Actual source code: ex9bus.c
1: static char help[] = "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: The equations for the stability analysis are described by the DAE
11: \dot{x} = f(x,y,t)
12: 0 = g(x,y,t)
14: where the generators are described by differential equations, while the algebraic
15: constraints define the network equations.
17: The generators are modeled with a 4th order differential equation describing the electrical
18: and mechanical dynamics. Each generator also has an exciter system modeled by 3rd order
19: diff. eqns. describing the exciter, voltage regulator, and the feedback stabilizer
20: mechanism.
22: The network equations are described by nodal current balance equations.
23: I(x,y) - Y*V = 0
25: where:
26: I(x,y) is the current injected from generators and loads.
27: Y is the admittance matrix, and
28: V is the voltage vector
29: */
31: /*
32: Include "petscts.h" so that we can use the TS ODE integrators. Note that this
33: file automatically includes:
34: petscsys.h - base PETSc routines
35: petscis.h - index sets
36: petscvec.h - vectors
37: petscmat.h - matrices
38: petscpc.h - preconditioners
39: petscksp.h - linear solvers
40: */
42: #include <petscts.h>
43: #include <petscdm.h>
44: #include <petscdmda.h>
45: #include <petscdmcomposite.h>
47: #define freq 60
48: #define w_s (2 * PETSC_PI * freq)
50: /* Sizes and indices */
51: const PetscInt nbus = 9; /* Number of network buses */
52: const PetscInt ngen = 3; /* Number of generators */
53: const PetscInt nload = 3; /* Number of loads */
54: const PetscInt gbus[3] = {0, 1, 2}; /* Buses at which generators are incident */
55: const PetscInt lbus[3] = {4, 5, 7}; /* Buses at which loads are incident */
57: /* Generator real and reactive powers (found via loadflow) */
58: const PetscScalar PG[3] = {0.716786142395021, 1.630000000000000, 0.850000000000000};
59: const PetscScalar QG[3] = {0.270702180178785, 0.066120127797275, -0.108402221791588};
60: /* Generator constants */
61: const PetscScalar H[3] = {23.64, 6.4, 3.01}; /* Inertia constant */
62: const PetscScalar Rs[3] = {0.0, 0.0, 0.0}; /* Stator Resistance */
63: const PetscScalar Xd[3] = {0.146, 0.8958, 1.3125}; /* d-axis reactance */
64: const PetscScalar Xdp[3] = {0.0608, 0.1198, 0.1813}; /* d-axis transient reactance */
65: const PetscScalar Xq[3] = {0.4360, 0.8645, 1.2578}; /* q-axis reactance Xq(1) set to 0.4360, value given in text 0.0969 */
66: const PetscScalar Xqp[3] = {0.0969, 0.1969, 0.25}; /* q-axis transient reactance */
67: const PetscScalar Td0p[3] = {8.96, 6.0, 5.89}; /* d-axis open circuit time constant */
68: const PetscScalar Tq0p[3] = {0.31, 0.535, 0.6}; /* q-axis open circuit time constant */
69: PetscScalar M[3]; /* M = 2*H/w_s */
70: PetscScalar D[3]; /* D = 0.1*M */
72: PetscScalar TM[3]; /* Mechanical Torque */
73: /* Exciter system constants */
74: const PetscScalar KA[3] = {20.0, 20.0, 20.0}; /* Voltage regulartor gain constant */
75: const PetscScalar TA[3] = {0.2, 0.2, 0.2}; /* Voltage regulator time constant */
76: const PetscScalar KE[3] = {1.0, 1.0, 1.0}; /* Exciter gain constant */
77: const PetscScalar TE[3] = {0.314, 0.314, 0.314}; /* Exciter time constant */
78: const PetscScalar KF[3] = {0.063, 0.063, 0.063}; /* Feedback stabilizer gain constant */
79: const PetscScalar TF[3] = {0.35, 0.35, 0.35}; /* Feedback stabilizer time constant */
80: const PetscScalar k1[3] = {0.0039, 0.0039, 0.0039};
81: const PetscScalar k2[3] = {1.555, 1.555, 1.555}; /* k1 and k2 for calculating the saturation function SE = k1*exp(k2*Efd) */
82: const PetscScalar VRMIN[3] = {-4.0, -4.0, -4.0};
83: const PetscScalar VRMAX[3] = {7.0, 7.0, 7.0};
84: PetscInt VRatmin[3];
85: PetscInt VRatmax[3];
87: PetscScalar Vref[3];
88: /* Load constants
89: We use a composite load model that describes the load and reactive powers at each time instant as follows
90: P(t) = \sum\limits_{i=0}^ld_nsegsp \ld_alphap_i*P_D0(\frac{V_m(t)}{V_m0})^\ld_betap_i
91: Q(t) = \sum\limits_{i=0}^ld_nsegsq \ld_alphaq_i*Q_D0(\frac{V_m(t)}{V_m0})^\ld_betaq_i
92: where
93: ld_nsegsp,ld_nsegsq - Number of individual load models for real and reactive power loads
94: ld_alphap,ld_alphap - Percentage contribution (weights) or loads
95: P_D0 - Real power load
96: Q_D0 - Reactive power load
97: V_m(t) - Voltage magnitude at time t
98: V_m0 - Voltage magnitude at t = 0
99: ld_betap, ld_betaq - exponents describing the load model for real and reactive part
101: Note: All loads have the same characteristic currently.
102: */
103: const PetscScalar PD0[3] = {1.25, 0.9, 1.0};
104: const PetscScalar QD0[3] = {0.5, 0.3, 0.35};
105: const PetscInt ld_nsegsp[3] = {3, 3, 3};
106: const PetscScalar ld_alphap[3] = {1.0, 0.0, 0.0};
107: const PetscScalar ld_betap[3] = {2.0, 1.0, 0.0};
108: const PetscInt ld_nsegsq[3] = {3, 3, 3};
109: const PetscScalar ld_alphaq[3] = {1.0, 0.0, 0.0};
110: const PetscScalar ld_betaq[3] = {2.0, 1.0, 0.0};
112: typedef struct {
113: DM dmgen, dmnet; /* DMs to manage generator and network subsystem */
114: DM dmpgrid; /* Composite DM to manage the entire power grid */
115: Mat Ybus; /* Network admittance matrix */
116: Vec V0; /* Initial voltage vector (Power flow solution) */
117: PetscReal tfaulton, tfaultoff; /* Fault on and off times */
118: PetscInt faultbus; /* Fault bus */
119: PetscScalar Rfault;
120: PetscReal t0, tmax;
121: PetscInt neqs_gen, neqs_net, neqs_pgrid;
122: Mat Sol; /* Matrix to save solution at each time step */
123: PetscInt stepnum;
124: PetscReal t;
125: SNES snes_alg;
126: IS is_diff; /* indices for differential equations */
127: IS is_alg; /* indices for algebraic equations */
128: PetscBool setisdiff; /* TS computes truncation error based only on the differential variables */
129: PetscBool semiexplicit; /* If the flag is set then a semi-explicit method is used using TSRK */
130: } Userctx;
132: /*
133: The first two events are for fault on and off, respectively. The following events are
134: to check the min/max limits on the state variable VR. A non windup limiter is used for
135: the VR limits.
