Rung 60: efficiencies per snapshot — a link, a process, a storage unit, a fuel unit under a primary-energy cap and a transformer with a fixed phase shift, each reading its coefficient per snapshot¶

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'}
  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'}
  line: {description: 'passive branches, each between two buses, their flow set by impedance'}
  transformer: {description: 'passive branches between two buses, their flow set by impedance and tap
      ratio, with a phase shift fixed or optimised'}
  cycle: {description: 'independent cycles of the passive network graph — the cycle basis, data prep'}
  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}
  Link_bus0: {description: the bus a link leaves, key: link, 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_bus: {description: the bus a storage unit sits on, key: storage_unit, 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}
  Transformer_bus0: {description: the bus a transformer's flow is measured at, key: transformer, values: bus}
  Transformer_bus1: {description: the bus at a transformer's other end, key: transformer, 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
  Link_p_nom:
    description: nominal power
    dims: [scenario, link]
  Link_p_nom_extendable:
    description: whether the nominal power is a decision
    dims: [link]
    dtype: bool
  Link_p_min_pu:
    description: least flow, per unit of nominal power — negative for a link that carries both ways
    dims: [scenario, snapshot, link]
  Link_p_max_pu:
    description: most flow, per unit of nominal power
    dims: [scenario, snapshot, link]
  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:1522`)
    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, in `snapshot_weightings.generators` units, which the file states as whole snapshots; zero
      for a port that delivers at once. Each scenario takes its own. PyPSA `1.3.0` groups the ports by
      delay over all scenarios and shifts each group in every one, so a delay that differs by scenario
      delivers the flow twice (`constraints.py:1269-1276`, PyPSA/PyPSA#1941)
    dims: [scenario, 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. Each scenario takes its own, as the delay
    dims: [scenario, link_output]
    dtype: bool
  Link_marginal_cost:
    description: cost of one unit of flow
    dims: [scenario, snapshot, link]
  Link_marginal_cost_quadratic:
    description: cost of the square of one unit of flow
    dims: [scenario, snapshot, link]
  Link_committable:
    description: whether flow is gated by an on/off status decision
    dims: [link]
    dtype: bool
  Process_p_nom:
    description: nominal internal power
    dims: [scenario, process]
  Process_p_nom_extendable:
    description: whether the nominal internal power is a decision
    dims: [process]
    dtype: bool
  Process_p_min_pu:
    description: least internal power, per unit of nominal power — negative for a process that runs both
      ways
    dims: [scenario, snapshot, process]
  Process_p_max_pu:
    description: most internal power, per unit of nominal power
    dims: [scenario, snapshot, process]
  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:1522`)
    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, in `snapshot_weightings.generators` units, which the file states as whole snapshots;
      zero for a port that transfers at once. Each scenario takes its own, as a link's
    dims: [scenario, 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. Each scenario takes its own, as the delay
    dims: [scenario, process_output]
    dtype: bool
  Process_marginal_cost:
    description: cost of one unit of internal power
    dims: [scenario, snapshot, process]
  Process_marginal_cost_quadratic:
    description: cost of the square of one unit of internal power
    dims: [scenario, snapshot, process]
  Process_committable:
    description: whether internal power is gated by an on/off status decision
    dims: [process]
    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]
  period_weight_years:
    description: PyPSA's `investment_period_weightings.years` — what a period's energy weighs in a `primary_energy`
      or `operational_limit` row; PyPSA reads it only under `multi_investment_periods`, so data prep feeds
      one otherwise
    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
  Line_active:
    description: whether a line stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, line]
    dtype: bool
  Process_active:
    description: whether a process stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, process]
    dtype: bool
  Transformer_active:
    description: whether a transformer stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, transformer]
    dtype: bool
  snapshot_weightings_stores:
    description: PyPSA's `snapshot_weightings.stores` — hours a snapshot stands for in a storage balance
    dims: [snapshot]
  snapshot_weightings_generators:
    description: PyPSA's `snapshot_weightings.generators` — hours a snapshot stands for in an energy total
    dims: [snapshot]
  StorageUnit_p_nom:
    description: nominal power
    dims: [scenario, storage_unit]
  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 (`consistency.py:1187`)
    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]
  Line_s_nom:
    description: nominal apparent power
    dims: [scenario, 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_cycle_weight:
    description: the line's series impedance, signed by its orientation in the cycle — the cycle basis,
      data prep; a line in no cycle has no row. PyPSA builds the cycle basis from the first scenario only
      (`networks.py:1354-1361`)
    dims: [line, cycle]
  Transformer_s_nom:
    description: nominal apparent power
    dims: [scenario, transformer]
  Transformer_s_nom_extendable:
    description: whether the nominal apparent power is a decision
    dims: [transformer]
    dtype: bool
  Transformer_s_max_pu:
    description: most flow either way, per unit of nominal apparent power
    dims: [scenario, snapshot, transformer]
  Transformer_cycle_weight:
    description: the transformer's effective series reactance, `x` times its tap ratio, signed by its
      orientation in the cycle — PyPSA's `x_pu_eff`, the cycle basis, data prep; a transformer in no cycle
      has no row. From the first scenario only, as a line's
    dims: [transformer, cycle]
  Transformer_phase_shift_weight:
    description: a fixed transformer's phase shift in radians at each snapshot, signed by its orientation
      in the cycle — a constant added to the cycle sum, data prep; zero for a varying transformer, whose
      shift is a decision instead, so the constant and the variable term never both count a shift. A transformer
      with no shift or in no cycle has no row
    dims: [snapshot, transformer, cycle]
  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]
  GlobalConstraint_counts_snapshot:
    description: 'whether a row counts a snapshot in a scenario — PyPSA''s `investment_period`: every
      snapshot where the row names none, and only that period''s where it names one, data prep. A row
      that names a period the run does not model has no label here, as PyPSA skips it (`global_constraints.py:377`);
      PyPSA reads the column only under `multi_investment_periods`, and fails on a row that names a period
      without it (`global_constraints.py:375`)'
    dims: [scenario, global_constraint, snapshot]
    dtype: bool
  Generator_primary_energy_weight:
    description: the constrained attribute per unit of energy at the bus — the carrier's `co2_emissions`
      over the generator's efficiency at the snapshot, data prep; a generator of an unweighted carrier
      has no row
    dims: [scenario, global_constraint, snapshot, generator]
variables:
  Generator_p:
    description: '`Generator-p` — output of a generator in a snapshot'
    dims: [scenario, snapshot, generator]
    where: Generator_active
  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
  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
  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
  Transformer_s:
    description: '`Transformer-s` — PyPSA''s `p0`, the flow measured at the `Transformer_bus0` end: a
      positive value withdraws there and injects at `Transformer_bus1`, lossless'
    dims: [scenario, snapshot, transformer]
    where: Transformer_active
  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
  Link_fix_p_lower:
    description: '`Link-fix-p-lower` — a fixed link carries at least its minimum, negative for the other
      way'
    dims: [scenario, snapshot, link]
    where: not Link_p_nom_extendable AND not Link_committable AND Link_active
    expression: Link_p >= Link_p_min_pu * Link_p_nom
  Link_fix_p_upper:
    description: '`Link-fix-p-upper` — a fixed link carries at most its nominal power'
    dims: [scenario, snapshot, link]
    where: not Link_p_nom_extendable AND not Link_committable AND Link_active
    expression: Link_p <= Link_p_max_pu * Link_p_nom
  Process_fix_p_lower:
    description: '`Process-fix-p-lower` — a fixed process runs at least its minimum, negative for the
      other way'
    dims: [scenario, snapshot, process]
    where: not Process_p_nom_extendable AND not Process_committable AND Process_active
    expression: Process_p >= Process_p_min_pu * Process_p_nom
  Process_fix_p_upper:
    description: '`Process-fix-p-upper` — a fixed process runs at most its nominal power'
    dims: [scenario, snapshot, process]
    where: not Process_p_nom_extendable AND not Process_committable AND Process_active
