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line.py
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line.py
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import importlib
import logging
from cvxopt import matrix, spmatrix, sparse, spdiag, printing # NOQA
from cvxopt import mul, div # NOQA
from .base import ModelBase
from ..consts import Gy # NOQA
from ..consts import deg2rad
from ..utils.math import polar, conj
logger = logging.getLogger(__name__)
pd = None
printing.options['dformat'] = '%.3f'
printing.options['width'] = -1
class Line(ModelBase):
"""AC transmission line lumped model"""
def __init__(self, system, name):
super().__init__(system, name)
self._group = 'Series'
self._name = 'Line'
self._data.update({
'r': 0.0,
'x': 1e-6,
'b': 0.0,
'g': 0.0,
'b1': 0.0,
'g1': 0.0,
'b2': 0.0,
'g2': 0.0,
'bus1': None,
'bus2': None,
'Vn2': 110.0,
'xcoord': None,
'ycoord': None,
'trasf': False,
'tap': 1.0,
'phi': 0,
'fn': 60,
'owner': 0,
'rate_a': 0,
})
self._units.update({
'r': 'pu',
'x': 'pu',
'b': 'pu',
'g': 'pu',
'b1': 'pu',
'g1': 'pu',
'b2': 'pu',
'g2': 'pu',
'bus1': 'na',
'bus2': 'na',
'Vn2': 'kV',
'xcoord': 'deg',
'ycoord': 'deg',
'trasf': 'na',
'tap': 'na',
'phi': 'deg',
'fn': 'Hz',
'owner': 'na',
'rate_a': 'pu',
})
self._descr.update({
'r': 'connection line resistance',
'x': 'connection line reactance',
'g': 'shared shunt conductance',
'b': 'shared shunt susceptance',
'g1': 'from-side conductance',
'b1': 'from-side susceptance',
'g2': 'to-side conductance',
'b2': 'to-side susceptance',
'bus1': 'idx of from bus',
'bus2': 'idx of to bus',
'Vn2': 'rated voltage of bus2',
'xcoord': 'x coordinates',
'ycoord': 'y coordinates',
'trasf': 'transformer branch flag',
'tap': 'transformer branch tap ratio',
'phi': 'transformer branch phase shift in rad',
'fn': 'rated frequency',
'owner': 'owner code',
'rate_a': 'phase a power flow limit',
})
self._params.extend([
'r', 'x', 'b', 'g', 'b1', 'g1', 'b2', 'g2', 'tap', 'phi', 'fn',
'rate_a'
])
self._service.extend([
'a', 'v', 'a1', 'a2', 'S1', 'S2', 'nb', 'gy_store', 'y1', 'y2',
'y12', 'm', 'm2', 'mconj'
])
self.calls.update({
'gcall': True,
'gycall': True,
'init0': True,
'pflow': True,
'series': True,
'flows': True
})
self._ac = {'bus1': ['a1', 'v1'], 'bus2': ['a2', 'v2']}
self._config['is_series'] = True
self.rebuild = True
self.Y = []
self.C = []
self.Bp = []
self.Bpp = []
self._init()
def setup(self):
self._param_to_matrix()
self.nb = int(self.system.Bus.n)
self.system.config.nseries += self.n
self.r += 1e-10
self.b += 1e-10
self.g1 += 0.5 * self.g
self.b1 += 0.5 * self.b
self.g2 += 0.5 * self.g
self.b2 += 0.5 * self.b
def build_y(self):
"""Build transmission line admittance matrix into self.Y"""
if not self.n:
return
self.y1 = mul(self.u, self.g1 + self.b1 * 1j)
self.y2 = mul(self.u, self.g2 + self.b2 * 1j)
self.y12 = div(self.u, self.r + self.x * 1j)
self.m = polar(self.tap, self.phi * deg2rad)
self.m2 = abs(self.m)**2
self.mconj = conj(self.m)
# build self and mutual admittances into Y
self.Y = spmatrix(
div(self.y12 + self.y1, self.m2), self.a1, self.a1,
(self.nb, self.nb), 'z')
self.Y -= spmatrix(
div(self.y12, self.mconj), self.a1, self.a2, (self.nb, self.nb),
'z')
self.Y -= spmatrix(
div(self.y12, self.m), self.a2, self.a1, (self.nb, self.nb), 'z')