136: */
137: PetscErrorCode EventFunction(TS ts, PetscReal t, Vec X, PetscReal *fvalue, PetscCtx ctx)
138: {
139: Userctx *user = (Userctx *)ctx;
140: Vec Xgen, Xnet;
141: PetscInt i, idx = 0;
142: const PetscScalar *xgen, *xnet;
143: PetscScalar Efd, RF, VR, Vr, Vi, Vm;
145: PetscFunctionBegin;
146: PetscCall(DMCompositeGetLocalVectors(user->dmpgrid, &Xgen, &Xnet));
147: PetscCall(DMCompositeScatter(user->dmpgrid, X, Xgen, Xnet));
149: PetscCall(VecGetArrayRead(Xgen, &xgen));
150: PetscCall(VecGetArrayRead(Xnet, &xnet));
152: /* Event for fault-on time */
153: fvalue[0] = t - user->tfaulton;
154: /* Event for fault-off time */
155: fvalue[1] = t - user->tfaultoff;
157: for (i = 0; i < ngen; i++) {
158: Efd = xgen[idx + 6];
159: RF = xgen[idx + 7];
160: VR = xgen[idx + 8];
162: Vr = xnet[2 * gbus[i]]; /* Real part of generator terminal voltage */
163: Vi = xnet[2 * gbus[i] + 1]; /* Imaginary part of the generator terminal voltage */
164: Vm = PetscSqrtScalar(Vr * Vr + Vi * Vi);
166: if (!VRatmax[i]) {
167: fvalue[2 + 2 * i] = PetscRealPart(VRMAX[i] - VR);
168: } else {
169: fvalue[2 + 2 * i] = PetscRealPart((VR - KA[i] * RF + KA[i] * KF[i] * Efd / TF[i] - KA[i] * (Vref[i] - Vm)) / TA[i]);
170: }
171: if (!VRatmin[i]) {
172: fvalue[2 + 2 * i + 1] = PetscRealPart(VRMIN[i] - VR);
173: } else {
174: fvalue[2 + 2 * i + 1] = PetscRealPart((VR - KA[i] * RF + KA[i] * KF[i] * Efd / TF[i] - KA[i] * (Vref[i] - Vm)) / TA[i]);
175: }
176: idx = idx + 9;
177: }
178: PetscCall(VecRestoreArrayRead(Xgen, &xgen));
179: PetscCall(VecRestoreArrayRead(Xnet, &xnet));
181: PetscCall(DMCompositeRestoreLocalVectors(user->dmpgrid, &Xgen, &Xnet));
182: PetscFunctionReturn(PETSC_SUCCESS);
183: }
185: PetscErrorCode PostEventFunction(TS ts, PetscInt nevents, PetscInt event_list[], PetscReal t, Vec X, PetscBool forwardsolve, PetscCtx ctx)
186: {
187: Userctx *user = (Userctx *)ctx;
188: Vec Xgen, Xnet;
189: PetscScalar *xgen, *xnet;
190: PetscInt row_loc, col_loc;
191: PetscScalar val;
192: PetscInt i, idx = 0, event_num;
193: PetscScalar fvalue;
194: PetscScalar Efd, RF, VR;
195: PetscScalar Vr, Vi, Vm;
197: PetscFunctionBegin;
198: PetscCall(DMCompositeGetLocalVectors(user->dmpgrid, &Xgen, &Xnet));
199: PetscCall(DMCompositeScatter(user->dmpgrid, X, Xgen, Xnet));
201: PetscCall(VecGetArray(Xgen, &xgen));
202: PetscCall(VecGetArray(Xnet, &xnet));
204: for (i = 0; i < nevents; i++) {
205: if (event_list[i] == 0) {
206: /* Apply disturbance - resistive fault at user->faultbus */
207: /* This is done by adding shunt conductance to the diagonal location
208: in the Ybus matrix */
209: row_loc = 2 * user->faultbus;
210: col_loc = 2 * user->faultbus + 1; /* Location for G */
211: val = 1 / user->Rfault;
212: PetscCall(MatSetValues(user->Ybus, 1, &row_loc, 1, &col_loc, &val, ADD_VALUES));
213: row_loc = 2 * user->faultbus + 1;
214: col_loc = 2 * user->faultbus; /* Location for G */
215: val = 1 / user->Rfault;
216: PetscCall(MatSetValues(user->Ybus, 1, &row_loc, 1, &col_loc, &val, ADD_VALUES));
218: PetscCall(MatAssemblyBegin(user->Ybus, MAT_FINAL_ASSEMBLY));
219: PetscCall(MatAssemblyEnd(user->Ybus, MAT_FINAL_ASSEMBLY));
221: /* Solve the algebraic equations */
222: PetscCall(SNESSolve(user->snes_alg, NULL, X));
223: } else if (event_list[i] == 1) {
224: /* Remove the fault */
225: row_loc = 2 * user->faultbus;
226: col_loc = 2 * user->faultbus + 1;
227: val = -1 / user->Rfault;
228: PetscCall(MatSetValues(user->Ybus, 1, &row_loc, 1, &col_loc, &val, ADD_VALUES));
229: row_loc = 2 * user->faultbus + 1;
230: col_loc = 2 * user->faultbus;
231: val = -1 / user->Rfault;
232: PetscCall(MatSetValues(user->Ybus, 1, &row_loc, 1, &col_loc, &val, ADD_VALUES));
234: PetscCall(MatAssemblyBegin(user->Ybus, MAT_FINAL_ASSEMBLY));
235: PetscCall(MatAssemblyEnd(user->Ybus, MAT_FINAL_ASSEMBLY));
237: /* Solve the algebraic equations */
238: PetscCall(SNESSolve(user->snes_alg, NULL, X));
240: /* Check the VR derivatives and reset flags if needed */
241: for (i = 0; i < ngen; i++) {
242: Efd = xgen[idx + 6];
243: RF = xgen[idx + 7];
244: VR = xgen[idx + 8];
246: Vr = xnet[2 * gbus[i]]; /* Real part of generator terminal voltage */
247: Vi = xnet[2 * gbus[i] + 1]; /* Imaginary part of the generator terminal voltage */
248: Vm = PetscSqrtScalar(Vr * Vr + Vi * Vi);
250: if (VRatmax[i]) {
251: fvalue = (VR - KA[i] * RF + KA[i] * KF[i] * Efd / TF[i] - KA[i] * (Vref[i] - Vm)) / TA[i];
252: if (fvalue < 0) {
253: VRatmax[i] = 0;
254: PetscCall(PetscPrintf(PETSC_COMM_SELF, "VR[%" PetscInt_FMT "]: dVR_dt went negative on fault clearing at time %g\n", i, (double)t));
255: }
256: }
257: if (VRatmin[i]) {
258: fvalue = (VR - KA[i] * RF + KA[i] * KF[i] * Efd / TF[i] - KA[i] * (Vref[i] - Vm)) / TA[i];
260: if (fvalue > 0) {
261: VRatmin[i] = 0;
262: PetscCall(PetscPrintf(PETSC_COMM_SELF, "VR[%" PetscInt_FMT "]: dVR_dt went positive on fault clearing at time %g\n", i, (double)t));
263: }
264: }
265: idx = idx + 9;
266: }
267: } else {
268: idx = (event_list[i] - 2) / 2;
269: event_num = (event_list[i] - 2) % 2;
270: if (event_num == 0) { /* Max VR */
271: if (!VRatmax[idx]) {
272: VRatmax[idx] = 1;
273: PetscCall(PetscPrintf(PETSC_COMM_SELF, "VR[%" PetscInt_FMT "]: hit upper limit at time %g\n", idx, (double)t));
274: } else {
275: VRatmax[idx] = 0;
276: PetscCall(PetscPrintf(PETSC_COMM_SELF, "VR[%" PetscInt_FMT "]: freeing variable as dVR_dt is negative at time %g\n", idx, (double)t));
277: }
278: } else {
279: if (!VRatmin[idx]) {
280: VRatmin[idx] = 1;
281: PetscCall(PetscPrintf(PETSC_COMM_SELF, "VR[%" PetscInt_FMT "]: hit lower limit at time %g\n", idx, (double)t));
282: } else {
283: VRatmin[idx] = 0;
284: PetscCall(PetscPrintf(PETSC_COMM_SELF, "VR[%" PetscInt_FMT "]: freeing variable as dVR_dt is positive at time %g\n", idx, (double)t));
285: }
286: }
287: }
288: }
290: PetscCall(VecRestoreArray(Xgen, &xgen));
