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Rung 34: maintenance of committable units — a fixed, an extendable and a modular committable generator, link and process, each taken off for one event

One rung of the PyPSA corpus: the file pypsa.yaml projected onto what this network builds, attached to that network, and held to what PyPSA solves it to.

✔ Verified against pypsa master at 51986084 — objective 6420.048611 on both sides; structure ✔ 101 constraints · 30 variables, name for name; size ✔ 503 rows · ✔ 277 columns · ✔ 1153 nonzeros; duals — integer model, no duals; model for model: 131 blocks equal, 0 documented splits, 1 recorded deviations.

Rows and columns, PyPSA against specsolve, name for name
row PyPSA specsolve
Bus-nodal_balance 12 12
Generator-com-ext-p-lower 4 4
Generator-com-ext-p-lower-nonneg 4 4
Generator-com-ext-p-upper-bigM 4 4
Generator-com-ext-p-upper-cap 4 4
Generator-com-mod-p-lower 4 4
Generator-com-mod-p-upper 4 4
Generator-com-p-lower 4 4
Generator-com-p-upper 4 4
Generator-com-transition-shut-down 12 12
Generator-com-transition-start-up 12 12
Generator-ext-p_nom-lower 2 2
Generator-ext-p_nom-upper 2 2
Generator-fix-p-lower 12 12
Generator-fix-p-upper 12 12
Generator-maint-event-count 3 3
Generator-maint-modstatus-lb 4 4
Generator-maint-modstatus-le-maint 4 4
Generator-maint-modstatus-le-status 4 4
Generator-maint-start-horizon 1 1
Generator-maint-status-lb 4 4
Generator-maint-status-le-maint 4 4
Generator-maint-status-le-status 4 4
Generator-maint-window 12 12
Generator-maintcap_lower_nommax 4 4
Generator-maintcap_lower_nommin 4 4
Generator-maintcap_upper 4 4
Generator-maintcap_upper_nommax 4 4
Generator-p_nom_modularity 1 1
Generator-shut_down-p-fixed-upper 8 8
Generator-shut_down-p_nom-variable-upper 4 4
Generator-start_up-p-fixed-upper 8 8
Generator-start_up-p_nom-variable-upper 4 4
Generator-status-p-fixed-upper 8 8
Generator-status-p_nom-variable-upper 4 4
Link-com-ext-p-lower 4 4
Link-com-ext-p-lower-nonneg 4 4
Link-com-ext-p-upper-bigM 4 4
Link-com-ext-p-upper-cap 4 4
Link-com-mod-p-lower 4 4
Link-com-mod-p-upper 4 4
Link-com-p-lower 4 4
Link-com-p-upper 4 4
Link-com-transition-shut-down 12 12
Link-com-transition-start-up 12 12
Link-ext-p_nom-lower 2 2
Link-ext-p_nom-upper 2 2
Link-fix-p-lower 4 4
Link-fix-p-upper 4 4
Link-maint-event-count 3 3
Link-maint-modstatus-lb 4 4
Link-maint-modstatus-le-maint 4 4
Link-maint-modstatus-le-status 4 4
Link-maint-start-horizon 1 1
Link-maint-status-lb 4 4
Link-maint-status-le-maint 4 4
Link-maint-status-le-status 4 4
Link-maint-window 12 12
Link-maintcap_lower_nommax 4 4
Link-maintcap_lower_nommin 4 4
Link-maintcap_upper 4 4
Link-maintcap_upper_nommax 4 4
Link-p_nom_modularity 1 1
Link-shut_down-p-fixed-upper 8 8
Link-shut_down-p_nom-variable-upper 4 4
Link-start_up-p-fixed-upper 8 8
Link-start_up-p_nom-variable-upper 4 4
Link-status-p-fixed-upper 8 8
Link-status-p_nom-variable-upper 4 4
Process-com-ext-p-lower 4 4
Process-com-ext-p-lower-nonneg 4 4
Process-com-ext-p-upper-bigM 4 4
Process-com-ext-p-upper-cap 4 4
Process-com-mod-p-lower 4 4
Process-com-mod-p-upper 4 4
Process-com-p-lower 4 4
Process-com-p-upper 4 4
Process-com-transition-shut-down 12 12
Process-com-transition-start-up 12 12
Process-ext-p_nom-lower 2 2
Process-ext-p_nom-upper 2 2
Process-maint-event-count 3 3
Process-maint-modstatus-lb 4 4
Process-maint-modstatus-le-maint 4 4
Process-maint-modstatus-le-status 4 4
Process-maint-start-horizon 1 1
Process-maint-status-lb 4 4
Process-maint-status-le-maint 4 4
Process-maint-status-le-status 4 4
Process-maint-window 12 12
Process-maintcap_lower_nommax 4 4
Process-maintcap_lower_nommin 4 4
Process-maintcap_upper 4 4
Process-maintcap_upper_nommax 4 4
Process-p_nom_modularity 1 1
Process-shut_down-p-fixed-upper 8 8
Process-shut_down-p_nom-variable-upper 4 4
Process-start_up-p-fixed-upper 8 8
Process-start_up-p_nom-variable-upper 4 4
Process-status-p-fixed-upper 8 8
Process-status-p_nom-variable-upper 4 4
column PyPSA specsolve
Generator-maintenance 12 12
Generator-maintenance_capacity 4 4
Generator-maintenance_start 12 12
Generator-maintenance_status 8 8
Generator-n_mod 1 1
Generator-p 24 24
Generator-p_nom 2 2
Generator-shut_down 12 12
Generator-start_up 12 12
Generator-status 12 12
Link-maintenance 12 12
Link-maintenance_capacity 4 4
Link-maintenance_start 12 12
Link-maintenance_status 8 8
Link-n_mod 1 1
Link-p 16 16
Link-p_nom 2 2
Link-shut_down 12 12
Link-start_up 12 12
Link-status 12 12
Process-maintenance 12 12
Process-maintenance_capacity 4 4
Process-maintenance_start 12 12
Process-maintenance_status 8 8
Process-n_mod 1 1
Process-p 12 12
Process-p_nom 2 2
Process-shut_down 12 12
Process-start_up 12 12
Process-status 12 12

The model

The same model, as math

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 periods 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.

Sets

Symbol Meaning
\(\Xi\) index \(\xi\) — scenario with \(\mathrm{Generator\_maintenance\_cover} \subseteq \Xi \times \mathcal{G} \times \mathcal{T} \times \mathcal{T},\ \mathrm{Link\_maintenance\_cover} \subseteq \Xi \times \mathcal{L} \times \mathcal{T} \times \mathcal{T},\ \mathrm{Process\_maintenance\_cover} \subseteq \Xi \times \mathcal{J} \times \mathcal{T} \times \mathcal{T}\), Generator_maintenance_cover is absent where the data has no row, Link_maintenance_cover is absent where the data has no row, Process_maintenance_cover is absent where the data has no row — the futures dispatch is chosen in, each with a weight
\(\mathcal{T}\) index \(t\) — snapshot with \(\mathrm{Generator\_maintenance\_cover} \subseteq \Xi \times \mathcal{G} \times \mathcal{T} \times \mathcal{T},\ \mathrm{Link\_maintenance\_cover} \subseteq \Xi \times \mathcal{L} \times \mathcal{T} \times \mathcal{T},\ \mathrm{Process\_maintenance\_cover} \subseteq \Xi \times \mathcal{J} \times \mathcal{T} \times \mathcal{T},\ \mathrm{period}: \mathcal{T} \to \mathcal{Y}\), Generator_maintenance_cover is absent where the data has no row, Link_maintenance_cover is absent where the data has no row, Process_maintenance_cover is absent where the data has no row — dispatch periods
\(\mathcal{N}\) index \(n\) — bus with \(\mathrm{bus}: \mathcal{G} \to \mathcal{N},\ \mathrm{bus0}: \mathcal{L} \to \mathcal{N},\ \mathrm{bus}: \mathcal{O} \to \mathcal{N},\ \mathrm{bus}: \mathcal{R} \to \mathcal{N},\ \mathrm{bus}: \mathcal{D} \to \mathcal{N}\) — network nodes
\(\mathcal{G}\) index \(g\) — generator with \(\mathrm{Generator\_maintenance\_cover} \subseteq \Xi \times \mathcal{G} \times \mathcal{T} \times \mathcal{T},\ \mathrm{bus}: \mathcal{G} \to \mathcal{N}\), Generator_maintenance_cover is absent where the data has no row — generating units, each on one bus
\(\mathcal{L}\) index \(l\) — link with \(\mathrm{Link\_maintenance\_cover} \subseteq \Xi \times \mathcal{L} \times \mathcal{T} \times \mathcal{T},\ \mathrm{bus0}: \mathcal{L} \to \mathcal{N},\ \mathrm{link}: \mathcal{O} \to \mathcal{L}\), Link_maintenance_cover is absent where the data has no row — controllable connections, each from one bus to the buses it delivers to
\(\mathcal{O}\) index \(o\) — link_output with \(\mathrm{link}: \mathcal{O} \to \mathcal{L},\ \mathrm{bus}: \mathcal{O} \to \mathcal{N}\) — 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
\(\mathcal{J}\) index \(j\) — process with \(\mathrm{Process\_maintenance\_cover} \subseteq \Xi \times \mathcal{J} \times \mathcal{T} \times \mathcal{T},\ \mathrm{process}: \mathcal{R} \to \mathcal{J}\), Process_maintenance_cover is absent where the data has no row — generalized multi-port converters, each with an internal power that every port draws or delivers at its own rate
\(\mathcal{R}\) index \(r\) — process_output with \(\mathrm{process}: \mathcal{R} \to \mathcal{J},\ \mathrm{bus}: \mathcal{R} \to \mathcal{N}\) — 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
\(\mathcal{D}\) index \(d\) — load with \(\mathrm{bus}: \mathcal{D} \to \mathcal{N}\) — demands, each on one bus
\(\mathcal{Y}\) index \(y\) — period with \(\mathrm{period}: \mathcal{T} \to \mathcal{Y}\) — investment periods — PyPSA's investment_periods

Parameters

Symbol Meaning
\(\mathrm{w}\) snapshot_weightings_objective over \(\mathcal{T}\) — PyPSA's snapshot_weightings.objective — hours a snapshot stands for in the cost
\(\mathrm{p}^{\mathrm{nom}}\) Generator_p_nom over \(\Xi \times \mathcal{G}\) — nominal power
\(\mathrm{ext}\) Generator_p_nom_extendable over \(\mathcal{G}\) — whether the nominal power is a decision
\(\underline{\mathrm{p}}\) Generator_p_min_pu over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — least output, per unit of nominal power
\(\overline{\mathrm{p}}\) Generator_p_max_pu over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — most output, per unit of nominal power — an availability profile
\(\mathrm{c}\) Generator_marginal_cost over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — cost of one unit of output
\(\mathrm{c}^{(2)}\) Generator_marginal_cost_quadratic over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — cost of the square of one unit of output
\(\mathrm{sgn}\) Generator_sign over \(\mathcal{G}\) — 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)
\(\mathrm{com}\) Generator_committable over \(\mathcal{G}\) — whether output is gated by an on/off status decision
\(\mathrm{u}^{0}\) Generator_status_initial over \(\Xi \times \mathcal{G}\) — one where the unit was on before the first snapshot, zero where off — PyPSA's up_time_before > 0, data prep
\(\mathrm{c}^{\mathrm{up}}\) Generator_start_up_cost over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — cost of one start in this snapshot
\(\mathrm{c}^{\mathrm{dn}}\) Generator_shut_down_cost over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — cost of one stop in this snapshot
\(\mathrm{c}^{\mathrm{on}}\) Generator_stand_by_cost over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — cost of one snapshot spent on
\(\mathrm{p}^{\mathrm{mod}}\) Generator_p_nom_mod over \(\mathcal{G}\), absent where the data has no row — the module size a build comes in whole numbers of; no value means the build is continuous
\(\mathrm{N}^{\mathrm{fix}}\) Generator_modules_installed over \(\Xi \times \mathcal{G}\) — how many whole modules a committable build has in place: Generator_p_nom / Generator_p_nom_mod where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build whose nominal power is not a whole number of modules
\(\mathrm{M}\) Generator_big_m over \(\Xi \times \mathcal{G}\), \(0\) where the data has no row — the bound a committed extendable generator's big-M rows release it by — the build cap p_nom_max times the highest p_max_pu, where the cap is finite and positive. Elsewhere it is committable_big_m times the highest p_max_pu, and where that keyword is not given, ten times the largest of the peak total load and the component's largest finite p_nom and p_nom_max, or 1e6 where there is none of them (components.py:1050-1121). Below the output a solve wants, it caps that output; data prep
\(\mathrm{nonneg}\) Generator_p_min_pu_nonneg over \(\mathcal{G}\) — true where none of the generator's own minimums-per-unit is negative — PyPSA's per-unit (p_min_pu >= 0).all() over every snapshot and scenario, data prep
\(\mathrm{mnt}\) Generator_maintainable over \(\mathcal{G}\) — whether a generator must be taken off for maintenance within the horizon — in any scenario, as PyPSA takes the union over them (components.py:1016-1019)
\(\gamma\) Generator_maintenance_pu over \(\Xi \times \mathcal{G}\) — the share of the build a maintenance event takes off
\(\mathrm{n}^{\mathrm{mnt}}\) Generator_maintenance_events over \(\Xi \times \mathcal{G}\) — how many maintenance events the horizon holds
\(\mathrm{blk}\) Generator_maintenance_start_blocked over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — true where no maintenance event may start, because the snapshots it would cover run past the end of the horizon or into one the generator does not stand in — PyPSA's active & ~valid, from maintenance_duration and the generator weightings, data prep
\(\mathrm{f}^{\mathrm{nom}}\) Link_p_nom over \(\Xi \times \mathcal{L}\) — nominal power
\(\mathrm{ext}^{f}\) Link_p_nom_extendable over \(\mathcal{L}\) — whether the nominal power is a decision
\(\underline{\mathrm{f}}\) Link_p_min_pu over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — least flow, per unit of nominal power — negative for a link that carries both ways
\(\overline{\mathrm{f}}\) Link_p_max_pu over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — most flow, per unit of nominal power
\(\eta\) Link_efficiency over \(\Xi \times \mathcal{T} \times \mathcal{O}\) — 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)
\(\mathrm{d}^{f}\) Link_output_delay over \(\mathcal{O}\) — 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)
\(\mathrm{cyc}^{f}\) Link_output_cyclic_delay over \(\mathcal{O}\) — 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
\(\mathrm{c}^{f}\) Link_marginal_cost over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — cost of one unit of flow
\(\mathrm{c}^{f,(2)}\) Link_marginal_cost_quadratic over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — cost of the square of one unit of flow
\(\mathrm{com}^{f}\) Link_committable over \(\mathcal{L}\) — whether flow is gated by an on/off status decision
\(\mathrm{u}^{f,0}\) Link_status_initial over \(\Xi \times \mathcal{L}\) — one where the link was on before the first snapshot, zero where off — PyPSA's up_time_before > 0, data prep
\(\mathrm{c}^{f,\mathrm{up}}\) Link_start_up_cost over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — cost of one start in this snapshot
\(\mathrm{c}^{f,\mathrm{dn}}\) Link_shut_down_cost over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — cost of one stop in this snapshot
\(\mathrm{c}^{f,\mathrm{on}}\) Link_stand_by_cost over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — cost of one snapshot spent on
\(\mathrm{f}^{\mathrm{mod}}\) Link_p_nom_mod over \(\mathcal{L}\), absent where the data has no row — the module size a build comes in whole numbers of; no value means the build is continuous
\(\mathrm{N}^{f,\mathrm{fix}}\) Link_modules_installed over \(\Xi \times \mathcal{L}\) — how many whole modules a committable build has in place: Link_p_nom / Link_p_nom_mod where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build whose nominal power is not a whole number of modules
\(\mathrm{M}^{f}\) Link_big_m over \(\Xi \times \mathcal{L}\), \(0\) where the data has no row — the bound a committed extendable link's big-M rows release it by — the build cap p_nom_max times the highest p_max_pu, where the cap is finite and positive. Elsewhere it is committable_big_m times the highest p_max_pu, and where that keyword is not given, ten times the largest of the peak total load and the component's largest finite p_nom and p_nom_max, or 1e6 where there is none of them (components.py:1050-1121). Below the flow a solve wants, it caps that flow; data prep
\(\mathrm{nonneg}^{f}\) Link_p_min_pu_nonneg over \(\mathcal{L}\) — true where none of the link's own minimums-per-unit is negative — PyPSA's per-unit (p_min_pu >= 0).all() over every snapshot and scenario, data prep
\(\mathrm{mnt}^{f}\) Link_maintainable over \(\mathcal{L}\) — whether a link must be taken off for maintenance within the horizon — in any scenario, as PyPSA takes the union over them (components.py:1016-1019)
\(\gamma^{f}\) Link_maintenance_pu over \(\Xi \times \mathcal{L}\) — the share of the build a maintenance event takes off
\(\mathrm{n}^{f,\mathrm{mnt}}\) Link_maintenance_events over \(\Xi \times \mathcal{L}\) — how many maintenance events the horizon holds
\(\mathrm{blk}^{f}\) Link_maintenance_start_blocked over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — true where no maintenance event may start, because the snapshots it would cover run past the end of the horizon or into one the link does not stand in — PyPSA's active & ~valid, from maintenance_duration and the generator weightings, data prep
\(\mathrm{z}^{\mathrm{nom}}\) Process_p_nom over \(\Xi \times \mathcal{J}\) — nominal internal power
\(\mathrm{ext}^{z}\) Process_p_nom_extendable over \(\mathcal{J}\) — whether the nominal internal power is a decision
\(\underline{\mathrm{z}}\) Process_p_min_pu over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — least internal power, per unit of nominal power — negative for a process that runs both ways
\(\overline{\mathrm{z}}\) Process_p_max_pu over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — most internal power, per unit of nominal power
\(\alpha\) Process_rate over \(\Xi \times \mathcal{T} \times \mathcal{R}\) — 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)
\(\mathrm{d}^{z}\) Process_output_delay over \(\mathcal{R}\) — 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
\(\mathrm{cyc}^{z}\) Process_output_cyclic_delay over \(\mathcal{R}\) — 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
\(\mathrm{c}^{z}\) Process_marginal_cost over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — cost of one unit of internal power
\(\mathrm{c}^{z,(2)}\) Process_marginal_cost_quadratic over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — cost of the square of one unit of internal power
\(\underline{\mathrm{z}}^{\mathrm{nom}}\) Process_p_nom_min over \(\Xi \times \mathcal{J}\) — least nominal power an extendable process may be built at
\(\overline{\mathrm{z}}^{\mathrm{nom}}\) Process_p_nom_max over \(\Xi \times \mathcal{J}\) — most nominal power an extendable process may be built at
\(\mathrm{c}^{\mathrm{cap},z}\) Process_capital_cost over \(\Xi \times \mathcal{J}\) — 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
\(\mathrm{com}^{z}\) Process_committable over \(\mathcal{J}\) — whether internal power is gated by an on/off status decision
\(\mathrm{u}^{z,0}\) Process_status_initial over \(\Xi \times \mathcal{J}\) — one where the process was on before the first snapshot, zero where off — PyPSA's up_time_before > 0, data prep
\(\mathrm{c}^{z,\mathrm{up}}\) Process_start_up_cost over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — cost of one start in this snapshot
\(\mathrm{c}^{z,\mathrm{dn}}\) Process_shut_down_cost over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — cost of one stop in this snapshot
\(\mathrm{c}^{z,\mathrm{on}}\) Process_stand_by_cost over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — cost of one snapshot spent on
\(\mathrm{z}^{\mathrm{mod}}\) Process_p_nom_mod over \(\mathcal{J}\), absent where the data has no row — the module size a build comes in whole numbers of; no value means the build is continuous
\(\mathrm{N}^{z,\mathrm{fix}}\) Process_modules_installed over \(\Xi \times \mathcal{J}\) — how many whole modules a committable build has in place: Process_p_nom / Process_p_nom_mod where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build whose nominal power is not a whole number of modules
\(\mathrm{M}^{z}\) Process_big_m over \(\Xi \times \mathcal{J}\), \(0\) where the data has no row — the bound a committed extendable process's big-M rows release it by — the build cap p_nom_max times the highest p_max_pu, where the cap is finite and positive. Elsewhere it is committable_big_m times the highest p_max_pu, and where that keyword is not given, ten times the largest of the peak total load and the component's largest finite p_nom and p_nom_max, or 1e6 where there is none of them (components.py:1050-1121). Below the internal power a solve wants, it caps that internal power; data prep
\(\mathrm{nonneg}^{z}\) Process_p_min_pu_nonneg over \(\mathcal{J}\) — true where none of the process's own minimums-per-unit is negative — PyPSA's per-unit (p_min_pu >= 0).all() over every snapshot and scenario, data prep
\(\mathrm{mnt}^{z}\) Process_maintainable over \(\mathcal{J}\) — whether a process must be taken off for maintenance within the horizon — in any scenario, as PyPSA takes the union over them (components.py:1016-1019)
\(\gamma^{z}\) Process_maintenance_pu over \(\Xi \times \mathcal{J}\) — the share of the build a maintenance event takes off
\(\mathrm{n}^{z,\mathrm{mnt}}\) Process_maintenance_events over \(\Xi \times \mathcal{J}\) — how many maintenance events the horizon holds
\(\mathrm{blk}^{z}\) Process_maintenance_start_blocked over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — true where no maintenance event may start, because the snapshots it would cover run past the end of the horizon or into one the process does not stand in — PyPSA's active & ~valid, from maintenance_duration and the generator weightings, data prep
\(\mathrm{load}\) Load_p_set over \(\Xi \times \mathcal{T} \times \mathcal{D}\) — demand
\(\mathrm{sgn}^{\mathrm{load}}\) Load_sign over \(\mathcal{D}\) — 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)
\(\mathrm{on}^{\mathrm{load}}\) Load_active over \(\mathcal{D}\) — 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)
\(\pi\) scenario_weight over \(\Xi\) — PyPSA's scenario_weightings.weight — the probability of a future
\(\mathrm{w}^{y}\) period_weight_objective over \(\mathcal{Y}\) — 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)
\(\mathrm{on}\) Generator_active over \(\mathcal{T} \times \mathcal{G}\) — whether a generator stands in a snapshot's period — PyPSA's active, from build year and lifetime, data prep
\(\mathrm{on}^{f}\) Link_active over \(\mathcal{T} \times \mathcal{L}\) — whether a link stands in a snapshot's period — PyPSA's active, data prep
\(\mathrm{on}^{z}\) Process_active over \(\mathcal{T} \times \mathcal{J}\) — whether a process stands in a snapshot's period — PyPSA's active, data prep
\(\mathrm{act}\) Generator_active_asset over \(\mathcal{G}\) — whether a generator 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)
\(\mathrm{act}^{f}\) Link_active_asset over \(\mathcal{L}\) — whether a link 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)
\(\mathrm{act}^{z}\) Process_active_asset over \(\mathcal{J}\) — whether a process 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)
\(\mathrm{W}\) Generator_capital_weight over \(\mathcal{G}\) — the sum of period weights a generator stands in — PyPSA's active * period_weighting, summed, data prep
\(\mathrm{W}^{f}\) Link_capital_weight over \(\mathcal{L}\) — the sum of period weights a link stands in — PyPSA's active * period_weighting, summed, data prep
\(\mathrm{W}^{z}\) Process_capital_weight over \(\mathcal{J}\) — the sum of period weights a process stands in — PyPSA's active * period_weighting, summed, data prep
\(\underline{\mathrm{p}}^{\mathrm{nom}}\) Generator_p_nom_min over \(\Xi \times \mathcal{G}\) — least nominal power an extendable generator may be built at
\(\overline{\mathrm{p}}^{\mathrm{nom}}\) Generator_p_nom_max over \(\Xi \times \mathcal{G}\) — most nominal power an extendable generator may be built at
\(\mathrm{c}^{\mathrm{cap}}\) Generator_capital_cost over \(\Xi \times \mathcal{G}\) — 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
\(\underline{\mathrm{f}}^{\mathrm{nom}}\) Link_p_nom_min over \(\Xi \times \mathcal{L}\) — least nominal power an extendable link may be built at
\(\overline{\mathrm{f}}^{\mathrm{nom}}\) Link_p_nom_max over \(\Xi \times \mathcal{L}\) — most nominal power an extendable link may be built at
\(\mathrm{c}^{\mathrm{cap},f}\) Link_capital_cost over \(\Xi \times \mathcal{L}\) — 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

