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: {
113: *Fr = Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
114: *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
115: return 0;
116: }
118: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
119: PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd, PetscScalar *Fq)
120: {
121: *Fd = Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
122: *Fq = Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
123: return 0;
124: }
126: /* Saves the solution at each time to a matrix */
127: PetscErrorCode SaveSolution(TS ts)
128: {
129: Userctx *user;
130: Vec X;
131: PetscScalar *mat;
132: const PetscScalar *x;
133: PetscInt idx;
134: PetscReal t;
136: TSGetApplicationContext(ts,&user);
137: TSGetTime(ts,&t);
138: TSGetSolution(ts,&X);
139: idx = user->stepnum*(user->neqs_pgrid+1);
140: MatDenseGetArray(user->Sol,&mat);
141: VecGetArrayRead(X,&x);
142: mat[idx] = t;
143: PetscArraycpy(mat+idx+1,x,user->neqs_pgrid);
144: MatDenseRestoreArray(user->Sol,&mat);
145: VecRestoreArrayRead(X,&x);
146: user->stepnum++;
147: return 0;
148: }
150: PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
151: {
152: Vec Xgen,Xnet;
153: PetscScalar *xgen,*xnet;
154: PetscInt i,idx=0;
155: PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
156: PetscScalar Eqp,Edp,delta;
157: PetscScalar Efd,RF,VR; /* Exciter variables */
158: PetscScalar Id,Iq; /* Generator dq axis currents */
159: PetscScalar theta,Vd,Vq,SE;
161: M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
162: D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
164: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
166: /* Network subsystem initialization */
167: VecCopy(user->V0,Xnet);
169: /* Generator subsystem initialization */
170: VecGetArray(Xgen,&xgen);
171: VecGetArray(Xnet,&xnet);
173: for (i=0; i < ngen; i++) {
174: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
175: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
176: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
177: IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
178: IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;
180: delta = PetscAtan2Real(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
182: theta = PETSC_PI/2.0 - delta;
184: Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
185: Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
187: Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
188: Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
190: Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
191: Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
193: TM[i] = PG[i];
195: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
196: xgen[idx] = Eqp;
197: xgen[idx+1] = Edp;
198: xgen[idx+2] = delta;
199: xgen[idx+3] = w_s;
201: idx = idx + 4;
203: xgen[idx] = Id;
204: xgen[idx+1] = Iq;
206: idx = idx + 2;
208: /* Exciter */
209: Efd = Eqp + (Xd[i] - Xdp[i])*Id;
210: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
211: VR = KE[i]*Efd + SE;
212: RF = KF[i]*Efd/TF[i];
214: xgen[idx] = Efd;
215: xgen[idx+1] = RF;
216: xgen[idx+2] = VR;
218: Vref[i] = Vm + (VR/KA[i]);
220: idx = idx + 3;
221: }
223: VecRestoreArray(Xgen,&xgen);
224: VecRestoreArray(Xnet,&xnet);
226: /* VecView(Xgen,0); */
227: DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet);
228: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
229: return 0;
230: }
232: PetscErrorCode InitialGuess(Vec X,Userctx *user, const PetscScalar PGv[])
233: {
234: Vec Xgen,Xnet;
235: PetscScalar *xgen,*xnet;
236: PetscInt i,idx=0;
237: PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
238: PetscScalar Eqp,Edp,delta;
239: PetscScalar Efd,RF,VR; /* Exciter variables */
240: PetscScalar Id,Iq; /* Generator dq axis currents */
241: PetscScalar theta,Vd,Vq,SE;
243: M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
244: D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
246: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
248: /* Network subsystem initialization */
249: VecCopy(user->V0,Xnet);
251: /* Generator subsystem initialization */
252: VecGetArray(Xgen,&xgen);
253: VecGetArray(Xnet,&xnet);
255: for (i=0; i < ngen; i++) {
256: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
257: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
258: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
259: IGr = (Vr*PGv[i] + Vi*QG[i])/Vm2;
260: IGi = (Vi*PGv[i] - Vr*QG[i])/Vm2;
262: delta = PetscAtan2Real(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
264: theta = PETSC_PI/2.0 - delta;
266: Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
267: Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
269: Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
270: Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
272: Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
273: Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
275: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
276: xgen[idx] = Eqp;
277: xgen[idx+1] = Edp;
278: xgen[idx+2] = delta;
279: xgen[idx+3] = w_s;
281: idx = idx + 4;
283: xgen[idx] = Id;
284: xgen[idx+1] = Iq;
286: idx = idx + 2;
288: /* Exciter */
289: Efd = Eqp + (Xd[i] - Xdp[i])*Id;
290: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
291: VR = KE[i]*Efd + SE;
