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
alg = 700
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(find(gencost[ipol, NCOST] > 3)):
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:
opt['grb_opt'] = gurobi_options([], 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 > 0)), ## 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
def qps_ipopt(H, c, A, l, u, xmin, xmax, x0, opt):
"""Quadratic Program Solver based on IPOPT.
Uses IPOPT to solve the following QP (quadratic programming) problem::
min 1/2 x'*H*x + c'*x
x
subject to::
l <= A*x <= u (linear constraints)
xmin <= x <= xmax (variable bounds)
Inputs (all optional except C{H}, C{C}, C{A} and C{L}):
- C{H} : matrix (possibly sparse) of quadratic cost coefficients
- C{C} : vector of linear cost coefficients
- C{A, l, u} : define the optional linear constraints. Default
values for the elements of C{l} and C{u} are -Inf and Inf,
respectively.
- C{xmin, xmax} : optional lower and upper bounds on the
C{x} variables, defaults are -Inf and Inf, respectively.
- C{x0} : optional starting value of optimization vector C{x}
- C{opt} : optional options structure with the following fields,
all of which are also optional (default values shown in parentheses)
- C{verbose} (0) - controls level of progress output displayed
- 0 = no progress output
- 1 = some progress output
- 2 = verbose progress output
- C{max_it} (0) - maximum number of iterations allowed
- 0 = use algorithm default
- C{ipopt_opt} - options struct for IPOPT, values in
C{verbose} and C{max_it} override these options
- C{problem} : The inputs can alternatively be supplied in a single
C{problem} dict with fields corresponding to the input arguments
described above: C{H, c, A, l, u, xmin, xmax, x0, opt}
Outputs:
- C{x} : solution vector
- C{f} : final objective function value
- C{exitflag} : exit flag
- 1 = first order optimality conditions satisfied
- 0 = maximum number of iterations reached
- -1 = numerically failed
- C{output} : output struct with the following fields:
- C{iterations} - number of iterations performed
- C{hist} - dict list with trajectories of the following:
C{feascond}, C{gradcond}, C{compcond}, C{costcond}, C{gamma},
C{stepsize}, C{obj}, C{alphap}, C{alphad}
- message - exit message
- C{lmbda} : dict containing the Langrange and Kuhn-Tucker
multipliers on the constraints, with fields:
- C{mu_l} - lower (left-hand) limit on linear constraints
- C{mu_u} - upper (right-hand) limit on linear constraints
- C{lower} - lower bound on optimization variables
- C{upper} - upper bound on optimization variables
Calling syntax options::
x, f, exitflag, output, lmbda = \
qps_ipopt(H, c, A, l, u, xmin, xmax, x0, opt)
x = qps_ipopt(H, c, A, l, u)
x = qps_ipopt(H, c, A, l, u, xmin, xmax)
x = qps_ipopt(H, c, A, l, u, xmin, xmax, x0)
x = qps_ipopt(H, c, A, l, u, xmin, xmax, x0, opt)
x = qps_ipopt(problem), where problem is a struct with fields:
H, c, A, l, u, xmin, xmax, x0, opt
all fields except 'c', 'A' and 'l' or 'u' are optional
x = qps_ipopt(...)
x, f = qps_ipopt(...)
x, f, exitflag = qps_ipopt(...)
x, f, exitflag, output = qps_ipopt(...)
x, f, exitflag, output, lmbda = qps_ipopt(...)
