build_bus.py

# -*- coding: utf-8 -*-

# Copyright (c) 2016-2020 by University of Kassel and Fraunhofer Institute for Energy Economics
# and Energy System Technology (IEE), Kassel. All rights reserved.


from collections import defaultdict, Counter
from itertools import chain

import numpy as np
import pandas as pd
from packaging import version

from pandapower.auxiliary import _sum_by_group
from pandapower.pypower.idx_bus import BUS_I, BASE_KV, PD, QD, GS, BS, VMAX, VMIN, BUS_TYPE, NONE, VM, VA,\
                               CID, CZD, bus_cols, REF

try:
    from numba import jit
except ImportError:
    from .pf.no_numba import jit


@jit(nopython=True, cache=False)
def ds_find(ar, bus):  # pragma: no cover
    while True:
        p = ar[bus]
        if p == bus:
            break
        bus = p
    return p


@jit(nopython=True, cache=False)
def ds_union(ar, bus1, bus2, bus_is_pv):  # pragma: no cover
    root1 = ds_find(ar, bus1)
    root2 = ds_find(ar, bus2)
    if root1 == root2:
        return
    if bus_is_pv[root2]:
        ar[root1] = root2
    else:
        ar[root2] = root1


@jit(nopython=True, cache=False)
def ds_create(ar, switch_bus, switch_elm, switch_et_bus, switch_closed, switch_z_ohm,
              bus_is_pv, bus_in_service):  # pragma: no cover
    for i in range(len(switch_bus)):
        if not switch_closed[i] or not switch_et_bus[i] or switch_z_ohm[i]>0:
            continue
        bus1 = switch_bus[i]
        bus2 = switch_elm[i]
        if bus_in_service[bus1] and bus_in_service[bus2]:
            ds_union(ar, bus1, bus2, bus_is_pv)


@jit(nopython=True, cache=False)
def fill_bus_lookup(ar, bus_lookup, bus_index):
    for i in range(len(bus_index)):
        bus_lookup[bus_index[i]] = i
    for b in bus_index:
        ds = ds_find(ar, b)
        bus_lookup[b] = bus_lookup[ar[ds]]


def create_bus_lookup_numba(net, bus_index, bus_is_idx, gen_is_mask, eg_is_mask):
    max_bus_idx = np.max(bus_index)
    # extract numpy arrays of switch table data
    switch = net["switch"]
    switch_bus = switch["bus"].values
    switch_elm = switch["element"].values
    switch_et_bus = switch["et"].values == "b"
    switch_closed = switch["closed"].values
    switch_z_ohm = switch['z_ohm'].values
    # create array for fast checking if a bus is in_service
    bus_in_service = np.zeros(max_bus_idx + 1, dtype=bool)
    bus_in_service[bus_is_idx] = True
    # create array for fast checking if a bus is pv bus
    bus_is_pv = np.zeros(max_bus_idx + 1, dtype=bool)
    bus_is_pv[net["ext_grid"]["bus"].values[eg_is_mask]] = True
    bus_is_pv[net["gen"]["bus"].values[gen_is_mask]] = True
    # create array that represents the disjoint set
    ar = np.arange(max_bus_idx + 1)
    ds_create(ar, switch_bus, switch_elm, switch_et_bus, switch_closed, switch_z_ohm, bus_is_pv, bus_in_service)
    # finally create and fill bus lookup
    bus_lookup = -np.ones(max_bus_idx + 1, dtype=int)
    fill_bus_lookup(ar, bus_lookup, bus_index)
    return bus_lookup


class DisjointSet(dict):
    def add(self, item):
        self[item] = item

    def find(self, item):
        parent = self[item]
        if self[parent] != parent:
            parent = self.find(parent)
            self[item] = parent
        return parent

    def union(self, item1, item2):
        p1 = self.find(item1)
        p2 = self.find(item2)
        self[p1] = p2


def create_consecutive_bus_lookup(net, bus_index):
    # create a mapping from arbitrary pp-index to a consecutive index starting at zero (ppc-index)
    consec_buses = np.arange(len(bus_index))
    # bus_lookup as dict:
    # bus_lookup = dict(zip(bus_index, consec_buses))
    # bus lookup as mask from pandapower -> pypower
    bus_lookup = -np.ones(max(bus_index) + 1, dtype=int)
    bus_lookup[bus_index] = consec_buses
    return bus_lookup 


