def pipsopf_solver(om, ppopt, out_opt=None):
"""Solves AC optimal power flow using PIPS.
Inputs are an OPF model object, a PYPOWER options vector and
a dict containing keys (can be empty) for each of the desired
optional output fields.
outputs are a C{results} dict, C{success} flag and C{raw} output dict.
C{results} is a PYPOWER case dict (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{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{success} is C{True} if solver converged successfully, C{False} otherwise
C{raw} is a raw output dict in form returned by MINOS
- xr final value of optimization variables
- pimul constraint multipliers
- info solver specific termination code
- output solver specific output information
@see: L{opf}, L{pips}
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
@author: Richard Lincoln
"""
##----- initialization -----
## optional output
if out_opt is None:
out_opt = {}
## options
verbose = ppopt['VERBOSE']
feastol = ppopt['PDIPM_FEASTOL']
gradtol = ppopt['PDIPM_GRADTOL']
comptol = ppopt['PDIPM_COMPTOL']
costtol = ppopt['PDIPM_COSTTOL']
max_it = ppopt['PDIPM_MAX_IT']
max_red = ppopt['SCPDIPM_RED_IT']
init = ppopt['INIT']
step_control = (ppopt['OPF_ALG'] == 565) ## OPF_ALG == 565, PIPS-sc
if feastol == 0:
feastol = ppopt['OPF_VIOLATION']
opt = { 'feastol': feastol,
'gradtol': gradtol,
'comptol': comptol,
'costtol': costtol,
'max_it': max_it,
'max_red': max_red,
'step_control': step_control,
'cost_mult': 1e-4,
'verbose': verbose }
## unpack data
ppc = om.get_ppc()
baseMVA, bus, gen, branch, gencost = \
ppc["baseMVA"], ppc["bus"], ppc["gen"], ppc["branch"], ppc["gencost"]
vv, _, nn, _ = om.get_idx()
## problem dimensions
nb = bus.shape[0] ## number of buses
nl = branch.shape[0] ## number of branches
ny = om.getN('var', 'y') ## number of piece-wise linear costs
## linear constraints
A, l, u = om.linear_constraints()
## bounds on optimization vars
x0, xmin, xmax = om.getv()
## build admittance matrices
Ybus, Yf, Yt = makeYbus(baseMVA, bus, branch)
## try to select an interior initial point if init is not available from a previous powerflow
if init != "pf":
ll, uu = xmin.copy(), xmax.copy()
ll[xmin == -Inf] = -1e10 ## replace Inf with numerical proxies
uu[xmax == Inf] = 1e10
x0 = (ll + uu) / 2
Varefs = bus[bus[:, BUS_TYPE] == REF, VA] * (pi / 180)
## angles set to first reference angle
x0[vv["i1"]["Va"]:vv["iN"]["Va"]] = Varefs[0]
if ny > 0:
ipwl = find(gencost[:, MODEL] == PW_LINEAR)
# PQ = r_[gen[:, PMAX], gen[:, QMAX]]
# c = totcost(gencost[ipwl, :], PQ[ipwl])
c = gencost.flatten('F')[sub2ind(gencost.shape, ipwl, NCOST+2*gencost[ipwl, NCOST])] ## largest y-value in CCV data
x0[vv["i1"]["y"]:vv["iN"]["y"]] = max(c) + 0.1 * abs(max(c))
# x0[vv["i1"]["y"]:vv["iN"]["y"]] = c + 0.1 * abs(c)
## find branches with flow limits
il = find((branch[:, RATE_A] != 0) & (branch[:, RATE_A] < 1e10))
nl2 = len(il) ## number of constrained lines
##----- run opf -----
f_fcn = lambda x, return_hessian=False: opf_costfcn(x, om, return_hessian)
gh_fcn = lambda x: opf_consfcn(x, om, Ybus, Yf[il, :], Yt[il,:], ppopt, il)