291: PetscCall(VecRestoreArray(Xnet, &xnet));
293: PetscCall(DMCompositeRestoreLocalVectors(user->dmpgrid, &Xgen, &Xnet));
294: PetscFunctionReturn(PETSC_SUCCESS);
295: }
297: /* Converts from machine frame (dq) to network (phase a real,imag) reference frame */
298: PetscErrorCode dq2ri(PetscScalar Fd, PetscScalar Fq, PetscScalar delta, PetscScalar *Fr, PetscScalar *Fi)
299: {
300: PetscFunctionBegin;
301: *Fr = Fd * PetscSinScalar(delta) + Fq * PetscCosScalar(delta);
302: *Fi = -Fd * PetscCosScalar(delta) + Fq * PetscSinScalar(delta);
303: PetscFunctionReturn(PETSC_SUCCESS);
304: }
306: /* Converts from network frame ([phase a real,imag) to machine (dq) reference frame */
307: PetscErrorCode ri2dq(PetscScalar Fr, PetscScalar Fi, PetscScalar delta, PetscScalar *Fd, PetscScalar *Fq)
308: {
309: PetscFunctionBegin;
310: *Fd = Fr * PetscSinScalar(delta) - Fi * PetscCosScalar(delta);
311: *Fq = Fr * PetscCosScalar(delta) + Fi * PetscSinScalar(delta);
312: PetscFunctionReturn(PETSC_SUCCESS);
313: }
315: /* Saves the solution at each time to a matrix */
316: PetscErrorCode SaveSolution(TS ts)
317: {
318: Userctx *user;
319: Vec X;
320: const PetscScalar *x;
321: PetscScalar *mat;
322: PetscInt idx;
323: PetscReal t;
325: PetscFunctionBegin;
326: PetscCall(TSGetApplicationContext(ts, &user));
327: PetscCall(TSGetTime(ts, &t));
328: PetscCall(TSGetSolution(ts, &X));
329: idx = user->stepnum * (user->neqs_pgrid + 1);
330: PetscCall(MatDenseGetArray(user->Sol, &mat));
331: PetscCall(VecGetArrayRead(X, &x));
332: mat[idx] = t;
333: PetscCall(PetscArraycpy(mat + idx + 1, x, user->neqs_pgrid));
334: PetscCall(MatDenseRestoreArray(user->Sol, &mat));
335: PetscCall(VecRestoreArrayRead(X, &x));
336: user->stepnum++;
337: PetscFunctionReturn(PETSC_SUCCESS);
338: }
340: PetscErrorCode SetInitialGuess(Vec X, Userctx *user)
341: {
342: Vec Xgen, Xnet;
343: PetscScalar *xgen;
344: const PetscScalar *xnet;
345: PetscInt i, idx = 0;
346: PetscScalar Vr, Vi, IGr, IGi, Vm, Vm2;
347: PetscScalar Eqp, Edp, delta;
348: PetscScalar Efd, RF, VR; /* Exciter variables */
349: PetscScalar Id, Iq; /* Generator dq axis currents */
350: PetscScalar theta, Vd, Vq, SE;
352: PetscFunctionBegin;
353: M[0] = 2 * H[0] / w_s;
354: M[1] = 2 * H[1] / w_s;
355: M[2] = 2 * H[2] / w_s;
356: D[0] = 0.1 * M[0];
357: D[1] = 0.1 * M[1];
358: D[2] = 0.1 * M[2];
360: PetscCall(DMCompositeGetLocalVectors(user->dmpgrid, &Xgen, &Xnet));
362: /* Network subsystem initialization */
363: PetscCall(VecCopy(user->V0, Xnet));
365: /* Generator subsystem initialization */
366: PetscCall(VecGetArrayWrite(Xgen, &xgen));
367: PetscCall(VecGetArrayRead(Xnet, &xnet));
369: for (i = 0; i < ngen; i++) {
370: Vr = xnet[2 * gbus[i]]; /* Real part of generator terminal voltage */
371: Vi = xnet[2 * gbus[i] + 1]; /* Imaginary part of the generator terminal voltage */
372: Vm = PetscSqrtScalar(Vr * Vr + Vi * Vi);
373: Vm2 = Vm * Vm;
374: IGr = (Vr * PG[i] + Vi * QG[i]) / Vm2;
375: IGi = (Vi * PG[i] - Vr * QG[i]) / Vm2;
377: delta = PetscAtan2Real(Vi + Xq[i] * IGr, Vr - Xq[i] * IGi); /* Machine angle */
379: theta = PETSC_PI / 2.0 - delta;
381: Id = IGr * PetscCosScalar(theta) - IGi * PetscSinScalar(theta); /* d-axis stator current */
382: Iq = IGr * PetscSinScalar(theta) + IGi * PetscCosScalar(theta); /* q-axis stator current */
384: Vd = Vr * PetscCosScalar(theta) - Vi * PetscSinScalar(theta);
385: Vq = Vr * PetscSinScalar(theta) + Vi * PetscCosScalar(theta);
387: Edp = Vd + Rs[i] * Id - Xqp[i] * Iq; /* d-axis transient EMF */
388: Eqp = Vq + Rs[i] * Iq + Xdp[i] * Id; /* q-axis transient EMF */
390: TM[i] = PG[i];
392: /* The generator variables are ordered as [Eqp,Edp,delta,w,Id,Iq] */
393: xgen[idx] = Eqp;
394: xgen[idx + 1] = Edp;
395: xgen[idx + 2] = delta;
396: xgen[idx + 3] = w_s;
398: idx = idx + 4;
400: xgen[idx] = Id;
401: xgen[idx + 1] = Iq;
403: idx = idx + 2;
405: /* Exciter */
406: Efd = Eqp + (Xd[i] - Xdp[i]) * Id;
407: SE = k1[i] * PetscExpScalar(k2[i] * Efd);
408: VR = KE[i] * Efd + SE;
409: RF = KF[i] * Efd / TF[i];
411: xgen[idx] = Efd;
412: xgen[idx + 1] = RF;
413: xgen[idx + 2] = VR;
415: Vref[i] = Vm + (VR / KA[i]);
417: VRatmin[i] = VRatmax[i] = 0;
419: idx = idx + 3;
420: }
421: PetscCall(VecRestoreArrayWrite(Xgen, &xgen));
422: PetscCall(VecRestoreArrayRead(Xnet, &xnet));
424: /* PetscCall(VecView(Xgen,0)); */
425: PetscCall(DMCompositeGather(user->dmpgrid, INSERT_VALUES, X, Xgen, Xnet));
426: PetscCall(DMCompositeRestoreLocalVectors(user->dmpgrid, &Xgen, &Xnet));
427: PetscFunctionReturn(PETSC_SUCCESS);
428: }
430: /* Computes F = [f(x,y);g(x,y)] */
431: PetscErrorCode ResidualFunction(Vec X, Vec F, Userctx *user)
432: {
433: Vec Xgen, Xnet, Fgen, Fnet;
434: const PetscScalar *xgen, *xnet;
435: PetscScalar *fgen, *fnet;
436: PetscInt i, idx = 0;
437: PetscScalar Vr, Vi, Vm, Vm2;
438: PetscScalar Eqp, Edp, delta, w; /* Generator variables */
439: PetscScalar Efd, RF, VR; /* Exciter variables */
440: PetscScalar Id, Iq; /* Generator dq axis currents */
441: PetscScalar Vd, Vq, SE;
442: PetscScalar IGr, IGi, IDr, IDi;
443: PetscScalar Zdq_inv[4], det;
444: PetscScalar PD, QD, Vm0, *v0;
446: PetscFunctionBegin;
447: PetscCall(VecZeroEntries(F));
448: PetscCall(DMCompositeGetLocalVectors(user->dmpgrid, &Xgen, &Xnet));
449: PetscCall(DMCompositeGetLocalVectors(user->dmpgrid, &Fgen, &Fnet));
450: PetscCall(DMCompositeScatter(user->dmpgrid, X, Xgen, Xnet));
451: PetscCall(DMCompositeScatter(user->dmpgrid, F, Fgen, Fnet));
453: /* Network current balance residual IG + Y*V + IL = 0. Only YV is added here.
454: The generator current injection, IG, and load current injection, ID are added later
455: */
456: /* Note that the values in Ybus are stored assuming the imaginary current balance
457: equation is ordered first followed by real current balance equation for each bus.
