Rung 21: a carrier's growth limit binds its non-generator builds — a storage unit and two stores over two 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 a risk preference is set.
  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, ordered: true}
  bus: {description: network nodes}
  generator: {description: 'generating units, each on one bus'}
  link: {description: 'controllable connections, each from one bus to the buses it delivers to'}
  link_output: {description: 'a link''s output ports, one label per port a link declares — PyPSA''s `bus1`,
      `bus2`, … columns read long, so a link of any number of output ports is one term in the balance,
      data prep'}
  process: {description: 'generalized multi-port converters, each with an internal power that every port
      draws or delivers at its own rate'}
  process_output: {description: 'a process''s ports, one label per port a process declares — PyPSA''s
      `bus0`, `bus1`, … each carry a signed `rate`, so a process of any number of ports is one term in
      the balance, data prep'}
  load: {description: 'demands, each on one bus'}
  storage_unit: {description: 'storage units, dispatch and store behind one bus connection'}
  store: {description: 'pure energy stores, each on one bus'}
  period: {description: investment periods — PyPSA's `investment_periods`, dtype: int, ordered: true}
  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_bus: {description: the bus a generator sits on, key: generator, values: bus}
  Link_output_link: {description: the link an output port belongs to, key: link_output, values: link}
  Link_output_bus: {description: 'the bus an output port delivers to — PyPSA''s `bus1`, `bus2`, … columns.
      A link of three output ports is three labels here rather than a third relation, so the file states
      any number of them', key: link_output, values: bus}
  Process_output_process: {description: the process a port belongs to, key: process_output, values: process}
  Process_output_bus: {description: 'the bus a port draws from or delivers to — PyPSA''s `bus0`, `bus1`,
      … columns. A process of three ports is three labels here rather than a third relation, so the file
      states any number of them', key: process_output, values: bus}
  Load_bus: {description: the bus a load sits on, key: load, values: bus}
  StorageUnit_carrier: {description: the carrier a storage unit converts from, key: storage_unit, values: carrier}
  StorageUnit_bus: {description: the bus a storage unit sits on, key: storage_unit, values: bus}
  Store_carrier: {description: the carrier a store holds, key: store, values: carrier}
  Store_bus: {description: the bus a store sits on, key: store, 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 (`constants.py:43`)
    dims: [generator]
  Generator_committable:
    description: whether output is gated by an on/off status decision
    dims: [generator]
    dtype: bool
  Link_efficiency:
    description: share of the flow that arrives at an output port, PyPSA's `efficiency`, `efficiency2`,
      … read long — negative where that port consumes rather than delivers. Read at the snapshot the flow
      arrives, so a delayed port delivers at its arrival snapshot's efficiency (`constraints.py:1498`)
    dims: [scenario, snapshot, link_output]
  Link_output_delay:
    description: snapshots a port's delivery lags its link's flow — PyPSA's `delay`, `delay2`, … read
      long, divided by the `snapshot_weightings.generators` value and rounded up in data prep; zero for
      a port that delivers at once. A port has the same delay in every scenario, because PyPSA refuses
      a delay that differs by scenario (`constants.py:52`)
    dims: [link_output]
    dtype: int
  Link_output_cyclic_delay:
    description: whether a delayed port's flow wraps from the end of its investment period — PyPSA's `cyclic_delay`,
      `cyclic_delay2`, …; where it does not, the flow still in transit at each period's first snapshots
      is lost. The flag is the same in every scenario, as the delay is
    dims: [link_output]
    dtype: bool
  Process_rate:
    description: the energy a port draws or delivers per unit of internal power, PyPSA's `rate0`, `rate1`,
      … read long — negative where the port withdraws, positive where it injects; a link is a process
      whose `bus0` rate is minus one and whose output rates are its efficiencies. Read at the snapshot
      the transfer arrives, so a delayed port transfers at its arrival snapshot's rate (`constraints.py:1498`)
    dims: [scenario, snapshot, process_output]
  Process_output_delay:
    description: snapshots a port's transfer lags its process's internal power — PyPSA's `delay0`, `delay1`,
      … read long, divided by the `snapshot_weightings.generators` value and rounded up in data prep;
      zero for a port that transfers at once. A port has the same delay in every scenario, as a link's
      port has
    dims: [process_output]
    dtype: int
  Process_output_cyclic_delay:
    description: whether a delayed port's transfer wraps from the end of its investment period — PyPSA's
      `cyclic_delay0`, `cyclic_delay1`, …; where it does not, the energy still in transit at each period's
      first snapshots is lost. The flag is the same in every scenario, as the delay is
    dims: [process_output]