292: RF = KF[i]*Efd/TF[i];
294: xgen[idx] = Efd;
295: xgen[idx+1] = RF;
296: xgen[idx+2] = VR;
298: idx = idx + 3;
299: }
301: VecRestoreArray(Xgen,&xgen);
302: VecRestoreArray(Xnet,&xnet);
304: /* VecView(Xgen,0); */
305: DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet);
306: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
307: return 0;
308: }
310: PetscErrorCode DICDPFiniteDifference(Vec X,Vec *DICDP, Userctx *user)
311: {
312: Vec Y;
313: PetscScalar PGv[3],eps;
314: PetscInt i,j;
316: eps = 1.e-7;
317: VecDuplicate(X,&Y);
319: for (i=0;i<ngen;i++) {
320: for (j=0;j<3;j++) PGv[j] = PG[j];
321: PGv[i] = PG[i]+eps;
322: InitialGuess(Y,user,PGv);
323: InitialGuess(X,user,PG);
325: VecAXPY(Y,-1.0,X);
326: VecScale(Y,1./eps);
327: VecCopy(Y,DICDP[i]);
328: }
329: VecDestroy(&Y);
330: return 0;
331: }
333: /* Computes F = [-f(x,y);g(x,y)] */
334: PetscErrorCode ResidualFunction(SNES snes,Vec X, Vec F, Userctx *user)
335: {
336: Vec Xgen,Xnet,Fgen,Fnet;
337: PetscScalar *xgen,*xnet,*fgen,*fnet;
338: PetscInt i,idx=0;
339: PetscScalar Vr,Vi,Vm,Vm2;
340: PetscScalar Eqp,Edp,delta,w; /* Generator variables */
341: PetscScalar Efd,RF,VR; /* Exciter variables */
342: PetscScalar Id,Iq; /* Generator dq axis currents */
343: PetscScalar Vd,Vq,SE;
344: PetscScalar IGr,IGi,IDr,IDi;
345: PetscScalar Zdq_inv[4],det;
346: PetscScalar PD,QD,Vm0,*v0;
347: PetscInt k;
349: VecZeroEntries(F);
350: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
351: DMCompositeGetLocalVectors(user->dmpgrid,&Fgen,&Fnet);
352: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
353: DMCompositeScatter(user->dmpgrid,F,Fgen,Fnet);
355: /* Network current balance residual IG + Y*V + IL = 0. Only YV is added here.
356: The generator current injection, IG, and load current injection, ID are added later
357: */
358: /* Note that the values in Ybus are stored assuming the imaginary current balance
359: equation is ordered first followed by real current balance equation for each bus.
360: Thus imaginary current contribution goes in location 2*i, and
361: real current contribution in 2*i+1
362: */
363: MatMult(user->Ybus,Xnet,Fnet);
365: VecGetArray(Xgen,&xgen);
366: VecGetArray(Xnet,&xnet);
367: VecGetArray(Fgen,&fgen);
368: VecGetArray(Fnet,&fnet);
370: /* Generator subsystem */
371: for (i=0; i < ngen; i++) {
372: Eqp = xgen[idx];
373: Edp = xgen[idx+1];
374: delta = xgen[idx+2];
375: w = xgen[idx+3];
376: Id = xgen[idx+4];
377: Iq = xgen[idx+5];
378: Efd = xgen[idx+6];
379: RF = xgen[idx+7];
380: VR = xgen[idx+8];
382: /* Generator differential equations */
383: fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i];
384: fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i];
385: fgen[idx+2] = -w + w_s;
386: fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i];
388: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
389: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
391: ri2dq(Vr,Vi,delta,&Vd,&Vq);
392: /* Algebraic equations for stator currents */
393: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
395: Zdq_inv[0] = Rs[i]/det;
396: Zdq_inv[1] = Xqp[i]/det;
397: Zdq_inv[2] = -Xdp[i]/det;
398: Zdq_inv[3] = Rs[i]/det;
400: fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id;
401: fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq;
403: /* Add generator current injection to network */
404: dq2ri(Id,Iq,delta,&IGr,&IGi);
406: fnet[2*gbus[i]] -= IGi;
407: fnet[2*gbus[i]+1] -= IGr;
409: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
411: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
413: /* Exciter differential equations */
414: fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i];
415: fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i];
416: fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
418: idx = idx + 9;
419: }
421: VecGetArray(user->V0,&v0);
422: for (i=0; i < nload; i++) {
423: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
424: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
425: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
426: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
427: PD = QD = 0.0;
428: for (k=0; k < ld_nsegsp[i]; k++) PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
429: for (k=0; k < ld_nsegsq[i]; k++) QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
431: /* Load currents */
432: IDr = (PD*Vr + QD*Vi)/Vm2;
433: IDi = (-QD*Vr + PD*Vi)/Vm2;
435: fnet[2*lbus[i]] += IDi;
436: fnet[2*lbus[i]+1] += IDr;
437: }
438: VecRestoreArray(user->V0,&v0);
440: VecRestoreArray(Xgen,&xgen);
441: VecRestoreArray(Xnet,&xnet);
442: VecRestoreArray(Fgen,&fgen);
443: VecRestoreArray(Fnet,&fnet);
445: DMCompositeGather(user->dmpgrid,INSERT_VALUES,F,Fgen,Fnet);
446: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
447: DMCompositeRestoreLocalVectors(user->dmpgrid,&Fgen,&Fnet);
448: return 0;
449: }
451: /* \dot{x} - f(x,y)
452: g(x,y) = 0
453: */
454: PetscErrorCode IFunction(TS ts,PetscReal t, Vec X, Vec Xdot, Vec F, Userctx *user)
455: {
456: SNES snes;
457: PetscScalar *f;
458: const PetscScalar *xdot;
459: PetscInt i;
461: user->t = t;
463: TSGetSNES(ts,&snes);
464: ResidualFunction(snes,X,F,user);
465: VecGetArray(F,&f);
466: VecGetArrayRead(Xdot,&xdot);
467: for (i=0;i < ngen;i++) {
468: f[9*i] += xdot[9*i];
