,*xnet;
426: PetscScalar *fgen,*fnet;
427: PetscInt i,idx=0;
428: PetscScalar Vr,Vi,Vm,Vm2;
429: PetscScalar Eqp,Edp,delta,w; /* Generator variables */
430: PetscScalar Efd,RF,VR; /* Exciter variables */
431: PetscScalar Id,Iq; /* Generator dq axis currents */
432: PetscScalar Vd,Vq,SE;
433: PetscScalar IGr,IGi,IDr,IDi;
434: PetscScalar Zdq_inv[4],det;
435: PetscScalar PD,QD,Vm0,*v0;
436: PetscInt k;
438: VecZeroEntries(F);
439: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
440: DMCompositeGetLocalVectors(user->dmpgrid,&Fgen,&Fnet);
441: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
442: DMCompositeScatter(user->dmpgrid,F,Fgen,Fnet);
444: /* Network current balance residual IG + Y*V + IL = 0. Only YV is added here.
445: The generator current injection, IG, and load current injection, ID are added later
446: */
447: /* Note that the values in Ybus are stored assuming the imaginary current balance
448: equation is ordered first followed by real current balance equation for each bus.
449: Thus imaginary current contribution goes in location 2*i, and
450: real current contribution in 2*i+1
451: */
452: MatMult(user->Ybus,Xnet,Fnet);
454: VecGetArrayRead(Xgen,&xgen);
455: VecGetArrayRead(Xnet,&xnet);
456: VecGetArrayWrite(Fgen,&fgen);
457: VecGetArrayWrite(Fnet,&fnet);
459: /* Generator subsystem */
460: for (i=0; i < ngen; i++) {
461: Eqp = xgen[idx];
462: Edp = xgen[idx+1];
463: delta = xgen[idx+2];
464: w = xgen[idx+3];
465: Id = xgen[idx+4];
466: Iq = xgen[idx+5];
467: Efd = xgen[idx+6];
468: RF = xgen[idx+7];
469: VR = xgen[idx+8];
471: /* Generator differential equations */
472: fgen[idx] = (-Eqp - (Xd[i] - Xdp[i])*Id + Efd)/Td0p[i];
473: fgen[idx+1] = (-Edp + (Xq[i] - Xqp[i])*Iq)/Tq0p[i];
474: fgen[idx+2] = w - w_s;
475: fgen[idx+3] = (TM[i] - Edp*Id - Eqp*Iq - (Xqp[i] - Xdp[i])*Id*Iq - D[i]*(w - w_s))/M[i];
477: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
478: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
480: ri2dq(Vr,Vi,delta,&Vd,&Vq);
481: /* Algebraic equations for stator currents */
482: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
484: Zdq_inv[0] = Rs[i]/det;
485: Zdq_inv[1] = Xqp[i]/det;
486: Zdq_inv[2] = -Xdp[i]/det;
487: Zdq_inv[3] = Rs[i]/det;
489: fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id;
490: fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq;
492: /* Add generator current injection to network */
493: dq2ri(Id,Iq,delta,&IGr,&IGi);
495: fnet[2*gbus[i]] -= IGi;
496: fnet[2*gbus[i]+1] -= IGr;
498: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
500: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
502: /* Exciter differential equations */
503: fgen[idx+6] = (-KE[i]*Efd - SE + VR)/TE[i];
504: fgen[idx+7] = (-RF + KF[i]*Efd/TF[i])/TF[i];
505: if (VRatmax[i]) fgen[idx+8] = VR - VRMAX[i];
506: else if (VRatmin[i]) fgen[idx+8] = VRMIN[i] - VR;
507: else fgen[idx+8] = (-VR + KA[i]*RF - KA[i]*KF[i]*Efd/TF[i] + KA[i]*(Vref[i] - Vm))/TA[i];
509: idx = idx + 9;
510: }
512: VecGetArray(user->V0,&v0);
513: for (i=0; i < nload; i++) {
514: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
515: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
516: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
517: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
518: PD = QD = 0.0;
519: for (k=0; k < ld_nsegsp[i]; k++) PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
520: for (k=0; k < ld_nsegsq[i]; k++) QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
522: /* Load currents */
523: IDr = (PD*Vr + QD*Vi)/Vm2;
524: IDi = (-QD*Vr + PD*Vi)/Vm2;
526: fnet[2*lbus[i]] += IDi;
527: fnet[2*lbus[i]+1] += IDr;
528: }
529: VecRestoreArray(user->V0,&v0);
531: VecRestoreArrayRead(Xgen,&xgen);
532: VecRestoreArrayRead(Xnet,&xnet);
533: VecRestoreArrayWrite(Fgen,&fgen);