hess_fcn = lambda x, lmbda, cost_mult: opf_hessfcn(x, lmbda, om, Ybus, Yf[il, :], Yt[il, :], ppopt, il, cost_mult)
solution = pips(f_fcn, x0, A, l, u, xmin, xmax, gh_fcn, hess_fcn, opt)
x, f, info, lmbda, output = solution["x"], solution["f"], \
solution["eflag"], solution["lmbda"], solution["output"]
success = (info > 0)
## update solution data
Va = x[vv["i1"]["Va"]:vv["iN"]["Va"]]
Vm = x[vv["i1"]["Vm"]:vv["iN"]["Vm"]]
Pg = x[vv["i1"]["Pg"]:vv["iN"]["Pg"]]
Qg = x[vv["i1"]["Qg"]:vv["iN"]["Qg"]]
V = Vm * exp(1j * Va)
##----- calculate return values -----
## update voltages & generator outputs
bus[:, VA] = Va * 180 / pi
bus[:, VM] = Vm
gen[:, PG] = Pg * baseMVA
gen[:, QG] = Qg * baseMVA
gen[:, VG] = Vm[ gen[:, GEN_BUS].astype(int) ]
## compute branch flows
Sf = V[ branch[:, F_BUS].astype(int) ] * conj(Yf * V) ## cplx pwr at "from" bus, p["u"].
St = V[ branch[:, T_BUS].astype(int) ] * conj(Yt * V) ## cplx pwr at "to" bus, p["u"].
branch[:, PF] = Sf.real * baseMVA
branch[:, QF] = Sf.imag * baseMVA
branch[:, PT] = St.real * baseMVA
branch[:, QT] = St.imag * baseMVA
## line constraint is actually on square of limit
## so we must fix multipliers
muSf = zeros(nl)
muSt = zeros(nl)
if len(il) > 0:
muSf[il] = \
2 * lmbda["ineqnonlin"][:nl2] * branch[il, RATE_A] / baseMVA
muSt[il] = \
2 * lmbda["ineqnonlin"][nl2:nl2+nl2] * branch[il, RATE_A] / baseMVA
## update Lagrange multipliers
bus[:, MU_VMAX] = lmbda["upper"][vv["i1"]["Vm"]:vv["iN"]["Vm"]]
bus[:, MU_VMIN] = lmbda["lower"][vv["i1"]["Vm"]:vv["iN"]["Vm"]]
gen[:, MU_PMAX] = lmbda["upper"][vv["i1"]["Pg"]:vv["iN"]["Pg"]] / baseMVA
gen[:, MU_PMIN] = lmbda["lower"][vv["i1"]["Pg"]:vv["iN"]["Pg"]] / baseMVA
gen[:, MU_QMAX] = lmbda["upper"][vv["i1"]["Qg"]:vv["iN"]["Qg"]] / baseMVA
gen[:, MU_QMIN] = lmbda["lower"][vv["i1"]["Qg"]:vv["iN"]["Qg"]] / baseMVA
bus[:, LAM_P] = \
lmbda["eqnonlin"][nn["i1"]["Pmis"]:nn["iN"]["Pmis"]] / baseMVA
bus[:, LAM_Q] = \
lmbda["eqnonlin"][nn["i1"]["Qmis"]:nn["iN"]["Qmis"]] / baseMVA
branch[:, MU_SF] = muSf / baseMVA
branch[:, MU_ST] = muSt / baseMVA
## package up results
nlnN = om.getN('nln')
## extract multipliers for nonlinear constraints
kl = find(lmbda["eqnonlin"] < 0)
ku = find(lmbda["eqnonlin"] > 0)
nl_mu_l = zeros(nlnN)
nl_mu_u = r_[zeros(2*nb), muSf, muSt]
nl_mu_l[kl] = -lmbda["eqnonlin"][kl]
nl_mu_u[ku] = lmbda["eqnonlin"][ku]
mu = {
'var': {'l': lmbda["lower"], 'u': lmbda["upper"]},
'nln': {'l': nl_mu_l, 'u': nl_mu_u},
'lin': {'l': lmbda["mu_l"], 'u': lmbda["mu_u"]} }
results = ppc
results["bus"], results["branch"], results["gen"], \
results["om"], results["x"], results["mu"], results["f"] = \
bus, branch, gen, om, x, mu, f
pimul = r_[
results["mu"]["nln"]["l"] - results["mu"]["nln"]["u"],
results["mu"]["lin"]["l"] - results["mu"]["lin"]["u"],
-ones(int(ny > 0)),
results["mu"]["var"]["l"] - results["mu"]["var"]["u"],
]
raw = {'xr': x, 'pimul': pimul, 'info': info, 'output': output}
return results, success, raw
def dcopf_solver(om, ppopt, out_opt=None):
"""Solves a DC optimal power flow.
