Actual source code: ex9busopt.c
1: static char help[] = "Application of adjoint sensitivity analysis for power grid stability analysis of WECC 9 bus system.\n\
2: This example is based on the 9-bus (node) example given in the book Power\n\
3: Systems Dynamics and Stability (Chapter 7) by P. Sauer and M. A. Pai.\n\
4: The power grid in this example consists of 9 buses (nodes), 3 generators,\n\
5: 3 loads, and 9 transmission lines. The network equations are written\n\
6: in current balance form using rectangular coordinates.\n\n";
8: /*
9: This code demonstrates how to solve a DAE-constrained optimization problem with TAO, TSAdjoint and TS.
10: The objectivie is to find optimal parameter PG for each generator to minizie the frequency violations due to faults.
11: The problem features discontinuities and a cost function in integral form.
12: The gradient is computed with the discrete adjoint of an implicit theta method, see ex9busadj.c for details.
13: */
15: #include <petsctao.h>
16: #include <petscts.h>
17: #include <petscdm.h>
18: #include <petscdmda.h>
19: #include <petscdmcomposite.h>
20: #include <petsctime.h>
22: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
24: #define freq 60
25: #define w_s (2*PETSC_PI*freq)
27: /* Sizes and indices */
28: const PetscInt nbus = 9; /* Number of network buses */
29: const PetscInt ngen = 3; /* Number of generators */
30: const PetscInt nload = 3; /* Number of loads */
31: const PetscInt gbus[3] = {0,1,2}; /* Buses at which generators are incident */
32: const PetscInt lbus[3] = {4,5,7}; /* Buses at which loads are incident */
34: /* Generator real and reactive powers (found via loadflow) */
35: PetscScalar PG[3] = { 0.69,1.59,0.69};
36: /* PetscScalar PG[3] = {0.716786142395021,1.630000000000000,0.850000000000000};*/
38: const PetscScalar QG[3] = {0.270702180178785,0.066120127797275,-0.108402221791588};
39: /* Generator constants */
40: const PetscScalar H[3] = {23.64,6.4,3.01}; /* Inertia constant */
41: const PetscScalar Rs[3] = {0.0,0.0,0.0}; /* Stator Resistance */
42: const PetscScalar Xd[3] = {0.146,0.8958,1.3125}; /* d-axis reactance */
43: const PetscScalar Xdp[3] = {0.0608,0.1198,0.1813}; /* d-axis transient reactance */
44: 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 */
45: const PetscScalar Xqp[3] = {0.0969,0.1969,0.25}; /* q-axis transient reactance */
46: const PetscScalar Td0p[3] = {8.96,6.0,5.89}; /* d-axis open circuit time constant */
47: const PetscScalar Tq0p[3] = {0.31,0.535,0.6}; /* q-axis open circuit time constant */
48: PetscScalar M[3]; /* M = 2*H/w_s */
49: PetscScalar D[3]; /* D = 0.1*M */
51: PetscScalar TM[3]; /* Mechanical Torque */
52: /* Exciter system constants */
53: const PetscScalar KA[3] = {20.0,20.0,20.0}; /* Voltage regulartor gain constant */
54: const PetscScalar TA[3] = {0.2,0.2,0.2}; /* Voltage regulator time constant */
55: const PetscScalar KE[3] = {1.0,1.0,1.0}; /* Exciter gain constant */
56: const PetscScalar TE[3] = {0.314,0.314,0.314}; /* Exciter time constant */
57: const PetscScalar KF[3] = {0.063,0.063,0.063}; /* Feedback stabilizer gain constant */
58: const PetscScalar TF[3] = {0.35,0.35,0.35}; /* Feedback stabilizer time constant */
59: const PetscScalar k1[3] = {0.0039,0.0039,0.0039};
60: const PetscScalar k2[3] = {1.555,1.555,1.555}; /* k1 and k2 for calculating the saturation function SE = k1*exp(k2*Efd) */
62: PetscScalar Vref[3];
63: /* Load constants
64: We use a composite load model that describes the load and reactive powers at each time instant as follows
65: P(t) = \sum\limits_{i=0}^ld_nsegsp \ld_alphap_i*P_D0(\frac{V_m(t)}{V_m0})^\ld_betap_i
66: Q(t) = \sum\limits_{i=0}^ld_nsegsq \ld_alphaq_i*Q_D0(\frac{V_m(t)}{V_m0})^\ld_betaq_i
67: where
68: ld_nsegsp,ld_nsegsq - Number of individual load models for real and reactive power loads
69: ld_alphap,ld_alphap - Percentage contribution (weights) or loads
70: P_D0 - Real power load
71: Q_D0 - Reactive power load
72: V_m(t) - Voltage magnitude at time t
73: V_m0 - Voltage magnitude at t = 0
74: ld_betap, ld_betaq - exponents describing the load model for real and reactive part
76: Note: All loads have the same characteristic currently.