534: VecRestoreArrayWrite(Fnet,&fnet);
536: DMCompositeGather(user->dmpgrid,INSERT_VALUES,F,Fgen,Fnet);
537: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
538: DMCompositeRestoreLocalVectors(user->dmpgrid,&Fgen,&Fnet);
539: return 0;
540: }
542: /* f(x,y)
543: g(x,y)
544: */
545: PetscErrorCode RHSFunction(TS ts,PetscReal t, Vec X, Vec F, void *ctx)
546: {
547: Userctx *user=(Userctx*)ctx;
549: user->t = t;
550: ResidualFunction(X,F,user);
551: return 0;
552: }
554: /* f(x,y) - \dot{x}
555: g(x,y) = 0
556: */
557: PetscErrorCode IFunction(TS ts,PetscReal t, Vec X, Vec Xdot, Vec F, void *ctx)
558: {
559: PetscScalar *f;
560: const PetscScalar *xdot;
561: PetscInt i;
563: RHSFunction(ts,t,X,F,ctx);
564: VecScale(F,-1.0);
565: VecGetArray(F,&f);
566: VecGetArrayRead(Xdot,&xdot);
567: for (i=0;i < ngen;i++) {
568: f[9*i] += xdot[9*i];
569: f[9*i+1] += xdot[9*i+1];
570: f[9*i+2] += xdot[9*i+2];
571: f[9*i+3] += xdot[9*i+3];
572: f[9*i+6] += xdot[9*i+6];
573: f[9*i+7] += xdot[9*i+7];
574: f[9*i+8] += xdot[9*i+8];
575: }
576: VecRestoreArray(F,&f);
577: VecRestoreArrayRead(Xdot,&xdot);
578: return 0;
579: }
581: /* This function is used for solving the algebraic system only during fault on and
582: off times. It computes the entire F and then zeros out the part corresponding to
583: differential equations
584: F = [0;g(y)];
585: */
586: PetscErrorCode AlgFunction(SNES snes, Vec X, Vec F, void *ctx)
587: {
588: Userctx *user=(Userctx*)ctx;
589: PetscScalar *f;
590: PetscInt i;
592: ResidualFunction(X,F,user);
593: VecGetArray(F,&f);
594: for (i=0; i < ngen; i++) {
595: f[9*i] = 0;
596: f[9*i+1] = 0;
597: f[9*i+2] = 0;
598: f[9*i+3] = 0;
599: f[9*i+6] = 0;
600: f[9*i+7] = 0;
601: f[9*i+8] = 0;
602: }
603: VecRestoreArray(F,&f);
604: return 0;
605: }
607: PetscErrorCode PostStage(TS ts, PetscReal t, PetscInt i, Vec *X)
608: {
609: Userctx *user;
611: TSGetApplicationContext(ts,&user);
612: SNESSolve(user->snes_alg,NULL,X[i]);
613: return 0;
614: }
616: PetscErrorCode PostEvaluate(TS ts)
617: {
618: Userctx *user;
619: Vec X;
621: TSGetApplicationContext(ts,&user);
622: TSGetSolution(ts,&X);
623: SNESSolve(user->snes_alg,NULL,X);
624: return 0;
625: }
627: PetscErrorCode PreallocateJacobian(Mat J, Userctx *user)
628: {
629: PetscInt *d_nnz;
630: PetscInt i,idx=0,start=0;
631: PetscInt ncols;
633: PetscMalloc1(user->neqs_pgrid,&d_nnz);
634: for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
635: /* Generator subsystem */
636: for (i=0; i < ngen; i++) {
638: d_nnz[idx] += 3;
639: d_nnz[idx+1] += 2;
640: d_nnz[idx+2] += 2;
641: d_nnz[idx+3] += 5;
642: d_nnz[idx+4] += 6;
643: d_nnz[idx+5] += 6;
645: d_nnz[user->neqs_gen+2*gbus[i]] += 3;
646: d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;
648: d_nnz[idx+6] += 2;
649: d_nnz[idx+7] += 2;
650: d_nnz[idx+8] += 5;
652: idx = idx + 9;
653: }
654: start = user->neqs_gen;
656: for (i=0; i < nbus; i++) {
657: MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL);
658: d_nnz[start+2*i] += ncols;
659: d_nnz[start+2*i+1] += ncols;
660: MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL);
661: }
662: MatSeqAIJSetPreallocation(J,0,d_nnz);
663: PetscFree(d_nnz);
664: return 0;
665: }
667: /*
668: J = [df_dx, df_dy
669: dg_dx, dg_dy]
670: */
671: PetscErrorCode ResidualJacobian(Vec X,Mat J,Mat B,void *ctx)
672: {
673: Userctx *user = (Userctx*)ctx;
674: Vec Xgen,Xnet;
675: const PetscScalar *xgen,*xnet;
676: PetscInt i,idx=0;
677: PetscScalar Vr,Vi,Vm,Vm2;
678: PetscScalar Eqp,Edp,delta; /* Generator variables */
679: PetscScalar Efd;
680: PetscScalar Id,Iq; /* Generator dq axis currents */
681: PetscScalar Vd,Vq;
682: PetscScalar val[10];
683: PetscInt row[2],col[10];
684: PetscInt net_start = user->neqs_gen;
685: PetscScalar Zdq_inv[4],det;
686: PetscScalar dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