self.Y += spmatrix(self.y12 + self.y2, self.a2, self.a2,
(self.nb, self.nb), 'z')
# avoid singularity
# for item in range(self.nb):
# if abs(self.Y[item, item]) == 0:
# self.Y[item, item] = 1e-6 + 0j
def build_b(self):
"""build Bp and Bpp for fast decoupled method"""
if not self.n:
return
method = self.system.pflow.config.method.lower()
# Build B prime matrix
y1 = mul(
self.u, self.g1
) # y1 neglects line charging shunt, and g1 is usually 0 in HV lines
y2 = mul(
self.u, self.g2
) # y2 neglects line charging shunt, and g2 is usually 0 in HV lines
m = polar(1.0, self.phi * deg2rad) # neglected tap ratio
self.mconj = conj(m)
m2 = matrix(1.0, (self.n, 1), 'z')
if method in ('fdxb', 'dcpf'):
# neglect line resistance in Bp in XB method
y12 = div(self.u, self.x * 1j)
else:
y12 = div(self.u, self.r + self.x * 1j)
self.Bp = spmatrix(
div(y12 + y1, m2), self.a1, self.a1, (self.nb, self.nb), 'z')
self.Bp -= spmatrix(
div(y12, conj(m)), self.a1, self.a2, (self.nb, self.nb), 'z')
self.Bp -= spmatrix(
div(y12, m), self.a2, self.a1, (self.nb, self.nb), 'z')
self.Bp += spmatrix(y12 + y2, self.a2, self.a2, (self.nb, self.nb),
'z')
self.Bp = self.Bp.imag()
# Build B double prime matrix
y1 = mul(
self.u, self.g1 + self.b1 * 1j
) # y1 neglected line charging shunt, and g1 is usually 0 in HV lines
y2 = mul(
self.u, self.g2 + self.b2 * 1j
) # y2 neglected line charging shunt, and g2 is usually 0 in HV lines
m = self.tap + 0j # neglected phase shifter
m2 = abs(m)**2 + 0j
if method in ('fdbx', 'fdpf', 'dcpf'):
# neglect line resistance in Bpp in BX method
y12 = div(self.u, self.x * 1j)
else:
y12 = div(self.u, self.r + self.x * 1j)
self.Bpp = spmatrix(
div(y12 + y1, m2), self.a1, self.a1, (self.nb, self.nb), 'z')
self.Bpp -= spmatrix(
div(y12, conj(m)), self.a1, self.a2, (self.nb, self.nb), 'z')
self.Bpp -= spmatrix(
div(y12, m), self.a2, self.a1, (self.nb, self.nb), 'z')
self.Bpp += spmatrix(y12 + y2, self.a2, self.a2, (self.nb, self.nb),
'z')
self.Bpp = self.Bpp.imag()
for item in range(self.nb):
if abs(self.Bp[item, item]) == 0:
self.Bp[item, item] = 1e-6 + 0j
if abs(self.Bpp[item, item]) == 0:
self.Bpp[item, item] = 1e-6 + 0j
def incidence(self):
"""Build incidence matrix into self.C"""
self.C = \
spmatrix(self.u, range(self.n), self.a1, (self.n, self.nb), 'd') -\
spmatrix(self.u, range(self.n), self.a2, (self.n, self.nb), 'd')
def connectivity(self, bus):
"""check connectivity of network using Goderya's algorithm"""
if not self.n:
return
n = self.nb
fr = self.a1
to = self.a2
os = [0] * self.n
# find islanded buses
diag = list(
matrix(
spmatrix(self.u, to, os, (n, 1), 'd') +
spmatrix(self.u, fr, os, (n, 1), 'd')))
nib = bus.n_islanded_buses = diag.count(0)
bus.islanded_buses = []
for idx in range(n):
if diag[idx] == 0:
bus.islanded_buses.append(idx)
# find islanded areas
temp = spmatrix(
list(self.u) * 4, fr + to + fr + to, to + fr + fr + to, (n, n),
'd')
cons = temp[0, :]
nelm = len(cons.J)
conn = spmatrix([], [], [], (1, n), 'd')
bus.island_sets = []
idx = islands = 0
enum = 0
while 1:
while 1:
cons = cons * temp
cons = sparse(cons) # remove zero values
new_nelm = len(cons.J)
if new_nelm == nelm:
break
nelm = new_nelm
if len(cons.J) == n: # all buses are interconnected
return
bus.island_sets.append(list(cons.J))
conn += cons
islands += 1
nconn = len(conn.J)
if nconn >= (n - nib):
