Actual source code: ex9busopt.c
petsc-3.12.0 2019-09-29
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 coordiantes.\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;
111: /* Converts from machine frame (dq) to network (phase a real,imag) reference frame */
112: PetscErrorCode dq2ri(PetscScalar Fd,PetscScalar Fq,PetscScalar delta,PetscScalar *Fr, PetscScalar *Fi)
113: {
115: *Fr = Fd*PetscSinScalar(delta) + Fq*PetscCosScalar(delta);
116: *Fi = -Fd*PetscCosScalar(delta) + Fq*PetscSinScalar(delta);
117: return(0);
118: }
120: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
121: PetscErrorCode ri2dq(PetscScalar Fr,PetscScalar Fi,PetscScalar delta,PetscScalar *Fd, PetscScalar *Fq)
122: {
124: *Fd = Fr*PetscSinScalar(delta) - Fi*PetscCosScalar(delta);
125: *Fq = Fr*PetscCosScalar(delta) + Fi*PetscSinScalar(delta);
126: return(0);
127: }
129: /* Saves the solution at each time to a matrix */
130: PetscErrorCode SaveSolution(TS ts)
131: {
132: PetscErrorCode ierr;
133: Userctx *user;
134: Vec X;
135: PetscScalar *mat;
136: const PetscScalar *x;
137: PetscInt idx;
138: PetscReal t;
141: TSGetApplicationContext(ts,&user);
142: TSGetTime(ts,&t);
143: TSGetSolution(ts,&X);
144: idx = user->stepnum*(user->neqs_pgrid+1);
145: MatDenseGetArray(user->Sol,&mat);
146: VecGetArrayRead(X,&x);
147: mat[idx] = t;
148: PetscArraycpy(mat+idx+1,x,user->neqs_pgrid);
149: MatDenseRestoreArray(user->Sol,&mat);
150: VecRestoreArrayRead(X,&x);
151: user->stepnum++;
152: return(0);
153: }
155: PetscErrorCode SetInitialGuess(Vec X,Userctx *user)
156: {
158: Vec Xgen,Xnet;
159: PetscScalar *xgen,*xnet;
160: PetscInt i,idx=0;
161: PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
162: PetscScalar Eqp,Edp,delta;
163: PetscScalar Efd,RF,VR; /* Exciter variables */
164: PetscScalar Id,Iq; /* Generator dq axis currents */
165: PetscScalar theta,Vd,Vq,SE;
168: M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
169: D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
171: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
173: /* Network subsystem initialization */
174: VecCopy(user->V0,Xnet);
176: /* Generator subsystem initialization */
177: VecGetArray(Xgen,&xgen);
178: VecGetArray(Xnet,&xnet);
180: for (i=0; i < ngen; i++) {
181: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
182: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
183: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
184: IGr = (Vr*PG[i] + Vi*QG[i])/Vm2;
185: IGi = (Vi*PG[i] - Vr*QG[i])/Vm2;
187: delta = PetscAtan2Real(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
189: theta = PETSC_PI/2.0 - delta;
191: Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
192: Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
194: Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
195: Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
197: Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
198: Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
200: TM[i] = PG[i];
202: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
203: xgen[idx] = Eqp;
204: xgen[idx+1] = Edp;
205: xgen[idx+2] = delta;
206: xgen[idx+3] = w_s;
208: idx = idx + 4;
210: xgen[idx] = Id;
211: xgen[idx+1] = Iq;
213: idx = idx + 2;
215: /* Exciter */
216: Efd = Eqp + (Xd[i] - Xdp[i])*Id;
217: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
218: VR = KE[i]*Efd + SE;
219: RF = KF[i]*Efd/TF[i];
221: xgen[idx] = Efd;
222: xgen[idx+1] = RF;
223: xgen[idx+2] = VR;
225: Vref[i] = Vm + (VR/KA[i]);
227: idx = idx + 3;
228: }
230: VecRestoreArray(Xgen,&xgen);
231: VecRestoreArray(Xnet,&xnet);
233: /* VecView(Xgen,0); */
234: DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet);
235: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
236: return(0);
237: }
239: PetscErrorCode InitialGuess(Vec X,Userctx *user, const PetscScalar PGv[])
240: {
242: Vec Xgen,Xnet;
243: PetscScalar *xgen,*xnet;
244: PetscInt i,idx=0;
245: PetscScalar Vr,Vi,IGr,IGi,Vm,Vm2;
246: PetscScalar Eqp,Edp,delta;
247: PetscScalar Efd,RF,VR; /* Exciter variables */
248: PetscScalar Id,Iq; /* Generator dq axis currents */
249: PetscScalar theta,Vd,Vq,SE;
252: M[0] = 2*H[0]/w_s; M[1] = 2*H[1]/w_s; M[2] = 2*H[2]/w_s;
253: D[0] = 0.1*M[0]; D[1] = 0.1*M[1]; D[2] = 0.1*M[2];
255: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
257: /* Network subsystem initialization */
258: VecCopy(user->V0,Xnet);
260: /* Generator subsystem initialization */
261: VecGetArray(Xgen,&xgen);
262: VecGetArray(Xnet,&xnet);
264: for (i=0; i < ngen; i++) {
265: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
266: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
267: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
268: IGr = (Vr*PGv[i] + Vi*QG[i])/Vm2;
269: IGi = (Vi*PGv[i] - Vr*QG[i])/Vm2;
271: delta = PetscAtan2Real(Vi+Xq[i]*IGr,Vr-Xq[i]*IGi); /* Machine angle */
273: theta = PETSC_PI/2.0 - delta;
275: Id = IGr*PetscCosScalar(theta) - IGi*PetscSinScalar(theta); /* d-axis stator current */
276: Iq = IGr*PetscSinScalar(theta) + IGi*PetscCosScalar(theta); /* q-axis stator current */
