def system_function(x, Y, pv_inds, slack_inds, s):
nb = Y.shape[0]
vX = x[:2*nb]
pF = powerflow(vX,Y)
C = PowerNetwork.get_C(pv_inds, slack_inds, nb)
pF += C.T.dot(x[2*nb:])
out = np.hstack([C.dot(x[:2*nb]), pF]) - s
return out
def lamed(self):
"""lamed, the Phoenician name for lambda. (As the word lambda is
reserved in Python.)"""
if self._lamed is None:
eH = powerflow(self.ev, self.extY)
resid = self.eb - eH
rresid = resid[self.reindr2eindr]
out = spsl.lsqr(self.C, rresid, atol=1e-14, btol=1e-14)
# assert out[3] < 1e-8
self._lamed = np.matrix(out[0]).T
return self._lamed
def lamed(self):
"""lamed, the Phoenician name for lambda. (As the word lambda is
reserved in Python.)"""
if self._lamed is None:
eH = powerflow(self.ev, self.extY)
resid = self.eb - eH
rresid = resid[self.reindr2eindr]
out = spsl.lsqr(self.C, rresid, atol=1e-14, btol=1e-14)
# assert out[3] < 1e-8
self._lamed = np.matrix(out[0]).T
return self._lamed
def dHdv(self):
"""Compute the reordered extended Jacobian matrix."""
if self._dHdv is None:
en = self.en
extY = self.extY
e2r = self.eindr2reindr
vM = self.ev[en:]
vTheta = self.ev[:en]
vC = vM * np.exp(1j * vTheta)
vA = np.exp(1j * vTheta)
s = powerflow(self.ev, extY)
s = s[:en] + 1j * s[en:]
ij = []
data = []
def add_element(i, j, val):
ij.append(i)
ij.append(j)
data.append(val)
for i, j in zip(*extY.nonzero()):
val = np.imag(vC[i] * np.conj(extY[i, j] * vC[j]))
add_element(e2r[i], e2r[j], val)
val = np.real(vC[i] * np.conj(extY[i, j] * vA[j]))
add_element(e2r[i], e2r[en + j], val)
val = np.real(-vC[i] * np.conj(extY[i, j] * vC[j]))
add_element(e2r[en + i], e2r[j], val)
val = np.imag(vC[i] * np.conj(extY[i, j] * vA[j]))
add_element(e2r[en + i], e2r[en + j], val)
extYvC = extY.dot(vC)
for i in xrange(en):
if s[i] == 0 and extYvC[i] == 0:
continue
add_element(e2r[i], e2r[i], -np.imag(s[i]))
add_element(e2r[i], e2r[en + i],
np.real(vA[i] * np.conj(extYvC[i])))
add_element(e2r[en + i], e2r[i], np.real(s[i]))
add_element(e2r[en + i], e2r[en + i],
np.imag(vA[i] * np.conj(extYvC[i])))
ij = np.reshape(ij, (2, len(ij) / 2), order='F')
self._dHdv = sps.csr_matrix((data, ij), shape=(2 * en, 2 * en))
return self._dHdv
def dHdv(self):
"""Compute the reordered extended Jacobian matrix."""
if self._dHdv is None:
en = self.en
extY = self.extY
e2r = self.eindr2reindr
vM = self.ev[en:]
vTheta = self.ev[:en]
vC = vM * np.exp(1j * vTheta)
vA = np.exp(1j*vTheta)
s = powerflow(self.ev, extY)
s = s[:en] + 1j * s[en:]
ij = []
data = []
def add_element(i,j,val):
ij.append(i)
ij.append(j)
data.append(val)
for i,j in zip(*extY.nonzero()):
val = np.imag(vC[i] * np.conj(extY[i,j] * vC[j]))
add_element(e2r[i], e2r[j], val)
val = np.real(vC[i] * np.conj(extY[i,j] * vA[j]))
add_element(e2r[i], e2r[en+j], val)
val = np.real(-vC[i] * np.conj(extY[i,j] * vC[j]))
add_element(e2r[en+i], e2r[j], val)
val = np.imag(vC[i] * np.conj(extY[i,j] * vA[j]))
add_element(e2r[en+i], e2r[en+j], val)
extYvC = extY.dot(vC)
for i in xrange(en):
if s[i] == 0 and extYvC[i] == 0:
continue
add_element(e2r[ i], e2r[ i], -np.imag(s[i]))
add_element(e2r[ i], e2r[en+i],
np.real(vA[i] * np.conj(extYvC[i])))
add_element(e2r[en+i], e2r[ i], np.real(s[i]))
add_element(e2r[en+i], e2r[en+i],
np.imag(vA[i] * np.conj(extYvC[i])))
ij = np.reshape(ij, (2, len(ij)/2), order='F')
self._dHdv = sps.csr_matrix((data, ij), shape=(2*en, 2*en))
return self._dHdv