794 lines
24 KiB
Python
794 lines
24 KiB
Python
from six import iteritems
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import pandas as pd
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import numpy as np
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import pypsa
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from pypsa.descriptors import (
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nominal_attrs,
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get_active_assets,
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)
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from helper import override_component_attrs
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from prepare_sector_network import prepare_costs
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from make_summary import (assign_carriers, assign_locations,
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calculate_cfs, calculate_nodal_cfs,
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calculate_nodal_costs)
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idx = pd.IndexSlice
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opt_name = {"Store": "e", "Line": "s", "Transformer": "s"}
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def calculate_costs(n, label, costs):
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investments = n.investment_periods
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cols = pd.MultiIndex.from_product(
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[
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costs.columns.levels[0],
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costs.columns.levels[1],
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costs.columns.levels[2],
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investments,
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],
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names=costs.columns.names[:3] + ["year"],
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)
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costs = costs.reindex(cols, axis=1)
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for c in n.iterate_components(
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n.branch_components | n.controllable_one_port_components ^ {"Load"}
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):
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capital_costs = c.df.capital_cost * c.df[opt_name.get(c.name, "p") + "_nom_opt"]
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active = pd.concat(
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[
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get_active_assets(n, c.name, inv_p).rename(inv_p)
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for inv_p in investments
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],
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axis=1,
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).astype(int)
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capital_costs = active.mul(capital_costs, axis=0)
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discount = (
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n.investment_period_weightings["objective_weightings"]
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/ n.investment_period_weightings["time_weightings"]
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)
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capital_costs_grouped = (
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capital_costs.groupby(c.df.carrier).sum().mul(discount)
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)
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capital_costs_grouped = pd.concat([capital_costs_grouped], keys=["capital"])
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capital_costs_grouped = pd.concat([capital_costs_grouped], keys=[c.list_name])
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costs = costs.reindex(capital_costs_grouped.index.union(costs.index))
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costs.loc[capital_costs_grouped.index, label] = capital_costs_grouped.values
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if c.name == "Link":
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p = (
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c.pnl.p0.multiply(n.snapshot_weightings.generator_weightings, axis=0)
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.groupby(level=0)
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.sum()
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)
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elif c.name == "Line":
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continue
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elif c.name == "StorageUnit":
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p_all = c.pnl.p.multiply(n.snapshot_weightings.store_weightings, axis=0)
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p_all[p_all < 0.0] = 0.0
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p = p_all.groupby(level=0).sum()
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else:
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p = (
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round(c.pnl.p, ndigits=2)
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.multiply(n.snapshot_weightings.generator_weightings, axis=0)
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.groupby(level=0)
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.sum()
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)
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# correct sequestration cost
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if c.name == "Store":
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items = c.df.index[
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(c.df.carrier == "co2 stored") & (c.df.marginal_cost <= -100.0)
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]
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c.df.loc[items, "marginal_cost"] = -20.0
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marginal_costs = p.mul(c.df.marginal_cost).T
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# marginal_costs = active.mul(marginal_costs, axis=0)
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marginal_costs_grouped = (
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marginal_costs.groupby(c.df.carrier).sum().mul(discount)
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)
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marginal_costs_grouped = pd.concat([marginal_costs_grouped], keys=["marginal"])
