# -*- coding: utf-8 -*-
# SPDX-FileCopyrightText: : 2017-2022 The PyPSA-Eur Authors
#
# SPDX-License-Identifier: MIT
"""
Solves linear optimal power flow for a network iteratively while updating
reactances.
Relevant Settings
-----------------
.. code:: yaml
solving:
tmpdir:
options:
formulation:
clip_p_max_pu:
load_shedding:
noisy_costs:
nhours:
min_iterations:
max_iterations:
skip_iterations:
track_iterations:
solver:
name:
.. seealso::
Documentation of the configuration file ``config.yaml`` at
:ref:`electricity_cf`, :ref:`solving_cf`, :ref:`plotting_cf`
Inputs
------
- ``networks/elec_s{simpl}_{clusters}_ec_l{ll}_{opts}.nc``: confer :ref:`prepare`
Outputs
-------
- ``results/networks/elec_s{simpl}_{clusters}_ec_l{ll}_{opts}.nc``: Solved PyPSA network including optimisation results
.. image:: ../img/results.png
:scale: 40 %
Description
-----------
Total annual system costs are minimised with PyPSA. The full formulation of the
linear optimal power flow (plus investment planning
is provided in the
`documentation of PyPSA <https://pypsa.readthedocs.io/en/latest/optimal_power_flow.html#linear-optimal-power-flow>`_.
The optimization is based on the ``pyomo=False`` setting in the :func:`network.lopf` and :func:`pypsa.linopf.ilopf` function.
Additionally, some extra constraints specified in :mod:`prepare_network` are added.
Solving the network in multiple iterations is motivated through the dependence of transmission line capacities and impedances.
As lines are expanded their electrical parameters change, which renders the optimisation bilinear even if the power flow
equations are linearized.
To retain the computational advantage of continuous linear programming, a sequential linear programming technique
is used, where in between iterations the line impedances are updated.
Details (and errors made through this heuristic) are discussed in the paper
- Fabian Neumann and Tom Brown. `Heuristics for Transmission Expansion Planning in Low-Carbon Energy System Models <https://arxiv.org/abs/1907.10548>`_), *16th International Conference on the European Energy Market*, 2019. `arXiv:1907.10548 <https://arxiv.org/abs/1907.10548>`_.
.. warning::
Capital costs of existing network components are not included in the objective function,
since for the optimisation problem they are just a constant term (no influence on optimal result).
Therefore, these capital costs are not included in ``network.objective``!
If you want to calculate the full total annual system costs add these to the objective value.
.. tip::
The rule :mod:`solve_all_networks` runs
for all ``scenario`` s in the configuration file
the rule :mod:`solve_network`.
"""
import logging
import re
from pathlib import Path
import numpy as np
import pandas as pd
import pypsa
from _helpers import configure_logging
from pypsa.descriptors import get_switchable_as_dense as get_as_dense
from pypsa.linopf import (
define_constraints,
define_variables,
get_var,
ilopf,
join_exprs,
linexpr,
network_lopf,
)
from vresutils.benchmark import memory_logger
logger = logging.getLogger(__name__)
def prepare_network(n, solve_opts):
if "clip_p_max_pu" in solve_opts:
for df in (n.generators_t.p_max_pu, n.storage_units_t.inflow):
df.where(df > solve_opts["clip_p_max_pu"], other=0.0, inplace=True)
load_shedding = solve_opts.get("load_shedding")
if load_shedding:
n.add("Carrier", "load", color="#dd2e23", nice_name="Load shedding")
buses_i = n.buses.query("carrier == 'AC'").index
if not np.isscalar(load_shedding):
load_shedding = 1e2 # Eur/kWh
# intersect between macroeconomic and surveybased
# willingness to pay
# http://journal.frontiersin.org/article/10.3389/fenrg.2015.00055/full)
n.madd(
"Generator",
buses_i,
" load",
bus=buses_i,
carrier="load",
sign=1e-3, # Adjust sign to measure p and p_nom in kW instead of MW
marginal_cost=load_shedding,
p_nom=1e9, # kW
)
if solve_opts.get("noisy_costs"):
for t in n.iterate_components(n.one_port_components):
# if 'capital_cost' in t.df:
# t.df['capital_cost'] += 1e1 + 2.*(np.random.random(len(t.df)) - 0.5)
if "marginal_cost" in t.df:
t.df["marginal_cost"] += 1e-2 + 2e-3 * (
np.random.random(len(t.df)) - 0.5
)
for t in n.iterate_components(["Line", "Link"]):
t.df["capital_cost"] += (
1e-1 + 2e-2 * (np.random.random(len(t.df)) - 0.5)
) * t.df["length"]
if solve_opts.get("nhours"):
nhours = solve_opts["nhours"]
n.set_snapshots(n.snapshots[:nhours])
n.snapshot_weightings[:] = 8760.0 / nhours
return n
def add_CCL_constraints(n, config):
agg_p_nom_limits = config["electricity"].get("agg_p_nom_limits")
try:
agg_p_nom_minmax = pd.read_csv(agg_p_nom_limits, index_col=list(range(2)))
except IOError:
logger.exception(
"Need to specify the path to a .csv file containing "
"aggregate capacity limits per country in "
"config['electricity']['agg_p_nom_limit']."
