pf.py

## Copyright 2015-2017 Tom Brown (FIAS), Jonas Hoersch (FIAS)

## This program is free software; you can redistribute it and/or
## modify it under the terms of the GNU General Public License as
## published by the Free Software Foundation; either version 3 of the
## License, or (at your option) any later version.

## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.

## You should have received a copy of the GNU General Public License
## along with this program.  If not, see <http://www.gnu.org/licenses/>.

"""Power flow functionality.
"""

# make the code as Python 3 compatible as possible
from __future__ import division, absolute_import
from six.moves import range
from six import iterkeys

__author__ = "Tom Brown (FIAS), Jonas Hoersch (FIAS)"
__copyright__ = "Copyright 2015-2017 Tom Brown (FIAS), Jonas Hoersch (FIAS), GNU GPL 3"

import logging
logger = logging.getLogger(__name__)

from scipy.sparse import issparse, csr_matrix, csc_matrix, hstack as shstack, vstack as svstack, dok_matrix

from numpy import r_, ones, zeros, newaxis
from scipy.sparse.linalg import spsolve
from numpy.linalg import norm

import numpy as np
import pandas as pd
import scipy as sp, scipy.sparse
import networkx as nx

import collections, six
from itertools import chain
import time

from .descriptors import get_switchable_as_dense, allocate_series_dataframes, Dict

def _as_snapshots(network, snapshots):
    if snapshots is None:
        snapshots = network.snapshots
    if (isinstance(snapshots, six.string_types) or
        not isinstance(snapshots, (collections.Sequence, pd.Index))):
        return pd.Index([snapshots])
    else:
        return pd.Index(snapshots)


def _allocate_pf_outputs(network, linear=False):

    to_allocate = {'Generator': ['p'],
                   'Load': ['p'],
                   'StorageUnit': ['p'],
                   'Store': ['p'],
                   'ShuntImpedance': ['p'],
                   'Bus': ['p', 'v_ang', 'v_mag_pu'],
                   'Line': ['p0', 'p1'],
                   'Transformer': ['p0', 'p1'],
                   'Link': ['p0', 'p1']}

    if not linear:
        for component, attrs in to_allocate.items():
            if "p" in attrs:
                attrs.append("q")
            if "p0" in attrs and component != 'Link':
                attrs.extend(["q0","q1"])

    allocate_series_dataframes(network, to_allocate)



def _network_prepare_and_run_pf(network, snapshots, skip_pre, linear=False, **kwargs):

    if linear:
        sub_network_pf_fun = sub_network_lpf
        sub_network_prepare_fun = calculate_B_H
    else:
        sub_network_pf_fun = sub_network_pf
        sub_network_prepare_fun = calculate_Y

    if not skip_pre:
        network.determine_network_topology()
        calculate_dependent_values(network)
        _allocate_pf_outputs(network, linear)

    snapshots = _as_snapshots(network, snapshots)

    #deal with links
    if not network.links.empty:
        p_set = get_switchable_as_dense(network, 'Link', 'p_set', snapshots)
        network.links_t.p0.loc[snapshots] = p_set.loc[snapshots]
        network.links_t.p1.loc[snapshots] = -p_set.loc[snapshots].multiply(network.links.efficiency)

    itdf = pd.DataFrame(index=snapshots, columns=network.sub_networks.index, dtype=int)
    difdf = pd.DataFrame(index=snapshots, columns=network.sub_networks.index)
    cnvdf = pd.DataFrame(index=snapshots, columns=network.sub_networks.index, dtype=bool)
    for sub_network in network.sub_networks.obj:
        if not skip_pre:
            find_bus_controls(sub_network)

            branches_i = sub_network.branches_i()
            if len(branches_i) > 0:
                sub_network_prepare_fun(sub_network, skip_pre=True)
        if not linear:
            itdf[sub_network.name], difdf[sub_network.name], cnvdf[sub_network.name] = sub_network_pf_fun(sub_network, snapshots=snapshots, skip_pre=True, **kwargs)
        else:
            sub_network_pf_fun(sub_network, snapshots=snapshots, skip_pre=True, **kwargs)

    if not linear:
        return Dict({ 'n_iter': itdf, 'error': difdf, 'converged': cnvdf })

def network_pf(network, snapshots=None, skip_pre=False, x_tol=1e-6, use_seed=False):
    """
    Full non-linear power flow for generic network.

    Parameters
    ----------
    snapshots : list-like|single snapshot
        A subset or an elements of network.snapshots on which to run
        the power flow, defaults to network.snapshots
    skip_pre: bool, default False
        Skip the preliminary steps of computing topology, calculating dependent values and finding bus controls.
    x_tol: float
        Tolerance for Newton-Raphson power flow.
    use_seed : bool, default False
        Use a seed for the initial guess for the Newton-Raphson algorithm.