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marginal_costs_grouped = pd.concat([marginal_costs_grouped], keys=[c.list_name])
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costs = costs.reindex(marginal_costs_grouped.index.union(costs.index))
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costs.loc[marginal_costs_grouped.index, label] = marginal_costs_grouped.values
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# add back in all hydro
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# costs.loc[("storage_units","capital","hydro"),label] = (0.01)*2e6*n.storage_units.loc[n.storage_units.group=="hydro","p_nom"].sum()
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# costs.loc[("storage_units","capital","PHS"),label] = (0.01)*2e6*n.storage_units.loc[n.storage_units.group=="PHS","p_nom"].sum()
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# costs.loc[("generators","capital","ror"),label] = (0.02)*3e6*n.generators.loc[n.generators.group=="ror","p_nom"].sum()
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return costs
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def calculate_cumulative_cost():
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planning_horizons = snakemake.config["scenario"]["planning_horizons"]
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cumulative_cost = pd.DataFrame(
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index=df["costs"].sum().index,
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columns=pd.Series(data=np.arange(0, 0.1, 0.01), name="social discount rate"),
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)
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# discount cost and express them in money value of planning_horizons[0]
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for r in cumulative_cost.columns:
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cumulative_cost[r] = [
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df["costs"].sum()[index] / ((1 + r) ** (index[-1] - planning_horizons[0]))
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for index in cumulative_cost.index
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]
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# integrate cost throughout the transition path
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for r in cumulative_cost.columns:
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for cluster in cumulative_cost.index.get_level_values(level=0).unique():
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for lv in cumulative_cost.index.get_level_values(level=1).unique():
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for sector_opts in cumulative_cost.index.get_level_values(
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level=2
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).unique():
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cumulative_cost.loc[
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(cluster, lv, sector_opts, "cumulative cost"), r
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] = np.trapz(
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cumulative_cost.loc[
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idx[cluster, lv, sector_opts, planning_horizons], r
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].values,
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x=planning_horizons,
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)
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return cumulative_cost
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def calculate_nodal_capacities(n, label, nodal_capacities):
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# Beware this also has extraneous locations for country (e.g. biomass) or continent-wide (e.g. fossil gas/oil) stuff
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for c in n.iterate_components(
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n.branch_components | n.controllable_one_port_components ^ {"Load"}
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):
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nodal_capacities_c = c.df.groupby(["location", "carrier"])[
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opt_name.get(c.name, "p") + "_nom_opt"
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].sum()
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index = pd.MultiIndex.from_tuples(
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[(c.list_name,) + t for t in nodal_capacities_c.index.to_list()]
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)
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nodal_capacities = nodal_capacities.reindex(index.union(nodal_capacities.index))
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nodal_capacities.loc[index, label] = nodal_capacities_c.values
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return nodal_capacities
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def calculate_capacities(n, label, capacities):
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investments = n.investment_periods
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cols = pd.MultiIndex.from_product(
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[
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capacities.columns.levels[0],
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capacities.columns.levels[1],
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capacities.columns.levels[2],
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investments,
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],
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names=capacities.columns.names[:3] + ["year"],
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)
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capacities = capacities.reindex(cols, axis=1)
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for c in n.iterate_components(
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n.branch_components | n.controllable_one_port_components ^ {"Load"}
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):
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active = pd.concat(
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[
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get_active_assets(n, c.name, inv_p).rename(inv_p)
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for inv_p in investments
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],
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axis=1,
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).astype(int)
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caps = c.df[opt_name.get(c.name, "p") + "_nom_opt"]
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caps = active.mul(caps, axis=0)