Conditions

Symbol Meaning
\(\mathrm{Generator\_com\_ext}\) Generator_com_ext over \(\mathcal{G} \times \mathcal{T}\) — a committable generator with an extendable, non-modular build that stands in the snapshot's period — PyPSA's com-ext rows, whose status is relaxed against the chosen build
\(\mathrm{Generator\_maint\_ext}\) Generator_maint_ext over \(\mathcal{G} \times \mathcal{T}\) — a maintainable generator with an extendable build, unless it is committable and modular, that stands in the snapshot's period — the maintenance rows against the chosen build
\(\mathrm{Generator\_committed}\) Generator_committed over \(\mathcal{G} \times \mathcal{T}\) — a committable generator that stands in the snapshot's period — every unit-commitment row's set
\(\mathrm{Link\_com\_ext}\) Link_com_ext over \(\mathcal{L} \times \mathcal{T}\) — a committable link with an extendable, non-modular build that stands in the snapshot's period — PyPSA's com-ext rows, whose status is relaxed against the chosen build
\(\mathrm{Link\_maint\_ext}\) Link_maint_ext over \(\mathcal{L} \times \mathcal{T}\) — a maintainable link with an extendable build, unless it is committable and modular, that stands in the snapshot's period — the maintenance rows against the chosen build
\(\mathrm{Link\_committed}\) Link_committed over \(\mathcal{L} \times \mathcal{T}\) — a committable link that stands in the snapshot's period — every unit-commitment row's set
\(\mathrm{Process\_com\_ext}\) Process_com_ext over \(\mathcal{J} \times \mathcal{T}\) — a committable process with an extendable, non-modular build that stands in the snapshot's period — PyPSA's com-ext rows, whose status is relaxed against the chosen build
\(\mathrm{Process\_maint\_ext}\) Process_maint_ext over \(\mathcal{J} \times \mathcal{T}\) — a maintainable process with an extendable build, unless it is committable and modular, that stands in the snapshot's period — the maintenance rows against the chosen build
\(\mathrm{Process\_committed}\) Process_committed over \(\mathcal{J} \times \mathcal{T}\) — a committable process that stands in the snapshot's period — every unit-commitment row's set

Variables

Symbol Meaning
\(p\) Generator_p over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — Generator-p — output of a generator in a snapshot
\(f\) Link_p over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — 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
\(z\) Process_p over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — 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
\(N\) Generator_n_mod over \(\mathcal{G}\) — Generator-n_mod — how many modules of an extendable modular build; none for a unit that is not active
\(u\) Generator_status over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — Generator-status — how much of a committable unit is on: an integer the rows below cap at one, or at the module count where the build is modular
\(\mathit{up}\) Generator_start_up over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — Generator-start_up — how much of a committable unit turns on this snapshot, capped as the status is
\(\mathit{dn}\) Generator_shut_down over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — Generator-shut_down — how much of a committable unit turns off this snapshot, capped as the status is
\(\mu\) Generator_maintenance over \(\Xi \times \mathcal{T} \times \mathcal{G}\), \(0\) where the mask leaves it out — Generator-maintenance — whether a maintainable generator is in maintenance: continuous, and one exactly where an event covers the snapshot
\(\mu^{\mathrm{up}}\) Generator_maintenance_start over \(\Xi \times \mathcal{T} \times \mathcal{G}\), \(0\) where the mask leaves it out — Generator-maintenance_start — whether a maintenance event starts in this snapshot
\(\mu^{\mathrm{nom}}\) Generator_maintenance_capacity over \(\Xi \times \mathcal{T} \times \mathcal{G}\), \(0\) where the mask leaves it out — Generator-maintenance_capacity — the chosen build while in maintenance, zero otherwise: the product the maintcap rows linearize
\(\mu^{u}\) Generator_maintenance_status over \(\Xi \times \mathcal{T} \times \mathcal{G}\), \(0\) where the mask leaves it out — Generator-maintenance_status — the status while in maintenance, zero otherwise: the product the maint-status rows linearize, so a unit in maintenance may also be off
\(N^{f}\) Link_n_mod over \(\mathcal{L}\) — Link-n_mod — how many modules of an extendable modular build; none for a unit that is not active
\(u^{f}\) Link_status over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-status — how much of a committable link is on: an integer the rows below cap at one, or at the module count where the build is modular
\(\mathit{up}^{f}\) Link_start_up over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-start_up — how much of a committable link turns on this snapshot, capped as the status is
\(\mathit{dn}^{f}\) Link_shut_down over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-shut_down — how much of a committable link turns off this snapshot, capped as the status is
\(\mu^{f}\) Link_maintenance over \(\Xi \times \mathcal{T} \times \mathcal{L}\), \(0\) where the mask leaves it out — Link-maintenance — whether a maintainable link is in maintenance: continuous, and one exactly where an event covers the snapshot
\(\mu^{f,\mathrm{up}}\) Link_maintenance_start over \(\Xi \times \mathcal{T} \times \mathcal{L}\), \(0\) where the mask leaves it out — Link-maintenance_start — whether a maintenance event starts in this snapshot
\(\mu^{f,\mathrm{nom}}\) Link_maintenance_capacity over \(\Xi \times \mathcal{T} \times \mathcal{L}\), \(0\) where the mask leaves it out — Link-maintenance_capacity — the chosen build while in maintenance, zero otherwise: the product the maintcap rows linearize
\(\mu^{f,u}\) Link_maintenance_status over \(\Xi \times \mathcal{T} \times \mathcal{L}\), \(0\) where the mask leaves it out — Link-maintenance_status — the status while in maintenance, zero otherwise: the product the maint-status rows linearize, so a unit in maintenance may also be off
\(N^{z}\) Process_n_mod over \(\mathcal{J}\) — Process-n_mod — how many modules of an extendable modular build; none for a unit that is not active
\(u^{z}\) Process_status over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — 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
\(\mathit{up}^{z}\) Process_start_up over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — Process-start_up — how much of a committable process turns on this snapshot, capped as the status is
\(\mathit{dn}^{z}\) Process_shut_down over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — Process-shut_down — how much of a committable process turns off this snapshot, capped as the status is
\(\mu^{z}\) Process_maintenance over \(\Xi \times \mathcal{T} \times \mathcal{J}\), \(0\) where the mask leaves it out — Process-maintenance — whether a maintainable process is in maintenance: continuous, and one exactly where an event covers the snapshot
\(\mu^{z,\mathrm{up}}\) Process_maintenance_start over \(\Xi \times \mathcal{T} \times \mathcal{J}\), \(0\) where the mask leaves it out — Process-maintenance_start — whether a maintenance event starts in this snapshot
\(\mu^{z,\mathrm{nom}}\) Process_maintenance_capacity over \(\Xi \times \mathcal{T} \times \mathcal{J}\), \(0\) where the mask leaves it out — Process-maintenance_capacity — the chosen build while in maintenance, zero otherwise: the product the maintcap rows linearize
\(\mu^{z,u}\) Process_maintenance_status over \(\Xi \times \mathcal{T} \times \mathcal{J}\), \(0\) where the mask leaves it out — Process-maintenance_status — the status while in maintenance, zero otherwise: the product the maint-status rows linearize, so a unit in maintenance may also be off
\(P\) Generator_p_nom_ext over \(\mathcal{G}\) — Generator-p_nom — nominal power where it is a decision, for a generator that is active; the parameter of the same PyPSA name carries the fixed regime
\(F\) Link_p_nom_ext over \(\mathcal{L}\) — Link-p_nom — nominal power where it is a decision, for a link that is active; the parameter of the same PyPSA name carries the fixed regime
\(Z\) Process_p_nom_ext over \(\mathcal{J}\) — Process-p_nom — nominal internal power where it is a decision, for a process that is active; the parameter of the same PyPSA name carries the fixed regime

Definitions

Symbol Meaning
\(\mathit{Generator\_previous\_status}\) Generator_previous_status over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — the commitment state a generator carries into a snapshot — off at the first snapshot it stands in past the first of the horizon, as PyPSA reads a status it did not build (constraints.py:298), and the state carried over otherwise
\(\mathit{Generator\_status\_carried\_over}\) Generator_status_carried_over over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — the state a generator carries over into a snapshot — the state it brought into the horizon at the first, the previous snapshot's after that
\(\mathit{Link\_previous\_status}\) Link_previous_status over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — the commitment state a link carries into a snapshot — off at the first snapshot it stands in past the first of the horizon, as PyPSA reads a status it did not build (constraints.py:298), and the state carried over otherwise
\(\mathit{Link\_status\_carried\_over}\) Link_status_carried_over over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — the state a link carries over into a snapshot — the state it brought into the horizon at the first, the previous snapshot's after that
\(\mathit{Process\_previous\_status}\) Process_previous_status over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — the commitment state a process carries into a snapshot — off at the first snapshot it stands in past the first of the horizon, as PyPSA reads a status it did not build (constraints.py:298), and the state carried over otherwise
\(\mathit{Process\_status\_carried\_over}\) Process_status_carried_over over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — the state a process carries over into a snapshot — the state it brought into the horizon at the first, the previous snapshot's after that
\(\mathit{Link\_output\_arrival}\) Link_output_arrival over \(\Xi \times \mathcal{T} \times \mathcal{O}\) — 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
\(\mathit{Process\_output\_arrival}\) Process_output_arrival over \(\Xi \times \mathcal{T} \times \mathcal{R}\) — 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
\(\mathit{Generator\_opex}\) Generator_opex over \(\Xi\)
\(\mathit{Generator\_commitment\_opex}\) Generator_commitment_opex over \(\Xi\)
\(\mathit{Link\_opex}\) Link_opex over \(\Xi\)
\(\mathit{Link\_commitment\_opex}\) Link_commitment_opex over \(\Xi\)
\(\mathit{Process\_opex}\) Process_opex over \(\Xi\)
\(\mathit{Process\_commitment\_opex}\) Process_commitment_opex over \(\Xi\)
\(\mathit{scenario\_opex}\) scenario_opex over \(\Xi\) — 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)
\(\mathit{Generator\_capex}\) Generator_capex (scalar)
\(\mathit{Link\_capex}\) Link_capex (scalar)
\(\mathit{Process\_capex}\) Process_capex (scalar)
\(\mathit{risk\_weighted\_opex}\) risk_weighted_opex (scalar)
\(\mathit{total\_cost}\) total_cost (scalar) — 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
\(\mathrm{Load\_demand}\) Load_demand over \(\Xi \times \mathcal{T} \times \mathcal{D}\) — 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)
\(\mathit{Generator\_injection}\) Generator_injection over \(\mathcal{N} \times \Xi \times \mathcal{T}\)
\(\mathit{Link\_injection}\) Link_injection over \(\mathcal{N} \times \Xi \times \mathcal{T}\)
\(\mathrm{Load\_injection}\) Load_injection over \(\mathcal{N} \times \Xi \times \mathcal{T}\)
\(\mathit{Process\_injection}\) Process_injection over \(\mathcal{N} \times \Xi \times \mathcal{T}\)
\(\mathit{Bus\_injection}\) Bus_injection over \(\Xi \times \mathcal{T} \times \mathcal{N}\) — 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

Notation

Symbol Meaning
\(t \ominus k\) edge='wrap' — \(t-k\), cyclic
\(t \boxminus_{v} k\) edge=v — \(t-k\), and \(v\) past the edge
\(t \ominus^{\mathrm{property}(t)} k\) within=subject[...] — \(t-k\) inside the group of \(t\)
\(\mathrm{pos}(t)\) position() — the position of \(t\), counted from \(0\); \(t\) is the label

