Solve network

Functions to add constraints and prepare the network for the solver. Associated with the solve_networks rule in the Snakefile.

add_battery_constraints(n)

Add constraint ensuring that charger = discharger, i.e. 1 * charger_size - efficiency * discharger_size = 0

Source code in workflow/scripts/solve_network.py

def add_battery_constraints(n: pypsa.Network):
    """
    Add constraint ensuring that charger = discharger, i.e.
    1 * charger_size - efficiency * discharger_size = 0
    """
    if not n.links.p_nom_extendable.any():
        return

    discharger_bool = n.links.index.str.contains("battery discharger")
    charger_bool = n.links.index.str.contains("battery charger")

    dischargers_ext = n.links[discharger_bool].query("p_nom_extendable").index
    chargers_ext = n.links[charger_bool].query("p_nom_extendable").index

    eff = n.links.efficiency[dischargers_ext].values
    lhs = n.model["Link-p_nom"].loc[chargers_ext] - n.model["Link-p_nom"].loc[dischargers_ext] * eff

    n.model.add_constraints(lhs == 0, name="Link-charger_ratio")

add_chp_constraints(n)

Add constraints to couple the heat and electricity output of CHP plants (using the cb and cv parameter). See the DEA technology cataloge

Parameters:

Name	Type	Description	Default
n	Network	the pypsa network object to which's model the constraints are added	required

Source code in workflow/scripts/solve_network.py

def add_chp_constraints(n: pypsa.Network):
    """Add constraints to couple the heat and electricity output of CHP plants
         (using the cb and cv parameter). See the DEA technology cataloge

    Args:
        n (pypsa.Network): the pypsa network object to which's model the constraints are added
    """
    electric = n.links.index.str.contains("CHP") & n.links.index.str.contains("generator")
    heat = n.links.index.str.contains("CHP") & n.links.index.str.contains("boiler")

    electric_ext = n.links[electric].query("p_nom_extendable").index
    heat_ext = n.links[heat].query("p_nom_extendable").index

    electric_fix = n.links[electric].query("~p_nom_extendable").index
    heat_fix = n.links[heat].query("~p_nom_extendable").index

    p = n.model["Link-p"]  # dimension: [time, link]

    # output ratio between heat and electricity and top_iso_fuel_line for extendable
    if not electric_ext.empty:
        p_nom = n.model["Link-p_nom"]

        lhs = (
            p_nom.loc[electric_ext]
            * (n.links.p_nom_ratio * n.links.efficiency)[electric_ext].values
            - p_nom.loc[heat_ext] * n.links.efficiency[heat_ext].values
        )
        n.model.add_constraints(lhs == 0, name="chplink-fix_p_nom_ratio")

        rename = {"Link-ext": "Link"}
        lhs = p.loc[:, electric_ext] + p.loc[:, heat_ext] - p_nom.rename(rename).loc[electric_ext]
        n.model.add_constraints(lhs <= 0, name="chplink-top_iso_fuel_line_ext")

    # top_iso_fuel_line for fixed
    if not electric_fix.empty:
        lhs = p.loc[:, electric_fix] + p.loc[:, heat_fix]
        rhs = n.links.p_nom[electric_fix]
        n.model.add_constraints(lhs <= rhs, name="chplink-top_iso_fuel_line_fix")

    # back-pressure
    if not n.links[electric].index.empty:
        lhs = (
            p.loc[:, heat] * (n.links.efficiency[heat] * n.links.c_b[electric].values)
            - p.loc[:, electric] * n.links.efficiency[electric]
        )
        n.model.add_constraints(lhs <= 0, name="chplink-backpressure")

add_co2_constraints_prices(network, co2_control)

Add co2 constraints or prices

Parameters:

Name	Type	Description	Default
network	Network	the network to which prices or constraints are to be added	required
co2_control	dict	the config	required

Raises:

Type	Description
ValueError	unrecognised co2 control option

Source code in workflow/scripts/solve_network.py

def add_co2_constraints_prices(network: pypsa.Network, co2_control: dict):
    """Add co2 constraints or prices

    Args:
        network (pypsa.Network): the network to which prices or constraints are to be added
        co2_control (dict): the config

    Raises:
        ValueError: unrecognised co2 control option
    """

    if co2_control["control"] is None:
        pass
    elif co2_control["control"] == "price":
        logger.info("Adding CO2 price to marginal costs of generators and storage units")
        add_emission_prices(network, emission_prices={"co2": co2_control["co2_pr_or_limit"]})

    elif co2_control["control"].startswith("budget"):
        co2_limit = co2_control["co2_pr_or_limit"]
        logger.info("Adding CO2 constraint based on scenario {co2_limit}")
        network.add(
            "GlobalConstraint",
            "co2_limit",
            type="primary_energy",
            carrier_attribute="co2_emissions",
            sense="<=",
            constant=co2_limit,
        )
    else:
        logger.error(f"Unhandled CO2 control config {co2_control} due to unknown control.")
        raise ValueError(f"Unhandled CO2 control config {co2_control} due to unknown control")

add_emission_prices(n, emission_prices={'co2': 0.0}, exclude_co2=False)

from pypsa-eur: add GHG price to marginal costs of generators and storage units

Parameters:

Name	Type	Description	Default
n	Network	the pypsa network	required
emission_prices	dict	emission prices per GHG. Defaults to {"co2": 0.0}.	{'co2': 0.0}
exclude_co2	bool	do not charge for CO2 emissions. Defaults to False.	False

Source code in workflow/scripts/solve_network.py

def add_emission_prices(n: pypsa.Network, emission_prices={"co2": 0.0}, exclude_co2=False):
    """from pypsa-eur: add GHG price to marginal costs of generators and storage units

    Args:
        n (pypsa.Network): the pypsa network
        emission_prices (dict, optional): emission prices per GHG. Defaults to {"co2": 0.0}.
        exclude_co2 (bool, optional): do not charge for CO2 emissions. Defaults to False.
    """
    if exclude_co2:
        emission_prices.pop("co2")
    em_price = (
        pd.Series(emission_prices).rename(lambda x: x + "_emissions")
        * n.carriers.filter(like="_emissions")
    ).sum(axis=1)

    n.meta.update({"emission_prices": emission_prices})

    gen_em_price = n.generators.carrier.map(em_price) / n.generators.efficiency

    n.generators["marginal_cost"] += gen_em_price
    n.generators_t["marginal_cost"] += gen_em_price[n.generators_t["marginal_cost"].columns]
    # storage units su
    su_em_price = n.storage_units.carrier.map(em_price) / n.storage_units.efficiency_dispatch
    n.storage_units["marginal_cost"] += su_em_price

    logger.info("Added emission prices to marginal costs of generators and storage units")
    logger.info(f"\tEmission prices: {emission_prices}")

add_land_use_constraint(n, planning_horizons)

Add land use constraints for renewable energy potential. This ensures that the brownfield + greenfield vre installations for each generator tech do not exceed the technical potential.

Parameters:

Name	Type	Description	Default
n	Network	the network object to add the constraints to	required
planning_horizons	str | int	the planning horizon year as string	required

Source code in workflow/scripts/solve_network.py

def add_land_use_constraint(n: pypsa.Network, planning_horizons: str | int) -> None:
    """
    Add land use constraints for renewable energy potential. This ensures that the brownfield +
     greenfield vre installations for each generator tech do not exceed the technical potential.