def create_bus_lookup_numpy(net, bus_index, bus_is_idx, gen_is_mask, eg_is_mask, closed_bb_switch_mask):
    bus_lookup = create_consecutive_bus_lookup(net, bus_index)
    net._fused_bb_switches = closed_bb_switch_mask & (net["switch"]["z_ohm"].values<=0)
    if net._fused_bb_switches.any():
        # Note: this might seem a little odd - first constructing a pp to ppc mapping without
        # fused busses and then update the entries. The alternative (to construct the final
        # mapping at once) would require to determine how to fuse busses and which busses
        # are not part of any opened bus-bus switches first. It turns out, that the latter takes
        # quite some time in the average usecase, where #busses >> #bus-bus switches.

        # Find PV / Slack nodes -> their bus must be kept when fused with a PQ node
        pv_list = [net["ext_grid"]["bus"].values[eg_is_mask], net["gen"]["bus"].values[gen_is_mask]]
        pv_ref = np.unique(np.hstack(pv_list))
        # get the pp-indices of the buses which are connected to a switch to be fused
        fbus = net["switch"]["bus"].values[net._fused_bb_switches]
        tbus = net["switch"]["element"].values[net._fused_bb_switches]

        # create a mapping to map each bus to itself at frist ...
        ds = DisjointSet({e: e for e in chain(fbus, tbus)})

        # ... to follow each bus along a possible chain of switches to its final bus and update the
        # map
        for f, t in zip(fbus, tbus):
            ds.union(f, t)

        # now we can find out how to fuse each bus by looking up the final bus of the chain they
        # are connected to
        v = defaultdict(set)
        for a in ds:
            v[ds.find(a)].add(a)
        # build sets of buses which will be fused
        disjoint_sets = [e for e in v.values() if len(e) > 1]

        # check if PV buses need to be fused
        # if yes: the sets with PV buses must be found (which is slow)
        # if no: the check can be omitted
        if any(i in fbus or i in tbus for i in pv_ref):
            # for every disjoint set
            for dj in disjoint_sets:
                # check if pv buses are in the disjoint set dj
                pv_buses_in_set = set(pv_ref) & dj
                nr_pv_bus = len(pv_buses_in_set)
                if nr_pv_bus == 0:
                    # no pv buses. Use any bus in dj
                    map_to = bus_lookup[dj.pop()]
                else:
                    # one pv bus. Get bus from pv_buses_in_set
                    map_to = bus_lookup[pv_buses_in_set.pop()]
                for bus in dj:
                    # update lookup
                    bus_lookup[bus] = map_to
        else:
            # no PV buses in set
            for dj in disjoint_sets:
                # use any bus in set
                map_to = bus_lookup[dj.pop()]
                for bus in dj:
                    # update bus lookup
                    bus_lookup[bus] = map_to
    return bus_lookup


def create_bus_lookup(net, bus_index, bus_is_idx, gen_is_mask, eg_is_mask, numba):   
    switches_with_pos_z_ohm = net["switch"]["z_ohm"].values > 0
    if switches_with_pos_z_ohm.any() or numba == False:
        # if there are any closed bus-bus switches find them
        closed_bb_switch_mask = ((net["switch"]["closed"].values == True) &
                                 (net["switch"]["et"].values == "b") &
                                 np.in1d(net["switch"]["bus"].values, bus_is_idx) &
                                 np.in1d(net["switch"]["element"].values, bus_is_idx))

    if switches_with_pos_z_ohm.any():
        net._impedance_bb_switches = closed_bb_switch_mask & switches_with_pos_z_ohm
    else:
        net._impedance_bb_switches = np.zeros(switches_with_pos_z_ohm.shape)

    if numba:
        bus_lookup = create_bus_lookup_numba(net, bus_index, bus_is_idx, 
                                             gen_is_mask, eg_is_mask)
    else:
        bus_lookup = create_bus_lookup_numpy(net, bus_index, bus_is_idx, 
                                             gen_is_mask, eg_is_mask, closed_bb_switch_mask)
    return bus_lookup