77: */
78: const PetscScalar PD0[3] = {1.25,0.9,1.0};
79: const PetscScalar QD0[3] = {0.5,0.3,0.35};
80: const PetscInt ld_nsegsp[3] = {3,3,3};
81: const PetscScalar ld_alphap[3] = {1.0,0.0,0.0};
82: const PetscScalar ld_betap[3] = {2.0,1.0,0.0};
83: const PetscInt ld_nsegsq[3] = {3,3,3};
84: const PetscScalar ld_alphaq[3] = {1.0,0.0,0.0};
85: const PetscScalar ld_betaq[3] = {2.0,1.0,0.0};
87: typedef struct {
88: DM dmgen, dmnet; /* DMs to manage generator and network subsystem */
89: DM dmpgrid; /* Composite DM to manage the entire power grid */
90: Mat Ybus; /* Network admittance matrix */
91: Vec V0; /* Initial voltage vector (Power flow solution) */
92: PetscReal tfaulton,tfaultoff; /* Fault on and off times */
93: PetscInt faultbus; /* Fault bus */
94: PetscScalar Rfault;
95: PetscReal t0,tmax;
96: PetscInt neqs_gen,neqs_net,neqs_pgrid;
97: Mat Sol; /* Matrix to save solution at each time step */
98: PetscInt stepnum;
99: PetscBool alg_flg;
100: PetscReal t;
101: IS is_diff; /* indices for differential equations */
102: IS is_alg; /* indices for algebraic equations */
103: PetscReal freq_u,freq_l; /* upper and lower frequency limit */
104: PetscInt pow; /* power coefficient used in the cost function */
105: PetscBool jacp_flg;
106: Mat J,Jacp;
107: Mat DRDU,DRDP;
108: } Userctx;
110: /* Converts from machine frame (dq) to network (phase a real,imag) reference frame */
111: PetscErrorCode dq2ri(PetscScalar Fd,PetscScalar Fq,PetscScalar delta,PetscScalar *Fr, PetscScalar *Fi)
112: {
114: *Fr = Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
115: *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
116: return(0);
117: }
119: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
120: PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd, PetscScalar *Fq)
121: {
123: *Fd = Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
124: *Fq = Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
125: return(0);
126: }
128: /* Saves the solution at each time to a matrix */
129: PetscErrorCode SaveSolution(TS ts)
130: {
131: PetscErrorCode ierr;
132: Userctx *user;
133: Vec X;
134: PetscScalar *mat;
135: const PetscScalar *x;
136: PetscInt idx;
137: PetscReal t;
140: TSGetApplicationContext(ts,&user);
141: TSGetTime(ts,&t);
142: TSGetSolution(ts,&X);
143: idx = user->stepnum*(user->neqs_pgrid+1);
144: MatDenseGetArray(user->Sol,&mat);
145: VecGetArrayRead(X,&x);
146: mat[idx] = t;
147: PetscArraycpy(mat+idx+1,x,user->neqs_pgrid);
148: MatDenseRestoreArray(user->Sol,&mat);
149: VecRestoreArrayRead(X,&x);
150: user->stepnum++;
151: return(0);
152: }
154: PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
155: {
157: Vec Xgen,Xnet;
158: PetscScalar *xgen,*xnet;
159: PetscInt i,idx=0;
160: PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
161: PetscScalar Eqp,Edp,delta;
162: PetscScalar Efd,RF,VR; /* Exciter variables */
163: PetscScalar Id,Iq; /* Generator dq axis currents */
164: PetscScalar theta,Vd,Vq,SE;
167: M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
168: D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
170: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
172: /* Network subsystem initialization */
173: VecCopy(user->V0,Xnet);
175: /* Generator subsystem initialization */
176: VecGetArray(Xgen,&xgen);
177: VecGetArray(Xnet,&xnet);
179: for (i=0; i < ngen; i++) {
180: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
181: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
182: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
183: IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
184: IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;
186: delta = PetscAtan2Real(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
188: theta = PETSC_PI/2.0 - delta;
190: Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
191: Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
193: Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
194: Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
196: Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
197: Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
199: TM[i] = PG[i];
201: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
202: xgen[idx] = Eqp;
203: xgen[idx+1] = Edp;
204: xgen[idx+2] = delta;
205: xgen[idx+3] = w_s;
207: idx = idx + 4;
209: xgen[idx] = Id;
210: xgen[idx+1] = Iq;
212: idx = idx + 2;
214: /* Exciter */
215: Efd = Eqp + (Xd[i] - Xdp[i])*Id;
216: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
217: VR = KE[i]*Efd + SE;
218: RF = KF[i]*Efd/TF[i];
220: xgen[idx] = Efd;
221: xgen[idx+1] = RF;
222: xgen[idx+2] = VR;
224: Vref[i] = Vm + (VR/KA[i]);
226: idx = idx + 3;
227: }
229: VecRestoreArray(Xgen,&xgen);
230: VecRestoreArray(Xnet,&xnet);
232: /* VecView(Xgen,0); */
233: DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet);
234: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
235: return(0);
236: }
238: PetscErrorCode InitialGuess(Vec X,Userctx *user, const PetscScalar PGv[])
239: {
241: Vec Xgen,Xnet;
242: PetscScalar *xgen,*xnet;
243: PetscInt i,idx=0;
244: PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
245: PetscScalar Eqp,Edp,delta;
246: PetscScalar Efd,RF,VR; /* Exciter variables */
247: PetscScalar Id,Iq; /* Generator dq axis currents */
248: PetscScalar theta,Vd,Vq,SE;
251: M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
252: D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
254: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
256: /* Network subsystem initialization */
257: VecCopy(user->V0,Xnet);
259: /* Generator subsystem initialization */
260: VecGetArray(Xgen,&xgen);
261: VecGetArray(Xnet,&xnet);
263: for (i=0; i < ngen; i++) {
264: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
265: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
266: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
267: IGr = (Vr*PGv[i] + Vi*QG[i])/Vm2;
268: IGi = (Vi*PGv[i] - Vr*QG[i])/Vm2;
270: delta = PetscAtan2Real(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
272: theta = PETSC_PI/2.0 - delta;
274: Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
275: Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
277: Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
278: Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
280: Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
281: Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
283: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
284: xgen[idx] = Eqp;
285: xgen[idx+1] = Edp;
286: xgen[idx+2] = delta;
287: xgen[idx+3] = w_s;
289: idx = idx + 4;
291: xgen[idx] = Id;
292: xgen[idx+1] = Iq;
294: idx = idx + 2;
296: /* Exciter */
297: Efd = Eqp + (Xd[i] - Xdp[i])*Id;
298: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
299: VR = KE[i]*Efd + SE;
300: RF = KF[i]*Efd/TF[i];
302: xgen[idx] = Efd;
303: xgen[idx+1] = RF;
304: xgen[idx+2] = VR;
306: idx = idx + 3;
307: }
309: VecRestoreArray(Xgen,&xgen);
310: VecRestoreArray(Xnet,&xnet);
312: /* VecView(Xgen,0); */
313: DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet);
314: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
315: return(0);
316: }
318: PetscErrorCode DICDPFiniteDifference(Vec X,Vec *DICDP, Userctx *user)
319: {
320: Vec Y;
321: PetscScalar PGv[3],eps;
323: PetscInt i,j;
326: eps = 1.e-7;
327: VecDuplicate(X,&Y);
329: for (i=0;i<ngen;i++) {
330: for (j=0;j<3;j++) PGv[j] = PG[j];
331: PGv[i] = PG[i]+eps;
332: InitialGuess(Y,user,PGv);
333: InitialGuess(X,user,PG);
335: VecAXPY(Y,-1.0,X);
336: VecScale(Y,1./eps);
337: VecCopy(Y,DICDP[i]);
338: }
339: VecDestroy(&Y);
340: return(0);
341: }
343: /* Computes F = [-f(x,y);g(x,y)] */
344: PetscErrorCode ResidualFunction(SNES snes,Vec X, Vec F, Userctx *user)
345: {
347: Vec Xgen,Xnet,Fgen,Fnet;
348: PetscScalar *xgen,*xnet,*fgen,*fnet;
349: PetscInt i,idx=0;
350: PetscScalar Vr,Vi,Vm,Vm2;
351: PetscScalar Eqp,Edp,delta,w; /* Generator variables */
352: PetscScalar Efd,RF,VR; /* Exciter variables */
353: PetscScalar Id,Iq; /* Generator dq axis currents */
354: PetscScalar Vd,Vq,SE;
355: PetscScalar IGr,IGi,IDr,IDi;
356: PetscScalar Zdq_inv[4],det;
357: PetscScalar PD,QD,Vm0,*v0;
358: PetscInt k;
361: VecZeroEntries(F);
362: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
363: DMCompositeGetLocalVectors(user->dmpgrid,&Fgen,&Fnet);
364: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
365: DMCompositeScatter(user->dmpgrid,F,Fgen,Fnet);
367: /* Network current balance residual IG + Y*V + IL = 0. Only YV is added here.