    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 (`constants.py:43`)
    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 (`constants.py:51`)
    dims: [load]
    dtype: bool
  scenario_weight:
    description: PyPSA's `scenario_weightings.weight` — the probability of a future
    dims: [scenario]
  period_weight_objective:
    description: PyPSA's `investment_period_weightings.objective` — what a period's cost weighs; PyPSA
      reads it only under `multi_investment_periods`, so data prep feeds one otherwise, whatever the column
      holds (`optimize.py:205-207`, `:264-266`)
    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
  Link_active:
    description: whether a link stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, link]
    dtype: bool
  StorageUnit_active:
    description: whether a storage unit stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, storage_unit]
    dtype: bool
  Store_active:
    description: whether a store stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, store]
    dtype: bool
  Process_active:
    description: whether a process stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, process]
    dtype: bool
  StorageUnit_active_asset:
    description: whether a storage unit is one of PyPSA's `active_assets` — its `active` flag alone, without
      build year and lifetime, so a unit that stands in no snapshot of the horizon still counts. PyPSA
      refuses one that differs by scenario (`constants.py:51`)
    dims: [storage_unit]
    dtype: bool
  Store_active_asset:
    description: whether a store is one of PyPSA's `active_assets` — its `active` flag alone, without
      build year and lifetime, so a unit that stands in no snapshot of the horizon still counts. PyPSA
      refuses one that differs by scenario (`constants.py:51`)
    dims: [store]
    dtype: bool
  StorageUnit_capital_weight:
    description: the sum of period weights a storage unit stands in — PyPSA's `active * period_weighting`,
      summed, data prep
    dims: [storage_unit]
  Store_capital_weight:
    description: the sum of period weights a store stands in — PyPSA's `active * period_weighting`, summed,
      data prep
    dims: [store]
  StorageUnit_first_active:
    description: one in the first period a storage unit stands in, zero elsewhere, data prep. PyPSA takes
      `active & (active.cumsum() == 1)` (`global_constraints.py:265`)
    dims: [period, storage_unit]
  Store_first_active:
    description: one in the first period a store stands in, zero elsewhere, data prep. PyPSA takes `active
      & (active.cumsum() == 1)` (`global_constraints.py:265`)
    dims: [period, store]
  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:227-231`), data prep. PyPSA
      reads it only under `multi_investment_periods` (`global_constraints.py:220-221`), so data prep feeds
      no value otherwise
    dims: [carrier]
    missing: neutral
  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]
  snapshot_weightings_stores:
    description: PyPSA's `snapshot_weightings.stores` — hours a snapshot stands for in a storage balance
    dims: [snapshot]
  StorageUnit_p_nom_min:
    description: least nominal power an extendable storage unit may be built at
    dims: [scenario, storage_unit]
  StorageUnit_p_nom_max:
    description: most nominal power an extendable storage unit may be built at
    dims: [scenario, storage_unit]
  StorageUnit_capital_cost:
    description: 'cost of one unit of nominal power for the modelled horizon — PyPSA''s `periodized_cost`:
      `overnight_cost` as an annuity over `lifetime` at `discount_rate`, times `nyears`, where it is given,
      and `capital_cost` where it is not, plus `fom_cost` (`components.py:1126-1147`, `costs.py:102-203`),
      data prep'
    dims: [scenario, storage_unit]
  Store_e_nom_min:
    description: least nominal capacity an extendable store may be built at
    dims: [scenario, store]
  Store_e_nom_max:
    description: most nominal capacity an extendable store may be built at
    dims: [scenario, store]
  Store_capital_cost:
    description: 'cost of one unit of nominal capacity for the modelled horizon — PyPSA''s `periodized_cost`:
      `overnight_cost` as an annuity over `lifetime` at `discount_rate`, times `nyears`, where it is given,
      and `capital_cost` where it is not, plus `fom_cost` (`components.py:1126-1147`, `costs.py:102-203`),
      data prep'
    dims: [scenario, store]
  StorageUnit_p_nom_extendable:
    description: whether the nominal power is a decision
    dims: [storage_unit]
    dtype: bool
  StorageUnit_p_min_pu:
    description: most storing, per unit of nominal power and negated
    dims: [scenario, snapshot, storage_unit]
  StorageUnit_p_max_pu:
    description: most dispatch, per unit of nominal power
    dims: [scenario, snapshot, storage_unit]
  StorageUnit_max_hours:
    description: energy capacity, as hours of dispatch at nominal power
    dims: [scenario, storage_unit]
  StorageUnit_efficiency_store:
    description: share of the power drawn from the bus that becomes charge
    dims: [scenario, snapshot, storage_unit]
  StorageUnit_efficiency_dispatch:
    description: share of the charge drawn down that reaches the bus
    dims: [scenario, snapshot, storage_unit]
  StorageUnit_sign:
    description: the sign net dispatch enters its bus's balance with — PyPSA's `sign`, `1` unless given.