    Returns
    -------
    Dictionary with keys 'n_iter', 'converged', 'error' and dataframe
    values indicating number of iterations, convergence status, and
    iteration error for each snapshot (rows) and sub_network (columns)
    """

    return _network_prepare_and_run_pf(network, snapshots, skip_pre, linear=False, x_tol=x_tol, use_seed=use_seed)


def newton_raphson_sparse(f, guess, dfdx, x_tol=1e-10, lim_iter=100):
    """Solve f(x) = 0 with initial guess for x and dfdx(x). dfdx(x) should
    return a sparse Jacobian.  Terminate if error on norm of f(x) is <
    x_tol or there were more than lim_iter iterations.

    """

    converged = False
    n_iter = 0
    F = f(guess)
    diff = norm(F,np.Inf)

    logger.debug("Error at iteration %d: %f", n_iter, diff)

    while diff > x_tol and n_iter < lim_iter:

        n_iter +=1

        guess = guess - spsolve(dfdx(guess),F)

        F = f(guess)
        diff = norm(F,np.Inf)

        logger.debug("Error at iteration %d: %f", n_iter, diff)

    if diff > x_tol:
        logger.warn("Warning, we didn't reach the required tolerance within %d iterations, error is at %f. See the section \"Troubleshooting\" in the documentation for tips to fix this. ", n_iter, diff)
    elif not np.isnan(diff):
        converged = True

    return guess, n_iter, diff, converged



def sub_network_pf(sub_network, snapshots=None, skip_pre=False, x_tol=1e-6, use_seed=False):
    """
    Non-linear power flow for connected sub-network.

    Parameters
    ----------
    snapshots : list-like|single snapshot
        A subset or an elements of network.snapshots on which to run
        the power flow, defaults to network.snapshots
    skip_pre: bool, default False
        Skip the preliminary steps of computing topology, calculating dependent values and finding bus controls.
    x_tol: float
        Tolerance for Newton-Raphson power flow.
    use_seed : bool, default False
        Use a seed for the initial guess for the Newton-Raphson algorithm.

    Returns
    -------
    Tuple of three pandas.Series indicating number of iterations,
    remaining error, and convergence status for each snapshot
    """

    snapshots = _as_snapshots(sub_network.network, snapshots)
    logger.info("Performing non-linear load-flow on {} sub-network {} for snapshots {}".format(sub_network.network.sub_networks.at[sub_network.name,"carrier"], sub_network, snapshots))

    # _sub_network_prepare_pf(sub_network, snapshots, skip_pre, calculate_Y)
    network = sub_network.network

    from .components import passive_branch_components, controllable_branch_components, controllable_one_port_components

    if not skip_pre:
        calculate_dependent_values(network)
        find_bus_controls(sub_network)
        _allocate_pf_outputs(network, linear=False)


    # get indices for the components on this subnetwork
    branches_i = sub_network.branches_i()
    buses_o = sub_network.buses_o

    if not skip_pre and len(branches_i) > 0:
        calculate_Y(sub_network, skip_pre=True)

    for n in ("q", "p"):
        # allow all one ports to dispatch as set
        for c in sub_network.iterate_components(controllable_one_port_components):
            c_n_set = get_switchable_as_dense(network, c.name, n + '_set', snapshots, c.ind)
            c.pnl[n].loc[snapshots, c.ind] = c_n_set

        # set the power injection at each node from controllable components
        network.buses_t[n].loc[snapshots, buses_o] = \
            sum([((c.pnl[n].loc[snapshots, c.ind] * c.df.loc[c.ind, 'sign'])
                  .groupby(c.df.loc[c.ind, 'bus'], axis=1).sum()
                  .reindex(columns=buses_o, fill_value=0.))
                 for c in sub_network.iterate_components(controllable_one_port_components)])

        if n == "p":
            network.buses_t[n].loc[snapshots, buses_o] += sum(
                [(- c.pnl[n+str(i)].loc[snapshots].groupby(c.df["bus"+str(i)], axis=1).sum()
                  .reindex(columns=buses_o, fill_value=0))
                 for c in network.iterate_components(controllable_branch_components)
                 for i in [0,1]])

    def f(guess):
        network.buses_t.v_ang.loc[now,sub_network.pvpqs] = guess[:len(sub_network.pvpqs)]

        network.buses_t.v_mag_pu.loc[now,sub_network.pqs] = guess[len(sub_network.pvpqs):]

        v_mag_pu = network.buses_t.v_mag_pu.loc[now,buses_o]
        v_ang = network.buses_t.v_ang.loc[now,buses_o]
        V = v_mag_pu*np.exp(1j*v_ang)

        mismatch = V*np.conj(sub_network.Y*V) - s

        F = r_[mismatch.real[1:],mismatch.imag[1+len(sub_network.pvs):]]

        return F


    def dfdx(guess):

        network.buses_t.v_ang.loc[now,sub_network.pvpqs] = guess[:len(sub_network.pvpqs)]

        network.buses_t.v_mag_pu.loc[now,sub_network.pqs] = guess[len(sub_network.pvpqs):]

        v_mag_pu = network.buses_t.v_mag_pu.loc[now,buses_o]
        v_ang = network.buses_t.v_ang.loc[now,buses_o]

        V = v_mag_pu*np.exp(1j*v_ang)

        index = r_[:len(buses_o)]