469: f[9*i+1] += xdot[9*i+1];
470: f[9*i+2] += xdot[9*i+2];
471: f[9*i+3] += xdot[9*i+3];
472: f[9*i+6] += xdot[9*i+6];
473: f[9*i+7] += xdot[9*i+7];
474: f[9*i+8] += xdot[9*i+8];
475: }
476: VecRestoreArray(F,&f);
477: VecRestoreArrayRead(Xdot,&xdot);
478: return 0;
479: }
481: /* This function is used for solving the algebraic system only during fault on and
482: off times. It computes the entire F and then zeros out the part corresponding to
483: differential equations
484: F = [0;g(y)];
485: */
486: PetscErrorCode AlgFunction(SNES snes, Vec X, Vec F, void *ctx)
487: {
488: Userctx *user=(Userctx*)ctx;
489: PetscScalar *f;
490: PetscInt i;
492: ResidualFunction(snes,X,F,user);
493: VecGetArray(F,&f);
494: for (i=0; i < ngen; i++) {
495: f[9*i] = 0;
496: f[9*i+1] = 0;
497: f[9*i+2] = 0;
498: f[9*i+3] = 0;
499: f[9*i+6] = 0;
500: f[9*i+7] = 0;
501: f[9*i+8] = 0;
502: }
503: VecRestoreArray(F,&f);
504: return 0;
505: }
507: PetscErrorCode PreallocateJacobian(Mat J, Userctx *user)
508: {
509: PetscInt *d_nnz;
510: PetscInt i,idx=0,start=0;
511: PetscInt ncols;
513: PetscMalloc1(user->neqs_pgrid,&d_nnz);
514: for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
515: /* Generator subsystem */
516: for (i=0; i < ngen; i++) {
518: d_nnz[idx] += 3;
519: d_nnz[idx+1] += 2;
520: d_nnz[idx+2] += 2;
521: d_nnz[idx+3] += 5;
522: d_nnz[idx+4] += 6;
523: d_nnz[idx+5] += 6;
525: d_nnz[user->neqs_gen+2*gbus[i]] += 3;
526: d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;
528: d_nnz[idx+6] += 2;
529: d_nnz[idx+7] += 2;
530: d_nnz[idx+8] += 5;
532: idx = idx + 9;
533: }
535: start = user->neqs_gen;
536: for (i=0; i < nbus; i++) {
537: MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL);
538: d_nnz[start+2*i] += ncols;
539: d_nnz[start+2*i+1] += ncols;
540: MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL);
541: }
543: MatSeqAIJSetPreallocation(J,0,d_nnz);
544: PetscFree(d_nnz);
545: return 0;
546: }
548: /*
549: J = [-df_dx, -df_dy
550: dg_dx, dg_dy]
551: */
552: PetscErrorCode ResidualJacobian(SNES snes,Vec X,Mat J,Mat B,void *ctx)
553: {
554: Userctx *user=(Userctx*)ctx;
555: Vec Xgen,Xnet;
556: PetscScalar *xgen,*xnet;
557: PetscInt i,idx=0;
558: PetscScalar Vr,Vi,Vm,Vm2;
559: PetscScalar Eqp,Edp,delta; /* Generator variables */
560: PetscScalar Efd; /* Exciter variables */
561: PetscScalar Id,Iq; /* Generator dq axis currents */
562: PetscScalar Vd,Vq;
563: PetscScalar val[10];
564: PetscInt row[2],col[10];
565: PetscInt net_start=user->neqs_gen;
566: PetscInt ncols;
567: const PetscInt *cols;
568: const PetscScalar *yvals;
569: PetscInt k;
570: PetscScalar Zdq_inv[4],det;
571: PetscScalar dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
572: PetscScalar dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
573: PetscScalar dSE_dEfd;
574: PetscScalar dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
575: PetscScalar PD,QD,Vm0,*v0,Vm4;
576: PetscScalar dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
577: PetscScalar dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;
579: MatZeroEntries(B);
580: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
581: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
583: VecGetArray(Xgen,&xgen);
584: VecGetArray(Xnet,&xnet);
586: /* Generator subsystem */
587: for (i=0; i < ngen; i++) {
588: Eqp = xgen[idx];
589: Edp = xgen[idx+1];
590: delta = xgen[idx+2];
591: Id = xgen[idx+4];
592: Iq = xgen[idx+5];
593: Efd = xgen[idx+6];
595: /* fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i]; */
596: row[0] = idx;
597: col[0] = idx; col[1] = idx+4; col[2] = idx+6;
598: val[0] = 1/ Td0p[i]; val[1] = (Xd[i] - Xdp[i])/ Td0p[i]; val[2] = -1/Td0p[i];
600: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
602: /* fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
603: row[0] = idx + 1;
604: col[0] = idx + 1; col[1] = idx+5;
605: val[0] = 1/Tq0p[i]; val[1] = -(Xq[i] - Xqp[i])/Tq0p[i];
606: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
608: /* fgen[idx+2] = - w + w_s; */
609: row[0] = idx + 2;
610: col[0] = idx + 2; col[1] = idx + 3;
611: val[0] = 0; val[1] = -1;
612: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
614: /* fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i]; */
615: row[0] = idx + 3;
616: col[0] = idx; col[1] = idx + 1; col[2] = idx + 3; col[3] = idx + 4; col[4] = idx + 5;
617: 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];
618: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
620: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
621: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
622: ri2dq(Vr,Vi,delta,&Vd,&Vq);
624: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
626: Zdq_inv[0] = Rs[i]/det;
627: Zdq_inv[1] = Xqp[i]/det;
628: Zdq_inv[2] = -Xdp[i]/det;
629: Zdq_inv[3] = Rs[i]/det;
631: dVd_dVr = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
632: dVq_dVr = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
633: dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
634: dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);
636: /* fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
637: row[0] = idx+4;
638: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
639: val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0]; val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