687: PetscScalar dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
688: PetscScalar dSE_dEfd;
689: PetscScalar dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
690: PetscInt ncols;
691: const PetscInt *cols;
692: const PetscScalar *yvals;
693: PetscInt k;
694: PetscScalar PD,QD,Vm0,Vm4;
695: const PetscScalar *v0;
696: PetscScalar dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
697: PetscScalar dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;
699: MatZeroEntries(B);
700: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
701: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
703: VecGetArrayRead(Xgen,&xgen);
704: VecGetArrayRead(Xnet,&xnet);
706: /* Generator subsystem */
707: for (i=0; i < ngen; i++) {
708: Eqp = xgen[idx];
709: Edp = xgen[idx+1];
710: delta = xgen[idx+2];
711: Id = xgen[idx+4];
712: Iq = xgen[idx+5];
713: Efd = xgen[idx+6];
715: /* fgen[idx] = (-Eqp - (Xd[i] - Xdp[i])*Id + Efd)/Td0p[i]; */
716: row[0] = idx;
717: col[0] = idx; col[1] = idx+4; col[2] = idx+6;
718: val[0] = -1/ Td0p[i]; val[1] = -(Xd[i] - Xdp[i])/ Td0p[i]; val[2] = 1/Td0p[i];
720: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
722: /* fgen[idx+1] = (-Edp + (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
723: row[0] = idx + 1;
724: col[0] = idx + 1; col[1] = idx+5;
725: val[0] = -1/Tq0p[i]; val[1] = (Xq[i] - Xqp[i])/Tq0p[i];
726: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
728: /* fgen[idx+2] = w - w_s; */
729: row[0] = idx + 2;
730: col[0] = idx + 2; col[1] = idx + 3;
731: val[0] = 0; val[1] = 1;
732: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
734: /* fgen[idx+3] = (TM[i] - Edp*Id - Eqp*Iq - (Xqp[i] - Xdp[i])*Id*Iq - D[i]*(w - w_s))/M[i]; */
735: row[0] = idx + 3;
736: col[0] = idx; col[1] = idx + 1; col[2] = idx + 3; col[3] = idx + 4; col[4] = idx + 5;
737: 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];
738: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
740: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
741: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
742: ri2dq(Vr,Vi,delta,&Vd,&Vq);
744: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
746: Zdq_inv[0] = Rs[i]/det;
747: Zdq_inv[1] = Xqp[i]/det;
748: Zdq_inv[2] = -Xdp[i]/det;
749: Zdq_inv[3] = Rs[i]/det;
751: dVd_dVr = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
752: dVq_dVr = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
753: dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
754: dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);
756: /* fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
757: row[0] = idx+4;
758: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
759: val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0]; val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
760: col[3] = idx + 4; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
761: 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;
762: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
764: /* fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
765: row[0] = idx+5;
766: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
767: val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2]; val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
768: col[3] = idx + 5; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
769: 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;
770: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
772: dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
773: dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
774: dIGr_dId = PetscSinScalar(delta); dIGr_dIq = PetscCosScalar(delta);
775: dIGi_dId = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);
777: /* fnet[2*gbus[i]] -= IGi; */
778: row[0] = net_start + 2*gbus[i];