278: Vd = Vr*PetscCosScalar(theta) - Vi*PetscSinScalar(theta);
279: Vq = Vr*PetscSinScalar(theta) + Vi*PetscCosScalar(theta);
281: Edp = Vd + Rs[i]*Id - Xqp[i]*Iq; /* d-axis transient EMF */
282: Eqp = Vq + Rs[i]*Iq + Xdp[i]*Id; /* q-axis transient EMF */
284: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
285: xgen[idx] = Eqp;
286: xgen[idx+1] = Edp;
287: xgen[idx+2] = delta;
288: xgen[idx+3] = w_s;
290: idx = idx + 4;
292: xgen[idx] = Id;
293: xgen[idx+1] = Iq;
295: idx = idx + 2;
297: /* Exciter */
298: Efd = Eqp + (Xd[i] - Xdp[i])*Id;
299: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
300: VR = KE[i]*Efd + SE;
301: RF = KF[i]*Efd/TF[i];
303: xgen[idx] = Efd;
304: xgen[idx+1] = RF;
305: xgen[idx+2] = VR;
307: idx = idx + 3;
308: }
310: VecRestoreArray(Xgen,&xgen);
311: VecRestoreArray(Xnet,&xnet);
313: /* VecView(Xgen,0); */
314: DMCompositeGather(user->dmpgrid,INSERT_VALUES,X,Xgen,Xnet);
315: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
316: return(0);
317: }
319: PetscErrorCode DICDPFiniteDifference(Vec X,Vec *DICDP, Userctx *user)
320: {
321: Vec Y;
322: PetscScalar PGv[3],eps;
324: 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: }
344: /* Computes F = [-f(x,y);g(x,y)] */
345: PetscErrorCode ResidualFunction(SNES snes,Vec X, Vec F, Userctx *user)
346: {
348: Vec Xgen,Xnet,Fgen,Fnet;
349: PetscScalar *xgen,*xnet,*fgen,*fnet;
350: PetscInt i,idx=0;
351: PetscScalar Vr,Vi,Vm,Vm2;
352: PetscScalar Eqp,Edp,delta,w; /* Generator variables */
353: PetscScalar Efd,RF,VR; /* Exciter variables */
354: PetscScalar Id,Iq; /* Generator dq axis currents */
355: PetscScalar Vd,Vq,SE;
356: PetscScalar IGr,IGi,IDr,IDi;
357: PetscScalar Zdq_inv[4],det;
358: PetscScalar PD,QD,Vm0,*v0;
359: PetscInt k;
362: VecZeroEntries(F);
363: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
364: DMCompositeGetLocalVectors(user->dmpgrid,&Fgen,&Fnet);
365: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
366: DMCompositeScatter(user->dmpgrid,F,Fgen,Fnet);
368: /* Network current balance residual IG + Y*V + IL = 0. Only YV is added here.
369: The generator current injection, IG, and load current injection, ID are added later
370: */
371: /* Note that the values in Ybus are stored assuming the imaginary current balance
372: equation is ordered first followed by real current balance equation for each bus.
373: Thus imaginary current contribution goes in location 2*i, and
374: real current contribution in 2*i+1
375: */
376: MatMult(user->Ybus,Xnet,Fnet);
378: VecGetArray(Xgen,&xgen);
379: VecGetArray(Xnet,&xnet);
380: VecGetArray(Fgen,&fgen);
381: VecGetArray(Fnet,&fnet);
383: /* Generator subsystem */
384: for (i=0; i < ngen; i++) {
385: Eqp = xgen[idx];
386: Edp = xgen[idx+1];
387: delta = xgen[idx+2];
388: w = xgen[idx+3];
389: Id = xgen[idx+4];
390: Iq = xgen[idx+5];
391: Efd = xgen[idx+6];
392: RF = xgen[idx+7];
393: VR = xgen[idx+8];
395: /* Generator differential equations */
396: fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i];
397: fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i];
398: fgen[idx+2] = -w + w_s;
399: fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i];
401: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
402: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
404: ri2dq(Vr,Vi,delta,&Vd,&Vq);
405: /* Algebraic equations for stator currents */
406: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
408: Zdq_inv[0] = Rs[i]/det;
409: Zdq_inv[1] = Xqp[i]/det;
410: Zdq_inv[2] = -Xdp[i]/det;
411: Zdq_inv[3] = Rs[i]/det;
413: fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id;
414: fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq;
416: /* Add generator current injection to network */
417: dq2ri(Id,Iq,delta,&IGr,&IGi);
419: fnet[2*gbus[i]] -= IGi;
420: fnet[2*gbus[i]+1] -= IGr;
422: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
424: SE = k1[i]*PetscExpScalar(k2[i]*Efd);
426: /* Exciter differential equations */
427: fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i];
428: fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i];
429: fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i];
431: idx = idx + 9;
432: }
434: VecGetArray(user->V0,&v0);
435: for (i=0; i < nload; i++) {
436: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
437: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
438: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2 = Vm*Vm;
439: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
440: PD = QD = 0.0;
441: for (k=0; k < ld_nsegsp[i]; k++) PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
442: for (k=0; k < ld_nsegsq[i]; k++) QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
444: /* Load currents */
445: IDr = (PD*Vr + QD*Vi)/Vm2;
446: IDi = (-QD*Vr + PD*Vi)/Vm2;
448: fnet[2*lbus[i]] += IDi;
449: fnet[2*lbus[i]+1] += IDr;
450: }
451: VecRestoreArray(user->V0,&v0);
453: VecRestoreArray(Xgen,&xgen);
454: VecRestoreArray(Xnet,&xnet);
455: VecRestoreArray(Fgen,&fgen);
456: VecRestoreArray(Fnet,&fnet);