Conditions

Generator_com_ext

\[ \mathrm{Generator\_com\_ext}_{g,t} \iff \mathrm{com}_{g} \wedge \mathrm{ext}_{g} \wedge \neg \left( \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \wedge \mathrm{on}_{t,g} \qquad \forall\, g \in \mathcal{G},\ t \in \mathcal{T} \]

Generator_maint_ext

\[ \mathrm{Generator\_maint\_ext}_{g,t} \iff \mathrm{mnt}_{g} \wedge \mathrm{ext}_{g} \wedge \neg \left( \mathrm{com}_{g} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \wedge \mathrm{on}_{t,g} \qquad \forall\, g \in \mathcal{G},\ t \in \mathcal{T} \]

Generator_committed

\[ \mathrm{Generator\_committed}_{g,t} \iff \mathrm{com}_{g} \wedge \mathrm{on}_{t,g} \qquad \forall\, g \in \mathcal{G},\ t \in \mathcal{T} \]

Link_com_ext

\[ \mathrm{Link\_com\_ext}_{l,t} \iff \mathrm{com}^{f}_{l} \wedge \mathrm{ext}^{f}_{l} \wedge \neg \left( \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right) \wedge \mathrm{on}^{f}_{t,l} \qquad \forall\, l \in \mathcal{L},\ t \in \mathcal{T} \]

Link_maint_ext

\[ \mathrm{Link\_maint\_ext}_{l,t} \iff \mathrm{mnt}^{f}_{l} \wedge \mathrm{ext}^{f}_{l} \wedge \neg \left( \mathrm{com}^{f}_{l} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right) \wedge \mathrm{on}^{f}_{t,l} \qquad \forall\, l \in \mathcal{L},\ t \in \mathcal{T} \]

Link_committed

\[ \mathrm{Link\_committed}_{l,t} \iff \mathrm{com}^{f}_{l} \wedge \mathrm{on}^{f}_{t,l} \qquad \forall\, l \in \mathcal{L},\ t \in \mathcal{T} \]

Process_com_ext

\[ \mathrm{Process\_com\_ext}_{j,t} \iff \mathrm{com}^{z}_{j} \wedge \mathrm{ext}^{z}_{j} \wedge \neg \left( \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right) \wedge \mathrm{on}^{z}_{t,j} \qquad \forall\, j \in \mathcal{J},\ t \in \mathcal{T} \]

Process_maint_ext

\[ \mathrm{Process\_maint\_ext}_{j,t} \iff \mathrm{mnt}^{z}_{j} \wedge \mathrm{ext}^{z}_{j} \wedge \neg \left( \mathrm{com}^{z}_{j} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right) \wedge \mathrm{on}^{z}_{t,j} \qquad \forall\, j \in \mathcal{J},\ t \in \mathcal{T} \]

Process_committed

\[ \mathrm{Process\_committed}_{j,t} \iff \mathrm{com}^{z}_{j} \wedge \mathrm{on}^{z}_{t,j} \qquad \forall\, j \in \mathcal{J},\ t \in \mathcal{T} \]

Variable domains

Generator_p

\[ p_{\xi,t,g} \in \mathbb{R} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{on}_{t,g} \]

Link_p

\[ f_{\xi,t,l} \in \mathbb{R} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{on}^{f}_{t,l} \]

Process_p

\[ z_{\xi,t,j} \in \mathbb{R} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{on}^{z}_{t,j} \]

Generator_n_mod

\[ N_{g} \ge 0, N_{g} \in \mathbb{Z} \qquad \forall\, g \in \mathcal{G} \,:\, \mathrm{ext}_{g} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \wedge \mathrm{act}_{g} \]

Generator_status

\[ u_{\xi,t,g} \ge 0, u_{\xi,t,g} \in \mathbb{Z} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \]

Generator_start_up

\[ \mathit{up}_{\xi,t,g} \ge 0, \mathit{up}_{\xi,t,g} \in \mathbb{Z} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \]

Generator_shut_down

\[ \mathit{dn}_{\xi,t,g} \ge 0, \mathit{dn}_{\xi,t,g} \in \mathbb{Z} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \]

Generator_maintenance

\[ 0 \le \mu_{\xi,t,g} \le 1 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}_{t,g} \]

Generator_maintenance_start

\[ \mu^{\mathrm{up}}_{\xi,t,g} \in \{0, 1\} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}_{t,g} \]

Generator_maintenance_capacity

\[ \mu^{\mathrm{nom}}_{\xi,t,g} \ge 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_maint\_ext}_{g,t} \]

Generator_maintenance_status

\[ \mu^{u}_{\xi,t,g} \ge 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{Generator\_committed}_{g,t} \wedge \neg \left( \mathrm{ext}_{g} \wedge \neg \left( \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \right) \]

Link_n_mod

\[ N^{f}_{l} \ge 0, N^{f}_{l} \in \mathbb{Z} \qquad \forall\, l \in \mathcal{L} \,:\, \mathrm{ext}^{f}_{l} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \wedge \mathrm{act}^{f}_{l} \]

Link_status

\[ u^{f}_{\xi,t,l} \ge 0, u^{f}_{\xi,t,l} \in \mathbb{Z} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \]

Link_start_up

\[ \mathit{up}^{f}_{\xi,t,l} \ge 0, \mathit{up}^{f}_{\xi,t,l} \in \mathbb{Z} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \]

Link_shut_down

\[ \mathit{dn}^{f}_{\xi,t,l} \ge 0, \mathit{dn}^{f}_{\xi,t,l} \in \mathbb{Z} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \]

Link_maintenance

\[ 0 \le \mu^{f}_{\xi,t,l} \le 1 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{mnt}^{f}_{l} \wedge \mathrm{on}^{f}_{t,l} \]

Link_maintenance_start

\[ \mu^{f,\mathrm{up}}_{\xi,t,l} \in \{0, 1\} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{mnt}^{f}_{l} \wedge \mathrm{on}^{f}_{t,l} \]

Link_maintenance_capacity

\[ \mu^{f,\mathrm{nom}}_{\xi,t,l} \ge 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_maint\_ext}_{l,t} \]

Link_maintenance_status

\[ \mu^{f,u}_{\xi,t,l} \ge 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{mnt}^{f}_{l} \wedge \mathrm{Link\_committed}_{l,t} \wedge \neg \left( \mathrm{ext}^{f}_{l} \wedge \neg \left( \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right) \right) \]

Process_n_mod

\[ N^{z}_{j} \ge 0, N^{z}_{j} \in \mathbb{Z} \qquad \forall\, j \in \mathcal{J} \,:\, \mathrm{ext}^{z}_{j} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \wedge \mathrm{act}^{z}_{j} \]

Process_status

\[ u^{z}_{\xi,t,j} \ge 0, u^{z}_{\xi,t,j} \in \mathbb{Z} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \]

Process_start_up

\[ \mathit{up}^{z}_{\xi,t,j} \ge 0, \mathit{up}^{z}_{\xi,t,j} \in \mathbb{Z} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \]

Process_shut_down

\[ \mathit{dn}^{z}_{\xi,t,j} \ge 0, \mathit{dn}^{z}_{\xi,t,j} \in \mathbb{Z} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \]

Process_maintenance

\[ 0 \le \mu^{z}_{\xi,t,j} \le 1 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{mnt}^{z}_{j} \wedge \mathrm{on}^{z}_{t,j} \]

Process_maintenance_start

\[ \mu^{z,\mathrm{up}}_{\xi,t,j} \in \{0, 1\} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{mnt}^{z}_{j} \wedge \mathrm{on}^{z}_{t,j} \]

Process_maintenance_capacity

\[ \mu^{z,\mathrm{nom}}_{\xi,t,j} \ge 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_maint\_ext}_{j,t} \]

Process_maintenance_status

\[ \mu^{z,u}_{\xi,t,j} \ge 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{mnt}^{z}_{j} \wedge \mathrm{Process\_committed}_{j,t} \wedge \neg \left( \mathrm{ext}^{z}_{j} \wedge \neg \left( \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right) \right) \]

Generator_p_nom_ext

\[ P_{g} \in \mathbb{R} \qquad \forall\, g \in \mathcal{G} \,:\, \mathrm{ext}_{g} \wedge \mathrm{act}_{g} \]

Link_p_nom_ext

\[ F_{l} \in \mathbb{R} \qquad \forall\, l \in \mathcal{L} \,:\, \mathrm{ext}^{f}_{l} \wedge \mathrm{act}^{f}_{l} \]

Process_p_nom_ext

\[ Z_{j} \in \mathbb{R} \qquad \forall\, j \in \mathcal{J} \,:\, \mathrm{ext}^{z}_{j} \wedge \mathrm{act}^{z}_{j} \]

Definitions

Generator_previous_status

\[ \mathit{Generator\_previous\_status}_{\xi,t,g} = \begin{cases} 0 & \text{if } \mathrm{pos}(t) > 0 \wedge \neg \mathrm{on}_{t - 1,g} \\ \mathit{Generator\_status\_carried\_over}_{\xi,t,g} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \]

Generator_status_carried_over

\[ \mathit{Generator\_status\_carried\_over}_{\xi,t,g} = \begin{cases} \mathrm{u}^{0}_{\xi,g} & \text{if } \mathrm{pos}(t) = 0 \\ u_{\xi,t - 1,g} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \]

Link_previous_status

\[ \mathit{Link\_previous\_status}_{\xi,t,l} = \begin{cases} 0 & \text{if } \mathrm{pos}(t) > 0 \wedge \neg \mathrm{on}^{f}_{t - 1,l} \\ \mathit{Link\_status\_carried\_over}_{\xi,t,l} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \]

Link_status_carried_over

\[ \mathit{Link\_status\_carried\_over}_{\xi,t,l} = \begin{cases} \mathrm{u}^{f,0}_{\xi,l} & \text{if } \mathrm{pos}(t) = 0 \\ u^{f}_{\xi,t - 1,l} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \]

Process_previous_status

\[ \mathit{Process\_previous\_status}_{\xi,t,j} = \begin{cases} 0 & \text{if } \mathrm{pos}(t) > 0 \wedge \neg \mathrm{on}^{z}_{t - 1,j} \\ \mathit{Process\_status\_carried\_over}_{\xi,t,j} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \]

Process_status_carried_over

\[ \mathit{Process\_status\_carried\_over}_{\xi,t,j} = \begin{cases} \mathrm{u}^{z,0}_{\xi,j} & \text{if } \mathrm{pos}(t) = 0 \\ u^{z}_{\xi,t - 1,j} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \]

Link_output_arrival

\[ \mathit{Link\_output\_arrival}_{\xi,t,o} = \begin{cases} f_{\xi,t \ominus^{\mathrm{period}(t)} \mathrm{d}^{f},\mathrm{link}(o)} \cdot \eta_{\xi,t,o} & \text{if } \mathrm{cyc}^{f}_{o} \\ f_{\xi,t \boxminus_{0}^{\mathrm{period}(t)} \mathrm{d}^{f},\mathrm{link}(o)} \cdot \eta_{\xi,t,o} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ o \in \mathcal{O} \]

Process_output_arrival

\[ \mathit{Process\_output\_arrival}_{\xi,t,r} = \begin{cases} z_{\xi,t \ominus^{\mathrm{period}(t)} \mathrm{d}^{z},\mathrm{process}(r)} \cdot \alpha_{\xi,t,r} & \text{if } \mathrm{cyc}^{z}_{r} \\ z_{\xi,t \boxminus_{0}^{\mathrm{period}(t)} \mathrm{d}^{z},\mathrm{process}(r)} \cdot \alpha_{\xi,t,r} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ r \in \mathcal{R} \]

Generator_opex

\[ \mathit{Generator\_opex}_{\xi} = \sum_{t \in \mathcal{T}} \sum_{g \in \mathcal{G}} p_{\xi,t,g} \cdot \mathrm{c}_{\xi,t,g} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{period}(t)} + \sum_{t \in \mathcal{T}} \sum_{g \in \mathcal{G}} p_{\xi,t,g} \cdot p_{\xi,t,g} \cdot \mathrm{c}^{(2)}_{\xi,t,g} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{period}(t)} \qquad \forall\, \xi \in \Xi \]

Generator_commitment_opex

\[ \mathit{Generator\_commitment\_opex}_{\xi} = \sum_{t \in \mathcal{T}} \sum_{g \in \mathcal{G}} u_{\xi,t,g} \cdot \mathrm{c}^{\mathrm{on}}_{\xi,t,g} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{period}(t)} + \sum_{t \in \mathcal{T}} \sum_{g \in \mathcal{G}} \mathit{up}_{\xi,t,g} \cdot \mathrm{c}^{\mathrm{up}}_{\xi,t,g} + \sum_{t \in \mathcal{T}} \sum_{g \in \mathcal{G}} \mathit{dn}_{\xi,t,g} \cdot \mathrm{c}^{\mathrm{dn}}_{\xi,t,g} \qquad \forall\, \xi \in \Xi \]

Link_opex

\[ \mathit{Link\_opex}_{\xi} = \sum_{t \in \mathcal{T}} \sum_{l \in \mathcal{L}} f_{\xi,t,l} \cdot \mathrm{c}^{f}_{\xi,t,l} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{period}(t)} + \sum_{t \in \mathcal{T}} \sum_{l \in \mathcal{L}} f_{\xi,t,l} \cdot f_{\xi,t,l} \cdot \mathrm{c}^{f,(2)}_{\xi,t,l} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{period}(t)} \qquad \forall\, \xi \in \Xi \]

Link_commitment_opex

\[ \mathit{Link\_commitment\_opex}_{\xi} = \sum_{t \in \mathcal{T}} \sum_{l \in \mathcal{L}} u^{f}_{\xi,t,l} \cdot \mathrm{c}^{f,\mathrm{on}}_{\xi,t,l} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{period}(t)} + \sum_{t \in \mathcal{T}} \sum_{l \in \mathcal{L}} \mathit{up}^{f}_{\xi,t,l} \cdot \mathrm{c}^{f,\mathrm{up}}_{\xi,t,l} + \sum_{t \in \mathcal{T}} \sum_{l \in \mathcal{L}} \mathit{dn}^{f}_{\xi,t,l} \cdot \mathrm{c}^{f,\mathrm{dn}}_{\xi,t,l} \qquad \forall\, \xi \in \Xi \]

Process_opex

\[ \mathit{Process\_opex}_{\xi} = \sum_{t \in \mathcal{T}} \sum_{j \in \mathcal{J}} z_{\xi,t,j} \cdot \mathrm{c}^{z}_{\xi,t,j} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{period}(t)} + \sum_{t \in \mathcal{T}} \sum_{j \in \mathcal{J}} z_{\xi,t,j} \cdot z_{\xi,t,j} \cdot \mathrm{c}^{z,(2)}_{\xi,t,j} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{period}(t)} \qquad \forall\, \xi \in \Xi \]

Process_commitment_opex

\[ \mathit{Process\_commitment\_opex}_{\xi} = \sum_{t \in \mathcal{T}} \sum_{j \in \mathcal{J}} u^{z}_{\xi,t,j} \cdot \mathrm{c}^{z,\mathrm{on}}_{\xi,t,j} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{period}(t)} + \sum_{t \in \mathcal{T}} \sum_{j \in \mathcal{J}} \mathit{up}^{z}_{\xi,t,j} \cdot \mathrm{c}^{z,\mathrm{up}}_{\xi,t,j} + \sum_{t \in \mathcal{T}} \sum_{j \in \mathcal{J}} \mathit{dn}^{z}_{\xi,t,j} \cdot \mathrm{c}^{z,\mathrm{dn}}_{\xi,t,j} \qquad \forall\, \xi \in \Xi \]

scenario_opex

\[ \mathit{scenario\_opex}_{\xi} = \mathit{Generator\_opex}_{\xi} + \mathit{Generator\_commitment\_opex}_{\xi} + \mathit{Link\_opex}_{\xi} + \mathit{Link\_commitment\_opex}_{\xi} + \mathit{Process\_opex}_{\xi} + \mathit{Process\_commitment\_opex}_{\xi} \qquad \forall\, \xi \in \Xi \]

Generator_capex

\[ \mathit{Generator\_capex} = \sum_{\xi \in \Xi,\ g \in \mathcal{G}} \pi_{\xi} \cdot P_{g} \cdot \mathrm{c}^{\mathrm{cap}}_{\xi,g} \cdot \mathrm{W}_{g} \]

Link_capex

\[ \mathit{Link\_capex} = \sum_{\xi \in \Xi,\ l \in \mathcal{L}} \pi_{\xi} \cdot F_{l} \cdot \mathrm{c}^{\mathrm{cap},f}_{\xi,l} \cdot \mathrm{W}^{f}_{l} \]

Process_capex

\[ \mathit{Process\_capex} = \sum_{\xi \in \Xi,\ j \in \mathcal{J}} \pi_{\xi} \cdot Z_{j} \cdot \mathrm{c}^{\mathrm{cap},z}_{\xi,j} \cdot \mathrm{W}^{z}_{j} \]

risk_weighted_opex

\[ \mathit{risk\_weighted\_opex} = \sum_{\xi \in \Xi} \pi_{\xi} \cdot \mathit{scenario\_opex}_{\xi} \]

total_cost

\[ \mathit{total\_cost} = \mathit{Generator\_capex} + \mathit{Link\_capex} + \mathit{Process\_capex} + \mathit{risk\_weighted\_opex} \]

Load_demand

\[ \mathrm{Load\_demand}_{\xi,t,d} = \begin{cases} \mathrm{sgn}^{\mathrm{load}}_{d} \cdot \mathrm{load}_{\xi,t,d} & \text{if } \mathrm{on}^{\mathrm{load}}_{d} \\ 0 & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ d \in \mathcal{D} \]

Generator_injection

\[ \mathit{Generator\_injection}_{n,\xi,t} = \sum_{g \in \mathcal{G} \,:\, \mathrm{bus}(g) = n} \mathrm{sgn}_{g} \cdot p_{\xi,t,g} \qquad \forall\, n \in \mathcal{N},\ \xi \in \Xi,\ t \in \mathcal{T} \]