bus.island_sets = [i for i in bus.island_sets if i != []]
break
for element in conn.J[idx:]:
if not diag[idx]:
enum += 1 # skip islanded buses
if element <= enum:
idx += 1
enum += 1
else:
break
cons = temp[enum, :]
def init0(self, dae):
self.copy_data_ext('Bus', 'a', dest='a', idx=None, astype=list)
self.copy_data_ext('Bus', 'v', dest='v', idx=None, astype=list)
method = self.system.pflow.config.method.lower()
self.build_y()
self.incidence()
if method in ('fdpf', 'fdbx', 'fdxb', 'dcpf'):
self.build_b()
def gcall(self, dae):
if self.system.pflow.config.method == 'DCPF':
return
if self.rebuild:
self.build_y()
self.rebuild = False
vc = polar(dae.y[self.v], dae.y[self.a])
Ic = self.Y * vc
S = mul(vc, conj(Ic))
dae.g[self.a] += S.real()
dae.g[self.v] += S.imag()
def gycall(self, dae):
gy = self.build_gy(dae)
dae.add_jac(Gy, gy.V, gy.I, gy.J)
def build_gy(self, dae):
"""Build line Jacobian matrix"""
if not self.n:
idx = range(dae.m)
dae.set_jac(Gy, 1e-6, idx, idx)
return
Vn = polar(1.0, dae.y[self.a])
Vc = mul(dae.y[self.v], Vn)
Ic = self.Y * Vc
diagVn = spdiag(Vn)
diagVc = spdiag(Vc)
diagIc = spdiag(Ic)
dS = self.Y * diagVn
dS = diagVc * conj(dS)
dS += conj(diagIc) * diagVn
dR = diagIc
dR -= self.Y * diagVc
dR = diagVc.H.T * dR
self.gy_store = sparse([[dR.imag(), dR.real()], [dS.real(),
dS.imag()]])
return self.gy_store
def seriesflow(self, dae):
"""
Compute the flow through the line after solving PF.
Compute terminal injections, line losses
"""
# Vm = dae.y[self.v]
# Va = dae.y[self.a]
# V1 = polar(Vm[self.a1], Va[self.a1])
# V2 = polar(Vm[self.a2], Va[self.a2])
I1 = mul(self.v1, div(self.y12 + self.y1, self.m2)) - mul(self.v2, div(self.y12, self.mconj))
I2 = mul(self.v2, self.y12 + self.y2) - mul(self.v1, div(self.y12, self.m))
self.I1_real = I1.real()
self.I1_imag = I1.imag()
self.I2_real = I2.real()
self.I2_imag = I2.imag()
self.S1 = mul(self.v1, conj(I1))
self.S2 = mul(self.v2, conj(I2))
self.P1 = self.S1.real()
self.P2 = self.S2.real()
self.Q1 = self.S1.imag()
self.Q2 = self.S2.imag()
self.chg1 = mul(self.g1 + 1j * self.b1, div(self.v1**2, self.m2))
self.chg2 = mul(self.g2 + 1j * self.b2, self.v2**2)
self.Pchg1 = self.chg1.real()
self.Pchg2 = self.chg2.real()
self.Qchg1 = self.chg1.imag()
self.Qchg2 = self.chg2.imag()
self._line_flows = matrix([self.P1, self.P2, self.Q1, self.Q2,
self.I1_real, self.I1_imag,
self.I2_real, self.I2_imag])
@property
def v1(self):
"""Return voltage phasors at the "from buses" (bus1)"""
Vm = self.system.dae.y[self.v]
Va = self.system.dae.y[self.a]
return polar(Vm[self.a1], Va[self.a1])
@property
def v2(self):
"""Return voltage phasors at the "to buses" (bus2)"""
Vm = self.system.dae.y[self.v]
Va = self.system.dae.y[self.a]
return polar(Vm[self.a2], Va[self.a2])
def switch(self, idx, u):
"""switch the status of Line idx"""
self.u[self.uid[idx]] = u
self.rebuild = True
self.system.dae.factorize = True
logger.debug('<Line> Status switch to {} on idx {}.'.format(u, idx))
def build_name_from_bus(self):
"""Rebuild line names from bus names"""
pass
def _varname_flow(self):
"""Build variable names for Pij, Pji, Qij, Qji, Sij, Sji"""
if not self.n:
return
mpq = self.system.dae.m + 2 * self.system.Bus.n
nl = self.n
# Pij
xy_idx = range(mpq, mpq + nl)
self.system.varname.append(
listname='unamey',
xy_idx=xy_idx,