    expression: Process_p <= Process_p_max_pu * Process_p_nom
  StorageUnit_fix_p_dispatch_lower:
    description: '`StorageUnit-fix-p_dispatch-lower` — dispatch is non-negative'
    dims: [scenario, snapshot, storage_unit]
    where: not StorageUnit_p_nom_extendable AND StorageUnit_active
    expression: StorageUnit_p_dispatch >= 0
  StorageUnit_fix_p_dispatch_upper:
    description: '`StorageUnit-fix-p_dispatch-upper` — a fixed unit dispatches at most its nominal power'
    dims: [scenario, snapshot, storage_unit]
    where: not StorageUnit_p_nom_extendable AND StorageUnit_active
    expression: StorageUnit_p_dispatch <= StorageUnit_p_max_pu * StorageUnit_p_nom
  StorageUnit_fix_p_store_lower:
    description: '`StorageUnit-fix-p_store-lower` — storing is non-negative'
    dims: [scenario, snapshot, storage_unit]
    where: not StorageUnit_p_nom_extendable AND StorageUnit_active
    expression: StorageUnit_p_store >= 0
  StorageUnit_fix_p_store_upper:
    description: '`StorageUnit-fix-p_store-upper` — a fixed unit stores at most its nominal power, the
      minimum-per-unit column carrying that cap negated'
    dims: [scenario, snapshot, storage_unit]
    where: not StorageUnit_p_nom_extendable AND StorageUnit_active
    expression: StorageUnit_p_store <= -StorageUnit_p_min_pu * StorageUnit_p_nom
  StorageUnit_fix_state_of_charge_lower:
    description: '`StorageUnit-fix-state_of_charge-lower` — charge is non-negative'
    dims: [scenario, snapshot, storage_unit]
    where: not StorageUnit_p_nom_extendable AND StorageUnit_active
    expression: StorageUnit_state_of_charge >= 0
  StorageUnit_fix_state_of_charge_upper:
    description: '`StorageUnit-fix-state_of_charge-upper` — a fixed unit holds at most its hours at nominal
      power'
    dims: [scenario, snapshot, storage_unit]
    where: not StorageUnit_p_nom_extendable AND StorageUnit_active
    expression: StorageUnit_state_of_charge <= StorageUnit_max_hours * StorageUnit_p_nom
  Line_fix_s_lower:
    description: '`Line-fix-s-lower` — a fixed line carries at least the negative of its rating, the loss
      counted against it'
    dims: [scenario, snapshot, line]
    where: not Line_s_nom_extendable AND Line_active
    expression: Line_s >= (-Line_s_max_pu) * Line_s_nom
  Line_fix_s_upper:
    description: '`Line-fix-s-upper` — a fixed line carries at most its rating, the loss included'
    dims: [scenario, snapshot, line]
    where: not Line_s_nom_extendable AND Line_active
    expression: Line_s <= Line_s_max_pu * Line_s_nom
  Transformer_fix_s_lower:
    description: '`Transformer-fix-s-lower` — a fixed transformer carries at least the negative of its
      rating, the loss counted against it'
    dims: [scenario, snapshot, transformer]
    where: not Transformer_s_nom_extendable AND Transformer_active
    expression: Transformer_s >= (-Transformer_s_max_pu) * Transformer_s_nom
  Transformer_fix_s_upper:
    description: '`Transformer-fix-s-upper` — a fixed transformer carries at most its rating, the loss
      included'
    dims: [scenario, snapshot, transformer]
    where: not Transformer_s_nom_extendable AND Transformer_active
    expression: Transformer_s <= Transformer_s_max_pu * Transformer_s_nom
  Kirchhoff_Voltage_Law:
    description: '`Kirchhoff-Voltage-Law` — around every independent cycle the impedance-weighted flows
      sum to nothing, which is what makes the linear power flow physical rather than transport. A transformer''s
      flow weighs its effective reactance, and its phase shift enters the cycle sum too: a constant where
      the shift is fixed, or the shift decision times its cycle weight where the shift is a phase-shifting
      transformer''s to choose'
    dims: [scenario, snapshot, cycle]
    expression: Cycle_angle_sum == 0
  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)
  GlobalConstraint_primary_energy_ub:
    description: '`primary_energy` — its total, at most its constant'
    dims: [scenario, global_constraint]
    where: GlobalConstraint_type == 'primary_energy' AND GlobalConstraint_sense == '<='
    expression: primary_energy <= 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:
  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'', by=snapshot_period,
          within=period)'}
      period_opening: {when: 'StorageUnit_state_of_charge_initial_per_period AND NOT StorageUnit_cyclic_state_of_charge_per_period
          AND position(snapshot, by=snapshot_period, within=period) == 0', expression: StorageUnit_state_of_charge_initial}
    otherwise: StorageUnit_retention * shift(StorageUnit_state_of_charge, along=snapshot, offset=1)
  primary_energy:
    dims: [scenario, global_constraint]
    expression: Generator_primary_energy
    description: what a `primary_energy` row totals — weighted generator energy over the snapshots it
      counts, less the charge left in weighted storage at the close; the initial charge it is compared