458: DMCompositeGather(user->dmpgrid,INSERT_VALUES,F,Fgen,Fnet);
459: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
460: DMCompositeRestoreLocalVectors(user->dmpgrid,&Fgen,&Fnet);
461: return(0);
462: }
464: /* \dot{x} - f(x,y)
465: g(x,y) = 0
466: */
467: PetscErrorCode IFunction(TS ts,PetscReal t, Vec X, Vec Xdot, Vec F, Userctx *user)
468: {
469: PetscErrorCode ierr;
470: SNES snes;
471: PetscScalar *f;
472: const PetscScalar *xdot;
473: PetscInt i;
476: user->t = t;
478: TSGetSNES(ts,&snes);
479: ResidualFunction(snes,X,F,user);
480: VecGetArray(F,&f);
481: VecGetArrayRead(Xdot,&xdot);
482: for (i=0;i < ngen;i++) {
483: f[9*i] += xdot[9*i];
484: f[9*i+1] += xdot[9*i+1];
485: f[9*i+2] += xdot[9*i+2];
486: f[9*i+3] += xdot[9*i+3];
487: f[9*i+6] += xdot[9*i+6];
488: f[9*i+7] += xdot[9*i+7];
489: f[9*i+8] += xdot[9*i+8];
490: }
491: VecRestoreArray(F,&f);
492: VecRestoreArrayRead(Xdot,&xdot);
493: return(0);
494: }
496: /* This function is used for solving the algebraic system only during fault on and
497: off times. It computes the entire F and then zeros out the part corresponding to
498: differential equations
499: F = [0;g(y)];
500: */
501: PetscErrorCode AlgFunction(SNES snes, Vec X, Vec F, void *ctx)
502: {
504: Userctx *user=(Userctx*)ctx;
505: PetscScalar *f;
506: PetscInt i;
509: ResidualFunction(snes,X,F,user);
510: VecGetArray(F,&f);
511: for (i=0; i < ngen; i++) {
512: f[9*i] = 0;
513: f[9*i+1] = 0;
514: f[9*i+2] = 0;
515: f[9*i+3] = 0;
516: f[9*i+6] = 0;
517: f[9*i+7] = 0;
518: f[9*i+8] = 0;
519: }
520: VecRestoreArray(F,&f);
521: return(0);
522: }
524: PetscErrorCode PreallocateJacobian(Mat J, Userctx *user)
525: {
527: PetscInt *d_nnz;
528: PetscInt i,idx=0,start=0;
529: PetscInt ncols;
532: PetscMalloc1(user->neqs_pgrid,&d_nnz);
533: for (i=0; i<user->neqs_pgrid; i++) d_nnz[i] = 0;
534: /* Generator subsystem */
535: for (i=0; i < ngen; i++) {
537: d_nnz[idx] += 3;
538: d_nnz[idx+1] += 2;
539: d_nnz[idx+2] += 2;
540: d_nnz[idx+3] += 5;
541: d_nnz[idx+4] += 6;
542: d_nnz[idx+5] += 6;
544: d_nnz[user->neqs_gen+2*gbus[i]] += 3;
545: d_nnz[user->neqs_gen+2*gbus[i]+1] += 3;
547: d_nnz[idx+6] += 2;
548: d_nnz[idx+7] += 2;
549: d_nnz[idx+8] += 5;
551: idx = idx + 9;
552: }
554: start = user->neqs_gen;
555: for (i=0; i < nbus; i++) {
556: MatGetRow(user->Ybus,2*i,&ncols,NULL,NULL);
557: d_nnz[start+2*i] += ncols;
558: d_nnz[start+2*i+1] += ncols;
559: MatRestoreRow(user->Ybus,2*i,&ncols,NULL,NULL);
560: }
562: MatSeqAIJSetPreallocation(J,0,d_nnz);
563: PetscFree(d_nnz);
564: return(0);
565: }
567: /*
568: J = [-df_dx, -df_dy
569: dg_dx, dg_dy]
570: */
571: PetscErrorCode ResidualJacobian(SNES snes,Vec X,Mat J,Mat B,void *ctx)
572: {
573: PetscErrorCode ierr;
574: Userctx *user=(Userctx*)ctx;
575: Vec Xgen,Xnet;
576: PetscScalar *xgen,*xnet;
577: PetscInt i,idx=0;
578: PetscScalar Vr,Vi,Vm,Vm2;
579: PetscScalar Eqp,Edp,delta; /* Generator variables */
580: PetscScalar Efd; /* Exciter variables */
581: PetscScalar Id,Iq; /* Generator dq axis currents */
582: PetscScalar Vd,Vq;
583: PetscScalar val[10];
584: PetscInt row[2],col[10];
585: PetscInt net_start=user->neqs_gen;
586: PetscInt ncols;
587: const PetscInt *cols;
588: const PetscScalar *yvals;
589: PetscInt k;
590: PetscScalar Zdq_inv[4],det;
591: PetscScalar dVd_dVr,dVd_dVi,dVq_dVr,dVq_dVi,dVd_ddelta,dVq_ddelta;
592: PetscScalar dIGr_ddelta,dIGi_ddelta,dIGr_dId,dIGr_dIq,dIGi_dId,dIGi_dIq;
593: PetscScalar dSE_dEfd;
594: PetscScalar dVm_dVd,dVm_dVq,dVm_dVr,dVm_dVi;
595: PetscScalar PD,QD,Vm0,*v0,Vm4;
596: PetscScalar dPD_dVr,dPD_dVi,dQD_dVr,dQD_dVi;
597: PetscScalar dIDr_dVr,dIDr_dVi,dIDi_dVr,dIDi_dVi;
600: MatZeroEntries(B);
601: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
602: DMCompositeScatter(user->dmpgrid,X,Xgen,Xnet);
604: VecGetArray(Xgen,&xgen);
605: VecGetArray(Xnet,&xnet);
607: /* Generator subsystem */
608: for (i=0; i < ngen; i++) {
609: Eqp = xgen[idx];
610: Edp = xgen[idx+1];
611: delta = xgen[idx+2];
612: Id = xgen[idx+4];
613: Iq = xgen[idx+5];
614: Efd = xgen[idx+6];
616: /* fgen[idx] = (Eqp + (Xd[i] - Xdp[i])*Id - Efd)/Td0p[i]; */
617: row[0] = idx;
618: col[0] = idx; col[1] = idx+4; col[2] = idx+6;
619: val[0] = 1/ Td0p[i]; val[1] = (Xd[i] - Xdp[i])/ Td0p[i]; val[2] = -1/Td0p[i];
621: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
623: /* fgen[idx+1] = (Edp - (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
624: row[0] = idx + 1;
625: col[0] = idx + 1; col[1] = idx+5;
626: val[0] = 1/Tq0p[i]; val[1] = -(Xq[i] - Xqp[i])/Tq0p[i];
627: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
629: /* fgen[idx+2] = - w + w_s; */
630: row[0] = idx + 2;
631: col[0] = idx + 2; col[1] = idx + 3;
632: val[0] = 0; val[1] = -1;
633: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
635: /* fgen[idx+3] = (-TM[i] + Edp*Id + Eqp*Iq + (Xqp[i] - Xdp[i])*Id*Iq + D[i]*(w - w_s))/M[i]; */
636: row[0] = idx + 3;
637: col[0] = idx; col[1] = idx + 1; col[2] = idx + 3; col[3] = idx + 4; col[4] = idx + 5;
638: 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];
639: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