779: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
780: val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
781: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
783: /* fnet[2*gbus[i]+1] -= IGr; */
784: row[0] = net_start + 2*gbus[i]+1;
785: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
786: val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
787: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
789: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
791: /* fgen[idx+6] = (-KE[i]*Efd - SE + VR)/TE[i]; */
792: /* SE = k1[i]*PetscExpScalar(k2[i]*Efd); */
794: dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);
796: row[0] = idx + 6;
797: col[0] = idx + 6; col[1] = idx + 8;
798: val[0] = (-KE[i] - dSE_dEfd)/TE[i]; val[1] = 1/TE[i];
799: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
801: /* Exciter differential equations */
803: /* fgen[idx+7] = (-RF + KF[i]*Efd/TF[i])/TF[i]; */
804: row[0] = idx + 7;
805: col[0] = idx + 6; col[1] = idx + 7;
806: val[0] = (KF[i]/TF[i])/TF[i]; val[1] = -1/TF[i];
807: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
809: /* fgen[idx+8] = (-VR + KA[i]*RF - KA[i]*KF[i]*Efd/TF[i] + KA[i]*(Vref[i] - Vm))/TA[i]; */
810: /* Vm = (Vd^2 + Vq^2)^0.5; */
812: row[0] = idx + 8;
813: if (VRatmax[i]) {
814: col[0] = idx + 8; val[0] = 1.0;
815: MatSetValues(J,1,row,1,col,val,INSERT_VALUES);
816: } else if (VRatmin[i]) {
817: col[0] = idx + 8; val[0] = -1.0;
818: MatSetValues(J,1,row,1,col,val,INSERT_VALUES);
819: } else {
820: dVm_dVd = Vd/Vm; dVm_dVq = Vq/Vm;
821: dVm_dVr = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
822: dVm_dVi = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
823: row[0] = idx + 8;
824: col[0] = idx + 6; col[1] = idx + 7; col[2] = idx + 8;
825: val[0] = -(KA[i]*KF[i]/TF[i])/TA[i]; val[1] = KA[i]/TA[i]; val[2] = -1/TA[i];
826: col[3] = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
827: val[3] = -KA[i]*dVm_dVr/TA[i]; val[4] = -KA[i]*dVm_dVi/TA[i];
828: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
829: }
830: idx = idx + 9;
831: }
833: for (i=0; i<nbus; i++) {
834: MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
835: row[0] = net_start + 2*i;
836: for (k=0; k<ncols; k++) {
837: col[k] = net_start + cols[k];
838: val[k] = yvals[k];
839: }
840: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
841: MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);
843: MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
844: row[0] = net_start + 2*i+1;
845: for (k=0; k<ncols; k++) {
846: col[k] = net_start + cols[k];
847: val[k] = yvals[k];
848: }
849: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
850: MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
851: }
853: MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
854: MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);
856: VecGetArrayRead(user->V0,&v0);
857: for (i=0; i < nload; i++) {
858: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
859: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
860: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm; Vm4 = Vm2*Vm2;
861: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
862: PD = QD = 0.0;
863: dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
864: for (k=0; k < ld_nsegsp[i]; k++) {
865: PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
866: dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
867: dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
868: }
869: for (k=0; k < ld_nsegsq[i]; k++) {
870: QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
871: dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
872: dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
873: }
875: /* IDr = (PD*Vr + QD*Vi)/Vm2; */
876: /* IDi = (-QD*Vr + PD*Vi)/Vm2; */
