Rung 17: process — generalized converters, one fixed and ramping, one extendable, one on a set schedule, all feeding a hub¶

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'}
  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}
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_ramp_limit_up:
    description: most a process may raise its internal power between snapshots, per unit of nominal power;
      no value means no limit — read at the later of the two snapshots, so the limit may change over time
    dims: [scenario, snapshot, process]
  Process_ramp_limit_down:
    description: most a process may lower its internal power between snapshots, per unit of nominal power;
      no value means no limit — read at the later of the two snapshots, so the limit may change over time
    dims: [scenario, snapshot, process]
  Process_p_set:
    description: a given internal power schedule; a process without one has no row here
    dims: [scenario, snapshot, process]
  Process_p_nom_min:
    description: least nominal power an extendable process may be built at
    dims: [scenario, process]
  Process_p_nom_max:
    description: most nominal power an extendable process may be built at
    dims: [scenario, process]
  Process_capital_cost:
    description: cost of one unit of nominal power — PyPSA's `capital_cost`, periodized as an annuity
      in data prep
    dims: [scenario, process]
  Process_p_nom_set:
    description: a given nominal power for an extendable process; one without a value has no row here
    dims: [scenario, process]
  Process_committable:
    description: whether internal power is gated by an on/off status decision
    dims: [process]
    dtype: bool
  Process_ramp_limit_start_up:
    description: most internal power in the snapshot a process starts, per unit of nominal power
    dims: [scenario, process]
  Process_ramp_limit_shut_down:
    description: most internal power in the snapshot before a process stops, per unit of nominal power
    dims: [scenario, process]
  Process_status_initial:
    description: one where the process was on before the first snapshot, zero where off — PyPSA's `up_time_before
      > 0`, data prep
    dims: [scenario, process]
    dtype: int
  Process_p_init:
    description: the internal power a process brought into the horizon — PyPSA's `p_init`, read only where
      the process came in running; no value means it is unknown, so the process carries no ramp row at
      the first snapshot
    dims: [scenario, process]
  Process_p_nom_mod:
    description: the module size a build comes in whole numbers of; no value means the build is continuous
    dims: [process]
  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
  Link_active:
    description: whether a link stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, link]
    dtype: bool
  Process_active:
    description: whether a process stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, process]
    dtype: bool
  Process_capital_weight:
    description: the sum of period weights a process stands in — PyPSA's `active * period_weighting`,
      summed, data prep
    dims: [process]
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
  Process_p_nom_ext:
    description: '`Process-p_nom` — nominal internal power where it is a decision; the parameter of the
      same PyPSA name carries the fixed regime'
    dims: [process]
    where: Process_p_nom_extendable
  CVaR_a:
    description: '`CVaR-a` — how far a scenario''s operating cost exceeds the tail''s start; nothing where
      it does not'
    dims: [scenario]
    bounds: {lower: 0}
  CVaR_theta:
    description: '`CVaR-theta` — where the tail starts, the value at risk'
    dims: []
  CVaR:
    description: '`CVaR` — the tail''s average cost, what the objective prices at `omega`'
    dims: []
  Process_status:
    description: '`Process-status` — how much of a committable process is on: an integer the rows below
      cap at one, or at the module count where the build is modular'
    dims: [scenario, snapshot, process]
    where: Process_committable AND Process_active
    domain: integer
    bounds: {lower: 0}
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
  Process_ext_p_lower:
    description: '`Process-ext-p-lower` — an extendable process runs at least its minimum of the chosen
      build, negative for the other way'
    dims: [scenario, snapshot, process]
    where: Process_p_nom_extendable AND not Process_committable AND Process_active
    expression: Process_p >= Process_p_min_pu * Process_p_nom_ext
  Process_ext_p_upper:
    description: '`Process-ext-p-upper` — an extendable process runs at most the chosen build'
    dims: [scenario, snapshot, process]
    where: Process_p_nom_extendable AND not Process_committable AND Process_active
    expression: Process_p <= Process_p_max_pu * Process_p_nom_ext
  Process_ext_p_nom_lower:
    description: '`Process-ext-p_nom-lower` — the chosen build is at least its floor in every scenario'
    dims: [scenario, process]
    where: Process_p_nom_extendable
    expression: Process_p_nom_ext >= Process_p_nom_min
  Process_ext_p_nom_upper:
    description: '`Process-ext-p_nom-upper` — the chosen build is at most its cap in every scenario; a
      cap of infinity is no row'
    dims: [scenario, process]
    where: Process_p_nom_extendable AND Process_p_nom_max
    expression: Process_p_nom_ext <= Process_p_nom_max
  Process_p_nom_set:
    description: '`Process-p_nom_set` — the chosen build pinned, wherever a value is given'
    dims: [scenario, process]
    where: Process_p_nom_extendable AND Process_p_nom_set
    expression: Process_p_nom_ext == Process_p_nom_set
  Process_p_ramp_limit_up:
    description: '`Process-p-ramp_limit_up` — a process raises internal power no faster than its ramp
      limit of the build, and a committed one no further than its start-up ramp in the snapshot it turns
      on. A process that came into the horizon running carries a row at the first snapshot only where
      its `p_init` gives the internal power it brought in, and no process carries one at the start of
      a later investment period — nor does any process a big M releases instead'
    dims: [scenario, snapshot, process]
    where: (Process_ramp_limit_up OR Process_ramp_limit_start_up) AND NOT (Process_committable AND Process_p_nom_extendable
      AND NOT (Process_p_nom_mod > 0)) AND (position(snapshot, by=snapshot_period, within=period) > 0
      OR (position(snapshot) == 0 AND (Process_status_initial == 0 OR Process_p_init))) AND Process_active
    expression: Process_p - Process_previous_p <= Process_ramp_up_allowance
  Process_p_ramp_limit_down:
    description: '`Process-p-ramp_limit_down` — a process lowers internal power no faster than its ramp
      limit of the build, and a committed one no further than its shut-down ramp in the snapshot it turns
      off. A process that came into the horizon running carries a row at the first snapshot only where
      its `p_init` gives the internal power it brought in, and no process carries one at the start of
      a later investment period — nor does any process a big M releases instead'
    dims: [scenario, snapshot, process]
    where: (Process_ramp_limit_down OR Process_ramp_limit_shut_down) AND NOT (Process_committable AND
      Process_p_nom_extendable AND NOT (Process_p_nom_mod > 0)) AND (position(snapshot, by=snapshot_period,
      within=period) > 0 OR (position(snapshot) == 0 AND (Process_status_initial == 0 OR Process_p_init)))
      AND Process_active
    expression: Process_previous_p - Process_p <= Process_ramp_down_allowance
  Process_p_set:
    description: '`Process-p_set` — internal power pinned to the given schedule, wherever one is given'
    dims: [scenario, snapshot, process]
    where: Process_p_set AND Process_active
    expression: Process_p == Process_p_set
  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:
  Process_previous_p:
    description: the internal power a process carries into a snapshot — at the first, the `p_init` it
      brought in where it came in running and nothing where it came in off; the previous snapshot's after
      that
    dims: [scenario, snapshot, process]
    cases:
      opening: {when: position(snapshot) == 0, expression: Process_status_initial * Process_p_init}
    otherwise: shift(Process_p, along=snapshot, offset=1)
  Process_ramp_up_allowance:
    description: how far a process may raise internal power between two snapshots — its ramp limit of
      the build while it stays on, plus its start-up ramp in the snapshot it turns on
    dims: [scenario, snapshot, process]
    cases:
      committed: {when: Process_committable, expression: Process_ramp_up_rate * Process_p_nom_committed
          * Process_previous_status + Process_start_up_rate * Process_p_nom_committed * (Process_status
          - Process_previous_status)}
    otherwise: Process_ramp_up_rate * Process_p_nom_effective
  Process_ramp_down_allowance:
    description: how far a process may lower internal power between two snapshots — its ramp limit of
      the build while it stays on, plus its shut-down ramp in the snapshot it turns off
    dims: [scenario, snapshot, process]