Inputs are an OPF model object, a PYPOWER options dict and
a dict containing fields (can be empty) for each of the desired
optional output fields.
Outputs are a C{results} dict, C{success} flag and C{raw} output dict.
C{results} is a PYPOWER case dict (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{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{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{success} is C{True} if solver converged successfully, C{False} otherwise.
C{raw} is a raw output dict in form returned by MINOS
- C{xr} final value of optimization variables
- C{pimul} constraint multipliers
- C{info} solver specific termination code
- C{output} solver specific output information
@see: L{opf}, L{qps_pypower}
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
@author: Richard Lincoln
"""
if out_opt is None:
out_opt = {}
## options
verbose = ppopt['VERBOSE']
alg = ppopt['OPF_ALG_DC']
if alg == 0:
if have_fcn('cplex'): ## use CPLEX by default, if available
alg = 500
elif have_fcn('mosek'): ## if not, then MOSEK, if available
alg = 600
elif have_fcn('gurobi'): ## if not, then Gurobi, if available
# Error in Gurobi pypower solver -> Issue with pypower 5.1.4. Gurobi won't work. Using alg 200 instead
# Reason for failure: In qps_gurobi of pypower len(H) raises Error:
# TypeError: sparse matrix length is ambiguous; use getnnz() or shape[0]
# Todo: Fix Gurobi and activate 700 again. ATM: Fallback on 200
# alg = 700
alg = 200
UserWarning("Gurobi not working with pypower 5.1.4")
else: ## otherwise PIPS
alg = 200
## unpack data
ppc = om.get_ppc()
baseMVA, bus, gen, branch, gencost = \
ppc["baseMVA"], ppc["bus"], ppc["gen"], ppc["branch"], ppc["gencost"]
cp = om.get_cost_params()
N, H, Cw = cp["N"], cp["H"], cp["Cw"]
fparm = array(c_[cp["dd"], cp["rh"], cp["kk"], cp["mm"]])
Bf = om.userdata('Bf')
Pfinj = om.userdata('Pfinj')
vv, ll, _, _ = om.get_idx()
## problem dimensions
ipol = find(gencost[:, MODEL] == POLYNOMIAL) ## polynomial costs
ipwl = find(gencost[:, MODEL] == PW_LINEAR) ## piece-wise linear costs
nb = bus.shape[0] ## number of buses
nl = branch.shape[0] ## number of branches
nw = N.shape[0] ## number of general cost vars, w
ny = om.getN('var', 'y') ## number of piece-wise linear costs
nxyz = om.getN('var') ## total number of control vars of all types
## linear constraints & variable bounds
A, l, u = om.linear_constraints()
x0, xmin, xmax = om.getv()
## set up objective function of the form: f = 1/2 * X'*HH*X + CC'*X
## where X = [x;y;z]. First set up as quadratic function of w,
## f = 1/2 * w'*HHw*w + CCw'*w, where w = diag(M) * (N*X - Rhat). We
## will be building on the (optionally present) user supplied parameters.
## piece-wise linear costs
any_pwl = int(ny > 0)
if any_pwl:
# Sum of y vars.
Npwl = sparse(
(ones(ny), (zeros(ny), arange(vv["i1"]["y"], vv["iN"]["y"]))),
(1, nxyz))
Hpwl = sparse((1, 1))
Cpwl = array([1])
fparm_pwl = array([[1, 0, 0, 1]])
else:
Npwl = None #zeros((0, nxyz))
Hpwl = None #array([])
Cpwl = array([])
fparm_pwl = zeros((0, 4))
## quadratic costs
npol = len(ipol)
if any(len(gencost[ipol, NCOST] > 3)) and sum(
gencost[find(gencost[ipol, NCOST] > 3)][:][NCOST + 1:]):
stderr.write('DC opf cannot handle polynomial costs with higher '
'than quadratic order.\n')
iqdr = find(gencost[ipol, NCOST] == 3)
ilin = find(gencost[ipol, NCOST] == 2)
polycf = zeros((npol, 3)) ## quadratic coeffs for Pg
if len(iqdr) > 0:
polycf[iqdr, :] = gencost[ipol[iqdr], COST:COST + 3]
if npol:
polycf[ilin, 1:3] = gencost[ipol[ilin], COST:COST + 2]
polycf = dot(polycf, diag([baseMVA**2, baseMVA, 1])) ## convert to p.u.
if npol:
Npol = sparse((ones(npol), (arange(npol), vv["i1"]["Pg"] + ipol)),
(npol, nxyz)) # Pg vars
Hpol = sparse((2 * polycf[:, 0], (arange(npol), arange(npol))),
(npol, npol))
else:
Npol = None
Hpol = None
Cpol = polycf[:, 1]
fparm_pol = ones((npol, 1)) * array([[1, 0, 0, 1]])
## combine with user costs
NN = vstack(
[n for n in [Npwl, Npol, N] if n is not None and n.shape[0] > 0],
"csr")
# FIXME: Zero dimension sparse matrices.
if (Hpwl is not None) and any_pwl and (npol + nw):
Hpwl = hstack([Hpwl, sparse((any_pwl, npol + nw))])
if Hpol is not None:
if any_pwl and npol:
Hpol = hstack([sparse((npol, any_pwl)), Hpol])
if npol and nw:
Hpol = hstack([Hpol, sparse((npol, nw))])
if (H is not None) and nw and (any_pwl + npol):
H = hstack([sparse((nw, any_pwl + npol)), H])
HHw = vstack(
[h for h in [Hpwl, Hpol, H] if h is not None and h.shape[0] > 0],
"csr")
CCw = r_[Cpwl, Cpol, Cw]
ffparm = r_[fparm_pwl, fparm_pol, fparm]
## transform quadratic coefficients for w into coefficients for X
nnw = any_pwl + npol + nw
M = sparse((ffparm[:, 3], (range(nnw), range(nnw))))
MR = M * ffparm[:, 1]
HMR = HHw * MR
MN = M * NN
HH = MN.T * HHw * MN
CC = MN.T * (CCw - HMR)
C0 = 0.5 * dot(MR, HMR) + sum(polycf[:, 2]) # Constant term of cost.
