def optimal_power_flow_energy_reserve(*args):
casedata = args[0] # Target power flow modelling
beta = args[1] # The reserve level
mpc = loadcase(casedata) # Import the power flow modelling
## convert to internal indexing
mpc = ext2int(mpc)
baseMVA, bus, gen, branch,gencost = mpc["baseMVA"], mpc["bus"], mpc["gen"], mpc["branch"],mpc["gencost"] #
nb = shape(mpc['bus'])[0] ## number of buses
nl = shape(mpc['branch'])[0] ## number of branches
ng = shape(mpc['gen'])[0] ## number of dispatchable injections
## Formualte the
stat = branch[:, BR_STATUS] ## ones at in-service branches
b = stat / branch[:, BR_X] ## series susceptance
tap = ones(nl) ## default tap ratio = 1
i = find(branch[:, TAP]) ## indices of non-zero tap ratios
tap[i] = branch[i, TAP] ## assign non-zero tap ratios
## build connection matrix Cft = Cf - Ct for line and from - to buses
f = branch[:, F_BUS] ## list of "from" buses
t = branch[:, T_BUS] ## list of "to" buses
i = r_[range(nl), range(nl)] ## double set of row indices
## connection matrix
Cft = sparse((r_[ones(nl), -ones(nl)], (i, r_[f, t])), (nl, nb))
## build Bf such that Bf * Va is the vector of real branch powers injected
## at each branch's "from" bus
Bf = sparse((r_[b, -b], (i, r_[f, t])), shape=(nl, nb)) ## = spdiags(b, 0, nl, nl) * Cft
## build Bbus
Bbus = Cft.T * Bf
# The distribution factor
Distribution_factor = sparse(Bf*inv(Bbus))
Cg = sparse((ones(ng), (gen[:, GEN_BUS], arange(ng))), (nb, ng)) # Sparse index generation method is different from the way of matlab
Cd = sparse((ones(nb), (bus[:, BUS_I], arange(nb))), (nb, nb)) # Sparse index load
Pd = sum(bus[:,PD]) # Total power demand
# Formulate the problem
lb = concatenate((gen[:,PMIN],zeros(ng))) # extend the
ub = concatenate((gen[:,PMAX],gen[:,PMAX]))
Aeq = sparse(concatenate((ones(ng),zeros(ng))))
beq = [Pd]
Aineq = sparse(hstack([Distribution_factor * Cg,zeros((nl,ng))]))
Aineq = vstack([Aineq, -Aineq])
# The ramp reserve requirement
Aineq = vstack([Aineq, sparse((r_[ones(ng), ones(ng)], (r_[arange(ng), arange(ng)], r_[arange(ng), ng+arange(ng)])), (ng, 2*ng))])
Aineq = vstack([Aineq, sparse((r_[-ones(ng), ones(ng)], (r_[arange(ng), arange(ng)], r_[arange(ng), ng+arange(ng)])), (ng, 2*ng))])
bineq = concatenate((branch[:, RATE_A] + Distribution_factor * Cd * bus[:, PD], branch[:, RATE_A] - Distribution_factor * Cd * bus[:, PD]))
bineq = concatenate((bineq, gen[:, PMAX]))
bineq = concatenate((bineq, -gen[:, PMIN]))
c = concatenate((gencost[:,5],zeros(ng)))
Q = diag(concatenate((gencost[:,4],zeros(ng))))
(Pg,obj) = miqp_gurobi(c = c,Q = Q, Aeq = Aeq, beq = beq, A = Aineq, b = bineq, xmin = lb,xmax = ub)
obj = obj + sum(gencost[:,6])
return Pg, obj
def draw_network(fignr=754): from matplotlib.pyplot import figure, show import networkx as nx casedata = get_topology() ppc = casedata ppopt = ppoption(PF_ALG=2) ppc = ext2int(ppc) figure(fignr) g = nx.Graph() i = ppc['bus'][:, BUS_I].astype(int) g.add_nodes_from(i, bgcolor='green') #nx.draw_networkx_nodes(g,pos=nx.spring_layout(g)) fr = ppc['branch'][:, F_BUS].astype(int) to = ppc['branch'][:, T_BUS].astype(int) g.add_edges_from(zip(fr, to), color='magenta') nx.draw(g, with_labels=True, node_size=1000,node_color='skyblue',width=0.5) show()
def draw_network(fignr=754):
from matplotlib.pyplot import figure, show
import networkx as nx
casedata = get_topology()
ppc = casedata
ppopt = ppoption(PF_ALG=2)
ppc = ext2int(ppc)
figure(fignr)
g = nx.Graph()
i = ppc['bus'][:, BUS_I].astype(int)
g.add_nodes_from(i, bgcolor='green')
#nx.draw_networkx_nodes(g,pos=nx.spring_layout(g))
fr = ppc['branch'][:, F_BUS].astype(int)
to = ppc['branch'][:, T_BUS].astype(int)
g.add_edges_from(zip(fr, to), color='magenta')
nx.draw(g,
with_labels=True,
node_size=1000,
node_color='skyblue',
width=0.5)
show()
def run(mpc):
"""
Gurobi based optimal power flow modelling and solution
:param mpc: The input case of optimal power flow
:return: obtained solution
"""
# Data format
from pypower.idx_brch import F_BUS, T_BUS, BR_R, BR_X, TAP, SHIFT, BR_STATUS, RATE_A
from pypower.idx_cost import MODEL, NCOST, PW_LINEAR, COST, POLYNOMIAL
from pypower.idx_bus import BUS_TYPE, REF, VA, VM, PD, GS, VMAX, VMIN, BUS_I, QD
from pypower.idx_gen import GEN_BUS, VG, PG, QG, PMAX, PMIN, QMAX, QMIN
from pypower.ext2int import ext2int
mpc = ext2int(mpc)
baseMVA, bus, gen, branch, gencost = mpc["baseMVA"], mpc["bus"], mpc[
"gen"], mpc["branch"], mpc["gencost"]
nb = shape(mpc['bus'])[0] # number of buses
nl = shape(mpc['branch'])[0] # number of branches
ng = shape(mpc['gen'])[0] # number of dispatchable injections
f = branch[:, F_BUS] ## list of "from" buses
t = branch[:, T_BUS] ## list of "to" buses
i = range(nl) ## double set of row indices
# Connection matrix
Cf = sparse((ones(nl), (i, f)), (nl, nb))
Ct = sparse((ones(nl), (i, t)), (nl, nb))
Cg = sparse((ones(ng), (gen[:, GEN_BUS], range(ng))), (nb, ng))
Branch_R = branch[:, BR_R]
Branch_X = branch[:, BR_X]
Cf = Cf.T
Ct = Ct.T
# Obtain the boundary information
Slmax = branch[:, RATE_A] / baseMVA
Pij_l = -Slmax
Qij_l = -Slmax
Iij_l = zeros(nl)
Vm_l = turn_to_power(bus[:, VMIN], 2)
Pg_l = gen[:, PMIN] / baseMVA
Qg_l = gen[:, QMIN] / baseMVA
Pij_u = Slmax
Qij_u = Slmax
Iij_u = Slmax
Vm_u = turn_to_power(bus[:, VMAX], 2)
Pg_u = 2 * gen[:, PMAX] / baseMVA
Qg_u = 2 * gen[:, QMAX] / baseMVA
lx = concatenate([Pij_l, Qij_l, Iij_l, Vm_l, Pg_l, Qg_l])
ux = concatenate([Pij_u, Qij_u, Iij_u, Vm_u, Pg_u, Qg_u])
model = Model("OPF")
# Define the decision variables
x = {}
nx = 3 * nl + nb + 2 * ng
for i in range(nx):
x[i] = model.addVar(lb=lx[i], ub=ux[i], vtype=GRB.CONTINUOUS)
# Add system level constraints
Aeq_p = hstack([
Ct - Cf,
zeros((nb, nl)), -diag(Ct * Branch_R) * Ct,
zeros((nb, nb)), Cg,
zeros((nb, ng))
])
beq_p = bus[:, PD] / baseMVA
# Add constraints for each sub system
Aeq_q = hstack([
zeros((nb, nl)), Ct - Cf, -diag(Ct * Branch_X) * Ct,
zeros((nb, nb)),
zeros((nb, ng)), Cg
])
beq_q = bus[:, QD] / baseMVA
Aeq_KVL = hstack([
-2 * diags(Branch_R), -2 * diags(Branch_X),
diags(turn_to_power(Branch_R, 2)) + diags(turn_to_power(Branch_X, 2)),
Cf.T - Ct.T,
zeros((nl, 2 * ng))
])
beq_KVL = zeros(nl)
Aeq = vstack([Aeq_p, Aeq_q, Aeq_KVL])
Aeq = Aeq.todense()
beq = concatenate([beq_p, beq_q, beq_KVL])
neq = len(beq)
for i in range(neq):
expr = 0
for j in range(nx):
expr += x[j] * Aeq[i, j]
model.addConstr(lhs=expr, sense=GRB.EQUAL, rhs=beq[i])
for i in range(nl):
model.addConstr(x[i] * x[i] + x[i + nl] * x[i + nl] <=
x[i + 2 * nl] * x[f[i] + 3 * nl],
name='"rc{0}"'.format(i))
obj = 0
for i in range(ng):
obj += gencost[i, 4] * x[i + 3 * nl + nb] * x[
i + 3 * nl + nb] * baseMVA * baseMVA + gencost[i, 5] * x[
i + 3 * nl + nb] * baseMVA + gencost[i, 6]
model.setObjective(obj)
model.Params.OutputFlag = 0
model.Params.LogToConsole = 0
model.Params.DisplayInterval = 1
model.optimize()
xx = []
for v in model.getVars():
xx.append(v.x)
obj = obj.getValue()
Pij = xx[0:nl]
Qij = xx[nl + 0:2 * nl]
Iij = xx[2 * nl:3 * nl]
Vi = xx[3 * nl:3 * nl + nb]
Pg = xx[3 * nl + nb:3 * nl + nb + ng]
Qg = xx[3 * nl + nb + ng:3 * nl + nb + 2 * ng]
# for i in range(nl): # branch indexing exchange
# if branch[i, F_BUS] > branch[i, T_BUS]:
# temp = branch[i, F_BUS]
# branch[i, F_BUS] = branch[i, T_BUS]
# branch[i, T_BUS] = temp
f = branch[:, F_BUS] ## list of "from" buses
t = branch[:, T_BUS] ## list of "to" buses
# i = range(nl) ## double set of row indices
area = ancestor_children_generation(f, t, range(nb))
Pi = Cg * Pg - bus[:, PD] / baseMVA
Qi = Cg * Qg - bus[:, QD] / baseMVA
for i in range(nb):
# If the bus is the root bus, only the children information is required.
if len(area[i]["Ai"]) == 0:
print(i)
expr = 0
for j in range(len(area[i]["Cbranch"][0])):
expr += Pij[area[i]["Cbranch"][0][j]]
print(expr - Pi[i])
expr = 0
for j in range(len(area[i]["Cbranch"][0])):
expr += Qij[area[i]["Cbranch"][0][j]]
print(expr - Qi[i])
elif len(area[i]["Cbranch"]) == 0: # This bus is the lead node
print(i)
print(Pij[area[i]["Abranch"][0][0]] -
Iij[area[i]["Abranch"][0][0]] *
Branch_R[area[i]["Abranch"][0][0]] + Pi[i])
print(Qij[area[i]["Abranch"][0][0]] -
Iij[area[i]["Abranch"][0][0]] *
Branch_X[area[i]["Abranch"][0][0]] + Qi[i])
print(Vi[int(area[i]["Ai"][0])] - Vi[i] -
2 * Branch_R[area[i]["Abranch"][0][0]] *
Pij[area[i]["Abranch"][0][0]] -
2 * Branch_X[area[i]["Abranch"][0][0]] *
Qij[area[i]["Abranch"][0][0]] +
Iij[area[i]["Abranch"][0][0]] *
(Branch_R[area[i]["Abranch"][0][0]]**2 +
Branch_X[area[i]["Abranch"][0][0]]**2))
print(
Pij[area[i]["Abranch"][0][0]] * Pij[area[i]["Abranch"][0][0]] +
Qij[area[i]["Abranch"][0][0]] * Qij[area[i]["Abranch"][0][0]]
<= Vi[int(area[i]["Ai"][0])] * Iij[area[i]["Abranch"][0][0]])
else:
print(i)
expr = 0
for j in range(len(area[i]["Cbranch"][0])):
expr += Pij[area[i]["Cbranch"][0][j]]
print(Pij[area[i]["Abranch"][0][0]] -
Iij[area[i]["Abranch"][0][0]] *
Branch_R[area[i]["Abranch"][0][0]] + Pi[i] - expr)
expr = 0
for j in range(len(area[i]["Cbranch"][0])):
expr += Qij[area[i]["Cbranch"][0][j]]
print(Qij[area[i]["Abranch"][0][0]] -
Iij[area[i]["Abranch"][0][0]] *
Branch_X[area[i]["Abranch"][0][0]] + Qi[i] - expr)
print(Vi[int(area[i]["Ai"][0])] - Vi[i] -
2 * Branch_R[area[i]["Abranch"][0][0]] *
Pij[area[i]["Abranch"][0][0]] -
2 * Branch_X[area[i]["Abranch"][0][0]] *
Qij[area[i]["Abranch"][0][0]] +
Iij[area[i]["Abranch"][0][0]] *
(Branch_R[area[i]["Abranch"][0][0]]**2 +
Branch_X[area[i]["Abranch"][0][0]]**2))
print(
Pij[area[i]["Abranch"][0][0]] * Pij[area[i]["Abranch"][0][0]] +
Qij[area[i]["Abranch"][0][0]] * Qij[area[i]["Abranch"][0][0]]
<= Vi[int(area[i]["Ai"][0])] * Iij[area[i]["Abranch"][0][0]])
obj = 0
for i in range(ng):
print(Pg[i] - Pi[int(gen[i, GEN_BUS])] -
bus[int(gen[i, GEN_BUS]), PD] / baseMVA)
print(Qg[i] - Qi[int(gen[i, GEN_BUS])] -
bus[int(gen[i, GEN_BUS]), QD] / baseMVA)
print(int(gen[i, GEN_BUS]))
obj += gencost[i, 4] * Pg[i] * Pg[i] * baseMVA * baseMVA + gencost[
i, 5] * Pg[i] * baseMVA + gencost[i, 6]
# Connection matrix
Cg = sparse((ones(ng), (gen[:, GEN_BUS], range(ng))), (nb, ng))
Branch_R = branch[:, BR_R]
Branch_X = branch[:, BR_X]
# Obtain the boundary information
Slmax = branch[:, RATE_A] / baseMVA
Pij_l = -Slmax
Qij_l = -Slmax
Iij_l = zeros(nl)
Vm_l = turn_to_power(bus[:, VMIN], 2)
Pg_l = gen[:, PMIN] / baseMVA
Qg_l = gen[:, QMIN] / baseMVA
Pi_l = -bus[:, PD] / baseMVA + Cg * Pg_l / baseMVA
Qi_l = -bus[:, QD] / baseMVA + Cg * Qg_l / baseMVA
Pij_u = Slmax
Qij_u = Slmax
Iij_u = Slmax
Vm_u = turn_to_power(bus[:, VMAX], 2)
Pg_u = 2 * gen[:, PMAX] / baseMVA
Qg_u = 2 * gen[:, QMAX] / baseMVA
Pi_u = -bus[:, PD] / baseMVA + Cg * Pg_u # Boundary error
Qi_u = -bus[:, QD] / baseMVA + Cg * Qg_u # Boundary error
model = Model("OPF")
# Define the decision variables, compact set
Pij = {}
Qij = {}
Iij = {}
Vi = {}
Pg = {}
Qg = {}
Pi = {}
Qi = {}
for i in range(nl):
Pij[i] = model.addVar(lb=Pij_l[i],
ub=Pij_u[i],
vtype=GRB.CONTINUOUS,
name="Pij{0}".format(i))
Qij[i] = model.addVar(lb=Qij_l[i],
ub=Qij_u[i],
vtype=GRB.CONTINUOUS,
name="Qij{0}".format(i))
Iij[i] = model.addVar(lb=Iij_l[i],
ub=Iij_u[i],
vtype=GRB.CONTINUOUS,
name="Iij{0}".format(i))
for i in range(nb):
Vi[i] = model.addVar(lb=Vm_l[i],
ub=Vm_u[i],
vtype=GRB.CONTINUOUS,
name="V{0}".format(i))
for i in range(ng):
Pg[i] = model.addVar(lb=Pg_l[i],
ub=Pg_u[i],
vtype=GRB.CONTINUOUS,
name="Pg{0}".format(i))
Qg[i] = model.addVar(lb=Qg_l[i],
ub=Qg_u[i],
vtype=GRB.CONTINUOUS,
name="Qg{0}".format(i))
for i in range(nb):
Pi[i] = model.addVar(lb=Pi_l[i],
ub=Pi_u[i],
vtype=GRB.CONTINUOUS,
name="Pi{0}".format(i))
Qi[i] = model.addVar(lb=Qi_l[i],
ub=Qi_u[i],
vtype=GRB.CONTINUOUS,
name="Qi{0}".format(i))
# For each area, before decomposition
# Add system level constraints
for i in range(nb):
# If the bus is the root bus, only the children information is required.
if len(area[i]["Ai"]) == 0:
expr = 0
for j in range(len(area[i]["Cbranch"][0])):
expr += Pij[area[i]["Cbranch"][0][j]]
model.addConstr(lhs=expr - Pi[i], sense=GRB.EQUAL, rhs=0)
expr = 0
for j in range(len(area[i]["Cbranch"][0])):
expr += Qij[area[i]["Cbranch"][0][j]]
model.addConstr(lhs=expr - Qi[i], sense=GRB.EQUAL, rhs=0)
elif len(area[i]["Cbranch"]) == 0: # This bus is the lead node
model.addConstr(lhs=Pij[area[i]["Abranch"][0][0]] -
Iij[area[i]["Abranch"][0][0]] *
Branch_R[area[i]["Abranch"][0][0]] + Pi[i],
sense=GRB.EQUAL,
rhs=0)
model.addConstr(lhs=Qij[area[i]["Abranch"][0][0]] -
Iij[area[i]["Abranch"][0][0]] *
Branch_X[area[i]["Abranch"][0][0]] + Qi[i],
sense=GRB.EQUAL,
rhs=0)
model.addConstr(lhs=Vi[int(area[i]["Ai"][0])] - Vi[i] -
2 * Branch_R[area[i]["Abranch"][0][0]] *
Pij[area[i]["Abranch"][0][0]] -
2 * Branch_X[area[i]["Abranch"][0][0]] *
Qij[area[i]["Abranch"][0][0]] +
Iij[area[i]["Abranch"][0][0]] *
(Branch_R[area[i]["Abranch"][0][0]]**2 +
Branch_X[area[i]["Abranch"][0][0]]**2),
sense=GRB.EQUAL,
rhs=0)
model.addConstr(
Pij[area[i]["Abranch"][0][0]] * Pij[area[i]["Abranch"][0][0]] +
Qij[area[i]["Abranch"][0][0]] * Qij[area[i]["Abranch"][0][0]]
<= Vi[area[i]["Ai"][0]] * Iij[area[i]["Abranch"][0][0]],
name="rc{0}".format(i))
else:
expr = 0
for j in range(len(area[i]["Cbranch"][0])):
expr += Pij[area[i]["Cbranch"][0][j]]
model.addConstr(lhs=Pij[area[i]["Abranch"][0][0]] -
Iij[area[i]["Abranch"][0][0]] *
Branch_R[area[i]["Abranch"][0][0]] + Pi[i] - expr,
sense=GRB.EQUAL,
rhs=0)
expr = 0
for j in range(len(area[i]["Cbranch"][0])):
expr += Qij[area[i]["Cbranch"][0][j]]
model.addConstr(lhs=Qij[area[i]["Abranch"][0][0]] -
Iij[area[i]["Abranch"][0][0]] *
Branch_X[area[i]["Abranch"][0][0]] + Qi[i] - expr,
sense=GRB.EQUAL,
rhs=0)
model.addConstr(lhs=Vi[int(area[i]["Ai"][0])] - Vi[i] -
2 * Branch_R[area[i]["Abranch"][0][0]] *
Pij[area[i]["Abranch"][0][0]] -
2 * Branch_X[area[i]["Abranch"][0][0]] *
Qij[area[i]["Abranch"][0][0]] +
Iij[area[i]["Abranch"][0][0]] *
(Branch_R[area[i]["Abranch"][0][0]]**2 +
Branch_X[area[i]["Abranch"][0][0]]**2),
sense=GRB.EQUAL,
rhs=0)
model.addConstr(
Pij[area[i]["Abranch"][0][0]] * Pij[area[i]["Abranch"][0][0]] +
Qij[area[i]["Abranch"][0][0]] * Qij[area[i]["Abranch"][0][0]]
<= Vi[area[i]["Ai"][0]] * Iij[area[i]["Abranch"][0][0]],
name="rc{0}".format(i))
obj = 0
for i in range(ng):
model.addConstr(lhs=Pg[i] - Pi[int(gen[i, GEN_BUS])],
sense=GRB.EQUAL,
rhs=bus[int(gen[i, GEN_BUS]), PD] / baseMVA)
model.addConstr(lhs=Qg[i] - Qi[int(gen[i, GEN_BUS])],
sense=GRB.EQUAL,
rhs=bus[int(gen[i, GEN_BUS]), QD] / baseMVA)
obj += gencost[i, 4] * Pg[i] * Pg[i] * baseMVA * baseMVA + gencost[
i, 5] * Pg[i] * baseMVA + gencost[i, 6]
model.setObjective(obj)
model.Params.OutputFlag = 0
model.Params.LogToConsole = 0
model.Params.DisplayInterval = 1
model.optimize()
Pij = []
Qij = []
Iij = []
Vi = []
Pg = []
Qg = []
Pi = []
Qi = []
for i in range(nl):
Pij.append(model.getVarByName("Pij{0}".format(i)).X)
Qij.append(model.getVarByName("Qij{0}".format(i)).X)
Iij.append(model.getVarByName("Iij{0}".format(i)).X)
for i in range(nb):
Vi.append(model.getVarByName("V{0}".format(i)).X)
Pi.append(model.getVarByName("Pi{0}".format(i)).X)
Qi.append(model.getVarByName("Qi{0}".format(i)).X)
for i in range(ng):
Pg.append(model.getVarByName("Pg{0}".format(i)).X)
Qg.append(model.getVarByName("Qg{0}".format(i)).X)
obj = obj.getValue()
primal_residual = []
for i in range(nl):
primal_residual.append(Pij[i] * Pij[i] + Qij[i] * Qij[i] -
Iij[i] * Vi[int(f[i])])
return obj, primal_residual
def Ybus(ppc):
ppc = ext2int(ppc)
baseMVA, bus, gen, branch = ppc["baseMVA"], ppc["bus"], ppc["gen"], ppc[
"branch"]
Ybus, Yf, Yt = makeYbus(baseMVA, bus, branch)
return Ybus
def run_sim(ppc, elements, dynopt=None, events=None, recorder=None):
"""
Run a time-domain simulation
Inputs:
ppc PYPOWER load flow case
elements Dictionary of dynamic model objects (machines, controllers, etc) with Object ID as key
events Events object
recorder Recorder object (empty)
Outputs:
recorder Recorder object (with data)
"""
#########
# SETUP #
#########
# Get version information
ver = pydyn_ver()
print('PYPOWER-Dynamics ' + ver['Version'] + ', ' + ver['Date'])
# Program options
if dynopt:
h = dynopt['h']
t_sim = dynopt['t_sim']
max_err = dynopt['max_err']
max_iter = dynopt['max_iter']
verbose = dynopt['verbose']
else:
# Default program options
h = 0.01 # step length (s)
t_sim = 5 # simulation time (s)
max_err = 0.0001 # Maximum error in network iteration (voltage mismatches)
max_iter = 25 # Maximum number of network iterations
verbose = False
if dynopt['sample_period']:
sample_rate = max(int(dynopt['sample_period'] / h) - 1, 0)
else:
sample_rate = 0
# Make lists of current injection sources (generators, external grids, etc) and controllers
sources = []
controllers = []
for element in elements.values():
if element.__module__ in [
'pydyn.sym_order6a', 'pydyn.sym_order6b', 'pydyn.sym_order4',
'pydyn.ext_grid', 'pydyn.vsc_average', 'pydyn.asym_1cage',
'pydyn.asym_2cage'
]:
sources.append(element)
if element.__module__ == 'pydyn.controller':
controllers.append(element)
# Set up interfaces
interfaces = init_interfaces(elements)
interfaces0 = init_interfaces0(elements)
# find events
events_controllers = []
# find blocks that create events in controllers
for element_id in elements.keys():
element = elements[element_id]
if element.__module__ == 'pydyn.controller':
for line in element.equations:
if line[1] == 'EVENT':
new_event = [element_id, line[0], line[2]] + line[3:]
events_controllers.append(new_event)
##################
# INITIALISATION #
##################
print('Initialising models...')