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capacities_grouped = (
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caps.groupby(c.df.carrier)
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.sum()
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.drop("load", errors="ignore")
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)
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capacities_grouped = pd.concat([capacities_grouped], keys=[c.list_name])
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capacities = capacities.reindex(
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capacities_grouped.index.union(capacities.index)
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)
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capacities.loc[capacities_grouped.index, label] = capacities_grouped.values
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return capacities
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def calculate_curtailment(n, label, curtailment):
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avail = (
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n.generators_t.p_max_pu.multiply(n.generators.p_nom_opt)
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.sum()
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.groupby(n.generators.carrier)
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.sum()
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)
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used = n.generators_t.p.sum().groupby(n.generators.carrier).sum()
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curtailment[label] = (((avail - used) / avail) * 100).round(3)
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return curtailment
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def calculate_energy(n, label, energy):
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for c in n.iterate_components(n.one_port_components | n.branch_components):
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if c.name in n.one_port_components:
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c_energies = (
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c.pnl.p.multiply(n.snapshot_weightings, axis=0)
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.sum()
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.multiply(c.df.sign)
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.groupby(c.df.carrier)
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.sum()
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)
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else:
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c_energies = pd.Series(0.0, c.df.carrier.unique())
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for port in [col[3:] for col in c.df.columns if col[:3] == "bus"]:
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totals = c.pnl["p" + port].multiply(n.snapshot_weightings, axis=0).sum()
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# remove values where bus is missing (bug in nomopyomo)
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no_bus = c.df.index[c.df["bus" + port] == ""]
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totals.loc[no_bus] = n.component_attrs[c.name].loc[
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"p" + port, "default"
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]
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c_energies -= totals.groupby(c.df.carrier).sum()
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c_energies = pd.concat([c_energies], keys=[c.list_name])
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energy = energy.reindex(c_energies.index.union(energy.index))
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energy.loc[c_energies.index, label] = c_energies
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return energy
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def calculate_supply(n, label, supply):
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"""calculate the max dispatch of each component at the buses aggregated by carrier"""
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bus_carriers = n.buses.carrier.unique()
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for i in bus_carriers:
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bus_map = n.buses.carrier == i
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bus_map.at[""] = False
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for c in n.iterate_components(n.one_port_components):
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items = c.df.index[c.df.bus.map(bus_map).fillna(False)]
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if len(items) == 0:
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continue
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s = (
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c.pnl.p[items]
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.max()
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.multiply(c.df.loc[items, "sign"])
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.groupby(c.df.loc[items, "carrier"])
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.sum()
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)
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s = pd.concat([s], keys=[c.list_name])
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s = pd.concat([s], keys=[i])
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supply = supply.reindex(s.index.union(supply.index))
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supply.loc[s.index, label] = s
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for c in n.iterate_components(n.branch_components):
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for end in [col[3:] for col in c.df.columns if col[:3] == "bus"]:
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items = c.df.index[c.df["bus" + end].map(bus_map, na_action=False)]
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if len(items) == 0:
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continue
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# lots of sign compensation for direction and to do maximums
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s = (-1) ** (1 - int(end)) * (
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(-1) ** int(end) * c.pnl["p" + end][items]
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).max().groupby(c.df.loc[items, "carrier"]).sum()
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s.index = s.index + end
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s = pd.concat([s], keys=[c.list_name])
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s = pd.concat([s], keys=[i])