        #make sparse diagonal matrices
        V_diag = csr_matrix((V,(index,index)))
        V_norm_diag = csr_matrix((V/abs(V),(index,index)))
        I_diag = csr_matrix((sub_network.Y*V,(index,index)))

        dS_dVa = 1j*V_diag*np.conj(I_diag - sub_network.Y*V_diag)

        dS_dVm = V_norm_diag*np.conj(I_diag) + V_diag * np.conj(sub_network.Y*V_norm_diag)

        J00 = dS_dVa[1:,1:].real
        J01 = dS_dVm[1:,1+len(sub_network.pvs):].real
        J10 = dS_dVa[1+len(sub_network.pvs):,1:].imag
        J11 = dS_dVm[1+len(sub_network.pvs):,1+len(sub_network.pvs):].imag

        J = svstack([
            shstack([J00, J01]),
            shstack([J10, J11])
        ], format="csr")

        return J


    #Set what we know: slack V and v_mag_pu for PV buses
    v_mag_pu_set = get_switchable_as_dense(network, 'Bus', 'v_mag_pu_set', snapshots)
    network.buses_t.v_mag_pu.loc[snapshots,sub_network.pvs] = v_mag_pu_set.loc[:,sub_network.pvs]
    network.buses_t.v_mag_pu.loc[snapshots,sub_network.slack_bus] = v_mag_pu_set.loc[:,sub_network.slack_bus]
    network.buses_t.v_ang.loc[snapshots,sub_network.slack_bus] = 0.

    if not use_seed:
        network.buses_t.v_mag_pu.loc[snapshots,sub_network.pqs] = 1.
        network.buses_t.v_ang.loc[snapshots,sub_network.pvpqs] = 0.

    ss = np.empty((len(snapshots), len(buses_o)), dtype=np.complex)
    roots = np.empty((len(snapshots), len(sub_network.pvpqs) + len(sub_network.pqs)))
    iters = pd.Series(0, index=snapshots)
    diffs = pd.Series(index=snapshots)
    convs = pd.Series(False, index=snapshots)
    for i, now in enumerate(snapshots):
        p = network.buses_t.p.loc[now,buses_o]
        q = network.buses_t.q.loc[now,buses_o]
        ss[i] = s = p + 1j*q

        #Make a guess for what we don't know: V_ang for PV and PQs and v_mag_pu for PQ buses
        guess = r_[network.buses_t.v_ang.loc[now,sub_network.pvpqs],network.buses_t.v_mag_pu.loc[now,sub_network.pqs]]

        #Now try and solve
        start = time.time()
        roots[i], n_iter, diff, converged = newton_raphson_sparse(f,guess,dfdx,x_tol=x_tol)
        logger.info("Newton-Raphson solved in %d iterations with error of %f in %f seconds", n_iter,diff,time.time()-start)
        iters[now] = n_iter
        diffs[now] = diff
        convs[now] = converged


    #now set everything
    network.buses_t.v_ang.loc[snapshots,sub_network.pvpqs] = roots[:,:len(sub_network.pvpqs)]
    network.buses_t.v_mag_pu.loc[snapshots,sub_network.pqs] = roots[:,len(sub_network.pvpqs):]

    v_mag_pu = network.buses_t.v_mag_pu.loc[snapshots,buses_o].values
    v_ang = network.buses_t.v_ang.loc[snapshots,buses_o].values

    V = v_mag_pu*np.exp(1j*v_ang)

    #add voltages to branches
    buses_indexer = buses_o.get_indexer
    branch_bus0 = []; branch_bus1 = []
    for c in sub_network.iterate_components(passive_branch_components):
        branch_bus0 += list(c.df.loc[c.ind, 'bus0'])
        branch_bus1 += list(c.df.loc[c.ind, 'bus1'])
    v0 = V[:,buses_indexer(branch_bus0)]
    v1 = V[:,buses_indexer(branch_bus1)]

    i0 = np.empty((len(snapshots), sub_network.Y0.shape[0]), dtype=np.complex)
    i1 = np.empty((len(snapshots), sub_network.Y1.shape[0]), dtype=np.complex)
    for i, now in enumerate(snapshots):
        i0[i] = sub_network.Y0*V[i]
        i1[i] = sub_network.Y1*V[i]

    s0 = pd.DataFrame(v0*np.conj(i0), columns=branches_i, index=snapshots)
    s1 = pd.DataFrame(v1*np.conj(i1), columns=branches_i, index=snapshots)
    for c in sub_network.iterate_components(passive_branch_components):
        s0t = s0.loc[:,c.name]
        s1t = s1.loc[:,c.name]
        c.pnl.p0.loc[snapshots,s0t.columns] = s0t.values.real
        c.pnl.q0.loc[snapshots,s0t.columns] = s0t.values.imag
        c.pnl.p1.loc[snapshots,s1t.columns] = s1t.values.real
        c.pnl.q1.loc[snapshots,s1t.columns] = s1t.values.imag

    s_calc = np.empty((len(snapshots), len(buses_o)), dtype=np.complex)
    for i in np.arange(len(snapshots)):
        s_calc[i] = V[i]*np.conj(sub_network.Y*V[i])
    slack_index = buses_o.get_loc(sub_network.slack_bus)
    network.buses_t.p.loc[snapshots,sub_network.slack_bus] = s_calc[:,slack_index].real
    network.buses_t.q.loc[snapshots,sub_network.slack_bus] = s_calc[:,slack_index].imag
    network.buses_t.q.loc[snapshots,sub_network.pvs] = s_calc[:,buses_indexer(sub_network.pvs)].imag