if not verbose:
ppopt = ppoption(VERBOSE=0, OUT_ALL=0)
else:
ppopt = ppoption()
#print('not verbose')
# Run power flow and update bus voltages and angles in PYPOWER case object
results, success = runpf(ppc, ppopt)
ppc["bus"][:, VM] = results["bus"][:, VM]
ppc["bus"][:, VA] = results["bus"][:, VA]
# Build Ybus matrix
ppc_int = ext2int(ppc)
baseMVA, bus, branch = ppc_int["baseMVA"], ppc_int["bus"], ppc_int[
"branch"]
Ybus, Yf, Yt = makeYbus(baseMVA, bus, branch)
# Build modified Ybus matrix
try:
Ybus = mod_Ybus(Ybus, elements, bus, ppc_int['gen'], baseMVA)
except:
bp()
Ybus = mod_Ybus(Ybus, elements, bus, ppc_int['gen'], baseMVA)
# Calculate initial voltage phasors
v0 = bus[:, VM] * (np.cos(np.radians(bus[:, VA])) +
1j * np.sin(np.radians(bus[:, VA])))
# Initialise sources from load flow
for source in sources:
if source.__module__ in ['pydyn.asym_1cage', 'pydyn.asym_2cage']:
# Asynchronous machine
source_bus = ppc_int['bus'][source.bus_no, 0].astype(np.int64)
v_source = v0[source_bus]
source.initialise(v_source, 0)
else:
# Generator or VSC
source_bus = ppc_int['gen'][source.gen_no, 0].astype(np.int64)
S_source = np.complex(results["gen"][source.gen_no, 1] / baseMVA,
results["gen"][source.gen_no, 2] / baseMVA)
v_source = v0[source_bus]
source.initialise(v_source, S_source)
# initialise bus
elements['bus'] = bus_int(ppc)
elements['sys_matrices'] = sys_matrices_int(ppc)
#elements['branch'] = ppc['branch']
# Do we need interfaces0?
# Interface controllers and machines (for initialisation)
#for intf in interfaces:
for k in range(len(interfaces)):
intf = interfaces[k]
intf0 = interfaces0[k]
int_type = intf[0]
var_name = intf0[1]
source_var = intf[1]
source_id = intf[2]
dest_var = intf[3]
dest_id = intf[4]
if int_type == 'OUTPUT':
# If an output, interface in the reverse direction for initialisation
#intf[2].signals[var_name] = intf[3].signals[var_name]
#if (intf0[2] != source_id) or (var_name != source_var) or (var_name != dest_var):
# bp()
elements[source_id].signals[source_var] = elements[
dest_id].signals[dest_var]
else:
# Inputs are interfaced in normal direction during initialisation
#intf[3].signals[var_name] = intf[2].signals[var_name]
#if (intf0[3] != dest_id) or (var_name != source_var) or (var_name != dest_var):
# bp()
elements[dest_id].signals[dest_var] = elements[source_id].signals[
source_var]
#try:
# element_source.signals[ var_name_source ] = element_dest.signals[ var_name_dest ]
#except:
# bp()
# Initialise controllers
for controller in controllers:
controller.initialise()
#############
# MAIN LOOP #
#############
sample_age = 0
if events == None:
print('Warning: no events!')
# Factorise Ybus matrix
Ybus_inv = splu(Ybus)
y1 = []
v_prev = v0
print('Simulating...')
for t in range(int(t_sim / h) + 1):
if np.mod(t, 1 / h) == 0 and verbose:
print('t=' + str(t * h) + 's')
# Interface controllers and machines
#for intf in interfaces:
for k in range(len(interfaces)):
intf = interfaces[k]
intf0 = interfaces0[k]
var_name = intf0[1]
source_var = intf[1]
source_id = intf[2]
dest_var = intf[3]
dest_id = intf[4]
#if var_name_dest not in element_dest.signals.keys():
#bp()
#element_dest.signals[ var_name_dest ] = element_source.signals[ var_name_source ]
#if (intf0[2] != source_id) or (var_name != source_var) or (var_name != dest_var) or (intf0[3] != dest_id):
# bp()
elements[dest_id].signals[dest_var] = elements[source_id].signals[
source_var]
#intf[3].signals[var_name] = intf[2].signals[var_name]
# Solve differential equations
for j in range(4):
# Solve step of differential equations
for element in elements.values():
try:
element.solve_step(h, j)
except:
bp()
element.solve_step(h, j)
# Interface with network equations
v_prev = solve_network(sources, v_prev, Ybus_inv, ppc_int,
len(bus), max_err, max_iter)
# check for events
for event_c in events_controllers:
new_event = None
ctrl = event_c[0]
ctrl_var = event_c[2]
var_result = event_c[1]
condition = elements[ctrl].signals[ctrl_var]
if condition >= 1:
#event_type = event_c[0]
#node = event_c[1]
new_event = [np.round(t * h, 5)] + event_c[3:]
#print(new_event)
try:
events.event_stack.append(new_event)
elements[ctrl].signals[var_result] = 1.0
#bp()
except:
bp()
else:
elements[ctrl].signals[var_result] = 0.0
if sample_age < sample_rate:
sample_age += 1
else:
sample_age = 0
if recorder != None:
# Record signals or states
recorder.record_variables(t * h, elements)
if events != None:
#if new_event != None:
# bp()
# Check event stack
ppc, refactorise = events.handle_events(np.round(t * h, 5),
elements, ppc, baseMVA)
if refactorise == True:
# Rebuild Ybus from new ppc_int
ppc_int = ext2int(ppc)
baseMVA, bus, branch = ppc_int["baseMVA"], ppc_int[
"bus"], ppc_int["branch"]
Ybus, Yf, Yt = makeYbus(baseMVA, bus, branch)
# Rebuild modified Ybus
Ybus = mod_Ybus(Ybus, elements, bus, ppc_int['gen'], baseMVA)
# Refactorise Ybus
Ybus_inv = splu(Ybus)
# Solve network equations
v_prev = solve_network(sources, v_prev, Ybus_inv, ppc_int,
len(bus), max_err, max_iter)
# update the voltage in 'bus' matrix
ppc['bus'][:, VM] = abs(v_prev)
ppc['bus'][:, VA] = 2 * np.arctan(v_prev.imag /
(abs(v_prev) + v_prev.real))
# update the system matrices
elements['bus'].update(ppc)
elements['sys_matrices'].update(ppc)
#bp()
return recorder
def run(mpc):
"""
Gurobi based optimal power flow modelling and solution
:param mpc: The input case of optimal power flow
:return: obtained solution
"""
mpc = ext2int(mpc)
baseMVA, bus, gen, branch, gencost = mpc["baseMVA"], mpc["bus"], mpc[
"gen"], mpc["branch"], mpc["gencost"]
nb = shape(mpc['bus'])[0] # number of buses
nl = shape(mpc['branch'])[0] # number of branches
ng = shape(mpc['gen'])[0] # number of dispatchable injections
f = branch[:, F_BUS] ## list of "from" buses
t = branch[:, T_BUS] ## list of "to" buses
# Modify the bus information
Branch_R = branch[:, BR_R]
Branch_X = branch[:, BR_X]
Slmax = branch[:, RATE_A] / baseMVA
gen[:, PMAX] = gen[:, PMAX] / baseMVA
gen[:, PMIN] = gen[:, PMIN] / baseMVA
gen[:, QMAX] = gen[:, QMAX] / baseMVA
gen[:, QMIN] = gen[:, QMIN] / baseMVA
gencost[:, 4] = gencost[:, 4] * baseMVA * baseMVA
gencost[:, 5] = gencost[:, 5] * baseMVA
bus[:, PD] = bus[:, PD] / baseMVA
bus[:, QD] = bus[:, QD] / baseMVA
area = ancestor_children_generation(f, t, nb, Branch_R, Branch_X, Slmax,
gen, bus, gencost, baseMVA)
# Initialize algorithm for each sub area
# 1) For each area, for self observation
# x:=[Pg,Qg,pi,qi,Pi,Qi,Vi,Ii]
# y:=[pi,qi,Pi,Qi,Vi,Ii,Pij,Qij,Vij,Iij]
f = f.tolist()
t = t.tolist()
for i in range(nb):
area[i]["PG"] = (area[i]["PGMAX"] + area[i]["PGMIN"]) / 2
area[i]["QG"] = (area[i]["QGMIN"] + area[i]["QGMAX"]) / 2
# Observation of x
area[i]["pi"] = area[i]["PG"] - area[i]["PD"]
area[i]["qi"] = area[i]["QG"] - area[i]["QD"]
area[i]["Pi"] = area[i]["pi"]
area[i]["Qi"] = area[i]["qi"]
area[i]["Vi"] = (area[i]["VMIN"] + area[i]["VMAX"]) / 2
if area[i]["TYPE"] != "ROOT":
area[i]["Ii"] = (area[i]["Pi"]**2 +
area[i]["Qi"]**2) / area[i]["Vi"]
# The self observation
area[i]["pi_y"] = area[i]["pi"]
area[i]["qi_y"] = area[i]["qi"]
if area[i]["TYPE"] != "ROOT":
area[i]["Vi_y"] = area[i]["Vi"]
area[i]["Ii_y"] = area[i]["Ii"]
area[i]["Pi_y"] = area[i]["Pi"]
area[i]["Qi_y"] = area[i]["Qi"]
# The multipliers
area[i]["mu_pi"] = area[i]["pi"] - area[i]["pi_y"]
area[i]["mu_qi"] = area[i]["qi"] - area[i]["qi_y"]
if area[i]["TYPE"] != "ROOT":
area[i]["mu_Vi"] = area[i]["Vi"] - area[i]["Vi_y"]
area[i]["mu_Ii"] = area[i]["Ii"] - area[i]["Ii_y"]
area[i]["mu_Pi"] = area[i]["Pi"] - area[i]["Pi_y"]
area[i]["mu_Qi"] = area[i]["Qi"] - area[i]["Qi_y"]
area[i]["COST"] = 0
# Spread the information to the observatory
observatory = []
# Store the voltage of parent bus and children power flow information
# 1)The ancestor bus voltage information is stored in the observotory
# 2)The children bus power and current information is stored in the observotory
for i in range(nl):
temp = {}
temp["Vij_x"] = area[int(f[i])]["Vi"]
temp["Pij_x"] = area[int(t[i])]["Pi"]
temp["Qij_x"] = area[int(t[i])]["Qi"]
temp["Iij_x"] = area[int(t[i])]["Ii"]
temp["Vij_y"] = area[int(f[i])]["Vi"]
temp["Pij_y"] = area[int(t[i])]["Pi"]
temp["Qij_y"] = area[int(t[i])]["Qi"]
temp["Iij_y"] = area[int(t[i])]["Ii"]
temp["mu_Vij"] = 0
temp["mu_Pij"] = 0
temp["mu_Qij"] = 0
temp["mu_Iij"] = 0
observatory.append(temp)
# Begin the iteration,
Gap = 1000
Gap_index = []
Dual_gap_index = []
Obj_index = []
k = 0
kmax = 10000
ru = 700
# The iteration
mu = 5
t = 2
while k <= kmax and Gap > 0.0001 * 2:
observatory0 = deepcopy(observatory)
area0 = deepcopy(area)
for i in range(nb):
(area, observatory) = sub_problem(area, observatory, i, ru / 2)
# # multiplier update
# for i in range(nb):
# area[i]["mu_pi"] += ru * (area[i]["pi"] - area[i]["pi_y"])
# area[i]["mu_qi"] += ru * (area[i]["qi"] - area[i]["qi_y"])
# if area[i]["TYPE"] != "ROOT":
# area[i]["mu_Vi"] += ru * (area[i]["Vi"] - area[i]["Vi_y"])
# area[i]["mu_Ii"] += ru * (area[i]["Ii"] - area[i]["Ii_y"])
# area[i]["mu_Pi"] += ru * (area[i]["Pi"] - area[i]["Pi_y"])
# area[i]["mu_Qi"] += ru * (area[i]["Qi"] - area[i]["Qi_y"])
# for i in range(nl):
# observatory[i]["mu_Vij"] += ru * (observatory[i]["Vij_x"] - observatory[i]["Vij_y"])
# observatory[i]["mu_Pij"] += ru * (observatory[i]["Pij_x"] - observatory[i]["Pij_y"])
# observatory[i]["mu_Qij"] += ru * (observatory[i]["Qij_x"] - observatory[i]["Qij_y"])
# observatory[i]["mu_Iij"] += ru * (observatory[i]["Iij_x"] - observatory[i]["Iij_y"])
# Calculate the gap
gap = 0
for i in range(nb):
gap += (area[i]["pi"] - area[i]["pi_y"])**2
gap += (area[i]["qi"] - area[i]["qi_y"])**2
if area[i]["TYPE"] != "ROOT":
gap += (area[i]["Vi"] - area[i]["Vi_y"])**2
gap += (area[i]["Ii"] - area[i]["Ii_y"])**2
gap += (area[i]["Pi"] - area[i]["Pi_y"])**2
gap += (area[i]["Qi"] - area[i]["Qi_y"])**2
for i in range(nl):
gap += (observatory[i]["Vij_x"] - observatory[i]["Vij_y"])**2
gap += (observatory[i]["Pij_x"] - observatory[i]["Pij_y"])**2
gap += (observatory[i]["Qij_x"] - observatory[i]["Qij_y"])**2
gap += (observatory[i]["Iij_x"] - observatory[i]["Iij_y"])**2
dual_gap = 0
for i in range(nb):
dual_gap += (area0[i]["pi_y"] - area[i]["pi_y"])**2
dual_gap += (area0[i]["qi_y"] - area[i]["qi_y"])**2
if area[i]["TYPE"] != "ROOT":
dual_gap += (area0[i]["Vi_y"] - area[i]["Vi_y"])**2
dual_gap += (area0[i]["Ii_y"] - area[i]["Ii_y"])**2
dual_gap += (area0[i]["Pi_y"] - area[i]["Pi_y"])**2
dual_gap += (area0[i]["Qi_y"] - area[i]["Qi_y"])**2
for i in range(nl):
dual_gap += (observatory0[i]["Vij_y"] - observatory[i]["Vij_y"])**2
dual_gap += (observatory0[i]["Pij_y"] - observatory[i]["Pij_y"])**2
dual_gap += (observatory0[i]["Qij_y"] - observatory[i]["Qij_y"])**2
dual_gap += (observatory0[i]["Iij_y"] - observatory[i]["Iij_y"])**2
# if dual_gap * mu < gap:
# ru = ru * t
# if gap * mu < dual_gap:
# ru = ru / t
Gap = sqrt(gap)
Gap_index.append(Gap)
Dual_gap_index.append(sqrt(dual_gap))
obj = 0
for i in range(nb):
obj += area[i]["COST"]
k = k + 1
print(k)
print(Gap)
print(obj)
print(sqrt(dual_gap))
# compute the objective function
obj = 0
for i in range(nb):
obj += area[i]["COST"]
Gap_index = array(Gap_index)
Dual_gap_index = array(Dual_gap_index)
plt.figure(1)
plt.subplot(211)
plt.plot(Gap_index)
plt.ylabel('Primal residual')
plt.subplot(212)
plt.plot(Dual_gap_index)
plt.ylabel('Dual residual')
plt.show()
return obj, area
def run(mpc):
"""
Gurobi based optimal power flow modelling and solution
:param mpc: The input case of optimal power flow
:return: obtained solution
"""
mpc = ext2int(mpc)
baseMVA, bus, gen, branch, gencost = mpc["baseMVA"], mpc["bus"], mpc["gen"], mpc["branch"], mpc["gencost"]
nb = shape(mpc['bus'])[0] # number of buses
nl = shape(mpc['branch'])[0] # number of branches
ng = shape(mpc['gen'])[0] # number of dispatchable injections
f = branch[:, F_BUS] ## list of "from" buses
t = branch[:, T_BUS] ## list of "to" buses
i = range(nl) ## double set of row indices
# Connection matrix
Cf = sparse((ones(nl), (i, f)), (nl, nb))
Ct = sparse((ones(nl), (i, t)), (nl, nb))
Cg = sparse((ones(ng), (gen[:, GEN_BUS], range(ng))), (nb, ng))
# Connection matrix
Cg = sparse((ones(ng), (gen[:, GEN_BUS], range(ng))), (nb, ng))
Branch_R = branch[:, BR_R]
Branch_X = branch[:, BR_X]
Slmax = branch[:, RATE_A] / baseMVA
gen[:, PMAX] = gen[:, PMAX] / baseMVA
gen[:, PMIN] = gen[:, PMIN] / baseMVA
gen[:, QMAX] = gen[:, QMAX] / baseMVA
gen[:, QMIN] = gen[:, QMIN] / baseMVA
gencost[:, 4] = gencost[:, 4] * baseMVA * baseMVA
gencost[:, 5] = gencost[:, 5] * baseMVA
bus[:, PD] = bus[:, PD] / baseMVA
bus[:, QD] = bus[:, QD] / baseMVA
area = ancestor_children_generation(f, t, nb, Branch_R, Branch_X, Slmax, gen, bus, gencost, baseMVA)
M = inf
# Formulate the centralized optimization problem according to the information provided by area
model = Model("OPF")
# Define the decision variables, compact set
# X variables
Pi_x = {}
Qi_x = {}
Ii_x = {}
Vi_x = {}
pi_x = {}
qi_x = {}
Pg = {}
Qg = {}
# Y variables
# Part 1), self observation
Pii_y = {}
Qii_y = {}
Iii_y = {}
Vii_y = {}
pii_y = {}
qii_y = {}
# Part 2), to the ancestor
Pij_y = {}
Qij_y = {}
Iij_y = {}
# Part 3), to the children. The definition is in accordance with the sequence of lines
Vij_y = {} # For the given branch
obj = 0
for i in range(nb): # The iteration from each bus
Pi_x[i] = model.addVar(lb=-area[i]["SMAX"], ub=area[i]["SMAX"], vtype=GRB.CONTINUOUS,
name="Pi_x{0}".format(i))
Qi_x[i] = model.addVar(lb=-area[i]["SMAX"], ub=area[i]["SMAX"], vtype=GRB.CONTINUOUS,
name="Qi_x{0}".format(i))
Ii_x[i] = model.addVar(lb=-area[i]["SMAX"], ub=area[i]["SMAX"], vtype=GRB.CONTINUOUS,
name="Ii_x{0}".format(i))
Vi_x[i] = model.addVar(lb=area[i]["VMIN"], ub=area[i]["VMAX"], vtype=GRB.CONTINUOUS,
name="Vi_x{0}".format(i))
pi_x[i] = model.addVar(lb=-M, ub=M, vtype=GRB.CONTINUOUS, name="pi_x{0}".format(i))
qi_x[i] = model.addVar(lb=-M, ub=M, vtype=GRB.CONTINUOUS, name="qi_x{0}".format(i))
Pg[i] = model.addVar(lb=area[i]["PGMIN"], ub=area[i]["PGMAX"], vtype=GRB.CONTINUOUS, name="Pgi{0}".format(i))
Qg[i] = model.addVar(lb=area[i]["QGMIN"], ub=area[i]["QGMAX"], vtype=GRB.CONTINUOUS, name="Qgi{0}".format(i))
Pii_y[i] = model.addVar(lb=-M, ub=M, vtype=GRB.CONTINUOUS, name="Pii_y{0}".format(i))
Qii_y[i] = model.addVar(lb=-M, ub=M, vtype=GRB.CONTINUOUS, name="Qii_y{0}".format(i))
Iii_y[i] = model.addVar(lb=-M, ub=M, vtype=GRB.CONTINUOUS, name="Iii_y{0}".format(i))
Vii_y[i] = model.addVar(lb=-M, ub=M, vtype=GRB.CONTINUOUS, name="Vii_y{0}".format(i))
pii_y[i] = model.addVar(lb=-M, ub=M, vtype=GRB.CONTINUOUS, name="pii_y{0}".format(i))
qii_y[i] = model.addVar(lb=-M, ub=M, vtype=GRB.CONTINUOUS, name="qii_y{0}".format(i))
# For each branch, the following observation variables should be introduced
# According to the sequence of lines
for i in range(nl):
Pij_y[i] = model.addVar(lb=-M, ub=M, vtype=GRB.CONTINUOUS, name="Pij_y{0}".format(i))
Qij_y[i] = model.addVar(lb=-M, ub=M, vtype=GRB.CONTINUOUS, name="Qij_y{0}".format(i))
Iij_y[i] = model.addVar(lb=-M, ub=M, vtype=GRB.CONTINUOUS, name="Iij_y{0}".format(i))
Vij_y[i] = model.addVar(lb=-M, ub=M, vtype=GRB.CONTINUOUS, name="Vij_y{0}".format(i))
for i in range(nb):
# Add constrain for each bus
model.addConstr(Pg[i] - pi_x[i] == area[i]["PD"])
model.addConstr(Qg[i] - qi_x[i] == area[i]["QD"])
model.addConstr(Pi_x[i] * Pi_x[i] + Qi_x[i] * Qi_x[i] <= Ii_x[i] * Vi_x[i])
# Update the objective function
obj += area[i]["a"] * Pg[i] * Pg[i] + area[i]["b"] * Pg[i] + area[i]["c"]
# Add constrain for the observation of each bus
# 1)Constrain for KCL equations
# 2)Constrain for KVL equations
if area[i]["TYPE"] == "ROOT":
# Only KCL equation is required
expr = 0
for j in range(len(area[i]["Ci"])):
expr += Pij_y[area[i]["Cbranch"][j]] - Iij_y[area[i]["Cbranch"][j]] * Branch_R[area[i]["Cbranch"][j]]
model.addConstr(pii_y[i] + expr == 0)
expr = 0
for j in range(len(area[i]["Ci"])):
expr += Qij_y[area[i]["Cbranch"][j]] - Iij_y[area[i]["Cbranch"][j]] * Branch_X[area[i]["Cbranch"][j]]
model.addConstr(qii_y[i] + expr == 0)
elif area[i]["TYPE"] == "LEAF": # Only KCL equation is required
model.addConstr(pii_y[i] - Pii_y[i] == 0)
model.addConstr(qii_y[i] - Qii_y[i] == 0)
model.addConstr(
Vij_y[area[i]["Abranch"]] - Vii_y[i] + 2 * area[i]["BR_R"] * Pii_y[i] + 2 * area[i]["BR_X"] * Qii_y[i] -
Iii_y[i] * (area[i]["BR_R"] ** 2 + area[i]["BR_X"] ** 2) == 0)
else:
expr = 0
for j in range(len(area[i]["Ci"])):
expr += Pij_y[area[i]["Cbranch"][j]] - Iij_y[area[i]["Cbranch"][j]] * Branch_R[area[i]["Cbranch"][j]]
model.addConstr(pii_y[i] - Pii_y[i] + expr == 0)
expr = 0
for j in range(len(area[i]["Ci"])):
expr += Qij_y[area[i]["Cbranch"][j]] - Iij_y[area[i]["Cbranch"][j]] * Branch_X[area[i]["Cbranch"][j]]
model.addConstr(qii_y[i] - Qii_y[i] + expr == 0)