    Args:
        n (pypsa.Network): the network object to add the constraints to
        planning_horizons (str | int): the planning horizon year as string
    """
    # warning: this will miss existing offwind which is not classed AC-DC and has carrier 'offwind'

    for carrier in [
        "solar",
        "solar thermal",
        "onwind",
        "offwind",
        "offwind-ac",
        "offwind-dc",
        "offwind-float",
    ]:
        ext_i = (n.generators.carrier == carrier) & ~n.generators.p_nom_extendable
        grouper = n.generators.loc[ext_i].index.str.replace(f" {carrier}.*$", "", regex=True)
        existing = n.generators.loc[ext_i, "p_nom"].groupby(grouper).sum()
        existing.index += f" {carrier}"
        n.generators.loc[existing.index, "p_nom_max"] -= existing

    # check if existing capacities are larger than technical potential
    existing_large = n.generators[n.generators["p_nom_min"] > n.generators["p_nom_max"]].index
    if len(existing_large):
        logger.warning(
            f"Existing capacities larger than technical potential for {existing_large},\
                        adjust technical potential to existing capacities"
        )
        n.generators.loc[existing_large, "p_nom_max"] = n.generators.loc[
            existing_large, "p_nom_min"
        ]

    n.generators["p_nom_max"] = n.generators["p_nom_max"].clip(lower=0)

add_operational_reserve_margin(n, config)

Build operational reserve margin constraints based on the formulation given in https://genxproject.github.io/GenX.jl/stable/Model_Reference/core/#GenX.operational_reserves_core!-Tuple{JuMP.Model,%20Dict,%20Dict}

The constraint is network wide and not at each node!

Parameters:

Name	Type	Description	Default
n	Network	the network object to optimize	required
config	dict	the configuration dictionary	required

Example

config.yaml requires to specify operational_reserve: operational_reserve: activate: true epsilon_load: 0.02 # percentage of load at each snapshot epsilon_vres: 0.02 # percentage of VRES at each snapshot contingency: 400000 # MW

Source code in workflow/scripts/solve_network.py

def add_operational_reserve_margin(n: pypsa.network, config):
    """
    Build operational reserve margin constraints based on the formulation given in
    https://genxproject.github.io/GenX.jl/stable/Model_Reference/core/#GenX.operational_reserves_core!-Tuple{JuMP.Model,%20Dict,%20Dict}

    The constraint is network wide and not at each node!

    Args:
        n (pypsa.Network): the network object to optimize
        config (dict): the configuration dictionary

    Example:
        config.yaml requires to specify operational_reserve:
        operational_reserve:
            activate: true
            epsilon_load: 0.02 # percentage of load at each snapshot
            epsilon_vres: 0.02 # percentage of VRES at each snapshot
            contingency: 400000 # MW
    """
    reserve_config = config["operational_reserve"]
    VRE_TECHS = config["Techs"].get("non_dispatchable", ["onwind", "offwind", "solar"])
    EPSILON_LOAD, EPSILON_VRES = reserve_config["epsilon_load"], reserve_config["epsilon_vres"]
    CONTINGENCY = float(reserve_config["contingency"])

    # AC producers
    ac_mask = n.generators.bus.map(n.buses.carrier) == "AC"
    ac_buses = n.buses.query("carrier =='AC'").index
    attached_carriers = filter_carriers(n, "AC")
    # conceivably a link could have a negative efficiency and flow towards bus0 - don't consider
    prod_links = n.links.query("carrier in @attached_carriers & not bus0 in @ac_buses")
    transport_links = prod_links.bus0.map(n.buses.carrier) == prod_links.bus1.map(n.buses.carrier)
    prod_links = prod_links.loc[transport_links == False]
    prod_gen = n.generators.loc[ac_mask]
    producers_all = prod_links.index.append(prod_gen.index)
    producers_all.name = "Producers-p"

    # RSERVES
    n.model.add_variables(0, np.inf, coords=[n.snapshots, prod_gen.index], name="Generator-r")
    n.model.add_variables(0, np.inf, coords=[n.snapshots, prod_links.index], name="Link-r")