878: dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
879: dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;
881: dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
882: dIDi_dVi = (-dQD_dVi*Vr + dPD_dVi*Vi + PD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vi)/Vm4;
884: /* fnet[2*lbus[i]] += IDi; */
885: row[0] = net_start + 2*lbus[i];
886: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
887: val[0] = dIDi_dVr; val[1] = dIDi_dVi;
888: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
889: /* fnet[2*lbus[i]+1] += IDr; */
890: row[0] = net_start + 2*lbus[i]+1;
891: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
892: val[0] = dIDr_dVr; val[1] = dIDr_dVi;
893: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
894: }
895: VecRestoreArrayRead(user->V0,&v0);
897: VecRestoreArrayRead(Xgen,&xgen);
898: VecRestoreArrayRead(Xnet,&xnet);
900: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
902: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
903: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
904: return 0;
905: }
907: /*
908: J = [I, 0
909: dg_dx, dg_dy]
910: */
911: PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
912: {
913: Userctx *user=(Userctx*)ctx;
915: ResidualJacobian(X,A,B,ctx);
916: MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
917: MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);
918: return 0;
919: }
921: /*
922: J = [-df_dx, -df_dy
923: dg_dx, dg_dy]
924: */
926: PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec X,Mat A,Mat B,void *ctx)
927: {
928: Userctx *user=(Userctx*)ctx;
930: user->t = t;
932: ResidualJacobian(X,A,B,user);
934: return 0;
935: }
937: /*
938: J = [df_dx-aI, df_dy
939: dg_dx, dg_dy]
940: */
942: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
943: {
944: PetscScalar atmp = (PetscScalar) a;
945: PetscInt i,row;
947: user->t = t;
949: RHSJacobian(ts,t,X,A,B,user);
950: MatScale(B,-1.0);
951: for (i=0;i < ngen;i++) {
952: row = 9*i;
953: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
954: row = 9*i+1;
955: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
956: row = 9*i+2;
957: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
958: row = 9*i+3;
959: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
960: row = 9*i+6;
961: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
962: row = 9*i+7;
963: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
964: row = 9*i+8;
965: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
966: }
967: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
968: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
969: return 0;
970: }
972: int main(int argc,char **argv)
973: {
974: TS ts;
975: SNES snes_alg;
976: PetscErrorCode ierr;
977: PetscMPIInt size;
978: Userctx user;
979: PetscViewer Xview,Ybusview,viewer;
980: Vec X,F_alg;
981: Mat J,A;
982: PetscInt i,idx,*idx2;
983: Vec Xdot;
984: PetscScalar *x,*mat,*amat;
985: const PetscScalar *rmat;
986: Vec vatol;
987: PetscInt *direction;
988: PetscBool *terminate;
989: const PetscInt *idx3;
990: PetscScalar *vatoli;
991: PetscInt k;
993: PetscInitialize(&argc,&argv,"petscoptions",help);
994: MPI_Comm_size(PETSC_COMM_WORLD,&size);
997: user.neqs_gen = 9*ngen; /* # eqs. for generator subsystem */
998: user.neqs_net = 2*nbus; /* # eqs. for network subsystem */
999: user.neqs_pgrid = user.neqs_gen + user.neqs_net;
1001: /* Create indices for differential and algebraic equations */
1003: PetscMalloc1(7*ngen,&idx2);
1004: for (i=0; i<ngen; i++) {
1005: 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;
1006: idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
1007: }
1008: ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
1009: ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
1010: PetscFree(idx2);
1012: /* Read initial voltage vector and Ybus */