368: The generator current injection, IG, and load current injection, ID are added later
369: */
370: /* Note that the values in Ybus are stored assuming the imaginary current balance
371: equation is ordered first followed by real current balance equation for each bus.
372: Thus imaginary current contribution goes in location 2*i, and
373: real current contribution in 2*i+1
374: */
375: MatMult(user->Ybus,Xnet,Fnet);
377: VecGetArray(Xgen,&xgen);
378: VecGetArray(Xnet,&xnet);
379: VecGetArray(Fgen,&fgen);
380: VecGetArray(Fnet,&fnet);
382: /* Generator subsystem */
383: for (i=0; i < ngen; i++) {
384: Eqp = xgen[idx];
385: Edp = xgen[idx+1];
386: delta = xgen[idx+2];
387: w = xgen[idx+3];
388: Id = xgen[idx+4];
389: Iq = xgen[idx+5];
390: Efd = xgen[idx+6];
391: RF = xgen[idx+7];
392: VR = xgen[idx+8];
394: /* Generator differential equations */
395: fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i];
396: fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i];
397: fgen[idx+2] = -w + w_s;
398: fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i];
400: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
401: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
403: ri2dq(Vr,Vi,delta,&Vd,&Vq);
404: /* Algebraic equations for stator currents */
405: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
407: Zdq_inv[0] = Rs[i]/det;
408: Zdq_inv[1] = Xqp[i]/det;
409: Zdq_inv[2] = -Xdp[i]/det;
410: Zdq_inv[3] = Rs[i]/det;
412: fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id;
413: fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq;
415: /* Add generator current injection to network */
416: dq2ri(Id,Iq,delta,&IGr,&IGi);
418: fnet[2*gbus[i]] -= IGi;
419: fnet[2*gbus[i]+1] -= IGr;
421: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
423: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
425: /* Exciter differential equations */
426: fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i];
427: fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i];
428: fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
430: idx = idx + 9;
431: }
433: VecGetArray(user->V0,&v0);
434: for (i=0; i < nload; i++) {
435: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
436: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
437: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
438: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
439: PD = QD = 0.0;
440: for (k=0; k < ld_nsegsp[i]; k++) PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
441: for (k=0; k < ld_nsegsq[i]; k++) QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
443: /* Load currents */
444: IDr = (PD*Vr + QD*Vi)/Vm2;
445: IDi = (-QD*Vr + PD*Vi)/Vm2;
447: fnet[2*lbus[i]] += IDi;
448: fnet[2*lbus[i]+1] += IDr;
449: }
450: VecRestoreArray(user->V0,&v0);
452: VecRestoreArray(Xgen,&xgen);
453: VecRestoreArray(Xnet,&xnet);
454: VecRestoreArray(Fgen,&fgen);
455: VecRestoreArray(Fnet,&fnet);
457: DMCompositeGather(user->dmpgrid,INSERT_VALUES,F,Fgen,Fnet);
458: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
459: DMCompositeRestoreLocalVectors(user->dmpgrid,&Fgen,&Fnet);
460: return(0);
461: }
463: /* \dot{x} - f(x,y)
464: g(x,y) = 0
465: */
466: PetscErrorCode IFunction(TS ts,PetscReal t, Vec X, Vec Xdot, Vec F, Userctx *user)
467: {
468: PetscErrorCode ierr;
469: SNES snes;
470: PetscScalar *f;
471: const PetscScalar *xdot;
472: PetscInt i;
475: user->t = t;
477: TSGetSNES(ts,&snes);
478: ResidualFunction(snes,X,F,user);
479: VecGetArray(F,&f);
480: VecGetArrayRead(Xdot,&xdot);
481: for (i=0;i < ngen;i++) {
482: f[9*i] += xdot[9*i];
483: f[9*i+1] += xdot[9*i+1];
484: f[9*i+2] += xdot[9*i+2];
485: f[9*i+3] += xdot[9*i+3];
486: f[9*i+6] += xdot[9*i+6];
487: f[9*i+7] += xdot[9*i+7];
488: f[9*i+8] += xdot[9*i+8];
489: }
490: VecRestoreArray(F,&f);
491: VecRestoreArrayRead(Xdot,&xdot);
492: return(0);
493: }
495: /* This function is used for solving the algebraic system only during fault on and
496: off times. It computes the entire F and then zeros out the part corresponding to
497: differential equations
498: F = [0;g(y)];
499: */
500: PetscErrorCode AlgFunction(SNES snes, Vec X, Vec F, void *ctx)
501: {
503: Userctx *user=(Userctx*)ctx;
504: PetscScalar *f;
505: PetscInt i;
508: ResidualFunction(snes,X,F,user);
509: VecGetArray(F,&f);
510: for (i=0; i < ngen; i++) {
511: f[9*i] = 0;
512: f[9*i+1] = 0;
513: f[9*i+2] = 0;
514: f[9*i+3] = 0;
515: f[9*i+6] = 0;
516: f[9*i+7] = 0;
517: f[9*i+8] = 0;
518: }
519: VecRestoreArray(F,&f);
520: return(0);
521: }
523: PetscErrorCode PreallocateJacobian(Mat J, Userctx *user)
524: {
526: PetscInt *d_nnz;
527: PetscInt i,idx=0,start=0;
528: PetscInt ncols;
531: PetscMalloc1(user->neqs_pgrid,&d_nnz);
532: for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
533: /* Generator subsystem */
534: for (i=0; i < ngen; i++) {
536: d_nnz[idx] += 3;
537: d_nnz[idx+1] += 2;
538: d_nnz[idx+2] += 2;
539: d_nnz[idx+3] += 5;
540: d_nnz[idx+4] += 6;
541: d_nnz[idx+5] += 6;
543: d_nnz[user->neqs_gen+2*gbus[i]] += 3;
544: d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;
546: d_nnz[idx+6] += 2;
547: d_nnz[idx+7] += 2;
548: d_nnz[idx+8] += 5;
550: idx = idx + 9;
551: }
553: start = user->neqs_gen;
554: for (i=0; i < nbus; i++) {
555: MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL);
556: d_nnz[start+2*i] += ncols;
557: d_nnz[start+2*i+1] += ncols;
558: MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL);
559: }
561: MatSeqAIJSetPreallocation(J,0,d_nnz);
562: PetscFree(d_nnz);
563: return(0);
564: }
566: /*