    #set shunt impedance powers
    shunt_impedances_i = sub_network.shunt_impedances_i()
    if len(shunt_impedances_i):
        #add voltages
        shunt_impedances_v_mag_pu = v_mag_pu[:,buses_indexer(network.shunt_impedances.loc[shunt_impedances_i, 'bus'])]
        network.shunt_impedances_t.p.loc[snapshots,shunt_impedances_i] = (shunt_impedances_v_mag_pu**2)*network.shunt_impedances.loc[shunt_impedances_i, 'g_pu'].values
        network.shunt_impedances_t.q.loc[snapshots,shunt_impedances_i] = (shunt_impedances_v_mag_pu**2)*network.shunt_impedances.loc[shunt_impedances_i, 'b_pu'].values

    #let slack generator take up the slack
    network.generators_t.p.loc[snapshots,sub_network.slack_generator] += network.buses_t.p.loc[snapshots,sub_network.slack_bus] - ss[:,slack_index].real
    network.generators_t.q.loc[snapshots,sub_network.slack_generator] += network.buses_t.q.loc[snapshots,sub_network.slack_bus] - ss[:,slack_index].imag

    #set the Q of the PV generators
    network.generators_t.q.loc[snapshots,network.buses.loc[sub_network.pvs, "generator"]] += np.asarray(network.buses_t.q.loc[snapshots,sub_network.pvs] - ss[:,buses_indexer(sub_network.pvs)].imag)

    return iters, diffs, convs


def network_lpf(network, snapshots=None, skip_pre=False):
    """
    Linear power flow for generic network.

    Parameters
    ----------
    snapshots : list-like|single snapshot
        A subset or an elements of network.snapshots on which to run
        the power flow, defaults to network.snapshots
    skip_pre: bool, default False
        Skip the preliminary steps of computing topology, calculating
        dependent values and finding bus controls.

    Returns
    -------
    None
    """

    _network_prepare_and_run_pf(network, snapshots, skip_pre, linear=True)


def apply_line_types(network):
    """Calculate line electrical parameters x, r, b, g from standard
    types.

    """

    lines_with_types = network.lines.index[network.lines.type != ""]

    if len(lines_with_types) == 0:
        return

    for attr in ["r","x"]:
        network.lines.loc[lines_with_types,attr] = network.lines.loc[lines_with_types,"type"].map(network.line_types[attr + "_per_length"])*network.lines.loc[lines_with_types,"length"]/network.lines.loc[lines_with_types,"num_parallel"]

    factor = 2*np.pi*1e-9*network.lines.loc[lines_with_types,"type"].map(network.line_types.f_nom)
    network.lines.loc[lines_with_types,"b"] = factor*network.lines.loc[lines_with_types,"type"].map(network.line_types["c_per_length"])*network.lines.loc[lines_with_types,"length"]*network.lines.loc[lines_with_types,"num_parallel"]





def apply_transformer_types(network):
    """Calculate transformer electrical parameters x, r, b, g from
    standard types.

    """

    trafos_with_types = network.transformers.index[network.transformers.type != ""]

    if len(trafos_with_types) == 0:
        return


    network.transformers.loc[trafos_with_types, "r"] = network.transformers.loc[trafos_with_types, "type"].map(network.transformer_types["vscr"])/100.

    z = network.transformers.loc[trafos_with_types, "type"].map(network.transformer_types["vsc"])/100.

    network.transformers.loc[trafos_with_types, "x"] = np.sqrt(z**2 - network.transformers.loc[trafos_with_types, "r"]**2)

    for attr in ["phase_shift","s_nom"]:
        network.transformers.loc[trafos_with_types, attr] = network.transformers.loc[trafos_with_types, "type"].map(network.transformer_types[attr])

    #NB: b and g are per unit of s_nom
    network.transformers.loc[trafos_with_types, "g"] = network.transformers.loc[trafos_with_types, "type"].map(network.transformer_types["pfe"])/(1000. * network.transformers.loc[trafos_with_types, "s_nom"])

    i0 = network.transformers.loc[trafos_with_types, "type"].map(network.transformer_types["i0"])/100.

    b_minus_squared = i0**2 - network.transformers.loc[trafos_with_types, "g"]**2

    #for some bizarre reason, some of the standard types in pandapower have i0^2 < g^2

    b_minus_squared[b_minus_squared < 0.] = 0.

    network.transformers.loc[trafos_with_types, "b"] = - np.sqrt(b_minus_squared)


    for attr in ["r","x"]:
        network.transformers.loc[trafos_with_types, attr] = network.transformers.loc[trafos_with_types, attr]/network.transformers.loc[trafos_with_types, "num_parallel"]

    for attr in ["b","g"]:
        network.transformers.loc[trafos_with_types, attr] = network.transformers.loc[trafos_with_types, attr]*network.transformers.loc[trafos_with_types, "num_parallel"]