      PyPSA refuses one that differs by scenario (`constants.py:43`)
    dims: [storage_unit]
  StorageUnit_retention:
    description: share of charge kept over a snapshot — PyPSA's `(1 - standing_loss) ** elapsed hours`,
      data prep
    dims: [scenario, snapshot, storage_unit]
  StorageUnit_inflow:
    description: energy arriving per hour, a river into a reservoir
    dims: [scenario, snapshot, storage_unit]
  StorageUnit_state_of_charge_initial:
    description: charge held before the first snapshot
    dims: [scenario, storage_unit]
  StorageUnit_cyclic_state_of_charge:
    description: whether the horizon closes on itself instead of opening on the initial charge
    dims: [scenario, storage_unit]
    dtype: bool
  StorageUnit_cyclic_state_of_charge_per_period:
    description: whether each investment period closes on itself instead of carrying its charge on to
      the next; it overrides `cyclic_state_of_charge` and `state_of_charge_initial_per_period`. PyPSA
      reads it only under `multi_investment_periods`, so data prep feeds false otherwise
    dims: [scenario, storage_unit]
    dtype: bool
  StorageUnit_state_of_charge_initial_per_period:
    description: whether each investment period opens on the initial charge instead of carrying the previous
      period's; PyPSA reads it only under `multi_investment_periods`, so data prep feeds false otherwise
    dims: [scenario, storage_unit]
    dtype: bool
  StorageUnit_opens_late:
    description: whether a snapshot is the first a storage unit stands in, where that is not the first
      of the horizon — PyPSA's `active.cumsum() == 1` over the snapshots it stands in, past the first
      snapshot, data prep; false in a run where every unit stands throughout
    dims: [snapshot, storage_unit]
    dtype: bool
  StorageUnit_inactive_snapshots:
    description: how many snapshots a storage unit does not stand in — PyPSA's `(~active).sum()`, data
      prep. A cyclic unit reaches back this many snapshots further, so it closes on the last snapshot
      it stands in
    dims: [storage_unit]
    dtype: int
  StorageUnit_marginal_cost:
    description: cost of one unit of dispatch
    dims: [scenario, snapshot, storage_unit]
  StorageUnit_marginal_cost_quadratic:
    description: cost of the square of one unit of dispatch; storing is not charged
    dims: [scenario, snapshot, storage_unit]
  StorageUnit_marginal_cost_storage:
    description: cost of one unit of charge held over one snapshot
    dims: [scenario, snapshot, storage_unit]
  Store_e_nom_extendable:
    description: whether the nominal energy capacity is a decision
    dims: [store]
    dtype: bool
  Store_e_min_pu:
    description: least energy held, per unit of nominal capacity — negative for a store that may go short
    dims: [scenario, snapshot, store]
  Store_e_max_pu:
    description: most energy held, per unit of nominal capacity
    dims: [scenario, snapshot, store]
  Store_sign:
    description: the sign the power a store delivers enters its bus's balance with — PyPSA's `sign`, `1`
      unless given. PyPSA refuses one that differs by scenario (`constants.py:43`)
    dims: [store]
  Store_retention:
    description: share of energy kept over a snapshot — PyPSA's `(1 - standing_loss) ** elapsed hours`,
      data prep
    dims: [scenario, snapshot, store]
  Store_e_initial:
    description: energy held before the first snapshot
    dims: [scenario, store]
  Store_e_cyclic:
    description: whether the horizon closes on itself instead of opening on the initial energy
    dims: [scenario, store]
    dtype: bool
  Store_e_cyclic_per_period:
    description: whether each investment period closes on itself instead of carrying its energy on to
      the next; it overrides `e_cyclic` and `e_initial_per_period`. PyPSA reads it only under `multi_investment_periods`,
      so data prep feeds false otherwise
    dims: [scenario, store]