model.addConstr(
Vij_y[area[i]["Abranch"]] - Vii_y[i] + 2 * area[i]["BR_R"] * Pii_y[i] + 2 * area[i]["BR_X"] * Qii_y[i] -
Iii_y[i] * (area[i]["BR_R"] ** 2 + area[i]["BR_X"] ** 2) == 0)
# Formulate consensus constraints
# Add constraints
# The introduction of Xii is to formulate the closed form of the solution
model.addConstr(Pii_y[i] == Pi_x[i])
model.addConstr(Qii_y[i] == Qi_x[i])
model.addConstr(Vii_y[i] == Vi_x[i])
model.addConstr(Iii_y[i] == Ii_x[i])
model.addConstr(pii_y[i] == pi_x[i])
model.addConstr(qii_y[i] == qi_x[i])
# For each branch
for i in range(nl): # which stands for the observatory for each line; The observatory constraints
model.addConstr(Vij_y[i] == Vi_x[f[i]])
model.addConstr(Pij_y[i] == Pi_x[t[i]])
model.addConstr(Qij_y[i] == Qi_x[t[i]])
model.addConstr(Iij_y[i] == Ii_x[t[i]])
# from the perspective of nodes
# for i in range(nb):
# if area[i]["nChildren"] != 0:
# for j in range(area[i]["nChildren"]):
# model.addConstr(Vi_x[i] == Vij_y[area[i]["Cbranch"][j]])
# if area[i]["TYPE"] != "ROOT":
# model.addConstr(Pi_x[i] == Pij_y[area[i]["Abranch"]])
# model.addConstr(Qi_x[i] == Qij_y[area[i]["Abranch"]])
# model.addConstr(Ii_x[i] == Iij_y[area[i]["Abranch"]])
model.setObjective(obj)
model.Params.OutputFlag = 1
model.Params.LogToConsole = 1
model.Params.DisplayInterval = 1
model.optimize()
Pi = []
Qi = []
Ii = []
Vi = []
pi = []
qi = []
pg = []
qg = []
for i in range(nb):
Pi.append(model.getVarByName("Pi_x{0}".format(i)).X)
Qi.append(model.getVarByName("Pi_x{0}".format(i)).X)
Ii.append(model.getVarByName("Ii_x{0}".format(i)).X)
Vi.append(model.getVarByName("Vi_x{0}".format(i)).X)
pi.append(model.getVarByName("pi_x{0}".format(i)).X)
qi.append(model.getVarByName("qi_x{0}".format(i)).X)
pg.append(model.getVarByName("Pgi{0}".format(i)).X)
qg.append(model.getVarByName("Qgi{0}".format(i)).X)
obj = obj.getValue()
primal_residual = []
for i in range(nb):
primal_residual.append(Pi[i] * Pi[i] + Qi[i] * Qi[i] - Ii[i] * Vi[i])
return obj, primal_residual
def run(mpc):
"""
Gurobi based optimal power flow modelling and solution
:param mpc: The input case of optimal power flow
:return: obtained solution
"""
# Data format
from pypower.idx_brch import F_BUS, T_BUS, BR_R, BR_X, TAP, SHIFT, BR_STATUS, RATE_A
from pypower.idx_cost import MODEL, NCOST, PW_LINEAR, COST, POLYNOMIAL
from pypower.idx_bus import BUS_TYPE, REF, VA, VM, PD, GS, VMAX, VMIN, BUS_I, QD
from pypower.idx_gen import GEN_BUS, VG, PG, QG, PMAX, PMIN, QMAX, QMIN
from pypower.ext2int import ext2int
mpc = ext2int(mpc)
baseMVA, bus, gen, branch, gencost = mpc["baseMVA"], mpc["bus"], mpc[
"gen"], mpc["branch"], mpc["gencost"]
nb = shape(mpc['bus'])[0] ## number of buses
nl = shape(mpc['branch'])[0] ## number of branches
ng = shape(mpc['gen'])[0] ## number of dispatchable injections
f = branch[:, F_BUS] ## list of "from" buses
t = branch[:, T_BUS] ## list of "to" buses
i = range(nl) ## double set of row indices
# Connection matrix
Cf = sparse((ones(nl), (i, f)), (nl, nb))
Ct = sparse((ones(nl), (i, t)), (nl, nb))
Cg = sparse((ones(ng), (gen[:, GEN_BUS], range(ng))), (nb, ng))
Branch_R = branch[:, BR_R]
Branch_X = branch[:, BR_X]
Cf = Cf.T
Ct = Ct.T
# Obtain the boundary information
Slmax = branch[:, RATE_A] / baseMVA
Pij_l = -Slmax
Qij_l = -Slmax
Iij_l = zeros(nl)
Vm_l = turn_to_power(bus[:, VMIN], 2)
Pg_l = gen[:, PMIN] / baseMVA
Qg_l = gen[:, QMIN] / baseMVA
Pij_u = Slmax
Qij_u = Slmax
Iij_u = Slmax
Vm_u = turn_to_power(bus[:, VMAX], 2)
Pg_u = 2 * gen[:, PMAX] / baseMVA
Qg_u = 2 * gen[:, QMAX] / baseMVA
lx = concatenate([Pij_l, Qij_l, Iij_l, Vm_l, Pg_l, Qg_l])
ux = concatenate([Pij_u, Qij_u, Iij_u, Vm_u, Pg_u, Qg_u])
model = Model("OPF")
# Define the decision variables
x = {}
nx = 3 * nl + nb + 2 * ng
for i in range(nx):
x[i] = model.addVar(lb=lx[i], ub=ux[i], vtype=GRB.CONTINUOUS)
# Add system level constraints
Aeq_p = hstack([
Ct - Cf,
zeros((nb, nl)), -diag(Ct * Branch_R) * Ct,
zeros((nb, nb)), Cg,
zeros((nb, ng))
])
beq_p = bus[:, PD] / baseMVA
# Add constraints for each sub system
Aeq_q = hstack([
zeros((nb, nl)), Ct - Cf, -diag(Ct * Branch_X) * Ct,
zeros((nb, nb)),
zeros((nb, ng)), Cg
])
beq_q = bus[:, QD] / baseMVA
Aeq_KVL = hstack([
-2 * diags(Branch_R), -2 * diags(Branch_X),
diags(turn_to_power(Branch_R, 2)) + diags(turn_to_power(Branch_X, 2)),
Cf.T - Ct.T,
zeros((nl, 2 * ng))
])
beq_KVL = zeros(nl)
Aeq = vstack([Aeq_p, Aeq_q, Aeq_KVL])
Aeq = Aeq.todense()
beq = concatenate([beq_p, beq_q, beq_KVL])
neq = len(beq)
for i in range(neq):
expr = 0
for j in range(nx):
expr += x[j] * Aeq[i, j]
model.addConstr(lhs=expr, sense=GRB.EQUAL, rhs=beq[i])
for i in range(nl):
model.addConstr(x[i] * x[i] + x[i + nl] * x[i + nl] <=
x[i + 2 * nl] * x[f[i] + 3 * nl],
name='"rc{0}"'.format(i))
obj = 0
for i in range(ng):
obj += gencost[i, 4] * x[i + 3 * nl + nb] * x[
i + 3 * nl + nb] * baseMVA * baseMVA + gencost[i, 5] * x[
i + 3 * nl + nb] * baseMVA + gencost[i, 6]
model.setObjective(obj)
model.Params.OutputFlag = 0
model.Params.LogToConsole = 0
model.Params.DisplayInterval = 1
model.optimize()
xx = []
for v in model.getVars():
xx.append(v.x)
obj = obj.getValue()
Pij = xx[0:nl]
Qij = xx[nl + 0:2 * nl]
Iij = xx[2 * nl:3 * nl]
Vi = xx[3 * nl:3 * nl + nb]
Pg = xx[3 * nl + nb:3 * nl + nb + ng]
Qg = xx[3 * nl + nb + ng:3 * nl + nb + 2 * ng]
primal_residual = []
for i in range(nl):
primal_residual.append(Pij[i] * Pij[i] + Qij[i] * Qij[i] -
Iij[i] * Vi[int(f[i])])
return xx, obj, primal_residual
def run(mpc):
"""
Gurobi based optimal power flow modelling and solution
:param mpc: The input case of optimal power flow
:return: obtained solution
"""
mpc = ext2int(mpc)
baseMVA, bus, gen, branch, gencost = mpc["baseMVA"], mpc["bus"], mpc[
"gen"], mpc["branch"], mpc["gencost"]
nb = shape(mpc['bus'])[0] # number of buses
nl = shape(mpc['branch'])[0] # number of branches
ng = shape(mpc['gen'])[0] # number of dispatchable injections
f = branch[:, F_BUS] ## list of "from" buses
t = branch[:, T_BUS] ## list of "to" buses
i = range(nl) ## double set of row indices
# Connection matrix
Cf = sparse((ones(nl), (i, f)), (nl, nb))
Ct = sparse((ones(nl), (i, t)), (nl, nb))
Cg = sparse((ones(ng), (gen[:, GEN_BUS], range(ng))), (nb, ng))
# Connection matrix
Cg = sparse((ones(ng), (gen[:, GEN_BUS], range(ng))), (nb, ng))
Branch_R = branch[:, BR_R]
Branch_X = branch[:, BR_X]
Slmax = branch[:, RATE_A] / baseMVA
gen[:, PMAX] = gen[:, PMAX] / baseMVA
gen[:, PMIN] = gen[:, PMIN] / baseMVA
gen[:, QMAX] = gen[:, QMAX] / baseMVA
gen[:, QMIN] = gen[:, QMIN] / baseMVA
gencost[:, 4] = gencost[:, 4] * baseMVA * baseMVA
gencost[:, 5] = gencost[:, 5] * baseMVA
bus[:, PD] = bus[:, PD] / baseMVA
bus[:, QD] = bus[:, QD] / baseMVA
area = ancestor_children_generation(f, t, nb, Branch_R, Branch_X, Slmax,
gen, bus, gencost, baseMVA)
# Formulate the centralized optimization problem according to the information provided by area
# Generate the initial value
# 1) For the x-update
Pi_x0 = [0] * nb
Qi_x0 = [0] * nb
Ii_x0 = [1] * nb
Vi_x0 = [0] * nb
pi_x0 = [0] * nb
qi_x0 = [0] * nb
Pg0 = [0] * nb
Qg0 = [0] * nb
# 2) For the y-update
Pi_y0 = [0] * nb
Qi_y0 = [0] * nb
Ii_y0 = [0] * nb
Vi_y0 = [1] * nb
pi_y0 = [0] * nb
qi_y0 = [0] * nb
Pij_y0 = [0] * nl
Qij_y0 = [0] * nl
Iij_y0 = [0] * nl
Vij_y0 = [0] * nl
# 3) The multiplier part
mu_Pi = [0] * nb
mu_Qi = [0] * nb
mu_Ii = [0] * nb
mu_Vi = [0] * nb
mu_pi = [0] * nb
mu_qi = [0] * nb
mu_Pij = [0] * nl
mu_Qij = [0] * nl
mu_Iij = [0] * nl
mu_Vij = [0] * nl
f = f.tolist()
t = t.tolist()
for i in range(nl):
f[i] = int(f[i])
t[i] = int(t[i])
for i in range(nl):
Pij_y0[i] = Pi_x0[t[i]]
Qij_y0[i] = Qi_x0[t[i]]
Iij_y0[i] = Ii_x0[t[i]]
Vij_y0[i] = Vi_x0[f[i]]
Gap = 1000
Gap_index = []
k = 0
kmax = 10000
ru = 1000
half_ru = ru / 2
# The iteration
while k <= kmax and Gap > 0.001:
# Y variables
# Part 1), self observation
modelY = Model("Yupdate")
Pi_y = {}
Qi_y = {}
Ii_y = {}
Vi_y = {}
pi_y = {}
qi_y = {}
# Part 2), to the ancestor
Pij_y = {}
Qij_y = {}
Iij_y = {}
# Part 3), to the children. The definition is in accordance with the sequence of lines
Vij_y = {} # For the given branch
for i in range(nb): # The iteration from each bus
Pi_y[i] = modelY.addVar(lb=-inf,
ub=inf,
vtype=GRB.CONTINUOUS,
name="Pi_y{0}".format(i))
Qi_y[i] = modelY.addVar(lb=-inf,
ub=inf,
vtype=GRB.CONTINUOUS,
name="Qi_y{0}".format(i))
Ii_y[i] = modelY.addVar(lb=-inf,
ub=inf,
vtype=GRB.CONTINUOUS,
name="Ii_y{0}".format(i))
Vi_y[i] = modelY.addVar(lb=-inf,
ub=inf,
vtype=GRB.CONTINUOUS,
name="Vi_y{0}".format(i))
pi_y[i] = modelY.addVar(lb=-inf,
ub=inf,
vtype=GRB.CONTINUOUS,
name="pi_y{0}".format(i))
qi_y[i] = modelY.addVar(lb=-inf,
ub=inf,
vtype=GRB.CONTINUOUS,
name="qi_y{0}".format(i))
for i in range(nl): # The information stored in the observatory
Pij_y[i] = modelY.addVar(lb=-inf,
ub=inf,
vtype=GRB.CONTINUOUS,
name="Pij_y{0}".format(i))
Qij_y[i] = modelY.addVar(lb=-inf,
ub=inf,
vtype=GRB.CONTINUOUS,
name="Qij_y{0}".format(i))
Iij_y[i] = modelY.addVar(lb=-inf,
ub=inf,
vtype=GRB.CONTINUOUS,
name="Iij_y{0}".format(i))
Vij_y[i] = modelY.addVar(lb=-inf,
ub=inf,
vtype=GRB.CONTINUOUS,
name="Vij_y{0}".format(i))
for i in range(nb):
# Add constrain for the observation of each bus
# 1)Constrain for KCL equations
# 2)Constrain for KVL equations
if area[i]["TYPE"] == "ROOT":
# Only KCL equation is required
expr = 0
for j in range(area[i]["nCi"]):
expr += Pij_y[area[i]["Cbranch"][j]] - Iij_y[
area[i]["Cbranch"][j]] * area[i]["BR_R_C"][j]
modelY.addConstr(pi_y[i] + expr == 0)
expr = 0
for j in range(area[i]["nCi"]):
expr += Qij_y[area[i]["Cbranch"][j]] - Iij_y[
area[i]["Cbranch"][j]] * area[i]["BR_X_C"][j]
modelY.addConstr(qi_y[i] + expr == 0)
elif area[i]["TYPE"] == "LEAF": # Only KCL equation is required
modelY.addConstr(pi_y[i] - Pi_y[i] == 0)
modelY.addConstr(qi_y[i] - Qi_y[i] == 0)
modelY.addConstr(
Vij_y[area[i]["Abranch"]] - Vi_y[i] +
2 * area[i]["BR_R"] * Pi_y[i] +
2 * area[i]["BR_X"] * Qi_y[i] - Ii_y[i] *
(area[i]["BR_R"]**2 + area[i]["BR_X"]**2) == 0)
else:
expr = 0
for j in range(area[i]["nCi"]):
expr += Pij_y[area[i]["Cbranch"][j]] - Iij_y[
area[i]["Cbranch"][j]] * area[i]["BR_R_C"][j]
modelY.addConstr(pi_y[i] - Pi_y[i] + expr == 0)
expr = 0
for j in range(area[i]["nCi"]):
expr += Qij_y[area[i]["Cbranch"][j]] - Iij_y[
area[i]["Cbranch"][j]] * area[i]["BR_X_C"][j]
modelY.addConstr(qi_y[i] - Qi_y[i] + expr == 0)
modelY.addConstr(
Vij_y[area[i]["Abranch"]] - Vi_y[i] +
2 * area[i]["BR_R"] * Pi_y[i] +
2 * area[i]["BR_X"] * Qi_y[i] - Ii_y[i] *
(area[i]["BR_R"]**2 + area[i]["BR_X"]**2) == 0)
objY = 0
for i in range(nb):
objY += mu_Pi[i] * Pi_y[i] + half_ru * (Pi_y[i] - Pi_x0[i]) * (Pi_y[i] - Pi_x0[i]) + \
mu_Qi[i] * Qi_y[i] + half_ru * (Qi_y[i] - Qi_x0[i]) * (Qi_y[i] - Qi_x0[i]) + \
mu_Ii[i] * Ii_y[i] + half_ru * (Ii_y[i] - Ii_x0[i]) * (Ii_y[i] - Ii_x0[i]) + \
mu_Vi[i] * Vi_y[i] + half_ru * (Vi_y[i] - Vi_x0[i]) * (Vi_y[i] - Vi_x0[i]) + \
mu_pi[i] * pi_y[i] + half_ru * (pi_y[i] - pi_x0[i]) * (pi_y[i] - pi_x0[i]) + \
mu_qi[i] * qi_y[i] + half_ru * (qi_y[i] - qi_x0[i]) * (qi_y[i] - qi_x0[i])
for i in range(nl):
objY += mu_Pij[i] * Pij_y[i] + half_ru * (Pij_y[i] - Pi_x0[t[i]]) * (Pij_y[i] - Pi_x0[t[i]]) + \
mu_Qij[i] * Qij_y[i] + half_ru * (Qij_y[i] - Qi_x0[t[i]]) * (Qij_y[i] - Qi_x0[t[i]]) + \
mu_Iij[i] * Iij_y[i] + half_ru * (Iij_y[i] - Ii_x0[t[i]]) * (Iij_y[i] - Ii_x0[t[i]]) + \
mu_Vij[i] * Vij_y[i] + half_ru * (Vij_y[i] - Vi_x0[f[i]]) * (Vij_y[i] - Vi_x0[f[i]])
modelY.setObjective(objY)
modelY.Params.OutputFlag = 0
modelY.Params.LogToConsole = 0
modelY.Params.DisplayInterval = 1
modelY.Params.LogFile = ""
modelY.optimize()
for i in range(nb):
Pi_y0[i] = modelY.getVarByName("Pi_y{0}".format(i)).X
Qi_y0[i] = modelY.getVarByName("Qi_y{0}".format(i)).X
Ii_y0[i] = modelY.getVarByName("Ii_y{0}".format(i)).X
Vi_y0[i] = modelY.getVarByName("Vi_y{0}".format(i)).X
pi_y0[i] = modelY.getVarByName("pi_y{0}".format(i)).X
qi_y0[i] = modelY.getVarByName("qi_y{0}".format(i)).X
for i in range(nl):
Pij_y0[i] = modelY.getVarByName("Pij_y{0}".format(i)).X
Qij_y0[i] = modelY.getVarByName("Qij_y{0}".format(i)).X
Iij_y0[i] = modelY.getVarByName("Iij_y{0}".format(i)).X
Vij_y0[i] = modelY.getVarByName("Vij_y{0}".format(i)).X
del modelY
# The sub problems
modelX = Model("Xupdate")
# Define the decision variables, compact set
# X variables
Pi_x = {}
Qi_x = {}
Ii_x = {}
Vi_x = {}
pi_x = {}
qi_x = {}
Pg = {}
Qg = {}
objX = 0
for i in range(nb): # The iteration from each bus
Pi_x[i] = modelX.addVar(lb=-area[i]["SMAX"],
ub=area[i]["SMAX"],
vtype=GRB.CONTINUOUS,
name="Pi_x{0}".format(i))
Qi_x[i] = modelX.addVar(lb=-area[i]["SMAX"],
ub=area[i]["SMAX"],
vtype=GRB.CONTINUOUS,
name="Qi_x{0}".format(i))
Ii_x[i] = modelX.addVar(lb=-area[i]["SMAX"],
ub=area[i]["SMAX"],
vtype=GRB.CONTINUOUS,
name="Ii_x{0}".format(i))
Vi_x[i] = modelX.addVar(lb=area[i]["VMIN"],
ub=area[i]["VMAX"],
vtype=GRB.CONTINUOUS,
name="Vi_x{0}".format(i))
pi_x[i] = modelX.addVar(lb=-inf,
ub=inf,
vtype=GRB.CONTINUOUS,
name="pi_x{0}".format(i))
qi_x[i] = modelX.addVar(lb=-inf,
ub=inf,
vtype=GRB.CONTINUOUS,
name="qi_x{0}".format(i))
Pg[i] = modelX.addVar(lb=area[i]["PGMIN"],
ub=area[i]["PGMAX"],
vtype=GRB.CONTINUOUS,
name="Pgi{0}".format(i))
Qg[i] = modelX.addVar(lb=area[i]["QGMIN"],
ub=area[i]["QGMAX"],
vtype=GRB.CONTINUOUS,
name="Qgi{0}".format(i))
# For each branch, the following observation variables should be introduced
# According to the sequence of line
for i in range(nb):
# Add constrain for each bus
modelX.addConstr(Pg[i] - pi_x[i] == area[i]["PD"])
modelX.addConstr(Qg[i] - qi_x[i] == area[i]["QD"])
modelX.addConstr(
Pi_x[i] * Pi_x[i] + Qi_x[i] * Qi_x[i] <= Ii_x[i] * Vi_x[i])
for i in range(nb):
# Update the objective function
objX += area[i]["a"] * Pg[i] * Pg[i] + area[i]["b"] * Pg[i] + area[i]["c"] - \
mu_Pi[i] * Pi_x[i] + half_ru * (Pi_x[i] - Pi_y0[i]) * (Pi_x[i] - Pi_y0[i]) - \
mu_Qi[i] * Qi_x[i] + half_ru * (Qi_x[i] - Qi_y0[i]) * (Qi_x[i] - Qi_y0[i]) - \
mu_Ii[i] * Ii_x[i] + half_ru * (Ii_x[i] - Ii_y0[i]) * (Ii_x[i] - Ii_y0[i]) - \
mu_Vi[i] * Vi_x[i] + half_ru * (Vi_x[i] - Vi_y0[i]) * (Vi_x[i] - Vi_y0[i]) - \
mu_pi[i] * pi_x[i] + half_ru * (pi_x[i] - pi_y0[i]) * (pi_x[i] - pi_y0[i]) - \
mu_qi[i] * qi_x[i] + half_ru * (qi_x[i] - qi_y0[i]) * (qi_x[i] - qi_y0[i])
for i in range(nl):
objX += -mu_Pij[i] * Pi_x[t[i]] + half_ru * (Pi_x[t[i]] - Pij_y0[i]) * (Pi_x[t[i]] - Pij_y0[i]) \
- mu_Qij[i] * Qi_x[t[i]] + half_ru * (Qi_x[t[i]] - Qij_y0[i]) * (Qi_x[t[i]] - Qij_y0[i]) \
- mu_Iij[i] * Ii_x[t[i]] + half_ru * (Ii_x[t[i]] - Iij_y0[i]) * (Ii_x[t[i]] - Iij_y0[i]) \
- mu_Vij[i] * Vi_x[f[i]] + half_ru * (Vi_x[f[i]] - Vij_y0[i]) * (Vi_x[f[i]] - Vij_y0[i])
modelX.setObjective(objX)
modelX.Params.OutputFlag = 0
modelX.Params.LogToConsole = 0
modelX.Params.DisplayInterval = 1
modelX.Params.LogFile = ""
modelX.optimize()
for i in range(nb):
Pi_x0[i] = modelX.getVarByName("Pi_x{0}".format(i)).X
Qi_x0[i] = modelX.getVarByName("Qi_x{0}".format(i)).X
Ii_x0[i] = modelX.getVarByName("Ii_x{0}".format(i)).X
Vi_x0[i] = modelX.getVarByName("Vi_x{0}".format(i)).X
pi_x0[i] = modelX.getVarByName("pi_x{0}".format(i)).X
qi_x0[i] = modelX.getVarByName("qi_x{0}".format(i)).X
Pg0[i] = modelX.getVarByName("Pgi{0}".format(i)).X
Qg0[i] = modelX.getVarByName("Qgi{0}".format(i)).X
del modelX
# Update mutiplier
for i in range(nb):
mu_Pi[i] += ru * (Pi_y0[i] - Pi_x0[i])
mu_Qi[i] += ru * (Qi_y0[i] - Qi_x0[i])
mu_Ii[i] += ru * (Ii_y0[i] - Ii_x0[i])
mu_Vi[i] += ru * (Vi_y0[i] - Vi_x0[i])
mu_pi[i] += ru * (pi_y0[i] - pi_x0[i])
mu_qi[i] += ru * (qi_y0[i] - qi_x0[i])
for i in range(nl):
mu_Pij[i] += ru * (Pij_y0[i] - Pi_x0[t[i]])
mu_Qij[i] += ru * (Qij_y0[i] - Qi_x0[t[i]])
mu_Iij[i] += ru * (Iij_y0[i] - Ii_x0[t[i]])
mu_Vij[i] += ru * (Vij_y0[i] - Vi_x0[f[i]])
# Update residual
residual = 0
for i in range(nb):
residual += abs(Pi_y0[i] - Pi_x0[i])
residual += abs(Qi_y0[i] - Qi_x0[i])
residual += abs(Ii_y0[i] - Ii_x0[i])
residual += abs(Vi_y0[i] - Vi_x0[i])
residual += abs(pi_y0[i] - pi_x0[i])
residual += abs(qi_y0[i] - qi_x0[i])
for i in range(nl):
residual += abs(Pij_y0[i] - Pi_x0[t[i]])
residual += abs(Qij_y0[i] - Qi_x0[t[i]])
residual += abs(Iij_y0[i] - Ii_x0[t[i]])
residual += abs(Vij_y0[i] - Vi_x0[f[i]])
obj = 0
for i in range(nb):
obj += area[i]["a"] * Pg0[i] * Pg0[i] + area[i]["b"] * Pg0[
i] + area[i]["c"]
Gap = residual
k = k + 1
print(k)
print(Gap)
print(obj)
obj = 0
for i in range(nb):
obj += area[i]["a"] * Pg0[i] * Pg0[i] + area[i]["b"] * Pg0[i] + area[
i]["c"]
primal_residual = []
for i in range(nb):
primal_residual.append(Pi_x0[i] * Pi_x0[i] + Qi_x0[i] * Qi_x0[i] -
Ii_x0[i] * Vi_x0[i])
return obj, primal_residual
def runpf(casedata=None, ppopt=None, fname='', solvedcase=''):
"""Runs a power flow.