1013: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
1014: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);
1016: VecCreate(PETSC_COMM_WORLD,&user.V0);
1017: VecSetSizes(user.V0,PETSC_DECIDE,user.neqs_net);
1018: VecLoad(user.V0,Xview);
1020: MatCreate(PETSC_COMM_WORLD,&user.Ybus);
1021: MatSetSizes(user.Ybus,PETSC_DECIDE,PETSC_DECIDE,user.neqs_net,user.neqs_net);
1022: MatSetType(user.Ybus,MATBAIJ);
1023: /* MatSetBlockSize(user.Ybus,2); */
1024: MatLoad(user.Ybus,Ybusview);
1026: /* Set run time options */
1027: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Transient stability fault options","");
1028: {
1029: user.tfaulton = 1.0;
1030: user.tfaultoff = 1.2;
1031: user.Rfault = 0.0001;
1032: user.setisdiff = PETSC_FALSE;
1033: user.semiexplicit = PETSC_FALSE;
1034: user.faultbus = 8;
1035: PetscOptionsReal("-tfaulton","","",user.tfaulton,&user.tfaulton,NULL);
1036: PetscOptionsReal("-tfaultoff","","",user.tfaultoff,&user.tfaultoff,NULL);
1037: PetscOptionsInt("-faultbus","","",user.faultbus,&user.faultbus,NULL);
1038: user.t0 = 0.0;
1039: user.tmax = 5.0;
1040: PetscOptionsReal("-t0","","",user.t0,&user.t0,NULL);
1041: PetscOptionsReal("-tmax","","",user.tmax,&user.tmax,NULL);
1042: PetscOptionsBool("-setisdiff","","",user.setisdiff,&user.setisdiff,NULL);
1043: PetscOptionsBool("-dae_semiexplicit","","",user.semiexplicit,&user.semiexplicit,NULL);
1044: }
1045: PetscOptionsEnd();
1047: PetscViewerDestroy(&Xview);
1048: PetscViewerDestroy(&Ybusview);
1050: /* Create DMs for generator and network subsystems */
1051: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
1052: DMSetOptionsPrefix(user.dmgen,"dmgen_");
1053: DMSetFromOptions(user.dmgen);
1054: DMSetUp(user.dmgen);
1055: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
1056: DMSetOptionsPrefix(user.dmnet,"dmnet_");
1057: DMSetFromOptions(user.dmnet);
1058: DMSetUp(user.dmnet);
1059: /* Create a composite DM packer and add the two DMs */
1060: DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
1061: DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
1062: DMCompositeAddDM(user.dmpgrid,user.dmgen);
1063: DMCompositeAddDM(user.dmpgrid,user.dmnet);
1065: DMCreateGlobalVector(user.dmpgrid,&X);
1067: MatCreate(PETSC_COMM_WORLD,&J);
1068: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,user.neqs_pgrid);
1069: MatSetFromOptions(J);
1070: PreallocateJacobian(J,&user);
1072: /* Create matrix to save solutions at each time step */
1073: user.stepnum = 0;
1075: MatCreateSeqDense(PETSC_COMM_SELF,user.neqs_pgrid+1,1002,NULL,&user.Sol);
1076: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1077: Create timestepping solver context
1078: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1079: TSCreate(PETSC_COMM_WORLD,&ts);
1080: TSSetProblemType(ts,TS_NONLINEAR);
1081: if (user.semiexplicit) {
1082: TSSetType(ts,TSRK);
1083: TSSetRHSFunction(ts,NULL,RHSFunction,&user);
1084: TSSetRHSJacobian(ts,J,J,RHSJacobian,&user);
1085: } else {
1086: TSSetType(ts,TSCN);
1087: TSSetEquationType(ts,TS_EQ_DAE_IMPLICIT_INDEX1);
1088: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&user);
1089: TSSetIJacobian(ts,J,J,(TSIJacobian)IJacobian,&user);
1090: }
1091: TSSetApplicationContext(ts,&user);
1093: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1094: Set initial conditions
1095: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1096: SetInitialGuess(X,&user);
1097: /* Just to set up the Jacobian structure */
1099: VecDuplicate(X,&Xdot);
1100: IJacobian(ts,0.0,X,Xdot,0.0,J,J,&user);
1101: VecDestroy(&Xdot);
1103: /* Save initial solution */
1105: idx=user.stepnum*(user.neqs_pgrid+1);
1106: MatDenseGetArray(user.Sol,&mat);
1107: VecGetArray(X,&x);
1109: mat[idx] = 0.0;
1111: PetscArraycpy(mat+idx+1,x,user.neqs_pgrid);
1112: MatDenseRestoreArray(user.Sol,&mat);