def get_voltage_init_vector(net, init_v, mode):
    if isinstance(init_v, str):
        if init_v == "results":
            # init voltage possible if bus results are available
            if net.res_bus.index.equals(net.bus.index):
                # init bus voltages from results if the sorting is correct
                return net["res_bus"]["vm_pu" if mode == "magnitude" else "va_degree"].values
            else:
                # cannot init from results, since sorting of results is different from element table
                UserWarning("Init from results not possible. Index of res_bus do not match with bus. "
                            "You should sort res_bus before calling runpp.")
                return None
        if init_v == "flat":
            if mode == "magnitude":
                net["_options"]["init_vm_pu"] = 0.
            else:
                net["_options"]["init_va_degree"] = 0.
            return None
    elif isinstance(init_v, (float, np.ndarray, list)):
        return init_v
    elif isinstance(init_v, pd.Series):
        if init_v.index.equals(net.bus.index):
            return init_v.loc[net.bus.index]
        else:
            raise UserWarning("Voltage starting vector indices do not match bus indices")


def _build_bus_ppc(net, ppc):
    """
    Generates the ppc["bus"] array and the lookup pandapower indices -> ppc indices
    """
    init_vm_pu = net["_options"]["init_vm_pu"]
    init_va_degree = net["_options"]["init_va_degree"]
    mode = net["_options"]["mode"]
    numba = net["_options"]["numba"] if "numba" in net["_options"] else False

    # get bus indices
    nr_xward = len(net.xward)
    nr_trafo3w = len(net.trafo3w)
    aux = dict()
    if nr_xward > 0 or nr_trafo3w > 0:
        bus_indices = [net["bus"].index.values, np.array([], dtype=np.int64)]
        max_idx = max(net["bus"].index) + 1
        if nr_xward > 0:
            aux_xward = np.arange(max_idx, max_idx+nr_xward, dtype=np.int64)
            aux["xward"] = aux_xward
            bus_indices.append(aux_xward)
        if nr_trafo3w:
            aux_trafo3w = np.arange(max_idx+nr_xward, max_idx+nr_xward+nr_trafo3w)
            aux["trafo3w"] = aux_trafo3w
            bus_indices.append(aux_trafo3w)
        bus_index = np.concatenate(bus_indices)
    else:
        bus_index = net["bus"].index.values
    # get in service elements


    if mode == "nx":
        bus_lookup = create_consecutive_bus_lookup(net, bus_index)
    else:
        _is_elements = net["_is_elements"]
        eg_is_mask = _is_elements['ext_grid']
        gen_is_mask = _is_elements['gen']
        bus_is_idx = _is_elements['bus_is_idx']
        bus_lookup = create_bus_lookup(net, bus_index, bus_is_idx,
                                       gen_is_mask, eg_is_mask, numba=numba)

    n_bus_ppc = len(bus_index)
    # init ppc with empty values
    ppc["bus"] = np.zeros(shape=(n_bus_ppc, bus_cols), dtype=float)
    ppc["bus"][:, :15] = np.array([0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0., 0.])  # changes of
    # voltage limits (2 and 0) must be considered in check_opf_data
    if mode == "sc":
        from pandapower.shortcircuit.idx_bus import bus_cols_sc
        bus_sc = np.empty(shape=(n_bus_ppc, bus_cols_sc), dtype=float)
        bus_sc.fill(np.nan)
        ppc["bus"] = np.hstack((ppc["bus"], bus_sc))

    # apply consecutive bus numbers
    ppc["bus"][:, BUS_I] = np.arange(n_bus_ppc)

    n_bus = len(net.bus.index)
    # init voltages from net
    ppc["bus"][:n_bus, BASE_KV] = net["bus"]["vn_kv"].values
    # set buses out of service (BUS_TYPE == 4)
    if nr_xward > 0 or nr_trafo3w > 0:
        in_service = np.concatenate([net["bus"]["in_service"].values,
                                    net["xward"]["in_service"].values,
                                    net["trafo3w"]["in_service"].values])
    else:
        in_service = net["bus"]["in_service"].values
    ppc["bus"][~in_service, BUS_TYPE] = NONE
    if mode != "nx":
        set_reference_buses(net, ppc, bus_lookup, mode)
    vm_pu = get_voltage_init_vector(net, init_vm_pu, "magnitude")
    if vm_pu is not None:
        ppc["bus"][:n_bus, VM] = vm_pu

    va_degree = get_voltage_init_vector(net, init_va_degree, "angle")
    if va_degree is not None:
        ppc["bus"][:n_bus, VA] = va_degree

    if mode == "sc":
        _add_c_to_ppc(net, ppc)