567: J = [-df_dx, -df_dy
568: dg_dx, dg_dy]
569: */
570: PetscErrorCode ResidualJacobian(SNES snes,Vec X,Mat J,Mat B,void *ctx)
571: {
572: PetscErrorCode ierr;
573: Userctx *user=(Userctx*)ctx;
574: Vec Xgen,Xnet;
575: PetscScalar *xgen,*xnet;
576: PetscInt i,idx=0;
577: PetscScalar Vr,Vi,Vm,Vm2;
578: PetscScalar Eqp,Edp,delta; /* Generator variables */
579: PetscScalar Efd; /* Exciter variables */
580: PetscScalar Id,Iq; /* Generator dq axis currents */
581: PetscScalar Vd,Vq;
582: PetscScalar val[10];
583: PetscInt row[2],col[10];
584: PetscInt net_start=user->neqs_gen;
585: PetscInt ncols;
586: const PetscInt *cols;
587: const PetscScalar *yvals;
588: PetscInt k;
589: PetscScalar Zdq_inv[4],det;
590: PetscScalar dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
591: PetscScalar dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
592: PetscScalar dSE_dEfd;
593: PetscScalar dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
594: PetscScalar PD,QD,Vm0,*v0,Vm4;
595: PetscScalar dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
596: PetscScalar dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;
599: MatZeroEntries(B);
600: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
601: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
603: VecGetArray(Xgen,&xgen);
604: VecGetArray(Xnet,&xnet);
606: /* Generator subsystem */
607: for (i=0; i < ngen; i++) {
608: Eqp = xgen[idx];
609: Edp = xgen[idx+1];
610: delta = xgen[idx+2];
611: Id = xgen[idx+4];
612: Iq = xgen[idx+5];
613: Efd = xgen[idx+6];
615: /* fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i]; */
616: row[0] = idx;
617: col[0] = idx; col[1] = idx+4; col[2] = idx+6;
618: val[0] = 1/ Td0p[i]; val[1] = (Xd[i] - Xdp[i])/ Td0p[i]; val[2] = -1/Td0p[i];
620: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
622: /* fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
623: row[0] = idx + 1;
624: col[0] = idx + 1; col[1] = idx+5;
625: val[0] = 1/Tq0p[i]; val[1] = -(Xq[i] - Xqp[i])/Tq0p[i];
626: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
628: /* fgen[idx+2] = - w + w_s; */
629: row[0] = idx + 2;
630: col[0] = idx + 2; col[1] = idx + 3;
631: val[0] = 0; val[1] = -1;
632: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
634: /* fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i]; */
635: row[0] = idx + 3;
636: col[0] = idx; col[1] = idx + 1; col[2] = idx + 3; col[3] = idx + 4; col[4] = idx + 5;
637: 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];
638: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
640: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
641: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
642: ri2dq(Vr,Vi,delta,&Vd,&Vq);
644: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
646: Zdq_inv[0] = Rs[i]/det;
647: Zdq_inv[1] = Xqp[i]/det;
648: Zdq_inv[2] = -Xdp[i]/det;
649: Zdq_inv[3] = Rs[i]/det;
651: dVd_dVr = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
652: dVq_dVr = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
653: dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
654: dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);
656: /* fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
657: row[0] = idx+4;
658: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
659: val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0]; val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
660: col[3] = idx + 4; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
661: 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;
662: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
664: /* fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
665: row[0] = idx+5;
666: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
667: val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2]; val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
668: col[3] = idx + 5; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
669: 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;
670: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
672: dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
673: dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
674: dIGr_dId = PetscSinScalar(delta); dIGr_dIq = PetscCosScalar(delta);
675: dIGi_dId = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);
677: /* fnet[2*gbus[i]] -= IGi; */
678: row[0] = net_start + 2*gbus[i];
679: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
680: val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
681: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
683: /* fnet[2*gbus[i]+1] -= IGr; */
684: row[0] = net_start + 2*gbus[i]+1;
685: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
686: val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
687: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
689: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
691: /* fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i]; */
692: /* SE = k1[i]*PetscExpScalar(k2[i]*Efd); */
693: dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);
695: row[0] = idx + 6;
696: col[0] = idx + 6; col[1] = idx + 8;
697: val[0] = (KE[i] + dSE_dEfd)/TE[i]; val[1] = -1/TE[i];
698: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
700: /* Exciter differential equations */
702: /* fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i]; */
703: row[0] = idx + 7;
704: col[0] = idx + 6; col[1] = idx + 7;
705: val[0] = (-KF[i]/TF[i])/TF[i]; val[1] = 1/TF[i];
706: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