Runs a power flow [full AC Newton's method by default] and optionally
returns the solved values in the data matrices, a flag which is C{True} if
the algorithm was successful in finding a solution, and the elapsed
time in seconds. All input arguments are optional. If C{casename} is
provided it specifies the name of the input data file or dict
containing the power flow data. The default value is 'case9'.
If the ppopt is provided it overrides the default PYPOWER options
vector and can be used to specify the solution algorithm and output
options among other things. If the 3rd argument is given the pretty
printed output will be appended to the file whose name is given in
C{fname}. If C{solvedcase} is specified the solved case will be written
to a case file in PYPOWER format with the specified name. If C{solvedcase}
ends with '.mat' it saves the case as a MAT-file otherwise it saves it
as a Python-file.
If the C{ENFORCE_Q_LIMS} options is set to C{True} [default is false] then
if any generator reactive power limit is violated after running the AC
power flow, the corresponding bus is converted to a PQ bus, with Qg at
the limit, and the case is re-run. The voltage magnitude at the bus
will deviate from the specified value in order to satisfy the reactive
power limit. If the reference bus is converted to PQ, the first
remaining PV bus will be used as the slack bus for the next iteration.
This may result in the real power output at this generator being
slightly off from the specified values.
Enforcing of generator Q limits inspired by contributions from Mu Lin,
Lincoln University, New Zealand (1/14/05).
@author: Ray Zimmerman (PSERC Cornell)
"""
## default arguments
if casedata is None:
casedata = join(dirname(__file__), 'case9')
ppopt = ppoption(ppopt)
## options
verbose = ppopt["VERBOSE"]
qlim = ppopt["ENFORCE_Q_LIMS"] ## enforce Q limits on gens?
dc = ppopt["PF_DC"] ## use DC formulation?
## read data
ppc = loadcase(casedata)
## add zero columns to branch for flows if needed
if ppc["branch"].shape[1] < QT:
ppc["branch"] = c_[ppc["branch"],
zeros((ppc["branch"].shape[0],
QT - ppc["branch"].shape[1] + 1))]
## convert to internal indexing
ppc = ext2int(ppc)
baseMVA, bus, gen, branch = \
ppc["baseMVA"], ppc["bus"], ppc["gen"], ppc["branch"]
## get bus index lists of each type of bus
ref, pv, pq = bustypes(bus, gen)
## generator info
on = find(gen[:, GEN_STATUS] > 0) ## which generators are on?
gbus = gen[on, GEN_BUS].astype(int) ## what buses are they at?
##----- run the power flow -----
t0 = time()
if verbose > 0:
v = ppver('all')
stdout.write('PYPOWER Version %s, %s' % (v["Version"], v["Date"]))
if dc: # DC formulation
if verbose:
stdout.write(' -- DC Power Flow\n')
## initial state
Va0 = bus[:, VA] * (pi / 180)
## build B matrices and phase shift injections
B, Bf, Pbusinj, Pfinj = makeBdc(baseMVA, bus, branch)
## compute complex bus power injections [generation - load]
## adjusted for phase shifters and real shunts
Pbus = makeSbus(baseMVA, bus,
gen).real - Pbusinj - bus[:, GS] / baseMVA
## "run" the power flow
Va = dcpf(B, Pbus, Va0, ref, pv, pq)
## update data matrices with solution
branch[:, [QF, QT]] = zeros((branch.shape[0], 2))
branch[:, PF] = (Bf * Va + Pfinj) * baseMVA
branch[:, PT] = -branch[:, PF]
bus[:, VM] = ones(bus.shape[0])
bus[:, VA] = Va * (180 / pi)
## update Pg for slack generator (1st gen at ref bus)
## (note: other gens at ref bus are accounted for in Pbus)
## Pg = Pinj + Pload + Gs
## newPg = oldPg + newPinj - oldPinj
refgen = zeros(len(ref), dtype=int)
for k in range(len(ref)):
temp = find(gbus == ref[k])
refgen[k] = on[temp[0]]
gen[refgen,
PG] = gen[refgen, PG] + (B[ref, :] * Va - Pbus[ref]) * baseMVA
success = 1
else: ## AC formulation
alg = ppopt['PF_ALG']
if verbose > 0:
if alg == 1:
solver = 'Newton'
elif alg == 2:
solver = 'fast-decoupled, XB'
elif alg == 3:
solver = 'fast-decoupled, BX'
elif alg == 4:
solver = 'Gauss-Seidel'
else:
solver = 'unknown'
print(' -- AC Power Flow (%s)\n' % solver)
## initial state
# V0 = ones(bus.shape[0]) ## flat start
V0 = bus[:, VM] * exp(1j * pi / 180 * bus[:, VA])
V0[gbus] = gen[on, VG] / abs(V0[gbus]) * V0[gbus]
if qlim:
ref0 = ref ## save index and angle of
Varef0 = bus[ref0, VA] ## original reference bus(es)
limited = [] ## list of indices of gens @ Q lims
fixedQg = zeros(gen.shape[0]) ## Qg of gens at Q limits
repeat = True
while repeat:
## build admittance matrices
Ybus, Yf, Yt = makeYbus(baseMVA, bus, branch)
## compute complex bus power injections [generation - load]
Sbus = makeSbus(baseMVA, bus, gen)
## run the power flow
alg = ppopt["PF_ALG"]
if alg == 1:
V, success, _ = newtonpf(Ybus, Sbus, V0, ref, pv, pq, ppopt)
elif alg == 2 or alg == 3:
Bp, Bpp = makeB(baseMVA, bus, branch, alg)
V, success, _ = fdpf(Ybus, Sbus, V0, Bp, Bpp, ref, pv, pq,
ppopt)
elif alg == 4:
V, success, _ = gausspf(Ybus, Sbus, V0, ref, pv, pq, ppopt)
else:
stderr.write('Only Newton'
's method, fast-decoupled, and '
'Gauss-Seidel power flow algorithms currently '
'implemented.\n')
## update data matrices with solution
bus, gen, branch = pfsoln(baseMVA, bus, gen, branch, Ybus, Yf, Yt,
V, ref, pv, pq)
if qlim: ## enforce generator Q limits
## find gens with violated Q constraints
gen_status = gen[:, GEN_STATUS] > 0
qg_max_lim = gen[:, QG] > gen[:, QMAX]
qg_min_lim = gen[:, QG] < gen[:, QMIN]
mx = find(gen_status & qg_max_lim)
mn = find(gen_status & qg_min_lim)
if len(mx) > 0 or len(
mn) > 0: ## we have some Q limit violations
# No PV generators
if len(pv) == 0:
if verbose:
if len(mx) > 0:
print(
'Gen %d [only one left] exceeds upper Q limit : INFEASIBLE PROBLEM\n'
% mx + 1)
else:
print(
'Gen %d [only one left] exceeds lower Q limit : INFEASIBLE PROBLEM\n'
% mn + 1)
success = 0
break
## one at a time?
if qlim == 2: ## fix largest violation, ignore the rest
k = argmax(r_[gen[mx, QG] - gen[mx, QMAX],
gen[mn, QMIN] - gen[mn, QG]])
if k > len(mx):
mn = mn[k - len(mx)]
mx = []
else:
mx = mx[k]
mn = []
if verbose and len(mx) > 0:
for i in range(len(mx)):
print('Gen ' + str(mx[i] + 1) +
' at upper Q limit, converting to PQ bus\n')
if verbose and len(mn) > 0:
for i in range(len(mn)):
print('Gen ' + str(mn[i] + 1) +
' at lower Q limit, converting to PQ bus\n')
## save corresponding limit values
fixedQg[mx] = gen[mx, QMAX]
fixedQg[mn] = gen[mn, QMIN]
mx = r_[mx, mn].astype(int)
## convert to PQ bus
gen[mx, QG] = fixedQg[mx] ## set Qg to binding
for i in range(
len(mx)
): ## [one at a time, since they may be at same bus]
gen[mx[i],
GEN_STATUS] = 0 ## temporarily turn off gen,
bi = gen[mx[i], GEN_BUS] ## adjust load accordingly,
bus[bi, [PD, QD]] = (bus[bi, [PD, QD]] -
gen[mx[i], [PG, QG]])
if len(ref) > 1 and any(bus[gen[mx, GEN_BUS],
BUS_TYPE] == REF):
raise ValueError('Sorry, PYPOWER cannot enforce Q '
'limits for slack buses in systems '
'with multiple slacks.')
bus[gen[mx, GEN_BUS].astype(int),
BUS_TYPE] = PQ ## & set bus type to PQ
## update bus index lists of each type of bus
ref_temp = ref
ref, pv, pq = bustypes(bus, gen)
if verbose and ref != ref_temp:
print('Bus %d is new slack bus\n' % ref)
limited = r_[limited, mx].astype(int)
else:
repeat = 0 ## no more generator Q limits violated
else:
repeat = 0 ## don't enforce generator Q limits, once is enough
if qlim and len(limited) > 0:
## restore injections from limited gens [those at Q limits]
gen[limited, QG] = fixedQg[limited] ## restore Qg value,
for i in range(
len(limited
)): ## [one at a time, since they may be at same bus]
bi = gen[limited[i], GEN_BUS] ## re-adjust load,
bus[bi,
[PD, QD]] = bus[bi, [PD, QD]] + gen[limited[i], [PG, QG]]
gen[limited[i], GEN_STATUS] = 1 ## and turn gen back on
if ref != ref0:
## adjust voltage angles to make original ref bus correct
bus[:, VA] = bus[:, VA] - bus[ref0, VA] + Varef0
ppc["et"] = time() - t0
ppc["success"] = success
##----- output results -----
## convert back to original bus numbering & print results
ppc["bus"], ppc["gen"], ppc["branch"] = bus, gen, branch
results = int2ext(ppc)
## zero out result fields of out-of-service gens & branches
if len(results["order"]["gen"]["status"]["off"]) > 0:
results["gen"][ix_(results["order"]["gen"]["status"]["off"],
[PG, QG])] = 0
if len(results["order"]["branch"]["status"]["off"]) > 0:
results["branch"][ix_(results["order"]["branch"]["status"]["off"],
[PF, QF, PT, QT])] = 0
if fname:
fd = None
try:
fd = open(fname, "a")
except Exception as detail:
stderr.write("Error opening %s: %s.\n" % (fname, detail))
finally:
if fd is not None:
printpf(results, fd, ppopt)
fd.close()
else:
printpf(results, stdout, ppopt)
## save solved case
if solvedcase:
savecase(solvedcase, results)
return results, success
def run_sim(ppc, elements, dynopt=None, events=None, recorder=None):
"""
Run a time-domain simulation
Inputs:
ppc PYPOWER load flow case
elements Dictionary of dynamic model objects (machines, controllers, etc) with Object ID as key
events Events object
recorder Recorder object (empty)
Outputs:
recorder Recorder object (with data)
"""
#########
# SETUP #
#########
# Get version information
ver = pydyn_ver()
print('PYPOWER-Dynamics ' + ver['Version'] + ', ' + ver['Date'])
# Program options
if dynopt:
h = dynopt['h']
t_sim = dynopt['t_sim']
max_err = dynopt['max_err']
max_iter = dynopt['max_iter']
verbose = dynopt['verbose']
else:
# Default program options
h = 0.01 # step length (s)
t_sim = 5 # simulation time (s)
max_err = 0.0001 # Maximum error in network iteration (voltage mismatches)
max_iter = 25 # Maximum number of network iterations
verbose = False
# Make lists of current injection sources (generators, external grids, etc) and controllers
sources = []
controllers = []
for element in elements.values():
if element.__module__ in [
'pydyn.sym_order6a', 'pydyn.sym_order6b', 'pydyn.sym_order4',
'pydyn.ext_grid', 'pydyn.vsc_average', 'pydyn.asym_1cage',
'pydyn.asym_2cage'
]:
sources.append(element)
if element.__module__ == 'pydyn.controller':
controllers.append(element)
# Set up interfaces
interfaces = init_interfaces(elements)
##################
# INITIALISATION #
##################
print('Initialising models...')
# Run power flow and update bus voltages and angles in PYPOWER case object
results, success = runpf(ppc)
ppc["bus"][:, VM] = results["bus"][:, VM]
ppc["bus"][:, VA] = results["bus"][:, VA]
# Build Ybus matrix
ppc_int = ext2int(ppc)
baseMVA, bus, branch = ppc_int["baseMVA"], ppc_int["bus"], ppc_int[
"branch"]
Ybus, Yf, Yt = makeYbus(baseMVA, bus, branch)
# Build modified Ybus matrix
Ybus = mod_Ybus(Ybus, elements, bus, ppc_int['gen'], baseMVA)
# Calculate initial voltage phasors
v0 = bus[:, VM] * (np.cos(np.radians(bus[:, VA])) +
1j * np.sin(np.radians(bus[:, VA])))
# Initialise sources from load flow
for source in sources:
if source.__module__ in ['pydyn.asym_1cage', 'pydyn.asym_2cage']:
# Asynchronous machine
source_bus = int(ppc_int['bus'][source.bus_no, 0])
v_source = v0[source_bus]
source.initialise(v_source, 0)
else:
# Generator or VSC
source_bus = int(ppc_int['gen'][source.gen_no, 0])
S_source = np.complex(results["gen"][source.gen_no, 1] / baseMVA,
results["gen"][source.gen_no, 2] / baseMVA)
v_source = v0[source_bus]
source.initialise(v_source, S_source)
# Interface controllers and machines (for initialisation)
for intf in interfaces:
int_type = intf[0]
var_name = intf[1]
if int_type == 'OUTPUT':
# If an output, interface in the reverse direction for initialisation
intf[2].signals[var_name] = intf[3].signals[var_name]
else:
# Inputs are interfaced in normal direction during initialisation
intf[3].signals[var_name] = intf[2].signals[var_name]
# Initialise controllers
for controller in controllers:
controller.initialise()
#############
# MAIN LOOP #
#############
if events == None:
print('Warning: no events!')
# Factorise Ybus matrix
Ybus_inv = splu(Ybus)
y1 = []
v_prev = v0
print('Simulating...')