641: Vr = xnet[2*gbus[i]]; /* Real part of generator terminal voltage */
642: Vi = xnet[2*gbus[i]+1]; /* Imaginary part of the generator terminal voltage */
643: ri2dq(Vr,Vi,delta,&Vd,&Vq);
645: det = Rs[i]*Rs[i] + Xdp[i]*Xqp[i];
647: Zdq_inv[0] = Rs[i]/det;
648: Zdq_inv[1] = Xqp[i]/det;
649: Zdq_inv[2] = -Xdp[i]/det;
650: Zdq_inv[3] = Rs[i]/det;
652: dVd_dVr = PetscSinScalar(delta); dVd_dVi = -PetscCosScalar(delta);
653: dVq_dVr = PetscCosScalar(delta); dVq_dVi = PetscSinScalar(delta);
654: dVd_ddelta = Vr*PetscCosScalar(delta) + Vi*PetscSinScalar(delta);
655: dVq_ddelta = -Vr*PetscSinScalar(delta) + Vi*PetscCosScalar(delta);
657: /* fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
658: row[0] = idx+4;
659: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
660: val[0] = -Zdq_inv[1]; val[1] = -Zdq_inv[0]; val[2] = Zdq_inv[0]*dVd_ddelta + Zdq_inv[1]*dVq_ddelta;
661: col[3] = idx + 4; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
662: 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;
663: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
665: /* fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
666: row[0] = idx+5;
667: col[0] = idx; col[1] = idx+1; col[2] = idx + 2;
668: val[0] = -Zdq_inv[3]; val[1] = -Zdq_inv[2]; val[2] = Zdq_inv[2]*dVd_ddelta + Zdq_inv[3]*dVq_ddelta;
669: col[3] = idx + 5; col[4] = net_start+2*gbus[i]; col[5] = net_start + 2*gbus[i]+1;
670: 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;
671: MatSetValues(J,1,row,6,col,val,INSERT_VALUES);
673: dIGr_ddelta = Id*PetscCosScalar(delta) - Iq*PetscSinScalar(delta);
674: dIGi_ddelta = Id*PetscSinScalar(delta) + Iq*PetscCosScalar(delta);
675: dIGr_dId = PetscSinScalar(delta); dIGr_dIq = PetscCosScalar(delta);
676: dIGi_dId = -PetscCosScalar(delta); dIGi_dIq = PetscSinScalar(delta);
678: /* fnet[2*gbus[i]] -= IGi; */
679: row[0] = net_start + 2*gbus[i];
680: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
681: val[0] = -dIGi_ddelta; val[1] = -dIGi_dId; val[2] = -dIGi_dIq;
682: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
684: /* fnet[2*gbus[i]+1] -= IGr; */
685: row[0] = net_start + 2*gbus[i]+1;
686: col[0] = idx+2; col[1] = idx + 4; col[2] = idx + 5;
687: val[0] = -dIGr_ddelta; val[1] = -dIGr_dId; val[2] = -dIGr_dIq;
688: MatSetValues(J,1,row,3,col,val,INSERT_VALUES);
690: Vm = PetscSqrtScalar(Vd*Vd + Vq*Vq);
692: /* fgen[idx+6] = (KE[i]*Efd + SE - VR)/TE[i]; */
693: /* SE = k1[i]*PetscExpScalar(k2[i]*Efd); */
694: dSE_dEfd = k1[i]*k2[i]*PetscExpScalar(k2[i]*Efd);
696: row[0] = idx + 6;
697: col[0] = idx + 6; col[1] = idx + 8;
698: val[0] = (KE[i] + dSE_dEfd)/TE[i]; val[1] = -1/TE[i];
699: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
701: /* Exciter differential equations */
703: /* fgen[idx+7] = (RF - KF[i]*Efd/TF[i])/TF[i]; */
704: row[0] = idx + 7;
705: col[0] = idx + 6; col[1] = idx + 7;
706: val[0] = (-KF[i]/TF[i])/TF[i]; val[1] = 1/TF[i];
707: MatSetValues(J,1,row,2,col,val,INSERT_VALUES);
709: /* fgen[idx+8] = (VR - KA[i]*RF + KA[i]*KF[i]*Efd/TF[i] - KA[i]*(Vref[i] - Vm))/TA[i]; */
710: /* Vm = (Vd^2 + Vq^2)^0.5; */
711: dVm_dVd = Vd/Vm; dVm_dVq = Vq/Vm;
712: dVm_dVr = dVm_dVd*dVd_dVr + dVm_dVq*dVq_dVr;
713: dVm_dVi = dVm_dVd*dVd_dVi + dVm_dVq*dVq_dVi;
714: row[0] = idx + 8;
715: col[0] = idx + 6; col[1] = idx + 7; col[2] = idx + 8;
716: val[0] = (KA[i]*KF[i]/TF[i])/TA[i]; val[1] = -KA[i]/TA[i]; val[2] = 1/TA[i];
717: col[3] = net_start + 2*gbus[i]; col[4] = net_start + 2*gbus[i]+1;
718: val[3] = KA[i]*dVm_dVr/TA[i]; val[4] = KA[i]*dVm_dVi/TA[i];
719: MatSetValues(J,1,row,5,col,val,INSERT_VALUES);
720: idx = idx + 9;
721: }
724: for (i=0; i<nbus; i++) {
725: MatGetRow(user->Ybus,2*i,&ncols,&cols,&yvals);
726: row[0] = net_start + 2*i;
727: for (k=0; k<ncols; k++) {
728: col[k] = net_start + cols[k];
729: val[k] = yvals[k];
730: }
731: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
732: MatRestoreRow(user->Ybus,2*i,&ncols,&cols,&yvals);
734: MatGetRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
735: row[0] = net_start + 2*i+1;
736: for (k=0; k<ncols; k++) {
737: col[k] = net_start + cols[k];
738: val[k] = yvals[k];
739: }
740: MatSetValues(J,1,row,ncols,col,val,INSERT_VALUES);
741: MatRestoreRow(user->Ybus,2*i+1,&ncols,&cols,&yvals);
742: }
744: MatAssemblyBegin(J,MAT_FLUSH_ASSEMBLY);
745: MatAssemblyEnd(J,MAT_FLUSH_ASSEMBLY);
748: VecGetArray(user->V0,&v0);
749: for (i=0; i < nload; i++) {
750: Vr = xnet[2*lbus[i]]; /* Real part of load bus voltage */
751: Vi = xnet[2*lbus[i]+1]; /* Imaginary part of the load bus voltage */
752: Vm = PetscSqrtScalar(Vr*Vr + Vi*Vi); Vm2= Vm*Vm; Vm4 = Vm2*Vm2;
753: Vm0 = PetscSqrtScalar(v0[2*lbus[i]]*v0[2*lbus[i]] + v0[2*lbus[i]+1]*v0[2*lbus[i]+1]);
754: PD = QD = 0.0;
755: dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
756: for (k=0; k < ld_nsegsp[i]; k++) {
757: PD += ld_alphap[k]*PD0[i]*PetscPowScalar((Vm/Vm0),ld_betap[k]);
758: dPD_dVr += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vr*PetscPowScalar(Vm,(ld_betap[k]-2));