708: /* fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i]; */
709: /* Vm = (Vd^2 + Vq^2)^0.5; */
710: dVm_dVd = Vd/Vm; dVm_dVq = Vq/Vm;
711: dVm_dVr = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
712: dVm_dVi = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
713: row[0] = idx + 8;
714: col[0] = idx + 6; col[1] = idx + 7; col[2] = idx + 8;
715: val[0] = (KA[i]*KF[i]/TF[i])/TA[i]; val[1] = -KA[i]/TA[i]; val[2] = 1/TA[i];
716: col[3] = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
717: val[3] = KA[i]*dVm_dVr/TA[i]; val[4] = KA[i]*dVm_dVi/TA[i];
718: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
719: idx = idx + 9;
720: }
722: for (i=0; i<nbus; i++) {
723: MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
724: row[0] = net_start + 2*i;
725: for (k=0; k<ncols; k++) {
726: col[k] = net_start + cols[k];
727: val[k] = yvals[k];
728: }
729: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
730: MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);
732: MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
733: row[0] = net_start + 2*i+1;
734: for (k=0; k<ncols; k++) {
735: col[k] = net_start + cols[k];
736: val[k] = yvals[k];
737: }
738: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
739: MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
740: }
742: MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
743: MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);
745: VecGetArray(user->V0,&v0);
746: for (i=0; i < nload; i++) {
747: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
748: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
749: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2= Vm*Vm; Vm4 = Vm2*Vm2;
750: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
751: PD = QD = 0.0;
752: dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
753: for (k=0; k < ld_nsegsp[i]; k++) {
754: PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
755: dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
756: dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
757: }
758: for (k=0; k < ld_nsegsq[i]; k++) {
759: QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
760: dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
761: dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
762: }
764: /* IDr = (PD*Vr + QD*Vi)/Vm2; */
765: /* IDi = (-QD*Vr + PD*Vi)/Vm2; */
767: dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
768: dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;
770: dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
771: dIDi_dVi = (-dQD_dVi*Vr + dPD_dVi*Vi + PD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vi)/Vm4;
773: /* fnet[2*lbus[i]] += IDi; */
774: row[0] = net_start + 2*lbus[i];
775: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
776: val[0] = dIDi_dVr; val[1] = dIDi_dVi;
777: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
778: /* fnet[2*lbus[i]+1] += IDr; */
779: row[0] = net_start + 2*lbus[i]+1;
780: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
781: val[0] = dIDr_dVr; val[1] = dIDr_dVi;
782: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
783: }
784: VecRestoreArray(user->V0,&v0);
786: VecRestoreArray(Xgen,&xgen);
787: VecRestoreArray(Xnet,&xnet);
789: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
791: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
792: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
793: return(0);
794: }
796: /*
797: J = [I, 0
798: dg_dx, dg_dy]
799: */
800: PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
801: {
803: Userctx *user=(Userctx*)ctx;
806: ResidualJacobian(snes,X,A,B,ctx);
807: MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
808: MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);
809: return(0);
810: }
812: /*
813: J = [a*I-df_dx, -df_dy
814: dg_dx, dg_dy]
815: */
817: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
818: {
820: SNES snes;
821: PetscScalar atmp = (PetscScalar) a;
822: PetscInt i,row;
825: user->t = t;
827: TSGetSNES(ts,&snes);
828: ResidualJacobian(snes,X,A,B,user);
829: for (i=0;i < ngen;i++) {
830: row = 9*i;
831: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
832: row = 9*i+1;
833: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
834: row = 9*i+2;
835: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
836: row = 9*i+3;
837: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
838: row = 9*i+6;
839: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
840: row = 9*i+7;
841: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
842: row = 9*i+8;
843: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
844: }
845: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
846: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
847: return(0);
848: }
850: /* Matrix JacobianP is constant so that it only needs to be evaluated once */
851: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A, void *ctx0)
852: {
854: PetscScalar a;
855: PetscInt row,col;
856: Userctx *ctx=(Userctx*)ctx0;
860: if (ctx->jacp_flg) {
861: MatZeroEntries(A);
863: for (col=0;col<3;col++) {
864: a = 1.0/M[col];
865: row = 9*col+3;
866: MatSetValues(A,1,&row,1,&col,&a,INSERT_VALUES);
867: }
869: ctx->jacp_flg = PETSC_FALSE;
871: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
872: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
873: }
874: return(0);
875: }
877: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,Userctx *user)
878: {
879: PetscErrorCode ierr;
880: const PetscScalar *u;
881: PetscInt idx;
882: Vec Xgen,Xnet;
883: PetscScalar *r,*xgen;