    # Define Reserve and weigh VRES by their mean availability ("capacity credit")
    vres_gen = prod_gen.query("carrier in @VRE_TECHS")
    non_vre = prod_gen.index.difference(vres_gen.index)
    # full capacity credit for non-VRE producers (questionable, maybe should be weighted by availability)
    summed_reserve = (n.model["Link-r"] * prod_links.efficiency).sum("Link") + n.model[
        "Generator-r"
    ].loc[:, non_vre].sum("Generator")

    # VRE capacity credit & margin reqs
    ext_idx = vres_gen.query("p_nom_extendable").index
    avail = n.generators_t.p_max_pu.loc[:, vres_gen.index]
    vres_idx = avail.columns

    if not vres_gen.empty:
        # Reserve score based on actual avail (perfect foresight) not mean/expected avail
        vre_reserve_score = (n.model["Generator-r"].loc[:, vres_gen.index] * avail).sum("Generator")
        summed_reserve += vre_reserve_score
    if not ext_idx.empty and not vres_idx.empty:
        # reqs from brownfield VRE generators. epsilon is the margin for VRES forecast error
        avail_factor = n.generators_t.p_max_pu[ext_idx]
        p_nom_vres = n.model["Generator-p_nom"].loc[ext_idx].rename({"Generator-ext": "Generator"})
        vre_req_ext = (p_nom_vres * (EPSILON_VRES * xr.DataArray(avail_factor))).sum("Generator")
    else:
        vre_req_ext = 0

    if not vres_idx.empty:
        # reqs extendable VRE generators
        avail_factor = n.generators_t.p_max_pu[vres_idx.difference(ext_idx)]
        renewable_capacity = n.generators.p_nom[vres_idx.difference(ext_idx)]
        vre_req_fix = (avail_factor * renewable_capacity).sum(axis=1)
    else:
        vre_req_fix = 0

    lhs = summed_reserve - vre_req_ext
    # Right-hand-side
    demand = get_as_dense(n, "Load", "p_set").sum(axis=1)
    rhs = EPSILON_LOAD * demand + EPSILON_VRES * vre_req_fix + CONTINGENCY

    n.model.add_constraints(lhs >= rhs, name="Reserve-margin")

    # Need additional constraints (reserve + dispatch <= p_nom): gen_r + gen_p <= gen_p_nom (capacity)
    to_constrain = {"Link": prod_links, "Generator": prod_gen}
    for component, producer in to_constrain.items():
        logger.info(f"adding secondary reserve constraint for {component}s")

        fix_i = producer.query("p_nom_extendable==False").index
        ext_i = producer.query("p_nom_extendable==True").index

        dispatch = n.model[f"{component}-p"].loc[:, producer.index]
        reserve = n.model[f"{component}-r"].loc[:, ext_i.union(fix_i)]

        capacity_variable = n.model[f"{component}-p_nom"].loc[ext_i]
        capacity_variable = capacity_variable.rename({f"{component}-ext": f"{component}"})
        capacity_fixed = getattr(n, component.lower() + "s").p_nom[fix_i]

        p_max_pu = get_as_dense(n, f"{component}", "p_max_pu")

        lhs = dispatch + reserve
        # MAY have to check what happens in case pmaxpu is not defined for all items
        rhs = capacity_variable * p_max_pu[ext_i] + (p_max_pu[fix_i] * capacity_fixed)
        n.model.add_constraints(
            lhs - rhs.loc[lhs.indexes] <= 0, name=f"{component}-p-reserve-upper"
        )

add_remind_paid_off_constraints(n)

Paid-off components can be placed wherever PyPSA wants but have a total limit.

Add constraints to ensure that the paid off capacity from REMIND is not exceeded across the network & that it does not exceed the technical potential.

Parameters:

Name	Type	Description	Default
n	Network	the network object to which's model the constraints are added	required

Source code in workflow/scripts/solve_network.py

def add_remind_paid_off_constraints(n: pypsa.Network) -> None:
    """
    Paid-off components can be placed wherever PyPSA wants but have a total limit.