Link_injection

\[ \mathit{Link\_injection}_{n,\xi,t} = -\left( \sum_{l \in \mathcal{L} \,:\, \mathrm{bus0}(l) = n} f_{\xi,t,l} \right) + \sum_{o \in \mathcal{O} \,:\, \mathrm{bus}(o) = n} \mathit{Link\_output\_arrival}_{\xi,t,o} \qquad \forall\, n \in \mathcal{N},\ \xi \in \Xi,\ t \in \mathcal{T} \]

Load_injection

\[ \mathrm{Load\_injection}_{n,\xi,t} = \sum_{d \in \mathcal{D} \,:\, \mathrm{bus}(d) = n} \mathrm{Load\_demand}_{\xi,t,d} \qquad \forall\, n \in \mathcal{N},\ \xi \in \Xi,\ t \in \mathcal{T} \]

Process_injection

\[ \mathit{Process\_injection}_{n,\xi,t} = \sum_{r \in \mathcal{R} \,:\, \mathrm{bus}(r) = n} \mathit{Process\_output\_arrival}_{\xi,t,r} \qquad \forall\, n \in \mathcal{N},\ \xi \in \Xi,\ t \in \mathcal{T} \]

Bus_injection

\[ \mathit{Bus\_injection}_{\xi,t,n} = \mathit{Generator\_injection}_{n,\xi,t} + \mathit{Link\_injection}_{n,\xi,t} + \mathrm{Load\_injection}_{n,\xi,t} + \mathit{Process\_injection}_{n,\xi,t} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ n \in \mathcal{N} \]

Objective

\[ \min \mathit{total\_cost} \]

Subject to

Generator_fix_p_lower

\[ p_{\xi,t,g} \ge \underline{\mathrm{p}}_{\xi,t,g} \cdot \mathrm{p}^{\mathrm{nom}}_{\xi,g} \cdot \left( 1 - \gamma_{\xi,g} \cdot \mu_{\xi,t,g} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \neg \mathrm{ext}_{g} \wedge \neg \mathrm{com}_{g} \wedge \mathrm{on}_{t,g} \]

Generator_fix_p_upper

\[ p_{\xi,t,g} \le \overline{\mathrm{p}}_{\xi,t,g} \cdot \mathrm{p}^{\mathrm{nom}}_{\xi,g} \cdot \left( 1 - \gamma_{\xi,g} \cdot \mu_{\xi,t,g} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \neg \mathrm{ext}_{g} \wedge \neg \mathrm{com}_{g} \wedge \mathrm{on}_{t,g} \]

Link_fix_p_lower

\[ f_{\xi,t,l} \ge \underline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \cdot \left( 1 - \gamma^{f}_{\xi,l} \cdot \mu^{f}_{\xi,t,l} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \neg \mathrm{ext}^{f}_{l} \wedge \neg \mathrm{com}^{f}_{l} \wedge \mathrm{on}^{f}_{t,l} \]

Link_fix_p_upper

\[ f_{\xi,t,l} \le \overline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \cdot \left( 1 - \gamma^{f}_{\xi,l} \cdot \mu^{f}_{\xi,t,l} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \neg \mathrm{ext}^{f}_{l} \wedge \neg \mathrm{com}^{f}_{l} \wedge \mathrm{on}^{f}_{t,l} \]

Generator_ext_p_nom_lower

\[ P_{g} \ge \underline{\mathrm{p}}^{\mathrm{nom}}_{\xi,g} \qquad \forall\, \xi \in \Xi,\ g \in \mathcal{G} \,:\, \mathrm{ext}_{g} \wedge \mathrm{act}_{g} \]

Generator_ext_p_nom_upper

\[ P_{g} \le \overline{\mathrm{p}}^{\mathrm{nom}}_{\xi,g} \qquad \forall\, \xi \in \Xi,\ g \in \mathcal{G} \,:\, \mathrm{ext}_{g} \wedge \mathrm{act}_{g} \wedge \overline{\mathrm{p}}^{\mathrm{nom}}_{\xi,g} \text{ is defined} \]

Link_ext_p_nom_lower

\[ F_{l} \ge \underline{\mathrm{f}}^{\mathrm{nom}}_{\xi,l} \qquad \forall\, \xi \in \Xi,\ l \in \mathcal{L} \,:\, \mathrm{ext}^{f}_{l} \wedge \mathrm{act}^{f}_{l} \]

Link_ext_p_nom_upper

\[ F_{l} \le \overline{\mathrm{f}}^{\mathrm{nom}}_{\xi,l} \qquad \forall\, \xi \in \Xi,\ l \in \mathcal{L} \,:\, \mathrm{ext}^{f}_{l} \wedge \mathrm{act}^{f}_{l} \wedge \overline{\mathrm{f}}^{\mathrm{nom}}_{\xi,l} \text{ is defined} \]

Process_ext_p_nom_lower

\[ Z_{j} \ge \underline{\mathrm{z}}^{\mathrm{nom}}_{\xi,j} \qquad \forall\, \xi \in \Xi,\ j \in \mathcal{J} \,:\, \mathrm{ext}^{z}_{j} \wedge \mathrm{act}^{z}_{j} \]

Process_ext_p_nom_upper

\[ Z_{j} \le \overline{\mathrm{z}}^{\mathrm{nom}}_{\xi,j} \qquad \forall\, \xi \in \Xi,\ j \in \mathcal{J} \,:\, \mathrm{ext}^{z}_{j} \wedge \mathrm{act}^{z}_{j} \wedge \overline{\mathrm{z}}^{\mathrm{nom}}_{\xi,j} \text{ is defined} \]

Generator_com_p_lower

\[ p_{\xi,t,g} \ge \underline{\mathrm{p}}_{\xi,t,g} \cdot \mathrm{p}^{\mathrm{nom}}_{\xi,g} \cdot \left( u_{\xi,t,g} - \gamma_{\xi,g} \cdot \mu^{u}_{\xi,t,g} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \wedge \neg \mathrm{ext}_{g} \wedge \neg \left( \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \]

Generator_com_p_upper

\[ p_{\xi,t,g} \le \overline{\mathrm{p}}_{\xi,t,g} \cdot \mathrm{p}^{\mathrm{nom}}_{\xi,g} \cdot \left( u_{\xi,t,g} - \gamma_{\xi,g} \cdot \mu^{u}_{\xi,t,g} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \wedge \neg \mathrm{ext}_{g} \wedge \neg \left( \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \]

Generator_com_transition_start_up

\[ \mathit{up}_{\xi,t,g} \ge u_{\xi,t,g} - \mathit{Generator\_previous\_status}_{\xi,t,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \]

Generator_com_transition_shut_down

\[ \mathit{dn}_{\xi,t,g} \ge \mathit{Generator\_previous\_status}_{\xi,t,g} - u_{\xi,t,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \]

Generator_p_nom_modularity

\[ P_{g} = \mathrm{p}^{\mathrm{mod}}_{g} \cdot N_{g} \qquad \forall\, g \in \mathcal{G} \,:\, \mathrm{ext}_{g} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \wedge \mathrm{act}_{g} \]

Generator_com_ext_p_upper_cap

\[ p_{\xi,t,g} \le \overline{\mathrm{p}}_{\xi,t,g} \cdot \left( P_{g} - \gamma_{\xi,g} \cdot \mu^{\mathrm{nom}}_{\xi,t,g} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_com\_ext}_{g,t} \]

Generator_com_ext_p_upper_big_m

\[ p_{\xi,t,g} \le \mathrm{M}_{\xi,g} \cdot u_{\xi,t,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_com\_ext}_{g,t} \]

Generator_com_ext_p_lower

\[ p_{\xi,t,g} \ge \underline{\mathrm{p}}_{\xi,t,g} \cdot \left( P_{g} - \gamma_{\xi,g} \cdot \mu^{\mathrm{nom}}_{\xi,t,g} \right) + \mathrm{M}_{\xi,g} \cdot u_{\xi,t,g} - \mathrm{M}_{\xi,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_com\_ext}_{g,t} \]

Generator_com_ext_p_lower_nonneg

\[ p_{\xi,t,g} \ge 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_com\_ext}_{g,t} \wedge \mathrm{nonneg}_{g} \]

Generator_com_mod_p_lower

\[ p_{\xi,t,g} \ge \underline{\mathrm{p}}_{\xi,t,g} \cdot \mathrm{p}^{\mathrm{mod}}_{g} \cdot \left( u_{\xi,t,g} - \gamma_{\xi,g} \cdot \mu^{u}_{\xi,t,g} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \]

Generator_com_mod_p_upper

\[ p_{\xi,t,g} \le \overline{\mathrm{p}}_{\xi,t,g} \cdot \mathrm{p}^{\mathrm{mod}}_{g} \cdot \left( u_{\xi,t,g} - \gamma_{\xi,g} \cdot \mu^{u}_{\xi,t,g} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \]

Generator_status_p_fixed_upper

\[ u_{\xi,t,g} \le \mathrm{N}^{\mathrm{fix}}_{\xi,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \wedge \neg \left( \mathrm{ext}_{g} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \]

Generator_start_up_p_fixed_upper

\[ \mathit{up}_{\xi,t,g} \le \mathrm{N}^{\mathrm{fix}}_{\xi,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \wedge \neg \left( \mathrm{ext}_{g} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \]

Generator_shut_down_p_fixed_upper

\[ \mathit{dn}_{\xi,t,g} \le \mathrm{N}^{\mathrm{fix}}_{\xi,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \wedge \neg \left( \mathrm{ext}_{g} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \]

Generator_status_p_nom_variable_upper

\[ u_{\xi,t,g} \le N_{g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \wedge \mathrm{ext}_{g} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \]

Generator_start_up_p_nom_variable_upper

\[ \mathit{up}_{\xi,t,g} \le N_{g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \wedge \mathrm{ext}_{g} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \]

Generator_shut_down_p_nom_variable_upper

\[ \mathit{dn}_{\xi,t,g} \le N_{g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_committed}_{g,t} \wedge \mathrm{ext}_{g} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \]

Generator_maint_event_count

\[ \sum_{t \in \mathcal{T}} \mu^{\mathrm{up}}_{\xi,t,g} = \mathrm{n}^{\mathrm{mnt}}_{\xi,g} \qquad \forall\, \xi \in \Xi,\ g \in \mathcal{G} \,:\, \mathrm{mnt}_{g} \]

Generator_maint_window

\[ \mu_{\xi,t,g} = \sum_{t' \in \mathcal{T} \,:\, \left( \xi,\ g,\ t',\ t \right) \in \mathrm{Generator\_maintenance\_cover}} \mu^{\mathrm{up}}_{\xi,t',g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}_{t,g} \]

Generator_maint_start_horizon

\[ \mu^{\mathrm{up}}_{\xi,t,g} = 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{on}_{t,g} \wedge \mathrm{blk}_{\xi,t,g} \]

Generator_maintcap_upper

\[ \mu^{\mathrm{nom}}_{\xi,t,g} \le P_{g} - \underline{\mathrm{p}}^{\mathrm{nom}}_{\xi,g} \cdot \left( 1 - \mu_{\xi,t,g} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_maint\_ext}_{g,t} \]

Generator_maintcap_upper_nommax

\[ \mu^{\mathrm{nom}}_{\xi,t,g} \le \overline{\mathrm{p}}^{\mathrm{nom}}_{\xi,g} \cdot \mu_{\xi,t,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_maint\_ext}_{g,t} \]

Generator_maintcap_lower_nommax

\[ \mu^{\mathrm{nom}}_{\xi,t,g} \ge P_{g} - \overline{\mathrm{p}}^{\mathrm{nom}}_{\xi,g} \cdot \left( 1 - \mu_{\xi,t,g} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_maint\_ext}_{g,t} \]

Generator_maintcap_lower_nommin

\[ \mu^{\mathrm{nom}}_{\xi,t,g} \ge \underline{\mathrm{p}}^{\mathrm{nom}}_{\xi,g} \cdot \mu_{\xi,t,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{Generator\_maint\_ext}_{g,t} \wedge \underline{\mathrm{p}}^{\mathrm{nom}}_{\xi,g} > 0 \]

Generator_maint_status_le_status

\[ \mu^{u}_{\xi,t,g} \le u_{\xi,t,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{Generator\_committed}_{g,t} \wedge \neg \mathrm{ext}_{g} \wedge \neg \left( \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \]

Generator_maint_status_le_maint

\[ \mu^{u}_{\xi,t,g} \le \mu_{\xi,t,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{Generator\_committed}_{g,t} \wedge \neg \mathrm{ext}_{g} \wedge \neg \left( \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \]

Generator_maint_status_lb

\[ \mu^{u}_{\xi,t,g} \ge u_{\xi,t,g} + \mu_{\xi,t,g} - 1 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{Generator\_committed}_{g,t} \wedge \neg \mathrm{ext}_{g} \wedge \neg \left( \mathrm{p}^{\mathrm{mod}}_{g} > 0 \right) \]

Generator_maint_modstatus_le_status

\[ \mu^{u}_{\xi,t,g} \le u_{\xi,t,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{Generator\_committed}_{g,t} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \]

Generator_maint_modstatus_le_maint

\[ \mu^{u}_{\xi,t,g} \le \frac{\overline{\mathrm{p}}^{\mathrm{nom}}_{\xi,g}}{\mathrm{p}^{\mathrm{mod}}_{g}} \cdot \mu_{\xi,t,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{Generator\_committed}_{g,t} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \]

Generator_maint_modstatus_lb

\[ \mu^{u}_{\xi,t,g} \ge u_{\xi,t,g} - \frac{\overline{\mathrm{p}}^{\mathrm{nom}}_{\xi,g}}{\mathrm{p}^{\mathrm{mod}}_{g}} \cdot \left( 1 - \mu_{\xi,t,g} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \mathrm{mnt}_{g} \wedge \mathrm{Generator\_committed}_{g,t} \wedge \mathrm{p}^{\mathrm{mod}}_{g} > 0 \]

Link_com_p_lower

\[ f_{\xi,t,l} \ge \underline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \cdot \left( u^{f}_{\xi,t,l} - \gamma^{f}_{\xi,l} \cdot \mu^{f,u}_{\xi,t,l} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \neg \mathrm{ext}^{f}_{l} \wedge \neg \left( \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right) \]

Link_com_p_upper

\[ f_{\xi,t,l} \le \overline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \cdot \left( u^{f}_{\xi,t,l} - \gamma^{f}_{\xi,l} \cdot \mu^{f,u}_{\xi,t,l} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \neg \mathrm{ext}^{f}_{l} \wedge \neg \left( \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right) \]

Link_com_transition_start_up

\[ \mathit{up}^{f}_{\xi,t,l} \ge u^{f}_{\xi,t,l} - \mathit{Link\_previous\_status}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \]

Link_com_transition_shut_down

\[ \mathit{dn}^{f}_{\xi,t,l} \ge \mathit{Link\_previous\_status}_{\xi,t,l} - u^{f}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \]

Link_p_nom_modularity

\[ F_{l} = \mathrm{f}^{\mathrm{mod}}_{l} \cdot N^{f}_{l} \qquad \forall\, l \in \mathcal{L} \,:\, \mathrm{ext}^{f}_{l} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \wedge \mathrm{act}^{f}_{l} \]

Link_com_ext_p_upper_cap

\[ f_{\xi,t,l} \le \overline{\mathrm{f}}_{\xi,t,l} \cdot \left( F_{l} - \gamma^{f}_{\xi,l} \cdot \mu^{f,\mathrm{nom}}_{\xi,t,l} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_com\_ext}_{l,t} \]

Link_com_ext_p_upper_big_m

\[ f_{\xi,t,l} \le \mathrm{M}^{f}_{\xi,l} \cdot u^{f}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_com\_ext}_{l,t} \]

Link_com_ext_p_lower

\[ f_{\xi,t,l} \ge \underline{\mathrm{f}}_{\xi,t,l} \cdot \left( F_{l} - \gamma^{f}_{\xi,l} \cdot \mu^{f,\mathrm{nom}}_{\xi,t,l} \right) + \mathrm{M}^{f}_{\xi,l} \cdot u^{f}_{\xi,t,l} - \mathrm{M}^{f}_{\xi,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_com\_ext}_{l,t} \]

Link_com_ext_p_lower_nonneg

\[ f_{\xi,t,l} \ge 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_com\_ext}_{l,t} \wedge \mathrm{nonneg}^{f}_{l} \]

Link_com_mod_p_lower

\[ f_{\xi,t,l} \ge \underline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{mod}}_{l} \cdot \left( u^{f}_{\xi,t,l} - \gamma^{f}_{\xi,l} \cdot \mu^{f,u}_{\xi,t,l} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \]

Link_com_mod_p_upper

\[ f_{\xi,t,l} \le \overline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{mod}}_{l} \cdot \left( u^{f}_{\xi,t,l} - \gamma^{f}_{\xi,l} \cdot \mu^{f,u}_{\xi,t,l} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \]

Link_status_p_fixed_upper

\[ u^{f}_{\xi,t,l} \le \mathrm{N}^{f,\mathrm{fix}}_{\xi,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \neg \left( \mathrm{ext}^{f}_{l} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right) \]

Link_start_up_p_fixed_upper

\[ \mathit{up}^{f}_{\xi,t,l} \le \mathrm{N}^{f,\mathrm{fix}}_{\xi,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \neg \left( \mathrm{ext}^{f}_{l} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right) \]

Link_shut_down_p_fixed_upper

\[ \mathit{dn}^{f}_{\xi,t,l} \le \mathrm{N}^{f,\mathrm{fix}}_{\xi,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \neg \left( \mathrm{ext}^{f}_{l} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right) \]

Link_status_p_nom_variable_upper

\[ u^{f}_{\xi,t,l} \le N^{f}_{l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \mathrm{ext}^{f}_{l} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \]

Link_start_up_p_nom_variable_upper

\[ \mathit{up}^{f}_{\xi,t,l} \le N^{f}_{l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \mathrm{ext}^{f}_{l} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \]

