Rung 51: a carrier's growth limit counts an asset in the first period it stands in only, not again after it retires¶

description: A plain `n.optimize()`, and its multi-period and stochastic classes, in one file. Every second-stage
  quantity spans a `scenario` (a future dispatch is chosen in) and every asset stands in the investment
  `period`s its build year and lifetime span. A parameter spans `scenario` exactly when PyPSA reads it
  per scenario. Capacity is chosen once, before the future is known, and paid once per active period at
  its cost in expectation over the scenarios; operation is the expectation over the scenarios' weights,
  with a share priced at the tail through the CVaR rows, which stand only where that share is positive.
  A plain run feeds one scenario, one period, all-active masks and unit weights, and the model collapses
  to the standard one. A security-constrained run copies each branch flow limit once per outage in an
  `outage` set that a plain run leaves empty. Which snapshots an asset is active in, a scenario's weight,
  and the outage factors are data prep.
dimensions:
  scenario: {description: 'the futures dispatch is chosen in, each with a weight'}
  snapshot: {description: dispatch periods, dtype: datetime}
  bus: {description: network nodes}
  generator: {description: 'generating units, each on one bus'}
  load: {description: 'demands, each on one bus'}
  period: {description: investment periods — PyPSA's `investment_periods`, dtype: int}
  carrier: {description: 'energy carriers, what a growth limit is set per'}
relations:
  snapshot_period: {description: the investment period a snapshot falls in, key: snapshot, values: period}
  Generator_carrier: {description: the carrier a generator converts from, key: generator, values: carrier}
  Generator_bus: {description: the bus a generator sits on, key: generator, values: bus}
  Load_bus: {description: the bus a load sits on, key: load, values: bus}
parameters:
  snapshot_weightings_objective:
    description: PyPSA's `snapshot_weightings.objective` — hours a snapshot stands for in the cost
    dims: [snapshot]
  Generator_p_nom:
    description: nominal power
    dims: [scenario, generator]
  Generator_p_nom_extendable:
    description: whether the nominal power is a decision
    dims: [generator]
    dtype: bool
  Generator_p_min_pu:
    description: least output, per unit of nominal power
    dims: [scenario, snapshot, generator]
  Generator_p_max_pu:
    description: most output, per unit of nominal power — an availability profile
    dims: [scenario, snapshot, generator]
  Generator_marginal_cost:
    description: cost of one unit of output
    dims: [scenario, snapshot, generator]
  Generator_marginal_cost_quadratic:
    description: cost of the square of one unit of output
    dims: [scenario, snapshot, generator]
  Generator_sign:
    description: the sign output enters its bus's balance with — PyPSA's `sign`, `1` unless given, `-1`
      for a unit that draws power. PyPSA refuses one that differs by scenario (`consistency.py:1187`)
    dims: [generator]
  Generator_committable:
    description: whether output is gated by an on/off status decision
    dims: [generator]
    dtype: bool
  Load_p_set:
    description: demand
    dims: [scenario, snapshot, load]
  Load_sign:
    description: the sign a load's demand enters its bus's balance with — PyPSA's `sign`, `-1` unless
      given, `1` for a load that feeds its bus. PyPSA refuses one that differs by scenario (`consistency.py:1187`)
    dims: [load]
  Load_active:
    description: whether a load stands in the model — PyPSA's `active`. A load has no build year and no
      lifetime, so the flag holds in every snapshot. PyPSA refuses one that differs by scenario (`consistency.py:1195`)
    dims: [load]
    dtype: bool
  scenario_weight:
    description: PyPSA's `scenario_weightings.weight` — the probability of a future
    dims: [scenario]
  CVaR_omega:
    description: PyPSA's `risk_preference['omega']` — the share of operating cost priced at the tail rather
      than in expectation; zero recovers the risk-neutral model
    dims: []
  period_weight_objective:
    description: PyPSA's `investment_period_weightings.objective` — what a period's cost weighs
    dims: [period]
  Generator_active:
    description: whether a generator stands in a snapshot's period — PyPSA's `active`, from build year