    if net._options["mode"] == "opf":
        if "max_vm_pu" in net.bus:
            ppc["bus"][:n_bus, VMAX] = net["bus"].max_vm_pu.values
        else:
            ppc["bus"][:n_bus, VMAX] = 2.  # changes of VMAX must be considered in check_opf_data
        if "min_vm_pu" in net.bus:
            ppc["bus"][:n_bus, VMIN] = net["bus"].min_vm_pu.values
        else:
            ppc["bus"][:n_bus, VMIN] = 0.  # changes of VMIN must be considered in check_opf_data

    if len(net.xward):
        _fill_auxiliary_buses(net, ppc, bus_lookup, "xward", "bus", aux)

    if len(net.trafo3w):
        _fill_auxiliary_buses(net, ppc, bus_lookup, "trafo3w", "hv_bus", aux)
    net["_pd2ppc_lookups"]["bus"] = bus_lookup
    net["_pd2ppc_lookups"]["aux"] = aux


def _fill_auxiliary_buses(net, ppc, bus_lookup, element, bus_column, aux):
    element_bus_idx = bus_lookup[net[element][bus_column].values]
    aux_idx = bus_lookup[aux[element]]
    ppc["bus"][aux_idx, BASE_KV] = ppc["bus"][element_bus_idx, BASE_KV]
    if net._options["mode"] == "opf":
        ppc["bus"][aux_idx, VMIN] = ppc["bus"][element_bus_idx, VMIN]
        ppc["bus"][aux_idx, VMAX] = ppc["bus"][element_bus_idx, VMAX]
    if net._options["init_vm_pu"] == "results":
        ppc["bus"][aux_idx, VM] = net["res_%s"%element]["vm_internal_pu"].values
    else:
        ppc["bus"][aux_idx, VM] = ppc["bus"][element_bus_idx, VM]
    if net._options["init_va_degree"] == "results":
        ppc["bus"][aux_idx, VA] = net["res_%s"%element]["va_internal_degree"].values
    else:
        ppc["bus"][aux_idx, VA] = ppc["bus"][element_bus_idx, VA]

def set_reference_buses(net, ppc, bus_lookup, mode):
    if mode == "nx":
        return
    eg_buses = bus_lookup[net.ext_grid.bus.values[net._is_elements["ext_grid"]]]
    ppc["bus"][eg_buses, BUS_TYPE] = REF
    if mode == "sc":
        gen_slacks = net._is_elements["gen"] #generators are slacks for short-circuit calculation
    else:
        gen_slacks = net._is_elements["gen"] & net.gen["slack"].values
    if gen_slacks.any():
        slack_buses = net.gen["bus"].values[gen_slacks]
        ppc["bus"][bus_lookup[slack_buses], BUS_TYPE] = REF


def _calc_pq_elements_and_add_on_ppc(net, ppc):
    # init values
    b, p, q = np.array([], dtype=int), np.array([]), np.array([])

    _is_elements = net["_is_elements"]
    voltage_depend_loads = net["_options"]["voltage_depend_loads"]
    for element in ["load", "sgen", "storage", "ward", "xward"]:
        tab = net[element]
        if len(tab):
            if element == "load" and voltage_depend_loads:
                cz = tab["const_z_percent"].values / 100.
                ci = tab["const_i_percent"].values / 100.
                if ((cz + ci) > 1).any():
                    raise ValueError("const_z_percent + const_i_percent need to be less or equal to " +
                                     "100%!")

                # cumulative sum of constant-current loads
                b_zip = tab["bus"].values
                load_counter = Counter(b_zip)

                bus_lookup = net["_pd2ppc_lookups"]["bus"]
                b_zip = bus_lookup[b_zip]
                load_counter = {bus_lookup[k]: v for k, v in load_counter.items()}
                b_zip, ci_sum, cz_sum = _sum_by_group(b_zip, ci, cz)

                for bus, no_loads in load_counter.items():
                    ci_sum[b_zip == bus] /= no_loads
                    cz_sum[b_zip == bus] /= no_loads

                ppc["bus"][b_zip, CID] = ci_sum
                ppc["bus"][b_zip, CZD] = cz_sum
            active = _is_elements[element]
            sign = -1 if element == "sgen" else 1
            if element.endswith("ward"):
                p = np.hstack([p, tab["ps_mw"].values * active * sign])
                q = np.hstack([q, tab["qs_mvar"].values * active * sign])
            else:
                scaling = tab["scaling"].values
                p = np.hstack([p, tab["p_mw"].values * active * scaling * sign])
                q = np.hstack([q, tab["q_mvar"].values * active * scaling * sign])
            b = np.hstack([b, tab["bus"].values])