458: Thus imaginary current contribution goes in location 2*i, and
459: real current contribution in 2*i+1
460: */
461: PetscCall(MatMult(user->Ybus, Xnet, Fnet));
463: PetscCall(VecGetArrayRead(Xgen, &xgen));
464: PetscCall(VecGetArrayRead(Xnet, &xnet));
465: PetscCall(VecGetArrayWrite(Fgen, &fgen));
466: PetscCall(VecGetArrayWrite(Fnet, &fnet));
468: /* Generator subsystem */
469: for (i = 0; i < ngen; i++) {
470: Eqp = xgen[idx];
471: Edp = xgen[idx + 1];
472: delta = xgen[idx + 2];
473: w = xgen[idx + 3];
474: Id = xgen[idx + 4];
475: Iq = xgen[idx + 5];
476: Efd = xgen[idx + 6];
477: RF = xgen[idx + 7];
478: VR = xgen[idx + 8];
480: /* Generator differential equations */
481: fgen[idx] = (-Eqp - (Xd[i] - Xdp[i]) * Id + Efd) / Td0p[i];
482: fgen[idx + 1] = (-Edp + (Xq[i] - Xqp[i]) * Iq) / Tq0p[i];
483: fgen[idx + 2] = w - w_s;
484: fgen[idx + 3] = (TM[i] - Edp * Id - Eqp * Iq - (Xqp[i] - Xdp[i]) * Id * Iq - D[i] * (w - w_s)) / M[i];
486: Vr = xnet[2 * gbus[i]]; /* Real part of generator terminal voltage */
487: Vi = xnet[2 * gbus[i] + 1]; /* Imaginary part of the generator terminal voltage */
489: PetscCall(ri2dq(Vr, Vi, delta, &Vd, &Vq));
490: /* Algebraic equations for stator currents */
491: det = Rs[i] * Rs[i] + Xdp[i] * Xqp[i];
493: Zdq_inv[0] = Rs[i] / det;
494: Zdq_inv[1] = Xqp[i] / det;
495: Zdq_inv[2] = -Xdp[i] / det;
496: Zdq_inv[3] = Rs[i] / det;
498: fgen[idx + 4] = Zdq_inv[0] * (-Edp + Vd) + Zdq_inv[1] * (-Eqp + Vq) + Id;
499: fgen[idx + 5] = Zdq_inv[2] * (-Edp + Vd) + Zdq_inv[3] * (-Eqp + Vq) + Iq;
501: /* Add generator current injection to network */
502: PetscCall(dq2ri(Id, Iq, delta, &IGr, &IGi));
504: fnet[2 * gbus[i]] -= IGi;
505: fnet[2 * gbus[i] + 1] -= IGr;
507: Vm = PetscSqrtScalar(Vd * Vd + Vq * Vq);
509: SE = k1[i] * PetscExpScalar(k2[i] * Efd);
511: /* Exciter differential equations */
512: fgen[idx + 6] = (-KE[i] * Efd - SE + VR) / TE[i];
513: fgen[idx + 7] = (-RF + KF[i] * Efd / TF[i]) / TF[i];
514: if (VRatmax[i]) fgen[idx + 8] = VR - VRMAX[i];
515: else if (VRatmin[i]) fgen[idx + 8] = VRMIN[i] - VR;
516: else fgen[idx + 8] = (-VR + KA[i] * RF - KA[i] * KF[i] * Efd / TF[i] + KA[i] * (Vref[i] - Vm)) / TA[i];
518: idx = idx + 9;
519: }
521: PetscCall(VecGetArray(user->V0, &v0));
522: for (i = 0; i < nload; i++) {
523: Vr = xnet[2 * lbus[i]]; /* Real part of load bus voltage */
524: Vi = xnet[2 * lbus[i] + 1]; /* Imaginary part of the load bus voltage */
525: Vm = PetscSqrtScalar(Vr * Vr + Vi * Vi);
526: Vm2 = Vm * Vm;
527: Vm0 = PetscSqrtScalar(v0[2 * lbus[i]] * v0[2 * lbus[i]] + v0[2 * lbus[i] + 1] * v0[2 * lbus[i] + 1]);
528: PD = QD = 0.0;
529: for (PetscInt k = 0; k < ld_nsegsp[i]; k++) PD += ld_alphap[k] * PD0[i] * PetscPowScalar(Vm / Vm0, ld_betap[k]);
530: for (PetscInt k = 0; k < ld_nsegsq[i]; k++) QD += ld_alphaq[k] * QD0[i] * PetscPowScalar(Vm / Vm0, ld_betaq[k]);
532: /* Load currents */
533: IDr = (PD * Vr + QD * Vi) / Vm2;
534: IDi = (-QD * Vr + PD * Vi) / Vm2;
536: fnet[2 * lbus[i]] += IDi;
537: fnet[2 * lbus[i] + 1] += IDr;
538: }
539: PetscCall(VecRestoreArray(user->V0, &v0));
541: PetscCall(VecRestoreArrayRead(Xgen, &xgen));
542: PetscCall(VecRestoreArrayRead(Xnet, &xnet));
543: PetscCall(VecRestoreArrayWrite(Fgen, &fgen));
544: PetscCall(VecRestoreArrayWrite(Fnet, &fnet));
546: PetscCall(DMCompositeGather(user->dmpgrid, INSERT_VALUES, F, Fgen, Fnet));
547: PetscCall(DMCompositeRestoreLocalVectors(user->dmpgrid, &Xgen, &Xnet));
548: PetscCall(DMCompositeRestoreLocalVectors(user->dmpgrid, &Fgen, &Fnet));
549: PetscFunctionReturn(PETSC_SUCCESS);
550: }
552: /* f(x,y)
553: g(x,y)
554: */
555: PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec X, Vec F, PetscCtx ctx)
556: {
557: Userctx *user = (Userctx *)ctx;
559: PetscFunctionBegin;
560: user->t = t;
561: PetscCall(ResidualFunction(X, F, user));
562: PetscFunctionReturn(PETSC_SUCCESS);
563: }
565: /* f(x,y) - \dot{x}
566: g(x,y) = 0
567: */
568: PetscErrorCode IFunction(TS ts, PetscReal t, Vec X, Vec Xdot, Vec F, PetscCtx ctx)
569: {
570: PetscScalar *f;
571: const PetscScalar *xdot;
572: PetscInt i;
574: PetscFunctionBegin;
575: PetscCall(RHSFunction(ts, t, X, F, ctx));
576: PetscCall(VecScale(F, -1.0));
577: PetscCall(VecGetArray(F, &f));
578: PetscCall(VecGetArrayRead(Xdot, &xdot));
579: for (i = 0; i < ngen; i++) {
580: f[9 * i] += xdot[9 * i];
581: f[9 * i + 1] += xdot[9 * i + 1];
582: f[9 * i + 2] += xdot[9 * i + 2];
583: f[9 * i + 3] += xdot[9 * i + 3];
584: f[9 * i + 6] += xdot[9 * i + 6];
585: f[9 * i + 7] += xdot[9 * i + 7];
586: f[9 * i + 8] += xdot[9 * i + 8];
587: }
588: PetscCall(VecRestoreArray(F, &f));
589: PetscCall(VecRestoreArrayRead(Xdot, &xdot));
590: PetscFunctionReturn(PETSC_SUCCESS);
591: }
593: /* This function is used for solving the algebraic system only during fault on and
594: off times. It computes the entire F and then zeros out the part corresponding to
595: differential equations
596: F = [0;g(y)];
597: */
598: PetscErrorCode AlgFunction(SNES snes, Vec X, Vec F, PetscCtx ctx)
599: {
600: Userctx *user = (Userctx *)ctx;
601: PetscScalar *f;
602: PetscInt i;
604: PetscFunctionBegin;
605: PetscCall(ResidualFunction(X, F, user));
606: PetscCall(VecGetArray(F, &f));
607: for (i = 0; i < ngen; i++) {
608: f[9 * i] = 0;
609: f[9 * i + 1] = 0;
610: f[9 * i + 2] = 0;
611: f[9 * i + 3] = 0;
612: f[9 * i + 6] = 0;
613: f[9 * i + 7] = 0;
614: f[9 * i + 8] = 0;
615: }
616: PetscCall(VecRestoreArray(F, &f));
617: PetscFunctionReturn(PETSC_SUCCESS);
618: }
620: PetscErrorCode PostStage(TS ts, PetscReal t, PetscInt i, Vec *X)
621: {
622: Userctx *user;
624: PetscFunctionBegin;
625: PetscCall(TSGetApplicationContext(ts, &user));
626: PetscCall(SNESSolve(user->snes_alg, NULL, X[i]));
627: PetscFunctionReturn(PETSC_SUCCESS);
628: }
630: PetscErrorCode PostEvaluate(TS ts)
631: {
632: Userctx *user;
633: Vec X;
635: PetscFunctionBegin;
636: PetscCall(TSGetApplicationContext(ts, &user));
637: PetscCall(TSGetSolution(ts, &X));
638: PetscCall(SNESSolve(user->snes_alg, NULL, X));
639: PetscFunctionReturn(PETSC_SUCCESS);
640: }
642: PetscErrorCode PreallocateJacobian(Mat J, Userctx *user)
643: {
644: PetscInt *d_nnz;
645: PetscInt i, idx = 0, start = 0;