    #deal with tap positions

    network.transformers.loc[trafos_with_types, "tap_ratio"] = 1 + (
        network.transformers.loc[trafos_with_types, "tap_position"] -
        network.transformers.loc[trafos_with_types, "type"].map(network.transformer_types["tap_neutral"])) * (
            network.transformers.loc[trafos_with_types, "type"].map(network.transformer_types["tap_step"])/100.)

    network.transformers.loc[trafos_with_types, "tap_side"] = network.transformers.loc[trafos_with_types, "type"].map(network.transformer_types["tap_side"])

    #TODO: status, rate_A


def wye_to_delta(z1,z2,z3):
    """Follows http://home.earthlink.net/~w6rmk/math/wyedelta.htm"""
    summand = z1*z2 + z2*z3 + z3*z1
    return (summand/z2,summand/z1,summand/z3)


def apply_transformer_t_model(network):
    """Convert given T-model parameters to PI-model parameters using wye-delta transformation"""

    z_series = network.transformers.r_pu + 1j*network.transformers.x_pu
    y_shunt = network.transformers.g_pu + 1j*network.transformers.b_pu

    ts = network.transformers.index[(network.transformers.model == "t") & (y_shunt != 0.)]

    if len(ts) == 0:
        return

    za,zb,zc = wye_to_delta(z_series.loc[ts]/2,z_series.loc[ts]/2,1/y_shunt.loc[ts])

    network.transformers.loc[ts,"r_pu"] = zc.real
    network.transformers.loc[ts,"x_pu"] = zc.imag
    network.transformers.loc[ts,"g_pu"] = (2/za).real
    network.transformers.loc[ts,"b_pu"] = (2/za).imag


def calculate_dependent_values(network):
    """Calculate per unit impedances and append voltages to lines and shunt impedances."""

    apply_line_types(network)
    apply_transformer_types(network)

    network.lines["v_nom"] = network.lines.bus0.map(network.buses.v_nom)

    network.lines["x_pu"] = network.lines.x/(network.lines.v_nom**2)
    network.lines["r_pu"] = network.lines.r/(network.lines.v_nom**2)
    network.lines["b_pu"] = network.lines.b*network.lines.v_nom**2
    network.lines["g_pu"] = network.lines.g*network.lines.v_nom**2

    #convert transformer impedances from base power s_nom to base = 1 MVA
    network.transformers["x_pu"] = network.transformers.x/network.transformers.s_nom
    network.transformers["r_pu"] = network.transformers.r/network.transformers.s_nom
    network.transformers["b_pu"] = network.transformers.b*network.transformers.s_nom
    network.transformers["g_pu"] = network.transformers.g*network.transformers.s_nom

    apply_transformer_t_model(network)

    network.shunt_impedances["v_nom"] = network.shunt_impedances["bus"].map(network.buses.v_nom)
    network.shunt_impedances["b_pu"] = network.shunt_impedances.b*network.shunt_impedances.v_nom**2
    network.shunt_impedances["g_pu"] = network.shunt_impedances.g*network.shunt_impedances.v_nom**2


def find_slack_bus(sub_network):
    """Find the slack bus in a connected sub-network."""

    gens = sub_network.generators()

    if len(gens) == 0:
        logger.warn("No generators in sub-network {}, better hope power is already balanced".format(sub_network.name))
        sub_network.slack_generator = None
        sub_network.slack_bus = sub_network.buses_i()[0]

    else:

        slacks = gens[gens.control == "Slack"].index

        if len(slacks) == 0:
            sub_network.slack_generator = gens.index[0]
            sub_network.network.generators.loc[sub_network.slack_generator,"control"] = "Slack"
            logger.debug("No slack generator found in sub-network {}, using {} as the slack generator".format(sub_network.name, sub_network.slack_generator))

        elif len(slacks) == 1:
            sub_network.slack_generator = slacks[0]
        else:
            sub_network.slack_generator = slacks[0]
            sub_network.network.generators.loc[slacks[1:],"control"] = "PV"
            logger.debug("More than one slack generator found in sub-network {}, using {} as the slack generator".format(sub_network.name, sub_network.slack_generator))

        sub_network.slack_bus = gens.bus[sub_network.slack_generator]

    #also put it into the dataframe
    sub_network.network.sub_networks.at[sub_network.name,"slack_bus"] = sub_network.slack_bus

    logger.info("Slack bus for sub-network {} is {}".format(sub_network.name, sub_network.slack_bus))


def find_bus_controls(sub_network):
    """Find slack and all PV and PQ buses for a sub_network.
    This function also fixes sub_network.buses_o, a DataFrame
    ordered by control type."""

    network = sub_network.network

    find_slack_bus(sub_network)

    gens = sub_network.generators()
    buses_i = sub_network.buses_i()

    #default bus control is PQ
    network.buses.loc[buses_i, "control"] = "PQ"

