Rung 53: a transmission_volume_expansion_limit row holds in every scenario under multi_investment_periods¶

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'}
  line: {description: 'passive branches, each between two buses, their flow set by impedance'}
  global_constraint: {description: 'PyPSA''s `GlobalConstraint` rows, one label per declared limit'}
  period: {description: investment periods — PyPSA's `investment_periods`, dtype: int}
relations:
  snapshot_period: {description: the investment period a snapshot falls in, key: snapshot, values: period}
  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}
  Line_bus0: {description: the bus a line's flow is measured at, key: line, values: bus}
  Line_bus1: {description: the bus at a line's other end, key: line, 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
  Line_active:
    description: whether a line stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, line]
    dtype: bool
  Line_capital_weight:
    description: the sum of period weights a line stands in — PyPSA's `active * period_weighting`, summed,
      data prep
    dims: [line]
  Line_s_nom_extendable:
    description: whether the nominal apparent power is a decision
    dims: [line]
    dtype: bool
  Line_s_max_pu:
    description: most flow either way, per unit of nominal apparent power
    dims: [scenario, snapshot, line]
  Line_s_nom_min:
    description: least nominal apparent power an extendable line may be built at
    dims: [scenario, line]
  Line_s_nom_max:
    description: most nominal apparent power an extendable line may be built at
    dims: [scenario, line]
  Line_capital_cost:
    description: cost of one unit of nominal apparent power — PyPSA's `capital_cost`, periodized as an
      annuity in data prep
    dims: [scenario, line]
  GlobalConstraint_type:
    description: which formula the row takes — `primary_energy`, `operational_limit`, `transmission_volume_expansion_limit`,
      `transmission_expansion_cost_limit` or `tech_capacity_expansion_limit`
    dims: [global_constraint]
    dtype: str
  GlobalConstraint_sense:
    description: which way the row binds in each scenario — `<=`, `>=` or `==`; PyPSA reads a row's sense
      per scenario (`global_constraints.py:556`, `:748`, `:860`)
    dims: [scenario, global_constraint]
    dtype: str
  GlobalConstraint_constant:
    description: the constant the total is held against; what a variable cannot carry — an initial charge,
      times its period's years for each counted period where the storage reopens per period, or a non-extendable
      build — is folded in here by data prep. PyPSA reads it per scenario (`global_constraints.py:557`,
      `:749`, `:861`)
    dims: [scenario, global_constraint]
  Line_volume_weight:
    description: the line's length where its carrier is in the row's set, the first scenario's length
      as PyPSA reads it (`global_constraints.py:835-836`) — data prep; a line outside it, or one that
      does not stand in the row's `investment_period`, has no row
    dims: [scenario, global_constraint, line]
variables:
  Generator_p:
    description: '`Generator-p` — output of a generator in a snapshot'
    dims: [scenario, snapshot, generator]
    where: Generator_active
  Line_s:
    description: '`Line-s` — PyPSA''s `p0`, the flow measured at the `Line_bus0` end: a positive value
      withdraws there and injects at `Line_bus1`, lossless'
    dims: [scenario, snapshot, line]
    where: Line_active
  Line_s_nom_ext:
    description: '`Line-s_nom` — nominal apparent power where it is a decision; the parameter of the same
      PyPSA name carries the fixed regime'
    dims: [line]
    where: Line_s_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
  Line_ext_s_lower:
    description: '`Line-ext-s-lower` — an extendable line carries at least the negative of its rating
      of the chosen build, the loss counted against it'
    dims: [scenario, snapshot, line]
    where: Line_s_nom_extendable AND Line_active
    expression: Line_s >= (-Line_s_max_pu) * Line_s_nom_ext
  Line_ext_s_upper:
    description: '`Line-ext-s-upper` — an extendable line carries at most its rating of the chosen build,
      the loss included'
    dims: [scenario, snapshot, line]
    where: Line_s_nom_extendable AND Line_active
    expression: Line_s <= Line_s_max_pu * Line_s_nom_ext
  Line_ext_s_nom_lower:
    description: '`Line-ext-s_nom-lower` — the chosen build is at least its floor in every scenario'
    dims: [scenario, line]
    where: Line_s_nom_extendable
    expression: Line_s_nom_ext >= Line_s_nom_min
  Line_ext_s_nom_upper:
    description: '`Line-ext-s_nom-upper` — the chosen build is at most its cap in every scenario; a cap
      of infinity is no row'
    dims: [scenario, line]
    where: Line_s_nom_extendable AND Line_s_nom_max
    expression: Line_s_nom_ext <= Line_s_nom_max
  GlobalConstraint_transmission_volume_expansion_limit_ub:
    description: '`transmission_volume_expansion_limit` — its total, at most its constant'
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'transmission_volume_expansion_limit' AND GlobalConstraint_sense ==
      '<='
    expression: transmission_volume_expansion <= GlobalConstraint_constant
  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
expressions:
  transmission_volume_expansion:
    dims: [scenario, global_constraint]
    expression: Line_transmission_volume_expansion
    description: what a `transmission_volume_expansion_limit` row totals — length times the chosen build
      of the row's branches
  total_cost:
    dims: []
    expression: Line_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
  Bus_injection:
    dims: [scenario, snapshot, bus]
    expression: (Generator_injection + Line_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
  Line_transmission_volume_expansion: {expression: 'sum(Line_s_nom_ext * Line_volume_weight, over=line)'}
  Line_capex: {expression: sum(scenario_weight * Line_s_nom_ext * Line_capital_cost * Line_capital_weight)}
  risk_weighted_opex: {expression: '(1 - CVaR_omega) * sum(scenario_weight * scenario_opex, over=scenario)
      + CVaR_omega * CVaR'}
  Generator_injection: {expression: 'sum(Generator_sign * Generator_p, by=Generator_bus, over=generator,
      into=bus)'}
  Line_injection: {expression: '(-sum(Line_s, by=Line_bus0, over=line, into=bus)) + sum(Line_s, by=Line_bus1,
      over=line, 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_53_scenario_period_volume_limit.yaml', sources) as solution:
    solution.objective  # 15005.0