884: PetscInt i;
887: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
888: DMCompositeScatter(user->dmpgrid,U,Xgen,Xnet);
890: VecGetArray(Xgen,&xgen);
892: VecGetArrayRead(U,&u);
893: VecGetArray(R,&r);
894: r[0] = 0.;
895: idx = 0;
896: for (i=0;i<ngen;i++) {
897: r[0] += PetscPowScalarInt(PetscMax(0.,PetscMax(xgen[idx+3]/(2.*PETSC_PI)-user->freq_u,user->freq_l-xgen[idx+3]/(2.*PETSC_PI))),user->pow);
898: idx += 9;
899: }
900: VecRestoreArrayRead(U,&u);
901: VecRestoreArray(R,&r);
902: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
903: return(0);
904: }
906: static PetscErrorCode DRDUJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDU,Mat B,Userctx *user)
907: {
909: Vec Xgen,Xnet,Dgen,Dnet;
910: PetscScalar *xgen,*dgen;
911: PetscInt i;
912: PetscInt idx;
913: Vec drdu_col;
914: PetscScalar *xarr;
917: VecDuplicate(U,&drdu_col);
918: MatDenseGetColumn(DRDU,0,&xarr);
919: VecPlaceArray(drdu_col,xarr);
920: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
921: DMCompositeGetLocalVectors(user->dmpgrid,&Dgen,&Dnet);
922: DMCompositeScatter(user->dmpgrid,U,Xgen,Xnet);
923: DMCompositeScatter(user->dmpgrid,drdu_col,Dgen,Dnet);
925: VecGetArray(Xgen,&xgen);
926: VecGetArray(Dgen,&dgen);
928: idx = 0;
929: for (i=0;i<ngen;i++) {
930: dgen[idx+3] = 0.;
931: if (xgen[idx+3]/(2.*PETSC_PI) > user->freq_u) dgen[idx+3] = user->pow*PetscPowScalarInt(xgen[idx+3]/(2.*PETSC_PI)-user->freq_u,user->pow-1)/(2.*PETSC_PI);
932: if (xgen[idx+3]/(2.*PETSC_PI) < user->freq_l) dgen[idx+3] = user->pow*PetscPowScalarInt(user->freq_l-xgen[idx+3]/(2.*PETSC_PI),user->pow-1)/(-2.*PETSC_PI);
933: idx += 9;
934: }
936: VecRestoreArray(Dgen,&dgen);
937: VecRestoreArray(Xgen,&xgen);
938: DMCompositeGather(user->dmpgrid,INSERT_VALUES,drdu_col,Dgen,Dnet);
939: DMCompositeRestoreLocalVectors(user->dmpgrid,&Dgen,&Dnet);
940: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
941: VecResetArray(drdu_col);
942: MatDenseRestoreColumn(DRDU,&xarr);
943: VecDestroy(&drdu_col);
944: return(0);
945: }
947: static PetscErrorCode DRDPJacobianTranspose(TS ts,PetscReal t,Vec U,Mat drdp,Userctx *user)
948: {
950: return(0);
951: }
953: PetscErrorCode ComputeSensiP(Vec lambda,Vec mu,Vec *DICDP,Userctx *user)
954: {
956: PetscScalar *x,*y,sensip;
957: PetscInt i;
960: VecGetArray(lambda,&x);
961: VecGetArray(mu,&y);
963: for (i=0;i<3;i++) {
964: VecDot(lambda,DICDP[i],&sensip);
965: sensip = sensip+y[i];
966: /* PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt %D th parameter: %g \n",i,(double)sensip); */
967: y[i] = sensip;
968: }
969: VecRestoreArray(mu,&y);
970: return(0);
971: }
973: int main(int argc,char **argv)
974: {
975: Userctx user;
976: Vec p;
977: PetscScalar *x_ptr;
978: PetscErrorCode ierr;
979: PetscMPIInt size;
980: PetscInt i;
981: PetscViewer Xview,Ybusview;
982: PetscInt *idx2;
983: Tao tao;
984: KSP ksp;
985: PC pc;
986: Vec lowerb,upperb;
988: PetscInitialize(&argc,&argv,"petscoptions",help);if (ierr) return ierr;
989: MPI_Comm_size(PETSC_COMM_WORLD,&size);
990: if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
992: user.jacp_flg = PETSC_TRUE;
993: user.neqs_gen = 9*ngen; /* # eqs. for generator subsystem */
994: user.neqs_net = 2*nbus; /* # eqs. for network subsystem */
995: user.neqs_pgrid = user.neqs_gen + user.neqs_net;
997: /* Create indices for differential and algebraic equations */
998: PetscMalloc1(7*ngen,&idx2);
999: for (i=0; i<ngen; i++) {
1000: 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;
1001: idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
1002: }
1003: ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
1004: ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
1005: PetscFree(idx2);
1007: /* Set run time options */
1008: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Transient stability fault options","");
1009: {
1010: user.tfaulton = 1.0;
1011: user.tfaultoff = 1.2;
1012: user.Rfault = 0.0001;
1013: user.faultbus = 8;
1014: PetscOptionsReal("-tfaulton","","",user.tfaulton,&user.tfaulton,NULL);
1015: PetscOptionsReal("-tfaultoff","","",user.tfaultoff,&user.tfaultoff,NULL);
1016: PetscOptionsInt("-faultbus","","",user.faultbus,&user.faultbus,NULL);
1017: user.t0 = 0.0;
1018: user.tmax = 1.3;
1019: PetscOptionsReal("-t0","","",user.t0,&user.t0,NULL);
1020: PetscOptionsReal("-tmax","","",user.tmax,&user.tmax,NULL);
1021: user.freq_u = 61.0;
1022: user.freq_l = 59.0;
1023: user.pow = 2;
1024: PetscOptionsReal("-frequ","","",user.freq_u,&user.freq_u,NULL);
1025: PetscOptionsReal("-freql","","",user.freq_l,&user.freq_l,NULL);
1026: PetscOptionsInt("-pow","","",user.pow,&user.pow,NULL);
1028: }
1029: PetscOptionsEnd();
1031: /* Create DMs for generator and network subsystems */
1032: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
1033: DMSetOptionsPrefix(user.dmgen,"dmgen_");
1034: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
1035: DMSetOptionsPrefix(user.dmnet,"dmnet_");
1036: DMSetFromOptions(user.dmnet);
1037: DMSetUp(user.dmnet);
1038: /* Create a composite DM packer and add the two DMs */
1039: DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
1040: DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
1041: DMSetFromOptions(user.dmgen);
1042: DMSetUp(user.dmgen);
1043: DMCompositeAddDM(user.dmpgrid,user.dmgen);
1044: DMCompositeAddDM(user.dmpgrid,user.dmnet);
1046: /* Read initial voltage vector and Ybus */
1047: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
1048: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);
1050: VecCreate(PETSC_COMM_WORLD,&user.V0);