for t in range(int(t_sim / h) + 1):
if np.mod(t, 1 / h) == 0:
print('t=' + str(t * h) + 's')
# Interface controllers and machines
for intf in interfaces:
var_name = intf[1]
intf[3].signals[var_name] = intf[2].signals[var_name]
# Solve differential equations
for j in range(4):
# Solve step of differential equations
for element in elements.values():
element.solve_step(h, j)
# Interface with network equations
v_prev = solve_network(sources, v_prev, Ybus_inv, ppc_int,
len(bus), max_err, max_iter)
if recorder != None:
# Record signals or states
recorder.record_variables(t * h, elements)
if events != None:
# Check event stack
ppc, refactorise = events.handle_events(np.round(t * h, 5),
elements, ppc, baseMVA)
if refactorise == True:
# Rebuild Ybus from new ppc_int
prev_ybus = Ybus.todense().copy()
ppc_int = ext2int(ppc)
baseMVA, bus, branch = ppc_int["baseMVA"], ppc_int[
"bus"], ppc_int["branch"]
Ybus, Yf, Yt = makeYbus(baseMVA, bus, branch)
# Rebuild modified Ybus
Ybus = mod_Ybus(Ybus, elements, bus, ppc_int['gen'], baseMVA)
ybus_delta = np.array(Ybus - prev_ybus)
# Refactorise Ybus
Ybus_inv = splu(Ybus)
# Solve network equations
v_prev = solve_network(sources, v_prev, Ybus_inv, ppc_int,
len(bus), max_err, max_iter)
return recorder
fnameWhole = "Net1_UKGDS_60.m"
convert_mcase(fname)
from Net1_UKGDS_60_subgrid import Net1_UKGDS_60_ as net
from Net1_UKGDS_60 import Net1_UKGDS_60_ as netWhole
t_f = 96
# time variation
t_ges = 1440 # all time in min
delta_t = 15 # time intervals in min
time = np.arange(delta_t, t_ges + delta_t, delta_t)
casedataWhole = netWhole()
convert_to_python_indices(casedataWhole)
ppc = casedataWhole
ppopt = ppoption(PF_ALG=2)
ppc = ext2int(ppc)
baseMVA, bus, gen, branch = ppc["baseMVA"], ppc["bus"], ppc["gen"], ppc[
"branch"]
baseMVA = 1000
Ybus, Yf, Yt = makeYbus(baseMVA, bus, branch) # nodal admittance matrix Ybus
condition = np.hstack((1, np.arange(16, 27, 1)))
Yws = Ybus[np.ix_(condition, condition)]
#Yws = Y
t_f = 96
slack_idx = 0
p0 = 1e-3
iterstop = 50
accuracy = 1e-9
roundY = None
def solveropfnlp_2(ppc, solver="ipopt"):
if solver == "ipopt":
opt = SolverFactory("ipopt", executable="/home/iso/PycharmProjects/opfLC_python3/Python3/py_solvers/ipopt-linux64/ipopt")
if solver == "bonmin":
opt = SolverFactory("bonmin", executable="/home/iso/PycharmProjects/opfLC_python3/Python3/py_solvers/bonmin-linux64/bonmin")
if solver == "knitro":
opt = SolverFactory("knitro", executable="D:/ICT/Artelys/Knitro 10.2.1/knitroampl/knitroampl")
ppc = ext2int(ppc) # convert to continuous indexing starting from 0
# Gather information about the system
# =============================================================
baseMVA, bus, gen, branch = \
ppc["baseMVA"], ppc["bus"], ppc["gen"], ppc["branch"]
nb = bus.shape[0] # number of buses
ng = gen.shape[0] # number of generators
nl = branch.shape[0] # number of lines
# generator buses
gb = tolist(np.array(gen[:, GEN_BUS]).astype(int))
sb = find((bus[:, BUS_TYPE] == REF)) # slack bus index
fr = branch[:, F_BUS].astype(int) # from bus indices
to = branch[:, T_BUS].astype(int) # to bus indices
tr = branch[:, TAP] # transformation ratios
tr[find(tr == 0)] = 1 # set to 1 transformation ratios that are 0
r = branch[:, BR_R] # branch resistances
x = branch[:, BR_X] # branch reactances
b = branch[:, BR_B] # branch susceptances
start_time = time.clock()
# Admittance matrix computation
# =============================================================
y = makeYbus(baseMVA, bus, branch)[0] # admittance matrix
yk = 1./(r+x*1j) # branch admittance
yft = yk + 0.5j*b # branch admittance + susceptance
gk = yk.real # branch resistance
yk = yk/tr # include /tr in yk
# Optimization
# =============================================================
branch[find(branch[:, RATE_A] == 0), RATE_A] = 9999 # set undefined Sflow limit to 9999
Smax = branch[:, RATE_A] / baseMVA # Max. Sflow
# Power demand parameters
Pd = bus[:, PD] / baseMVA
Qd = bus[:, QD] / baseMVA
# Max and min Pg and Qg
Pg_max = zeros(nb)
Pg_max[gb] = gen[:, PMAX] / baseMVA
Pg_min = zeros(nb)
Pg_min[gb] = gen[:, PMIN] / baseMVA
Qg_max = zeros(nb)
Qg_max[gb] = gen[:, QMAX] / baseMVA
Qg_min = zeros(nb)
Qg_min[gb] = gen[:, QMIN] / baseMVA
# Vmax and Vmin vectors
Vmax = bus[:, VMAX]
Vmin = bus[:, VMIN]
vm = bus[:, VM]
va = bus[:, VA]*pi/180
# create a new optimization model
model = ConcreteModel()
# Define sets
# ------------
model.bus = Set(ordered=True, initialize=range(nb)) # Set of all buses
model.gen = Set(ordered=True, initialize=gb) # Set of buses with generation
model.line = Set(ordered=True, initialize=range(nl)) # Set of all lines
# Define variables
# -----------------
# Voltage magnitudes vector (vm)
model.vm = Var(model.bus)
# Voltage angles vector (va)
model.va = Var(model.bus)
# Reactive power generation, synchronous machines(SM) (Qg)
model.Qg = Var(model.gen)
Qg0 = zeros(nb)
Qg0[gb] = gen[:, QG]/baseMVA
# Active power generation, synchronous machines(SM) (Pg)
model.Pg = Var(model.gen)
Pg0 = zeros(nb)
Pg0[gb] = gen[:, PG] / baseMVA
# Active and reactive power from at all branches
model.Pf = Var(model.line)
model.Qf = Var(model.line)
# Active and reactive power to at all branches
model.Pt = Var(model.line)
model.Qt = Var(model.line)
# Warm start the problem
# ------------------------
for i in range(nb):
model.vm[i] = vm[i]
model.va[i] = va[i]
if i in gb:
model.Pg[i] = Pg0[i]
model.Qg[i] = Qg0[i]
for i in range(nl):
model.Pf[i] = vm[fr[i]] ** 2 * abs(yft[i]) / (tr[i] ** 2) * np.cos(-ang(yft[i])) -\
vm[fr[i]] * vm[to[i]] * abs(yk[i]) * np.cos(va[fr[i]] - va[to[i]] - ang(yk[i]))
model.Qf[i] = vm[fr[i]] ** 2 * abs(yft[i]) / (tr[i] ** 2) * np.sin(-ang(yft[i])) -\
vm[fr[i]] * vm[to[i]] * abs(yk[i]) * np.sin(va[fr[i]] - va[to[i]] - ang(yk[i]))
model.Pt[i] = vm[to[i]] ** 2 * abs(yft[i]) * np.cos(-ang(yft[i])) -\
vm[to[i]] * vm[fr[i]] * abs(yk[i]) * np.cos(va[to[i]] - va[fr[i]] - ang(yk[i]))
model.Qt[i] = vm[to[i]] ** 2 * abs(yft[i]) * np.sin(-ang(yft[i])) -\
vm[to[i]] * vm[fr[i]] * abs(yk[i]) * np.sin(va[to[i]] - va[fr[i]] - ang(yk[i]))
# Define constraints
# ----------------------------
# Equalities:
# ------------
# Active power flow equalities
def powerflowact(model, i):
if i in gb:
return model.Pg[i]-Pd[i] == sum(model.vm[i]*model.vm[j]*abs(y[i, j]) *
cos(model.va[i] - model.va[j] - ang(y[i, j])) for j in range(nb))
else:
return sum(model.vm[i]*model.vm[j]*abs(y[i, j]) * cos(model.va[i] - model.va[j] -
ang(y[i, j])) for j in range(nb)) == -Pd[i]
model.const1 = Constraint(model.bus, rule=powerflowact)
# Reactive power flow equalities
def powerflowreact(model, i):
if i in gb:
return model.Qg[i]-Qd[i] == sum(model.vm[i]*model.vm[j]*abs(y[i, j]) *
sin(model.va[i] - model.va[j] - ang(y[i, j])) for j in range(nb))
else:
return sum(model.vm[i]*model.vm[j]*abs(y[i, j]) * sin(model.va[i] - model.va[j] -
ang(y[i, j])) for j in range(nb)) == -Qd[i]
model.const2 = Constraint(model.bus, rule=powerflowreact)
# Active power from
def pfrom(model, i):
return model.Pf[i] == model.vm[fr[i]] ** 2 * abs(yft[i]) / (tr[i] ** 2) * np.cos(-ang(yft[i])) - \
model.vm[fr[i]] * model.vm[to[i]] * abs(yk[i]) * \
cos(model.va[fr[i]] - model.va[to[i]] - ang(yk[i]))
model.const3 = Constraint(model.line, rule=pfrom)
# Reactive power from
def qfrom(model, i):
return model.Qf[i] == model.vm[fr[i]] ** 2 * abs(yft[i]) / (tr[i] ** 2) * np.sin(-ang(yft[i])) - \
model.vm[fr[i]] * model.vm[to[i]] * abs(yk[i]) * \
sin(model.va[fr[i]] - model.va[to[i]] - ang(yk[i]))
model.const4 = Constraint(model.line, rule=qfrom)
# Active power to
def pto(model, i):
return model.Pt[i] == model.vm[to[i]] ** 2 * abs(yft[i]) * np.cos(-ang(yft[i])) - \
model.vm[to[i]] * model.vm[fr[i]] * abs(yk[i]) * \
cos(model.va[to[i]] - model.va[fr[i]] - ang(yk[i]))
model.const5 = Constraint(model.line, rule=pto)
# Reactive power to
def qto(model, i):
return model.Qt[i] == model.vm[to[i]] ** 2 * abs(yft[i]) * np.sin(-ang(yft[i])) - \
model.vm[to[i]] * model.vm[fr[i]] * abs(yk[i]) * \
sin(model.va[to[i]] - model.va[fr[i]] - ang(yk[i]))
model.const6 = Constraint(model.line, rule=qto)
# Slack bus phase angle
model.const7 = Constraint(expr=model.va[sb[0]] == 0)
# Inequalities:
# ----------------
# Active power generator limits Pg_min <= Pg <= Pg_max
def genplimits(model, i):
return Pg_min[i] <= model.Pg[i] <= Pg_max[i]
model.const8 = Constraint(model.gen, rule=genplimits)
# Reactive power generator limits Qg_min <= Qg <= Qg_max
def genqlimits(model, i):
return Qg_min[i] <= model.Qg[i] <= Qg_max[i]
model.const9 = Constraint(model.gen, rule=genqlimits)
# Voltage constraints ( Vmin <= V <= Vmax )
def vlimits(model, i):
return Vmin[i] <= model.vm[i] <= Vmax[i]
model.const10 = Constraint(model.bus, rule=vlimits)
# Sfrom line limit
def sfrommax(model, i):
return model.Pf[i]**2 + model.Qf[i]**2 <= Smax[i]**2
model.const11 = Constraint(model.line, rule=sfrommax)
# Sto line limit
def stomax(model, i):
return model.Pt[i]**2 + model.Qt[i]**2 <= Smax[i]**2
model.const12 = Constraint(model.line, rule=stomax)
# Set objective function
# ------------------------
def obj_fun(model):
return sum(gk[i] * ((model.vm[fr[i]] / tr[i])**2 + model.vm[to[i]]**2 -
2/tr[i] * model.vm[fr[i]] * model.vm[to[i]] *
cos(model.va[fr[i]] - model.va[to[i]])) for i in range(nl))
model.obj = Objective(rule=obj_fun, sense=minimize)
mt = time.clock() - start_time # Modeling time
# Execute solve command with the selected solver
# ------------------------------------------------
start_time = time.clock()
results = opt.solve(model, tee=True)
et = time.clock() - start_time # Elapsed time
print(results)
# Update the case info with the optimized variables
# ==================================================
for i in range(nb):
bus[i, VM] = model.vm[i].value # Bus voltage magnitudes
bus[i, VA] = model.va[i].value*180/pi # Bus voltage angles
# Include Pf - Qf - Pt - Qt in the branch matrix
branchsol = zeros((nl, 17))
branchsol[:, :-4] = branch
for i in range(nl):
branchsol[i, PF] = model.Pf[i].value * baseMVA
branchsol[i, QF] = model.Qf[i].value * baseMVA
branchsol[i, PT] = model.Pt[i].value * baseMVA
branchsol[i, QT] = model.Qt[i].value * baseMVA
# Update gen matrix variables
for i in range(ng):
gen[i, PG] = model.Pg[gb[i]].value * baseMVA
gen[i, QG] = model.Qg[gb[i]].value * baseMVA
gen[i, VG] = bus[gb[i], VM]
# Convert to external (original) numbering and save case results
ppc = int2ext(ppc)
ppc['bus'][:, 1:] = bus[:, 1:]
branchsol[:, 0:2] = ppc['branch'][:, 0:2]
ppc['branch'] = branchsol
ppc['gen'][:, 1:] = gen[:, 1:]
ppc['obj'] = value(obj_fun(model))
ppc['ploss'] = value(obj_fun(model)) * baseMVA
ppc['et'] = et
ppc['mt'] = mt
ppc['success'] = 1
# ppc solved case is returned
return ppc
def run(mpc):
"""
Gurobi based optimal power flow modelling and solution
:param mpc: The input case of optimal power flow
:return: obtained solution
"""
# Data format
from pypower.idx_brch import F_BUS, T_BUS, BR_R, BR_X, TAP, SHIFT, BR_STATUS, RATE_A
from pypower.idx_cost import MODEL, NCOST, PW_LINEAR, COST, POLYNOMIAL
from pypower.idx_bus import BUS_TYPE, REF, VA, VM, PD, GS, VMAX, VMIN, BUS_I, QD
from pypower.idx_gen import GEN_BUS, VG, PG, QG, PMAX, PMIN, QMAX, QMIN
from pypower.ext2int import ext2int
mpc = ext2int(mpc)
baseMVA, bus, gen, branch, gencost = mpc["baseMVA"], mpc["bus"], mpc[
"gen"], mpc["branch"], mpc["gencost"]
nb = shape(mpc['bus'])[0] # number of buses
nl = shape(mpc['branch'])[0] # number of branches
ng = shape(mpc['gen'])[0] # number of dispatchable injections
for i in range(nl): # branch indexing exchange
if branch[i, F_BUS] > branch[i, T_BUS]:
temp = branch[i, F_BUS]
branch[i, F_BUS] = branch[i, T_BUS]
branch[i, T_BUS] = temp
f = branch[:, F_BUS] ## list of "from" buses
t = branch[:, T_BUS] ## list of "to" buses
area = ancestor_children_generation(f, t, range(nb))
# Connection matrix
Cg = sparse((ones(ng), (gen[:, GEN_BUS], range(ng))), (nb, ng))
Branch_R = branch[:, BR_R]
Branch_X = branch[:, BR_X]
# Obtain the boundary information
Slmax = branch[:, RATE_A] / baseMVA
Pij_l = -Slmax
Qij_l = -Slmax
Iij_l = zeros(nl)
Vm_l = turn_to_power(bus[:, VMIN], 2)
Pg_l = gen[:, PMIN] / baseMVA
Qg_l = gen[:, QMIN] / baseMVA
Pi_l = -bus[:, PD] / baseMVA + Cg * Pg_l
Qi_l = -bus[:, QD] / baseMVA + Cg * Qg_l
Pij_u = Slmax
Qij_u = Slmax
Iij_u = Slmax
Vm_u = turn_to_power(bus[:, VMAX], 2)
Pg_u = 2 * gen[:, PMAX] / baseMVA
Qg_u = 2 * gen[:, QMAX] / baseMVA
Pi_u = -bus[:, PD] / baseMVA + Cg * Pg_u
Qi_u = -bus[:, QD] / baseMVA + Cg * Qg_u
#
model = Model("OPF")
# Define the decision variables, compact set
Pij = {}
Qij = {}
Iij = {}
Vi = {}
Pg = {}
Qg = {}
Pi = {}
Qi = {}
for i in range(nl):
Pij[i] = model.addVar(lb=Pij_l[i],
ub=Pij_u[i],
vtype=GRB.CONTINUOUS,
name="Pij{0}".format(i))
Qij[i] = model.addVar(lb=Qij_l[i],
ub=Qij_u[i],
vtype=GRB.CONTINUOUS,
name="Qij{0}".format(i))
Iij[i] = model.addVar(lb=Iij_l[i],
ub=Iij_u[i],
vtype=GRB.CONTINUOUS,
name="Iij{0}".format(i))
for i in range(nb):
Vi[i] = model.addVar(lb=Vm_l[i],
ub=Vm_u[i],
vtype=GRB.CONTINUOUS,
name="V{0}".format(i))
for i in range(ng):
Pg[i] = model.addVar(lb=Pg_l[i],
ub=Pg_u[i],
vtype=GRB.CONTINUOUS,
name="Pg{0}".format(i))
Qg[i] = model.addVar(lb=Qg_l[i],
ub=Qg_u[i],
vtype=GRB.CONTINUOUS,
name="Qg{0}".format(i))
for i in range(nb):
Pi[i] = model.addVar(lb=Pi_l[i],
ub=Pi_u[i],
vtype=GRB.CONTINUOUS,
name="Pi{0}".format(i))
Qi[i] = model.addVar(lb=Qi_l[i],
ub=Qi_u[i],
vtype=GRB.CONTINUOUS,
name="Qi{0}".format(i))
# For each area, before decomposition
# Add system level constraints
for i in range(nb):
# If the bus is the root bus, only the children information is required.
if len(area[i]["Ai"]) == 0:
print(i)
expr = 0
for j in range(len(area[i]["Cbranch"][0])):
expr += Pij[area[i]["Cbranch"][0][j]]
model.addConstr(lhs=expr - Pi[i], sense=GRB.EQUAL, rhs=0)
expr = 0
for j in range(len(area[i]["Cbranch"][0])):
expr += Qij[area[i]["Cbranch"][0][j]]
model.addConstr(lhs=expr - Qi[i], sense=GRB.EQUAL, rhs=0)
elif len(area[i]["Cbranch"]) == 0: # This bus is the lead node
model.addConstr(lhs=Pij[area[i]["Abranch"][0][0]] -
Iij[area[i]["Abranch"][0][0]] *
Branch_R[area[i]["Abranch"][0][0]] + Pi[i],
sense=GRB.EQUAL,
rhs=0)
model.addConstr(lhs=Qij[area[i]["Abranch"][0][0]] -
Iij[area[i]["Abranch"][0][0]] *
Branch_X[area[i]["Abranch"][0][0]] + Qi[i],
sense=GRB.EQUAL,
rhs=0)
model.addConstr(lhs=Vi[int(area[i]["Ai"][0])] - Vi[i] -
2 * Branch_R[area[i]["Abranch"][0][0]] *
Pij[area[i]["Abranch"][0][0]] -
2 * Branch_X[area[i]["Abranch"][0][0]] *
Qij[area[i]["Abranch"][0][0]] +
Iij[area[i]["Abranch"][0][0]] *
(Branch_R[area[i]["Abranch"][0][0]]**2 +
Branch_X[area[i]["Abranch"][0][0]]**2),
sense=GRB.EQUAL,
rhs=0)
model.addConstr(
Pij[area[i]["Abranch"][0][0]] * Pij[area[i]["Abranch"][0][0]] +
Qij[area[i]["Abranch"][0][0]] * Qij[area[i]["Abranch"][0][0]]
<= Vi[int(area[i]["Ai"][0])] * Iij[area[i]["Abranch"][0][0]])
else:
expr = 0
for j in range(len(area[i]["Cbranch"][0])):
expr += Pij[area[i]["Cbranch"][0][j]]
model.addConstr(lhs=Pij[area[i]["Abranch"][0][0]] -
Iij[area[i]["Abranch"][0][0]] *
Branch_R[area[i]["Abranch"][0][0]] + Pi[i] - expr,
sense=GRB.EQUAL,
rhs=0)
expr = 0
for j in range(len(area[i]["Cbranch"][0])):
expr += Qij[area[i]["Cbranch"][0][j]]
model.addConstr(Qij[area[i]["Abranch"][0][0]] -
Iij[area[i]["Abranch"][0][0]] *
Branch_X[area[i]["Abranch"][0][0]] + Qi[i] - expr,
sense=GRB.EQUAL,
rhs=0)
model.addConstr(lhs=Vi[int(area[i]["Ai"][0])] - Vi[i] -
2 * Branch_R[area[i]["Abranch"][0][0]] *
Pij[area[i]["Abranch"][0][0]] -
2 * Branch_X[area[i]["Abranch"][0][0]] *
Qij[area[i]["Abranch"][0][0]] +
Iij[area[i]["Abranch"][0][0]] *
(Branch_R[area[i]["Abranch"][0][0]]**2 +
Branch_X[area[i]["Abranch"][0][0]]**2),
sense=GRB.EQUAL,
rhs=0)
model.addConstr(
Pij[area[i]["Abranch"][0][0]] * Pij[area[i]["Abranch"][0][0]] +
Qij[area[i]["Abranch"][0][0]] * Qij[area[i]["Abranch"][0][0]]
<= Vi[int(area[i]["Ai"][0])] * Iij[area[i]["Abranch"][0][0]])
obj = 0
for i in range(ng):
model.addConstr(lhs=Pg[i] - Pi[int(gen[i, GEN_BUS])],
sense=GRB.EQUAL,
rhs=bus[int(gen[i, GEN_BUS]), PD] / baseMVA)
model.addConstr(lhs=Qg[i] - Qi[int(gen[i, GEN_BUS])],
sense=GRB.EQUAL,
rhs=bus[int(gen[i, GEN_BUS]), QD] / baseMVA)
obj += gencost[i, 4] * Pg[i] * Pg[i] * baseMVA * baseMVA + gencost[
i, 5] * Pg[i] * baseMVA + gencost[i, 6]
model.setObjective(obj)
model.Params.OutputFlag = 0
model.Params.LogToConsole = 0
model.Params.DisplayInterval = 1
model.optimize()
Pij = []
Qij = []
Iij = []
Vi = []
Pg = []
Qg = []
Pi = []
Qi = []
for i in range(nl):
Pij.append(model.getVarByName("Pij{0}".format(i)).X)
Qij.append(model.getVarByName("Qij{0}".format(i)).X)
Iij.append(model.getVarByName("Iij{0}".format(i)).X)
for i in range(nb):
Vi.append(model.getVarByName("V{0}".format(i)).X)
Pi.append(model.getVarByName("Pi{0}".format(i)).X)
Qi.append(model.getVarByName("Qi{0}".format(i)).X)
for i in range(ng):
Pg.append(model.getVarByName("Pg{0}".format(i)).X)
Qg.append(model.getVarByName("Qg{0}".format(i)).X)
obj = obj.getValue()
primal_residual = []
for i in range(nl):
primal_residual.append(Pij[i] * Pij[i] + Qij[i] * Qij[i] -
Iij[i] * Vi[int(f[i])])
return obj, primal_residual
def opf(*args):
"""Solves an optimal power flow.
Returns a C{results} dict.
The data for the problem can be specified in one of three ways:
1. a string (ppc) containing the file name of a PYPOWER case
which defines the data matrices baseMVA, bus, gen, branch, and
gencost (areas is not used at all, it is only included for
backward compatibility of the API).
2. a dict (ppc) containing the data matrices as fields.
3. the individual data matrices themselves.
The optional user parameters for user constraints (C{A, l, u}), user costs
(C{N, fparm, H, Cw}), user variable initializer (C{z0}), and user variable
limits (C{zl, zu}) can also be specified as fields in a case dict,
either passed in directly or defined in a case file referenced by name.
When specified, C{A, l, u} represent additional linear constraints on the
optimization variables, C{l <= A*[x z] <= u}. If the user specifies an C{A}
matrix that has more columns than the number of "C{x}" (OPF) variables,
then there are extra linearly constrained "C{z}" variables. For an
explanation of the formulation used and instructions for forming the
C{A} matrix, see the MATPOWER manual.
A generalized cost on all variables can be applied if input arguments
C{N}, C{fparm}, C{H} and C{Cw} are specified. First, a linear transformation
of the optimization variables is defined by means of C{r = N * [x z]}.
Then, to each element of C{r} a function is applied as encoded in the
C{fparm} matrix (see MATPOWER manual). If the resulting vector is named
C{w}, then C{H} and C{Cw} define a quadratic cost on w:
C{(1/2)*w'*H*w + Cw * w}. C{H} and C{N} should be sparse matrices and C{H}
should also be symmetric.
The optional C{ppopt} vector specifies PYPOWER options. If the OPF
algorithm is not explicitly set in the options PYPOWER will use the default
solver, based on a primal-dual interior point method. For the AC OPF this
is C{OPF_ALG = 560}. For the DC OPF, the default is C{OPF_ALG_DC = 200}.
See L{ppoption} for more details on the available OPF solvers and other OPF
options and their default values.
The solved case is returned in a single results dict (described
below). Also returned are the final objective function value (C{f}) and a
flag which is C{True} if the algorithm was successful in finding a solution
(success). Additional optional return values are an algorithm specific
return status (C{info}), elapsed time in seconds (C{et}), the constraint
vector (C{g}), the Jacobian matrix (C{jac}), and the vector of variables
(C{xr}) as well as the constraint multipliers (C{pimul}).
The single results dict is a PYPOWER case struct (ppc) with the
usual baseMVA, bus, branch, gen, gencost fields, along with the
following additional fields:
- C{order} see 'help ext2int' for details of this field
- C{et} elapsed time in seconds for solving OPF
- C{success} 1 if solver converged successfully, 0 otherwise
- C{om} OPF model object, see 'help opf_model'
- C{x} final value of optimization variables (internal order)
- C{f} final objective function value
- C{mu} shadow prices on ...
- C{var}
- C{l} lower bounds on variables
- C{u} upper bounds on variables
- C{nln}
- C{l} lower bounds on nonlinear constraints
- C{u} upper bounds on nonlinear constraints
- C{lin}
- C{l} lower bounds on linear constraints
- C{u} upper bounds on linear constraints
- C{g} (optional) constraint values
- C{dg} (optional) constraint 1st derivatives
- C{df} (optional) obj fun 1st derivatives (not yet implemented)
- C{d2f} (optional) obj fun 2nd derivatives (not yet implemented)
- C{raw} raw solver output in form returned by MINOS, and more
- C{xr} final value of optimization variables
- C{pimul} constraint multipliers
- C{info} solver specific termination code
- C{output} solver specific output information
- C{alg} algorithm code of solver used
- C{var}
- C{val} optimization variable values, by named block
- C{Va} voltage angles
- C{Vm} voltage magnitudes (AC only)
- C{Pg} real power injections
- C{Qg} reactive power injections (AC only)
- C{y} constrained cost variable (only if have pwl costs)
- (other) any user defined variable blocks
- C{mu} variable bound shadow prices, by named block
- C{l} lower bound shadow prices
- C{Va}, C{Vm}, C{Pg}, C{Qg}, C{y}, (other)
- C{u} upper bound shadow prices
- C{Va}, C{Vm}, C{Pg}, C{Qg}, C{y}, (other)
- C{nln} (AC only)
- C{mu} shadow prices on nonlinear constraints, by named block
- C{l} lower bounds
- C{Pmis} real power mismatch equations
- C{Qmis} reactive power mismatch equations
- C{Sf} flow limits at "from" end of branches
- C{St} flow limits at "to" end of branches
- C{u} upper bounds
- C{Pmis}, C{Qmis}, C{Sf}, C{St}
- C{lin}
- C{mu} shadow prices on linear constraints, by named block
- C{l} lower bounds
- C{Pmis} real power mistmatch equations (DC only)
- C{Pf} flow limits at "from" end of branches (DC only)
- C{Pt} flow limits at "to" end of branches (DC only)
- C{PQh} upper portion of gen PQ-capability curve(AC only)
- C{PQl} lower portion of gen PQ-capability curve(AC only)
- C{vl} constant power factor constraint for loads
- C{ycon} basin constraints for CCV for pwl costs
- (other) any user defined constraint blocks
- C{u} upper bounds
- C{Pmis}, C{Pf}, C{Pf}, C{PQh}, C{PQl}, C{vl}, C{ycon},
- (other)
- C{cost} user defined cost values, by named block
@see: L{runopf}, L{dcopf}, L{uopf}, L{caseformat}
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
@author: Richard Lincoln
"""
##----- initialization -----
t0 = time() ## start timer
## process input arguments
ppc, ppopt = opf_args2(*args)
## add zero columns to bus, gen, branch for multipliers, etc if needed
nb = shape(ppc['bus'])[0] ## number of buses
nl = shape(ppc['branch'])[0] ## number of branches
ng = shape(ppc['gen'])[0] ## number of dispatchable injections
if shape(ppc['bus'])[1] < MU_VMIN + 1:
ppc['bus'] = c_[ppc['bus'],
zeros((nb, MU_VMIN + 1 - shape(ppc['bus'])[1]))]
if shape(ppc['gen'])[1] < MU_QMIN + 1:
ppc['gen'] = c_[ppc['gen'],
zeros((ng, MU_QMIN + 1 - shape(ppc['gen'])[1]))]
if shape(ppc['branch'])[1] < MU_ANGMAX + 1:
ppc['branch'] = c_[ppc['branch'],
zeros(
(nl, MU_ANGMAX + 1 - shape(ppc['branch'])[1]))]
##----- convert to internal numbering, remove out-of-service stuff -----
ppc = ext2int(ppc)
##----- construct OPF model object -----
om = opf_setup(ppc, ppopt)
##----- execute the OPF -----
results, success, raw = opf_execute(om, ppopt)
##----- revert to original ordering, including out-of-service stuff -----
results = int2ext(results)
## zero out result fields of out-of-service gens & branches
if len(results['order']['gen']['status']['off']) > 0:
results['gen'][ix_(results['order']['gen']['status']['off'],
[PG, QG, MU_PMAX, MU_PMIN])] = 0
if len(results['order']['branch']['status']['off']) > 0:
results['branch'][ix_(
results['order']['branch']['status']['off'],
[PF, QF, PT, QT, MU_SF, MU_ST, MU_ANGMIN, MU_ANGMAX])] = 0
##----- finish preparing output -----
et = time() - t0 ## compute elapsed time
results['et'] = et
results['success'] = success
results['raw'] = raw
return results
def runpf(casedata=None, ppopt=None, fname='', solvedcase=''):
"""Runs a power flow.