)
logger.info(
"Adding per carrier generation capacity constraints for " "individual countries"
)
gen_country = n.generators.bus.map(n.buses.country)
# cc means country and carrier
p_nom_per_cc = (
pd.DataFrame(
{
"p_nom": linexpr((1, get_var(n, "Generator", "p_nom"))),
"country": gen_country,
"carrier": n.generators.carrier,
}
)
.dropna(subset=["p_nom"])
.groupby(["country", "carrier"])
.p_nom.apply(join_exprs)
)
minimum = agg_p_nom_minmax["min"].dropna()
if not minimum.empty:
minconstraint = define_constraints(
n, p_nom_per_cc[minimum.index], ">=", minimum, "agg_p_nom", "min"
)
maximum = agg_p_nom_minmax["max"].dropna()
if not maximum.empty:
maxconstraint = define_constraints(
n, p_nom_per_cc[maximum.index], "<=", maximum, "agg_p_nom", "max"
)
def add_EQ_constraints(n, o, scaling=1e-1):
float_regex = "[0-9]*\.?[0-9]+"
level = float(re.findall(float_regex, o)[0])
if o[-1] == "c":
ggrouper = n.generators.bus.map(n.buses.country)
lgrouper = n.loads.bus.map(n.buses.country)
sgrouper = n.storage_units.bus.map(n.buses.country)
else:
ggrouper = n.generators.bus
lgrouper = n.loads.bus
sgrouper = n.storage_units.bus
load = (
n.snapshot_weightings.generators
@ n.loads_t.p_set.groupby(lgrouper, axis=1).sum()
)
inflow = (
n.snapshot_weightings.stores
@ n.storage_units_t.inflow.groupby(sgrouper, axis=1).sum()
)
inflow = inflow.reindex(load.index).fillna(0.0)
rhs = scaling * (level * load - inflow)
lhs_gen = (
linexpr(
(n.snapshot_weightings.generators * scaling, get_var(n, "Generator", "p").T)
)
.T.groupby(ggrouper, axis=1)
.apply(join_exprs)
)
lhs_spill = (
linexpr(
(
-n.snapshot_weightings.stores * scaling,
get_var(n, "StorageUnit", "spill").T,
)
)
.T.groupby(sgrouper, axis=1)
.apply(join_exprs)
)
lhs_spill = lhs_spill.reindex(lhs_gen.index).fillna("")
lhs = lhs_gen + lhs_spill
define_constraints(n, lhs, ">=", rhs, "equity", "min")
def add_BAU_constraints(n, config):
mincaps = pd.Series(config["electricity"]["BAU_mincapacities"])
lhs = (
linexpr((1, get_var(n, "Generator", "p_nom")))
.groupby(n.generators.carrier)
.apply(join_exprs)
)
define_constraints(n, lhs, ">=", mincaps[lhs.index], "Carrier", "bau_mincaps")
def add_SAFE_constraints(n, config):
peakdemand = (
1.0 + config["electricity"]["SAFE_reservemargin"]
) * n.loads_t.p_set.sum(axis=1).max()
conv_techs = config["plotting"]["conv_techs"]
exist_conv_caps = n.generators.query(
"~p_nom_extendable & carrier in @conv_techs"
).p_nom.sum()
ext_gens_i = n.generators.query("carrier in @conv_techs & p_nom_extendable").index
lhs = linexpr((1, get_var(n, "Generator", "p_nom")[ext_gens_i])).sum()
rhs = peakdemand - exist_conv_caps
define_constraints(n, lhs, ">=", rhs, "Safe", "mintotalcap")
def add_operational_reserve_margin_constraint(n, config):
reserve_config = config["electricity"]["operational_reserve"]
EPSILON_LOAD = reserve_config["epsilon_load"]
EPSILON_VRES = reserve_config["epsilon_vres"]
CONTINGENCY = reserve_config["contingency"]
# Reserve Variables
reserve = get_var(n, "Generator", "r")
lhs = linexpr((1, reserve)).sum(1)
# Share of extendable renewable capacities
ext_i = n.generators.query("p_nom_extendable").index
vres_i = n.generators_t.p_max_pu.columns
if not ext_i.empty and not vres_i.empty:
capacity_factor = n.generators_t.p_max_pu[vres_i.intersection(ext_i)]
renewable_capacity_variables = get_var(n, "Generator", "p_nom")[
vres_i.intersection(ext_i)
]
lhs += linexpr(
(-EPSILON_VRES * capacity_factor, renewable_capacity_variables)
).sum(1)
# Total demand at t
demand = n.loads_t.p.sum(1)
# VRES potential of non extendable generators
capacity_factor = n.generators_t.p_max_pu[vres_i.difference(ext_i)]
renewable_capacity = n.generators.p_nom[vres_i.difference(ext_i)]
potential = (capacity_factor * renewable_capacity).sum(1)
# Right-hand-side
rhs = EPSILON_LOAD * demand + EPSILON_VRES * potential + CONTINGENCY
define_constraints(n, lhs, ">=", rhs, "Reserve margin")
def update_capacity_constraint(n):
gen_i = n.generators.index
ext_i = n.generators.query("p_nom_extendable").index
fix_i = n.generators.query("not p_nom_extendable").index
dispatch = get_var(n, "Generator", "p")
reserve = get_var(n, "Generator", "r")
capacity_fixed = n.generators.p_nom[fix_i]
p_max_pu = get_as_dense(n, "Generator", "p_max_pu")
lhs = linexpr((1, dispatch), (1, reserve))
if not ext_i.empty:
capacity_variable = get_var(n, "Generator", "p_nom")
lhs += linexpr((-p_max_pu[ext_i], capacity_variable)).reindex(
columns=gen_i, fill_value=""
)
rhs = (p_max_pu[fix_i] * capacity_fixed).reindex(columns=gen_i, fill_value=0)
define_constraints(n, lhs, "<=", rhs, "Generators", "updated_capacity_constraint")
def add_operational_reserve_margin(n, sns, config):
"""
Build reserve margin constraints based on the formulation given in
https://genxproject.github.io/GenX/dev/core/#Reserves.