646: PetscInt ncols;
648: PetscFunctionBegin;
649: PetscCall(PetscMalloc1(user->neqs_pgrid, &d_nnz));
650: for (i = 0; i < user->neqs_pgrid; i++) d_nnz[i] = 0;
651: /* Generator subsystem */
652: for (i = 0; i < ngen; i++) {
653: d_nnz[idx] += 3;
654: d_nnz[idx + 1] += 2;
655: d_nnz[idx + 2] += 2;
656: d_nnz[idx + 3] += 5;
657: d_nnz[idx + 4] += 6;
658: d_nnz[idx + 5] += 6;
660: d_nnz[user->neqs_gen + 2 * gbus[i]] += 3;
661: d_nnz[user->neqs_gen + 2 * gbus[i] + 1] += 3;
663: d_nnz[idx + 6] += 2;
664: d_nnz[idx + 7] += 2;
665: d_nnz[idx + 8] += 5;
667: idx = idx + 9;
668: }
669: start = user->neqs_gen;
671: for (i = 0; i < nbus; i++) {
672: PetscCall(MatGetRow(user->Ybus, 2 * i, &ncols, NULL, NULL));
673: d_nnz[start + 2 * i] += ncols;
674: d_nnz[start + 2 * i + 1] += ncols;
675: PetscCall(MatRestoreRow(user->Ybus, 2 * i, &ncols, NULL, NULL));
676: }
677: PetscCall(MatSeqAIJSetPreallocation(J, 0, d_nnz));
678: PetscCall(PetscFree(d_nnz));
679: PetscFunctionReturn(PETSC_SUCCESS);
680: }
682: /*
683: J = [df_dx, df_dy
684: dg_dx, dg_dy]
685: */
686: PetscErrorCode ResidualJacobian(Vec X, Mat J, Mat B, PetscCtx ctx)
687: {
688: Userctx *user = (Userctx *)ctx;
689: Vec Xgen, Xnet;
690: const PetscScalar *xgen, *xnet;
691: PetscInt i, idx = 0;
692: PetscScalar Vr, Vi, Vm, Vm2;
693: PetscScalar Eqp, Edp, delta; /* Generator variables */
694: PetscScalar Efd;
695: PetscScalar Id, Iq; /* Generator dq axis currents */
696: PetscScalar Vd, Vq;
697: PetscScalar val[10];
698: PetscInt row[2], col[10];
699: PetscInt net_start = user->neqs_gen;
700: PetscScalar Zdq_inv[4], det;
701: PetscScalar dVd_dVr, dVd_dVi, dVq_dVr, dVq_dVi, dVd_ddelta, dVq_ddelta;
702: PetscScalar dIGr_ddelta, dIGi_ddelta, dIGr_dId, dIGr_dIq, dIGi_dId, dIGi_dIq;
703: PetscScalar dSE_dEfd;
704: PetscScalar dVm_dVd, dVm_dVq, dVm_dVr, dVm_dVi;
705: PetscInt ncols;
706: const PetscInt *cols;
707: const PetscScalar *yvals;
708: PetscScalar PD, QD, Vm0, Vm4;
709: const PetscScalar *v0;
710: PetscScalar dPD_dVr, dPD_dVi, dQD_dVr, dQD_dVi;
711: PetscScalar dIDr_dVr, dIDr_dVi, dIDi_dVr, dIDi_dVi;
713: PetscFunctionBegin;
714: PetscCall(MatZeroEntries(B));
715: PetscCall(DMCompositeGetLocalVectors(user->dmpgrid, &Xgen, &Xnet));
716: PetscCall(DMCompositeScatter(user->dmpgrid, X, Xgen, Xnet));
718: PetscCall(VecGetArrayRead(Xgen, &xgen));
719: PetscCall(VecGetArrayRead(Xnet, &xnet));
721: /* Generator subsystem */
722: for (i = 0; i < ngen; i++) {
723: Eqp = xgen[idx];
724: Edp = xgen[idx + 1];
725: delta = xgen[idx + 2];
726: Id = xgen[idx + 4];
727: Iq = xgen[idx + 5];
728: Efd = xgen[idx + 6];
730: /* fgen[idx] = (-Eqp - (Xd[i] - Xdp[i])*Id + Efd)/Td0p[i]; */
731: row[0] = idx;
732: col[0] = idx;
733: col[1] = idx + 4;
734: col[2] = idx + 6;
735: val[0] = -1 / Td0p[i];
736: val[1] = -(Xd[i] - Xdp[i]) / Td0p[i];
737: val[2] = 1 / Td0p[i];
739: PetscCall(MatSetValues(J, 1, row, 3, col, val, INSERT_VALUES));
741: /* fgen[idx+1] = (-Edp + (Xq[i] - Xqp[i])*Iq)/Tq0p[i]; */
742: row[0] = idx + 1;
743: col[0] = idx + 1;
744: col[1] = idx + 5;
745: val[0] = -1 / Tq0p[i];
746: val[1] = (Xq[i] - Xqp[i]) / Tq0p[i];
747: PetscCall(MatSetValues(J, 1, row, 2, col, val, INSERT_VALUES));
749: /* fgen[idx+2] = w - w_s; */
750: row[0] = idx + 2;
751: col[0] = idx + 2;
752: col[1] = idx + 3;
753: val[0] = 0;
754: val[1] = 1;
755: PetscCall(MatSetValues(J, 1, row, 2, col, val, INSERT_VALUES));
757: /* fgen[idx+3] = (TM[i] - Edp*Id - Eqp*Iq - (Xqp[i] - Xdp[i])*Id*Iq - D[i]*(w - w_s))/M[i]; */
758: row[0] = idx + 3;
759: col[0] = idx;
760: col[1] = idx + 1;
761: col[2] = idx + 3;
762: col[3] = idx + 4;
763: col[4] = idx + 5;
764: val[0] = -Iq / M[i];
765: val[1] = -Id / M[i];
766: val[2] = -D[i] / M[i];
767: val[3] = (-Edp - (Xqp[i] - Xdp[i]) * Iq) / M[i];
768: val[4] = (-Eqp - (Xqp[i] - Xdp[i]) * Id) / M[i];
769: PetscCall(MatSetValues(J, 1, row, 5, col, val, INSERT_VALUES));
771: Vr = xnet[2 * gbus[i]]; /* Real part of generator terminal voltage */
772: Vi = xnet[2 * gbus[i] + 1]; /* Imaginary part of the generator terminal voltage */
773: PetscCall(ri2dq(Vr, Vi, delta, &Vd, &Vq));
775: det = Rs[i] * Rs[i] + Xdp[i] * Xqp[i];
777: Zdq_inv[0] = Rs[i] / det;
778: Zdq_inv[1] = Xqp[i] / det;
779: Zdq_inv[2] = -Xdp[i] / det;
780: Zdq_inv[3] = Rs[i] / det;
782: dVd_dVr = PetscSinScalar(delta);
783: dVd_dVi = -PetscCosScalar(delta);
784: dVq_dVr = PetscCosScalar(delta);
785: dVq_dVi = PetscSinScalar(delta);
786: dVd_ddelta = Vr * PetscCosScalar(delta) + Vi * PetscSinScalar(delta);
787: dVq_ddelta = -Vr * PetscSinScalar(delta) + Vi * PetscCosScalar(delta);
789: /* fgen[idx+4] = Zdq_inv[0]*(-Edp + Vd) + Zdq_inv[1]*(-Eqp + Vq) + Id; */
790: row[0] = idx + 4;
791: col[0] = idx;
792: col[1] = idx + 1;
793: col[2] = idx + 2;
794: val[0] = -Zdq_inv[1];
795: val[1] = -Zdq_inv[0];
796: val[2] = Zdq_inv[0] * dVd_ddelta + Zdq_inv[1] * dVq_ddelta;
797: col[3] = idx + 4;
798: col[4] = net_start + 2 * gbus[i];
799: col[5] = net_start + 2 * gbus[i] + 1;
800: val[3] = 1;
801: val[4] = Zdq_inv[0] * dVd_dVr + Zdq_inv[1] * dVq_dVr;
802: val[5] = Zdq_inv[0] * dVd_dVi + Zdq_inv[1] * dVq_dVi;
803: PetscCall(MatSetValues(J, 1, row, 6, col, val, INSERT_VALUES));
805: /* fgen[idx+5] = Zdq_inv[2]*(-Edp + Vd) + Zdq_inv[3]*(-Eqp + Vq) + Iq; */
806: row[0] = idx + 5;
807: col[0] = idx;
808: col[1] = idx + 1;
809: col[2] = idx + 2;
810: val[0] = -Zdq_inv[3];
811: val[1] = -Zdq_inv[2];
812: val[2] = Zdq_inv[2] * dVd_ddelta + Zdq_inv[3] * dVq_ddelta;
813: col[3] = idx + 5;
814: col[4] = net_start + 2 * gbus[i];
815: col[5] = net_start + 2 * gbus[i] + 1;
816: val[3] = 1;
817: val[4] = Zdq_inv[2] * dVd_dVr + Zdq_inv[3] * dVq_dVr;
818: val[5] = Zdq_inv[2] * dVd_dVi + Zdq_inv[3] * dVq_dVi;
819: PetscCall(MatSetValues(J, 1, row, 6, col, val, INSERT_VALUES));
821: dIGr_ddelta = Id * PetscCosScalar(delta) - Iq * PetscSinScalar(delta);
822: dIGi_ddelta = Id * PetscSinScalar(delta) + Iq * PetscCosScalar(delta);
823: dIGr_dId = PetscSinScalar(delta);
824: dIGr_dIq = PetscCosScalar(delta);
825: dIGi_dId = -PetscCosScalar(delta);
826: dIGi_dIq = PetscSinScalar(delta);
828: /* fnet[2*gbus[i]] -= IGi; */
829: row[0] = net_start + 2 * gbus[i];
830: col[0] = idx + 2;
831: col[1] = idx + 4;