    #find all buses with one or more gens with PV
    pvs = gens[gens.control == 'PV'].index.to_series().groupby(gens.bus).first()
    network.buses.loc[pvs.index, "control"] = "PV"
    network.buses.loc[pvs.index, "generator"] = pvs

    network.buses.loc[sub_network.slack_bus, "control"] = "Slack"
    network.buses.loc[sub_network.slack_bus, "generator"] = sub_network.slack_generator

    buses_control = network.buses.loc[buses_i, "control"]
    sub_network.pvs = buses_control.index[buses_control == "PV"]
    sub_network.pqs = buses_control.index[buses_control == "PQ"]

    sub_network.pvpqs = sub_network.pvs.append(sub_network.pqs)

    # order buses
    sub_network.buses_o = sub_network.pvpqs.insert(0, sub_network.slack_bus)


def calculate_B_H(sub_network,skip_pre=False):
    """Calculate B and H matrices for AC or DC sub-networks."""

    from .components import passive_branch_components

    network = sub_network.network

    if not skip_pre:
        calculate_dependent_values(network)
        find_bus_controls(sub_network)

    if network.sub_networks.at[sub_network.name,"carrier"] == "DC":
        attribute="r_pu"
    else:
        attribute="x_pu"

    #following leans heavily on pypower.makeBdc

    #susceptances
    b = 1./np.concatenate([(c.df.loc[c.ind, attribute]*c.df.loc[c.ind, "tap_ratio"]).values if c.name == "Transformer"
                           else c.df.loc[c.ind, attribute].values
                           for c in sub_network.iterate_components(passive_branch_components)])


    if np.isnan(b).any():
        logger.warn("Warning! Some series impedances are zero - this will cause a singularity in LPF!")
    b_diag = csr_matrix((b, (r_[:len(b)], r_[:len(b)])))

    #incidence matrix
    sub_network.K = sub_network.incidence_matrix(busorder=sub_network.buses_o)

    sub_network.H = b_diag*sub_network.K.T

    #weighted Laplacian
    sub_network.B = sub_network.K * sub_network.H


    sub_network.p_branch_shift = -b*np.concatenate([(c.df.loc[c.ind, "phase_shift"]).values*np.pi/180. if c.name == "Transformer"
                                                    else np.zeros((len(c.ind),))
                                                    for c in sub_network.iterate_components(passive_branch_components)])

    sub_network.p_bus_shift = sub_network.K * sub_network.p_branch_shift

def calculate_PTDF(sub_network,skip_pre=False):
    """
    Calculate the Power Transfer Distribution Factor (PTDF) for
    sub_network.

    Sets sub_network.PTDF as a (dense) numpy array.

    Parameters
    ----------
    sub_network : pypsa.SubNetwork
    skip_pre: bool, default False
        Skip the preliminary steps of computing topology, calculating dependent values,
        finding bus controls and computing B and H.

    """

    if not skip_pre:
        calculate_B_H(sub_network)

    #calculate inverse of B with slack removed

    n_pvpq = len(sub_network.pvpqs)
    index = np.r_[:n_pvpq]

    I = csc_matrix((np.ones(n_pvpq), (index, index)))

    B_inverse = spsolve(sub_network.B[1:, 1:],I)

    #exception for two-node networks, where B_inverse is a 1d array
    if issparse(B_inverse):
        B_inverse = B_inverse.toarray()
    elif B_inverse.shape == (1,):
        B_inverse = B_inverse.reshape((1,1))

    #add back in zeroes for slack
    B_inverse = np.hstack((np.zeros((n_pvpq,1)),B_inverse))
    B_inverse = np.vstack((np.zeros(n_pvpq+1),B_inverse))

    sub_network.PTDF = sub_network.H*B_inverse


def calculate_Y(sub_network,skip_pre=False):
    """Calculate bus admittance matrices for AC sub-networks."""

    if not skip_pre:
        calculate_dependent_values(sub_network.network)

    if sub_network.network.sub_networks.at[sub_network.name,"carrier"] != "AC":
        logger.warn("Non-AC networks not supported for Y!")
        return

    branches = sub_network.branches()
    buses_o = sub_network.buses_o

    network = sub_network.network

    #following leans heavily on pypower.makeYbus
    #Copyright Richard Lincoln, Ray Zimmerman, BSD-style licence

    num_branches = len(branches)
    num_buses = len(buses_o)

    y_se = 1/(branches["r_pu"] + 1.j*branches["x_pu"])

    y_sh = branches["g_pu"]+ 1.j*branches["b_pu"]

    tau = branches["tap_ratio"].fillna(1.)

    #catch some transformers falsely set with tau = 0 by pypower
    tau[tau==0] = 1.

    #define the HV tap ratios
    tau_hv = pd.Series(1.,branches.index)
    tau_hv[branches.tap_side==0] = tau[branches.tap_side==0]

    #define the LV tap ratios
    tau_lv = pd.Series(1.,branches.index)
    tau_lv[branches.tap_side==1] = tau[branches.tap_side==1]


    phase_shift = np.exp(1.j*branches["phase_shift"].fillna(0.)*np.pi/180.)