640: col[3] = idx + 4; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
641: 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;
642: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
644: /* fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
645: row[0] = idx+5;
646: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
647: val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2]; val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
648: col[3] = idx + 5; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
649: 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;
650: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
652: dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
653: dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
654: dIGr_dId = PetscSinScalar(delta); dIGr_dIq = PetscCosScalar(delta);
655: dIGi_dId = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);
657: /* fnet[2*gbus[i]] -= IGi; */
658: row[0] = net_start + 2*gbus[i];
659: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
660: val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
661: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
663: /* fnet[2*gbus[i]+1] -= IGr; */
664: row[0] = net_start + 2*gbus[i]+1;
665: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
666: val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
667: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
669: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
671: /* fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i]; */
672: /* SE = k1[i]*PetscExpScalar(k2[i]*Efd); */
673: dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);
675: row[0] = idx + 6;
676: col[0] = idx + 6; col[1] = idx + 8;
677: val[0] = (KE[i] + dSE_dEfd)/TE[i]; val[1] = -1/TE[i];
678: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
680: /* Exciter differential equations */
682: /* fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i]; */
683: row[0] = idx + 7;
684: col[0] = idx + 6; col[1] = idx + 7;
685: val[0] = (-KF[i]/TF[i])/TF[i]; val[1] = 1/TF[i];
686: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
688: /* fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i]; */
689: /* Vm = (Vd^2 + Vq^2)^0.5; */
690: dVm_dVd = Vd/Vm; dVm_dVq = Vq/Vm;
691: dVm_dVr = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
692: dVm_dVi = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
693: row[0] = idx + 8;
694: col[0] = idx + 6; col[1] = idx + 7; col[2] = idx + 8;
695: val[0] = (KA[i]*KF[i]/TF[i])/TA[i]; val[1] = -KA[i]/TA[i]; val[2] = 1/TA[i];
696: col[3] = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
697: val[3] = KA[i]*dVm_dVr/TA[i]; val[4] = KA[i]*dVm_dVi/TA[i];
698: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
699: idx = idx + 9;
700: }
702: for (i=0; i<nbus; i++) {
703: MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
704: row[0] = net_start + 2*i;
705: for (k=0; k<ncols; k++) {
706: col[k] = net_start + cols[k];
707: val[k] = yvals[k];
708: }
709: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
710: MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);
712: MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
713: row[0] = net_start + 2*i+1;
714: for (k=0; k<ncols; k++) {
715: col[k] = net_start + cols[k];
716: val[k] = yvals[k];
717: }
718: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
719: MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
720: }
722: MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
723: MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);
725: VecGetArray(user->V0,&v0);
726: for (i=0; i < nload; i++) {
727: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
728: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
729: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2= Vm*Vm; Vm4 = Vm2*Vm2;
730: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
731: PD = QD = 0.0;
732: dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
733: for (k=0; k < ld_nsegsp[i]; k++) {
734: PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
735: dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
736: dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
737: }
738: for (k=0; k < ld_nsegsq[i]; k++) {
739: QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
740: dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
741: dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
742: }
744: /* IDr = (PD*Vr + QD*Vi)/Vm2; */
745: /* IDi = (-QD*Vr + PD*Vi)/Vm2; */
747: dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
748: dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;
750: dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
751: dIDi_dVi = (-dQD_dVi*Vr + dPD_dVi*Vi + PD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vi)/Vm4;
753: /* fnet[2*lbus[i]] += IDi; */
754: row[0] = net_start + 2*lbus[i];
755: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
756: val[0] = dIDi_dVr; val[1] = dIDi_dVi;
757: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
758: /* fnet[2*lbus[i]+1] += IDr; */
759: row[0] = net_start + 2*lbus[i]+1;
760: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
761: val[0] = dIDr_dVr; val[1] = dIDr_dVi;
762: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
763: }