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supply = supply.reindex(s.index.union(supply.index))
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supply.loc[s.index, label] = s
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return supply
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def calculate_supply_energy(n, label, supply_energy):
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"""calculate the total energy supply/consuption of each component at the buses aggregated by carrier"""
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investments = n.investment_periods
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cols = pd.MultiIndex.from_product(
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[
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supply_energy.columns.levels[0],
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supply_energy.columns.levels[1],
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supply_energy.columns.levels[2],
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investments,
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],
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names=supply_energy.columns.names[:3] + ["year"],
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)
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supply_energy = supply_energy.reindex(cols, axis=1)
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bus_carriers = n.buses.carrier.unique()
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for i in bus_carriers:
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bus_map = n.buses.carrier == i
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bus_map.at[""] = False
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for c in n.iterate_components(n.one_port_components):
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items = c.df.index[c.df.bus.map(bus_map).fillna(False)]
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if len(items) == 0:
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continue
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if c.name == "Generator":
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weightings = n.snapshot_weightings.generator_weightings
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else:
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weightings = n.snapshot_weightings.store_weightings
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if i in ["oil", "co2", "H2"]:
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if c.name=="Load":
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c.df.loc[items, "carrier"] = [load.split("-202")[0] for load in items]
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if i=="oil" and c.name=="Generator":
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c.df.loc[items, "carrier"] = "imported oil"
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s = (
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c.pnl.p[items]
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.multiply(weightings, axis=0)
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.groupby(level=0)
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.sum()
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.multiply(c.df.loc[items, "sign"])
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.groupby(c.df.loc[items, "carrier"], axis=1)
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.sum()
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.T
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)
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s = pd.concat([s], keys=[c.list_name])
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s = pd.concat([s], keys=[i])
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supply_energy = supply_energy.reindex(
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s.index.union(supply_energy.index, sort=False)
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)
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supply_energy.loc[s.index, label] = s.values
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for c in n.iterate_components(n.branch_components):
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for end in [col[3:] for col in c.df.columns if col[:3] == "bus"]:
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items = c.df.index[c.df["bus" + str(end)].map(bus_map, na_action=False)]
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if len(items) == 0:
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continue
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s = (
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(-1)
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* c.pnl["p" + end]
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.reindex(items, axis=1)
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.multiply(n.snapshot_weightings.objective_weightings, axis=0)
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.groupby(level=0)
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.sum()
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.groupby(c.df.loc[items, "carrier"], axis=1)
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.sum()
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).T
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s.index = s.index + end
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s = pd.concat([s], keys=[c.list_name])
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s = pd.concat([s], keys=[i])
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supply_energy = supply_energy.reindex(
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s.index.union(supply_energy.index, sort=False)
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)
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supply_energy.loc[s.index, label] = s.values
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return supply_energy
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def calculate_metrics(n, label, metrics):
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metrics = metrics.reindex(
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pd.Index(
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[
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"line_volume",
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"line_volume_limit",
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"line_volume_AC",
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"line_volume_DC",
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"line_volume_shadow",
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"co2_shadow",
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]
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).union(metrics.index)