    dtype: bool
  Store_e_initial_per_period:
    description: whether each investment period opens on the initial energy instead of carrying the previous
      period's; PyPSA reads it only under `multi_investment_periods`, so data prep feeds false otherwise
    dims: [scenario, store]
    dtype: bool
  Store_opens_late:
    description: whether a snapshot is the first a store stands in, where that is not the first of the
      horizon — PyPSA's `active.cumsum() == 1` over the snapshots it stands in, past the first snapshot,
      data prep; false in a run where every store stands throughout
    dims: [snapshot, store]
    dtype: bool
  Store_inactive_snapshots:
    description: how many snapshots a store does not stand in — PyPSA's `(~active).sum()`, data prep.
      A cyclic store reaches back this many snapshots further, so it closes on the last snapshot it stands
      in
    dims: [store]
    dtype: int
  Store_marginal_cost:
    description: cost of one unit of power delivered
    dims: [scenario, snapshot, store]
  Store_marginal_cost_quadratic:
    description: cost of the square of the net power delivered, so charging costs as much as delivering
    dims: [scenario, snapshot, store]
  Store_marginal_cost_storage:
    description: cost of one unit of energy held over one snapshot
    dims: [scenario, snapshot, store]
variables:
  Generator_p:
    description: '`Generator-p` — output of a generator in a snapshot'
    dims: [scenario, snapshot, generator]
    where: Generator_active
  StorageUnit_p_dispatch:
    description: '`StorageUnit-p_dispatch` — power delivered to the bus'
    dims: [scenario, snapshot, storage_unit]
    where: StorageUnit_active
  StorageUnit_p_store:
    description: '`StorageUnit-p_store` — power drawn from the bus into charge'
    dims: [scenario, snapshot, storage_unit]
    where: StorageUnit_active
  StorageUnit_state_of_charge:
    description: '`StorageUnit-state_of_charge` — energy held at the end of a snapshot'
    dims: [scenario, snapshot, storage_unit]
    where: StorageUnit_active
  Store_e:
    description: '`Store-e` — energy held at the end of a snapshot'
    dims: [scenario, snapshot, store]
    where: Store_active
  Store_p:
    description: '`Store-p` — power delivered to the bus; charging is negative'
    dims: [scenario, snapshot, store]
    where: Store_active
  StorageUnit_p_nom_ext:
    description: '`StorageUnit-p_nom` — nominal power where it is a decision, for a storage unit that
      is active; the parameter of the same PyPSA name carries the fixed regime'
    dims: [storage_unit]
    where: StorageUnit_p_nom_extendable AND StorageUnit_active_asset
  Store_e_nom_ext:
    description: '`Store-e_nom` — nominal capacity where it is a decision, for a store that is active;
      the parameter of the same PyPSA name carries the fixed regime'
    dims: [store]
    where: Store_e_nom_extendable AND Store_active_asset
  Link_p:
    description: '`Link-p` — PyPSA''s `p0`, the flow measured at the `Link_bus0` end: a positive value
      withdraws there and injects at every bus the link''s output ports deliver to'
    dims: [scenario, snapshot, link]
    where: Link_active
  Process_p:
    description: '`Process-p` — PyPSA''s internal power `p`: a positive value drives every port at its
      own rate, withdrawing where the rate is negative and injecting where it is positive'
    dims: [scenario, snapshot, process]
    where: Process_active
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
  StorageUnit_ext_p_dispatch_lower:
    description: '`StorageUnit-ext-p_dispatch-lower` — dispatch is non-negative'
    dims: [scenario, snapshot, storage_unit]
    where: StorageUnit_ext
    expression: StorageUnit_p_dispatch >= 0
  StorageUnit_ext_p_dispatch_upper:
    description: '`StorageUnit-ext-p_dispatch-upper` — an extendable unit dispatches at most the chosen
      build'