759: dPD_dVi += ld_alphap[k]*ld_betap[k]*PD0[i]*PetscPowScalar((1/Vm0),ld_betap[k])*Vi*PetscPowScalar(Vm,(ld_betap[k]-2));
760: }
761: for (k=0; k < ld_nsegsq[i]; k++) {
762: QD += ld_alphaq[k]*QD0[i]*PetscPowScalar((Vm/Vm0),ld_betaq[k]);
763: dQD_dVr += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vr*PetscPowScalar(Vm,(ld_betaq[k]-2));
764: dQD_dVi += ld_alphaq[k]*ld_betaq[k]*QD0[i]*PetscPowScalar((1/Vm0),ld_betaq[k])*Vi*PetscPowScalar(Vm,(ld_betaq[k]-2));
765: }
767: /* IDr = (PD*Vr + QD*Vi)/Vm2; */
768: /* IDi = (-QD*Vr + PD*Vi)/Vm2; */
770: dIDr_dVr = (dPD_dVr*Vr + dQD_dVr*Vi + PD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vr)/Vm4;
771: dIDr_dVi = (dPD_dVi*Vr + dQD_dVi*Vi + QD)/Vm2 - ((PD*Vr + QD*Vi)*2*Vi)/Vm4;
773: dIDi_dVr = (-dQD_dVr*Vr + dPD_dVr*Vi - QD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vr)/Vm4;
774: dIDi_dVi = (-dQD_dVi*Vr + dPD_dVi*Vi + PD)/Vm2 - ((-QD*Vr + PD*Vi)*2*Vi)/Vm4;
777: /* fnet[2*lbus[i]] += IDi; */
778: row[0] = net_start + 2*lbus[i];
779: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
780: val[0] = dIDi_dVr; val[1] = dIDi_dVi;
781: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
782: /* fnet[2*lbus[i]+1] += IDr; */
783: row[0] = net_start + 2*lbus[i]+1;
784: col[0] = net_start + 2*lbus[i]; col[1] = net_start + 2*lbus[i]+1;
785: val[0] = dIDr_dVr; val[1] = dIDr_dVi;
786: MatSetValues(J,1,row,2,col,val,ADD_VALUES);
787: }
788: VecRestoreArray(user->V0,&v0);
790: VecRestoreArray(Xgen,&xgen);
791: VecRestoreArray(Xnet,&xnet);
793: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
795: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
796: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
797: return(0);
798: }
800: /*
801: J = [I, 0
802: dg_dx, dg_dy]
803: */
804: PetscErrorCode AlgJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
805: {
807: Userctx *user=(Userctx*)ctx;
810: ResidualJacobian(snes,X,A,B,ctx);
811: MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
812: MatZeroRowsIS(A,user->is_diff,1.0,NULL,NULL);
813: return(0);
814: }
816: /*
817: J = [a*I-df_dx, -df_dy
818: dg_dx, dg_dy]
819: */
821: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,Userctx *user)
822: {
824: SNES snes;
825: PetscScalar atmp = (PetscScalar) a;
826: PetscInt i,row;
829: user->t = t;
831: TSGetSNES(ts,&snes);
832: ResidualJacobian(snes,X,A,B,user);
833: for (i=0;i < ngen;i++) {
834: row = 9*i;
835: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
836: row = 9*i+1;
837: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
838: row = 9*i+2;
839: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
840: row = 9*i+3;
841: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
842: row = 9*i+6;
843: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
844: row = 9*i+7;
845: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
846: row = 9*i+8;
847: MatSetValues(A,1,&row,1,&row,&atmp,ADD_VALUES);
848: }
849: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
850: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
851: return(0);
852: }
854: /* Matrix JacobianP is constant so that it only needs to be evaluated once */
855: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A, void *ctx0)
856: {
858: PetscScalar a;
859: PetscInt row,col;
860: Userctx *ctx=(Userctx*)ctx0;
864: if (ctx->jacp_flg) {
865: MatZeroEntries(A);
867: for (col=0;col<3;col++) {
868: a = 1.0/M[col];
869: row = 9*col+3;
870: MatSetValues(A,1,&row,1,&col,&a,INSERT_VALUES);
871: }
873: ctx->jacp_flg = PETSC_FALSE;
875: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
876: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
877: }
878: return(0);
879: }
881: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,Userctx *user)
882: {
884: PetscScalar *u,*r;
885: PetscInt idx;
886: Vec Xgen,Xnet;
887: PetscScalar *xgen;
888: PetscInt i;
891: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
892: DMCompositeScatter(user->dmpgrid,U,Xgen,Xnet);
894: VecGetArray(Xgen,&xgen);
896: VecGetArray(U,&u);
897: VecGetArray(R,&r);
898: r[0] = 0.;
899: idx = 0;
900: for (i=0;i<ngen;i++) {
901: 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);
902: idx += 9;
903: }
904: VecRestoreArray(R,&r);
905: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
906: return(0);
907: }
909: static PetscErrorCode DRDUJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDU,Mat B,Userctx *user)
910: {
912: Vec Xgen,Xnet,Dgen,Dnet;
913: PetscScalar *xgen,*dgen;
914: PetscInt i;
915: PetscInt idx;
916: Vec drdu_col;
917: PetscScalar *xarr;
920: VecDuplicate(U,&drdu_col);
921: MatDenseGetColumn(DRDU,0,&xarr);
922: VecPlaceArray(drdu_col,xarr);
923: DMCompositeGetLocalVectors(user->dmpgrid,&Xgen,&Xnet);
924: DMCompositeGetLocalVectors(user->dmpgrid,&Dgen,&Dnet);
925: DMCompositeScatter(user->dmpgrid,U,Xgen,Xnet);
926: DMCompositeScatter(user->dmpgrid,drdu_col,Dgen,Dnet);
928: VecGetArray(Xgen,&xgen);
929: VecGetArray(Dgen,&dgen);
931: idx = 0;
932: for (i=0;i<ngen;i++) {
933: dgen[idx+3] = 0.;
934: 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);
935: 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);