    Add constraints to ensure that the paid off capacity from REMIND is not
    exceeded across the network & that it does not exceed the technical potential.

    Args:
        n (pypsa.Network): the network object to which's model the constraints are added
    """

    if not n.config["run"].get("is_remind_coupled", False):
        logger.info("Skipping paid off constraints as REMIND is not coupled")
        return

    # In coupled-mode components (Generators, Links,..) have limits p/e_nom_rcl & a tech_group
    # These columns are added by `add_existing_baseyear.add_paid_off_capacity`.
    # p/e_nom_rcl is the availale paid-off capacity per tech group and is nan for non paid-off (usual) generators.
    # rcl is a legacy name from Aodenweller
    for component in ["Generator", "Link", "Store"]:

        prefix = "e" if component == "Store" else "p"
        paid_off_col = f"{prefix}_nom_max_rcl"

        paid_off = getattr(n, component.lower() + "s").copy()
        # if there are no paid_off components
        if paid_off_col not in paid_off.columns:
            continue
        else:
            paid_off.dropna(subset=[paid_off_col], inplace=True)

        paid_off_totals = paid_off.set_index("tech_group")[paid_off_col].drop_duplicates()

        # LHS: p_nom per technology grp < totals
        groupers = [paid_off["tech_group"]]
        grouper_lhs = xr.DataArray(pd.MultiIndex.from_arrays(groupers), dims=[f"{component}-ext"])
        p_nom_groups = (
            n.model[f"{component}-{prefix}_nom"].loc[paid_off.index].groupby(grouper_lhs).sum()
        )

        # get indices to sort RHS. the grouper is multi-indexed (legacy from PyPSA-Eur)
        idx = p_nom_groups.indexes["group"]
        idx = [x[0] for x in idx]

        # Add constraint
        if not p_nom_groups.empty:
            n.model.add_constraints(
                p_nom_groups <= paid_off_totals[idx].values,
                name=f"paidoff_cap_totals_{component.lower()}",
            )

    # === ensure normal e/p_nom_max is respected for (paid_off + normal) components
    # e.g. if PV has 100MW tech potential at nodeA, paid_off+normal p_nom_opt <100MW
    for component in ["Generator", "Link", "Store"]:
        paidoff_comp = getattr(n, component.lower() + "s").copy()

        prefix = "e" if component == "Store" else "p"
        paid_off_col = f"{prefix}_nom_max_rcl"
        # if there are no paid_off components
        if paid_off_col not in paidoff_comp.columns:
            continue
        else:
            paidoff_comp.dropna(subset=[paid_off_col], inplace=True)

        # techs that only exist as paid-off don't have usual counterparts
        remind_only_techs = n.config["existing_capacities"].get("remind_only_tech_groups", [])
        paidoff_comp = paidoff_comp.query("tech_group not in @remind_only_techs")

        if paidoff_comp.empty:
            continue

        # find equivalent usual (not paid-off) components
        usual_comps_idx = paidoff_comp.index.str.replace("_paid_off", "")
        usual_comps = getattr(n, component.lower() + "s").loc[usual_comps_idx].copy()
        usual_comps = usual_comps[~usual_comps.p_nom_max.isin([np.inf, np.nan])]

        paid_off_wlimits = paidoff_comp.loc[usual_comps.index + "_paid_off"]
        to_constrain = pd.concat([usual_comps, paid_off_wlimits], axis=0)
        if to_constrain.empty:
            continue
        to_constrain.rename_axis(index=f"{component}-ext", inplace=True)
        # otherwise n.model query will fail. This is needed in case freeze_compoents was used
        # it is fine so long as p_nom is zero for the frozen components
        to_constrain = to_constrain.query("p_nom_extendable==True")
        to_constrain["grouper"] = to_constrain.index.str.replace("_paid_off", "")

        grouper = xr.DataArray(to_constrain.grouper, dims=[f"{component}-ext"])

        lhs = n.model[f"{component}-{prefix}_nom"].loc[to_constrain.index].groupby(grouper).sum()
        # RHS
        idx = lhs.indexes["grouper"]

        if not lhs.empty:
            n.model.add_constraints(
                lhs <= usual_comps.loc[idx].p_nom_max.values,
                name=f"constrain_paidoff&usual_{component}_potential",
            )

add_transmission_constraints(n)