    dims: [scenario, snapshot, storage_unit]
    where: StorageUnit_ext
    expression: StorageUnit_p_dispatch <= StorageUnit_p_max_pu * StorageUnit_p_nom_ext
  StorageUnit_ext_p_store_lower:
    description: '`StorageUnit-ext-p_store-lower` — storing is non-negative'
    dims: [scenario, snapshot, storage_unit]
    where: StorageUnit_ext
    expression: StorageUnit_p_store >= 0
  StorageUnit_ext_p_store_upper:
    description: '`StorageUnit-ext-p_store-upper` — an extendable unit stores at most the chosen build,
      the minimum-per-unit column carrying that cap negated'
    dims: [scenario, snapshot, storage_unit]
    where: StorageUnit_ext
    expression: StorageUnit_p_store <= -StorageUnit_p_min_pu * StorageUnit_p_nom_ext
  StorageUnit_ext_state_of_charge_lower:
    description: '`StorageUnit-ext-state_of_charge-lower` — charge is non-negative'
    dims: [scenario, snapshot, storage_unit]
    where: StorageUnit_ext
    expression: StorageUnit_state_of_charge >= 0
  StorageUnit_ext_state_of_charge_upper:
    description: '`StorageUnit-ext-state_of_charge-upper` — an extendable unit holds at most its hours
      at the chosen build'
    dims: [scenario, snapshot, storage_unit]
    where: StorageUnit_ext
    expression: StorageUnit_state_of_charge <= StorageUnit_max_hours * StorageUnit_p_nom_ext
  StorageUnit_ext_p_nom_lower:
    description: '`StorageUnit-ext-p_nom-lower` — the chosen build is at least its floor in every scenario'
    dims: [scenario, storage_unit]
    where: StorageUnit_p_nom_extendable AND StorageUnit_active_asset
    expression: StorageUnit_p_nom_ext >= StorageUnit_p_nom_min
  StorageUnit_ext_p_nom_upper:
    description: '`StorageUnit-ext-p_nom-upper` — the chosen build is at most its cap in every scenario;
      a cap of infinity is no row'
    dims: [scenario, storage_unit]
    where: StorageUnit_p_nom_extendable AND StorageUnit_active_asset AND StorageUnit_p_nom_max
    expression: StorageUnit_p_nom_ext <= StorageUnit_p_nom_max
  StorageUnit_energy_balance:
    description: '`StorageUnit-energy_balance` — the charge carried in, plus what is stored after its
      efficiency, less what dispatch draws down before its own, plus inflow not spilled'
    dims: [scenario, snapshot, storage_unit]
    where: StorageUnit_active
    expression: StorageUnit_state_of_charge == ((StorageUnit_charge_carried_in + ((StorageUnit_efficiency_store
      * StorageUnit_p_store) * snapshot_weightings_stores)) - ((StorageUnit_p_dispatch * snapshot_weightings_stores)
      / StorageUnit_efficiency_dispatch)) + (StorageUnit_inflow * snapshot_weightings_stores)
  Store_ext_e_lower:
    description: '`Store-ext-e-lower` — an extendable store holds at least its floor of the chosen build'
    dims: [scenario, snapshot, store]
    where: Store_e_nom_extendable AND Store_active
    expression: Store_e >= Store_e_min_pu * Store_e_nom_ext
  Store_ext_e_upper:
    description: '`Store-ext-e-upper` — an extendable store holds at most the chosen build'
    dims: [scenario, snapshot, store]
    where: Store_e_nom_extendable AND Store_active
    expression: Store_e <= Store_e_max_pu * Store_e_nom_ext
  Store_ext_e_nom_lower:
    description: '`Store-ext-e_nom-lower` — the chosen build is at least its floor in every scenario'
    dims: [scenario, store]
    where: Store_e_nom_extendable AND Store_active_asset
    expression: Store_e_nom_ext >= Store_e_nom_min
  Store_ext_e_nom_upper:
    description: '`Store-ext-e_nom-upper` — the chosen build is at most its cap in every scenario; a cap
      of infinity is no row'
    dims: [scenario, store]
    where: Store_e_nom_extendable AND Store_active_asset AND Store_e_nom_max
    expression: Store_e_nom_ext <= Store_e_nom_max
  Store_energy_balance:
    description: '`Store-energy_balance` — the energy carried in, less what is delivered to the bus'
    dims: [scenario, snapshot, store]
    where: Store_active