1051: VecSetSizes(user.V0,PETSC_DECIDE,user.neqs_net);
1052: VecLoad(user.V0,Xview);
1054: MatCreate(PETSC_COMM_WORLD,&user.Ybus);
1055: MatSetSizes(user.Ybus,PETSC_DECIDE,PETSC_DECIDE,user.neqs_net,user.neqs_net);
1056: MatSetType(user.Ybus,MATBAIJ);
1057: /* MatSetBlockSize(ctx->Ybus,2); */
1058: MatLoad(user.Ybus,Ybusview);
1060: PetscViewerDestroy(&Xview);
1061: PetscViewerDestroy(&Ybusview);
1063: /* Allocate space for Jacobians */
1064: MatCreate(PETSC_COMM_WORLD,&user.J);
1065: MatSetSizes(user.J,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,user.neqs_pgrid);
1066: MatSetFromOptions(user.J);
1067: PreallocateJacobian(user.J,&user);
1069: MatCreate(PETSC_COMM_WORLD,&user.Jacp);
1070: MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,3);
1071: MatSetFromOptions(user.Jacp);
1072: MatSetUp(user.Jacp);
1073: MatZeroEntries(user.Jacp); /* initialize to zeros */
1075: MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,3,1,NULL,&user.DRDP);
1076: MatSetUp(user.DRDP);
1077: MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,1,NULL,&user.DRDU);
1078: MatSetUp(user.DRDU);
1080: /* Create TAO solver and set desired solution method */
1081: TaoCreate(PETSC_COMM_WORLD,&tao);
1082: TaoSetType(tao,TAOBLMVM);
1083: /*
1084: Optimization starts
1085: */
1086: /* Set initial solution guess */
1087: VecCreateSeq(PETSC_COMM_WORLD,3,&p);
1088: VecGetArray(p,&x_ptr);
1089: x_ptr[0] = PG[0]; x_ptr[1] = PG[1]; x_ptr[2] = PG[2];
1090: VecRestoreArray(p,&x_ptr);
1092: TaoSetInitialVector(tao,p);
1093: /* Set routine for function and gradient evaluation */
1094: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);
1096: /* Set bounds for the optimization */
1097: VecDuplicate(p,&lowerb);
1098: VecDuplicate(p,&upperb);
1099: VecGetArray(lowerb,&x_ptr);
1100: x_ptr[0] = 0.5; x_ptr[1] = 0.5; x_ptr[2] = 0.5;
1101: VecRestoreArray(lowerb,&x_ptr);
1102: VecGetArray(upperb,&x_ptr);
1103: x_ptr[0] = 2.0; x_ptr[1] = 2.0; x_ptr[2] = 2.0;
1104: VecRestoreArray(upperb,&x_ptr);
1105: TaoSetVariableBounds(tao,lowerb,upperb);
1107: /* Check for any TAO command line options */
1108: TaoSetFromOptions(tao);
1109: TaoGetKSP(tao,&ksp);
1110: if (ksp) {
1111: KSPGetPC(ksp,&pc);
1112: PCSetType(pc,PCNONE);
1113: }
1115: /* SOLVE THE APPLICATION */
1116: TaoSolve(tao);
1118: VecView(p,PETSC_VIEWER_STDOUT_WORLD);
1119: /* Free TAO data structures */
1120: TaoDestroy(&tao);
1122: DMDestroy(&user.dmgen);
1123: DMDestroy(&user.dmnet);
1124: DMDestroy(&user.dmpgrid);
1125: ISDestroy(&user.is_diff);
1126: ISDestroy(&user.is_alg);
1128: MatDestroy(&user.J);
1129: MatDestroy(&user.Jacp);
1130: MatDestroy(&user.Ybus);
1131: /* MatDestroy(&user.Sol); */
1132: VecDestroy(&user.V0);
1133: VecDestroy(&p);
1134: VecDestroy(&lowerb);
1135: VecDestroy(&upperb);
1136: MatDestroy(&user.DRDU);
1137: MatDestroy(&user.DRDP);
1138: PetscFinalize();
1139: return ierr;
1140: }
1142: /* ------------------------------------------------------------------ */
1143: /*
1144: FormFunction - Evaluates the function and corresponding gradient.
1146: Input Parameters:
1147: tao - the Tao context
1148: X - the input vector
1149: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
1151: Output Parameters:
1152: f - the newly evaluated function
1153: G - the newly evaluated gradient
1154: */
1155: PetscErrorCode FormFunctionGradient(Tao tao,Vec P,PetscReal *f,Vec G,void *ctx0)
1156: {
1157: TS ts,quadts;
1158: SNES snes_alg;
1160: Userctx *ctx = (Userctx*)ctx0;
1161: Vec X;
1162: PetscInt i;
1163: /* sensitivity context */
1164: PetscScalar *x_ptr;
1165: Vec lambda[1],q;
1166: Vec mu[1];
1167: PetscInt steps1,steps2,steps3;
1168: Vec DICDP[3];
1169: Vec F_alg;
1170: PetscInt row_loc,col_loc;
1171: PetscScalar val;
1172: Vec Xdot;
1175: VecGetArrayRead(P,(const PetscScalar**)&x_ptr);
1176: PG[0] = x_ptr[0];
1177: PG[1] = x_ptr[1];
1178: PG[2] = x_ptr[2];
1179: VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);
1181: ctx->stepnum = 0;
1183: DMCreateGlobalVector(ctx->dmpgrid,&X);
1185: /* Create matrix to save solutions at each time step */
1186: /* MatCreateSeqDense(PETSC_COMM_SELF,ctx->neqs_pgrid+1,1002,NULL,&ctx->Sol); */
1187: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1188: Create timestepping solver context
1189: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1190: TSCreate(PETSC_COMM_WORLD,&ts);
1191: TSSetProblemType(ts,TS_NONLINEAR);
1192: TSSetType(ts,TSCN);
1193: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,ctx);
1194: TSSetIJacobian(ts,ctx->J,ctx->J,(TSIJacobian)IJacobian,ctx);
1195: TSSetApplicationContext(ts,ctx);
1196: /* Set RHS JacobianP */
1197: TSSetRHSJacobianP(ts,ctx->Jacp,RHSJacobianP,ctx);
1199: TSCreateQuadratureTS(ts,PETSC_FALSE,&quadts);
1200: TSSetRHSFunction(quadts,NULL,(TSRHSFunction)CostIntegrand,ctx);
1201: TSSetRHSJacobian(quadts,ctx->DRDU,ctx->DRDU,(TSRHSJacobian)DRDUJacobianTranspose,ctx);
1202: TSSetRHSJacobianP(quadts,ctx->DRDP,(TSRHSJacobianP)DRDPJacobianTranspose,ctx);
1204: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1205: Set initial conditions
1206: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1207: SetInitialGuess(X,ctx);
1209: /* Approximate DICDP with finite difference, we want to zero out network variables */
1210: for (i=0;i<3;i++) {
1211: VecDuplicate(X,&DICDP[i]);
1212: }
1213: DICDPFiniteDifference(X,DICDP,ctx);
1215: VecDuplicate(X,&F_alg);
1216: SNESCreate(PETSC_COMM_WORLD,&snes_alg);
1217: SNESSetFunction(snes_alg,F_alg,AlgFunction,ctx);
1218: MatZeroEntries(ctx->J);
1219: SNESSetJacobian(snes_alg,ctx->J,ctx->J,AlgJacobian,ctx);