764: VecRestoreArray(user->V0,&v0);
766: VecRestoreArray(Xgen,&xgen);
767: VecRestoreArray(Xnet,&xnet);
769: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
771: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
772: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
773: return 0;
774: }
776: /*
777: J = [I, 0
778: dg_dx, dg_dy]
779: */
780: PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
781: {
782: Userctx *user=(Userctx*)ctx;
784: ResidualJacobian(snes,X,A,B,ctx);
785: MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
786: MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);
787: return 0;
788: }
790: /*
791: J = [a*I-df_dx, -df_dy
792: dg_dx, dg_dy]
793: */
795: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
796: {
797: SNES snes;
798: PetscScalar atmp = (PetscScalar) a;
799: PetscInt i,row;
801: user->t = t;
803: TSGetSNES(ts,&snes);
804: ResidualJacobian(snes,X,A,B,user);
805: for (i=0;i < ngen;i++) {
806: row = 9*i;
807: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
808: row = 9*i+1;
809: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
810: row = 9*i+2;
811: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
812: row = 9*i+3;
813: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
814: row = 9*i+6;
815: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
816: row = 9*i+7;
817: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
818: row = 9*i+8;
819: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
820: }
821: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
822: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
823: return 0;
824: }
826: /* Matrix JacobianP is constant so that it only needs to be evaluated once */
827: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A, void *ctx0)
828: {
829: PetscScalar a;
830: PetscInt row,col;
831: Userctx *ctx=(Userctx*)ctx0;
835: if (ctx->jacp_flg) {
836: MatZeroEntries(A);
838: for (col=0;col<3;col++) {
839: a = 1.0/M[col];
840: row = 9*col+3;
841: MatSetValues(A,1,&row,1,&col,&a,INSERT_VALUES);
842: }
844: ctx->jacp_flg = PETSC_FALSE;
846: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
847: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
848: }
849: return 0;
850: }
852: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,Userctx *user)
853: {
854: const PetscScalar *u;
855: PetscInt idx;
856: Vec Xgen,Xnet;
857: PetscScalar *r,*xgen;
858: PetscInt i;
860: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
861: DMCompositeScatter(user->dmpgrid,U,Xgen,Xnet);
863: VecGetArray(Xgen,&xgen);
865: VecGetArrayRead(U,&u);
866: VecGetArray(R,&r);
867: r[0] = 0.;
868: idx = 0;
869: for (i=0;i<ngen;i++) {
870: 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);
871: idx += 9;
872: }
873: VecRestoreArrayRead(U,&u);
874: VecRestoreArray(R,&r);
875: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
876: return 0;
877: }
879: static PetscErrorCode DRDUJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDU,Mat B,Userctx *user)
880: {
881: Vec Xgen,Xnet,Dgen,Dnet;
882: PetscScalar *xgen,*dgen;
883: PetscInt i;
884: PetscInt idx;
885: Vec drdu_col;
886: PetscScalar *xarr;
888: VecDuplicate(U,&drdu_col);
889: MatDenseGetColumn(DRDU,0,&xarr);
890: VecPlaceArray(drdu_col,xarr);
891: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
892: DMCompositeGetLocalVectors(user->dmpgrid,&Dgen,&Dnet);
893: DMCompositeScatter(user->dmpgrid,U,Xgen,Xnet);
894: DMCompositeScatter(user->dmpgrid,drdu_col,Dgen,Dnet);
896: VecGetArray(Xgen,&xgen);
897: VecGetArray(Dgen,&dgen);
899: idx = 0;
900: for (i=0;i<ngen;i++) {
901: dgen[idx+3] = 0.;
902: 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);
903: 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);
904: idx += 9;
905: }
907: VecRestoreArray(Dgen,&dgen);
908: VecRestoreArray(Xgen,&xgen);
909: DMCompositeGather(user->dmpgrid,INSERT_VALUES,drdu_col,Dgen,Dnet);
910: DMCompositeRestoreLocalVectors(user->dmpgrid,&Dgen,&Dnet);
911: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
912: VecResetArray(drdu_col);
913: MatDenseRestoreColumn(DRDU,&xarr);
914: VecDestroy(&drdu_col);
915: return 0;
916: }
918: static PetscErrorCode DRDPJacobianTranspose(TS ts,PetscReal t,Vec U,Mat drdp,Userctx *user)
919: {
920: return 0;
921: }
923: PetscErrorCode ComputeSensiP(Vec lambda,Vec mu,Vec *DICDP,Userctx *user)
924: {
925: PetscScalar *x,*y,sensip;
926: PetscInt i;
928: VecGetArray(lambda,&x);
929: VecGetArray(mu,&y);
931: for (i=0;i<3;i++) {
932: VecDot(lambda,DICDP[i],&sensip);
933: sensip = sensip+y[i];
934: /* PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt %D th parameter: %g \n",i,(double)sensip); */
935: y[i] = sensip;
936: }
937: VecRestoreArray(mu,&y);
938: return 0;
939: }
941: int main(int argc,char **argv)
942: {
943: Userctx user;
944: Vec p;
945: PetscScalar *x_ptr;
946: PetscErrorCode ierr;
947: PetscMPIInt size;
948: PetscInt i;
949: PetscViewer Xview,Ybusview;
950: PetscInt *idx2;
951: Tao tao;
952: KSP ksp;
953: PC pc;
954: Vec lowerb,upperb;
956: PetscInitialize(&argc,&argv,"petscoptions",help);
957: MPI_Comm_size(PETSC_COMM_WORLD,&size);
960: user.jacp_flg = PETSC_TRUE;
961: user.neqs_gen = 9*ngen; /* # eqs. for generator subsystem */
962: user.neqs_net = 2*nbus; /* # eqs. for network subsystem */
963: user.neqs_pgrid = user.neqs_gen + user.neqs_net;