    # sum up p & q of bus elements
    if b.size:
        bus_lookup = net["_pd2ppc_lookups"]["bus"]
        b = bus_lookup[b]
        b, vp, vq = _sum_by_group(b, p, q)
        ppc["bus"][b, PD] = vp
        ppc["bus"][b, QD] = vq


def _calc_shunts_and_add_on_ppc(net, ppc):
    # init values
    b, p, q = np.array([], dtype=int), np.array([]), np.array([])
    bus_lookup = net["_pd2ppc_lookups"]["bus"]
    # get in service elements
    _is_elements = net["_is_elements"]

    s = net["shunt"]
    if len(s) > 0:
        vl = _is_elements["shunt"]
        v_ratio = (ppc["bus"][bus_lookup[s["bus"].values], BASE_KV] / s["vn_kv"].values) ** 2
        q = np.hstack([q, s["q_mvar"].values * s["step"].values * v_ratio * vl])
        p = np.hstack([p, s["p_mw"].values * s["step"].values * v_ratio * vl])
        b = np.hstack([b, s["bus"].values])

    w = net["ward"]
    if len(w) > 0:
        vl = _is_elements["ward"]
        q = np.hstack([q, w["qz_mvar"].values * vl])
        p = np.hstack([p, w["pz_mw"].values * vl])
        b = np.hstack([b, w["bus"].values])

    xw = net["xward"]
    if len(xw) > 0:
        vl = _is_elements["xward"]
        q = np.hstack([q, xw["qz_mvar"].values * vl])
        p = np.hstack([p, xw["pz_mw"].values * vl])
        b = np.hstack([b, xw["bus"].values])

    loss_location = net._options["trafo3w_losses"].lower()
    trafo3w = net["trafo3w"]
    if loss_location == "star" and len(trafo3w) > 0:

        pfe_mw = trafo3w["pfe_kw"].values * 1e-3
        i0 = trafo3w["i0_percent"].values
        sn_mva = trafo3w["sn_hv_mva"].values

        q_mvar = (sn_mva * i0 / 100.) ** 2 - pfe_mw **2
        q_mvar[q_mvar<0] = 0
        q_mvar= np.sqrt(q_mvar)

        vn_hv_trafo = trafo3w["vn_hv_kv"].values
        vn_hv_bus = ppc["bus"][bus_lookup[trafo3w.hv_bus.values], BASE_KV]
        v_ratio = (vn_hv_bus / vn_hv_trafo) ** 2

        q = np.hstack([q, q_mvar * v_ratio])
        p = np.hstack([p, pfe_mw * v_ratio])
        b = np.hstack([b, net._pd2ppc_lookups["aux"]["trafo3w"]])

    # if array is not empty
    if b.size:
        b = bus_lookup[b]
        b, vp, vq = _sum_by_group(b, p, q)

        ppc["bus"][b, GS] = vp
        ppc["bus"][b, BS] = -vq


def _add_gen_impedances_ppc(net, ppc):
    _add_ext_grid_sc_impedance(net, ppc)
    _add_gen_sc_impedance(net, ppc)


def _add_ext_grid_sc_impedance(net, ppc):
    from pandapower.shortcircuit.idx_bus import C_MAX, C_MIN
    mode = net._options["mode"]
    bus_lookup = net["_pd2ppc_lookups"]["bus"]
    if mode == "sc":
        case = net._options["case"]
    else:
        case = "max"
    eg = net["ext_grid"][net._is_elements["ext_grid"]]
    if len(eg) == 0:
        return
    eg_buses = eg.bus.values
    eg_buses_ppc = bus_lookup[eg_buses]

    if mode == "sc":
        c = ppc["bus"][eg_buses_ppc, C_MAX] if case == "max" else ppc["bus"][eg_buses_ppc, C_MIN]
    else:
        c = 1.
    if not "s_sc_%s_mva" % case in eg:
        raise ValueError("short circuit apparent power s_sc_%s_mva needs to be specified for "% case +
                         "external grid" )
    s_sc = eg["s_sc_%s_mva" % case].values
    if not "rx_%s" % case in eg:
        raise ValueError("short circuit R/X rate rx_%s needs to be specified for external grid" %
                         case)
    rx = eg["rx_%s" % case].values