    #build the admittance matrix elements for each branch
    Y11 = (y_se + 0.5*y_sh)/tau_lv**2
    Y10 = -y_se/tau_lv/tau_hv/phase_shift
    Y01 = -y_se/tau_lv/tau_hv/np.conj(phase_shift)
    Y00 = (y_se + 0.5*y_sh)/tau_hv**2

    #bus shunt impedances
    b_sh = network.shunt_impedances.b_pu.groupby(network.shunt_impedances.bus).sum().reindex(buses_o, fill_value = 0.)
    g_sh = network.shunt_impedances.g_pu.groupby(network.shunt_impedances.bus).sum().reindex(buses_o, fill_value = 0.)
    Y_sh = g_sh + 1.j*b_sh

    #get bus indices
    bus0 = buses_o.get_indexer(branches.bus0)
    bus1 = buses_o.get_indexer(branches.bus1)

    #connection matrices
    C0 = csr_matrix((ones(num_branches), (np.arange(num_branches), bus0)), (num_branches, num_buses))
    C1 = csr_matrix((ones(num_branches), (np.arange(num_branches), bus1)), (num_branches, num_buses))

    #build Y{0,1} such that Y{0,1} * V is the vector complex branch currents

    i = r_[np.arange(num_branches), np.arange(num_branches)]
    sub_network.Y0 = csr_matrix((r_[Y00,Y01],(i,r_[bus0,bus1])), (num_branches,num_buses))
    sub_network.Y1 = csr_matrix((r_[Y10,Y11],(i,r_[bus0,bus1])), (num_branches,num_buses))

    #now build bus admittance matrix
    sub_network.Y = C0.T * sub_network.Y0 + C1.T * sub_network.Y1 + \
       csr_matrix((Y_sh, (np.arange(num_buses), np.arange(num_buses))))



def aggregate_multi_graph(sub_network):
    """Aggregate branches between same buses and replace with a single
branch with aggregated properties (e.g. s_nom is summed, length is
averaged).

    """

    network = sub_network.network

    count = 0
    seen = []
    graph = sub_network.graph()
    for u,v in graph.edges():
        if (u,v) in seen:
            continue
        line_objs = list(graph.adj[u][v].keys())
        if len(line_objs) > 1:
            lines = network.lines.loc[[l[1] for l in line_objs]]
            aggregated = {}

            attr_inv = ["x","r"]
            attr_sum = ["s_nom","b","g","s_nom_max","s_nom_min"]
            attr_mean = ["capital_cost","length","terrain_factor"]

            for attr in attr_inv:
                aggregated[attr] = 1/(1/lines[attr]).sum()

            for attr in attr_sum:
                aggregated[attr] = lines[attr].sum()

            for attr in attr_mean:
                aggregated[attr] = lines[attr].mean()

            count += len(line_objs) - 1

            #remove all but first line
            for line in line_objs[1:]:
                network.remove("Line",line[1])

            rep = line_objs[0]

            for key,value in aggregated.items():
                setattr(rep,key,value)

            seen.append((u,v))

    logger.info("Removed %d excess lines from sub-network %s and replaced with aggregated lines", count,sub_network.name)




def find_tree(sub_network):
    """Get the spanning tree of the graph, choose the node with the
    highest degree as a central "tree slack" and then see for each
    branch which paths from the slack to each node go through the
    branch.

    """

    branches_bus0 = sub_network.branches()["bus0"]
    branches_i = branches_bus0.index
    buses_i = sub_network.buses_i()

    graph = sub_network.graph()
    sub_network.tree = nx.minimum_spanning_tree(graph)

    #find bus with highest degree to use as slack

    tree_slack_bus = None
    slack_degree = -1

    for bus,degree in sub_network.tree.degree_iter():
        if degree > slack_degree:
            tree_slack_bus = bus
            slack_degree = degree

    logger.info("Tree slack bus is %s with degree %d.", tree_slack_bus, slack_degree)

    #determine which buses are supplied in tree through branch from slack

    #matrix to store tree structure
    sub_network.T = dok_matrix((len(branches_i),len(buses_i)))

    for j,bus in enumerate(buses_i):
        path = nx.shortest_path(sub_network.tree,bus,tree_slack_bus)
        for i in range(len(path)-1):
            branch = next(iterkeys(graph[path[i]][path[i+1]]))
            branch_i = branches_i.get_loc(branch)
            sign = +1 if branches_bus0.iat[branch_i] == path[i] else -1
            sub_network.T[branch_i,j] = sign


def find_cycles(sub_network):
    """
    Find all cycles in the sub_network and record them in sub_network.C.

    networkx collects the cycles with more than 2 edges; then the 2-edge cycles
    from the MultiGraph must be collected separately (for cases where there
    are multiple lines between the same pairs of buses).