Example::
H = [ 1003.1 4.3 6.3 5.9;
4.3 2.2 2.1 3.9;
6.3 2.1 3.5 4.8;
5.9 3.9 4.8 10 ]
c = zeros((4, 1))
A = [ 1 1 1 1
0.17 0.11 0.10 0.18 ]
l = [1, 0.10]
u = [1, Inf]
xmin = zeros((4, 1))
x0 = [1, 0, 0, 1]
opt = {'verbose': 2)
x, f, s, out, lambda = qps_ipopt(H, c, A, l, u, xmin, [], x0, opt)
Problem from U{http://www.jmu.edu/docs/sasdoc/sashtml/iml/chap8/sect12.htm}
@see: C{pyipopt}, L{ipopt_options}
@author: Ray Zimmerman (PSERC Cornell)
"""
##----- input argument handling -----
## gather inputs
if isinstance(H, dict): ## problem struct
p = H
if 'opt' in p: opt = p['opt']
if 'x0' in p: x0 = p['x0']
if 'xmax' in p: xmax = p['xmax']
if 'xmin' in p: xmin = p['xmin']
if 'u' in p: u = p['u']
if 'l' in p: l = p['l']
if 'A' in p: A = p['A']
if 'c' in p: c = p['c']
if 'H' in p: H = p['H']
else: ## individual args
assert H is not None
assert c is not None
assert A is not None
assert l is not None
if opt is None:
opt = {}
# if x0 is None:
# x0 = array([])
# if xmax is None:
# xmax = array([])
# if xmin is None:
# xmin = array([])
## define nx, set default values for missing optional inputs
if len(H) == 0 or not any(any(H)):
if len(A) == 0 and len(xmin) == 0 and len(xmax) == 0:
stderr.write(
'qps_ipopt: LP problem must include constraints or variable bounds\n'
)
else:
if len(A) > 0:
nx = shape(A)[1]
elif len(xmin) > 0:
nx = len(xmin)
else: # if len(xmax) > 0
nx = len(xmax)
H = sparse((nx, nx))
else:
nx = shape(H)[0]
if len(c) == 0:
c = zeros(nx)
if len(A) > 0 and (len(l) == 0 or all(l == -Inf)) and \
(len(u) == 0 or all(u == Inf)):
A = None ## no limits => no linear constraints
nA = shape(A)[0] ## number of original linear constraints
if nA:
if len(u) == 0: ## By default, linear inequalities are ...
u = Inf * ones(nA) ## ... unbounded above and ...
if len(l) == 0:
l = -Inf * ones(nA) ## ... unbounded below.
if len(x0) == 0:
x0 = zeros(nx)
## default options
if 'verbose' in opt:
verbose = opt['verbose']
else:
verbose = 0
if 'max_it' in opt:
max_it = opt['max_it']
else:
max_it = 0
## make sure args are sparse/full as expected by IPOPT
if len(H) > 0:
if not issparse(H):
H = sparse(H)
if not issparse(A):
A = sparse(A)
##----- run optimization -----
## set options dict for IPOPT
options = {}
if 'ipopt_opt' in opt:
options['ipopt'] = ipopt_options(opt['ipopt_opt'])
else:
options['ipopt'] = ipopt_options()
options['ipopt']['jac_c_constant'] = 'yes'
options['ipopt']['jac_d_constant'] = 'yes'
options['ipopt']['hessian_constant'] = 'yes'
options['ipopt']['least_square_init_primal'] = 'yes'
options['ipopt']['least_square_init_duals'] = 'yes'
# options['ipopt']['mehrotra_algorithm'] = 'yes' ## default 'no'
if verbose:
options['ipopt']['print_level'] = min(12, verbose * 2 + 1)
else:
options['ipopt']['print_level = 0']
if max_it:
options['ipopt']['max_iter'] = max_it
## define variable and constraint bounds, if given
if nA:
options['cu'] = u
options['cl'] = l
if len(xmin) > 0:
options['lb'] = xmin
if len(xmax) > 0:
options['ub'] = xmax
## assign function handles
funcs = {}
funcs['objective'] = lambda x: 0.5 * x.T * H * x + c.T * x
funcs['gradient'] = lambda x: H * x + c
funcs['constraints'] = lambda x: A * x
funcs['jacobian'] = lambda x: A
funcs['jacobianstructure'] = lambda: A
funcs['hessian'] = lambda x, sigma, lmbda: tril(H)
funcs['hessianstructure'] = lambda: tril(H)
## run the optimization
x, info = pyipopt(x0, funcs, options)
if info['status'] == 0 | info['status'] == 1:
eflag = 1
else:
eflag = 0
output = {}
if 'iter' in info:
output['iterations'] = info['iter']
output['info'] = info['status']
f = funcs['objective'](x)
## repackage lmbdas
kl = find(info['lmbda'] < 0) ## lower bound binding
ku = find(info['lmbda'] > 0) ## upper bound binding
mu_l = zeros(nA)
mu_l[kl] = -info['lmbda'][kl]
mu_u = zeros(nA)
mu_u[ku] = info['lmbda'][ku]
lmbda = {
'mu_l': mu_l,
'mu_u': mu_u,
'lower': info['zl'],
'upper': info['zu']
}
return x, f, eflag, output, lmbda
def qps_ipopt(H, c, A, l, u, xmin, xmax, x0, opt):
"""Quadratic Program Solver based on IPOPT.