965: /* Create indices for differential and algebraic equations */
966: PetscMalloc1(7*ngen,&idx2);
967: for (i=0; i<ngen; i++) {
968: 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;
969: idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
970: }
971: ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
972: ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
973: PetscFree(idx2);
975: /* Set run time options */
976: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Transient stability fault options","");
977: {
978: user.tfaulton = 1.0;
979: user.tfaultoff = 1.2;
980: user.Rfault = 0.0001;
981: user.faultbus = 8;
982: PetscOptionsReal("-tfaulton","","",user.tfaulton,&user.tfaulton,NULL);
983: PetscOptionsReal("-tfaultoff","","",user.tfaultoff,&user.tfaultoff,NULL);
984: PetscOptionsInt("-faultbus","","",user.faultbus,&user.faultbus,NULL);
985: user.t0 = 0.0;
986: user.tmax = 1.3;
987: PetscOptionsReal("-t0","","",user.t0,&user.t0,NULL);
988: PetscOptionsReal("-tmax","","",user.tmax,&user.tmax,NULL);
989: user.freq_u = 61.0;
990: user.freq_l = 59.0;
991: user.pow = 2;
992: PetscOptionsReal("-frequ","","",user.freq_u,&user.freq_u,NULL);
993: PetscOptionsReal("-freql","","",user.freq_l,&user.freq_l,NULL);
994: PetscOptionsInt("-pow","","",user.pow,&user.pow,NULL);
996: }
997: PetscOptionsEnd();
999: /* Create DMs for generator and network subsystems */
1000: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
1001: DMSetOptionsPrefix(user.dmgen,"dmgen_");
1002: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
1003: DMSetOptionsPrefix(user.dmnet,"dmnet_");
1004: DMSetFromOptions(user.dmnet);
1005: DMSetUp(user.dmnet);
1006: /* Create a composite DM packer and add the two DMs */
1007: DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
1008: DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
1009: DMSetFromOptions(user.dmgen);
1010: DMSetUp(user.dmgen);
1011: DMCompositeAddDM(user.dmpgrid,user.dmgen);
1012: DMCompositeAddDM(user.dmpgrid,user.dmnet);
1014: /* Read initial voltage vector and Ybus */
1015: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
1016: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);
1018: VecCreate(PETSC_COMM_WORLD,&user.V0);
1019: VecSetSizes(user.V0,PETSC_DECIDE,user.neqs_net);
1020: VecLoad(user.V0,Xview);
1022: MatCreate(PETSC_COMM_WORLD,&user.Ybus);
1023: MatSetSizes(user.Ybus,PETSC_DECIDE,PETSC_DECIDE,user.neqs_net,user.neqs_net);
1024: MatSetType(user.Ybus,MATBAIJ);
1025: /* MatSetBlockSize(ctx->Ybus,2); */
1026: MatLoad(user.Ybus,Ybusview);
1028: PetscViewerDestroy(&Xview);
1029: PetscViewerDestroy(&Ybusview);
1031: /* Allocate space for Jacobians */
1032: MatCreate(PETSC_COMM_WORLD,&user.J);
1033: MatSetSizes(user.J,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,user.neqs_pgrid);
1034: MatSetFromOptions(user.J);
1035: PreallocateJacobian(user.J,&user);
1037: MatCreate(PETSC_COMM_WORLD,&user.Jacp);
1038: MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,3);
1039: MatSetFromOptions(user.Jacp);
1040: MatSetUp(user.Jacp);
1041: MatZeroEntries(user.Jacp); /* initialize to zeros */
1043: MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,3,1,NULL,&user.DRDP);
1044: MatSetUp(user.DRDP);
1045: MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,1,NULL,&user.DRDU);
1046: MatSetUp(user.DRDU);
1048: /* Create TAO solver and set desired solution method */
1049: TaoCreate(PETSC_COMM_WORLD,&tao);
1050: TaoSetType(tao,TAOBLMVM);
1051: /*
1052: Optimization starts
1053: */
1054: /* Set initial solution guess */
1055: VecCreateSeq(PETSC_COMM_WORLD,3,&p);
1056: VecGetArray(p,&x_ptr);
1057: x_ptr[0] = PG[0]; x_ptr[1] = PG[1]; x_ptr[2] = PG[2];
1058: VecRestoreArray(p,&x_ptr);
1060: TaoSetSolution(tao,p);
1061: /* Set routine for function and gradient evaluation */
1062: TaoSetObjectiveAndGradient(tao,NULL,FormFunctionGradient,&user);
1064: /* Set bounds for the optimization */
1065: VecDuplicate(p,&lowerb);
1066: VecDuplicate(p,&upperb);
1067: VecGetArray(lowerb,&x_ptr);
1068: x_ptr[0] = 0.5; x_ptr[1] = 0.5; x_ptr[2] = 0.5;
1069: VecRestoreArray(lowerb,&x_ptr);
1070: VecGetArray(upperb,&x_ptr);
1071: x_ptr[0] = 2.0; x_ptr[1] = 2.0; x_ptr[2] = 2.0;
1072: VecRestoreArray(upperb,&x_ptr);
1073: TaoSetVariableBounds(tao,lowerb,upperb);
1075: /* Check for any TAO command line options */
1076: TaoSetFromOptions(tao);
1077: TaoGetKSP(tao,&ksp);
1078: if (ksp) {
1079: KSPGetPC(ksp,&pc);
1080: PCSetType(pc,PCNONE);
1081: }
1083: /* SOLVE THE APPLICATION */
1084: TaoSolve(tao);
1086: VecView(p,PETSC_VIEWER_STDOUT_WORLD);
1087: /* Free TAO data structures */
1088: TaoDestroy(&tao);
1090: DMDestroy(&user.dmgen);
1091: DMDestroy(&user.dmnet);
1092: DMDestroy(&user.dmpgrid);
1093: ISDestroy(&user.is_diff);
1094: ISDestroy(&user.is_alg);
1096: MatDestroy(&user.J);
1097: MatDestroy(&user.Jacp);
1098: MatDestroy(&user.Ybus);
1099: /* MatDestroy(&user.Sol); */
1100: VecDestroy(&user.V0);
1101: VecDestroy(&p);
1102: VecDestroy(&lowerb);
1103: VecDestroy(&upperb);
1104: MatDestroy(&user.DRDU);
1105: MatDestroy(&user.DRDP);
1106: PetscFinalize();
1107: return 0;
1108: }
1110: /* ------------------------------------------------------------------ */
1111: /*
1112: FormFunction - Evaluates the function and corresponding gradient.