    """
    branches_bus0 = sub_network.branches()["bus0"]
    branches_i = branches_bus0.index

    #reduce to a non-multi-graph for cycles with > 2 edges
    mgraph = sub_network.graph()
    graph = nx.OrderedGraph(mgraph)

    cycles = nx.cycle_basis(graph)

    #number of 2-edge cycles
    num_multi = len(mgraph.edges()) - len(graph.edges())

    sub_network.C = dok_matrix((len(branches_bus0),len(cycles)+num_multi))

    for j,cycle in enumerate(cycles):

        for i in range(len(cycle)):
            branch = next(iterkeys(mgraph[cycle[i]][cycle[(i+1)%len(cycle)]]))
            branch_i = branches_i.get_loc(branch)
            sign = +1 if branches_bus0.iat[branch_i] == cycle[i] else -1
            sub_network.C[branch_i,j] += sign

    #counter for multis
    c = len(cycles)

    #add multi-graph 2-edge cycles for multiple branches between same pairs of buses
    for u,v in graph.edges():
        bs = list(mgraph[u][v].keys())
        if len(bs) > 1:
            first = bs[0]
            first_i = branches_i.get_loc(first)
            for b in bs[1:]:
                b_i = branches_i.get_loc(b)
                sign = -1 if branches_bus0.iat[b_i] == branches_bus0.iat[first_i] else +1
                sub_network.C[first_i,c] = 1
                sub_network.C[b_i,c] = sign
                c+=1

def sub_network_lpf(sub_network, snapshots=None, skip_pre=False):
    """
    Linear power flow for connected sub-network.

    Parameters
    ----------
    snapshots : list-like|single snapshot
        A subset or an elements of network.snapshots on which to run
        the power flow, defaults to network.snapshots
    skip_pre: bool, default False
        Skip the preliminary steps of computing topology, calculating
        dependent values and finding bus controls.

    Returns
    -------
    None
    """

    snapshots = _as_snapshots(sub_network.network, snapshots)
    logger.info("Performing linear load-flow on %s sub-network %s for snapshot(s) %s",
                sub_network.network.sub_networks.at[sub_network.name,"carrier"], sub_network, snapshots)

    from .components import \
        one_port_components, controllable_one_port_components, \
        passive_branch_components, controllable_branch_components

    network = sub_network.network


    if not skip_pre:
        calculate_dependent_values(network)
        find_bus_controls(sub_network)
        _allocate_pf_outputs(network, linear=True)


    # get indices for the components on this subnetwork
    buses_o = sub_network.buses_o
    branches_i = sub_network.branches_i()

    # allow all shunt impedances to dispatch as set
    shunt_impedances_i = sub_network.shunt_impedances_i()
    network.shunt_impedances_t.p.loc[snapshots, shunt_impedances_i] = \
        network.shunt_impedances.g_pu.loc[shunt_impedances_i].values

    # allow all one ports to dispatch as set
    for c in sub_network.iterate_components(controllable_one_port_components):
        c_p_set = get_switchable_as_dense(network, c.name, 'p_set', snapshots, c.ind)
        c.pnl.p.loc[snapshots, c.ind] = c_p_set

    # set the power injection at each node
    network.buses_t.p.loc[snapshots, buses_o] = \
        sum([((c.pnl.p.loc[snapshots, c.ind] * c.df.loc[c.ind, 'sign'])
              .groupby(c.df.loc[c.ind, 'bus'], axis=1).sum()
              .reindex(columns=buses_o, fill_value=0.))
             for c in sub_network.iterate_components(one_port_components)]
            +
            [(- c.pnl["p"+str(i)].loc[snapshots].groupby(c.df["bus"+str(i)], axis=1).sum()
              .reindex(columns=buses_o, fill_value=0))
             for c in network.iterate_components(controllable_branch_components)
             for i in [0,1]])

    if not skip_pre and len(branches_i) > 0:
        calculate_B_H(sub_network, skip_pre=True)

    v_diff = np.zeros((len(snapshots), len(buses_o)))
    if len(branches_i) > 0:
        p = network.buses_t['p'].loc[snapshots, buses_o].values - sub_network.p_bus_shift
        v_diff[:,1:] = spsolve(sub_network.B[1:, 1:], p[:,1:].T).T
        flows = pd.DataFrame(v_diff * sub_network.H.T,
                             columns=branches_i, index=snapshots) + sub_network.p_branch_shift

        for c in sub_network.iterate_components(passive_branch_components):
            f = flows.loc[:, c.name]
            c.pnl.p0.loc[snapshots, f.columns] = f
            c.pnl.p1.loc[snapshots, f.columns] = -f

    if network.sub_networks.at[sub_network.name,"carrier"] == "DC":
        network.buses_t.v_mag_pu.loc[snapshots, buses_o] = 1 + v_diff
        network.buses_t.v_ang.loc[snapshots, buses_o] = 0.
    else:
        network.buses_t.v_ang.loc[snapshots, buses_o] = v_diff
        network.buses_t.v_mag_pu.loc[snapshots, buses_o] = 1.

    # set slack bus power to pick up remained
    slack_adjustment = (- network.buses_t.p.loc[snapshots, buses_o[1:]].sum(axis=1)
                        - network.buses_t.p.loc[snapshots, buses_o[0]])
    network.buses_t.p.loc[snapshots, buses_o[0]] += slack_adjustment

    # let slack generator take up the slack
    if sub_network.slack_generator is not None:
        network.generators_t.p.loc[snapshots, sub_network.slack_generator] += slack_adjustment



def network_batch_lpf(network,snapshots=None):
    """Batched linear power flow with numpy.dot for several snapshots."""

    raise NotImplementedError("Batch linear power flow not supported yet.")