Add constraint ensuring that transmission lines p_nom are the same for both directions, i.e. p_nom positive = p_nom negative

Parameters:

Name	Type	Description	Default
n	Network	the network object to optimize	required

Source code in workflow/scripts/solve_network.py

def add_transmission_constraints(n: pypsa.Network):
    """
    Add constraint ensuring that transmission lines p_nom are the same for both directions, i.e.
    p_nom positive = p_nom negative

    Args:
        n (pypsa.Network): the network object to optimize
    """

    if not n.links.p_nom_extendable.any():
        return

    positive_bool = n.links.index.str.contains("positive")
    negative_bool = n.links.index.str.contains("reversed")

    positive_ext = n.links[positive_bool].query("p_nom_extendable").index
    negative_ext = n.links[negative_bool].query("p_nom_extendable").index

    lhs = n.model["Link-p_nom"].loc[positive_ext]
    rhs = n.model["Link-p_nom"].loc[negative_ext]

    n.model.add_constraints(lhs == rhs, name="Link-transmission")

extra_functionality(n, _)

Add supplementary constraints to the network model. 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.

Parameters:

Name	Type	Description	Default
n	Network	the network object to optimize	required

Source code in workflow/scripts/solve_network.py

def extra_functionality(n: pypsa.Network, _) -> None:
    """
    Add supplementary constraints to the network model. ``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.

    Args:
        n (pypsa.Network): the network object to optimize
    """
    config = n.config
    add_battery_constraints(n)
    add_transmission_constraints(n)
    add_chp_constraints(n)
    if config["run"].get("is_remind_coupled", False):
        logger.info("Adding remind paid off constraints")
        add_remind_paid_off_constraints(n)

    reserve = config.get("operational_reserve", {})
    if reserve.get("activate", False):
        logger.info("Adding operational reserve margin constraints")
        add_operational_reserve_margin(n, config)

    logger.info("Added extra functionality to the network model")

freeze_components(n, config, exclude=['H2 turbine'])

Set p_nom_extendable=False for the components in the network. Applies to vre_techs and conventional technologies not in the exclude list.

Parameters:

Name	Type	Description	Default
n	Network	the network object	required
config	dict	the configuration dictionary	required
exclude	list	list of technologies to exclude from freezing. Defaults to ["OCGT"]	['H2 turbine']

Source code in workflow/scripts/solve_network.py

def freeze_components(n: pypsa.Network, config: dict, exclude: list = ["H2 turbine"]):
    """Set p_nom_extendable=False for the components in the network.
    Applies to vre_techs and conventional technologies not in the exclude list.

    Args:
        n (pypsa.Network): the network object
        config (dict): the configuration dictionary
        exclude (list, optional): list of technologies to exclude from freezing.
            Defaults to ["OCGT"]
    """

    # Freeze VRE and conventional techs
    freeze = config["Techs"]["vre_techs"] + config["Techs"]["conv_techs"]
    freeze = [f for f in freeze if f not in exclude]
    if "coal boiler" in freeze:
        freeze += ["coal boiler central", "coal boiler decentral"]
    if "gas boiler" in freeze:
        freeze += ["gas boiler central", "gas boiler decentral"]