    z_grid = c / s_sc
    x_grid = z_grid / np.sqrt(rx ** 2 + 1)
    r_grid = rx * x_grid
    eg["r"] = r_grid
    eg["x"] = x_grid

    y_grid = 1 / (r_grid + x_grid * 1j)
    buses, gs, bs = _sum_by_group(eg_buses_ppc, y_grid.real, y_grid.imag)
    ppc["bus"][buses, GS] = gs
    ppc["bus"][buses, BS] = bs


def _add_gen_sc_impedance(net, ppc):
    from pandapower.shortcircuit.idx_bus import C_MAX
    gen = net["gen"][net._is_elements["gen"]]
    if len(gen) == 0:
        return
    gen_buses = gen.bus.values
    bus_lookup = net["_pd2ppc_lookups"]["bus"]
    gen_buses_ppc = bus_lookup[gen_buses]
    vn_gen = gen.vn_kv.values
    sn_gen = gen.sn_mva.values

    rdss_pu = gen.rdss_pu.values
    xdss_pu = gen.xdss_pu.values 
    gens_without_r = np.isnan(rdss_pu)
    if gens_without_r.any():
        #  use the estimations from the IEC standard for generators without defined rdss_pu
        lv_gens = (vn_gen <= 1.) & gens_without_r
        hv_gens = (vn_gen > 1.) & gens_without_r
        large_hv_gens = (sn_gen >= 100) & hv_gens
        small_hv_gens = (sn_gen < 100) & hv_gens
        rdss_pu[lv_gens] = 0.15 * xdss_pu[lv_gens]
        rdss_pu[large_hv_gens] = 0.05 * xdss_pu[large_hv_gens]
        rdss_pu[small_hv_gens] = 0.07 * xdss_pu[small_hv_gens]
          
    vn_net = ppc["bus"][gen_buses_ppc, BASE_KV]
    cmax = ppc["bus"][gen_buses_ppc, C_MAX]
    phi_gen = np.arccos(gen.cos_phi.values)
    kg = vn_gen / vn_net * cmax / (1 + xdss_pu * np.sin(phi_gen))

    z_gen = (rdss_pu + xdss_pu * 1j) * kg / sn_gen
    y_gen = 1 / z_gen

    buses, gs, bs = _sum_by_group(gen_buses_ppc, y_gen.real, y_gen.imag)
    ppc["bus"][buses, GS] = gs
    ppc["bus"][buses, BS] = bs


def _add_motor_impedances_ppc(net, ppc):
    sgen = net.sgen[net._is_elements["sgen"]]
    if "motor" not in sgen.type.values:
        return
    motor = sgen[sgen.type == "motor"]
    for par in ["sn_mva", "rx", "k"]:
        if any(pd.isnull(motor[par])):
            raise UserWarning("%s needs to be specified for all motors in net.sgen.%s" % (par, par))
    bus_lookup = net["_pd2ppc_lookups"]["bus"]
    motor_buses = motor.bus.values
    motor_buses_ppc = bus_lookup[motor_buses]

    z_motor = 1 / (motor.sn_mva.values * 1e-3) / motor.k  # vn_kv**2 becomes 1**2=1 in per unit
    x_motor = z_motor / np.sqrt(motor.rx ** 2 + 1)
    r_motor = motor.rx * x_motor
    y_motor = 1 / (r_motor + x_motor * 1j)

    buses, gs, bs = _sum_by_group(motor_buses_ppc, y_motor.real, y_motor.imag)
    ppc["bus"][buses, GS] = gs
    ppc["bus"][buses, BS] = bs


def _add_c_to_ppc(net, ppc):
    from pandapower.shortcircuit.idx_bus import C_MAX, C_MIN
    ppc["bus"][:, C_MAX] = 1.1
    ppc["bus"][:, C_MIN] = 1.
    lv_buses = np.where(ppc["bus"][:, BASE_KV] < 1.)
    if len(lv_buses) > 0:
        lv_tol_percent = net["_options"]["lv_tol_percent"]
        if lv_tol_percent == 10:
            c_ns = 1.1
        elif lv_tol_percent == 6:
            c_ns = 1.05
        else:
            raise ValueError("Voltage tolerance in the low voltage grid has" +
                             " to be either 6% or 10% according to IEC 60909")
        ppc["bus"][lv_buses, C_MAX] = c_ns
        ppc["bus"][lv_buses, C_MIN] = .95