832: col[2] = idx + 5;
833: val[0] = -dIGi_ddelta;
834: val[1] = -dIGi_dId;
835: val[2] = -dIGi_dIq;
836: PetscCall(MatSetValues(J, 1, row, 3, col, val, INSERT_VALUES));
838: /* fnet[2*gbus[i]+1] -= IGr; */
839: row[0] = net_start + 2 * gbus[i] + 1;
840: col[0] = idx + 2;
841: col[1] = idx + 4;
842: col[2] = idx + 5;
843: val[0] = -dIGr_ddelta;
844: val[1] = -dIGr_dId;
845: val[2] = -dIGr_dIq;
846: PetscCall(MatSetValues(J, 1, row, 3, col, val, INSERT_VALUES));
848: Vm = PetscSqrtScalar(Vd * Vd + Vq * Vq);
850: /* fgen[idx+6] = (-KE[i]*Efd - SE + VR)/TE[i]; */
851: /* SE = k1[i]*PetscExpScalar(k2[i]*Efd); */
853: dSE_dEfd = k1[i] * k2[i] * PetscExpScalar(k2[i] * Efd);
855: row[0] = idx + 6;
856: col[0] = idx + 6;
857: col[1] = idx + 8;
858: val[0] = (-KE[i] - dSE_dEfd) / TE[i];
859: val[1] = 1 / TE[i];
860: PetscCall(MatSetValues(J, 1, row, 2, col, val, INSERT_VALUES));
862: /* Exciter differential equations */
864: /* fgen[idx+7] = (-RF + KF[i]*Efd/TF[i])/TF[i]; */
865: row[0] = idx + 7;
866: col[0] = idx + 6;
867: col[1] = idx + 7;
868: val[0] = (KF[i] / TF[i]) / TF[i];
869: val[1] = -1 / TF[i];
870: PetscCall(MatSetValues(J, 1, row, 2, col, val, INSERT_VALUES));
872: /* fgen[idx+8] = (-VR + KA[i]*RF - KA[i]*KF[i]*Efd/TF[i] + KA[i]*(Vref[i] - Vm))/TA[i]; */
873: /* Vm = (Vd^2 + Vq^2)^0.5; */
875: row[0] = idx + 8;
876: if (VRatmax[i]) {
877: col[0] = idx + 8;
878: val[0] = 1.0;
879: PetscCall(MatSetValues(J, 1, row, 1, col, val, INSERT_VALUES));
880: } else if (VRatmin[i]) {
881: col[0] = idx + 8;
882: val[0] = -1.0;
883: PetscCall(MatSetValues(J, 1, row, 1, col, val, INSERT_VALUES));
884: } else {
885: dVm_dVd = Vd / Vm;
886: dVm_dVq = Vq / Vm;
887: dVm_dVr = dVm_dVd * dVd_dVr + dVm_dVq * dVq_dVr;
888: dVm_dVi = dVm_dVd * dVd_dVi + dVm_dVq * dVq_dVi;
889: row[0] = idx + 8;
890: col[0] = idx + 6;
891: col[1] = idx + 7;
892: col[2] = idx + 8;
893: val[0] = -(KA[i] * KF[i] / TF[i]) / TA[i];
894: val[1] = KA[i] / TA[i];
895: val[2] = -1 / TA[i];
896: col[3] = net_start + 2 * gbus[i];
897: col[4] = net_start + 2 * gbus[i] + 1;
898: val[3] = -KA[i] * dVm_dVr / TA[i];
899: val[4] = -KA[i] * dVm_dVi / TA[i];
900: PetscCall(MatSetValues(J, 1, row, 5, col, val, INSERT_VALUES));
901: }
902: idx = idx + 9;
903: }
905: for (i = 0; i < nbus; i++) {
906: PetscCall(MatGetRow(user->Ybus, 2 * i, &ncols, &cols, &yvals));
907: row[0] = net_start + 2 * i;
908: for (PetscInt k = 0; k < ncols; k++) {
909: col[k] = net_start + cols[k];
910: val[k] = yvals[k];
911: }
912: PetscCall(MatSetValues(J, 1, row, ncols, col, val, INSERT_VALUES));
913: PetscCall(MatRestoreRow(user->Ybus, 2 * i, &ncols, &cols, &yvals));
915: PetscCall(MatGetRow(user->Ybus, 2 * i + 1, &ncols, &cols, &yvals));
916: row[0] = net_start + 2 * i + 1;
917: for (PetscInt k = 0; k < ncols; k++) {
918: col[k] = net_start + cols[k];
919: val[k] = yvals[k];
920: }
921: PetscCall(MatSetValues(J, 1, row, ncols, col, val, INSERT_VALUES));
922: PetscCall(MatRestoreRow(user->Ybus, 2 * i + 1, &ncols, &cols, &yvals));
923: }
925: PetscCall(MatAssemblyBegin(J, MAT_FLUSH_ASSEMBLY));
926: PetscCall(MatAssemblyEnd(J, MAT_FLUSH_ASSEMBLY));
928: PetscCall(VecGetArrayRead(user->V0, &v0));
929: for (i = 0; i < nload; i++) {
930: Vr = xnet[2 * lbus[i]]; /* Real part of load bus voltage */
931: Vi = xnet[2 * lbus[i] + 1]; /* Imaginary part of the load bus voltage */
932: Vm = PetscSqrtScalar(Vr * Vr + Vi * Vi);
933: Vm2 = Vm * Vm;
934: Vm4 = Vm2 * Vm2;
935: Vm0 = PetscSqrtScalar(v0[2 * lbus[i]] * v0[2 * lbus[i]] + v0[2 * lbus[i] + 1] * v0[2 * lbus[i] + 1]);
936: PD = QD = 0.0;
937: dPD_dVr = dPD_dVi = dQD_dVr = dQD_dVi = 0.0;
938: for (PetscInt k = 0; k < ld_nsegsp[i]; k++) {
939: PD += ld_alphap[k] * PD0[i] * PetscPowScalar(Vm / Vm0, ld_betap[k]);
940: dPD_dVr += ld_alphap[k] * ld_betap[k] * PD0[i] * PetscPowScalar(1 / Vm0, ld_betap[k]) * Vr * PetscPowScalar(Vm, ld_betap[k] - 2);
941: dPD_dVi += ld_alphap[k] * ld_betap[k] * PD0[i] * PetscPowScalar(1 / Vm0, ld_betap[k]) * Vi * PetscPowScalar(Vm, ld_betap[k] - 2);
942: }
943: for (PetscInt k = 0; k < ld_nsegsq[i]; k++) {
944: QD += ld_alphaq[k] * QD0[i] * PetscPowScalar(Vm / Vm0, ld_betaq[k]);
945: dQD_dVr += ld_alphaq[k] * ld_betaq[k] * QD0[i] * PetscPowScalar(1 / Vm0, ld_betaq[k]) * Vr * PetscPowScalar(Vm, ld_betaq[k] - 2);
946: dQD_dVi += ld_alphaq[k] * ld_betaq[k] * QD0[i] * PetscPowScalar(1 / Vm0, ld_betaq[k]) * Vi * PetscPowScalar(Vm, ld_betaq[k] - 2);
947: }
949: /* IDr = (PD*Vr + QD*Vi)/Vm2; */
950: /* IDi = (-QD*Vr + PD*Vi)/Vm2; */
952: dIDr_dVr = (dPD_dVr * Vr + dQD_dVr * Vi + PD) / Vm2 - ((PD * Vr + QD * Vi) * 2 * Vr) / Vm4;
953: dIDr_dVi = (dPD_dVi * Vr + dQD_dVi * Vi + QD) / Vm2 - ((PD * Vr + QD * Vi) * 2 * Vi) / Vm4;
955: dIDi_dVr = (-dQD_dVr * Vr + dPD_dVr * Vi - QD) / Vm2 - ((-QD * Vr + PD * Vi) * 2 * Vr) / Vm4;
956: dIDi_dVi = (-dQD_dVi * Vr + dPD_dVi * Vi + PD) / Vm2 - ((-QD * Vr + PD * Vi) * 2 * Vi) / Vm4;
958: /* fnet[2*lbus[i]] += IDi; */
959: row[0] = net_start + 2 * lbus[i];
960: col[0] = net_start + 2 * lbus[i];
961: col[1] = net_start + 2 * lbus[i] + 1;
962: val[0] = dIDi_dVr;
963: val[1] = dIDi_dVi;
964: PetscCall(MatSetValues(J, 1, row, 2, col, val, ADD_VALUES));
965: /* fnet[2*lbus[i]+1] += IDr; */
966: row[0] = net_start + 2 * lbus[i] + 1;
967: col[0] = net_start + 2 * lbus[i];
968: col[1] = net_start + 2 * lbus[i] + 1;
969: val[0] = dIDr_dVr;
970: val[1] = dIDr_dVi;
971: PetscCall(MatSetValues(J, 1, row, 2, col, val, ADD_VALUES));
972: }
973: PetscCall(VecRestoreArrayRead(user->V0, &v0));
975: PetscCall(VecRestoreArrayRead(Xgen, &xgen));
976: PetscCall(VecRestoreArrayRead(Xnet, &xnet));
978: PetscCall(DMCompositeRestoreLocalVectors(user->dmpgrid, &Xgen, &Xnet));
980: PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
981: PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
982: PetscFunctionReturn(PETSC_SUCCESS);
983: }
985: /*
986: J = [I, 0
987: dg_dx, dg_dy]
988: */
989: PetscErrorCode AlgJacobian(SNES snes, Vec X, Mat A, Mat B, PetscCtx ctx)
990: {
991: Userctx *user = (Userctx *)ctx;
993: PetscFunctionBegin;
994: PetscCall(ResidualJacobian(X, A, B, ctx));
995: PetscCall(MatSetOption(A, MAT_KEEP_NONZERO_PATTERN, PETSC_TRUE));