Uses IPOPT to solve the following QP (quadratic programming) problem::
min 1/2 x'*H*x + c'*x
x
subject to::
l <= A*x <= u (linear constraints)
xmin <= x <= xmax (variable bounds)
Inputs (all optional except C{H}, C{C}, C{A} and C{L}):
- C{H} : matrix (possibly sparse) of quadratic cost coefficients
- C{C} : vector of linear cost coefficients
- C{A, l, u} : define the optional linear constraints. Default
values for the elements of C{l} and C{u} are -Inf and Inf,
respectively.
- C{xmin, xmax} : optional lower and upper bounds on the
C{x} variables, defaults are -Inf and Inf, respectively.
- C{x0} : optional starting value of optimization vector C{x}
- C{opt} : optional options structure with the following fields,
all of which are also optional (default values shown in parentheses)
- C{verbose} (0) - controls level of progress output displayed
- 0 = no progress output
- 1 = some progress output
- 2 = verbose progress output
- C{max_it} (0) - maximum number of iterations allowed
- 0 = use algorithm default
- C{ipopt_opt} - options struct for IPOPT, values in
C{verbose} and C{max_it} override these options
- C{problem} : The inputs can alternatively be supplied in a single
C{problem} dict with fields corresponding to the input arguments
described above: C{H, c, A, l, u, xmin, xmax, x0, opt}
Outputs:
- C{x} : solution vector
- C{f} : final objective function value
- C{exitflag} : exit flag
- 1 = first order optimality conditions satisfied
- 0 = maximum number of iterations reached
- -1 = numerically failed
- C{output} : output struct with the following fields:
- C{iterations} - number of iterations performed
- C{hist} - dict list with trajectories of the following:
C{feascond}, C{gradcond}, C{compcond}, C{costcond}, C{gamma},
C{stepsize}, C{obj}, C{alphap}, C{alphad}
- message - exit message
- C{lmbda} : dict containing the Langrange and Kuhn-Tucker
multipliers on the constraints, with fields:
- C{mu_l} - lower (left-hand) limit on linear constraints
- C{mu_u} - upper (right-hand) limit on linear constraints
- C{lower} - lower bound on optimization variables
- C{upper} - upper bound on optimization variables
Calling syntax options::
x, f, exitflag, output, lmbda = \
qps_ipopt(H, c, A, l, u, xmin, xmax, x0, opt)
x = qps_ipopt(H, c, A, l, u)
x = qps_ipopt(H, c, A, l, u, xmin, xmax)
x = qps_ipopt(H, c, A, l, u, xmin, xmax, x0)
x = qps_ipopt(H, c, A, l, u, xmin, xmax, x0, opt)
x = qps_ipopt(problem), where problem is a struct with fields:
H, c, A, l, u, xmin, xmax, x0, opt
all fields except 'c', 'A' and 'l' or 'u' are optional
x = qps_ipopt(...)
x, f = qps_ipopt(...)
x, f, exitflag = qps_ipopt(...)
x, f, exitflag, output = qps_ipopt(...)
x, f, exitflag, output, lmbda = qps_ipopt(...)