"""
define_variables(n, 0, np.inf, "Generator", "r", axes=[sns, n.generators.index])
add_operational_reserve_margin_constraint(n, config)
update_capacity_constraint(n)
def add_battery_constraints(n):
nodes = n.buses.index[n.buses.carrier == "battery"]
if nodes.empty or ("Link", "p_nom") not in n.variables.index:
return
link_p_nom = get_var(n, "Link", "p_nom")
lhs = linexpr(
(1, link_p_nom[nodes + " charger"]),
(
-n.links.loc[nodes + " discharger", "efficiency"].values,
link_p_nom[nodes + " discharger"].values,
),
)
define_constraints(n, lhs, "=", 0, "Link", "charger_ratio")
def extra_functionality(n, snapshots):
"""
Collects supplementary constraints which will be passed to
``pypsa.linopf.network_lopf``.
If you want to enforce additional custom constraints, this is a good
location to add them. The arguments ``opts`` and
``snakemake.config`` are expected to be attached to the network.
"""
opts = n.opts
config = n.config
if "BAU" in opts and n.generators.p_nom_extendable.any():
add_BAU_constraints(n, config)
if "SAFE" in opts and n.generators.p_nom_extendable.any():
add_SAFE_constraints(n, config)
if "CCL" in opts and n.generators.p_nom_extendable.any():
add_CCL_constraints(n, config)
reserve = config["electricity"].get("operational_reserve", {})
if reserve.get("activate"):
add_operational_reserve_margin(n, snapshots, config)
for o in opts:
if "EQ" in o:
add_EQ_constraints(n, o)
add_battery_constraints(n)
def solve_network(n, config, opts="", **kwargs):
solver_options = config["solving"]["solver"].copy()
solver_name = solver_options.pop("name")
cf_solving = config["solving"]["options"]
track_iterations = cf_solving.get("track_iterations", False)
min_iterations = cf_solving.get("min_iterations", 4)
max_iterations = cf_solving.get("max_iterations", 6)
# add to network for extra_functionality
n.config = config
n.opts = opts
skip_iterations = cf_solving.get("skip_iterations", False)
if not n.lines.s_nom_extendable.any():
skip_iterations = True
logger.info("No expandable lines found. Skipping iterative solving.")
if skip_iterations:
network_lopf(
n,
solver_name=solver_name,
solver_options=solver_options,
extra_functionality=extra_functionality,
**kwargs
)
else:
ilopf(
n,
solver_name=solver_name,
solver_options=solver_options,
track_iterations=track_iterations,
min_iterations=min_iterations,
max_iterations=max_iterations,
extra_functionality=extra_functionality,
**kwargs
)
return n
if __name__ == "__main__":
if "snakemake" not in globals():
from _helpers import mock_snakemake
snakemake = mock_snakemake(
"solve_network", simpl="", clusters="5", ll="copt", opts="Co2L-BAU-CCL-24H"
)
configure_logging(snakemake)
tmpdir = snakemake.config["solving"].get("tmpdir")
if tmpdir is not None:
Path(tmpdir).mkdir(parents=True, exist_ok=True)
opts = snakemake.wildcards.opts.split("-")
solve_opts = snakemake.config["solving"]["options"]
fn = getattr(snakemake.log, "memory", None)
with memory_logger(filename=fn, interval=30.0) as mem:
n = pypsa.Network(snakemake.input[0])
n = prepare_network(n, solve_opts)
n = solve_network(
n,
snakemake.config,
opts,
solver_dir=tmpdir,
solver_logfile=snakemake.log.solver,
)
n.meta = dict(snakemake.config, **dict(wildcards=dict(snakemake.wildcards)))
n.export_to_netcdf(snakemake.output[0])
logger.info("Maximum memory usage: {}".format(mem.mem_usage))