/**
* Returns two matrices containing partial derivatives of the complex bus power injections w.r.t
* voltage magnitude and voltage angle respectively (for all buses). If YBUS is a sparse matrix,
* the return values will be also. The following explains the expressions used to form the
* matrices:
*
* <p>S = diag(V) * conj(Ibus) = diag(conj(Ibus)) * V
*
* <p>Partials of V & Ibus w.r.t. voltage magnitudes dV/dVm = diag(V./abs(V)) dI/dVm = Ybus *
* dV/dVm = Ybus * diag(V./abs(V))
*
* <p>Partials of V & Ibus w.r.t. voltage angles dV/dVa = j * diag(V) dI/dVa = Ybus * dV/dVa =
* Ybus * j * diag(V)
*
* <p>Partials of S w.r.t. voltage magnitudes dS/dVm = diag(V) * conj(dI/dVm) + diag(conj(Ibus)) *
* dV/dVm = diag(V) * conj(Ybus * diag(V./abs(V))) + conj(diag(Ibus)) * diag(V./abs(V))
*
* <p>Partials of S w.r.t. voltage angles dS/dVa = diag(V) * conj(dI/dVa) + diag(conj(Ibus)) *
* dV/dVa = diag(V) * conj(Ybus * j * diag(V)) + conj(diag(Ibus)) * j * diag(V) = -j * diag(V) *
* conj(Ybus * diag(V)) + conj(diag(Ibus)) * j * diag(V) = j * diag(V) * conj(diag(Ibus) - Ybus *
* diag(V))
*
* @param Ybus
* @param V
* @return
*/
@SuppressWarnings("static-access")
public static DComplexMatrix2D[] jp_dSbus_dV(DComplexMatrix2D Ybus, DComplexMatrix1D V) {
int n;
int[] ib;
DComplexMatrix1D Ibus, absV, Vnorm;
DComplexMatrix2D[] dSbus_dV;
SparseRCDComplexMatrix2D diagV, diagIbus, diagVnorm, rhs, dS_dVa, conjInorm, dS_dVm, addend;
n = (int) V.size();
ib = Djp_util.irange(n);
Ibus = Ybus.zMult(V, null);
diagV = new SparseRCDComplexMatrix2D(n, n, ib, ib, V.toArray(), false, false);
diagIbus = new SparseRCDComplexMatrix2D(n, n, ib, ib, Ibus.toArray(), false, false);
absV = V.copy().assign(cfunc.abs);
Vnorm = V.copy().assign(absV, cfunc.div);
diagVnorm = new SparseRCDComplexMatrix2D(n, n, ib, ib, Vnorm.toArray(), false, false);
rhs = (SparseRCDComplexMatrix2D) Ybus.zMult(diagV, null);
rhs.assign(diagIbus, cfunc.swapArgs(cfunc.minus)).assign(cfunc.conj);
dS_dVa = (SparseRCDComplexMatrix2D) diagV.zMult(rhs, null);
dS_dVa.assign(cfunc.mult(new double[] {0, 1}));
conjInorm = (SparseRCDComplexMatrix2D) Ybus.zMult(diagVnorm, null);
conjInorm.assign(cfunc.conj);
dS_dVm = (SparseRCDComplexMatrix2D) diagV.zMult(conjInorm, null);
diagIbus.assign(cfunc.conj);
addend = (SparseRCDComplexMatrix2D) diagVnorm.zMult(diagIbus, null);
dS_dVm.assign(addend, cfunc.plus);
dSbus_dV = new DComplexMatrix2D[] {dS_dVm, dS_dVa};
return dSbus_dV;
}
/**
* Solves for bus voltages given the full system admittance matrix (for all buses), the complex
* bus power injection vector (for all buses), the initial vector of complex bus voltages, and
* column vectors with the lists of bus indices for the swing bus, PV buses, and PQ buses,
* respectively. The bus voltage vector contains the set point for generator (including ref bus)
* buses, and the reference angle of the swing bus, as well as an initial guess for remaining
* magnitudes and angles. JPOPT is a JPOWER options vector which can be used to set the
* termination tolerance, maximum number of iterations, and output options (see JPOPTION for
* details). Uses default options if this parameter is not given. Returns the final complex
* voltages, a flag which indicates whether it converged or not, and the number of iterations
* performed.