1220: SNESSetOptionsPrefix(snes_alg,"alg_");
1221: SNESSetFromOptions(snes_alg);
1222: ctx->alg_flg = PETSC_TRUE;
1223: /* Solve the algebraic equations */
1224: SNESSolve(snes_alg,NULL,X);
1226: /* Just to set up the Jacobian structure */
1227: VecDuplicate(X,&Xdot);
1228: IJacobian(ts,0.0,X,Xdot,0.0,ctx->J,ctx->J,ctx);
1229: VecDestroy(&Xdot);
1231: ctx->stepnum++;
1233: /*
1234: Save trajectory of solution so that TSAdjointSolve() may be used
1235: */
1236: TSSetSaveTrajectory(ts);
1238: TSSetTimeStep(ts,0.01);
1239: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
1240: TSSetFromOptions(ts);
1241: /* TSSetPostStep(ts,SaveSolution); */
1243: /* Prefault period */
1244: ctx->alg_flg = PETSC_FALSE;
1245: TSSetTime(ts,0.0);
1246: TSSetMaxTime(ts,ctx->tfaulton);
1247: TSSolve(ts,X);
1248: TSGetStepNumber(ts,&steps1);
1250: /* Create the nonlinear solver for solving the algebraic system */
1251: /* Note that although the algebraic system needs to be solved only for
1252: Idq and V, we reuse the entire system including xgen. The xgen
1253: variables are held constant by setting their residuals to 0 and
1254: putting a 1 on the Jacobian diagonal for xgen rows
1255: */
1256: MatZeroEntries(ctx->J);
1258: /* Apply disturbance - resistive fault at ctx->faultbus */
1259: /* This is done by adding shunt conductance to the diagonal location
1260: in the Ybus matrix */
1261: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
1262: val = 1/ctx->Rfault;
1263: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1264: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
1265: val = 1/ctx->Rfault;
1266: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1268: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1269: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1271: ctx->alg_flg = PETSC_TRUE;
1272: /* Solve the algebraic equations */
1273: SNESSolve(snes_alg,NULL,X);
1275: ctx->stepnum++;
1277: /* Disturbance period */
1278: ctx->alg_flg = PETSC_FALSE;
1279: TSSetTime(ts,ctx->tfaulton);
1280: TSSetMaxTime(ts,ctx->tfaultoff);
1281: TSSolve(ts,X);
1282: TSGetStepNumber(ts,&steps2);
1283: steps2 -= steps1;
1285: /* Remove the fault */
1286: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1;
1287: val = -1/ctx->Rfault;
1288: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1289: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus;
1290: val = -1/ctx->Rfault;
1291: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1293: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1294: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1296: MatZeroEntries(ctx->J);
1298: ctx->alg_flg = PETSC_TRUE;
1300: /* Solve the algebraic equations */
1301: SNESSolve(snes_alg,NULL,X);
1303: ctx->stepnum++;
1305: /* Post-disturbance period */
1306: ctx->alg_flg = PETSC_TRUE;
1307: TSSetTime(ts,ctx->tfaultoff);
1308: TSSetMaxTime(ts,ctx->tmax);
1309: TSSolve(ts,X);
1310: TSGetStepNumber(ts,&steps3);
1311: steps3 -= steps2;
1312: steps3 -= steps1;
1314: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1315: Adjoint model starts here
1316: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1317: TSSetPostStep(ts,NULL);
1318: MatCreateVecs(ctx->J,&lambda[0],NULL);
1319: /* Set initial conditions for the adjoint integration */
1320: VecZeroEntries(lambda[0]);
1322: MatCreateVecs(ctx->Jacp,&mu[0],NULL);
1323: VecZeroEntries(mu[0]);
1324: TSSetCostGradients(ts,1,lambda,mu);
1326: TSAdjointSetSteps(ts,steps3);
1327: TSAdjointSolve(ts);
1329: MatZeroEntries(ctx->J);
1330: /* Applying disturbance - resistive fault at ctx->faultbus */
1331: /* This is done by deducting shunt conductance to the diagonal location
1332: in the Ybus matrix */
1333: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
1334: val = 1./ctx->Rfault;
1335: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1336: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
1337: val = 1./ctx->Rfault;
1338: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1340: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1341: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1343: /* Set number of steps for the adjoint integration */
1344: TSAdjointSetSteps(ts,steps2);
1345: TSAdjointSolve(ts);
1347: MatZeroEntries(ctx->J);
1348: /* remove the fault */
1349: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
1350: val = -1./ctx->Rfault;
1351: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1352: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
1353: val = -1./ctx->Rfault;
1354: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1356: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1357: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1359: /* Set number of steps for the adjoint integration */
1360: TSAdjointSetSteps(ts,steps1);
1361: TSAdjointSolve(ts);
1363: ComputeSensiP(lambda[0],mu[0],DICDP,ctx);
1364: VecCopy(mu[0],G);
1366: TSGetQuadratureTS(ts,NULL,&quadts);
1367: TSGetSolution(quadts,&q);
1368: VecGetArray(q,&x_ptr);
1369: *f = x_ptr[0];
1370: x_ptr[0] = 0;
1371: VecRestoreArray(q,&x_ptr);
1373: VecDestroy(&lambda[0]);
1374: VecDestroy(&mu[0]);
1376: SNESDestroy(&snes_alg);
1377: VecDestroy(&F_alg);
1378: VecDestroy(&X);
1379: TSDestroy(&ts);
1380: for (i=0;i<3;i++) {
1381: VecDestroy(&DICDP[i]);
1382: }
1383: return(0);
1384: }
1386: /*TEST
1388: build:
1389: requires: double !complex !defined(PETSC_USE_64BIT_INDICES)
1391: test:
1392: args: -viewer_binary_skip_info -tao_monitor -tao_gttol .2
1393: localrunfiles: petscoptions X.bin Ybus.bin
1395: TEST*/