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)
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metrics.at["line_volume_DC", label] = (n.links.length * n.links.p_nom_opt)[
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n.links.carrier == "DC"
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].sum()
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metrics.at["line_volume_AC", label] = (n.lines.length * n.lines.s_nom_opt).sum()
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metrics.at["line_volume", label] = metrics.loc[
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["line_volume_AC", "line_volume_DC"], label
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].sum()
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if hasattr(n, "line_volume_limit"):
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metrics.at["line_volume_limit", label] = n.line_volume_limit
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metrics.at["line_volume_shadow", label] = n.line_volume_limit_dual
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if "CO2Limit" in n.global_constraints.index:
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metrics.at["co2_shadow", label] = n.global_constraints.at["CO2Limit", "mu"]
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return metrics
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def calculate_prices(n, label, prices):
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prices = prices.reindex(prices.index.union(n.buses.carrier.unique()))
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# WARNING: this is time-averaged, see weighted_prices for load-weighted average
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prices[label] = (
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n.buses_t.marginal_price.mean()
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.groupby(n.buses.carrier)
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.mean()
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)
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return prices
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def calculate_weighted_prices(n, label, weighted_prices):
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# Warning: doesn't include storage units as loads
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weighted_prices = weighted_prices.reindex(
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pd.Index(
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[
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"electricity",
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"heat",
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"space heat",
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"urban heat",
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"space urban heat",
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"gas",
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"H2",
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]
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)
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)
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link_loads = {
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"electricity": [
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"heat pump",
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"resistive heater",
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"battery charger",
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"H2 Electrolysis",
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],
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"heat": ["water tanks charger"],
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"urban heat": ["water tanks charger"],
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"space heat": [],
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"space urban heat": [],
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"gas": ["OCGT", "gas boiler", "CHP electric", "CHP heat"],
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"H2": ["Sabatier", "H2 Fuel Cell"],
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}
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for carrier in link_loads:
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if carrier == "electricity":
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suffix = ""
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elif carrier[:5] == "space":
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suffix = carrier[5:]
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else:
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suffix = " " + carrier
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buses = n.buses.index[n.buses.index.str[2:] == suffix]
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if buses.empty:
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continue
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if carrier in ["H2", "gas"]:
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load = pd.DataFrame(index=n.snapshots, columns=buses, data=0.0)
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else:
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load = n.loads_t.p_set.reindex(buses, axis=1)
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for tech in link_loads[carrier]:
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names = n.links.index[n.links.index.to_series().str[-len(tech) :] == tech]
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if names.empty:
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continue
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load += (
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|
n.links_t.p0[names].groupby(n.links.loc[names, "bus0"], axis=1).sum()
|
|
)
|
|
|
|
# Add H2 Store when charging
|
|
# if carrier == "H2":
|
|
# stores = n.stores_t.p[buses+ " Store"].groupby(n.stores.loc[buses+ " Store","bus"],axis=1).sum(axis=1)
|
|
# stores[stores > 0.] = 0.
|
|
# load += -stores
|
|
|
|
weighted_prices.loc[carrier, label] = (
|
|
load * n.buses_t.marginal_price[buses]
|
|
).sum().sum() / load.sum().sum()
|
|
|
|
if carrier[:5] == "space":
|
|
print(load * n.buses_t.marginal_price[buses])
|
|
|
|
return weighted_prices
|
|
|
|
|
|
def calculate_market_values(n, label, market_values):
|
|
# Warning: doesn't include storage units
|
|
|
|
carrier = "AC"
|
|
|
|
buses = n.buses.index[n.buses.carrier == carrier]
|
|
|
|
## First do market value of generators ##
|
|
|
|
generators = n.generators.index[n.buses.loc[n.generators.bus, "carrier"] == carrier]
|
|
|
|
techs = n.generators.loc[generators, "carrier"].value_counts().index
|
|
|
|
market_values = market_values.reindex(market_values.index.union(techs))