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

"""Rung 53: a `transmission_volume_expansion_limit` row holds in every scenario under `multi_investment_periods`.

PyPSA 1.3.0 builds no such row on a network with scenarios and investment
periods (PyPSA/PyPSA#1939). The two futures are identical, so the oracle is the
same network without scenarios, which PyPSA solves with the row.
"""

from __future__ import annotations

from datetime import datetime

import pandas as pd

ISSUE = 1939
OPTIMIZE = {'multi_investment_periods': True}


def network():
    """Two periods, a cheap unit behind an extendable line whose volume a limit of 60 caps."""
    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', ['hill', 'town'])
    n.add('Carrier', 'AC')
    n.add('Generator', 'hydro53', bus='hill', p_nom=100, marginal_cost=5)
    n.add('Generator', 'diesel53', bus='town', p_nom=100, marginal_cost=90)
    n.add(
        'Line',
        'tie53',
        bus0='hill',
        bus1='town',
        x=0.1,
        carrier='AC',
        length=3,
        s_nom_extendable=True,
        s_nom_max=100,
        capital_cost=1,
        build_year=2020,
        lifetime=30,
    )
    n.add('Load', 'town_load', bus='town', p_set=[40, 50, 60, 45])
    n.add(
        'GlobalConstraint',
        'volume53',
        type='transmission_volume_expansion_limit',
        carrier_attribute='AC',
        sense='<=',
        constant=60,
    )
    return n


def build():
    """The same network over two identical futures."""
    n = network()
    n.set_scenarios({'calm': 0.6, 'stormy': 0.4})
    return n


def oracle():
    """The network without scenarios: the futures are identical, so the expected cost is its cost."""
    return [(1.0, network())]

n = build()
n.optimize(solver_name='highs')
n.objective  # wrong in pypsa 1.3.0, PyPSA/PyPSA#1939