Link_shut_down_p_nom_variable_upper

\[ \mathit{dn}^{f}_{\xi,t,l} \le N^{f}_{l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \mathrm{ext}^{f}_{l} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \]

Link_maint_event_count

\[ \sum_{t \in \mathcal{T}} \mu^{f,\mathrm{up}}_{\xi,t,l} = \mathrm{n}^{f,\mathrm{mnt}}_{\xi,l} \qquad \forall\, \xi \in \Xi,\ l \in \mathcal{L} \,:\, \mathrm{mnt}^{f}_{l} \]

Link_maint_window

\[ \mu^{f}_{\xi,t,l} = \sum_{t' \in \mathcal{T} \,:\, \left( \xi,\ l,\ t',\ t \right) \in \mathrm{Link\_maintenance\_cover}} \mu^{f,\mathrm{up}}_{\xi,t',l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{mnt}^{f}_{l} \wedge \mathrm{on}^{f}_{t,l} \]

Link_maint_start_horizon

\[ \mu^{f,\mathrm{up}}_{\xi,t,l} = 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{mnt}^{f}_{l} \wedge \mathrm{on}^{f}_{t,l} \wedge \mathrm{blk}^{f}_{\xi,t,l} \]

Link_maintcap_upper

\[ \mu^{f,\mathrm{nom}}_{\xi,t,l} \le F_{l} - \underline{\mathrm{f}}^{\mathrm{nom}}_{\xi,l} \cdot \left( 1 - \mu^{f}_{\xi,t,l} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_maint\_ext}_{l,t} \]

Link_maintcap_upper_nommax

\[ \mu^{f,\mathrm{nom}}_{\xi,t,l} \le \overline{\mathrm{f}}^{\mathrm{nom}}_{\xi,l} \cdot \mu^{f}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_maint\_ext}_{l,t} \]

Link_maintcap_lower_nommax

\[ \mu^{f,\mathrm{nom}}_{\xi,t,l} \ge F_{l} - \overline{\mathrm{f}}^{\mathrm{nom}}_{\xi,l} \cdot \left( 1 - \mu^{f}_{\xi,t,l} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_maint\_ext}_{l,t} \]

Link_maintcap_lower_nommin

\[ \mu^{f,\mathrm{nom}}_{\xi,t,l} \ge \underline{\mathrm{f}}^{\mathrm{nom}}_{\xi,l} \cdot \mu^{f}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_maint\_ext}_{l,t} \wedge \underline{\mathrm{f}}^{\mathrm{nom}}_{\xi,l} > 0 \]

Link_maint_status_le_status

\[ \mu^{f,u}_{\xi,t,l} \le u^{f}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{mnt}^{f}_{l} \wedge \mathrm{Link\_committed}_{l,t} \wedge \neg \mathrm{ext}^{f}_{l} \wedge \neg \left( \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right) \]

Link_maint_status_le_maint

\[ \mu^{f,u}_{\xi,t,l} \le \mu^{f}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{mnt}^{f}_{l} \wedge \mathrm{Link\_committed}_{l,t} \wedge \neg \mathrm{ext}^{f}_{l} \wedge \neg \left( \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right) \]

Link_maint_status_lb

\[ \mu^{f,u}_{\xi,t,l} \ge u^{f}_{\xi,t,l} + \mu^{f}_{\xi,t,l} - 1 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{mnt}^{f}_{l} \wedge \mathrm{Link\_committed}_{l,t} \wedge \neg \mathrm{ext}^{f}_{l} \wedge \neg \left( \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right) \]

Link_maint_modstatus_le_status

\[ \mu^{f,u}_{\xi,t,l} \le u^{f}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{mnt}^{f}_{l} \wedge \mathrm{Link\_committed}_{l,t} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \]

Link_maint_modstatus_le_maint

\[ \mu^{f,u}_{\xi,t,l} \le \frac{\overline{\mathrm{f}}^{\mathrm{nom}}_{\xi,l}}{\mathrm{f}^{\mathrm{mod}}_{l}} \cdot \mu^{f}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{mnt}^{f}_{l} \wedge \mathrm{Link\_committed}_{l,t} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \]

Link_maint_modstatus_lb

\[ \mu^{f,u}_{\xi,t,l} \ge u^{f}_{\xi,t,l} - \frac{\overline{\mathrm{f}}^{\mathrm{nom}}_{\xi,l}}{\mathrm{f}^{\mathrm{mod}}_{l}} \cdot \left( 1 - \mu^{f}_{\xi,t,l} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{mnt}^{f}_{l} \wedge \mathrm{Link\_committed}_{l,t} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \]

Process_com_p_lower

\[ z_{\xi,t,j} \ge \underline{\mathrm{z}}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \cdot \left( u^{z}_{\xi,t,j} - \gamma^{z}_{\xi,j} \cdot \mu^{z,u}_{\xi,t,j} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \neg \mathrm{ext}^{z}_{j} \wedge \neg \left( \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right) \]

Process_com_p_upper

\[ z_{\xi,t,j} \le \overline{\mathrm{z}}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \cdot \left( u^{z}_{\xi,t,j} - \gamma^{z}_{\xi,j} \cdot \mu^{z,u}_{\xi,t,j} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \neg \mathrm{ext}^{z}_{j} \wedge \neg \left( \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right) \]

Process_com_transition_start_up

\[ \mathit{up}^{z}_{\xi,t,j} \ge u^{z}_{\xi,t,j} - \mathit{Process\_previous\_status}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \]

Process_com_transition_shut_down

\[ \mathit{dn}^{z}_{\xi,t,j} \ge \mathit{Process\_previous\_status}_{\xi,t,j} - u^{z}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \]

Process_p_nom_modularity

\[ Z_{j} = \mathrm{z}^{\mathrm{mod}}_{j} \cdot N^{z}_{j} \qquad \forall\, j \in \mathcal{J} \,:\, \mathrm{ext}^{z}_{j} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \wedge \mathrm{act}^{z}_{j} \]

Process_com_ext_p_upper_cap

\[ z_{\xi,t,j} \le \overline{\mathrm{z}}_{\xi,t,j} \cdot \left( Z_{j} - \gamma^{z}_{\xi,j} \cdot \mu^{z,\mathrm{nom}}_{\xi,t,j} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_com\_ext}_{j,t} \]

Process_com_ext_p_upper_big_m

\[ z_{\xi,t,j} \le \mathrm{M}^{z}_{\xi,j} \cdot u^{z}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_com\_ext}_{j,t} \]

Process_com_ext_p_lower

\[ z_{\xi,t,j} \ge \underline{\mathrm{z}}_{\xi,t,j} \cdot \left( Z_{j} - \gamma^{z}_{\xi,j} \cdot \mu^{z,\mathrm{nom}}_{\xi,t,j} \right) + \mathrm{M}^{z}_{\xi,j} \cdot u^{z}_{\xi,t,j} - \mathrm{M}^{z}_{\xi,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_com\_ext}_{j,t} \]

Process_com_ext_p_lower_nonneg

\[ z_{\xi,t,j} \ge 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_com\_ext}_{j,t} \wedge \mathrm{nonneg}^{z}_{j} \]

Process_com_mod_p_lower

\[ z_{\xi,t,j} \ge \underline{\mathrm{z}}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{mod}}_{j} \cdot \left( u^{z}_{\xi,t,j} - \gamma^{z}_{\xi,j} \cdot \mu^{z,u}_{\xi,t,j} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \]

Process_com_mod_p_upper

\[ z_{\xi,t,j} \le \overline{\mathrm{z}}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{mod}}_{j} \cdot \left( u^{z}_{\xi,t,j} - \gamma^{z}_{\xi,j} \cdot \mu^{z,u}_{\xi,t,j} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \]

Process_status_p_fixed_upper

\[ u^{z}_{\xi,t,j} \le \mathrm{N}^{z,\mathrm{fix}}_{\xi,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \neg \left( \mathrm{ext}^{z}_{j} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right) \]

Process_start_up_p_fixed_upper

\[ \mathit{up}^{z}_{\xi,t,j} \le \mathrm{N}^{z,\mathrm{fix}}_{\xi,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \neg \left( \mathrm{ext}^{z}_{j} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right) \]

Process_shut_down_p_fixed_upper

\[ \mathit{dn}^{z}_{\xi,t,j} \le \mathrm{N}^{z,\mathrm{fix}}_{\xi,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \neg \left( \mathrm{ext}^{z}_{j} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right) \]

Process_status_p_nom_variable_upper

\[ u^{z}_{\xi,t,j} \le N^{z}_{j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \mathrm{ext}^{z}_{j} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \]

Process_start_up_p_nom_variable_upper

\[ \mathit{up}^{z}_{\xi,t,j} \le N^{z}_{j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \mathrm{ext}^{z}_{j} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \]

Process_shut_down_p_nom_variable_upper

\[ \mathit{dn}^{z}_{\xi,t,j} \le N^{z}_{j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \mathrm{ext}^{z}_{j} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \]

Process_maint_event_count

\[ \sum_{t \in \mathcal{T}} \mu^{z,\mathrm{up}}_{\xi,t,j} = \mathrm{n}^{z,\mathrm{mnt}}_{\xi,j} \qquad \forall\, \xi \in \Xi,\ j \in \mathcal{J} \,:\, \mathrm{mnt}^{z}_{j} \]

Process_maint_window

\[ \mu^{z}_{\xi,t,j} = \sum_{t' \in \mathcal{T} \,:\, \left( \xi,\ j,\ t',\ t \right) \in \mathrm{Process\_maintenance\_cover}} \mu^{z,\mathrm{up}}_{\xi,t',j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{mnt}^{z}_{j} \wedge \mathrm{on}^{z}_{t,j} \]

Process_maint_start_horizon

\[ \mu^{z,\mathrm{up}}_{\xi,t,j} = 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{mnt}^{z}_{j} \wedge \mathrm{on}^{z}_{t,j} \wedge \mathrm{blk}^{z}_{\xi,t,j} \]

Process_maintcap_upper

\[ \mu^{z,\mathrm{nom}}_{\xi,t,j} \le Z_{j} - \underline{\mathrm{z}}^{\mathrm{nom}}_{\xi,j} \cdot \left( 1 - \mu^{z}_{\xi,t,j} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_maint\_ext}_{j,t} \]

Process_maintcap_upper_nommax

\[ \mu^{z,\mathrm{nom}}_{\xi,t,j} \le \overline{\mathrm{z}}^{\mathrm{nom}}_{\xi,j} \cdot \mu^{z}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_maint\_ext}_{j,t} \]

Process_maintcap_lower_nommax

\[ \mu^{z,\mathrm{nom}}_{\xi,t,j} \ge Z_{j} - \overline{\mathrm{z}}^{\mathrm{nom}}_{\xi,j} \cdot \left( 1 - \mu^{z}_{\xi,t,j} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_maint\_ext}_{j,t} \]

Process_maintcap_lower_nommin

\[ \mu^{z,\mathrm{nom}}_{\xi,t,j} \ge \underline{\mathrm{z}}^{\mathrm{nom}}_{\xi,j} \cdot \mu^{z}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_maint\_ext}_{j,t} \wedge \underline{\mathrm{z}}^{\mathrm{nom}}_{\xi,j} > 0 \]

Process_maint_status_le_status

\[ \mu^{z,u}_{\xi,t,j} \le u^{z}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{mnt}^{z}_{j} \wedge \mathrm{Process\_committed}_{j,t} \wedge \neg \mathrm{ext}^{z}_{j} \wedge \neg \left( \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right) \]

Process_maint_status_le_maint

\[ \mu^{z,u}_{\xi,t,j} \le \mu^{z}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{mnt}^{z}_{j} \wedge \mathrm{Process\_committed}_{j,t} \wedge \neg \mathrm{ext}^{z}_{j} \wedge \neg \left( \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right) \]

Process_maint_status_lb

\[ \mu^{z,u}_{\xi,t,j} \ge u^{z}_{\xi,t,j} + \mu^{z}_{\xi,t,j} - 1 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{mnt}^{z}_{j} \wedge \mathrm{Process\_committed}_{j,t} \wedge \neg \mathrm{ext}^{z}_{j} \wedge \neg \left( \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right) \]

Process_maint_modstatus_le_status

\[ \mu^{z,u}_{\xi,t,j} \le u^{z}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{mnt}^{z}_{j} \wedge \mathrm{Process\_committed}_{j,t} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \]

Process_maint_modstatus_le_maint

\[ \mu^{z,u}_{\xi,t,j} \le \frac{\overline{\mathrm{z}}^{\mathrm{nom}}_{\xi,j}}{\mathrm{z}^{\mathrm{mod}}_{j}} \cdot \mu^{z}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{mnt}^{z}_{j} \wedge \mathrm{Process\_committed}_{j,t} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \]

Process_maint_modstatus_lb

\[ \mu^{z,u}_{\xi,t,j} \ge u^{z}_{\xi,t,j} - \frac{\overline{\mathrm{z}}^{\mathrm{nom}}_{\xi,j}}{\mathrm{z}^{\mathrm{mod}}_{j}} \cdot \left( 1 - \mu^{z}_{\xi,t,j} \right) \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{mnt}^{z}_{j} \wedge \mathrm{Process\_committed}_{j,t} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \]

Bus_nodal_balance

\[ \mathit{Bus\_injection}_{\xi,t,n} = 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ n \in \mathcal{N} \]

The spec, differential/pypsa/rungs/rung_34_committable_maintenance.yaml — the file projected onto what this rung builds:

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'}
  period: {description: investment periods — PyPSA's `investment_periods`, dtype: int, ordered: true}
sets:
  Generator_maintenance_cover:
    description: >-
      the snapshots a maintenance event covers, by the snapshot it starts in —
      in a scenario, the start and the snapshots after it, until their generator
      weightings reach that scenario's `maintenance_duration`, data prep; no
      rows for a generator that is not maintainable
    dims: { scenario: scenario, generator: generator, start: snapshot, covered: snapshot }
    missing: absent
  Link_maintenance_cover:
    description: >-
      the snapshots a maintenance event covers, by the snapshot it starts in —
      in a scenario, the start and the snapshots after it, until their generator
      weightings reach that scenario's `maintenance_duration`, data prep; no
      rows for a link that is not maintainable
    dims: { scenario: scenario, link: link, start: snapshot, covered: snapshot }
    missing: absent
  Process_maintenance_cover:
    description: >-
      the snapshots a maintenance event covers, by the snapshot it starts in —
      in a scenario, the start and the snapshots after it, until their generator
      weightings reach that scenario's `maintenance_duration`, data prep; no
      rows for a process that is not maintainable
    dims: { scenario: scenario, process: process, start: snapshot, covered: snapshot }
    missing: absent