|
|
|
|
for tech in techs:
|
|
gens = generators[n.generators.loc[generators, "carrier"] == tech]
|
|
|
|
dispatch = (
|
|
n.generators_t.p[gens]
|
|
.groupby(n.generators.loc[gens, "bus"], axis=1)
|
|
.sum()
|
|
.reindex(columns=buses, fill_value=0.0)
|
|
)
|
|
|
|
revenue = dispatch * n.buses_t.marginal_price[buses]
|
|
|
|
market_values.at[tech, label] = revenue.sum().sum() / dispatch.sum().sum()
|
|
|
|
## Now do market value of links ##
|
|
|
|
for i in ["0", "1"]:
|
|
all_links = n.links.index[n.buses.loc[n.links["bus" + i], "carrier"] == carrier]
|
|
|
|
techs = n.links.loc[all_links, "carrier"].value_counts().index
|
|
|
|
market_values = market_values.reindex(market_values.index.union(techs))
|
|
|
|
for tech in techs:
|
|
links = all_links[n.links.loc[all_links, "carrier"] == tech]
|
|
|
|
dispatch = (
|
|
n.links_t["p" + i][links]
|
|
.groupby(n.links.loc[links, "bus" + i], axis=1)
|
|
.sum()
|
|
.reindex(columns=buses, fill_value=0.0)
|
|
)
|
|
|
|
revenue = dispatch * n.buses_t.marginal_price[buses]
|
|
|
|
market_values.at[tech, label] = revenue.sum().sum() / dispatch.sum().sum()
|
|
|
|
return market_values
|
|
|
|
|
|
def calculate_price_statistics(n, label, price_statistics):
|
|
|
|
price_statistics = price_statistics.reindex(
|
|
price_statistics.index.union(
|
|
pd.Index(["zero_hours", "mean", "standard_deviation"])
|
|
)
|
|
)
|
|
|
|
buses = n.buses.index[n.buses.carrier == "AC"]
|
|
|
|
threshold = 0.1 # higher than phoney marginal_cost of wind/solar
|
|
|
|
df = pd.DataFrame(data=0.0, columns=buses, index=n.snapshots)
|
|
|
|
df[n.buses_t.marginal_price[buses] < threshold] = 1.0
|
|
|
|
price_statistics.at["zero_hours", label] = df.sum().sum() / (
|
|
df.shape[0] * df.shape[1]
|
|
)
|
|
|
|
price_statistics.at["mean", label] = (
|
|
n.buses_t.marginal_price[buses].unstack().mean()
|
|
)
|
|
|
|
price_statistics.at["standard_deviation", label] = (
|
|
n.buses_t.marginal_price[buses].unstack().std()
|
|
)
|
|
|
|
return price_statistics
|
|
|
|
|
|
def calculate_co2_emissions(n, label, df):
|
|
|
|
carattr = "co2_emissions"
|
|
emissions = n.carriers.query(f"{carattr} != 0")[carattr]
|
|
|
|
if emissions.empty:
|
|
return
|
|
|
|
weightings = n.snapshot_weightings.mul(
|
|
n.investment_period_weightings["time_weightings"]
|
|
.reindex(n.snapshots)
|
|
.fillna(method="bfill")
|
|
.fillna(1.0),
|
|
axis=0,
|
|
)
|
|
|
|
# generators
|
|
gens = n.generators.query("carrier in @emissions.index")
|
|
if not gens.empty:
|
|
em_pu = gens.carrier.map(emissions) / gens.efficiency
|
|
em_pu = (
|
|
weightings["generator_weightings"].to_frame("weightings")
|
|
@ em_pu.to_frame("weightings").T
|
|
)
|
|
emitted = n.generators_t.p[gens.index].mul(em_pu)
|
|
|
|
emitted_grouped = (
|
|
emitted.groupby(level=0)
|
|
.sum()
|
|
.groupby(n.generators.carrier, axis=1)
|
|
.sum()
|
|
.T
|
|
)
|
|
|
|
df = df.reindex(emitted_grouped.index.union(df.index))
|
|
|
|
df.loc[emitted_grouped.index, label] = emitted_grouped.values
|
|
|
|
if any(n.stores.carrier == "co2"):
|
|
co2_i = n.stores[n.stores.carrier == "co2"].index
|
|
df[label] = n.stores_t.e.groupby(level=0).last()[co2_i].iloc[:, 0]
|
|
|
|
return df
|
|
|
|
|
|
|
|
|
|
def calculate_cumulative_capacities(n, label, cum_cap):
|
|
# TODO
|
|
|
|
investments = n.investment_periods
|
|
cols = pd.MultiIndex.from_product(
|
|
[
|
|
cum_cap.columns.levels[0],
|
|
cum_cap.columns.levels[1],
|
|
cum_cap.columns.levels[2],
|
|
investments,
|
|
],
|
|
names=cum_cap.columns.names[:3] + ["year"],
|
|
)
|
|
cum_cap = cum_cap.reindex(cols, axis=1)
|
|
|
|
learn_i = n.carriers[n.carriers.learning_rate != 0].index
|
|
|
|
for c, attr in nominal_attrs.items():
|
|
if "carrier" not in n.df(c) or n.df(c).empty:
|
|
continue
|
|
caps = (
|
|
n.df(c)[n.df(c).carrier.isin(learn_i)]
|
|
.groupby([n.df(c).carrier, n.df(c).build_year])[
|
|
opt_name.get(c, "p") + "_nom_opt"
|
|
]
|
|
.sum()
|
|
)
|
|
|
|
if caps.empty:
|
|
continue
|
|
|
|
caps = round(
|
|
caps.unstack().reindex(columns=investments).fillna(0).cumsum(axis=1)
|
|
)
|
|
cum_cap = cum_cap.reindex(caps.index.union(cum_cap.index))
|
|
|
|
cum_cap.loc[caps.index, label] = caps.values
|
|
|
|
return cum_cap
|
|
|
|
|
|
|
|
|
|
|
|
outputs = [
|
|
"nodal_costs",
|
|
"nodal_capacities",
|
|
"nodal_cfs",
|
|
"cfs",
|
|
"costs",
|
|
"capacities",
|
|
"curtailment",
|
|
"energy",
|
|
"supply",
|
|
"supply_energy",
|
|
"prices",
|
|
"weighted_prices",
|
|
"price_statistics",
|
|
"market_values",
|
|
"metrics",
|
|
"co2_emissions",
|
|
"cumulative_capacities",
|
|
]
|
|
|
|
|
|
def make_summaries(networks_dict):
|
|
|
|
columns = pd.MultiIndex.from_tuples(
|
|
networks_dict.keys(), names=["cluster", "lv", "opt", "year"]
|
|
)
|
|
df = {}
|
|
|
|
for output in outputs:
|
|
df[output] = pd.DataFrame(columns=columns, dtype=float)
|
|
|
|
overrides = override_component_attrs(snakemake.input.overrides)
|
|
for label, filename in iteritems(networks_dict):
|
|
print(label, filename)
|
|
try:
|
|
n = pypsa.Network(
|
|
filename, override_component_attrs=overrides
|
|
)
|
|
except OSError:
|
|
print(label, " not solved yet.")
|
|
continue
|
|
# del networks_dict[label]
|
|
|
|
if not hasattr(n, "objective"):
|
|
print(label, " not solved correctly. Check log if infeasible or unbounded.")
|
|
continue
|
|
assign_carriers(n)
|
|
assign_locations(n)
|
|
|
|
for output in outputs:
|
|
df[output] = globals()["calculate_" + output](n, label, df[output])
|
|
|
|
return df
|
|
|
|
|
|
def to_csv(df):
|
|
|
|
for key in df:
|
|
df[key] = df[key].apply(lambda x: pd.to_numeric(x))
|
|
df[key].to_csv(snakemake.output[key])
|
|
|
|
|
|
#%%
|
|
if __name__ == "__main__":
|
|
# Detect running outside of snakemake and mock snakemake for testing
|
|
if "snakemake" not in globals():
|
|
from helper import mock_snakemake
|
|
snakemake = mock_snakemake('make_summary_perfect')
|
|
|
|
networks_dict = {
|
|
(clusters, lv, opts+sector_opts) :
|
|
snakemake.config['results_dir'] + snakemake.config['run'] + f'/postnetworks/elec_s{simpl}_{clusters}_lv{lv}_{opts}_{sector_opts}_brownfield_all_years.nc' \
|
|
for simpl in snakemake.config['scenario']['simpl'] \
|
|
for clusters in snakemake.config['scenario']['clusters'] \
|
|
for opts in snakemake.config['scenario']['opts'] \
|
|
for sector_opts in snakemake.config['scenario']['sector_opts'] \
|
|
for lv in snakemake.config['scenario']['lv'] \
|
|
}
|
|
|
|
|
|
print(networks_dict)
|
|
|
|
Nyears = 1
|
|
|
|
costs_db = prepare_costs(
|
|
snakemake.input.costs,
|
|
snakemake.config["costs"]["USD2013_to_EUR2013"],
|
|
snakemake.config["costs"]["discountrate"],
|
|
Nyears,
|
|
snakemake.config["costs"]["lifetime"],
|
|
)
|
|
|
|
df = make_summaries(networks_dict)
|
|
|
|
df["metrics"].loc["total costs"] = df["costs"].sum().groupby(level=[0, 1, 2]).sum()
|
|
|
|
to_csv(df)
|