1114: Input Parameters:
1115: tao - the Tao context
1116: X - the input vector
1117: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient()
1119: Output Parameters:
1120: f - the newly evaluated function
1121: G - the newly evaluated gradient
1122: */
1123: PetscErrorCode FormFunctionGradient(Tao tao,Vec P,PetscReal *f,Vec G,void *ctx0)
1124: {
1125: TS ts,quadts;
1126: SNES snes_alg;
1127: Userctx *ctx = (Userctx*)ctx0;
1128: Vec X;
1129: PetscInt i;
1130: /* sensitivity context */
1131: PetscScalar *x_ptr;
1132: Vec lambda[1],q;
1133: Vec mu[1];
1134: PetscInt steps1,steps2,steps3;
1135: Vec DICDP[3];
1136: Vec F_alg;
1137: PetscInt row_loc,col_loc;
1138: PetscScalar val;
1139: Vec Xdot;
1141: VecGetArrayRead(P,(const PetscScalar**)&x_ptr);
1142: PG[0] = x_ptr[0];
1143: PG[1] = x_ptr[1];
1144: PG[2] = x_ptr[2];
1145: VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);
1147: ctx->stepnum = 0;
1149: DMCreateGlobalVector(ctx->dmpgrid,&X);
1151: /* Create matrix to save solutions at each time step */
1152: /* MatCreateSeqDense(PETSC_COMM_SELF,ctx->neqs_pgrid+1,1002,NULL,&ctx->Sol); */
1153: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1154: Create timestepping solver context
1155: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1156: TSCreate(PETSC_COMM_WORLD,&ts);
1157: TSSetProblemType(ts,TS_NONLINEAR);
1158: TSSetType(ts,TSCN);
1159: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,ctx);
1160: TSSetIJacobian(ts,ctx->J,ctx->J,(TSIJacobian)IJacobian,ctx);
1161: TSSetApplicationContext(ts,ctx);
1162: /* Set RHS JacobianP */
1163: TSSetRHSJacobianP(ts,ctx->Jacp,RHSJacobianP,ctx);
1165: TSCreateQuadratureTS(ts,PETSC_FALSE,&quadts);
1166: TSSetRHSFunction(quadts,NULL,(TSRHSFunction)CostIntegrand,ctx);
1167: TSSetRHSJacobian(quadts,ctx->DRDU,ctx->DRDU,(TSRHSJacobian)DRDUJacobianTranspose,ctx);
1168: TSSetRHSJacobianP(quadts,ctx->DRDP,(TSRHSJacobianP)DRDPJacobianTranspose,ctx);
1170: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1171: Set initial conditions
1172: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1173: SetInitialGuess(X,ctx);
1175: /* Approximate DICDP with finite difference, we want to zero out network variables */
1176: for (i=0;i<3;i++) {
1177: VecDuplicate(X,&DICDP[i]);
1178: }
1179: DICDPFiniteDifference(X,DICDP,ctx);
1181: VecDuplicate(X,&F_alg);
1182: SNESCreate(PETSC_COMM_WORLD,&snes_alg);
1183: SNESSetFunction(snes_alg,F_alg,AlgFunction,ctx);
1184: MatZeroEntries(ctx->J);
1185: SNESSetJacobian(snes_alg,ctx->J,ctx->J,AlgJacobian,ctx);
1186: SNESSetOptionsPrefix(snes_alg,"alg_");
1187: SNESSetFromOptions(snes_alg);
1188: ctx->alg_flg = PETSC_TRUE;
1189: /* Solve the algebraic equations */
1190: SNESSolve(snes_alg,NULL,X);
1192: /* Just to set up the Jacobian structure */
1193: VecDuplicate(X,&Xdot);
1194: IJacobian(ts,0.0,X,Xdot,0.0,ctx->J,ctx->J,ctx);
1195: VecDestroy(&Xdot);
1197: ctx->stepnum++;
1199: /*
1200: Save trajectory of solution so that TSAdjointSolve() may be used
1201: */
1202: TSSetSaveTrajectory(ts);
1204: TSSetTimeStep(ts,0.01);
1205: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
1206: TSSetFromOptions(ts);
1207: /* TSSetPostStep(ts,SaveSolution); */
1209: /* Prefault period */
1210: ctx->alg_flg = PETSC_FALSE;
1211: TSSetTime(ts,0.0);
1212: TSSetMaxTime(ts,ctx->tfaulton);
1213: TSSolve(ts,X);
1214: TSGetStepNumber(ts,&steps1);
1216: /* Create the nonlinear solver for solving the algebraic system */
1217: /* Note that although the algebraic system needs to be solved only for
1218: Idq and V, we reuse the entire system including xgen. The xgen
1219: variables are held constant by setting their residuals to 0 and
1220: putting a 1 on the Jacobian diagonal for xgen rows
1221: */
1222: MatZeroEntries(ctx->J);
1224: /* Apply disturbance - resistive fault at ctx->faultbus */
1225: /* This is done by adding shunt conductance to the diagonal location
1226: in the Ybus matrix */
1227: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
1228: val = 1/ctx->Rfault;