properties:
  snapshot:
    period:
      description: the investment period a snapshot falls in
      into: period
  generator:
    bus:
      description: the bus a generator sits on
      into: bus
  link:
    bus0:
      description: the bus a link leaves
      into: bus
  link_output:
    link:
      description: the link an output port belongs to
      into: link
    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
        property, so the file states any number of them
      into: bus
  process_output:
    process:
      description: the process a port belongs to
      into: process
    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 property, so the file states any number of them
      into: bus
  load:
    bus:
      description: the bus a load sits on
      into: 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
  Generator_status_initial:
    description: one where the unit was on before the first snapshot, zero where off — PyPSA's `up_time_before
      > 0`, data prep
    dims: [scenario, generator]
    dtype: int
  Generator_start_up_cost:
    description: cost of one start in this snapshot
    dims: [scenario, snapshot, generator]
  Generator_shut_down_cost:
    description: cost of one stop in this snapshot
    dims: [scenario, snapshot, generator]
  Generator_stand_by_cost:
    description: cost of one snapshot spent on
    dims: [scenario, snapshot, generator]
  Generator_p_nom_mod:
    description: the module size a build comes in whole numbers of; no value means the build is continuous
    dims: [generator]
    missing: absent
  Generator_modules_installed:
    description: 'how many whole modules a committable build has in place: `Generator_p_nom / Generator_p_nom_mod`
      where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build
      whose nominal power is not a whole number of modules'
    dims: [scenario, generator]
  Generator_big_m:
    description: the bound a committed extendable generator's big-M rows release it by — the build cap
      `p_nom_max` times the highest `p_max_pu`, where the cap is finite and positive. Elsewhere it is
      `committable_big_m` times the highest `p_max_pu`, and where that keyword is not given, ten times
      the largest of the peak total load and the component's largest finite `p_nom` and `p_nom_max`, or
      1e6 where there is none of them (`components.py:1050-1121`). Below the output a solve wants, it
      caps that output; data prep
    dims: [scenario, generator]
    missing: 0
  Generator_p_min_pu_nonneg:
    description: true where none of the generator's own minimums-per-unit is negative — PyPSA's per-unit
      `(p_min_pu >= 0).all()` over every snapshot and scenario, data prep
    dims: [generator]
    dtype: bool
  Generator_maintainable:
    description: whether a generator must be taken off for maintenance within the horizon — in any scenario,
      as PyPSA takes the union over them (`components.py:1016-1019`)
    dims: [generator]
    dtype: bool
  Generator_maintenance_pu:
    description: the share of the build a maintenance event takes off
    dims: [scenario, generator]
  Generator_maintenance_events:
    description: how many maintenance events the horizon holds
    dims: [scenario, generator]
    dtype: int
  Generator_maintenance_start_blocked:
    description: true where no maintenance event may start, because the snapshots it would cover run past
      the end of the horizon or into one the generator does not stand in — PyPSA's `active & ~valid`,
      from `maintenance_duration` and the generator weightings, data prep
    dims: [scenario, snapshot, 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: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
  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
  Link_status_initial:
    description: one where the link was on before the first snapshot, zero where off — PyPSA's `up_time_before
      > 0`, data prep
    dims: [scenario, link]
    dtype: int
  Link_start_up_cost:
    description: cost of one start in this snapshot
    dims: [scenario, snapshot, link]
  Link_shut_down_cost:
    description: cost of one stop in this snapshot
    dims: [scenario, snapshot, link]
  Link_stand_by_cost:
    description: cost of one snapshot spent on
    dims: [scenario, snapshot, link]
  Link_p_nom_mod:
    description: the module size a build comes in whole numbers of; no value means the build is continuous
    dims: [link]
    missing: absent
  Link_modules_installed:
    description: 'how many whole modules a committable build has in place: `Link_p_nom / Link_p_nom_mod`
      where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build
      whose nominal power is not a whole number of modules'
    dims: [scenario, link]
  Link_big_m:
    description: the bound a committed extendable link's big-M rows release it by — the build cap `p_nom_max`
      times the highest `p_max_pu`, where the cap is finite and positive. Elsewhere it is `committable_big_m`
      times the highest `p_max_pu`, and where that keyword is not given, ten times the largest of the
      peak total load and the component's largest finite `p_nom` and `p_nom_max`, or 1e6 where there is
      none of them (`components.py:1050-1121`). Below the flow a solve wants, it caps that flow; data
      prep
    dims: [scenario, link]
    missing: 0
  Link_p_min_pu_nonneg:
    description: true where none of the link's own minimums-per-unit is negative — PyPSA's per-unit `(p_min_pu
      >= 0).all()` over every snapshot and scenario, data prep
    dims: [link]
    dtype: bool
  Link_maintainable:
    description: whether a link must be taken off for maintenance within the horizon — in any scenario,
      as PyPSA takes the union over them (`components.py:1016-1019`)
    dims: [link]
    dtype: bool
  Link_maintenance_pu:
    description: the share of the build a maintenance event takes off
    dims: [scenario, link]
  Link_maintenance_events:
    description: how many maintenance events the horizon holds
    dims: [scenario, link]
    dtype: int
  Link_maintenance_start_blocked:
    description: true where no maintenance event may start, because the snapshots it would cover run past
      the end of the horizon or into one the link does not stand in — PyPSA's `active & ~valid`, from
      `maintenance_duration` and the generator weightings, data prep
    dims: [scenario, snapshot, 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: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
  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_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 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, process]
  Process_committable:
    description: whether internal power is gated by an on/off status decision
    dims: [process]
    dtype: bool
  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_start_up_cost:
    description: cost of one start in this snapshot
    dims: [scenario, snapshot, process]
  Process_shut_down_cost:
    description: cost of one stop in this snapshot
    dims: [scenario, snapshot, process]
  Process_stand_by_cost:
    description: cost of one snapshot spent on
    dims: [scenario, snapshot, 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]
    missing: absent
  Process_modules_installed:
    description: 'how many whole modules a committable build has in place: `Process_p_nom / Process_p_nom_mod`
      where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build
      whose nominal power is not a whole number of modules'
    dims: [scenario, process]
  Process_big_m:
    description: the bound a committed extendable process's big-M rows release it by — the build cap `p_nom_max`
      times the highest `p_max_pu`, where the cap is finite and positive. Elsewhere it is `committable_big_m`
      times the highest `p_max_pu`, and where that keyword is not given, ten times the largest of the
      peak total load and the component's largest finite `p_nom` and `p_nom_max`, or 1e6 where there is
      none of them (`components.py:1050-1121`). Below the internal power a solve wants, it caps that internal
      power; data prep
    dims: [scenario, process]
    missing: 0
  Process_p_min_pu_nonneg:
    description: true where none of the process's own minimums-per-unit is negative — PyPSA's per-unit
      `(p_min_pu >= 0).all()` over every snapshot and scenario, data prep
    dims: [process]
    dtype: bool
  Process_maintainable:
    description: whether a process must be taken off for maintenance within the horizon — in any scenario,
      as PyPSA takes the union over them (`components.py:1016-1019`)
    dims: [process]
    dtype: bool
  Process_maintenance_pu:
    description: the share of the build a maintenance event takes off
    dims: [scenario, process]
  Process_maintenance_events:
    description: how many maintenance events the horizon holds
    dims: [scenario, process]
    dtype: int
  Process_maintenance_start_blocked:
    description: true where no maintenance event may start, because the snapshots it would cover run past
      the end of the horizon or into one the process does not stand in — PyPSA's `active & ~valid`, from
      `maintenance_duration` and the generator weightings, data prep
    dims: [scenario, snapshot, 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 (`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
  Process_active:
    description: whether a process stands in a snapshot's period — PyPSA's `active`, data prep
    dims: [snapshot, process]
    dtype: bool
  Generator_active_asset:
    description: whether a generator 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: [generator]
    dtype: bool
  Link_active_asset:
    description: whether a link 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: [link]
    dtype: bool
  Process_active_asset:
    description: whether a process 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: [process]
    dtype: bool
  Generator_capital_weight:
    description: the sum of period weights a generator stands in — PyPSA's `active * period_weighting`,
      summed, data prep
    dims: [generator]
  Link_capital_weight:
    description: the sum of period weights a link stands in — PyPSA's `active * period_weighting`, summed,
      data prep
    dims: [link]
  Process_capital_weight:
    description: the sum of period weights a process stands in — PyPSA's `active * period_weighting`,
      summed, data prep
    dims: [process]
  Generator_p_nom_min:
    description: least nominal power an extendable generator may be built at
    dims: [scenario, generator]
  Generator_p_nom_max:
    description: most nominal power an extendable generator may be built at
    dims: [scenario, generator]
  Generator_capital_cost:
    description: 'cost of one unit of nominal power 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, generator]
  Link_p_nom_min:
    description: least nominal power an extendable link may be built at
    dims: [scenario, link]
  Link_p_nom_max:
    description: most nominal power an extendable link may be built at
    dims: [scenario, link]
  Link_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, link]
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
  Generator_n_mod:
    description: '`Generator-n_mod` — how many modules of an extendable modular build; none for a unit
      that is not active'
    dims: [generator]
    where: Generator_p_nom_extendable AND Generator_p_nom_mod > 0 AND Generator_active_asset
    domain: integer
    bounds: {lower: 0}
  Generator_status:
    description: '`Generator-status` — how much of a committable unit is on: an integer the rows below
      cap at one, or at the module count where the build is modular'
    dims: [scenario, snapshot, generator]
    where: Generator_committed
    domain: integer
    bounds: {lower: 0}
  Generator_start_up:
    description: '`Generator-start_up` — how much of a committable unit turns on this snapshot, capped
      as the status is'
    dims: [scenario, snapshot, generator]
    where: Generator_committed
    domain: integer
    bounds: {lower: 0}
  Generator_shut_down:
    description: '`Generator-shut_down` — how much of a committable unit turns off this snapshot, capped
      as the status is'
    dims: [scenario, snapshot, generator]
    where: Generator_committed
    domain: integer
    bounds: {lower: 0}
  Generator_maintenance:
    description: '`Generator-maintenance` — whether a maintainable generator is in maintenance: continuous,
      and one exactly where an event covers the snapshot'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_active
    missing: 0
    bounds: {lower: 0, upper: 1}
  Generator_maintenance_start:
    description: '`Generator-maintenance_start` — whether a maintenance event starts in this snapshot'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_active
    missing: 0
    domain: binary
  Generator_maintenance_capacity:
    description: '`Generator-maintenance_capacity` — the chosen build while in maintenance, zero otherwise:
      the product the `maintcap` rows linearize'
    dims: [scenario, snapshot, generator]
    where: Generator_maint_ext
    missing: 0
    bounds: {lower: 0}
  Generator_maintenance_status:
    description: '`Generator-maintenance_status` — the status while in maintenance, zero otherwise: the
      product the `maint-status` rows linearize, so a unit in maintenance may also be off'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committed AND NOT (Generator_p_nom_extendable AND NOT
      (Generator_p_nom_mod > 0))
    missing: 0
    bounds: {lower: 0}
  Link_n_mod:
    description: '`Link-n_mod` — how many modules of an extendable modular build; none for a unit that
      is not active'
    dims: [link]
    where: Link_p_nom_extendable AND Link_p_nom_mod > 0 AND Link_active_asset
    domain: integer
    bounds: {lower: 0}
  Link_status:
    description: '`Link-status` — how much of a committable link is on: an integer the rows below cap
      at one, or at the module count where the build is modular'
    dims: [scenario, snapshot, link]
    where: Link_committed
    domain: integer
    bounds: {lower: 0}
  Link_start_up:
    description: '`Link-start_up` — how much of a committable link turns on this snapshot, capped as the
      status is'
    dims: [scenario, snapshot, link]
    where: Link_committed
    domain: integer
    bounds: {lower: 0}
  Link_shut_down:
    description: '`Link-shut_down` — how much of a committable link turns off this snapshot, capped as
      the status is'
    dims: [scenario, snapshot, link]
    where: Link_committed
    domain: integer
    bounds: {lower: 0}
  Link_maintenance:
    description: '`Link-maintenance` — whether a maintainable link is in maintenance: continuous, and
      one exactly where an event covers the snapshot'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_active
    missing: 0
    bounds: {lower: 0, upper: 1}
  Link_maintenance_start:
    description: '`Link-maintenance_start` — whether a maintenance event starts in this snapshot'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_active
    missing: 0
    domain: binary
  Link_maintenance_capacity:
    description: '`Link-maintenance_capacity` — the chosen build while in maintenance, zero otherwise:
      the product the `maintcap` rows linearize'
    dims: [scenario, snapshot, link]
    where: Link_maint_ext
    missing: 0
    bounds: {lower: 0}
  Link_maintenance_status:
    description: '`Link-maintenance_status` — the status while in maintenance, zero otherwise: the product
      the `maint-status` rows linearize, so a unit in maintenance may also be off'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committed AND NOT (Link_p_nom_extendable AND NOT (Link_p_nom_mod
      > 0))
    missing: 0
    bounds: {lower: 0}
  Process_n_mod:
    description: '`Process-n_mod` — how many modules of an extendable modular build; none for a unit that
      is not active'
    dims: [process]
    where: Process_p_nom_extendable AND Process_p_nom_mod > 0 AND Process_active_asset
    domain: integer
    bounds: {lower: 0}
  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_committed
    domain: integer
    bounds: {lower: 0}
  Process_start_up:
    description: '`Process-start_up` — how much of a committable process turns on this snapshot, capped
      as the status is'
    dims: [scenario, snapshot, process]
    where: Process_committed
    domain: integer
    bounds: {lower: 0}
  Process_shut_down:
    description: '`Process-shut_down` — how much of a committable process turns off this snapshot, capped
      as the status is'
    dims: [scenario, snapshot, process]
    where: Process_committed
    domain: integer
    bounds: {lower: 0}
  Process_maintenance:
    description: '`Process-maintenance` — whether a maintainable process is in maintenance: continuous,
      and one exactly where an event covers the snapshot'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_active
    missing: 0
    bounds: {lower: 0, upper: 1}
  Process_maintenance_start:
    description: '`Process-maintenance_start` — whether a maintenance event starts in this snapshot'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_active
    missing: 0
    domain: binary
  Process_maintenance_capacity:
    description: '`Process-maintenance_capacity` — the chosen build while in maintenance, zero otherwise:
      the product the `maintcap` rows linearize'
    dims: [scenario, snapshot, process]
    where: Process_maint_ext
    missing: 0
    bounds: {lower: 0}
  Process_maintenance_status:
    description: '`Process-maintenance_status` — the status while in maintenance, zero otherwise: the
      product the `maint-status` rows linearize, so a unit in maintenance may also be off'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committed AND NOT (Process_p_nom_extendable AND NOT (Process_p_nom_mod
      > 0))
    missing: 0
    bounds: {lower: 0}
  Generator_p_nom_ext:
    description: '`Generator-p_nom` — nominal power where it is a decision, for a generator that is active;
      the parameter of the same PyPSA name carries the fixed regime'
    dims: [generator]
    where: Generator_p_nom_extendable AND Generator_active_asset
  Link_p_nom_ext:
    description: '`Link-p_nom` — nominal power where it is a decision, for a link that is active; the
      parameter of the same PyPSA name carries the fixed regime'
    dims: [link]
    where: Link_p_nom_extendable AND Link_active_asset
  Process_p_nom_ext:
    description: '`Process-p_nom` — nominal internal power where it is a decision, for a process that
      is active; the parameter of the same PyPSA name carries the fixed regime'
    dims: [process]
    where: Process_p_nom_extendable AND Process_active_asset
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 * (1 - Generator_maintenance_pu *
      Generator_maintenance)
  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 * (1 - Generator_maintenance_pu *
      Generator_maintenance)
  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 * (1 - Link_maintenance_pu * Link_maintenance)
  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 * (1 - Link_maintenance_pu * Link_maintenance)
  Generator_ext_p_nom_lower:
    description: '`Generator-ext-p_nom-lower` — the chosen build is at least its floor in every scenario'
    dims: [scenario, generator]
    where: Generator_p_nom_extendable AND Generator_active_asset
    expression: Generator_p_nom_ext >= Generator_p_nom_min
  Generator_ext_p_nom_upper:
    description: '`Generator-ext-p_nom-upper` — the chosen build is at most its cap in every scenario;
      a cap of infinity is no row'
    dims: [scenario, generator]
    where: Generator_p_nom_extendable AND Generator_active_asset AND Generator_p_nom_max
    expression: Generator_p_nom_ext <= Generator_p_nom_max
  Link_ext_p_nom_lower:
    description: '`Link-ext-p_nom-lower` — the chosen build is at least its floor in every scenario'
    dims: [scenario, link]
    where: Link_p_nom_extendable AND Link_active_asset
    expression: Link_p_nom_ext >= Link_p_nom_min
  Link_ext_p_nom_upper:
    description: '`Link-ext-p_nom-upper` — the chosen build is at most its cap in every scenario; a cap
      of infinity is no row'
    dims: [scenario, link]
    where: Link_p_nom_extendable AND Link_active_asset AND Link_p_nom_max
    expression: Link_p_nom_ext <= Link_p_nom_max
  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 AND Process_active_asset
    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_active_asset AND Process_p_nom_max
    expression: Process_p_nom_ext <= Process_p_nom_max
  Generator_com_p_lower:
    description: '`Generator-com-p-lower` — a committed unit outputs at least its minimum; off, at least
      nothing'
    dims: [scenario, snapshot, generator]
    where: Generator_committed AND NOT Generator_p_nom_extendable AND NOT (Generator_p_nom_mod > 0)
    expression: Generator_p >= Generator_p_min_pu * Generator_p_nom * (Generator_status - Generator_maintenance_pu
      * Generator_maintenance_status)
  Generator_com_p_upper:
    description: '`Generator-com-p-upper` — a committed unit outputs at most what is available; off, at
      most nothing'
    dims: [scenario, snapshot, generator]
    where: Generator_committed AND NOT Generator_p_nom_extendable AND NOT (Generator_p_nom_mod > 0)
    expression: Generator_p <= Generator_p_max_pu * Generator_p_nom * (Generator_status - Generator_maintenance_pu
      * Generator_maintenance_status)
  Generator_com_transition_start_up:
    description: '`Generator-com-transition-start-up` — turning on is a start, counted against the state
      the unit carried into the snapshot'
    dims: [scenario, snapshot, generator]
    where: Generator_committed
    expression: Generator_start_up >= Generator_status - Generator_previous_status
  Generator_com_transition_shut_down:
    description: '`Generator-com-transition-shut-down` — turning off is a stop, counted against the state
      the unit carried into the snapshot'
    dims: [scenario, snapshot, generator]
    where: Generator_committed
    expression: Generator_shut_down >= Generator_previous_status - Generator_status
  Generator_p_nom_modularity:
    description: '`Generator-p_nom_modularity` — the chosen build is a whole number of modules'
    dims: [generator]
    where: Generator_p_nom_extendable AND Generator_p_nom_mod > 0 AND Generator_active_asset
    expression: Generator_p_nom_ext == Generator_p_nom_mod * Generator_n_mod
  Generator_com_ext_p_upper_cap:
    description: '`Generator-com-ext-p-upper-cap` — a committed extendable unit outputs at most what is
      available of the chosen build, whatever its status'
    dims: [scenario, snapshot, generator]
    where: Generator_com_ext
    expression: Generator_p <= Generator_p_max_pu * (Generator_p_nom_ext - Generator_maintenance_pu *
      Generator_maintenance_capacity)
  Generator_com_ext_p_upper_big_m:
    description: '`Generator-com-ext-p-upper-bigM` — off, a unit outputs nothing; on, the big M is no
      bound'
    dims: [scenario, snapshot, generator]
    where: Generator_com_ext
    expression: Generator_p <= Generator_big_m * Generator_status
  Generator_com_ext_p_lower:
    description: '`Generator-com-ext-p-lower` — a committed extendable unit outputs at least its minimum
      of the chosen build; off, the big M releases the row'
    dims: [scenario, snapshot, generator]
    where: Generator_com_ext
    expression: Generator_p >= Generator_p_min_pu * (Generator_p_nom_ext - Generator_maintenance_pu *
      Generator_maintenance_capacity) + Generator_big_m * Generator_status - Generator_big_m
  Generator_com_ext_p_lower_nonneg:
    description: '`Generator-com-ext-p-lower-nonneg` — where no minimum-per-unit is negative, output is
      also plainly non-negative, a row the big-M lower cannot assert while the unit is off'
    dims: [scenario, snapshot, generator]
    where: Generator_com_ext AND Generator_p_min_pu_nonneg
    expression: Generator_p >= 0
  Generator_com_mod_p_lower:
    description: '`Generator-com-mod-p-lower` — a committed modular unit outputs at least its minimum
      of one module, whether the build is fixed or a decision'
    dims: [scenario, snapshot, generator]
    where: Generator_committed AND Generator_p_nom_mod > 0
    expression: Generator_p >= Generator_p_min_pu * Generator_p_nom_mod * (Generator_status - Generator_maintenance_pu
      * Generator_maintenance_status)
  Generator_com_mod_p_upper:
    description: '`Generator-com-mod-p-upper` — a committed modular unit outputs at most one module''s
      share, whether the build is fixed or a decision'
    dims: [scenario, snapshot, generator]
    where: Generator_committed AND Generator_p_nom_mod > 0
    expression: Generator_p <= Generator_p_max_pu * Generator_p_nom_mod * (Generator_status - Generator_maintenance_pu
      * Generator_maintenance_status)
  Generator_status_p_fixed_upper:
    description: '`Generator-status-p-fixed-upper` — a status is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, generator]
    where: Generator_committed AND NOT (Generator_p_nom_extendable AND Generator_p_nom_mod > 0)
    expression: Generator_status <= Generator_modules_installed
  Generator_start_up_p_fixed_upper:
    description: '`Generator-start_up-p-fixed-upper` — a start is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, generator]
    where: Generator_committed AND NOT (Generator_p_nom_extendable AND Generator_p_nom_mod > 0)
    expression: Generator_start_up <= Generator_modules_installed
  Generator_shut_down_p_fixed_upper:
    description: '`Generator-shut_down-p-fixed-upper` — a stop is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, generator]
    where: Generator_committed AND NOT (Generator_p_nom_extendable AND Generator_p_nom_mod > 0)
    expression: Generator_shut_down <= Generator_modules_installed
  Generator_status_p_nom_variable_upper:
    description: '`Generator-status-p_nom-variable-upper` — a modular unit is on only where a module is
      built'
    dims: [scenario, snapshot, generator]
    where: Generator_committed AND Generator_p_nom_extendable AND Generator_p_nom_mod > 0
    expression: Generator_status <= Generator_n_mod
  Generator_start_up_p_nom_variable_upper:
    description: '`Generator-start_up-p_nom-variable-upper` — a modular unit starts only where a module
      is built'
    dims: [scenario, snapshot, generator]
    where: Generator_committed AND Generator_p_nom_extendable AND Generator_p_nom_mod > 0
    expression: Generator_start_up <= Generator_n_mod
  Generator_shut_down_p_nom_variable_upper:
    description: '`Generator-shut_down-p_nom-variable-upper` — a modular unit stops only where a module
      is built'
    dims: [scenario, snapshot, generator]
    where: Generator_committed AND Generator_p_nom_extendable AND Generator_p_nom_mod > 0
    expression: Generator_shut_down <= Generator_n_mod
  Generator_maint_event_count:
    description: '`Generator-maint-event-count` — a maintainable generator holds its number of maintenance
      events over the horizon'
    dims: [scenario, generator]
    where: Generator_maintainable
    expression: sum(Generator_maintenance_start, over=snapshot) == Generator_maintenance_events
  Generator_maint_window:
    description: '`Generator-maint-window` — a generator is in maintenance exactly where an event it started
      covers the snapshot; two events do not overlap, since the maintenance status is at most one'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_active
    expression: Generator_maintenance == sum(Generator_maintenance_start, over=start, by=Generator_maintenance_cover[covered])
  Generator_maint_start_horizon:
    description: '`Generator-maint-start-horizon` — no event starts where it could not run its whole duration'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_active AND Generator_maintenance_start_blocked
    expression: Generator_maintenance_start == 0
  Generator_maintcap_upper:
    description: '`Generator-maintcap_upper` — the build taken off is at most the chosen build in maintenance,
      and at most the build less its floor out of it'
    dims: [scenario, snapshot, generator]
    where: Generator_maint_ext
    expression: Generator_maintenance_capacity <= Generator_p_nom_ext - Generator_p_nom_min * (1 - Generator_maintenance)
  Generator_maintcap_upper_nommax:
    description: '`Generator-maintcap_upper_nommax` — out of maintenance, no build is taken off'
    dims: [scenario, snapshot, generator]
    where: Generator_maint_ext
    expression: Generator_maintenance_capacity <= Generator_p_nom_max * Generator_maintenance
  Generator_maintcap_lower_nommax:
    description: '`Generator-maintcap_lower_nommax` — in maintenance, the whole chosen build is taken
      off'
    dims: [scenario, snapshot, generator]
    where: Generator_maint_ext
    expression: Generator_maintenance_capacity >= Generator_p_nom_ext - Generator_p_nom_max * (1 - Generator_maintenance)
  Generator_maintcap_lower_nommin:
    description: '`Generator-maintcap_lower_nommin` — in maintenance, at least the floor of the build
      is taken off'
    dims: [scenario, snapshot, generator]
    where: Generator_maint_ext AND Generator_p_nom_min > 0
    expression: Generator_maintenance_capacity >= Generator_p_nom_min * Generator_maintenance
  Generator_maint_status_le_status:
    description: '`Generator-maint-status-le-status` — the status in maintenance is at most the status'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committed AND NOT Generator_p_nom_extendable AND NOT (Generator_p_nom_mod
      > 0)
    expression: Generator_maintenance_status <= Generator_status
  Generator_maint_status_le_maint:
    description: '`Generator-maint-status-le-maint` — out of maintenance, the status in maintenance is
      zero'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committed AND NOT Generator_p_nom_extendable AND NOT (Generator_p_nom_mod
      > 0)
    expression: Generator_maintenance_status <= Generator_maintenance
  Generator_maint_status_lb:
    description: '`Generator-maint-status-lb` — on and in maintenance, the status in maintenance is one'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committed AND NOT Generator_p_nom_extendable AND NOT (Generator_p_nom_mod