Runs a power flow [full AC Newton's method by default] and optionally
returns the solved values in the data matrices, a flag which is C{True} if
the algorithm was successful in finding a solution, and the elapsed
time in seconds. All input arguments are optional. If C{casename} is
provided it specifies the name of the input data file or dict
containing the power flow data. The default value is 'case9'.
If the ppopt is provided it overrides the default PYPOWER options
vector and can be used to specify the solution algorithm and output
options among other things. If the 3rd argument is given the pretty
printed output will be appended to the file whose name is given in
C{fname}. If C{solvedcase} is specified the solved case will be written
to a case file in PYPOWER format with the specified name. If C{solvedcase}
ends with '.mat' it saves the case as a MAT-file otherwise it saves it
as a Python-file.
If the C{ENFORCE_Q_LIMS} options is set to C{True} [default is false] then
if any generator reactive power limit is violated after running the AC
power flow, the corresponding bus is converted to a PQ bus, with Qg at
the limit, and the case is re-run. The voltage magnitude at the bus
will deviate from the specified value in order to satisfy the reactive
power limit. If the reference bus is converted to PQ, the first
remaining PV bus will be used as the slack bus for the next iteration.
This may result in the real power output at this generator being
slightly off from the specified values.
Enforcing of generator Q limits inspired by contributions from Mu Lin,
Lincoln University, New Zealand (1/14/05).
@author: Ray Zimmerman (PSERC Cornell)
"""
## default arguments
if casedata is None:
casedata = join(dirname(__file__), 'case9')
ppopt = ppoption(ppopt)
## options
verbose = ppopt["VERBOSE"]
qlim = ppopt["ENFORCE_Q_LIMS"] ## enforce Q limits on gens?
dc = ppopt["PF_DC"] ## use DC formulation?
## read data
ppc = loadcase(casedata)
## add zero columns to branch for flows if needed
if ppc["branch"].shape[1] < QT:
ppc["branch"] = c_[ppc["branch"],
zeros((ppc["branch"].shape[0],
QT - ppc["branch"].shape[1] + 1))]
## convert to internal indexing
ppc = ext2int(ppc)
baseMVA, bus, gen, branch = \
ppc["baseMVA"], ppc["bus"], ppc["gen"], ppc["branch"]
## get bus index lists of each type of bus
ref, pv, pq = bustypes(bus, gen)
## generator info
on = find(gen[:, GEN_STATUS] > 0) ## which generators are on?
gbus = gen[on, GEN_BUS].astype(int) ## what buses are they at?
##----- run the power flow -----
t0 = time()
if verbose > 0:
v = ppver('all')
stdout.write('PYPOWER Version %s, %s' % (v["Version"], v["Date"]))
if dc: # DC formulation
if verbose:
stdout.write(' -- DC Power Flow\n')
## initial state
Va0 = bus[:, VA] * (pi / 180)
## build B matrices and phase shift injections
B, Bf, Pbusinj, Pfinj = makeBdc(baseMVA, bus, branch)
## compute complex bus power injections [generation - load]
## adjusted for phase shifters and real shunts
Pbus = makeSbus(baseMVA, bus, gen).real - Pbusinj - bus[:, GS] / baseMVA
## "run" the power flow
Va = dcpf(B, Pbus, Va0, ref, pv, pq)
## update data matrices with solution
branch[:, [QF, QT]] = zeros((branch.shape[0], 2))
branch[:, PF] = (Bf * Va + Pfinj) * baseMVA
branch[:, PT] = -branch[:, PF]
bus[:, VM] = ones(bus.shape[0])
bus[:, VA] = Va * (180 / pi)
## update Pg for slack generator (1st gen at ref bus)
## (note: other gens at ref bus are accounted for in Pbus)
## Pg = Pinj + Pload + Gs
## newPg = oldPg + newPinj - oldPinj
refgen = zeros(len(ref), dtype=int)
for k in range(len(ref)):
temp = find(gbus == ref[k])
refgen[k] = on[temp[0]]
gen[refgen, PG] = gen[refgen, PG] + (B[ref, :] * Va - Pbus[ref]) * baseMVA
success = 1
else: ## AC formulation
alg = ppopt['PF_ALG']
if verbose > 0:
if alg == 1:
solver = 'Newton'
elif alg == 2:
solver = 'fast-decoupled, XB'
elif alg == 3:
solver = 'fast-decoupled, BX'
elif alg == 4:
solver = 'Gauss-Seidel'
else:
solver = 'unknown'
print(' -- AC Power Flow (%s)\n' % solver)
## initial state
# V0 = ones(bus.shape[0]) ## flat start
V0 = bus[:, VM] * exp(1j * pi/180 * bus[:, VA])
V0[gbus] = gen[on, VG] / abs(V0[gbus]) * V0[gbus]
if qlim:
ref0 = ref ## save index and angle of
Varef0 = bus[ref0, VA] ## original reference bus(es)
limited = [] ## list of indices of gens @ Q lims
fixedQg = zeros(gen.shape[0]) ## Qg of gens at Q limits
repeat = True
while repeat:
## build admittance matrices
Ybus, Yf, Yt = makeYbus(baseMVA, bus, branch)
## compute complex bus power injections [generation - load]
Sbus = makeSbus(baseMVA, bus, gen)
## run the power flow
alg = ppopt["PF_ALG"]
if alg == 1:
V, success, _ = newtonpf(Ybus, Sbus, V0, ref, pv, pq, ppopt)
elif alg == 2 or alg == 3:
Bp, Bpp = makeB(baseMVA, bus, branch, alg)
V, success, _ = fdpf(Ybus, Sbus, V0, Bp, Bpp, ref, pv, pq, ppopt)
elif alg == 4:
V, success, _ = gausspf(Ybus, Sbus, V0, ref, pv, pq, ppopt)
else:
stderr.write('Only Newton''s method, fast-decoupled, and '
'Gauss-Seidel power flow algorithms currently '
'implemented.\n')
## update data matrices with solution
bus, gen, branch = pfsoln(baseMVA, bus, gen, branch, Ybus, Yf, Yt, V, ref, pv, pq)
if qlim: ## enforce generator Q limits
## find gens with violated Q constraints
gen_status = gen[:, GEN_STATUS] > 0
qg_max_lim = gen[:, QG] > gen[:, QMAX]
qg_min_lim = gen[:, QG] < gen[:, QMIN]
mx = find( gen_status & qg_max_lim )
mn = find( gen_status & qg_min_lim )
if len(mx) > 0 or len(mn) > 0: ## we have some Q limit violations
# No PV generators
if len(pv) == 0:
if verbose:
if len(mx) > 0:
print('Gen %d [only one left] exceeds upper Q limit : INFEASIBLE PROBLEM\n' % mx + 1)
else:
print('Gen %d [only one left] exceeds lower Q limit : INFEASIBLE PROBLEM\n' % mn + 1)
success = 0
break
## one at a time?
if qlim == 2: ## fix largest violation, ignore the rest
k = argmax(r_[gen[mx, QG] - gen[mx, QMAX],
gen[mn, QMIN] - gen[mn, QG]])
if k > len(mx):
mn = mn[k - len(mx)]
mx = []
else:
mx = mx[k]
mn = []
if verbose and len(mx) > 0:
for i in range(len(mx)):
print('Gen ' + str(mx[i] + 1) + ' at upper Q limit, converting to PQ bus\n')
if verbose and len(mn) > 0:
for i in range(len(mn)):
print('Gen ' + str(mn[i] + 1) + ' at lower Q limit, converting to PQ bus\n')
## save corresponding limit values
fixedQg[mx] = gen[mx, QMAX]
fixedQg[mn] = gen[mn, QMIN]
mx = r_[mx, mn].astype(int)
## convert to PQ bus
gen[mx, QG] = fixedQg[mx] ## set Qg to binding
for i in range(len(mx)): ## [one at a time, since they may be at same bus]
gen[mx[i], GEN_STATUS] = 0 ## temporarily turn off gen,
bi = gen[mx[i], GEN_BUS] ## adjust load accordingly,
bus[bi, [PD, QD]] = (bus[bi, [PD, QD]] - gen[mx[i], [PG, QG]])
if len(ref) > 1 and any(bus[gen[mx, GEN_BUS], BUS_TYPE] == REF):
raise ValueError('Sorry, PYPOWER cannot enforce Q '
'limits for slack buses in systems '
'with multiple slacks.')
bus[gen[mx, GEN_BUS].astype(int), BUS_TYPE] = PQ ## & set bus type to PQ
## update bus index lists of each type of bus
ref_temp = ref
ref, pv, pq = bustypes(bus, gen)
if verbose and ref != ref_temp:
print('Bus %d is new slack bus\n' % ref)
limited = r_[limited, mx].astype(int)
else:
repeat = 0 ## no more generator Q limits violated
else:
repeat = 0 ## don't enforce generator Q limits, once is enough
if qlim and len(limited) > 0:
## restore injections from limited gens [those at Q limits]
gen[limited, QG] = fixedQg[limited] ## restore Qg value,
for i in range(len(limited)): ## [one at a time, since they may be at same bus]
bi = gen[limited[i], GEN_BUS] ## re-adjust load,
bus[bi, [PD, QD]] = bus[bi, [PD, QD]] + gen[limited[i], [PG, QG]]
gen[limited[i], GEN_STATUS] = 1 ## and turn gen back on
if ref != ref0:
## adjust voltage angles to make original ref bus correct
bus[:, VA] = bus[:, VA] - bus[ref0, VA] + Varef0
ppc["et"] = time() - t0
ppc["success"] = success
##----- output results -----
## convert back to original bus numbering & print results
ppc["bus"], ppc["gen"], ppc["branch"] = bus, gen, branch
results = int2ext(ppc)
## zero out result fields of out-of-service gens & branches
if len(results["order"]["gen"]["status"]["off"]) > 0:
results["gen"][ix_(results["order"]["gen"]["status"]["off"], [PG, QG])] = 0
if len(results["order"]["branch"]["status"]["off"]) > 0:
results["branch"][ix_(results["order"]["branch"]["status"]["off"], [PF, QF, PT, QT])] = 0
if fname:
fd = None
try:
fd = open(fname, "a")
except Exception as detail:
stderr.write("Error opening %s: %s.\n" % (fname, detail))
finally:
if fd is not None:
printpf(results, fd, ppopt)
fd.close()
else:
printpf(results, stdout, ppopt)
## save solved case
if solvedcase:
savecase(solvedcase, results)
return results, success
def t_ext2int2ext(quiet=False):
"""Tests C{ext2int} and C{int2ext}.
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
t_begin(85, quiet)
##----- ppc = e2i_data/i2e_data(ppc) -----
t = 'ppc = e2i_data(ppc) : '
ppce = loadcase(t_case_ext())
ppci = loadcase(t_case_int())
ppc = e2i_data(ppce)
t_is(ppc['bus'], ppci['bus'], 12, [t, 'bus'])
t_is(ppc['branch'], ppci['branch'], 12, [t, 'branch'])
t_is(ppc['gen'], ppci['gen'], 12, [t, 'gen'])
t_is(ppc['gencost'], ppci['gencost'], 12, [t, 'gencost'])
t_is(ppc['areas'], ppci['areas'], 12, [t, 'areas'])
t_is(ppc['A'], ppci['A'], 12, [t, 'A'])
t_is(ppc['N'], ppci['N'], 12, [t, 'N'])
t = 'ppc = e2i_data(ppc) - repeat : '
ppc = e2i_data(ppc)
t_is(ppc['bus'], ppci['bus'], 12, [t, 'bus'])
t_is(ppc['branch'], ppci['branch'], 12, [t, 'branch'])
t_is(ppc['gen'], ppci['gen'], 12, [t, 'gen'])
t_is(ppc['gencost'], ppci['gencost'], 12, [t, 'gencost'])
t_is(ppc['areas'], ppci['areas'], 12, [t, 'areas'])
t_is(ppc['A'], ppci['A'], 12, [t, 'A'])
t_is(ppc['N'], ppci['N'], 12, [t, 'N'])
t = 'ppc = i2e_data(ppc) : '
ppc = i2e_data(ppc)
t_is(ppc['bus'], ppce['bus'], 12, [t, 'bus'])
t_is(ppc['branch'], ppce['branch'], 12, [t, 'branch'])
t_is(ppc['gen'], ppce['gen'], 12, [t, 'gen'])
t_is(ppc['gencost'], ppce['gencost'], 12, [t, 'gencost'])
t_is(ppc['areas'], ppce['areas'], 12, [t, 'areas'])
t_is(ppc['A'], ppce['A'], 12, [t, 'A'])
t_is(ppc['N'], ppce['N'], 12, [t, 'N'])
##----- val = e2i_data/i2e_data(ppc, val, ...) -----
t = 'val = e2i_data(ppc, val, \'bus\')'
ppc = e2i_data(ppce)
got = e2i_data(ppc, ppce['xbus'], 'bus')
ex = ppce['xbus']
ex = delete(ex, 5, 0)
t_is(got, ex, 12, t)
t = 'val = i2e_data(ppc, val, oldval, \'bus\')'
tmp = ones(ppce['xbus'].shape)
tmp[5, :] = ppce['xbus'][5, :]
got = i2e_data(ppc, ex, tmp, 'bus')
t_is(got, ppce['xbus'], 12, t)
t = 'val = e2i_data(ppc, val, \'bus\', 1)'
got = e2i_data(ppc, ppce['xbus'], 'bus', 1)
ex = ppce['xbus']
ex = delete(ex, 5, 1)
t_is(got, ex, 12, t)
t = 'val = i2e_data(ppc, val, oldval, \'bus\', 1)'
tmp = ones(ppce['xbus'].shape)
tmp[:, 5] = ppce['xbus'][:, 5]
got = i2e_data(ppc, ex, tmp, 'bus', 1)
t_is(got, ppce['xbus'], 12, t)
t = 'val = e2i_data(ppc, val, \'gen\')'
got = e2i_data(ppc, ppce['xgen'], 'gen')
ex = ppce['xgen'][[3, 1, 0], :]
t_is(got, ex, 12, t)
t = 'val = i2e_data(ppc, val, oldval, \'gen\')'
tmp = ones(ppce['xgen'].shape)
tmp[2, :] = ppce['xgen'][2, :]
got = i2e_data(ppc, ex, tmp, 'gen')
t_is(got, ppce['xgen'], 12, t)
t = 'val = e2i_data(ppc, val, \'gen\', 1)'
got = e2i_data(ppc, ppce['xgen'], 'gen', 1)
ex = ppce['xgen'][:, [3, 1, 0]]
t_is(got, ex, 12, t)
t = 'val = i2e_data(ppc, val, oldval, \'gen\', 1)'
tmp = ones(ppce['xgen'].shape)
tmp[:, 2] = ppce['xgen'][:, 2]
got = i2e_data(ppc, ex, tmp, 'gen', 1)
t_is(got, ppce['xgen'], 12, t)
t = 'val = e2i_data(ppc, val, \'branch\')'
got = e2i_data(ppc, ppce['xbranch'], 'branch')
ex = ppce['xbranch']
ex = delete(ex, 6, 0)
t_is(got, ex, 12, t)
t = 'val = i2e_data(ppc, val, oldval, \'branch\')'
tmp = ones(ppce['xbranch'].shape)
tmp[6, :] = ppce['xbranch'][6, :]
got = i2e_data(ppc, ex, tmp, 'branch')
t_is(got, ppce['xbranch'], 12, t)
t = 'val = e2i_data(ppc, val, \'branch\', 1)'
got = e2i_data(ppc, ppce['xbranch'], 'branch', 1)
ex = ppce['xbranch']
ex = delete(ex, 6, 1)
t_is(got, ex, 12, t)
t = 'val = i2e_data(ppc, val, oldval, \'branch\', 1)'
tmp = ones(ppce['xbranch'].shape)
tmp[:, 6] = ppce['xbranch'][:, 6]
got = i2e_data(ppc, ex, tmp, 'branch', 1)
t_is(got, ppce['xbranch'], 12, t)
t = 'val = e2i_data(ppc, val, {\'branch\', \'gen\', \'bus\'})'
got = e2i_data(ppc, ppce['xrows'], ['branch', 'gen', 'bus'])
ex = r_[ppce['xbranch'][list(range(6)) + list(range(7, 10)), :4],
ppce['xgen'][[3, 1, 0], :],
ppce['xbus'][list(range(5)) + list(range(6, 10)), :4],
-1 * ones((2, 4))]
t_is(got, ex, 12, t)
t = 'val = i2e_data(ppc, val, oldval, {\'branch\', \'gen\', \'bus\'})'
tmp1 = ones(ppce['xbranch'][:, :4].shape)
tmp1[6, :4] = ppce['xbranch'][6, :4]
tmp2 = ones(ppce['xgen'].shape)
tmp2[2, :] = ppce['xgen'][2, :]
tmp3 = ones(ppce['xbus'][:, :4].shape)
tmp3[5, :4] = ppce['xbus'][5, :4]
tmp = r_[tmp1, tmp2, tmp3]
got = i2e_data(ppc, ex, tmp, ['branch', 'gen', 'bus'])
t_is(got, ppce['xrows'], 12, t)
t = 'val = e2i_data(ppc, val, {\'branch\', \'gen\', \'bus\'}, 1)'
got = e2i_data(ppc, ppce['xcols'], ['branch', 'gen', 'bus'], 1)
ex = r_[ppce['xbranch'][list(range(6)) + list(range(7, 10)), :4],
ppce['xgen'][[3, 1, 0], :],
ppce['xbus'][list(range(5)) + list(range(6, 10)), :4],
-1 * ones((2, 4))].T
t_is(got, ex, 12, t)
t = 'val = i2e_data(ppc, val, oldval, {\'branch\', \'gen\', \'bus\'}, 1)'
tmp1 = ones(ppce['xbranch'][:, :4].shape)
tmp1[6, :4] = ppce['xbranch'][6, :4]
tmp2 = ones(ppce['xgen'].shape)
tmp2[2, :] = ppce['xgen'][2, :]
tmp3 = ones(ppce['xbus'][:, :4].shape)
tmp3[5, :4] = ppce['xbus'][5, :4]
tmp = r_[tmp1, tmp2, tmp3].T
got = i2e_data(ppc, ex, tmp, ['branch', 'gen', 'bus'], 1)
t_is(got, ppce['xcols'], 12, t)
##----- ppc = e2i_field/i2e_field(ppc, field, ...) -----
t = 'ppc = e2i_field(ppc, field, \'bus\')'
ppc = e2i_field(ppce)
ex = ppce['xbus']
ex = delete(ex, 5, 0)
got = e2i_field(ppc, 'xbus', 'bus')
t_is(got['xbus'], ex, 12, t)
t = 'ppc = i2e_field(ppc, field, \'bus\')'
got = i2e_field(got, 'xbus', ordering='bus')
t_is(got['xbus'], ppce['xbus'], 12, t)
t = 'ppc = e2i_field(ppc, field, \'bus\', 1)'
ex = ppce['xbus']
ex = delete(ex, 5, 1)
got = e2i_field(ppc, 'xbus', 'bus', 1)
t_is(got['xbus'], ex, 12, t)
t = 'ppc = i2e_field(ppc, field, \'bus\', 1)'
got = i2e_field(got, 'xbus', ordering='bus', dim=1)
t_is(got['xbus'], ppce['xbus'], 12, t)
t = 'ppc = e2i_field(ppc, field, \'gen\')'
ex = ppce['xgen'][[3, 1, 0], :]
got = e2i_field(ppc, 'xgen', 'gen')
t_is(got['xgen'], ex, 12, t)
t = 'ppc = i2e_field(ppc, field, \'gen\')'
got = i2e_field(got, 'xgen', ordering='gen')
t_is(got['xgen'], ppce['xgen'], 12, t)
t = 'ppc = e2i_field(ppc, field, \'gen\', 1)'
ex = ppce['xgen'][:, [3, 1, 0]]
got = e2i_field(ppc, 'xgen', 'gen', 1)
t_is(got['xgen'], ex, 12, t)
t = 'ppc = i2e_field(ppc, field, \'gen\', 1)'
got = i2e_field(got, 'xgen', ordering='gen', dim=1)
t_is(got['xgen'], ppce['xgen'], 12, t)
t = 'ppc = e2i_field(ppc, field, \'branch\')'
ex = ppce['xbranch']
ex = delete(ex, 6, 0)
got = e2i_field(ppc, 'xbranch', 'branch')
t_is(got['xbranch'], ex, 12, t)
t = 'ppc = i2e_field(ppc, field, \'branch\')'
got = i2e_field(got, 'xbranch', ordering='branch')
t_is(got['xbranch'], ppce['xbranch'], 12, t)
t = 'ppc = e2i_field(ppc, field, \'branch\', 1)'
ex = ppce['xbranch']
ex = delete(ex, 6, 1)
got = e2i_field(ppc, 'xbranch', 'branch', 1)
t_is(got['xbranch'], ex, 12, t)
t = 'ppc = i2e_field(ppc, field, \'branch\', 1)'
got = i2e_field(got, 'xbranch', ordering='branch', dim=1)
t_is(got['xbranch'], ppce['xbranch'], 12, t)
t = 'ppc = e2i_field(ppc, field, {\'branch\', \'gen\', \'bus\'})'
ex = r_[ppce['xbranch'][list(range(6)) + list(range(7, 10)), :4],
ppce['xgen'][[3, 1, 0], :],
ppce['xbus'][list(range(5)) + list(range(6, 10)), :4],
-1 * ones((2, 4))]
got = e2i_field(ppc, 'xrows', ['branch', 'gen', 'bus'])
t_is(got['xrows'], ex, 12, t)
t = 'ppc = i2e_field(ppc, field, {\'branch\', \'gen\', \'bus\'})'
got = i2e_field(got, 'xrows', ordering=['branch', 'gen', 'bus'])
t_is(got['xrows'], ppce['xrows'], 12, t)
t = 'ppc = e2i_field(ppc, field, {\'branch\', \'gen\', \'bus\'}, 1)'
ex = r_[ppce['xbranch'][list(range(6)) + list(range(7, 10)), :4],
ppce['xgen'][[3, 1, 0], :],
ppce['xbus'][list(range(5)) + list(range(6, 10)), :4],
-1 * ones((2, 4))].T
got = e2i_field(ppc, 'xcols', ['branch', 'gen', 'bus'], 1)
t_is(got['xcols'], ex, 12, t)
t = 'ppc = i2e_field(ppc, field, {\'branch\', \'gen\', \'bus\'})'
got = i2e_field(got, 'xcols', ordering=['branch', 'gen', 'bus'], dim=1)
t_is(got['xcols'], ppce['xcols'], 12, t)
t = 'ppc = e2i_field(ppc, {\'field1\', \'field2\'}, ordering)'
ex = ppce['x']['more'][[3, 1, 0], :]
got = e2i_field(ppc, ['x', 'more'], 'gen')
t_is(got['x']['more'], ex, 12, t)
t = 'ppc = i2e_field(ppc, {\'field1\', \'field2\'}, ordering)'
got = i2e_field(got, ['x', 'more'], ordering='gen')
t_is(got['x']['more'], ppce['x']['more'], 12, t)
t = 'ppc = e2i_field(ppc, {\'field1\', \'field2\'}, ordering, 1)'
ex = ppce['x']['more'][:, [3, 1, 0]]
got = e2i_field(ppc, ['x', 'more'], 'gen', 1)
t_is(got['x']['more'], ex, 12, t)
t = 'ppc = i2e_field(ppc, {\'field1\', \'field2\'}, ordering, 1)'
got = i2e_field(got, ['x', 'more'], ordering='gen', dim=1)
t_is(got['x']['more'], ppce['x']['more'], 12, t)
##----- more ppc = ext2int/int2ext(ppc) -----
t = 'ppc = ext2int(ppc) - bus/gen/branch only : '
ppce = loadcase(t_case_ext())
ppci = loadcase(t_case_int())
del ppce['gencost']
del ppce['areas']
del ppce['A']
del ppce['N']
del ppci['gencost']
del ppci['areas']
del ppci['A']
del ppci['N']
ppc = ext2int(ppce)
t_is(ppc['bus'], ppci['bus'], 12, [t, 'bus'])
t_is(ppc['branch'], ppci['branch'], 12, [t, 'branch'])
t_is(ppc['gen'], ppci['gen'], 12, [t, 'gen'])
t = 'ppc = ext2int(ppc) - no areas/A : '
ppce = loadcase(t_case_ext())
ppci = loadcase(t_case_int())
del ppce['areas']
del ppce['A']
del ppci['areas']
del ppci['A']
ppc = ext2int(ppce)
t_is(ppc['bus'], ppci['bus'], 12, [t, 'bus'])
t_is(ppc['branch'], ppci['branch'], 12, [t, 'branch'])
t_is(ppc['gen'], ppci['gen'], 12, [t, 'gen'])
t_is(ppc['gencost'], ppci['gencost'], 12, [t, 'gencost'])
t_is(ppc['N'], ppci['N'], 12, [t, 'N'])
t = 'ppc = ext2int(ppc) - Qg cost, no N : '
ppce = loadcase(t_case_ext())
ppci = loadcase(t_case_int())
del ppce['N']
del ppci['N']
ppce['gencost'] = c_[ppce['gencost'], ppce['gencost']]
ppci['gencost'] = c_[ppci['gencost'], ppci['gencost']]
ppc = ext2int(ppce)
t_is(ppc['bus'], ppci['bus'], 12, [t, 'bus'])
t_is(ppc['branch'], ppci['branch'], 12, [t, 'branch'])
t_is(ppc['gen'], ppci['gen'], 12, [t, 'gen'])
t_is(ppc['gencost'], ppci['gencost'], 12, [t, 'gencost'])
t_is(ppc['areas'], ppci['areas'], 12, [t, 'areas'])
t_is(ppc['A'], ppci['A'], 12, [t, 'A'])
t = 'ppc = ext2int(ppc) - A, N are DC sized : '
ppce = loadcase(t_case_ext())
ppci = loadcase(t_case_int())
eVmQgcols = list(range(10, 20)) + list(range(24, 28))
iVmQgcols = list(range(9, 18)) + list(range(21, 24))
ppce['A'] = delete(ppce['A'], eVmQgcols, 1)
ppce['N'] = delete(ppce['N'], eVmQgcols, 1)
ppci['A'] = delete(ppci['A'], iVmQgcols, 1)
ppci['N'] = delete(ppci['N'], iVmQgcols, 1)
ppc = ext2int(ppce)
t_is(ppc['bus'], ppci['bus'], 12, [t, 'bus'])
t_is(ppc['branch'], ppci['branch'], 12, [t, 'branch'])
t_is(ppc['gen'], ppci['gen'], 12, [t, 'gen'])
t_is(ppc['gencost'], ppci['gencost'], 12, [t, 'gencost'])
t_is(ppc['areas'], ppci['areas'], 12, [t, 'areas'])
t_is(ppc['A'], ppci['A'], 12, [t, 'A'])
t_is(ppc['N'], ppci['N'], 12, [t, 'N'])
t = 'ppc = int2ext(ppc) - A, N are DC sized : '
ppc = int2ext(ppc)
t_is(ppc['bus'], ppce['bus'], 12, [t, 'bus'])
t_is(ppc['branch'], ppce['branch'], 12, [t, 'branch'])
t_is(ppc['gen'], ppce['gen'], 12, [t, 'gen'])
t_is(ppc['gencost'], ppce['gencost'], 12, [t, 'gencost'])
t_is(ppc['areas'], ppce['areas'], 12, [t, 'areas'])
t_is(ppc['A'], ppce['A'], 12, [t, 'A'])
t_is(ppc['N'], ppce['N'], 12, [t, 'N'])
t_end()
def opf(*args):
"""Solves an optimal power flow.