## set up input for QP solver
opt = {'alg': alg, 'verbose': verbose}
if (alg == 200) or (alg == 250):
## try to select an interior initial point
Varefs = bus[bus[:, BUS_TYPE] == REF, VA] * (pi / 180.0)
lb, ub = xmin.copy(), xmax.copy()
lb[xmin == -Inf] = -1e10 ## replace Inf with numerical proxies
ub[xmax == Inf] = 1e10
x0 = (lb + ub) / 2
# angles set to first reference angle
x0[vv["i1"]["Va"]:vv["iN"]["Va"]] = Varefs[0]
if ny > 0:
ipwl = find(gencost[:, MODEL] == PW_LINEAR)
# largest y-value in CCV data
c = gencost.flatten('F')[sub2ind(gencost.shape, ipwl,
NCOST + 2 * gencost[ipwl, NCOST])]
x0[vv["i1"]["y"]:vv["iN"]["y"]] = max(c) + 0.1 * abs(max(c))
## set up options
feastol = ppopt['PDIPM_FEASTOL']
gradtol = ppopt['PDIPM_GRADTOL']
comptol = ppopt['PDIPM_COMPTOL']
costtol = ppopt['PDIPM_COSTTOL']
max_it = ppopt['PDIPM_MAX_IT']
max_red = ppopt['SCPDIPM_RED_IT']
if feastol == 0:
feastol = ppopt['OPF_VIOLATION'] ## = OPF_VIOLATION by default
opt["pips_opt"] = {
'feastol': feastol,
'gradtol': gradtol,
'comptol': comptol,
'costtol': costtol,
'max_it': max_it,
'max_red': max_red,
'cost_mult': 1
}
# elif alg == 400:
# opt['ipopt_opt'] = ipopt_options([], ppopt)
# elif alg == 500:
# opt['cplex_opt'] = cplex_options([], ppopt)
# elif alg == 600:
# opt['mosek_opt'] = mosek_options([], ppopt)
# elif alg == 700:
# ppopt['GRB_OPT'] = 0
# ppopt['GRB_METHOD'] = "automatic"
# ppopt['GRB_TIMELIMIT'] = Inf
# ppopt['GRB_THREADS'] = 0
# opt['GRB_OPT'] = gurobi_options(None, ppopt)
# else:
# raise ValueError("Unrecognised solver [%d]." % alg)
##----- run opf -----
x, f, info, output, lmbda = \
qps_pypower(HH, CC, A, l, u, xmin, xmax, x0, opt)
success = (info == 1)
##----- calculate return values -----
if not any(isnan(x)):
## update solution data
Va = x[vv["i1"]["Va"]:vv["iN"]["Va"]]
Pg = x[vv["i1"]["Pg"]:vv["iN"]["Pg"]]
f = f + C0
## update voltages & generator outputs
bus[:, VA] = Va * 180 / pi
gen[:, PG] = Pg * baseMVA
## compute branch flows
branch[:, [QF, QT]] = zeros((nl, 2))
branch[:, PF] = (Bf * Va + Pfinj) * baseMVA
branch[:, PT] = -branch[:, PF]
## package up results
mu_l = lmbda["mu_l"]
mu_u = lmbda["mu_u"]
muLB = lmbda["lower"]
muUB = lmbda["upper"]
## update Lagrange multipliers
il = find((branch[:, RATE_A] != 0) & (branch[:, RATE_A] < 1e10))
bus[:, [LAM_P, LAM_Q, MU_VMIN, MU_VMAX]] = zeros((nb, 4))
gen[:, [MU_PMIN, MU_PMAX, MU_QMIN, MU_QMAX]] = zeros((gen.shape[0], 4))
branch[:, [MU_SF, MU_ST]] = zeros((nl, 2))
bus[:, LAM_P] = (mu_u[ll["i1"]["Pmis"]:ll["iN"]["Pmis"]] -
mu_l[ll["i1"]["Pmis"]:ll["iN"]["Pmis"]]) / baseMVA
branch[il, MU_SF] = mu_u[ll["i1"]["Pf"]:ll["iN"]["Pf"]] / baseMVA
branch[il, MU_ST] = mu_u[ll["i1"]["Pt"]:ll["iN"]["Pt"]] / baseMVA
gen[:, MU_PMIN] = muLB[vv["i1"]["Pg"]:vv["iN"]["Pg"]] / baseMVA
gen[:, MU_PMAX] = muUB[vv["i1"]["Pg"]:vv["iN"]["Pg"]] / baseMVA
pimul = r_[mu_l - mu_u, -ones(
(ny)), ## dummy entry corresponding to linear cost row in A
muLB - muUB]
mu = {'var': {'l': muLB, 'u': muUB}, 'lin': {'l': mu_l, 'u': mu_u}}
results = deepcopy(ppc)
results["bus"], results["branch"], results["gen"], \
results["om"], results["x"], results["mu"], results["f"] = \
bus, branch, gen, om, x, mu, f
raw = {'xr': x, 'pimul': pimul, 'info': info, 'output': output}
return results, success, raw