    expression: Store_e == Store_energy_carried_in - Store_p * snapshot_weightings_stores
  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:1404-1405`, `:1514`), 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:
  StorageUnit_charge_carried_in:
    description: the charge a unit opens a snapshot with — at the first snapshot it stands in, its last
      such snapshot's less standing loss where it is cyclic and the given initial charge, which no standing
      loss has touched yet, where it is not; the previous snapshot's less standing loss otherwise. A unit
      built in a later period opens in that period, and a cyclic one that retires closes on its own last
      snapshot. Per period, the same holds with each investment period as the horizon
    dims: [scenario, snapshot, storage_unit]
    cases:
      cyclic: {when: StorageUnit_cyclic_state_of_charge AND NOT StorageUnit_cyclic_state_of_charge_per_period
          AND NOT StorageUnit_state_of_charge_initial_per_period AND (position(snapshot) == 0 OR StorageUnit_opens_late),
        expression: 'StorageUnit_retention * shift(shift(StorageUnit_state_of_charge, along=snapshot,
          offset=1, edge=''wrap''), along=snapshot, offset=StorageUnit_inactive_snapshots, edge=''wrap'')'}
      opening: {when: NOT StorageUnit_cyclic_state_of_charge AND NOT StorageUnit_cyclic_state_of_charge_per_period
          AND NOT StorageUnit_state_of_charge_initial_per_period AND (position(snapshot) == 0 OR StorageUnit_opens_late),
        expression: StorageUnit_state_of_charge_initial}
      period_cyclic: {when: StorageUnit_cyclic_state_of_charge_per_period, expression: 'StorageUnit_retention
          * shift(StorageUnit_state_of_charge, along=snapshot, offset=1, edge=''wrap'', within=snapshot_period[period])'}
      period_opening: {when: 'StorageUnit_state_of_charge_initial_per_period AND NOT StorageUnit_cyclic_state_of_charge_per_period
          AND position(snapshot, within=snapshot_period[period]) == 0', expression: StorageUnit_state_of_charge_initial}
    otherwise: StorageUnit_retention * shift(StorageUnit_state_of_charge, along=snapshot, offset=1)
  Store_energy_carried_in:
    description: the energy a store opens a snapshot with — at the first snapshot it stands in, its last
      such snapshot's less standing loss where it is cyclic and the given initial energy, which no standing
      loss has touched yet, where it is not; the previous snapshot's less standing loss otherwise. A store
      built in a later period opens in that period, and a cyclic one that retires closes on its own last
      snapshot. Per period, the same holds with each investment period as the horizon
    dims: [scenario, snapshot, store]
    cases:
      cyclic: {when: Store_e_cyclic AND NOT Store_e_cyclic_per_period AND NOT Store_e_initial_per_period
          AND (position(snapshot) == 0 OR Store_opens_late), expression: 'Store_retention * shift(shift(Store_e,
          along=snapshot, offset=1, edge=''wrap''), along=snapshot, offset=Store_inactive_snapshots, edge=''wrap'')'}
      opening: {when: NOT Store_e_cyclic AND NOT Store_e_cyclic_per_period AND NOT Store_e_initial_per_period
          AND (position(snapshot) == 0 OR Store_opens_late), expression: Store_e_initial}
      period_cyclic: {when: Store_e_cyclic_per_period, expression: 'Store_retention * shift(Store_e, along=snapshot,
          offset=1, edge=''wrap'', within=snapshot_period[period])'}
      period_opening: {when: 'Store_e_initial_per_period AND NOT Store_e_cyclic_per_period AND position(snapshot,
          within=snapshot_period[period]) == 0', expression: Store_e_initial}
    otherwise: Store_retention * shift(Store_e, along=snapshot, offset=1)
  Link_output_arrival:
    description: what a link delivers to an output port at a snapshot — its flow delayed by the port's
      `delay` within its investment period, times the port's efficiency at the snapshot the flow arrives;