Example::
H = [ 1003.1 4.3 6.3 5.9;
4.3 2.2 2.1 3.9;
6.3 2.1 3.5 4.8;
5.9 3.9 4.8 10 ]
c = zeros((4, 1))
A = [ 1 1 1 1
0.17 0.11 0.10 0.18 ]
l = [1, 0.10]
u = [1, Inf]
xmin = zeros((4, 1))
x0 = [1, 0, 0, 1]
opt = {'verbose': 2)
x, f, s, out, lambda = qps_ipopt(H, c, A, l, u, xmin, [], x0, opt)
Problem from U{http://www.jmu.edu/docs/sasdoc/sashtml/iml/chap8/sect12.htm}
@see: C{pyipopt}, L{ipopt_options}
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
##----- input argument handling -----
## gather inputs
if isinstance(H, dict): ## problem struct
p = H
if 'opt' in p: opt = p['opt']
if 'x0' in p: x0 = p['x0']
if 'xmax' in p: xmax = p['xmax']
if 'xmin' in p: xmin = p['xmin']
if 'u' in p: u = p['u']
if 'l' in p: l = p['l']
if 'A' in p: A = p['A']
if 'c' in p: c = p['c']
if 'H' in p: H = p['H']
else: ## individual args
assert H is not None
assert c is not None
assert A is not None
assert l is not None
if opt is None:
opt = {}
# if x0 is None:
# x0 = array([])
# if xmax is None:
# xmax = array([])
# if xmin is None:
# xmin = array([])
## define nx, set default values for missing optional inputs
if len(H) == 0 or not any(any(H)):
if len(A) == 0 and len(xmin) == 0 and len(xmax) == 0:
stderr.write('qps_ipopt: LP problem must include constraints or variable bounds\n')
else:
if len(A) > 0:
nx = shape(A)[1]
elif len(xmin) > 0:
nx = len(xmin)
else: # if len(xmax) > 0
nx = len(xmax)
H = sparse((nx, nx))
else:
nx = shape(H)[0]
if len(c) == 0:
c = zeros(nx)
if len(A) > 0 and (len(l) == 0 or all(l == -Inf)) and \
(len(u) == 0 or all(u == Inf)):
A = None ## no limits => no linear constraints
nA = shape(A)[0] ## number of original linear constraints
if nA:
if len(u) == 0: ## By default, linear inequalities are ...
u = Inf * ones(nA) ## ... unbounded above and ...
if len(l) == 0:
l = -Inf * ones(nA) ## ... unbounded below.
if len(x0) == 0:
x0 = zeros(nx)
## default options
if 'verbose' in opt:
verbose = opt['verbose']
else:
verbose = 0
if 'max_it' in opt:
max_it = opt['max_it']
else:
max_it = 0
## make sure args are sparse/full as expected by IPOPT
if len(H) > 0:
if not issparse(H):
H = sparse(H)
if not issparse(A):
A = sparse(A)
##----- run optimization -----
## set options dict for IPOPT
options = {}
if 'ipopt_opt' in opt:
options['ipopt'] = ipopt_options(opt['ipopt_opt'])
else:
options['ipopt'] = ipopt_options()
options['ipopt']['jac_c_constant'] = 'yes'
options['ipopt']['jac_d_constant'] = 'yes'
options['ipopt']['hessian_constant'] = 'yes'
options['ipopt']['least_square_init_primal'] = 'yes'
options['ipopt']['least_square_init_duals'] = 'yes'
# options['ipopt']['mehrotra_algorithm'] = 'yes' ## default 'no'
if verbose:
options['ipopt']['print_level'] = min(12, verbose * 2 + 1)
else:
options['ipopt']['print_level = 0']
if max_it:
options['ipopt']['max_iter'] = max_it
## define variable and constraint bounds, if given
if nA:
options['cu'] = u
options['cl'] = l
if len(xmin) > 0:
options['lb'] = xmin
if len(xmax) > 0:
options['ub'] = xmax
## assign function handles
funcs = {}
funcs['objective'] = lambda x: 0.5 * x.T * H * x + c.T * x
funcs['gradient'] = lambda x: H * x + c
funcs['constraints'] = lambda x: A * x
funcs['jacobian'] = lambda x: A
funcs['jacobianstructure'] = lambda : A
funcs['hessian'] = lambda x, sigma, lmbda: tril(H)
funcs['hessianstructure'] = lambda : tril(H)
## run the optimization
x, info = pyipopt(x0, funcs, options)
if info['status'] == 0 | info['status'] == 1:
eflag = 1
else:
eflag = 0
output = {}
if 'iter' in info:
output['iterations'] = info['iter']
output['info'] = info['status']
f = funcs['objective'](x)
## repackage lmbdas
kl = find(info['lmbda'] < 0) ## lower bound binding
ku = find(info['lmbda'] > 0) ## upper bound binding
mu_l = zeros(nA)
mu_l[kl] = -info['lmbda'][kl]
mu_u = zeros(nA)
mu_u[ku] = info['lmbda'][ku]
lmbda = {
'mu_l': mu_l,
'mu_u': mu_u,
'lower': info['zl'],
'upper': info['zu']
}
return x, f, eflag, output, lmbda
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)
"""
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
alg = 700
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(find(gencost[ipol, NCOST] > 3)):
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:
opt['grb_opt'] = gurobi_options([], 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(int(ny > 0)), ## 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