      and lifetime, data prep
    dims: [snapshot, generator]
    dtype: bool
  Generator_capital_weight:
    description: the sum of period weights a generator stands in — PyPSA's `active * period_weighting`,
      summed, data prep
    dims: [generator]
  Generator_first_active:
    description: one in the first period a generator stands in, zero elsewhere, data prep. PyPSA `1.3.0`
      takes `active.cumsum() == 1`, which also counts a generator that has retired in every later period
      (`global_constraints.py:276`, PyPSA/PyPSA#1938)
    dims: [period, generator]
  Carrier_max_growth:
    description: most capacity of a carrier that may be added in a period; no value means no limit. The
      least over the scenarios, as PyPSA takes it (`global_constraints.py:226-230`), data prep. PyPSA
      reads it only under `multi_investment_periods` (`global_constraints.py:219-220`), so data prep feeds
      no value otherwise
    dims: [carrier]
  Carrier_max_relative_growth:
    description: share of the previous period's additions that may be added on top — the least over the
      scenarios, as PyPSA takes it, data prep
    dims: [carrier]
  Generator_p_nom_min:
    description: least nominal power an extendable generator may be built at
    dims: [scenario, generator]
  Generator_p_nom_max:
    description: most nominal power an extendable generator may be built at
    dims: [scenario, generator]
  Generator_capital_cost:
    description: cost of one unit of nominal power — PyPSA's `capital_cost`, periodized as an annuity
      in data prep
    dims: [scenario, generator]
variables:
  Generator_p:
    description: '`Generator-p` — output of a generator in a snapshot'
    dims: [scenario, snapshot, generator]
    where: Generator_active
  Generator_p_nom_ext:
    description: '`Generator-p_nom` — nominal power where it is a decision; the parameter of the same
      PyPSA name carries the fixed regime'
    dims: [generator]
    where: Generator_p_nom_extendable
  CVaR_a:
    description: '`CVaR-a` — how far a scenario''s operating cost exceeds the tail''s start; nothing where
      it does not'
    dims: [scenario]
    bounds: {lower: 0}
  CVaR_theta:
    description: '`CVaR-theta` — where the tail starts, the value at risk'
    dims: []
  CVaR:
    description: '`CVaR` — the tail''s average cost, what the objective prices at `omega`'
    dims: []
constraints:
  Generator_fix_p_lower:
    description: '`Generator-fix-p-lower` — a fixed generator outputs at least its minimum'
    dims: [scenario, snapshot, generator]
    where: not Generator_p_nom_extendable AND not Generator_committable AND Generator_active
    expression: Generator_p >= Generator_p_min_pu * Generator_p_nom
  Generator_fix_p_upper:
    description: '`Generator-fix-p-upper` — a fixed generator outputs at most what is available'
    dims: [scenario, snapshot, generator]
    where: not Generator_p_nom_extendable AND not Generator_committable AND Generator_active
    expression: Generator_p <= Generator_p_max_pu * Generator_p_nom
  Generator_ext_p_lower:
    description: '`Generator-ext-p-lower` — an extendable generator outputs at least its minimum of the
      chosen build'
    dims: [scenario, snapshot, generator]
    where: Generator_p_nom_extendable AND not Generator_committable AND Generator_active
    expression: Generator_p >= Generator_p_min_pu * Generator_p_nom_ext
  Generator_ext_p_upper:
    description: '`Generator-ext-p-upper` — an extendable generator outputs at most what is available
      of the chosen build'
    dims: [scenario, snapshot, generator]
    where: Generator_p_nom_extendable AND not Generator_committable AND Generator_active
    expression: Generator_p <= Generator_p_max_pu * Generator_p_nom_ext
  Generator_ext_p_nom_lower:
    description: '`Generator-ext-p_nom-lower` — the chosen build is at least its floor in every scenario'
    dims: [scenario, generator]
    where: Generator_p_nom_extendable
    expression: Generator_p_nom_ext >= Generator_p_nom_min
  Generator_ext_p_nom_upper:
    description: '`Generator-ext-p_nom-upper` — the chosen build is at most its cap in every scenario;
      a cap of infinity is no row'
    dims: [scenario, generator]
    where: Generator_p_nom_extendable AND Generator_p_nom_max
    expression: Generator_p_nom_ext <= Generator_p_nom_max
  Bus_nodal_balance:
    description: '`Bus-nodal_balance` — what is generated at a bus, storage dispatch and stores included,
      less what the links take away, plus what arrives over them after losses and any delay at every port
      they deliver to, each process port drawing or delivering at its own rate and each passive branch
      carrying its flow, meets the load there, less half of every incident line''s and transformer''s
      loss — PyPSA dissipates a branch''s loss half at either end. Each generator, storage unit, store
      and load term enters with its component''s `sign` (`constraints.py:1428-1429`, `:1538`), and an
      inactive load not at all. A bus nothing is attached to has no row; PyPSA refuses one that carries
      load, and this file does not yet.'
    dims: [scenario, snapshot, bus]
    expression: Bus_injection == 0
  Carrier_growth_limit:
    description: '`Carrier-growth_limit` — what a carrier adds across its extendable components in a period,
      counting each build in the first period it stands in, is at most its allowance plus a share of what
      it added the period before; the first period has no predecessor, so `edge=0` leaves it the bare
      allowance'
    dims: [carrier, period]
    where: Carrier_max_growth
    expression: Carrier_additions - shift(Carrier_additions, along=period, offset=1, edge=0) * Carrier_relative_growth
      <= Carrier_max_growth
expressions:
  total_cost:
    dims: []
    expression: Generator_capex + risk_weighted_opex
    description: what the system costs — capacity once per active period at its expected cost over the
      scenarios, operation in expectation over the scenarios, and a share of it at the tail
  Carrier_additions:
    dims: [period, carrier]
    expression: Generator_additions
    description: what a carrier adds in a period — every extendable component of that carrier, counting
      each build in the first period it stands in. Like PyPSA, it sums only the components that carry
      a carrier attribute, so a transformer, which has none, counts in no carrier
  Carrier_relative_growth:
    description: the share of the previous period's additions a carrier's growth limit reads — PyPSA's
      `max_relative_growth` clipped at zero, so a negative share adds nothing and never tightens the limit
    dims: [carrier]
    cases:
      positive: {when: Carrier_max_relative_growth > 0, expression: Carrier_max_relative_growth}
    otherwise: 0
  Bus_injection:
    dims: [scenario, snapshot, bus]
    expression: Generator_injection + Load_injection
    description: what every component puts into a bus, less what it takes out of it; PyPSA writes each
      term into the balance, and a load on its right-hand side
  Generator_capex: {expression: sum(scenario_weight * Generator_p_nom_ext * Generator_capital_cost * Generator_capital_weight)}
  risk_weighted_opex: {expression: '(1 - CVaR_omega) * sum(scenario_weight * scenario_opex, over=scenario)
      + CVaR_omega * CVaR'}
  Generator_additions: {expression: 'sum(Generator_p_nom_ext * Generator_first_active, by=Generator_carrier,
      over=generator, into=carrier)'}
  Generator_injection: {expression: 'sum(Generator_sign * Generator_p, by=Generator_bus, over=generator,
      into=bus)'}
  Load_injection: {expression: 'sum(Load_demand, by=Load_bus, over=load, into=bus)'}
  scenario_opex:
    dims: [scenario]
    expression: Generator_opex
    description: what a future costs to run — every operating term, weighted by the snapshot's hours and
      its period, before the scenario's own weight; a start and a stop cost what they cost, unweighted,
      as PyPSA adds them (`optimize.py:414-429`)
  Load_demand:
    description: what a load draws from its bus's balance — its demand times its sign where it is active,
      nothing where it is not, since PyPSA drops an inactive load from the balance (`constraints.py:1537-1538`)
    dims: [scenario, snapshot, load]
    cases:
      active: {when: Load_active, expression: Load_sign * Load_p_set}
    otherwise: 0
  Generator_opex: {expression: 'sum(sum(((Generator_p * Generator_marginal_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=generator),
      over=snapshot) + sum(sum((((Generator_p * Generator_p) * Generator_marginal_cost_quadratic) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=generator),
      over=snapshot)'}
objective: {sense: minimize, expression: total_cost}