Returns a C{results} dict.
The data for the problem can be specified in one of three ways:
1. a string (ppc) containing the file name of a PYPOWER case
which defines the data matrices baseMVA, bus, gen, branch, and
gencost (areas is not used at all, it is only included for
backward compatibility of the API).
2. a dict (ppc) containing the data matrices as fields.
3. the individual data matrices themselves.
The optional user parameters for user constraints (C{A, l, u}), user costs
(C{N, fparm, H, Cw}), user variable initializer (C{z0}), and user variable
limits (C{zl, zu}) can also be specified as fields in a case dict,
either passed in directly or defined in a case file referenced by name.
When specified, C{A, l, u} represent additional linear constraints on the
optimization variables, C{l <= A*[x z] <= u}. If the user specifies an C{A}
matrix that has more columns than the number of "C{x}" (OPF) variables,
then there are extra linearly constrained "C{z}" variables. For an
explanation of the formulation used and instructions for forming the
C{A} matrix, see the MATPOWER manual.
A generalized cost on all variables can be applied if input arguments
C{N}, C{fparm}, C{H} and C{Cw} are specified. First, a linear transformation
of the optimization variables is defined by means of C{r = N * [x z]}.
Then, to each element of C{r} a function is applied as encoded in the
C{fparm} matrix (see MATPOWER manual). If the resulting vector is named
C{w}, then C{H} and C{Cw} define a quadratic cost on w:
C{(1/2)*w'*H*w + Cw * w}. C{H} and C{N} should be sparse matrices and C{H}
should also be symmetric.
The optional C{ppopt} vector specifies PYPOWER options. If the OPF
algorithm is not explicitly set in the options PYPOWER will use the default
solver, based on a primal-dual interior point method. For the AC OPF this
is C{OPF_ALG = 560}. For the DC OPF, the default is C{OPF_ALG_DC = 200}.
See L{ppoption} for more details on the available OPF solvers and other OPF
options and their default values.
The solved case is returned in a single results dict (described
below). Also returned are the final objective function value (C{f}) and a
flag which is C{True} if the algorithm was successful in finding a solution
(success). Additional optional return values are an algorithm specific
return status (C{info}), elapsed time in seconds (C{et}), the constraint
vector (C{g}), the Jacobian matrix (C{jac}), and the vector of variables
(C{xr}) as well as the constraint multipliers (C{pimul}).
The single results dict is a PYPOWER case struct (ppc) with the
usual baseMVA, bus, branch, gen, gencost fields, along with the
following additional fields:
- C{order} see 'help ext2int' for details of this field
- C{et} elapsed time in seconds for solving OPF
- C{success} 1 if solver converged successfully, 0 otherwise
- C{om} OPF model object, see 'help opf_model'
- C{x} final value of optimization variables (internal order)
- C{f} final objective function value
- C{mu} shadow prices on ...
- C{var}
- C{l} lower bounds on variables
- C{u} upper bounds on variables
- C{nln}
- C{l} lower bounds on nonlinear constraints
- C{u} upper bounds on nonlinear constraints
- C{lin}
- C{l} lower bounds on linear constraints
- C{u} upper bounds on linear constraints
- C{g} (optional) constraint values
- C{dg} (optional) constraint 1st derivatives
- C{df} (optional) obj fun 1st derivatives (not yet implemented)
- C{d2f} (optional) obj fun 2nd derivatives (not yet implemented)
- C{raw} raw solver output in form returned by MINOS, and more
- C{xr} final value of optimization variables
- C{pimul} constraint multipliers
- C{info} solver specific termination code
- C{output} solver specific output information
- C{alg} algorithm code of solver used
- C{var}
- C{val} optimization variable values, by named block
- C{Va} voltage angles
- C{Vm} voltage magnitudes (AC only)
- C{Pg} real power injections
- C{Qg} reactive power injections (AC only)
- C{y} constrained cost variable (only if have pwl costs)
- (other) any user defined variable blocks
- C{mu} variable bound shadow prices, by named block
- C{l} lower bound shadow prices
- C{Va}, C{Vm}, C{Pg}, C{Qg}, C{y}, (other)
- C{u} upper bound shadow prices
- C{Va}, C{Vm}, C{Pg}, C{Qg}, C{y}, (other)
- C{nln} (AC only)
- C{mu} shadow prices on nonlinear constraints, by named block
- C{l} lower bounds
- C{Pmis} real power mismatch equations
- C{Qmis} reactive power mismatch equations
- C{Sf} flow limits at "from" end of branches
- C{St} flow limits at "to" end of branches
- C{u} upper bounds
- C{Pmis}, C{Qmis}, C{Sf}, C{St}
- C{lin}
- C{mu} shadow prices on linear constraints, by named block
- C{l} lower bounds
- C{Pmis} real power mistmatch equations (DC only)
- C{Pf} flow limits at "from" end of branches (DC only)
- C{Pt} flow limits at "to" end of branches (DC only)
- C{PQh} upper portion of gen PQ-capability curve(AC only)
- C{PQl} lower portion of gen PQ-capability curve(AC only)
- C{vl} constant power factor constraint for loads
- C{ycon} basin constraints for CCV for pwl costs
- (other) any user defined constraint blocks
- C{u} upper bounds
- C{Pmis}, C{Pf}, C{Pf}, C{PQh}, C{PQl}, C{vl}, C{ycon},
- (other)
- C{cost} user defined cost values, by named block
@see: L{runopf}, L{dcopf}, L{uopf}, L{caseformat}
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
@author: Richard Lincoln
"""
##----- initialization -----
t0 = time() ## start timer
## process input arguments
ppc, ppopt = opf_args2(*args)
## add zero columns to bus, gen, branch for multipliers, etc if needed
nb = shape(ppc['bus'])[0] ## number of buses
nl = shape(ppc['branch'])[0] ## number of branches
ng = shape(ppc['gen'])[0] ## number of dispatchable injections
if shape(ppc['bus'])[1] < MU_VMIN + 1:
ppc['bus'] = c_[ppc['bus'], zeros((nb, MU_VMIN + 1 - shape(ppc['bus'])[1]))]
if shape(ppc['gen'])[1] < MU_QMIN + 1:
ppc['gen'] = c_[ppc['gen'], zeros((ng, MU_QMIN + 1 - shape(ppc['gen'])[1]))]
if shape(ppc['branch'])[1] < MU_ANGMAX + 1:
ppc['branch'] = c_[ppc['branch'], zeros((nl, MU_ANGMAX + 1 - shape(ppc['branch'])[1]))]
##----- convert to internal numbering, remove out-of-service stuff -----
ppc = ext2int(ppc)
##----- construct OPF model object -----
om = opf_setup(ppc, ppopt)
##----- execute the OPF -----
results, success, raw = opf_execute(om, ppopt)
##----- revert to original ordering, including out-of-service stuff -----
results = int2ext(results)
## zero out result fields of out-of-service gens & branches
if len(results['order']['gen']['status']['off']) > 0:
results['gen'][ ix_(results['order']['gen']['status']['off'], [PG, QG, MU_PMAX, MU_PMIN]) ] = 0
if len(results['order']['branch']['status']['off']) > 0:
results['branch'][ ix_(results['order']['branch']['status']['off'], [PF, QF, PT, QT, MU_SF, MU_ST, MU_ANGMIN, MU_ANGMAX]) ] = 0
##----- finish preparing output -----
et = time() - t0 ## compute elapsed time
results['et'] = et
results['success'] = success
results['raw'] = raw
return results
def solveropfnlp_4(ppc, solver="ipopt"):
if solver == "ipopt":
opt = SolverFactory(
"ipopt",
executable=
"/home/iso/PycharmProjects/opfLC_python3/Python3/py_solvers/ipopt-linux64/ipopt"
)
if solver == "bonmin":
opt = SolverFactory(
"bonmin",
executable=
"/home/iso/PycharmProjects/opfLC_python3/Python3/py_solvers/bonmin-linux64/bonmin"
)
if solver == "knitro":
opt = SolverFactory(
"knitro",
executable="D:/ICT/Artelys/Knitro 10.2.1/knitroampl/knitroampl")
ppc = ext2int(ppc) # convert to continuous indexing starting from 0
# Gather information about the system
# =============================================================
baseMVA, bus, gen, branch = \
ppc["baseMVA"], ppc["bus"], ppc["gen"], ppc["branch"]
nb = bus.shape[0] # number of buses
ng = gen.shape[0] # number of generators
nl = branch.shape[0] # number of lines
# generator buses
gb = tolist(np.array(gen[:, GEN_BUS]).astype(int))
sb = find((bus[:, BUS_TYPE] == REF)) # slack bus index
fr = branch[:, F_BUS].astype(int) # from bus indices
to = branch[:, T_BUS].astype(int) # to bus indices
tr0 = copy(branch[:, TAP]) # transformation ratios
tr0[find(tr0 == 0)] = 1 # set to 1 transformation ratios that are 0
tp = find(branch[:, TAP] != 0) # lines with tap changers
ntp = find(branch[:, TAP] == 0) # lines without tap changers
# Tap changer settings
dudtap = 0.01 # Voltage per unit variation with tap changes
tapmax = 10 # Highest tap changer setting
tapmin = -10 # Lowest tap changer setting
# Shunt element options
stepmax = 1 # maximum step of the shunt element
Bs0 = bus[:, BS] / baseMVA # shunt elements susceptance
sd = find(bus[:, BS] != 0) # buses with shunt devices
r = branch[:, BR_R] # branch resistances
x = branch[:, BR_X] # branch reactances
b = branch[:, BR_B] # branch susceptances
start_time = time.clock()
# Admittance matrix computation
# =============================================================
# Set tap ratios and shunt elements to neutral position
branch[:, TAP] = 1
bus[:, BS] = 0
y = makeYbus(baseMVA, bus, branch)[0] # admittance matrix
yk = 1. / (r + x * 1j) # branch admittance
yft = yk + 0.5j * b # branch admittance + susceptance
gk = yk.real # branch resistance
# Optimization
# =============================================================
branch[find(branch[:, RATE_A] == 0),
RATE_A] = 9999 # set undefined Sflow limit to 9999
Smax = branch[:, RATE_A] / baseMVA # Max. Sflow
# Power demand parameters
Pd = bus[:, PD] / baseMVA
Qd = bus[:, QD] / baseMVA
# Max and min Pg and Qg
Pg_max = zeros(nb)
Pg_max[gb] = gen[:, PMAX] / baseMVA
Pg_min = zeros(nb)
Pg_min[gb] = gen[:, PMIN] / baseMVA
Qg_max = zeros(nb)
Qg_max[gb] = gen[:, QMAX] / baseMVA
Qg_min = zeros(nb)
Qg_min[gb] = gen[:, QMIN] / baseMVA
# Vmax and Vmin vectors
Vmax = bus[:, VMAX]
Vmin = bus[:, VMIN]
vm = bus[:, VM]
va = bus[:, VA] * pi / 180
# create a new optimization model
model = ConcreteModel()
# Define sets
# ------------
model.bus = Set(ordered=True, initialize=range(nb)) # Set of all buses
model.gen = Set(ordered=True,
initialize=gb) # Set of buses with generation
model.line = Set(ordered=True, initialize=range(nl)) # Set of all lines
model.taps = Set(ordered=True,
initialize=tp) # Set of all lines with tap changers
model.shunt = Set(ordered=True,
initialize=sd) # Set of buses with shunt elements
# Define variables
# -----------------
# Voltage magnitudes vector (vm)
model.vm = Var(model.bus)
# Voltage angles vector (va)
model.va = Var(model.bus)
# Reactive power generation, synchronous machines(SM) (Qg)
model.Qg = Var(model.gen)
Qg0 = zeros(nb)
Qg0[gb] = gen[:, QG] / baseMVA
# Active power generation, synchronous machines(SM) (Pg)
model.Pg = Var(model.gen)
Pg0 = zeros(nb)
Pg0[gb] = gen[:, PG] / baseMVA
# Active and reactive power from at all branches
model.Pf = Var(model.line)
model.Qf = Var(model.line)
# Active and reactive power to at all branches
model.Pt = Var(model.line)
model.Qt = Var(model.line)
# Transformation ratios
model.tr = Var(model.taps)
# Tap changer positions + their bounds
model.tap = Var(model.taps, bounds=(tapmin, tapmax))
# Shunt susceptance
model.Bs = Var(model.shunt)
# Shunt positions + their bounds
model.s = Var(model.shunt, bounds=(0, stepmax))
# Warm start the problem
# ------------------------
for i in range(nb):
model.vm[i] = vm[i]
model.va[i] = va[i]
if i in gb:
model.Pg[i] = Pg0[i]
model.Qg[i] = Qg0[i]
for i in range(nl):
model.Pf[i] = vm[fr[i]] ** 2 * abs(yft[i]) / (tr0[i] ** 2) * np.cos(-ang(yft[i])) -\
vm[fr[i]] * vm[to[i]] * abs(yk[i]) / tr0[i] * np.cos(va[fr[i]] - va[to[i]] - ang(yk[i]))
model.Qf[i] = vm[fr[i]] ** 2 * abs(yft[i]) / (tr0[i] ** 2) * np.sin(-ang(yft[i])) -\
vm[fr[i]] * vm[to[i]] * abs(yk[i]) / tr0[i] * np.sin(va[fr[i]] - va[to[i]] - ang(yk[i]))
model.Pt[i] = vm[to[i]] ** 2 * abs(yft[i]) * np.cos(-ang(yft[i])) -\
vm[to[i]] * vm[fr[i]] * abs(yk[i]) / tr0[i] * np.cos(va[to[i]] - va[fr[i]] - ang(yk[i]))
model.Qt[i] = vm[to[i]] ** 2 * abs(yft[i]) * np.sin(-ang(yft[i])) -\
vm[to[i]] * vm[fr[i]] * abs(yk[i]) / tr0[i] * np.sin(va[to[i]] - va[fr[i]] - ang(yk[i]))
for i in tp:
model.tr[i] = tr0[i]
for i in sd:
model.Bs[i] = Bs0[i]
# Define constraints
# ----------------------------
# Equalities:
# ------------
# Active power flow equalities
def powerflowact(model, i):
bfrom_i = tp[find(fr[tp] == i)] # branches from bus i with transformer
bto_i = tp[find(to[tp] == i)] # branches to bus i with transformer
allbut_i = find(bus[:, BUS_I] != i) # Set of other buses
if i in gb:
return model.Pg[i]-Pd[i] == sum(model.vm[i] * model.vm[j] * abs(y[i, j]) *
cos(model.va[i] - model.va[j] - ang(y[i, j])) for j in allbut_i) - \
sum(model.vm[i] * model.vm[to[j]] * abs(yk[j]) * cos(model.va[i] -
model.va[to[j]] - ang(yk[j])) * (1 / model.tr[j] - 1) for j in bfrom_i) - \
sum(model.vm[i] * model.vm[fr[j]] * abs(yk[j]) * cos(model.va[i] -
model.va[fr[j]] - ang(yk[j])) * (1 / model.tr[j] - 1) for j in bto_i) + \
model.vm[i] ** 2 * (sum(abs(yk[j]) * (1 / model.tr[j]**2 - 1) *
np.cos(- ang(yk[j])) for j in bfrom_i) + real(y[i, i]))
else:
return sum(model.vm[i] * model.vm[j] * abs(y[i, j]) *
cos(model.va[i] - model.va[j] - ang(y[i, j])) for j in allbut_i) - \
sum(model.vm[i] * model.vm[to[j]] * abs(yk[j]) * cos(model.va[i] -
model.va[to[j]] - ang(yk[j])) * (1 / model.tr[j] - 1) for j in bfrom_i) - \
sum(model.vm[i] * model.vm[fr[j]] * abs(yk[j]) * cos(model.va[i] -
model.va[fr[j]] - ang(yk[j])) * (1 / model.tr[j] - 1) for j in bto_i) + \
model.vm[i] ** 2 * (sum(abs(yk[j]) * (1 / model.tr[j]**2 - 1) *
np.cos(- ang(yk[j])) for j in bfrom_i) + real(y[i, i])) == -Pd[i]
model.const1 = Constraint(model.bus, rule=powerflowact)
# Reactive power flow equalities
def powerflowreact(model, i):
bfrom_i = tp[find(fr[tp] == i)] # branches from bus i with transformer
bto_i = tp[find(to[tp] == i)] # branches to bus i with transformer
allbut_i = find(bus[:, BUS_I] != i) # Set of other buses
sh = sd[find(sd == i)] # Detect shunt elements
if i in gb:
return model.Qg[i]-Qd[i] == \
sum(model.vm[i] * model.vm[j] * abs(y[i, j]) *
sin(model.va[i] - model.va[j] - ang(y[i, j])) for j in allbut_i) - \
sum(model.vm[i] * model.vm[to[j]] * abs(yk[j]) * sin(model.va[i] - model.va[to[j]] - ang(yk[j]))
* (1 / model.tr[j] - 1) for j in bfrom_i) - \
sum(model.vm[i] * model.vm[fr[j]] * abs(yk[j]) * sin(model.va[i] - model.va[fr[j]] - ang(yk[j]))
* (1 / model.tr[j] - 1) for j in bto_i) + \
model.vm[i] ** 2 * (sum(abs(yk[j]) * (1 / model.tr[j] ** 2 - 1) * np.sin(- ang(yk[j]))
for j in bfrom_i) - imag(y[i, i]) - sum(model.Bs[j] for j in sh))
else:
return sum(model.vm[i] * model.vm[j] * abs(y[i, j]) *
sin(model.va[i] - model.va[j] - ang(y[i, j])) for j in allbut_i) - \
sum(model.vm[i] * model.vm[to[j]] * abs(yk[j]) * sin(model.va[i] -
model.va[to[j]] - ang(yk[j])) * (1 / model.tr[j] - 1) for j in bfrom_i) - \
sum(model.vm[i] * model.vm[fr[j]] * abs(yk[j]) * sin(model.va[i] -
model.va[fr[j]] - ang(yk[j])) * (1 / model.tr[j] - 1) for j in bto_i) + \
model.vm[i] ** 2 * (sum(abs(yk[j]) * (1 / model.tr[j] ** 2 - 1) * np.sin(- ang(yk[j]))
for j in bfrom_i) - imag(y[i, i]) - sum(model.Bs[j] for j in sh)) == - Qd[i]
model.const2 = Constraint(model.bus, rule=powerflowreact)
# Active power from
def pfrom(model, i):
if i in tp:
return model.Pf[i] == model.vm[fr[i]] ** 2 * abs(yft[i]) / (model.tr[i] ** 2) * np.cos(-ang(yft[i])) - \
model.vm[fr[i]] * model.vm[to[i]] * abs(yk[i]) / model.tr[i] * \
cos(model.va[fr[i]] - model.va[to[i]] - ang(yk[i]))
else:
return model.Pf[i] == model.vm[fr[i]] ** 2 * abs(yft[i]) / tr0[i] ** 2 * np.cos(-ang(yft[i])) - \
model.vm[fr[i]] * model.vm[to[i]] * abs(yk[i]) / tr0[i] * \
cos(model.va[fr[i]] - model.va[to[i]] - ang(yk[i]))
model.const3 = Constraint(model.line, rule=pfrom)
# Reactive power from
def qfrom(model, i):
if i in tp:
return model.Qf[i] == model.vm[fr[i]] ** 2 * abs(yft[i]) / (model.tr[i] ** 2) * np.sin(-ang(yft[i])) - \
model.vm[fr[i]] * model.vm[to[i]] * abs(yk[i]) / model.tr[i] * \
sin(model.va[fr[i]] - model.va[to[i]] - ang(yk[i]))
else:
return model.Qf[i] == model.vm[fr[i]] ** 2 * abs(yft[i]) / tr0[i] ** 2 * np.sin(-ang(yft[i])) - \
model.vm[fr[i]] * model.vm[to[i]] * abs(yk[i]) / tr0[i] * \
sin(model.va[fr[i]] - model.va[to[i]] - ang(yk[i]))
model.const4 = Constraint(model.line, rule=qfrom)
# Active power to
def pto(model, i):
if i in tp:
return model.Pt[i] == model.vm[to[i]] ** 2 * abs(yft[i]) * np.cos(-ang(yft[i])) - \
model.vm[to[i]] * model.vm[fr[i]] * abs(yk[i]) / model.tr[i] * \
cos(model.va[to[i]] - model.va[fr[i]] - ang(yk[i]))
else:
return model.Pt[i] == model.vm[to[i]] ** 2 * abs(yft[i]) * np.cos(-ang(yft[i])) - \
model.vm[to[i]] * model.vm[fr[i]] * abs(yk[i]) / tr0[i] * \
cos(model.va[to[i]] - model.va[fr[i]] - ang(yk[i]))
model.const5 = Constraint(model.line, rule=pto)
# Reactive power to
def qto(model, i):
if i in tp:
return model.Qt[i] == model.vm[to[i]] ** 2 * abs(yft[i]) * np.sin(-ang(yft[i])) - \
model.vm[to[i]] * model.vm[fr[i]] * abs(yk[i]) / model.tr[i] * \
sin(model.va[to[i]] - model.va[fr[i]] - ang(yk[i]))
else:
return model.Qt[i] == model.vm[to[i]] ** 2 * abs(yft[i]) * np.sin(-ang(yft[i])) - \
model.vm[to[i]] * model.vm[fr[i]] * abs(yk[i]) / tr0[i] * \
sin(model.va[to[i]] - model.va[fr[i]] - ang(yk[i]))
model.const6 = Constraint(model.line, rule=qto)
# Slack bus phase angle
model.const7 = Constraint(expr=model.va[sb[0]] == 0)