      against is folded into the row's constant
  total_cost:
    dims: []
    expression: 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) + Link_injection) + Load_injection) + Process_injection)
      + StorageUnit_injection) + Transformer_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
  Cycle_angle_sum:
    dims: [scenario, snapshot, cycle]
    expression: Line_angle_sum + Transformer_angle_sum
    description: 'the voltage angle differences around a cycle: every branch flow times its cycle weight,
      and every transformer phase shift'
  Generator_primary_energy: {expression: 'sum(sum((Generator_p * GlobalConstraint_energy_weight) * Generator_primary_energy_weight,
      over=snapshot), over=generator)'}
  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)'}
  Link_injection: {expression: '-sum(Link_p, by=Link_bus0, over=link, into=bus) + sum(Link_output_arrival,
      by=Link_output_bus, over=link_output, into=bus)'}
  Load_injection: {expression: 'sum(Load_demand, by=Load_bus, over=load, into=bus)'}
  Process_injection: {expression: 'sum(Process_output_arrival, by=Process_output_bus, over=process_output,
      into=bus)'}
  StorageUnit_injection: {expression: 'sum(StorageUnit_sign * (StorageUnit_p_dispatch - StorageUnit_p_store),
      by=StorageUnit_bus, over=storage_unit, into=bus)'}
  Transformer_injection: {expression: '(-sum(Transformer_s, by=Transformer_bus0, over=transformer, into=bus))
      + sum(Transformer_s, by=Transformer_bus1, over=transformer, into=bus)'}
  Line_angle_sum: {expression: 'sum(Line_s * Line_cycle_weight, over=line)'}
  Transformer_angle_sum: {expression: 'sum(Transformer_s * Transformer_cycle_weight, over=transformer)
      + sum(Transformer_phase_shift_weight, over=transformer)'}
  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, over=link,
          into=link_output), along=snapshot, offset=Link_output_delay, edge=''wrap'', by=snapshot_period,
          within=period) * Link_efficiency'}
    otherwise: shift(at(Link_p, by=Link_output_link, over=link, into=link_output), along=snapshot, offset=Link_output_delay,
      edge=0, by=snapshot_period, within=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,
          over=process, into=process_output), along=snapshot, offset=Process_output_delay, edge=''wrap'',
          by=snapshot_period, within=period) * Process_rate'}
    otherwise: shift(at(Process_p, by=Process_output_process, over=process, into=process_output), along=snapshot,
      offset=Process_output_delay, edge=0, by=snapshot_period, within=period) * Process_rate
  GlobalConstraint_energy_weight:
    description: what one unit of power at a snapshot counts for in a row — the generator weighting times
      the years of the snapshot's period, where the row counts the snapshot, and nothing where it does
      not
    dims: [scenario, global_constraint, snapshot]
    cases:
      counted: {when: GlobalConstraint_counts_snapshot, expression: 'snapshot_weightings_generators *
          at(period_weight_years, by=snapshot_period, over=period, into=snapshot)'}
    otherwise: 0
  scenario_opex:
    dims: [scenario]
    expression: ((Generator_opex + Link_opex) + Process_opex) + StorageUnit_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)'}
  Link_opex: {expression: 'sum(sum(((Link_p * Link_marginal_cost) * snapshot_weightings_objective) * at(period_weight_objective,
      by=snapshot_period, over=period, into=snapshot), over=link), over=snapshot) + sum(sum((((Link_p
      * Link_p) * Link_marginal_cost_quadratic) * snapshot_weightings_objective) * at(period_weight_objective,
      by=snapshot_period, over=period, into=snapshot), over=link), over=snapshot)'}
  Process_opex: {expression: 'sum(sum(((Process_p * Process_marginal_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=process), over=snapshot)
      + sum(sum((((Process_p * Process_p) * Process_marginal_cost_quadratic) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=process), over=snapshot)'}
  StorageUnit_opex: {expression: '(sum(sum(((StorageUnit_p_dispatch * StorageUnit_marginal_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), 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, over=period,
      into=snapshot), 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, over=period,
      into=snapshot), over=storage_unit), 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'),
    'Link_bus0': relation(n, 'Link', 'bus0'),
    'Load_bus': relation(n, 'Load', 'bus'),
    'StorageUnit_bus': relation(n, 'StorageUnit', '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'),
    'snapshot_weightings_generators': weighting(n, 'generators'),
}

with sps.solve('differential/pypsa/rungs/rung_60_efficiency_per_snapshot.yaml', sources) as solution:
    solution.objective  # 130562.094184