936: idx += 9;
937: }
939: VecRestoreArray(Dgen,&dgen);
940: VecRestoreArray(Xgen,&xgen);
941: DMCompositeGather(user->dmpgrid,INSERT_VALUES,drdu_col,Dgen,Dnet);
942: DMCompositeRestoreLocalVectors(user->dmpgrid,&Dgen,&Dnet);
943: DMCompositeRestoreLocalVectors(user->dmpgrid,&Xgen,&Xnet);
944: VecResetArray(drdu_col);
945: MatDenseRestoreColumn(DRDU,&xarr);
946: VecDestroy(&drdu_col);
947: return(0);
948: }
950: static PetscErrorCode DRDPJacobianTranspose(TS ts,PetscReal t,Vec U,Mat drdp,Userctx *user)
951: {
953: return(0);
954: }
956: PetscErrorCode ComputeSensiP(Vec lambda,Vec mu,Vec *DICDP,Userctx *user)
957: {
959: PetscScalar *x,*y,sensip;
960: PetscInt i;
963: VecGetArray(lambda,&x);
964: VecGetArray(mu,&y);
966: for (i=0;i<3;i++) {
967: VecDot(lambda,DICDP[i],&sensip);
968: sensip = sensip+y[i];
969: /* PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt %D th parameter: %g \n",i,(double)sensip); */
970: y[i] = sensip;
971: }
972: VecRestoreArray(mu,&y);
973: return(0);
974: }
976: int main(int argc,char **argv)
977: {
978: Userctx user;
979: Vec p;
980: PetscScalar *x_ptr;
981: PetscErrorCode ierr;
982: PetscMPIInt size;
983: PetscInt i;
984: PetscViewer Xview,Ybusview;
985: PetscInt *idx2;
986: Tao tao;
987: KSP ksp;
988: PC pc;
989: Vec lowerb,upperb;
991: PetscInitialize(&argc,&argv,"petscoptions",help);if (ierr) return ierr;
992: MPI_Comm_size(PETSC_COMM_WORLD,&size);
993: if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
995: user.jacp_flg = PETSC_TRUE;
996: user.neqs_gen = 9*ngen; /* # eqs. for generator subsystem */
997: user.neqs_net = 2*nbus; /* # eqs. for network subsystem */
998: user.neqs_pgrid = user.neqs_gen + user.neqs_net;
1000: /* Create indices for differential and algebraic equations */
1001: PetscMalloc1(7*ngen,&idx2);
1002: for (i=0; i<ngen; i++) {
1003: 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;
1004: idx2[7*i+4] = 9*i+6; idx2[7*i+5] = 9*i+7; idx2[7*i+6] = 9*i+8;
1005: }
1006: ISCreateGeneral(PETSC_COMM_WORLD,7*ngen,idx2,PETSC_COPY_VALUES,&user.is_diff);
1007: ISComplement(user.is_diff,0,user.neqs_pgrid,&user.is_alg);
1008: PetscFree(idx2);
1010: /* Set run time options */
1011: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Transient stability fault options","");
1012: {
1013: user.tfaulton = 1.0;
1014: user.tfaultoff = 1.2;
1015: user.Rfault = 0.0001;
1016: user.faultbus = 8;
1017: PetscOptionsReal("-tfaulton","","",user.tfaulton,&user.tfaulton,NULL);
1018: PetscOptionsReal("-tfaultoff","","",user.tfaultoff,&user.tfaultoff,NULL);
1019: PetscOptionsInt("-faultbus","","",user.faultbus,&user.faultbus,NULL);
1020: user.t0 = 0.0;
1021: user.tmax = 1.3;
1022: PetscOptionsReal("-t0","","",user.t0,&user.t0,NULL);
1023: PetscOptionsReal("-tmax","","",user.tmax,&user.tmax,NULL);
1024: user.freq_u = 61.0;
1025: user.freq_l = 59.0;
1026: user.pow = 2;
1027: PetscOptionsReal("-frequ","","",user.freq_u,&user.freq_u,NULL);
1028: PetscOptionsReal("-freql","","",user.freq_l,&user.freq_l,NULL);
1029: PetscOptionsInt("-pow","","",user.pow,&user.pow,NULL);
1031: }
1032: PetscOptionsEnd();
1034: /* Create DMs for generator and network subsystems */
1035: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_gen,1,1,NULL,&user.dmgen);
1036: DMSetOptionsPrefix(user.dmgen,"dmgen_");
1037: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,user.neqs_net,1,1,NULL,&user.dmnet);
1038: DMSetOptionsPrefix(user.dmnet,"dmnet_");
1039: DMSetFromOptions(user.dmnet);
1040: DMSetUp(user.dmnet);
1041: /* Create a composite DM packer and add the two DMs */
1042: DMCompositeCreate(PETSC_COMM_WORLD,&user.dmpgrid);
1043: DMSetOptionsPrefix(user.dmpgrid,"pgrid_");
1044: DMSetFromOptions(user.dmgen);
1045: DMSetUp(user.dmgen);
1046: DMCompositeAddDM(user.dmpgrid,user.dmgen);
1047: DMCompositeAddDM(user.dmpgrid,user.dmnet);
1049: /* Read initial voltage vector and Ybus */
1050: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);
1051: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);
1053: VecCreate(PETSC_COMM_WORLD,&user.V0);
1054: VecSetSizes(user.V0,PETSC_DECIDE,user.neqs_net);
1055: VecLoad(user.V0,Xview);
1057: MatCreate(PETSC_COMM_WORLD,&user.Ybus);
1058: MatSetSizes(user.Ybus,PETSC_DECIDE,PETSC_DECIDE,user.neqs_net,user.neqs_net);
1059: MatSetType(user.Ybus,MATBAIJ);
1060: /* MatSetBlockSize(ctx->Ybus,2); */
1061: MatLoad(user.Ybus,Ybusview);
1063: PetscViewerDestroy(&Xview);
1064: PetscViewerDestroy(&Ybusview);
1066: /* Allocate space for Jacobians */
1067: MatCreate(PETSC_COMM_WORLD,&user.J);
1068: MatSetSizes(user.J,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,user.neqs_pgrid);
1069: MatSetFromOptions(user.J);
1070: PreallocateJacobian(user.J,&user);
1072: MatCreate(PETSC_COMM_WORLD,&user.Jacp);
1073: MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,3);
1074: MatSetFromOptions(user.Jacp);
1075: MatSetUp(user.Jacp);
1076: MatZeroEntries(user.Jacp); /* initialize to zeros */
1078: MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,3,1,NULL,&user.DRDP);
1079: MatSetUp(user.DRDP);