    # very ugly -> how to make more robust?
    to_fix = {
        "OCGT": "gas OCGT",
        "CCGT": "gas CCGT",
        "CCGT-CCS": "gas ccs",
        "coal power plant": "coal",
        "coal-CCS": "coal ccs",
    }
    freeze += [to_fix[k] for k in to_fix if k in freeze]

    for comp in ["generators", "links"]:
        query = "carrier in @freeze & p_nom_extendable == True"
        components = getattr(n, comp)
        # p_nom_max_rcl.isna(): exclude paid_off as needed
        if "p_nom_max_rcl" in components.columns:
            query += " & p_nom_max_rcl.isna()"
        mask = components.query(query).index
        components.loc[mask, "p_nom_extendable"] = False

prepare_network(n, solve_opts, config, plan_year, co2_pathway)

prepare the network for the solver, Args: n (pypsa.Network): the network object to optimize solve_opts (dict): solving options config (dict): the snakemake configuration dictionary plan_year (int): planning horizon year for which network is solved co2_pathway (str): the CO2 pathway name to use

Returns:

Type	Description
Network	pypsa.Network: network object with additional constraints

Source code in workflow/scripts/solve_network.py

def prepare_network(
    n: pypsa.Network, solve_opts: dict, config: dict, plan_year: int, co2_pathway: str
) -> pypsa.Network:
    """prepare the network for the solver,
    Args:
        n (pypsa.Network): the network object to optimize
        solve_opts (dict): solving options
        config (dict): the snakemake configuration dictionary
        plan_year (int): planning horizon year for which network is solved
        co2_pathway (str): the CO2 pathway name to use

    Returns:
        pypsa.Network: network object with additional constraints
    """

    co2_opts = ConfigManager(config).fetch_co2_restriction(co2_pathway, int(plan_year))
    add_co2_constraints_prices(n, co2_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)

    # TODO duplicated with freeze components
    if solve_opts.get("load_shedding"):
        n.add("Carrier", "Load Shedding")
        buses_i = n.buses.query("carrier == 'AC'").index
        n.add(
            "Generator",
            buses_i,
            " load",
            bus=buses_i,
            carrier="Load Shedding",
            marginal_cost=solve_opts.get("voll", 1e5),  # EUR/MWh
            # intersect between macroeconomic and surveybased
            # willingness to pay
            # http://journal.frontiersin.org/article/10.3389/fenrg.2015.00055/full
            p_nom=1e6,  # MW
        )

    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 config["run"].get("is_remind_coupled", False) & (
        config["existing_capacities"].get("freeze_new", False)
    ):
        freeze_components(
            n,
            config,
            exclude=config["existing_capacities"].get("never_freeze", []),
        )

    if solve_opts.get("nhours"):
        nhours = solve_opts["nhours"]
        n.set_snapshots(n.snapshots[:nhours])
        n.snapshot_weightings[:] = YEAR_HRS / nhours

    if config["existing_capacities"].get("add", False):
        add_land_use_constraint(n, plan_year)

    return n

set_transmission_limit(n, kind, factor, n_years=1)

Set global transimission limit constraints - adapted from pypsa-eur

Parameters:

Name	Type	Description	Default
n	Network	the network object	required
kind	str	the kind of limit to set, either 'c' for cost or 'v' for volume or l for length	required
factor	float or str	the factor to apply to the base year quantity, per year	required
n_years	int	the number of years to consider for the limit. Defaults to 1.	1

Source code in workflow/scripts/solve_network.py

def set_transmission_limit(n: pypsa.Network, kind: str, factor: float, n_years=1):
    """
    Set global transimission limit constraints - adapted from pypsa-eur

    Args:
        n (pypsa.Network): the network object
        kind (str): the kind of limit to set, either 'c' for cost or 'v' for volume or l for length
        factor (float or str): the factor to apply to the base year quantity, per year
        n_years (int, optional): the number of years to consider for the limit. Defaults to 1.
    """
    logger.info(
        f"Adding global transmission limit for {kind} with factor {factor}/year & {n_years} years"
    )
    links_dc = n.links.query("carrier in ['AC','DC']").index
    # links_dc_rev = n.links.query("carrier in ['AC','DC'] & Link.str.contains('reverse')").index