from differential.pypsa.prep import relation, static, varying, weighting


n = build()  # the network from the PyPSA tab

sources = {
    'snapshot': pl.Series('snapshot', list(timesteps(n)), dtype=pl.Datetime('us')),
    'bus': pl.Series('bus', list(names(n.buses.index).astype(str)), dtype=pl.String),
        **{
            dim: pl.Series(dim, list(names(n.static(component).index).astype(str)), dtype=pl.String)
            for component, dim in DIM.items()
        },
        **scenarios(n),
        **periods(n),
        **carriers(n, multi),
    'Generator_bus': relation(n, 'Generator', 'bus'),
    'Load_bus': relation(n, 'Load', 'bus'),
    'snapshot_weightings_objective': weighting(n, 'objective'),
    'Generator_sign': per_component('Generator', first_scenario(n.generators['sign'])),
    'Load_p_set': varying(n, 'Load', 'p_set'),
    'Load_sign': per_component('Load', first_scenario(loads['sign'])),
    'Load_active': per_component('Load', first_scenario(loads['active']), bool),
}

with sps.solve('differential/pypsa/rungs/rung_51_growth_retired_asset.yaml', sources) as solution:
    solution.objective  # 3432.5

# SPDX-FileCopyrightText: mathspec Contributors
#
# SPDX-License-Identifier: MIT

"""Rung 51: a carrier's growth limit counts an asset in the first period it stands in only, not again after it retires.

PyPSA 1.3.0 counts an asset that retires in every later period too (PyPSA/PyPSA#1938).
The oracle gives each build its own carrier with the same limit: each carrier
then has one asset, which PyPSA counts in its first period, and a retired one
counted again repeats a row it already has.
"""

from __future__ import annotations

from datetime import datetime

import pandas as pd

ISSUE = 1938
OPTIMIZE = {'multi_investment_periods': True}


def network(carriers: dict[str, str]):
    """Two periods, a solar unit that stands in 2020 only and one built in 2030, each under the carrier named for it."""
    import pypsa

    n = pypsa.Network()
    n.snapshots = pd.MultiIndex.from_tuples(
        [(2020, datetime(2020, 1, 1, t)) for t in range(2)] + [(2030, datetime(2030, 1, 1, t)) for t in range(2)]
    )
    n.investment_periods = [2020, 2030]
    n.investment_period_weightings['objective'] = [1.0, 0.5]
    n.investment_period_weightings['years'] = [10.0, 10.0]
    n.snapshot_weightings['objective'] = [2.0, 1.5, 2.5, 2.0]
    n.add('Bus', 'grid')
    n.add('Carrier', 'gas')
    for carrier in sorted(set(carriers.values())):
        n.add('Carrier', carrier, max_growth=10)
    for name, build_year in (('solar_old', 2020), ('solar_new', 2030)):
        n.add(
            'Generator',
            name,
            bus='grid',
            carrier=carriers[name],
            p_nom_extendable=True,
            p_nom_max=50,
            marginal_cost=1,
            capital_cost=5,
            build_year=build_year,
            lifetime=10,
        )
    n.add('Generator', 'backup', bus='grid', carrier='gas', p_nom=100, marginal_cost=80)
    n.add('Load', 'town', bus='grid', p_set=[15, 20, 15, 20])
    return n


def build():
    """Both solar units under one carrier with `max_growth = 10`; the old one retires after 2020."""
    return network({'solar_old': 'solar', 'solar_new': 'solar'})


def oracle():
    """The same network with a carrier per build: PyPSA counts each build in its first period only."""
    return [(1.0, network({'solar_old': 'solar20', 'solar_new': 'solar30'}))]

n = build()
n.optimize(solver_name='highs')
n.objective  # wrong in pypsa 1.3.0, PyPSA/PyPSA#1938