1080: MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,user.neqs_pgrid,1,NULL,&user.DRDU);
1081: MatSetUp(user.DRDU);
1083: /* Create TAO solver and set desired solution method */
1084: TaoCreate(PETSC_COMM_WORLD,&tao);
1085: TaoSetType(tao,TAOBLMVM);
1086: /*
1087: Optimization starts
1088: */
1089: /* Set initial solution guess */
1090: VecCreateSeq(PETSC_COMM_WORLD,3,&p);
1091: VecGetArray(p,&x_ptr);
1092: x_ptr[0] = PG[0]; x_ptr[1] = PG[1]; x_ptr[2] = PG[2];
1093: VecRestoreArray(p,&x_ptr);
1095: TaoSetInitialVector(tao,p);
1096: /* Set routine for function and gradient evaluation */
1097: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);
1099: /* Set bounds for the optimization */
1100: VecDuplicate(p,&lowerb);
1101: VecDuplicate(p,&upperb);
1102: VecGetArray(lowerb,&x_ptr);
1103: x_ptr[0] = 0.5; x_ptr[1] = 0.5; x_ptr[2] = 0.5;
1104: VecRestoreArray(lowerb,&x_ptr);
1105: VecGetArray(upperb,&x_ptr);
1106: x_ptr[0] = 2.0; x_ptr[1] = 2.0; x_ptr[2] = 2.0;
1107: VecRestoreArray(upperb,&x_ptr);
1108: TaoSetVariableBounds(tao,lowerb,upperb);
1110: /* Check for any TAO command line options */
1111: TaoSetFromOptions(tao);
1112: TaoGetKSP(tao,&ksp);
1113: if (ksp) {
1114: KSPGetPC(ksp,&pc);
1115: PCSetType(pc,PCNONE);
1116: }
1118: /* SOLVE THE APPLICATION */
1119: TaoSolve(tao);
1121: VecView(p,PETSC_VIEWER_STDOUT_WORLD);
1122: /* Free TAO data structures */
1123: TaoDestroy(&tao);
1125: DMDestroy(&user.dmgen);
1126: DMDestroy(&user.dmnet);
1127: DMDestroy(&user.dmpgrid);
1128: ISDestroy(&user.is_diff);
1129: ISDestroy(&user.is_alg);
1131: MatDestroy(&user.J);
1132: MatDestroy(&user.Jacp);
1133: MatDestroy(&user.Ybus);
1134: /* MatDestroy(&user.Sol); */
1135: VecDestroy(&user.V0);
1136: VecDestroy(&p);
1137: VecDestroy(&lowerb);
1138: VecDestroy(&upperb);
1139: MatDestroy(&user.DRDU);
1140: MatDestroy(&user.DRDP);
1141: PetscFinalize();
1142: return ierr;
1143: }
1145: /* ------------------------------------------------------------------ */
1146: /*
1147: FormFunction - Evaluates the function and corresponding gradient.
1149: Input Parameters:
1150: tao - the Tao context
1151: X - the input vector
1152: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
1154: Output Parameters:
1155: f - the newly evaluated function
1156: G - the newly evaluated gradient
1157: */
1158: PetscErrorCode FormFunctionGradient(Tao tao,Vec P,PetscReal *f,Vec G,void *ctx0)
1159: {
1160: TS ts,quadts;
1161: SNES snes_alg;
1163: Userctx *ctx = (Userctx*)ctx0;
1164: Vec X;
1165: PetscInt i;
1166: /* sensitivity context */
1167: PetscScalar *x_ptr;
1168: Vec lambda[1],q;
1169: Vec mu[1];
1170: PetscInt steps1,steps2,steps3;
1171: Vec DICDP[3];
1172: Vec F_alg;
1173: PetscInt row_loc,col_loc;
1174: PetscScalar val;
1175: Vec Xdot;
1178: VecGetArrayRead(P,(const PetscScalar**)&x_ptr);
1179: PG[0] = x_ptr[0];
1180: PG[1] = x_ptr[1];
1181: PG[2] = x_ptr[2];
1182: VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);
1184: ctx->stepnum = 0;
1186: DMCreateGlobalVector(ctx->dmpgrid,&X);
1188: /* Create matrix to save solutions at each time step */
1189: /* MatCreateSeqDense(PETSC_COMM_SELF,ctx->neqs_pgrid+1,1002,NULL,&ctx->Sol); */
1190: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1191: Create timestepping solver context
1192: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1193: TSCreate(PETSC_COMM_WORLD,&ts);
1194: TSSetProblemType(ts,TS_NONLINEAR);
1195: TSSetType(ts,TSCN);
1196: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,ctx);
1197: TSSetIJacobian(ts,ctx->J,ctx->J,(TSIJacobian)IJacobian,ctx);
1198: TSSetApplicationContext(ts,ctx);
1199: /* Set RHS JacobianP */
1200: TSSetRHSJacobianP(ts,ctx->Jacp,RHSJacobianP,ctx);
1202: TSCreateQuadratureTS(ts,PETSC_FALSE,&quadts);
1203: TSSetRHSFunction(quadts,NULL,(TSRHSFunction)CostIntegrand,ctx);
1204: TSSetRHSJacobian(quadts,ctx->DRDU,ctx->DRDU,(TSRHSJacobian)DRDUJacobianTranspose,ctx);
1205: TSSetRHSJacobianP(quadts,ctx->DRDP,(TSRHSJacobianP)DRDPJacobianTranspose,ctx);
1207: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1208: Set initial conditions
1209: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1210: SetInitialGuess(X,ctx);
1212: /* Approximate DICDP with finite difference, we want to zero out network variables */
1213: for (i=0;i<3;i++) {
1214: VecDuplicate(X,&DICDP[i]);
1215: }
1216: DICDPFiniteDifference(X,DICDP,ctx);
1218: VecDuplicate(X,&F_alg);
1219: SNESCreate(PETSC_COMM_WORLD,&snes_alg);
1220: SNESSetFunction(snes_alg,F_alg,AlgFunction,ctx);
1221: MatZeroEntries(ctx->J);
1222: SNESSetJacobian(snes_alg,ctx->J,ctx->J,AlgJacobian,ctx);
1223: SNESSetOptionsPrefix(snes_alg,"alg_");
1224: SNESSetFromOptions(snes_alg);
1225: ctx->alg_flg = PETSC_TRUE;
1226: /* Solve the algebraic equations */
1227: SNESSolve(snes_alg,NULL,X);
1229: /* Just to set up the Jacobian structure */
1230: VecDuplicate(X,&Xdot);
1231: IJacobian(ts,0.0,X,Xdot,0.0,ctx->J,ctx->J,ctx);
1232: VecDestroy(&Xdot);
1234: ctx->stepnum++;
1236: /*
1237: Save trajectory of solution so that TSAdjointSolve() may be used
1238: */
1239: TSSetSaveTrajectory(ts);