      where the port is `cyclic_delay` the delayed flow wraps from the period's end, and where it is not
      the flow still in transit at the period's first snapshots is lost. A port that does not delay (`delay`
      zero) delivers its flow unshifted, cyclic or not
    dims: [scenario, snapshot, link_output]
    cases:
      wrapping: {when: Link_output_cyclic_delay, expression: 'shift(at(Link_p, by=Link_output_link[link]),
          along=snapshot, offset=Link_output_delay, edge=''wrap'', within=snapshot_period[period]) * Link_efficiency'}
    otherwise: shift(at(Link_p, by=Link_output_link[link]), along=snapshot, offset=Link_output_delay,
      edge=0, within=snapshot_period[period]) * Link_efficiency
  Process_output_arrival:
    description: what a process transfers at a port at a snapshot — its internal power delayed by the
      port's `delay` within its investment period, times the port's rate at the snapshot the transfer
      arrives; where the port is `cyclic_delay` the delayed transfer wraps from the period's end, and
      where it is not the energy still in transit at the period's first snapshots is lost. A port that
      does not delay (`delay` zero) transfers at once, cyclic or not
    dims: [scenario, snapshot, process_output]
    cases:
      wrapping: {when: Process_output_cyclic_delay, expression: 'shift(at(Process_p, by=Process_output_process[process]),
          along=snapshot, offset=Process_output_delay, edge=''wrap'', within=snapshot_period[period])
          * Process_rate'}
    otherwise: shift(at(Process_p, by=Process_output_process[process]), along=snapshot, offset=Process_output_delay,
      edge=0, within=snapshot_period[period]) * Process_rate
  Generator_opex: {expression: 'sum(sum(((Generator_p * Generator_marginal_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period[period]), over=generator), over=snapshot) + sum(sum((((Generator_p
      * Generator_p) * Generator_marginal_cost_quadratic) * snapshot_weightings_objective) * at(period_weight_objective,
      by=snapshot_period[period]), over=generator), over=snapshot)'}
  StorageUnit_opex: {expression: '(sum(sum(((StorageUnit_p_dispatch * StorageUnit_marginal_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period[period]), over=storage_unit), over=snapshot) +
      sum(sum((((StorageUnit_p_dispatch * StorageUnit_p_dispatch) * StorageUnit_marginal_cost_quadratic)
      * snapshot_weightings_objective) * at(period_weight_objective, by=snapshot_period[period]), over=storage_unit),
      over=snapshot)) + sum(sum(((StorageUnit_state_of_charge * StorageUnit_marginal_cost_storage) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period[period]), over=storage_unit), over=snapshot)'}
  Store_opex: {expression: 'sum(sum(((Store_p * Store_marginal_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period[period]), over=store), over=snapshot) + sum(sum((((Store_p
      * Store_p) * Store_marginal_cost_quadratic) * snapshot_weightings_objective) * at(period_weight_objective,
      by=snapshot_period[period]), over=store), over=snapshot) + sum(sum(((Store_e * Store_marginal_cost_storage)
      * snapshot_weightings_objective) * at(period_weight_objective, by=snapshot_period[period]), over=store),
      over=snapshot)'}
  scenario_opex:
    dims: [scenario]
    expression: (Generator_opex + StorageUnit_opex) + Store_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:415-432`)
  StorageUnit_capex: {expression: sum(scenario_weight * StorageUnit_p_nom_ext * StorageUnit_capital_cost
      * StorageUnit_capital_weight)}
  Store_capex: {expression: sum(scenario_weight * Store_e_nom_ext * Store_capital_cost * Store_capital_weight)}
  risk_weighted_opex: {expression: 'sum(scenario_weight * scenario_opex, over=scenario)'}
  total_cost:
    dims: []
    expression: (StorageUnit_capex + Store_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