*
* @param Ybus
* @param Sbus
* @param V0
* @param ref
* @param pv
* @param pq
* @param jpopt
* @return
*/
@SuppressWarnings("static-access")
public static Object[] jp_newtonpf(
DComplexMatrix2D Ybus,
DComplexMatrix1D Sbus,
DComplexMatrix1D V0,
int ref,
int[] pv,
int[] pq,
Map<String, Double> jpopt) {
int i, max_it, verbose, npv, npq, j1, j2, j3, j4, j5, j6;
int[] pvpq;
double tol, normF;
boolean converged;
DoubleMatrix1D F, dx;
DoubleMatrix2D J11, J12, J21, J22, J1, J2, J;
DComplexMatrix1D mis, V, Va, Vm, dxz;
DComplexMatrix2D dSbus_dVm, dSbus_dVa;
DComplexMatrix2D[] dSbus_dV;
SparseRCDoubleMatrix2D JJ;
/* options */
tol = jpopt.get("PF_TOL");
max_it = jpopt.get("PF_MAX_IT").intValue();
verbose = jpopt.get("VERBOSE").intValue();
/* initialize */
pvpq = Djp_util.icat(pv, pq);
converged = false;
i = 0;
V = V0;
Va = V.copy().assign(cfunc.arg);
Vm = V.copy().assign(cfunc.abs);
/* set up indexing for updating V */
npv = pv.length;
npq = pq.length;
j1 = 0;
j2 = npv; // j1:j2 - V angle of pv buses
j3 = j2;
j4 = j2 + npq; // j3:j4 - V angle of pq buses
j5 = j4;
j6 = j4 + npq; // j5:j6 - V mag of pq buses
/* evaluate F(x0) */
mis = Ybus.zMult(V, null).assign(cfunc.conj);
mis.assign(V, cfunc.mult).assign(Sbus, cfunc.minus);
F =
DoubleFactory1D.sparse.make(
new DoubleMatrix1D[] {
mis.viewSelection(pvpq).getRealPart(), mis.viewSelection(pq).getImaginaryPart()
});
/* check tolerance */
normF = DenseDoubleAlgebra.DEFAULT.norm(F, Norm.Infinity);
if (verbose > 0) System.out.print("(Newton)\n");
if (verbose > 1) {
System.out.printf("\n it max P & Q mismatch (p.u.)");
System.out.printf("\n---- ---------------------------");
System.out.printf("\n%3d %10.3e", i, normF);
}
if (normF < tol) {
converged = true;
if (verbose > 1) System.out.printf("\nConverged!\n");
}
/* do Newton iterations */
while ((!converged) & (i < max_it)) {
/* update iteration counter */
i += 1;
/* evaluate Jacobian */
dSbus_dV = Djp_dSbus_dV.jp_dSbus_dV(Ybus, V);
dSbus_dVm = dSbus_dV[0];
dSbus_dVa = dSbus_dV[1];
J11 = dSbus_dVa.getRealPart().viewSelection(pvpq, pvpq).copy();
J12 = dSbus_dVm.getRealPart().viewSelection(pvpq, pq).copy();
J21 = dSbus_dVa.getImaginaryPart().viewSelection(pq, pvpq).copy();
J22 = dSbus_dVm.getImaginaryPart().viewSelection(pq, pq).copy();
J1 = DoubleFactory2D.sparse.appendColumns(J11, J12);
J2 = DoubleFactory2D.sparse.appendColumns(J21, J22);
J = DoubleFactory2D.sparse.appendRows(J1, J2);
JJ = new SparseRCDoubleMatrix2D(J.rows(), J.columns());
JJ.assign(J);
dx = SparseDoubleAlgebra.DEFAULT.solve(JJ, F).assign(dfunc.neg);
dxz = Djp_util.complex(dx, null);
/* update voltage */
if (npv > 0)
Va.viewSelection(pv).assign(dxz.viewSelection(Djp_util.irange(j1, j2)), cfunc.plus);
if (npq > 0) {
Va.viewSelection(pq).assign(dxz.viewSelection(Djp_util.irange(j3, j4)), cfunc.plus);
Vm.viewSelection(pq).assign(dxz.viewSelection(Djp_util.irange(j5, j6)), cfunc.plus);
}
V = Djp_util.polar(Vm.getRealPart(), Va.getRealPart());
/* update Vm and Va again in case we wrapped around with a negative Vm */
Va = V.copy().assign(cfunc.arg);
Vm = V.copy().assign(cfunc.abs);
/* evalute F(x) */
mis = Ybus.zMult(V, null).assign(cfunc.conj);
mis.assign(V, cfunc.mult).assign(Sbus, cfunc.minus);
F =
DoubleFactory1D.sparse.make(
new DoubleMatrix1D[] {
mis.viewSelection(pvpq).getRealPart(), mis.viewSelection(pq).getImaginaryPart()
});
/* check for convergence */
normF = DenseDoubleAlgebra.DEFAULT.norm(F, Norm.Infinity);
if (verbose > 1) System.out.printf("\n%3d %10.3e", i, normF);
if (normF < tol) {
converged = true;
if (verbose > 0)
System.out.printf("\nNewton's method power flow converged in %d iterations.\n", i);
}
}
if (verbose > 0)
if (!converged)
System.out.printf("\nNewton''s method power did not converge in %d iterations.\n", i);
return new Object[] {V, converged, i};
}