var_name='Pij',
element_name=self.name)
self.system.varname.append(
listname='fnamey',
xy_idx=xy_idx,
var_name='P_{ij}',
element_name=self.name)
# Pji
xy_idx = range(mpq + nl, mpq + 2 * nl)
self.system.varname.append(
listname='unamey',
xy_idx=xy_idx,
var_name='Pji',
element_name=self.name)
self.system.varname.append(
listname='fnamey',
xy_idx=xy_idx,
var_name='P_{ji}',
element_name=self.name)
# Qij
xy_idx = range(mpq + 2 * nl, mpq + 3 * nl)
self.system.varname.append(
listname='unamey',
xy_idx=xy_idx,
var_name='Qij',
element_name=self.name)
self.system.varname.append(
listname='fnamey',
xy_idx=xy_idx,
var_name='Q_{ij}',
element_name=self.name)
# Qji
xy_idx = range(mpq + 3 * nl, mpq + 4 * nl)
self.system.varname.append(
listname='unamey',
xy_idx=xy_idx,
var_name='Qji',
element_name=self.name)
self.system.varname.append(
listname='fnamey',
xy_idx=xy_idx,
var_name='Q_{ji}',
element_name=self.name)
# Iij Real
xy_idx = range(mpq + 4 * nl, mpq + 5 * nl)
self.system.varname.append(
listname='unamey',
xy_idx=xy_idx,
var_name='Iij_Re',
element_name=self.name)
self.system.varname.append(
listname='fnamey',
xy_idx=xy_idx,
var_name='\\Re(I_{ij})',
element_name=self.name)
# Iij Imag
xy_idx = range(mpq + 5 * nl, mpq + 6 * nl)
self.system.varname.append(
listname='unamey',
xy_idx=xy_idx,
var_name='Iij_Im',
element_name=self.name)
self.system.varname.append(
listname='fnamey',
xy_idx=xy_idx,
var_name='\\Im(I_{ij})',
element_name=self.name)
# Iji Real
xy_idx = range(mpq + 6 * nl, mpq + 7 * nl)
self.system.varname.append(
listname='unamey',
xy_idx=xy_idx,
var_name='Iji_Re',
element_name=self.name)
self.system.varname.append(
listname='fnamey',
xy_idx=xy_idx,
var_name='\\Re(I_{ji})',
element_name=self.name)
# Iji Imag
xy_idx = range(mpq + 7 * nl, mpq + 8 * nl)
self.system.varname.append(
listname='unamey',
xy_idx=xy_idx,
var_name='Iji_Im',
element_name=self.name)
self.system.varname.append(
listname='fnamey',
xy_idx=xy_idx,
var_name='\\Im(I_{ji})',
element_name=self.name)
def get_flow_by_idx(self, idx, bus):
"""Return seriesflow based on the external idx on the `bus` side"""
P, Q = [], []
if not isinstance(idx, list):
idx = [idx]
if not isinstance(bus, list):
bus = [bus]
for line_idx, bus_idx in zip(idx, bus):
line_int = self.uid[line_idx]
if bus_idx == self.bus1[line_int]:
P.append(self.P1[line_int])
Q.append(self.Q1[line_int])
elif bus_idx == self.bus2[line_int]:
P.append(self.P2[line_int])
Q.append(self.Q2[line_int])
return matrix(P), matrix(Q)
def leaf_bus(self, df=False):
"""
Return leaf bus idx, line idx, and the line foreign key
Returns
-------
(list, list, list) or DataFrame
"""
# leafs - leaf bus idx
# lines - line idx
# fkey - the foreign key of Line, in 'bus1' or 'bus2', linking the bus
leafs, lines, fkeys = list(), list(), list()
# convert to unique, ordered list
buses = sorted(list(set(self.bus1 + self.bus2)))
links = self.link_bus(buses)
for bus, link in zip(buses, links):
line = link[0]
fkey = link[1]
if line is None:
continue
if len(line) == 1:
leafs.append(bus)
lines.extend(line)
fkeys.extend(fkey)
# output formatting
if df is False:
return leafs, lines, fkeys
else:
_data = {'Bus idx': leafs, 'Line idx': lines, 'fkey': fkeys}
if globals()['pd'] is None:
globals()['pd'] = importlib.import_module('pandas')
return pd.DataFrame(data=_data)