996: PetscCall(MatZeroRowsIS(A, user->is_diff, 1.0, NULL, NULL));
997: PetscFunctionReturn(PETSC_SUCCESS);
998: }
1000: /*
1001: J = [-df_dx, -df_dy
1002: dg_dx, dg_dy]
1003: */
1005: PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec X, Mat A, Mat B, PetscCtx ctx)
1006: {
1007: Userctx *user = (Userctx *)ctx;
1009: PetscFunctionBegin;
1010: user->t = t;
1012: PetscCall(ResidualJacobian(X, A, B, user));
1013: PetscFunctionReturn(PETSC_SUCCESS);
1014: }
1016: /*
1017: J = [df_dx-aI, df_dy
1018: dg_dx, dg_dy]
1019: */
1021: PetscErrorCode IJacobian(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal a, Mat A, Mat B, Userctx *user)
1022: {
1023: PetscScalar atmp = (PetscScalar)a;
1024: PetscInt i, row;
1026: PetscFunctionBegin;
1027: user->t = t;
1029: PetscCall(RHSJacobian(ts, t, X, A, B, user));
1030: PetscCall(MatScale(B, -1.0));
1031: for (i = 0; i < ngen; i++) {
1032: row = 9 * i;
1033: PetscCall(MatSetValues(A, 1, &row, 1, &row, &atmp, ADD_VALUES));
1034: row = 9 * i + 1;
1035: PetscCall(MatSetValues(A, 1, &row, 1, &row, &atmp, ADD_VALUES));
1036: row = 9 * i + 2;
1037: PetscCall(MatSetValues(A, 1, &row, 1, &row, &atmp, ADD_VALUES));
1038: row = 9 * i + 3;
1039: PetscCall(MatSetValues(A, 1, &row, 1, &row, &atmp, ADD_VALUES));
1040: row = 9 * i + 6;
1041: PetscCall(MatSetValues(A, 1, &row, 1, &row, &atmp, ADD_VALUES));
1042: row = 9 * i + 7;
1043: PetscCall(MatSetValues(A, 1, &row, 1, &row, &atmp, ADD_VALUES));
1044: row = 9 * i + 8;
1045: PetscCall(MatSetValues(A, 1, &row, 1, &row, &atmp, ADD_VALUES));
1046: }
1047: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
1048: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
1049: PetscFunctionReturn(PETSC_SUCCESS);
1050: }
1052: int main(int argc, char **argv)
1053: {
1054: TS ts;
1055: SNES snes_alg;
1056: PetscMPIInt size;
1057: Userctx user;
1058: PetscViewer Xview, Ybusview, viewer;
1059: Vec X, F_alg;
1060: Mat J, A;
1061: PetscInt i, idx, *idx2;
1062: Vec Xdot;
1063: PetscScalar *x, *mat, *amat;
1064: const PetscScalar *rmat;
1065: Vec vatol;
1066: PetscInt *direction;
1067: PetscBool *terminate;
1068: const PetscInt *idx3;
1069: PetscScalar *vatoli;
1071: PetscFunctionBeginUser;
1072: PetscCall(PetscInitialize(&argc, &argv, "petscoptions", help));
1073: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
1074: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");
1076: user.neqs_gen = 9 * ngen; /* # eqs. for generator subsystem */
1077: user.neqs_net = 2 * nbus; /* # eqs. for network subsystem */
1078: user.neqs_pgrid = user.neqs_gen + user.neqs_net;
1080: /* Create indices for differential and algebraic equations */
1082: PetscCall(PetscMalloc1(7 * ngen, &idx2));
1083: for (i = 0; i < ngen; i++) {
1084: idx2[7 * i] = 9 * i;
1085: idx2[7 * i + 1] = 9 * i + 1;
1086: idx2[7 * i + 2] = 9 * i + 2;
1087: idx2[7 * i + 3] = 9 * i + 3;
1088: idx2[7 * i + 4] = 9 * i + 6;
1089: idx2[7 * i + 5] = 9 * i + 7;
1090: idx2[7 * i + 6] = 9 * i + 8;
1091: }
1092: PetscCall(ISCreateGeneral(PETSC_COMM_WORLD, 7 * ngen, idx2, PETSC_COPY_VALUES, &user.is_diff));
1093: PetscCall(ISComplement(user.is_diff, 0, user.neqs_pgrid, &user.is_alg));
1094: PetscCall(PetscFree(idx2));
1096: /* Read initial voltage vector and Ybus */
1097: PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, "X.bin", FILE_MODE_READ, &Xview));
1098: PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, "Ybus.bin", FILE_MODE_READ, &Ybusview));
1100: PetscCall(VecCreate(PETSC_COMM_WORLD, &user.V0));
1101: PetscCall(VecSetSizes(user.V0, PETSC_DECIDE, user.neqs_net));
1102: PetscCall(VecLoad(user.V0, Xview));
1104: PetscCall(MatCreate(PETSC_COMM_WORLD, &user.Ybus));
1105: PetscCall(MatSetSizes(user.Ybus, PETSC_DECIDE, PETSC_DECIDE, user.neqs_net, user.neqs_net));
1106: PetscCall(MatSetType(user.Ybus, MATBAIJ));
1107: /* PetscCall(MatSetBlockSize(user.Ybus,2)); */
1108: PetscCall(MatLoad(user.Ybus, Ybusview));
1110: /* Set run time options */
1111: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Transient stability fault options", "");
1112: {
1113: user.tfaulton = 1.0;
1114: user.tfaultoff = 1.2;
1115: user.Rfault = 0.0001;
1116: user.setisdiff = PETSC_FALSE;
1117: user.semiexplicit = PETSC_FALSE;
1118: user.faultbus = 8;
1119: PetscCall(PetscOptionsReal("-tfaulton", "", "", user.tfaulton, &user.tfaulton, NULL));
1120: PetscCall(PetscOptionsReal("-tfaultoff", "", "", user.tfaultoff, &user.tfaultoff, NULL));
1121: PetscCall(PetscOptionsInt("-faultbus", "", "", user.faultbus, &user.faultbus, NULL));
1122: user.t0 = 0.0;
1123: user.tmax = 5.0;
1124: PetscCall(PetscOptionsReal("-t0", "", "", user.t0, &user.t0, NULL));
1125: PetscCall(PetscOptionsReal("-tmax", "", "", user.tmax, &user.tmax, NULL));
1126: PetscCall(PetscOptionsBool("-setisdiff", "", "", user.setisdiff, &user.setisdiff, NULL));
1127: PetscCall(PetscOptionsBool("-dae_semiexplicit", "", "", user.semiexplicit, &user.semiexplicit, NULL));
1128: }
1129: PetscOptionsEnd();
1131: PetscCall(PetscViewerDestroy(&Xview));
1132: PetscCall(PetscViewerDestroy(&Ybusview));
1134: /* Create DMs for generator and network subsystems */
1135: PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, user.neqs_gen, 1, 1, NULL, &user.dmgen));
1136: PetscCall(DMSetOptionsPrefix(user.dmgen, "dmgen_"));
1137: PetscCall(DMSetFromOptions(user.dmgen));
1138: PetscCall(DMSetUp(user.dmgen));
1139: PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, user.neqs_net, 1, 1, NULL, &user.dmnet));
1140: PetscCall(DMSetOptionsPrefix(user.dmnet, "dmnet_"));
1141: PetscCall(DMSetFromOptions(user.dmnet));
1142: PetscCall(DMSetUp(user.dmnet));
1143: /* Create a composite DM packer and add the two DMs */
1144: PetscCall(DMCompositeCreate(PETSC_COMM_WORLD, &user.dmpgrid));
1145: PetscCall(DMSetOptionsPrefix(user.dmpgrid, "pgrid_"));
1146: PetscCall(DMCompositeAddDM(user.dmpgrid, user.dmgen));
1147: PetscCall(DMCompositeAddDM(user.dmpgrid, user.dmnet));
1149: PetscCall(DMCreateGlobalVector(user.dmpgrid, &X));
1151: PetscCall(MatCreate(PETSC_COMM_WORLD, &J));
1152: PetscCall(MatSetSizes(J, PETSC_DECIDE, PETSC_DECIDE, user.neqs_pgrid, user.neqs_pgrid));
1153: PetscCall(MatSetFromOptions(J));
1154: PetscCall(PreallocateJacobian(J, &user));