    _lines_s_nom = (
        np.sqrt(3)
        * n.lines.type.map(n.line_types.i_nom)
        * n.lines.num_parallel
        * n.lines.bus0.map(n.buses.v_nom)
    )
    lines_s_nom = n.lines.s_nom.where(n.lines.type == "", _lines_s_nom)

    col = "capital_cost" if kind == "c" else "length"
    ref = lines_s_nom @ n.lines[col] + n.links.loc[links_dc, "p_nom"] @ n.links.loc[links_dc, col]

    if factor == "opt" or float(factor) ** n_years > 1.0:
        n.lines["s_nom_min"] = lines_s_nom
        n.lines["s_nom_extendable"] = True

        n.links.loc[links_dc, "p_nom_extendable"] = True

    elif float(factor) ** n_years == 1.0:
        # if factor is 1.0, then we do not need to extend
        n.lines["s_nom_min"] = lines_s_nom
        n.lines["s_nom_extendable"] = False
        n.links.loc[links_dc, "p_nom_extendable"] = False

        # factor = 1 + 1e-7  # to avoid numerical issues with the constraints

    elif float(factor) ** n_years < 1.0:
        n.lines["s_nom_min"] = 0
        n.links.loc[links_dc, "p_nom_min"] = 0
        # n.links.loc[links_dc_rev, "p_nom_min"] = 0

    if factor != "opt":
        con_type = "expansion_cost" if kind == "c" else "volume_expansion"
        rhs = float(factor) ** n_years * ref
        logger.info(
            f"Adding global transmission limit for {kind} to {float(factor)**n_years} current value"
        )
        n.add(
            "GlobalConstraint",
            f"l{kind}_limit",
            type=f"transmission_{con_type}_limit",
            sense="<=",
            constant=rhs,
            carrier_attribute="AC, DC",
        )

solve_network(n, config, solving, opts='', **kwargs)

perform the optimisation Args: n (pypsa.Network): the pypsa network object config (dict): the configuration dictionary solving (dict): the solving configuration dictionary opts (str): optional wildcards such as ll (not used in pypsa-china)

Returns:

Type	Description
Network	pypsa.Network: the optimized network

Source code in workflow/scripts/solve_network.py

def solve_network(
    n: pypsa.Network, config: dict, solving: dict, opts: str = "", **kwargs
) -> pypsa.Network:
    """perform the optimisation
    Args:
        n (pypsa.Network): the pypsa network object
        config (dict): the configuration dictionary
        solving (dict): the solving configuration dictionary
        opts (str): optional wildcards such as ll (not used in pypsa-china)

    Returns:
        pypsa.Network: the optimized network
    """
    set_of_options = solving["solver"]["options"]
    solver_options = solving["solver_options"][set_of_options] if set_of_options else {}
    solver_name = solving["solver"]["name"]
    cf_solving = 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)
    transmission_losses = cf_solving.get("transmission_losses", 0)

    # 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:
        status, condition = n.optimize(
            solver_name=solver_name,
            transmission_losses=transmission_losses,
            extra_functionality=extra_functionality,
            **solver_options,
            **kwargs,
        )
    else:
        status, condition = n.optimize.optimize_transmission_expansion_iteratively(
            solver_name=solver_name,
            track_iterations=track_iterations,
            min_iterations=min_iterations,
            max_iterations=max_iterations,
            transmission_losses=transmission_losses,
            extra_functionality=extra_functionality,
            **solver_options,
            **kwargs,
        )

    if status != "ok":
        logger.warning(f"Solving status '{status}' with termination condition '{condition}'")
    if "infeasible" in condition:
        raise RuntimeError("Solving status 'infeasible'")

    return n