  StorageUnit_additions: {expression: 'sum(StorageUnit_p_nom_ext * StorageUnit_first_active, over=storage_unit,
      by=StorageUnit_carrier[carrier])'}
  Store_additions: {expression: 'sum(Store_e_nom_ext * Store_first_active, over=store, by=Store_carrier[carrier])'}
  Carrier_additions:
    dims: [period, carrier]
    expression: StorageUnit_additions + Store_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
  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:1513-1514`)
    dims: [scenario, snapshot, load]
    cases:
      active: {when: Load_active, expression: Load_sign * Load_p_set}
    otherwise: 0
  Generator_injection: {expression: 'sum(Generator_sign * Generator_p, over=generator, by=Generator_bus[bus])'}
  Link_injection: {expression: 'sum(Link_output_arrival, over=link_output, by=Link_output_bus[bus])'}
  Load_injection: {expression: 'sum(Load_demand, over=load, by=Load_bus[bus])'}
  Process_injection: {expression: 'sum(Process_output_arrival, over=process_output, by=Process_output_bus[bus])'}
  StorageUnit_injection: {expression: 'sum(StorageUnit_sign * (StorageUnit_p_dispatch - StorageUnit_p_store),
      over=storage_unit, by=StorageUnit_bus[bus])'}
  Store_injection: {expression: 'sum(Store_sign * Store_p, over=store, by=Store_bus[bus])'}
  Bus_injection:
    dims: [scenario, snapshot, bus]
    expression: ((((Generator_injection + Link_injection) + Load_injection) + Process_injection) + StorageUnit_injection)
      + Store_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
conditions:
  StorageUnit_ext: {description: a storage unit with an extendable build that stands in the snapshot's
      period — PyPSA's `ext` rows, condition: StorageUnit_p_nom_extendable AND StorageUnit_active}
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, multi),
        **carriers(n, multi),
    'Generator_bus': relation(n, 'Generator', 'bus'),
    'Load_bus': relation(n, 'Load', 'bus'),
    'StorageUnit_bus': relation(n, 'StorageUnit', 'bus'),
    'Store_bus': relation(n, 'Store', '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),
    'snapshot_weightings_stores': weighting(n, 'stores'),
}

with sps.solve('differential/pypsa/rungs/rung_21_carrier_growth.yaml', sources) as solution:
    solution.objective  # 8452.5

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

"""Rung 21: a carrier's growth limit binds its non-generator builds — a storage unit and two stores over two periods."""

from __future__ import annotations

from datetime import datetime

import pandas as pd

OPTIMIZE = {'multi_investment_periods': True}


def build():
    """A whole network, not the spine: cheap solar only at the first snapshot of each period, so battery capacity pays off but its growth is capped."""
    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', 'solar')
    n.add('Carrier', 'gas')
    n.add('Carrier', 'battery', max_growth=20, max_relative_growth=0.5)
    n.add('Generator', 'solar', bus='grid', carrier='solar', p_nom=100, marginal_cost=1, p_max_pu=[1, 0, 1, 0])
    n.add('Generator', 'backup', bus='grid', carrier='gas', p_nom=200, marginal_cost=80)
    n.add(
        'StorageUnit',
        'bat20',
        bus='grid',
        carrier='battery',
        p_nom_extendable=True,
        p_nom_max=100,
        max_hours=4,
        capital_cost=50,
        build_year=2020,
        lifetime=30,
    )
    n.add(
        'Store',
        'tank20',
        bus='grid',
        carrier='battery',
        e_nom_extendable=True,
        e_nom_max=10,
        capital_cost=10,
        build_year=2020,
        lifetime=30,
    )
    n.add(
        'Store',
        'tank30',
        bus='grid',
        carrier='battery',
        e_nom_extendable=True,
        e_nom_max=100,
        capital_cost=8,
        build_year=2030,
        lifetime=30,
    )
    n.add('Load', 'town', bus='grid', p_set=[40, 60, 40, 80])
    return n