1156: /* Create matrix to save solutions at each time step */
1157: user.stepnum = 0;
1159: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, user.neqs_pgrid + 1, 1002, NULL, &user.Sol));
1160: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1161: Create timestepping solver context
1162: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1163: PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
1164: PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
1165: if (user.semiexplicit) {
1166: PetscCall(TSSetType(ts, TSRK));
1167: PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, &user));
1168: PetscCall(TSSetRHSJacobian(ts, J, J, RHSJacobian, &user));
1169: } else {
1170: PetscCall(TSSetType(ts, TSCN));
1171: PetscCall(TSSetEquationType(ts, TS_EQ_DAE_IMPLICIT_INDEX1));
1172: PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, &user));
1173: PetscCall(TSSetIJacobian(ts, J, J, (TSIJacobianFn *)IJacobian, &user));
1174: }
1175: PetscCall(TSSetApplicationContext(ts, &user));
1177: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1178: Set initial conditions
1179: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
1180: PetscCall(SetInitialGuess(X, &user));
1181: /* Just to set up the Jacobian structure */
1183: PetscCall(VecDuplicate(X, &Xdot));
1184: PetscCall(IJacobian(ts, 0.0, X, Xdot, 0.0, J, J, &user));
1185: PetscCall(VecDestroy(&Xdot));
1187: /* Save initial solution */
1189: idx = user.stepnum * (user.neqs_pgrid + 1);
1190: PetscCall(MatDenseGetArray(user.Sol, &mat));
1191: PetscCall(VecGetArray(X, &x));
1193: mat[idx] = 0.0;
1195: PetscCall(PetscArraycpy(mat + idx + 1, x, user.neqs_pgrid));
1196: PetscCall(MatDenseRestoreArray(user.Sol, &mat));
1197: PetscCall(VecRestoreArray(X, &x));
1198: user.stepnum++;
1200: PetscCall(TSSetMaxTime(ts, user.tmax));
1201: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
1202: PetscCall(TSSetTimeStep(ts, 0.01));
1203: PetscCall(TSSetFromOptions(ts));
1204: PetscCall(TSSetPostStep(ts, SaveSolution));
1205: PetscCall(TSSetSolution(ts, X));
1207: PetscCall(PetscMalloc1(2 * ngen + 2, &direction));
1208: PetscCall(PetscMalloc1(2 * ngen + 2, &terminate));
1209: direction[0] = direction[1] = 1;
1210: terminate[0] = terminate[1] = PETSC_FALSE;
1211: for (i = 0; i < ngen; i++) {
1212: direction[2 + 2 * i] = -1;
1213: direction[2 + 2 * i + 1] = 1;
1214: terminate[2 + 2 * i] = terminate[2 + 2 * i + 1] = PETSC_FALSE;
1215: }
1217: PetscCall(TSSetEventHandler(ts, 2 * ngen + 2, direction, terminate, EventFunction, PostEventFunction, (void *)&user));
1219: if (user.semiexplicit) {
1220: /* Use a semi-explicit approach with the time-stepping done by an explicit method and the
1221: algrebraic part solved via PostStage and PostEvaluate callbacks
1222: */
1223: PetscCall(TSSetType(ts, TSRK));
1224: PetscCall(TSSetPostStage(ts, PostStage));
1225: PetscCall(TSSetPostEvaluate(ts, PostEvaluate));
1226: }
1228: if (user.setisdiff) {
1229: /* Create vector of absolute tolerances and set the algebraic part to infinity */
1230: PetscCall(VecDuplicate(X, &vatol));
1231: PetscCall(VecSet(vatol, 100000.0));
1232: PetscCall(VecGetArray(vatol, &vatoli));
1233: PetscCall(ISGetIndices(user.is_diff, &idx3));
1234: for (PetscInt k = 0; k < 7 * ngen; k++) vatoli[idx3[k]] = 1e-2;
1235: PetscCall(VecRestoreArray(vatol, &vatoli));
1236: }
1238: /* Create the nonlinear solver for solving the algebraic system */
1239: /* Note that although the algebraic system needs to be solved only for
1240: Idq and V, we reuse the entire system including xgen. The xgen
1241: variables are held constant by setting their residuals to 0 and
1242: putting a 1 on the Jacobian diagonal for xgen rows
1243: */
1245: PetscCall(VecDuplicate(X, &F_alg));
1246: PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes_alg));
1247: PetscCall(SNESSetFunction(snes_alg, F_alg, AlgFunction, &user));
1248: PetscCall(SNESSetJacobian(snes_alg, J, J, AlgJacobian, &user));
1249: PetscCall(SNESSetFromOptions(snes_alg));
1251: user.snes_alg = snes_alg;
1253: /* Solve */
1254: PetscCall(TSSolve(ts, X));
1256: PetscCall(MatAssemblyBegin(user.Sol, MAT_FINAL_ASSEMBLY));
1257: PetscCall(MatAssemblyEnd(user.Sol, MAT_FINAL_ASSEMBLY));
1259: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, user.neqs_pgrid + 1, user.stepnum, NULL, &A));
1260: PetscCall(MatDenseGetArrayRead(user.Sol, &rmat));
1261: PetscCall(MatDenseGetArray(A, &amat));
1262: PetscCall(PetscArraycpy(amat, rmat, user.stepnum * (user.neqs_pgrid + 1)));
1263: PetscCall(MatDenseRestoreArray(A, &amat));
1264: PetscCall(MatDenseRestoreArrayRead(user.Sol, &rmat));
1265: PetscCall(PetscViewerBinaryOpen(PETSC_COMM_SELF, "out.bin", FILE_MODE_WRITE, &viewer));
1266: PetscCall(MatView(A, viewer));
1267: PetscCall(PetscViewerDestroy(&viewer));
1268: PetscCall(MatDestroy(&A));
1270: PetscCall(PetscFree(direction));
1271: PetscCall(PetscFree(terminate));
1272: PetscCall(SNESDestroy(&snes_alg));
1273: PetscCall(VecDestroy(&F_alg));
1274: PetscCall(MatDestroy(&J));
1275: PetscCall(MatDestroy(&user.Ybus));
1276: PetscCall(MatDestroy(&user.Sol));
1277: PetscCall(VecDestroy(&X));
1278: PetscCall(VecDestroy(&user.V0));
1279: PetscCall(DMDestroy(&user.dmgen));
1280: PetscCall(DMDestroy(&user.dmnet));
1281: PetscCall(DMDestroy(&user.dmpgrid));
1282: PetscCall(ISDestroy(&user.is_diff));
1283: PetscCall(ISDestroy(&user.is_alg));
1284: PetscCall(TSDestroy(&ts));
1285: if (user.setisdiff) PetscCall(VecDestroy(&vatol));
1286: PetscCall(PetscFinalize());
1287: return 0;
1288: }
1290: /*TEST
1292: build:
1293: requires: double !complex !defined(PETSC_USE_64BIT_INDICES)
1295: test:
1296: suffix: implicit
1297: args: -ts_monitor -snes_monitor
1298: localrunfiles: petscoptions X.bin Ybus.bin
1300: test:
1301: suffix: semiexplicit
1302: args: -ts_monitor -dae_semiexplicit -snes_error_if_not_converged -ts_rk_type 2a
1303: localrunfiles: petscoptions X.bin Ybus.bin
1305: test:
1306: suffix: steprestart
1307: # needs ARKIMEX methods with all implicit stages since the mass matrix is not the identity
1308: args: -ts_monitor -snes_monitor -ts_type arkimex -ts_arkimex_type prssp2
1309: localrunfiles: petscoptions X.bin Ybus.bin
1311: TEST*/