1229: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1230: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
1231: val = 1/ctx->Rfault;
1232: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1234: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1235: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1237: ctx->alg_flg = PETSC_TRUE;
1238: /* Solve the algebraic equations */
1239: SNESSolve(snes_alg,NULL,X);
1241: ctx->stepnum++;
1243: /* Disturbance period */
1244: ctx->alg_flg = PETSC_FALSE;
1245: TSSetTime(ts,ctx->tfaulton);
1246: TSSetMaxTime(ts,ctx->tfaultoff);
1247: TSSolve(ts,X);
1248: TSGetStepNumber(ts,&steps2);
1249: steps2 -= steps1;
1251: /* Remove the fault */
1252: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1;
1253: val = -1/ctx->Rfault;
1254: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1255: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus;
1256: val = -1/ctx->Rfault;
1257: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1259: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1260: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1262: MatZeroEntries(ctx->J);
1264: ctx->alg_flg = PETSC_TRUE;
1266: /* Solve the algebraic equations */
1267: SNESSolve(snes_alg,NULL,X);
1269: ctx->stepnum++;
1271: /* Post-disturbance period */
1272: ctx->alg_flg = PETSC_TRUE;
1273: TSSetTime(ts,ctx->tfaultoff);
1274: TSSetMaxTime(ts,ctx->tmax);
1275: TSSolve(ts,X);
1276: TSGetStepNumber(ts,&steps3);
1277: steps3 -= steps2;
1278: steps3 -= steps1;
1280: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1281: Adjoint model starts here
1282: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1283: TSSetPostStep(ts,NULL);
1284: MatCreateVecs(ctx->J,&lambda[0],NULL);
1285: /* Set initial conditions for the adjoint integration */
1286: VecZeroEntries(lambda[0]);
1288: MatCreateVecs(ctx->Jacp,&mu[0],NULL);
1289: VecZeroEntries(mu[0]);
1290: TSSetCostGradients(ts,1,lambda,mu);
1292: TSAdjointSetSteps(ts,steps3);
1293: TSAdjointSolve(ts);
1295: MatZeroEntries(ctx->J);
1296: /* Applying disturbance - resistive fault at ctx->faultbus */
1297: /* This is done by deducting shunt conductance to the diagonal location
1298: in the Ybus matrix */
1299: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
1300: val = 1./ctx->Rfault;
1301: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1302: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
1303: val = 1./ctx->Rfault;
1304: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1306: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1307: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1309: /* Set number of steps for the adjoint integration */
1310: TSAdjointSetSteps(ts,steps2);
1311: TSAdjointSolve(ts);
1313: MatZeroEntries(ctx->J);
1314: /* remove the fault */
1315: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
1316: val = -1./ctx->Rfault;
1317: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1318: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
1319: val = -1./ctx->Rfault;
1320: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1322: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1323: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1325: /* Set number of steps for the adjoint integration */
1326: TSAdjointSetSteps(ts,steps1);
1327: TSAdjointSolve(ts);
1329: ComputeSensiP(lambda[0],mu[0],DICDP,ctx);
1330: VecCopy(mu[0],G);
1332: TSGetQuadratureTS(ts,NULL,&quadts);
1333: TSGetSolution(quadts,&q);
1334: VecGetArray(q,&x_ptr);
1335: *f = x_ptr[0];
1336: x_ptr[0] = 0;
1337: VecRestoreArray(q,&x_ptr);
1339: VecDestroy(&lambda[0]);
1340: VecDestroy(&mu[0]);
1342: SNESDestroy(&snes_alg);
1343: VecDestroy(&F_alg);
1344: VecDestroy(&X);
1345: TSDestroy(&ts);
1346: for (i=0;i<3;i++) {
1347: VecDestroy(&DICDP[i]);
1348: }
1349: return 0;
1350: }
1352: /*TEST
1354: build:
1355: requires: double !complex !defined(PETSC_USE_64BIT_INDICES)
1357: test:
1358: args: -viewer_binary_skip_info -tao_monitor -tao_gttol .2
1359: localrunfiles: petscoptions X.bin Ybus.bin
1361: TEST*/