1113: VecRestoreArray(X,&x);
1114: user.stepnum++;
1116: TSSetMaxTime(ts,user.tmax);
1117: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
1118: TSSetTimeStep(ts,0.01);
1119: TSSetFromOptions(ts);
1120: TSSetPostStep(ts,SaveSolution);
1121: TSSetSolution(ts,X);
1123: PetscMalloc1((2*ngen+2),&direction);
1124: PetscMalloc1((2*ngen+2),&terminate);
1125: direction[0] = direction[1] = 1;
1126: terminate[0] = terminate[1] = PETSC_FALSE;
1127: for (i=0; i < ngen;i++) {
1128: direction[2+2*i] = -1; direction[2+2*i+1] = 1;
1129: terminate[2+2*i] = terminate[2+2*i+1] = PETSC_FALSE;
1130: }
1132: TSSetEventHandler(ts,2*ngen+2,direction,terminate,EventFunction,PostEventFunction,(void*)&user);
1134: if (user.semiexplicit) {
1135: /* Use a semi-explicit approach with the time-stepping done by an explicit method and the
1136: algrebraic part solved via PostStage and PostEvaluate callbacks
1137: */
1138: TSSetType(ts,TSRK);
1139: TSSetPostStage(ts,PostStage);
1140: TSSetPostEvaluate(ts,PostEvaluate);
1141: }
1143: if (user.setisdiff) {
1144: /* Create vector of absolute tolerances and set the algebraic part to infinity */
1145: VecDuplicate(X,&vatol);
1146: VecSet(vatol,100000.0);
1147: VecGetArray(vatol,&vatoli);
1148: ISGetIndices(user.is_diff,&idx3);
1149: for (k=0; k < 7*ngen; k++) vatoli[idx3[k]] = 1e-2;
1150: VecRestoreArray(vatol,&vatoli);
1151: }
1153: /* Create the nonlinear solver for solving the algebraic system */
1154: /* Note that although the algebraic system needs to be solved only for
1155: Idq and V, we reuse the entire system including xgen. The xgen
1156: variables are held constant by setting their residuals to 0 and
1157: putting a 1 on the Jacobian diagonal for xgen rows
1158: */
1160: VecDuplicate(X,&F_alg);
1161: SNESCreate(PETSC_COMM_WORLD,&snes_alg);
1162: SNESSetFunction(snes_alg,F_alg,AlgFunction,&user);
1163: SNESSetJacobian(snes_alg,J,J,AlgJacobian,&user);
1164: SNESSetFromOptions(snes_alg);
1166: user.snes_alg=snes_alg;
1168: /* Solve */
1169: TSSolve(ts,X);
1171: MatAssemblyBegin(user.Sol,MAT_FINAL_ASSEMBLY);
1172: MatAssemblyEnd(user.Sol,MAT_FINAL_ASSEMBLY);
1174: MatCreateSeqDense(PETSC_COMM_SELF,user.neqs_pgrid+1,user.stepnum,NULL,&A);
1175: MatDenseGetArrayRead(user.Sol,&rmat);
1176: MatDenseGetArray(A,&amat);
1177: PetscArraycpy(amat,rmat,user.stepnum*(user.neqs_pgrid+1));
1178: MatDenseRestoreArray(A,&amat);
1179: MatDenseRestoreArrayRead(user.Sol,&rmat);
1180: PetscViewerBinaryOpen(PETSC_COMM_SELF,"out.bin",FILE_MODE_WRITE,&viewer);
1181: MatView(A,viewer);
1182: PetscViewerDestroy(&viewer);
1183: MatDestroy(&A);
1185: PetscFree(direction);
1186: PetscFree(terminate);
1187: SNESDestroy(&snes_alg);
1188: VecDestroy(&F_alg);
1189: MatDestroy(&J);
1190: MatDestroy(&user.Ybus);
1191: MatDestroy(&user.Sol);
1192: VecDestroy(&X);
1193: VecDestroy(&user.V0);
1194: DMDestroy(&user.dmgen);
1195: DMDestroy(&user.dmnet);
1196: DMDestroy(&user.dmpgrid);
1197: ISDestroy(&user.is_diff);
1198: ISDestroy(&user.is_alg);
1199: TSDestroy(&ts);
1200: if (user.setisdiff) {
1201: VecDestroy(&vatol);
1202: }
1203: PetscFinalize();
1204: return 0;
1205: }
1207: /*TEST
1209: build:
1210: requires: double !complex !defined(PETSC_USE_64BIT_INDICES)
1212: test:
1213: suffix: implicit
1214: args: -ts_monitor -snes_monitor_short
1215: localrunfiles: petscoptions X.bin Ybus.bin
1217: test:
1218: suffix: semiexplicit
1219: args: -ts_monitor -snes_monitor_short -dae_semiexplicit -ts_rk_type 2a
1220: localrunfiles: petscoptions X.bin Ybus.bin
1222: test:
1223: suffix: steprestart
1224: # needs ARKIMEX methods with all implicit stages since the mass matrix is not the identity
1225: args: -ts_monitor -snes_monitor_short -ts_type arkimex -ts_arkimex_type prssp2
1226: localrunfiles: petscoptions X.bin Ybus.bin
1228: TEST*/