# Transformation ratio equalities
def trfunc(model, i):
return model.tr[i] == 1 + dudtap * model.tap[i]
model.const8 = Constraint(model.taps, rule=trfunc)
# Shunt susceptance equality
def shuntfunc(model, i):
return model.Bs[i] == model.s[i] / stepmax * Bs0[i]
model.const9 = Constraint(model.shunt, rule=shuntfunc)
# Inequalities:
# ----------------
# Active power generator limits Pg_min <= Pg <= Pg_max
def genplimits(model, i):
return Pg_min[i] <= model.Pg[i] <= Pg_max[i]
model.const10 = Constraint(model.gen, rule=genplimits)
# Reactive power generator limits Qg_min <= Qg <= Qg_max
def genqlimits(model, i):
return Qg_min[i] <= model.Qg[i] <= Qg_max[i]
model.const11 = Constraint(model.gen, rule=genqlimits)
# Voltage constraints ( Vmin <= V <= Vmax )
def vlimits(model, i):
return Vmin[i] <= model.vm[i] <= Vmax[i]
model.const12 = Constraint(model.bus, rule=vlimits)
# Sfrom line limit
def sfrommax(model, i):
return model.Pf[i]**2 + model.Qf[i]**2 <= Smax[i]**2
model.const13 = Constraint(model.line, rule=sfrommax)
# Sto line limit
def stomax(model, i):
return model.Pt[i]**2 + model.Qt[i]**2 <= Smax[i]**2
model.const14 = Constraint(model.line, rule=stomax)
# Set objective function
# ------------------------
def obj_fun(model):
return sum(gk[i] * ((model.vm[fr[i]] / model.tr[i])**2 + model.vm[to[i]]**2 -
2 / model.tr[i] * model.vm[fr[i]] * model.vm[to[i]] *
cos(model.va[fr[i]] - model.va[to[i]])) for i in tp) + \
sum(gk[i] * ((model.vm[fr[i]] / tr0[i]) ** 2 + model.vm[to[i]] ** 2 -
2 / tr0[i] * model.vm[fr[i]] * model.vm[to[i]] *
cos(model.va[fr[i]] - model.va[to[i]])) for i in ntp)
model.obj = Objective(rule=obj_fun, sense=minimize)
mt = time.clock() - start_time # Modeling time
# Execute solve command with the selected solver
# ------------------------------------------------
start_time = time.clock()
results = opt.solve(model, tee=True)
et = time.clock() - start_time # Elapsed time
print(results)
# Update the case info with the optimized variables and approximate the continuous variables to discrete values
# ==============================================================================================================
for i in range(nb):
if i in sd:
bus[i, BS] = round(model.s[i].value) * Bs0[i] * baseMVA
bus[i, VM] = model.vm[i].value # Bus voltage magnitudes
bus[i, VA] = model.va[i].value * 180 / pi # Bus voltage angles
# Update transformation ratios
for i in range(nl):
if i in tp:
branch[i, TAP] = 1 + dudtap * round(model.tap[i].value)
# Update gen matrix variables
for i in range(ng):
gen[i, PG] = model.Pg[gb[i]].value * baseMVA
gen[i, QG] = model.Qg[gb[i]].value * baseMVA
gen[i, VG] = bus[gb[i], VM]
# Convert to external (original) numbering and save case results
ppc = int2ext(ppc)
ppc['bus'][:, 1:] = bus[:, 1:]
branch[:, 0:2] = ppc['branch'][:, 0:2]
ppc['branch'] = branch
ppc['gen'][:, 1:] = gen[:, 1:]
# Execute a second optimization with only the discrete approximated values (requires solveropfnlp_2)
sol = solveropfnlp_2(ppc)
sol['mt'] = sol['mt'] + mt
sol['et'] = sol['et'] + et
sol['tap'] = zeros((tp.shape[0], 1))
for i in range(tp.shape[0]):
sol['tap'][i] = round(model.tap[tp[i]].value)
sol['shunt'] = zeros((sd.shape[0], 1))
for i in range(sd.shape[0]):
sol['shunt'][i] = round(model.s[sd[i]].value)
# ppc solved case is returned
return sol
if __name__ == "__main__":
from unit_commitment.test_cases import case118
test_case = case118.case118()
from pypower.case118 import case118
from pypower.idx_brch import F_BUS, T_BUS, BR_X, TAP, SHIFT, BR_STATUS, RATE_A
from pypower.idx_cost import MODEL, NCOST, PW_LINEAR, COST, POLYNOMIAL
from pypower.idx_bus import BUS_TYPE, REF, VA, VM, PD, GS, VMAX, VMIN, BUS_I
from pypower.idx_gen import GEN_BUS, VG, PG, QG, PMAX, PMIN, QMAX, QMIN
from numpy import flatnonzero as find
casedata = case118()
mpc = loadcase.loadcase(casedata)
mpc = ext2int.ext2int(mpc)
baseMVA, bus, gen, branch, gencost = mpc["baseMVA"], mpc["bus"], mpc[
"gen"], mpc["branch"], mpc["gencost"] #
nb = shape(mpc['bus'])[0] ## number of buses
nl = shape(mpc['branch'])[0] ## number of branches
ng = shape(mpc['gen'])[0] ## number of dispatchable injections
## Formualte the
stat = branch[:, BR_STATUS] ## ones at in-service branches
b = stat / branch[:, BR_X] ## series susceptance
tap = ones(nl) ## default tap ratio = 1
i = find(branch[:, TAP]) ## indices of non-zero tap ratios
tap[i] = branch[i, TAP] ## assign non-zero tap ratios
## build connection matrix Cft = Cf - Ct for line and from - to buses
def runcpf(basecasedata=None,
targetcasedata=None,
ppopt=None,
fname='',
solvedcase=''):
# default arguments
if basecasedata is None:
basecasedata = join(dirname(__file__), 'case9')
if targetcasedata is None:
targetcasedata = join(dirname(__file__), 'case9target')
ppopt = ppoption(ppopt)
# options
verbose = ppopt["VERBOSE"]
step = ppopt["CPF_STEP"]
parameterization = ppopt["CPF_PARAMETERIZATION"]
adapt_step = ppopt["CPF_ADAPT_STEP"]
cb_args = ppopt["CPF_USER_CALLBACK_ARGS"]
# set up callbacks
callback_names = ["cpf_default_callback"]
if len(ppopt["CPF_USER_CALLBACK"]) > 0:
if isinstance(ppopt["CPF_USER_CALLBACK"], list):
callback_names = r_[callback_names, ppopt["CPF_USER_CALLBACK"]]
else:
callback_names.append(ppopt["CPF_USER_CALLBACK"])
callbacks = []
for callback_name in callback_names:
callbacks.append(getattr(cpf_callbacks, callback_name))
# read base case data
ppcbase = loadcase(basecasedata)
nb = ppcbase["bus"].shape[0]
# add zero columns to branch for flows if needed
if ppcbase["branch"].shape[1] < QT:
ppcbase["branch"] = c_[ppcbase["branch"],
zeros((ppcbase["branch"].shape[0],
QT - ppcbase["branch"].shape[1] + 1))]
# convert to internal indexing
ppcbase = ext2int(ppcbase)
baseMVAb, busb, genb, branchb = \
ppcbase["baseMVA"], ppcbase["bus"], ppcbase["gen"], ppcbase["branch"]
# get bus index lists of each type of bus
ref, pv, pq = bustypes(busb, genb)
# generator info
onb = find(genb[:, GEN_STATUS] > 0) # which generators are on?
gbusb = genb[onb, GEN_BUS].astype(int) # what buses are they at?
# read target case data
ppctarget = loadcase(targetcasedata)
# add zero columns to branch for flows if needed
if ppctarget["branch"].shape[1] < QT:
ppctarget["branch"] = c_[ppctarget["branch"],
zeros(
(ppctarget["branch"].shape[0],
QT - ppctarget["branch"].shape[1] + 1))]
# convert to internal indexing
ppctarget = ext2int(ppctarget)
baseMVAt, bust, gent, brancht = \
ppctarget["baseMVA"], ppctarget["bus"], ppctarget["gen"], ppctarget["branch"]
# get bus index lists of each type of bus
# ref, pv, pq = bustypes(bust, gent)
# generator info
ont = find(gent[:, GEN_STATUS] > 0) # which generators are on?
gbust = gent[ont, GEN_BUS].astype(int) # what buses are they at?
# ----- run the power flow -----
t0 = time()
if verbose > 0:
v = ppver('all')
stdout.write('PYPOWER Version %s, %s' % (v["Version"], v["Date"]))
stdout.write(' -- AC Continuation Power Flow\n')
# initial state
# V0 = ones(bus.shape[0]) ## flat start
V0 = busb[:, VM] * exp(1j * pi / 180 * busb[:, VA])
vcb = ones(V0.shape) # create mask of voltage-controlled buses
vcb[pq] = 0 # exclude PQ buses
k = find(vcb[gbusb]) # in-service gens at v-c buses
V0[gbusb[k]] = genb[onb[k], VG] / abs(V0[gbusb[k]]) * V0[gbusb[k]]
# build admittance matrices
Ybus, Yf, Yt = makeYbus(baseMVAb, busb, branchb)
# compute base case complex bus power injections (generation - load)
Sbusb = makeSbus(baseMVAb, busb, genb)
# compute target case complex bus power injections (generation - load)
Sbust = makeSbus(baseMVAt, bust, gent)
# scheduled transfer
Sxfr = Sbust - Sbusb
# Run the base case power flow solution
if verbose > 2:
ppopt_pf = ppoption(ppopt, VERBOSE=max(0, verbose - 1))
else:
ppopt_pf = ppoption(ppopt, VERBOSE=max(0, verbose - 2))
lam = 0
V, success, iterations = newtonpf(Ybus, Sbusb, V0, ref, pv, pq, ppopt_pf)
if verbose > 2:
print('step %3d : lambda = %6.3f\n' % (0, 0))
elif verbose > 1:
print('step %3d : lambda = %6.3f, %2d Newton steps\n',
(0, 0, iterations))
lamprv = lam # lam at previous step
Vprv = V # V at previous step
continuation = 1
cont_steps = 0
# input args for callbacks
cb_data = {
"ppc_base": ppcbase,
"ppc_target": ppctarget,
"Sxfr": Sxfr,
"Ybus": Ybus,
"Yf": Yf,
"Yt": Yt,
"ref": ref,
"pv": pv,
"pq": pq,
"ppopt": ppopt
}
cb_state = {}
# invoke callbacks
for k in range(len(callbacks)):
cb_state, _ = callbacks[k](cont_steps, V, lam, V, lam, cb_data,
cb_state, cb_args)
if linalg.norm(Sxfr) == 0:
if verbose:
print(
'base case and target case have identical load and generation\n'
)
continuation = 0
V0 = V
lam0 = lam
# tangent predictor z = [dx;dlam]
z = zeros(2 * len(V) + 1)
z[-1] = 1.0
while continuation:
cont_steps = cont_steps + 1
# prediction for next step
V0, lam0, z = cpf_predictor(V, lam, Ybus, Sxfr, pv, pq, step, z, Vprv,
lamprv, parameterization)
# save previous voltage, lambda before updating
Vprv = V
lamprv = lam
# correction
V, success, i, lam = cpf_corrector(Ybus, Sbusb, V0, ref, pv, pq, lam0,
Sxfr, Vprv, lamprv, z, step,
parameterization, ppopt_pf)
if not success:
continuation = 0
if verbose:
print(
'step %3d : lambda = %6.3f, corrector did not converge in %d iterations\n'
% (cont_steps, lam, i))
break
if verbose > 2:
print('step %3d : lambda = %6.3f\n' % (cont_steps, lam))
elif verbose > 1:
print('step %3d : lambda = %6.3f, %2d corrector Newton steps\n' %
(cont_steps, lam, i))
# invoke callbacks
for k in range(len(callbacks)):
cb_state, _ = callbacks[k](cont_steps, V, lam, V0, lam0, cb_data,
cb_state, cb_args)
if isinstance(ppopt["CPF_STOP_AT"], str):
if ppopt["CPF_STOP_AT"].upper() == "FULL":
if abs(lam) < 1e-8: # traced the full continuation curve
if verbose:
print(
'\nTraced full continuation curve in %d continuation steps\n'
% cont_steps)
continuation = 0
elif lam < lamprv and lam - step < 0: # next step will overshoot
step = lam # modify step-size
parameterization = 1 # change to natural parameterization
adapt_step = False # disable step-adaptivity
else: # == 'NOSE'
if lam < lamprv: # reached the nose point
if verbose:
print(
'\nReached steady state loading limit in %d continuation steps\n'
% cont_steps)
continuation = 0
else:
if lam < lamprv:
if verbose:
print(
'\nReached steady state loading limit in %d continuation steps\n'
% cont_steps)
continuation = 0
elif abs(ppopt["CPF_STOP_AT"] -
lam) < 1e-8: # reached desired lambda
if verbose:
print(
'\nReached desired lambda %3.2f in %d continuation steps\n'
% (ppopt["CPF_STOP_AT"], cont_steps))
continuation = 0
# will reach desired lambda in next step
elif lam + step > ppopt["CPF_STOP_AT"]:
step = ppopt["CPF_STOP_AT"] - lam # modify step-size
parameterization = 1 # change to natural parameterization
adapt_step = False # disable step-adaptivity
if adapt_step and continuation:
pvpq = r_[pv, pq]
# Adapt stepsize
cpf_error = linalg.norm(
r_[angle(V[pq]), abs(V[pvpq]), lam] -
r_[angle(V0[pq]), abs(V0[pvpq]), lam0], inf)
if cpf_error < ppopt["CPF_ERROR_TOL"]:
# Increase stepsize
step = step * ppopt["CPF_ERROR_TOL"] / cpf_error
if step > ppopt["CPF_STEP_MAX"]:
step = ppopt["CPF_STEP_MAX"]
else:
# decrese stepsize
step = step * ppopt["CPF_ERROR_TOL"] / cpf_error
if step < ppopt["CPF_STEP_MIN"]:
step = ppopt["CPF_STEP_MIN"]
# invoke callbacks
if success:
cpf_results = {}
for k in range(len(callbacks)):
cb_state, cpf_results = callbacks[k](cont_steps,
V,
lam,
V0,
lam0,
cb_data,
cb_state,
cb_args,
results=cpf_results,
is_final=True)
else:
cpf_results["iterations"] = i
# update bus and gen matrices to reflect the loading and generation
# at the noise point
bust[:, PD] = busb[:, PD] + lam * (bust[:, PD] - busb[:, PD])
bust[:, QD] = busb[:, QD] + lam * (bust[:, QD] - busb[:, QD])
gent[:, PG] = genb[:, PG] + lam * (gent[:, PG] - genb[:, PG])
# update data matrices with solution
bust, gent, brancht = pfsoln(baseMVAt, bust, gent, brancht, Ybus, Yf, Yt,
V, ref, pv, pq)
ppctarget["et"] = time() - t0
ppctarget["success"] = success
# ----- output results -----
# convert back to original bus numbering & print results
ppctarget["bus"], ppctarget["gen"], ppctarget[
"branch"] = bust, gent, brancht
if success:
n = cpf_results["iterations"] + 1
cpf_results["V_p"] = i2e_data(ppctarget, cpf_results["V_p"],
full((nb, n), nan), "bus", 0)
cpf_results["V_c"] = i2e_data(ppctarget, cpf_results["V_c"],
full((nb, n), nan), "bus", 0)
results = int2ext(ppctarget)
results["cpf"] = cpf_results
# zero out result fields of out-of-service gens & branches
if len(results["order"]["gen"]["status"]["off"]) > 0:
results["gen"][ix_(results["order"]["gen"]["status"]["off"],
[PG, QG])] = 0
if len(results["order"]["branch"]["status"]["off"]) > 0:
results["branch"][ix_(results["order"]["branch"]["status"]["off"],
[PF, QF, PT, QT])] = 0
if fname:
fd = None
try:
fd = open(fname, "a")
except Exception as detail:
stderr.write("Error opening %s: %s.\n" % (fname, detail))
finally:
if fd is not None:
printpf(results, fd, ppopt)
fd.close()
else:
printpf(results, stdout, ppopt)
# save solved case
if solvedcase:
savecase(solvedcase, results)
return results, success
def run_sim(ppc, elements, dynopt = None, events = None, recorder = None):
"""
Run a time-domain simulation
Inputs:
ppc PYPOWER load flow case
elements Dictionary of dynamic model objects (machines, controllers, etc) with Object ID as key
events Events object
recorder Recorder object (empty)
Outputs:
recorder Recorder object (with data)
"""
#########
# SETUP #
#########
# Get version information
ver = pydyn_ver()
print('PYPOWER-Dynamics ' + ver['Version'] + ', ' + ver['Date'])
# Program options
if dynopt:
h = dynopt['h']
t_sim = dynopt['t_sim']
max_err = dynopt['max_err']
max_iter = dynopt['max_iter']
verbose = dynopt['verbose']
else:
# Default program options
h = 0.01 # step length (s)
t_sim = 5 # simulation time (s)
max_err = 0.0001 # Maximum error in network iteration (voltage mismatches)
max_iter = 25 # Maximum number of network iterations
verbose = False
# Make lists of current injection sources (generators, external grids, etc) and controllers
sources = []
controllers = []
for element in elements.values():
if element.__module__ in ['pydyn.sym_order6a', 'pydyn.sym_order6b', 'pydyn.sym_order4', 'pydyn.ext_grid', 'pydyn.vsc_average', 'pydyn.asym_1cage', 'pydyn.asym_2cage']:
sources.append(element)
if element.__module__ == 'pydyn.controller':
controllers.append(element)
# Set up interfaces
interfaces = init_interfaces(elements)
##################
# INITIALISATION #
##################
print('Initialising models...')
# Run power flow and update bus voltages and angles in PYPOWER case object
results, success = runpf(ppc)
ppc["bus"][:, VM] = results["bus"][:, VM]
ppc["bus"][:, VA] = results["bus"][:, VA]
# Build Ybus matrix
ppc_int = ext2int(ppc)
baseMVA, bus, branch = ppc_int["baseMVA"], ppc_int["bus"], ppc_int["branch"]
Ybus, Yf, Yt = makeYbus(baseMVA, bus, branch)
# Build modified Ybus matrix
Ybus = mod_Ybus(Ybus, elements, bus, ppc_int['gen'], baseMVA)
# Calculate initial voltage phasors
v0 = bus[:, VM] * (np.cos(np.radians(bus[:, VA])) + 1j * np.sin(np.radians(bus[:, VA])))
# Initialise sources from load flow
for source in sources:
if source.__module__ in ['pydyn.asym_1cage', 'pydyn.asym_2cage']:
# Asynchronous machine
source_bus = ppc_int['bus'][source.bus_no,0]
v_source = v0[source_bus]
source.initialise(v_source,0)
else:
# Generator or VSC
source_bus = ppc_int['gen'][source.gen_no,0]
S_source = np.complex(results["gen"][source.gen_no, 1] / baseMVA, results["gen"][source.gen_no, 2] / baseMVA)
v_source = v0[source_bus]
source.initialise(v_source,S_source)
# Interface controllers and machines (for initialisation)
for intf in interfaces:
int_type = intf[0]
var_name = intf[1]
if int_type == 'OUTPUT':
# If an output, interface in the reverse direction for initialisation
intf[2].signals[var_name] = intf[3].signals[var_name]
else:
# Inputs are interfaced in normal direction during initialisation
intf[3].signals[var_name] = intf[2].signals[var_name]
# Initialise controllers
for controller in controllers:
controller.initialise()
#############
# MAIN LOOP #
#############
if events == None:
print('Warning: no events!')
# Factorise Ybus matrix
Ybus_inv = splu(Ybus)
y1 = []
v_prev = v0
print('Simulating...')
for t in range(int(t_sim / h) + 1):
if np.mod(t,1/h) == 0:
print('t=' + str(t*h) + 's')
# Interface controllers and machines
for intf in interfaces:
var_name = intf[1]
intf[3].signals[var_name] = intf[2].signals[var_name]
# Solve differential equations
for j in range(4):
# Solve step of differential equations
for element in elements.values():
element.solve_step(h,j)
# Interface with network equations
v_prev = solve_network(sources, v_prev, Ybus_inv, ppc_int, len(bus), max_err, max_iter)
if recorder != None:
# Record signals or states
recorder.record_variables(t*h, elements)
if events != None:
# Check event stack
ppc, refactorise = events.handle_events(np.round(t*h,5), elements, ppc, baseMVA)
if refactorise == True:
# Rebuild Ybus from new ppc_int
ppc_int = ext2int(ppc)
baseMVA, bus, branch = ppc_int["baseMVA"], ppc_int["bus"], ppc_int["branch"]
Ybus, Yf, Yt = makeYbus(baseMVA, bus, branch)
# Rebuild modified Ybus
Ybus = mod_Ybus(Ybus, elements, bus, ppc_int['gen'], baseMVA)
# Refactorise Ybus
Ybus_inv = splu(Ybus)
# Solve network equations
v_prev = solve_network(sources, v_prev, Ybus_inv, ppc_int, len(bus), max_err, max_iter)
return recorder