1241: TSSetTimeStep(ts,0.01);
1242: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
1243: TSSetFromOptions(ts);
1244: /* TSSetPostStep(ts,SaveSolution); */
1247: /* Prefault period */
1248: ctx->alg_flg = PETSC_FALSE;
1249: TSSetTime(ts,0.0);
1250: TSSetMaxTime(ts,ctx->tfaulton);
1251: TSSolve(ts,X);
1252: TSGetStepNumber(ts,&steps1);
1254: /* Create the nonlinear solver for solving the algebraic system */
1255: /* Note that although the algebraic system needs to be solved only for
1256: Idq and V, we reuse the entire system including xgen. The xgen
1257: variables are held constant by setting their residuals to 0 and
1258: putting a 1 on the Jacobian diagonal for xgen rows
1259: */
1260: MatZeroEntries(ctx->J);
1262: /* Apply disturbance - resistive fault at ctx->faultbus */
1263: /* This is done by adding shunt conductance to the diagonal location
1264: in the Ybus matrix */
1265: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
1266: val = 1/ctx->Rfault;
1267: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1268: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
1269: val = 1/ctx->Rfault;
1270: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1272: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1273: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1275: ctx->alg_flg = PETSC_TRUE;
1276: /* Solve the algebraic equations */
1277: SNESSolve(snes_alg,NULL,X);
1279: ctx->stepnum++;
1281: /* Disturbance period */
1282: ctx->alg_flg = PETSC_FALSE;
1283: TSSetTime(ts,ctx->tfaulton);
1284: TSSetMaxTime(ts,ctx->tfaultoff);
1285: TSSolve(ts,X);
1286: TSGetStepNumber(ts,&steps2);
1287: steps2 -= steps1;
1289: /* Remove the fault */
1290: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1;
1291: val = -1/ctx->Rfault;
1292: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1293: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus;
1294: val = -1/ctx->Rfault;
1295: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1297: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1298: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1300: MatZeroEntries(ctx->J);
1302: ctx->alg_flg = PETSC_TRUE;
1304: /* Solve the algebraic equations */
1305: SNESSolve(snes_alg,NULL,X);
1307: ctx->stepnum++;
1309: /* Post-disturbance period */
1310: ctx->alg_flg = PETSC_TRUE;
1311: TSSetTime(ts,ctx->tfaultoff);
1312: TSSetMaxTime(ts,ctx->tmax);
1313: TSSolve(ts,X);
1314: TSGetStepNumber(ts,&steps3);
1315: steps3 -= steps2;
1316: steps3 -= steps1;
1318: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1319: Adjoint model starts here
1320: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1321: TSSetPostStep(ts,NULL);
1322: MatCreateVecs(ctx->J,&lambda[0],NULL);
1323: /* Set initial conditions for the adjoint integration */
1324: VecZeroEntries(lambda[0]);
1326: MatCreateVecs(ctx->Jacp,&mu[0],NULL);
1327: VecZeroEntries(mu[0]);
1328: TSSetCostGradients(ts,1,lambda,mu);
1330: TSAdjointSetSteps(ts,steps3);
1331: TSAdjointSolve(ts);
1333: MatZeroEntries(ctx->J);
1334: /* Applying disturbance - resistive fault at ctx->faultbus */
1335: /* This is done by deducting shunt conductance to the diagonal location
1336: in the Ybus matrix */
1337: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
1338: val = 1./ctx->Rfault;
1339: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1340: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
1341: val = 1./ctx->Rfault;
1342: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1344: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1345: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1348: /* Set number of steps for the adjoint integration */
1349: TSAdjointSetSteps(ts,steps2);
1350: TSAdjointSolve(ts);
1352: MatZeroEntries(ctx->J);
1353: /* remove the fault */
1354: row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
1355: val = -1./ctx->Rfault;
1356: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1357: row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
1358: val = -1./ctx->Rfault;
1359: MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);
1361: MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1362: MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);
1364: /* Set number of steps for the adjoint integration */
1365: TSAdjointSetSteps(ts,steps1);
1366: TSAdjointSolve(ts);
1368: ComputeSensiP(lambda[0],mu[0],DICDP,ctx);
1369: VecCopy(mu[0],G);
1371: TSGetQuadratureTS(ts,NULL,&quadts);
1372: TSGetSolution(quadts,&q);
1373: VecGetArray(q,&x_ptr);
1374: *f = x_ptr[0];
1375: x_ptr[0] = 0;
1376: VecRestoreArray(q,&x_ptr);
1378: VecDestroy(&lambda[0]);
1379: VecDestroy(&mu[0]);
1381: SNESDestroy(&snes_alg);
1382: VecDestroy(&F_alg);
1383: VecDestroy(&X);
1384: TSDestroy(&ts);
1385: for (i=0;i<3;i++) {
1386: VecDestroy(&DICDP[i]);
1387: }
1388: return(0);
1389: }
1391: /*TEST
1393: build:
1394: requires: double !complex !define(PETSC_USE_64BIT_INDICES)
1396: test:
1397: args: -viewer_binary_skip_info -tao_monitor -tao_gttol .2
1398: localrunfiles: petscoptions X.bin Ybus.bin
1400: TEST*/