      > 0)
    expression: Generator_maintenance_status >= Generator_status + Generator_maintenance - 1
  Generator_maint_modstatus_le_status:
    description: '`Generator-maint-modstatus-le-status` — the modules on in maintenance are at most the
      modules on'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committed AND Generator_p_nom_mod > 0
    expression: Generator_maintenance_status <= Generator_status
  Generator_maint_modstatus_le_maint:
    description: '`Generator-maint-modstatus-le-maint` — out of maintenance, no module is on in maintenance;
      in it, at most the modules the build cap holds'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committed AND Generator_p_nom_mod > 0
    expression: Generator_maintenance_status <= Generator_p_nom_max / Generator_p_nom_mod * Generator_maintenance
  Generator_maint_modstatus_lb:
    description: '`Generator-maint-modstatus-lb` — in maintenance, every module on is on in maintenance'
    dims: [scenario, snapshot, generator]
    where: Generator_maintainable AND Generator_committed AND Generator_p_nom_mod > 0
    expression: Generator_maintenance_status >= Generator_status - Generator_p_nom_max / Generator_p_nom_mod
      * (1 - Generator_maintenance)
  Link_com_p_lower:
    description: '`Link-com-p-lower` — a committed link flows at least its minimum; off, at least nothing'
    dims: [scenario, snapshot, link]
    where: Link_committed AND NOT Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0)
    expression: Link_p >= Link_p_min_pu * Link_p_nom * (Link_status - Link_maintenance_pu * Link_maintenance_status)
  Link_com_p_upper:
    description: '`Link-com-p-upper` — a committed link flows at most what is available; off, at most
      nothing'
    dims: [scenario, snapshot, link]
    where: Link_committed AND NOT Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0)
    expression: Link_p <= Link_p_max_pu * Link_p_nom * (Link_status - Link_maintenance_pu * Link_maintenance_status)
  Link_com_transition_start_up:
    description: '`Link-com-transition-start-up` — turning on is a start, counted against the state the
      link carried into the snapshot'
    dims: [scenario, snapshot, link]
    where: Link_committed
    expression: Link_start_up >= Link_status - Link_previous_status
  Link_com_transition_shut_down:
    description: '`Link-com-transition-shut-down` — turning off is a stop, counted against the state the
      link carried into the snapshot'
    dims: [scenario, snapshot, link]
    where: Link_committed
    expression: Link_shut_down >= Link_previous_status - Link_status
  Link_p_nom_modularity:
    description: '`Link-p_nom_modularity` — the chosen build is a whole number of modules'
    dims: [link]
    where: Link_p_nom_extendable AND Link_p_nom_mod > 0 AND Link_active_asset
    expression: Link_p_nom_ext == Link_p_nom_mod * Link_n_mod
  Link_com_ext_p_upper_cap:
    description: '`Link-com-ext-p-upper-cap` — a committed extendable link flows at most what is available
      of the chosen build, whatever its status'
    dims: [scenario, snapshot, link]
    where: Link_com_ext
    expression: Link_p <= Link_p_max_pu * (Link_p_nom_ext - Link_maintenance_pu * Link_maintenance_capacity)
  Link_com_ext_p_upper_big_m:
    description: '`Link-com-ext-p-upper-bigM` — off, a link flows nothing; on, the big M is no bound'
    dims: [scenario, snapshot, link]
    where: Link_com_ext
    expression: Link_p <= Link_big_m * Link_status
  Link_com_ext_p_lower:
    description: '`Link-com-ext-p-lower` — a committed extendable link flows at least its minimum of the
      chosen build; off, the big M releases the row'
    dims: [scenario, snapshot, link]
    where: Link_com_ext
    expression: Link_p >= Link_p_min_pu * (Link_p_nom_ext - Link_maintenance_pu * Link_maintenance_capacity)
      + Link_big_m * Link_status - Link_big_m
  Link_com_ext_p_lower_nonneg:
    description: '`Link-com-ext-p-lower-nonneg` — where no minimum-per-unit is negative, flow is also
      plainly non-negative, a row the big-M lower cannot assert while the link is off'
    dims: [scenario, snapshot, link]
    where: Link_com_ext AND Link_p_min_pu_nonneg
    expression: Link_p >= 0
  Link_com_mod_p_lower:
    description: '`Link-com-mod-p-lower` — a committed modular link flows at least its minimum of one
      module, whether the build is fixed or a decision'
    dims: [scenario, snapshot, link]
    where: Link_committed AND Link_p_nom_mod > 0
    expression: Link_p >= Link_p_min_pu * Link_p_nom_mod * (Link_status - Link_maintenance_pu * Link_maintenance_status)
  Link_com_mod_p_upper:
    description: '`Link-com-mod-p-upper` — a committed modular link flows at most one module''s share,
      whether the build is fixed or a decision'
    dims: [scenario, snapshot, link]
    where: Link_committed AND Link_p_nom_mod > 0
    expression: Link_p <= Link_p_max_pu * Link_p_nom_mod * (Link_status - Link_maintenance_pu * Link_maintenance_status)
  Link_status_p_fixed_upper:
    description: '`Link-status-p-fixed-upper` — a status is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, link]
    where: Link_committed AND NOT (Link_p_nom_extendable AND Link_p_nom_mod > 0)
    expression: Link_status <= Link_modules_installed
  Link_start_up_p_fixed_upper:
    description: '`Link-start_up-p-fixed-upper` — a start is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, link]
    where: Link_committed AND NOT (Link_p_nom_extendable AND Link_p_nom_mod > 0)
    expression: Link_start_up <= Link_modules_installed
  Link_shut_down_p_fixed_upper:
    description: '`Link-shut_down-p-fixed-upper` — a stop is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, link]
    where: Link_committed AND NOT (Link_p_nom_extendable AND Link_p_nom_mod > 0)
    expression: Link_shut_down <= Link_modules_installed
  Link_status_p_nom_variable_upper:
    description: '`Link-status-p_nom-variable-upper` — a modular link is on only where a module is built'
    dims: [scenario, snapshot, link]
    where: Link_committed AND Link_p_nom_extendable AND Link_p_nom_mod > 0
    expression: Link_status <= Link_n_mod
  Link_start_up_p_nom_variable_upper:
    description: '`Link-start_up-p_nom-variable-upper` — a modular link starts only where a module is
      built'
    dims: [scenario, snapshot, link]
    where: Link_committed AND Link_p_nom_extendable AND Link_p_nom_mod > 0
    expression: Link_start_up <= Link_n_mod
  Link_shut_down_p_nom_variable_upper:
    description: '`Link-shut_down-p_nom-variable-upper` — a modular link stops only where a module is
      built'
    dims: [scenario, snapshot, link]
    where: Link_committed AND Link_p_nom_extendable AND Link_p_nom_mod > 0
    expression: Link_shut_down <= Link_n_mod
  Link_maint_event_count:
    description: '`Link-maint-event-count` — a maintainable link holds its number of maintenance events
      over the horizon'
    dims: [scenario, link]
    where: Link_maintainable
    expression: sum(Link_maintenance_start, over=snapshot) == Link_maintenance_events
  Link_maint_window:
    description: '`Link-maint-window` — a link is in maintenance exactly where an event it started covers
      the snapshot; two events do not overlap, since the maintenance status is at most one'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_active
    expression: Link_maintenance == sum(Link_maintenance_start, over=start, by=Link_maintenance_cover[covered])
  Link_maint_start_horizon:
    description: '`Link-maint-start-horizon` — no event starts where it could not run its whole duration'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_active AND Link_maintenance_start_blocked
    expression: Link_maintenance_start == 0
  Link_maintcap_upper:
    description: '`Link-maintcap_upper` — the build taken off is at most the chosen build in maintenance,
      and at most the build less its floor out of it'
    dims: [scenario, snapshot, link]
    where: Link_maint_ext
    expression: Link_maintenance_capacity <= Link_p_nom_ext - Link_p_nom_min * (1 - Link_maintenance)
  Link_maintcap_upper_nommax:
    description: '`Link-maintcap_upper_nommax` — out of maintenance, no build is taken off'
    dims: [scenario, snapshot, link]
    where: Link_maint_ext
    expression: Link_maintenance_capacity <= Link_p_nom_max * Link_maintenance
  Link_maintcap_lower_nommax:
    description: '`Link-maintcap_lower_nommax` — in maintenance, the whole chosen build is taken off'
    dims: [scenario, snapshot, link]
    where: Link_maint_ext
    expression: Link_maintenance_capacity >= Link_p_nom_ext - Link_p_nom_max * (1 - Link_maintenance)
  Link_maintcap_lower_nommin:
    description: '`Link-maintcap_lower_nommin` — in maintenance, at least the floor of the build is taken
      off'
    dims: [scenario, snapshot, link]
    where: Link_maint_ext AND Link_p_nom_min > 0
    expression: Link_maintenance_capacity >= Link_p_nom_min * Link_maintenance
  Link_maint_status_le_status:
    description: '`Link-maint-status-le-status` — the status in maintenance is at most the status'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committed AND NOT Link_p_nom_extendable AND NOT (Link_p_nom_mod
      > 0)
    expression: Link_maintenance_status <= Link_status
  Link_maint_status_le_maint:
    description: '`Link-maint-status-le-maint` — out of maintenance, the status in maintenance is zero'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committed AND NOT Link_p_nom_extendable AND NOT (Link_p_nom_mod
      > 0)
    expression: Link_maintenance_status <= Link_maintenance
  Link_maint_status_lb:
    description: '`Link-maint-status-lb` — on and in maintenance, the status in maintenance is one'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committed AND NOT Link_p_nom_extendable AND NOT (Link_p_nom_mod
      > 0)
    expression: Link_maintenance_status >= Link_status + Link_maintenance - 1
  Link_maint_modstatus_le_status:
    description: '`Link-maint-modstatus-le-status` — the modules on in maintenance are at most the modules
      on'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committed AND Link_p_nom_mod > 0
    expression: Link_maintenance_status <= Link_status
  Link_maint_modstatus_le_maint:
    description: '`Link-maint-modstatus-le-maint` — out of maintenance, no module is on in maintenance;
      in it, at most the modules the build cap holds'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committed AND Link_p_nom_mod > 0
    expression: Link_maintenance_status <= Link_p_nom_max / Link_p_nom_mod * Link_maintenance
  Link_maint_modstatus_lb:
    description: '`Link-maint-modstatus-lb` — in maintenance, every module on is on in maintenance'
    dims: [scenario, snapshot, link]
    where: Link_maintainable AND Link_committed AND Link_p_nom_mod > 0
    expression: Link_maintenance_status >= Link_status - Link_p_nom_max / Link_p_nom_mod * (1 - Link_maintenance)
  Process_com_p_lower:
    description: '`Process-com-p-lower` — a committed process runs at least its minimum; off, at least
      nothing'
    dims: [scenario, snapshot, process]
    where: Process_committed AND NOT Process_p_nom_extendable AND NOT (Process_p_nom_mod > 0)
    expression: Process_p >= Process_p_min_pu * Process_p_nom * (Process_status - Process_maintenance_pu
      * Process_maintenance_status)
  Process_com_p_upper:
    description: '`Process-com-p-upper` — a committed process runs at most what is available; off, at
      most nothing'
    dims: [scenario, snapshot, process]
    where: Process_committed AND NOT Process_p_nom_extendable AND NOT (Process_p_nom_mod > 0)
    expression: Process_p <= Process_p_max_pu * Process_p_nom * (Process_status - Process_maintenance_pu
      * Process_maintenance_status)
  Process_com_transition_start_up:
    description: '`Process-com-transition-start-up` — turning on is a start, counted against the state
      the process carried into the snapshot'
    dims: [scenario, snapshot, process]
    where: Process_committed
    expression: Process_start_up >= Process_status - Process_previous_status
  Process_com_transition_shut_down:
    description: '`Process-com-transition-shut-down` — turning off is a stop, counted against the state
      the process carried into the snapshot'
    dims: [scenario, snapshot, process]
    where: Process_committed
    expression: Process_shut_down >= Process_previous_status - Process_status
  Process_p_nom_modularity:
    description: '`Process-p_nom_modularity` — the chosen build is a whole number of modules'
    dims: [process]
    where: Process_p_nom_extendable AND Process_p_nom_mod > 0 AND Process_active_asset
    expression: Process_p_nom_ext == Process_p_nom_mod * Process_n_mod
  Process_com_ext_p_upper_cap:
    description: '`Process-com-ext-p-upper-cap` — a committed extendable process runs at most what is
      available of the chosen build, whatever its status'
    dims: [scenario, snapshot, process]
    where: Process_com_ext
    expression: Process_p <= Process_p_max_pu * (Process_p_nom_ext - Process_maintenance_pu * Process_maintenance_capacity)
  Process_com_ext_p_upper_big_m:
    description: '`Process-com-ext-p-upper-bigM` — off, a process does not run; on, the big M is no bound'
    dims: [scenario, snapshot, process]
    where: Process_com_ext
    expression: Process_p <= Process_big_m * Process_status
  Process_com_ext_p_lower:
    description: '`Process-com-ext-p-lower` — a committed extendable process runs at least its minimum
      of the chosen build; off, the big M releases the row'
    dims: [scenario, snapshot, process]
    where: Process_com_ext
    expression: Process_p >= Process_p_min_pu * (Process_p_nom_ext - Process_maintenance_pu * Process_maintenance_capacity)
      + Process_big_m * Process_status - Process_big_m
  Process_com_ext_p_lower_nonneg:
    description: '`Process-com-ext-p-lower-nonneg` — where no minimum-per-unit is negative, internal power
      is also plainly non-negative, a row the big-M lower cannot assert while the process is off'
    dims: [scenario, snapshot, process]
    where: Process_com_ext AND Process_p_min_pu_nonneg
    expression: Process_p >= 0
  Process_com_mod_p_lower:
    description: '`Process-com-mod-p-lower` — a committed modular process runs at least its minimum of
      one module, whether the build is fixed or a decision'
    dims: [scenario, snapshot, process]
    where: Process_committed AND Process_p_nom_mod > 0
    expression: Process_p >= Process_p_min_pu * Process_p_nom_mod * (Process_status - Process_maintenance_pu
      * Process_maintenance_status)
  Process_com_mod_p_upper:
    description: '`Process-com-mod-p-upper` — a committed modular process runs at most one module''s share,
      whether the build is fixed or a decision'
    dims: [scenario, snapshot, process]
    where: Process_committed AND Process_p_nom_mod > 0
    expression: Process_p <= Process_p_max_pu * Process_p_nom_mod * (Process_status - Process_maintenance_pu
      * Process_maintenance_status)
  Process_status_p_fixed_upper:
    description: '`Process-status-p-fixed-upper` — a status is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, process]
    where: Process_committed AND NOT (Process_p_nom_extendable AND Process_p_nom_mod > 0)
    expression: Process_status <= Process_modules_installed
  Process_start_up_p_fixed_upper:
    description: '`Process-start_up-p-fixed-upper` — a start is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, process]
    where: Process_committed AND NOT (Process_p_nom_extendable AND Process_p_nom_mod > 0)
    expression: Process_start_up <= Process_modules_installed
  Process_shut_down_p_fixed_upper:
    description: '`Process-shut_down-p-fixed-upper` — a stop is at most the modules in place, an explicit
      row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
      modules where it is'
    dims: [scenario, snapshot, process]
    where: Process_committed AND NOT (Process_p_nom_extendable AND Process_p_nom_mod > 0)
    expression: Process_shut_down <= Process_modules_installed
  Process_status_p_nom_variable_upper:
    description: '`Process-status-p_nom-variable-upper` — a modular process is on only where a module
      is built'
    dims: [scenario, snapshot, process]
    where: Process_committed AND Process_p_nom_extendable AND Process_p_nom_mod > 0
    expression: Process_status <= Process_n_mod
  Process_start_up_p_nom_variable_upper:
    description: '`Process-start_up-p_nom-variable-upper` — a modular process starts only where a module
      is built'
    dims: [scenario, snapshot, process]
    where: Process_committed AND Process_p_nom_extendable AND Process_p_nom_mod > 0
    expression: Process_start_up <= Process_n_mod
  Process_shut_down_p_nom_variable_upper:
    description: '`Process-shut_down-p_nom-variable-upper` — a modular process stops only where a module
      is built'
    dims: [scenario, snapshot, process]
    where: Process_committed AND Process_p_nom_extendable AND Process_p_nom_mod > 0
    expression: Process_shut_down <= Process_n_mod
  Process_maint_event_count:
    description: '`Process-maint-event-count` — a maintainable process holds its number of maintenance
      events over the horizon'
    dims: [scenario, process]
    where: Process_maintainable
    expression: sum(Process_maintenance_start, over=snapshot) == Process_maintenance_events
  Process_maint_window:
    description: '`Process-maint-window` — a process is in maintenance exactly where an event it started
      covers the snapshot; two events do not overlap, since the maintenance status is at most one'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_active
    expression: Process_maintenance == sum(Process_maintenance_start, over=start, by=Process_maintenance_cover[covered])
  Process_maint_start_horizon:
    description: '`Process-maint-start-horizon` — no event starts where it could not run its whole duration'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_active AND Process_maintenance_start_blocked
    expression: Process_maintenance_start == 0
  Process_maintcap_upper:
    description: '`Process-maintcap_upper` — the build taken off is at most the chosen build in maintenance,
      and at most the build less its floor out of it'
    dims: [scenario, snapshot, process]
    where: Process_maint_ext
    expression: Process_maintenance_capacity <= Process_p_nom_ext - Process_p_nom_min * (1 - Process_maintenance)
  Process_maintcap_upper_nommax:
    description: '`Process-maintcap_upper_nommax` — out of maintenance, no build is taken off'
    dims: [scenario, snapshot, process]
    where: Process_maint_ext
    expression: Process_maintenance_capacity <= Process_p_nom_max * Process_maintenance
  Process_maintcap_lower_nommax:
    description: '`Process-maintcap_lower_nommax` — in maintenance, the whole chosen build is taken off'
    dims: [scenario, snapshot, process]
    where: Process_maint_ext
    expression: Process_maintenance_capacity >= Process_p_nom_ext - Process_p_nom_max * (1 - Process_maintenance)
  Process_maintcap_lower_nommin:
    description: '`Process-maintcap_lower_nommin` — in maintenance, at least the floor of the build is
      taken off'
    dims: [scenario, snapshot, process]
    where: Process_maint_ext AND Process_p_nom_min > 0
    expression: Process_maintenance_capacity >= Process_p_nom_min * Process_maintenance
  Process_maint_status_le_status:
    description: '`Process-maint-status-le-status` — the status in maintenance is at most the status'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committed AND NOT Process_p_nom_extendable AND NOT (Process_p_nom_mod
      > 0)
    expression: Process_maintenance_status <= Process_status
  Process_maint_status_le_maint:
    description: '`Process-maint-status-le-maint` — out of maintenance, the status in maintenance is zero'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committed AND NOT Process_p_nom_extendable AND NOT (Process_p_nom_mod
      > 0)
    expression: Process_maintenance_status <= Process_maintenance
  Process_maint_status_lb:
    description: '`Process-maint-status-lb` — on and in maintenance, the status in maintenance is one'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committed AND NOT Process_p_nom_extendable AND NOT (Process_p_nom_mod
      > 0)
    expression: Process_maintenance_status >= Process_status + Process_maintenance - 1
  Process_maint_modstatus_le_status:
    description: '`Process-maint-modstatus-le-status` — the modules on in maintenance are at most the
      modules on'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committed AND Process_p_nom_mod > 0
    expression: Process_maintenance_status <= Process_status
  Process_maint_modstatus_le_maint:
    description: '`Process-maint-modstatus-le-maint` — out of maintenance, no module is on in maintenance;
      in it, at most the modules the build cap holds'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committed AND Process_p_nom_mod > 0
    expression: Process_maintenance_status <= Process_p_nom_max / Process_p_nom_mod * Process_maintenance
  Process_maint_modstatus_lb:
    description: '`Process-maint-modstatus-lb` — in maintenance, every module on is on in maintenance'
    dims: [scenario, snapshot, process]
    where: Process_maintainable AND Process_committed AND Process_p_nom_mod > 0
    expression: Process_maintenance_status >= Process_status - Process_p_nom_max / Process_p_nom_mod *
      (1 - Process_maintenance)
  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
expressions:
  Generator_previous_status:
    description: the commitment state a generator carries into a snapshot — off at the first snapshot
      it stands in past the first of the horizon, as PyPSA reads a status it did not build (`constraints.py:298`),
      and the state carried over otherwise
    dims: [scenario, snapshot, generator]
    cases:
      opening_late: {when: 'position(snapshot) > 0 AND NOT shift(Generator_active, along=snapshot, offset=1)',
        expression: 0}
    otherwise: Generator_status_carried_over
  Generator_status_carried_over:
    description: the state a generator carries over into a snapshot — the state it brought into the horizon
      at the first, the previous snapshot's after that
    dims: [scenario, snapshot, generator]
    cases:
      opening: {when: position(snapshot) == 0, expression: Generator_status_initial}
    otherwise: shift(Generator_status, along=snapshot, offset=1)
  Link_previous_status:
    description: the commitment state a link carries into a snapshot — off at the first snapshot it stands
      in past the first of the horizon, as PyPSA reads a status it did not build (`constraints.py:298`),
      and the state carried over otherwise
    dims: [scenario, snapshot, link]
    cases:
      opening_late: {when: 'position(snapshot) > 0 AND NOT shift(Link_active, along=snapshot, offset=1)',
        expression: 0}
    otherwise: Link_status_carried_over
  Link_status_carried_over:
    description: the state a link carries over into a snapshot — the state it brought into the horizon
      at the first, the previous snapshot's after that
    dims: [scenario, snapshot, link]
    cases:
      opening: {when: position(snapshot) == 0, expression: Link_status_initial}
    otherwise: shift(Link_status, along=snapshot, offset=1)
  Process_previous_status:
    description: the commitment state a process carries into a snapshot — off at the first snapshot it
      stands in past the first of the horizon, as PyPSA reads a status it did not build (`constraints.py:298`),
      and the state carried over otherwise
    dims: [scenario, snapshot, process]
    cases:
      opening_late: {when: 'position(snapshot) > 0 AND NOT shift(Process_active, along=snapshot, offset=1)',
        expression: 0}
    otherwise: Process_status_carried_over
  Process_status_carried_over:
    description: the state a process carries over 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)
  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]),
          along=snapshot, offset=Link_output_delay, edge=''wrap'', within=snapshot[period]) * Link_efficiency'}
    otherwise: shift(at(Link_p, by=link_output[link]), along=snapshot, offset=Link_output_delay,
      edge=0, within=snapshot[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]),
          along=snapshot, offset=Process_output_delay, edge=''wrap'', within=snapshot[period])
          * Process_rate'}
    otherwise: shift(at(Process_p, by=process_output[process]), along=snapshot, offset=Process_output_delay,
      edge=0, within=snapshot[period]) * Process_rate
  Generator_opex: {expression: 'sum(sum(((Generator_p * Generator_marginal_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot[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]), over=generator), over=snapshot)'}
  Generator_commitment_opex: {expression: 'sum(sum(((Generator_status * Generator_stand_by_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot[period]), over=generator), over=snapshot) + sum(sum(Generator_start_up
      * Generator_start_up_cost, over=generator), over=snapshot) + sum(sum(Generator_shut_down * Generator_shut_down_cost,
      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=link), over=snapshot) + sum(sum((((Link_p * Link_p) * Link_marginal_cost_quadratic)
      * snapshot_weightings_objective) * at(period_weight_objective, by=snapshot[period]), over=link),
      over=snapshot)'}
  Link_commitment_opex: {expression: 'sum(sum(((Link_status * Link_stand_by_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot[period]), over=link), over=snapshot) + sum(sum(Link_start_up
      * Link_start_up_cost, over=link), over=snapshot) + sum(sum(Link_shut_down * Link_shut_down_cost,
      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=process), over=snapshot) + sum(sum((((Process_p
      * Process_p) * Process_marginal_cost_quadratic) * snapshot_weightings_objective) * at(period_weight_objective,
      by=snapshot[period]), over=process), over=snapshot)'}
  Process_commitment_opex: {expression: 'sum(sum(((Process_status * Process_stand_by_cost) * snapshot_weightings_objective)
      * at(period_weight_objective, by=snapshot[period]), over=process), over=snapshot) + sum(sum(Process_start_up
      * Process_start_up_cost, over=process), over=snapshot) + sum(sum(Process_shut_down * Process_shut_down_cost,
      over=process), over=snapshot)'}
  scenario_opex:
    dims: [scenario]
    expression: ((((Generator_opex + Generator_commitment_opex) + Link_opex) + Link_commitment_opex) +
      Process_opex) + Process_commitment_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`)
  Generator_capex: {expression: sum(scenario_weight * Generator_p_nom_ext * Generator_capital_cost * Generator_capital_weight)}
  Link_capex: {expression: sum(scenario_weight * Link_p_nom_ext * Link_capital_cost * Link_capital_weight)}
  Process_capex: {expression: sum(scenario_weight * Process_p_nom_ext * Process_capital_cost * Process_capital_weight)}
  risk_weighted_opex: {expression: 'sum(scenario_weight * scenario_opex, over=scenario)'}
  total_cost:
    dims: []
    expression: ((Generator_capex + Link_capex) + 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
  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])'}
  Link_injection: {expression: '-sum(Link_p, over=link, by=link[bus0]) + sum(Link_output_arrival,
      over=link_output, by=link_output[bus])'}
  Load_injection: {expression: 'sum(Load_demand, over=load, by=load[bus])'}
  Process_injection: {expression: 'sum(Process_output_arrival, over=process_output, by=process_output[bus])'}
  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
conditions:
  Generator_com_ext: {description: 'a committable generator with an extendable, non-modular build that
      stands in the snapshot''s period — PyPSA''s `com-ext` rows, whose status is relaxed against the
      chosen build', condition: Generator_committable AND Generator_p_nom_extendable AND NOT (Generator_p_nom_mod
      > 0) AND Generator_active}
  Generator_maint_ext: {description: 'a maintainable generator with an extendable build, unless it is
      committable and modular, that stands in the snapshot''s period — the maintenance rows against the
      chosen build', condition: Generator_maintainable AND Generator_p_nom_extendable AND NOT (Generator_committable
      AND Generator_p_nom_mod > 0) AND Generator_active}
  Generator_committed: {description: a committable generator that stands in the snapshot's period — every
      unit-commitment row's set, condition: Generator_committable AND Generator_active}
  Link_com_ext: {description: 'a committable link with an extendable, non-modular build that stands in
      the snapshot''s period — PyPSA''s `com-ext` rows, whose status is relaxed against the chosen build',
    condition: Link_committable AND Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0) AND Link_active}
  Link_maint_ext: {description: 'a maintainable link with an extendable build, unless it is committable
      and modular, that stands in the snapshot''s period — the maintenance rows against the chosen build',
    condition: Link_maintainable AND Link_p_nom_extendable AND NOT (Link_committable AND Link_p_nom_mod
      > 0) AND Link_active}
  Link_committed: {description: a committable link that stands in the snapshot's period — every unit-commitment
      row's set, condition: Link_committable AND Link_active}
  Process_com_ext: {description: 'a committable process with an extendable, non-modular build that stands
      in the snapshot''s period — PyPSA''s `com-ext` rows, whose status is relaxed against the chosen
      build', condition: Process_committable AND Process_p_nom_extendable AND NOT (Process_p_nom_mod >
      0) AND Process_active}
  Process_maint_ext: {description: 'a maintainable process with an extendable build, unless it is committable
      and modular, that stands in the snapshot''s period — the maintenance rows against the chosen build',
    condition: Process_maintainable AND Process_p_nom_extendable AND NOT (Process_committable AND Process_p_nom_mod
      > 0) AND Process_active}
  Process_committed: {description: a committable process that stands in the snapshot's period — every
      unit-commitment row's set, condition: Process_committable AND Process_active}
objective: {sense: minimize, expression: total_cost}