    cases:
      committed: {when: Process_committable, expression: Process_ramp_down_rate * Process_p_nom_committed
          * Process_status + Process_shut_down_rate * Process_p_nom_committed * (Process_previous_status
          - Process_status)}
    otherwise: Process_ramp_down_rate * Process_p_nom_effective
  total_cost:
    dims: []
    expression: Process_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 + Link_injection) + Load_injection) + Process_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
  Process_p_nom_effective:
    description: the build a process's limits are taken against — the chosen one where it is extendable,
      the given one otherwise
    dims: [scenario, process]
    cases:
      extendable: {when: Process_p_nom_extendable, expression: Process_p_nom_ext}
    otherwise: Process_p_nom
  Process_previous_status:
    description: the commitment state a process carries into a snapshot — the state it brought into the
      horizon at the first, the previous snapshot's after that
    dims: [scenario, snapshot, process]
    cases:
      opening: {when: position(snapshot) == 0, expression: Process_status_initial}
    otherwise: shift(Process_status, along=snapshot, offset=1)
  Process_ramp_up_rate:
    description: the ramp limit a process's up row reads — PyPSA's `ramp_limit_up`, or the full build
      where it has none, since a start-up ramp alone builds the row
    dims: [scenario, snapshot, process]
    cases:
      given: {when: Process_ramp_limit_up, expression: Process_ramp_limit_up}
    otherwise: 1
  Process_ramp_down_rate:
    description: the ramp limit a process's down row reads — PyPSA's `ramp_limit_down`, or the full build
      where it has none, since a shut-down ramp alone builds the row
    dims: [scenario, snapshot, process]
    cases:
      given: {when: Process_ramp_limit_down, expression: Process_ramp_limit_down}
    otherwise: 1
  Process_start_up_rate:
    description: the start-up ramp a process's up row reads — PyPSA's `ramp_limit_start_up`, or the full
      build where it has none
    dims: [scenario, process]
    cases:
      given: {when: Process_ramp_limit_start_up, expression: Process_ramp_limit_start_up}
    otherwise: 1
  Process_shut_down_rate:
    description: the shut-down ramp a process's down row reads — PyPSA's `ramp_limit_shut_down`, or the
      full build where it has none
    dims: [scenario, process]
    cases:
      given: {when: Process_ramp_limit_shut_down, expression: Process_ramp_limit_shut_down}
    otherwise: 1
  Process_p_nom_committed:
    description: the build a committed process's ramp rows are taken against — one module where the build
      is extendable and modular, the given build otherwise
    dims: [scenario, process]
    cases:
      modular_build: {when: Process_p_nom_extendable AND Process_p_nom_mod > 0, expression: Process_p_nom_mod}
    otherwise: Process_p_nom
  Process_capex: {expression: sum(scenario_weight * Process_p_nom_ext * Process_capital_cost * Process_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)'}
  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)'}
  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
  scenario_opex:
    dims: [scenario]
    expression: (Generator_opex + Link_opex) + Process_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)'}
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'),
    '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_17_process.yaml', sources) as solution:
    solution.objective  # 9730.0

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

"""Rung 17: process — generalized converters, one fixed and ramping, one extendable, one on a set schedule, all feeding a hub."""

from __future__ import annotations

from math import nan

import spine


def build():
    """The spine plus this rung's additions, as a ``pypsa.Network``."""
    n = spine.build()
    n.add('Bus', 'hub')
    n.add(
        'Process',
        'conv_fix',
        bus0='north',
        bus1='hub',
        p_nom=50,
        marginal_cost=2,
        ramp_limit_up=0.3,
        ramp_limit_down=0.3,
    )
    n.add(
        'Process',
        'conv_ext',
        bus0='south',
        bus1='hub',
        p_nom_extendable=True,
        capital_cost=20,
        p_nom_min=5,
        p_nom_max=40,
        marginal_cost=1,
        p_nom_set=25,
    )
    n.add('Process', 'conv_set', bus0='north', bus1='hub', p_nom=20, marginal_cost=3, p_set=[10, nan, nan, nan])
    n.add('Load', 'hub_load', bus='hub', p_set=[15, 20, 25, 10])
    return n

n = build()
n.optimize(solver_name='highs')
n.objective  # 9730.0