The prep — every table the spec declares, from the network — and the solve:

from differential.pypsa.prep import prop, 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': prop(n, 'Generator', 'bus'),
    'link.bus0': prop(n, 'Link', 'bus0'),
    'load.bus': prop(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_34_committable_maintenance.yaml', sources) as solution:
    solution.objective  # 6420.048611

The network, rung_34_committable_maintenance.py in the corpus — the spine plus what this rung adds:

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

"""Rung 34: maintenance of committable units — a fixed, an extendable and a modular committable generator, link and process, each taken off for one event."""

from __future__ import annotations

import spine


def build():
    """The spine plus an east bus and nine maintainable committable components, with a dear peaker to cover them."""
    n = spine.build()
    n.add('Bus', 'east')
    committable = {'committable': True, 'maintainable': True}
    n.add(
        'Generator',
        'unit',
        bus='north',
        p_nom=60,
        p_min_pu=0.3,
        marginal_cost=5,
        start_up_cost=10,
        maintenance_duration=2,
        **committable,
    )
    n.add(
        'Generator',
        'unit_ext',
        bus='south',
        p_nom_extendable=True,
        p_nom_min=5,
        p_nom_max=50,
        capital_cost=10,
        p_min_pu=0.2,
        marginal_cost=4,
        maintenance_duration=3,
        maintenance_pu=0.5,
        **committable,
    )
    n.add(
        'Generator',
        'unit_mod',
        bus='south',
        p_nom_extendable=True,
        p_nom_mod=10,
        p_nom_max=30,
        capital_cost=8,
        p_min_pu=0.5,
        marginal_cost=3,
        maintenance_duration=1,
        **committable,
    )
    for component, ports in (('Link', {}), ('Process', {'rate0': -1.25})):
        n.add(
            component,
            f'{component.lower()}_unit',
            bus0='north',
            bus1='east',
            p_nom=40,
            p_min_pu=0.2,
            marginal_cost=1,
            maintenance_duration=2,
            **ports,
            **committable,
        )
        n.add(
            component,
            f'{component.lower()}_ext',
            bus0='south',
            bus1='east',
            p_nom_extendable=True,
            p_nom_min=5,
            p_nom_max=30,
            capital_cost=5,
            p_min_pu=0.2,
            maintenance_duration=3,
            maintenance_pu=0.5,
            **ports,
            **committable,
        )
        n.add(
            component,
            f'{component.lower()}_mod',
            bus0='north',
            bus1='east',
            p_nom_extendable=True,
            p_nom_mod=10,
            p_nom_max=20,
            capital_cost=3,
            p_min_pu=0.5,
            maintenance_duration=1,
            **ports,
            **committable,
        )
    n.add('Generator', 'east_peak', bus='east', p_nom=100, marginal_cost=60)
    n.add('Load', 'east_load', bus='east', p_set=[50, 60, 40, 55])
    return n
n = build()
n.optimize(solver_name='highs')
n.objective  # 6420.048611

The data

Every table this spec declares was first declared by a lower rung; its values here are in the prep above.