Rung 67: linearized commitment of a link and a process — both tightened where start and stop cost the same, and an extendable link the tightening skips¶
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 47777.333333 on both sides; structure ✔ 39 constraints · 10 variables, name for name; size ✔ 184 rows · ✔ 65 columns · ✔ 420 nonzeros; duals ✔ 184 rows, 2 negated, 6 inside PyPSA's range; model for model: 49 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-fix-p-lower |
12 | 12 |
Generator-fix-p-upper |
12 | 12 |
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-p-before |
3 | 3 |
Link-com-p-current |
3 | 3 |
Link-com-p-lower |
4 | 4 |
Link-com-p-upper |
4 | 4 |
Link-com-partly-shut-down |
3 | 3 |
Link-com-partly-start-up |
3 | 3 |
Link-com-transition-shut-down |
8 | 8 |
Link-com-transition-start-up |
8 | 8 |
Link-com-up-time |
3 | 3 |
Link-ext-p_nom-lower |
1 | 1 |
Link-ext-p_nom-upper |
1 | 1 |
Link-fix-p-lower |
4 | 4 |
Link-fix-p-upper |
4 | 4 |
Link-p-ramp_limit_down |
4 | 4 |
Link-p-ramp_limit_up |
4 | 4 |
Link-shut_down-p-fixed-upper |
8 | 8 |
Link-start_up-p-fixed-upper |
8 | 8 |
Link-status-p-fixed-upper |
8 | 8 |
Process-com-p-before |
3 | 3 |
Process-com-p-current |
3 | 3 |
Process-com-p-lower |
4 | 4 |
Process-com-p-upper |
4 | 4 |
Process-com-partly-shut-down |
3 | 3 |
Process-com-partly-start-up |
3 | 3 |
Process-com-transition-shut-down |
4 | 4 |
Process-com-transition-start-up |
4 | 4 |
Process-com-up-time |
3 | 3 |
Process-p-ramp_limit_down |
4 | 4 |
Process-p-ramp_limit_up |
4 | 4 |
Process-shut_down-p-fixed-upper |
4 | 4 |
Process-start_up-p-fixed-upper |
4 | 4 |
Process-status-p-fixed-upper |
4 | 4 |
| column | PyPSA | specsolve |
|---|---|---|
Generator-p |
12 | 12 |
Link-p |
12 | 12 |
Link-p_nom |
1 | 1 |
Link-shut_down |
8 | 8 |
Link-start_up |
8 | 8 |
Link-status |
8 | 8 |
Process-p |
4 | 4 |
Process-shut_down |
4 | 4 |
Process-start_up |
4 | 4 |
Process-status |
4 | 4 |
The model¶
The same model, as math
n.optimize(linearized_unit_commitment=True), as a patch over examples/pypsa.yaml. The status, its starts and its stops of a committable generator, link and process are shares in [0, 1] rather than integers, and four rows PyPSA adds only under the keyword tighten the relaxation of a unit with a fixed build whose start and stop cost the same in every snapshot and every scenario (constraints.py:599-699). A modular committable unit is refused, as PyPSA refuses it. Every other row is the integer run's.
Sets¶
| Symbol | Meaning |
|---|---|
| \(\Xi\) | index \(\xi\) — scenario — the futures dispatch is chosen in, each with a weight |
| \(\mathcal{T}\) | index \(t\) — snapshot with \(\mathrm{snapshot\_period}: \mathcal{T} \to \mathcal{Y}\) — dispatch periods |
| \(\mathcal{N}\) | index \(n\) — bus with \(\mathrm{Generator\_bus}: \mathcal{G} \to \mathcal{N},\ \mathrm{Link\_bus0}: \mathcal{L} \to \mathcal{N},\ \mathrm{Link\_output\_bus}: \mathcal{O} \to \mathcal{N},\ \mathrm{Process\_output\_bus}: \mathcal{R} \to \mathcal{N},\ \mathrm{Load\_bus}: \mathcal{D} \to \mathcal{N}\) — network nodes |
| \(\mathcal{G}\) | index \(g\) — generator with \(\mathrm{Generator\_bus}: \mathcal{G} \to \mathcal{N}\) — generating units, each on one bus |
| \(\mathcal{L}\) | index \(l\) — link with \(\mathrm{Link\_bus0}: \mathcal{L} \to \mathcal{N},\ \mathrm{Link\_output\_link}: \mathcal{O} \to \mathcal{L}\) — controllable connections, each from one bus to the buses it delivers to |
| \(\mathcal{O}\) | index \(o\) — link_output with \(\mathrm{Link\_output\_link}: \mathcal{O} \to \mathcal{L},\ \mathrm{Link\_output\_bus}: \mathcal{O} \to \mathcal{N}\) — 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 \(\mathrm{Process\_output\_process}: \mathcal{R} \to \mathcal{J}\) — 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 \(\mathrm{Process\_output\_process}: \mathcal{R} \to \mathcal{J},\ \mathrm{Process\_output\_bus}: \mathcal{R} \to \mathcal{N}\) — 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 \(\mathrm{Load\_bus}: \mathcal{D} \to \mathcal{N}\) — demands, each on one bus |
| \(\mathcal{Y}\) | index \(y\) — period with \(\mathrm{snapshot\_period}: \mathcal{T} \to \mathcal{Y}\) — 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 |
| \(\mathrm{ru}^{f}\) | Link_ramp_limit_up over \(\Xi \times \mathcal{T} \times \mathcal{L}\), neutral where the data has no row — most a link may raise its flow between snapshots, per unit of nominal power; no value means no limit — read at the later of the two snapshots, so the limit may change over time |
| \(\mathrm{rd}^{f}\) | Link_ramp_limit_down over \(\Xi \times \mathcal{T} \times \mathcal{L}\), neutral where the data has no row — most a link may lower its flow between snapshots, per unit of nominal power; no value means no limit — read at the later of the two snapshots, so the limit may change over time |
| \(\mathrm{f}^{\mathrm{nom}}\) | 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 |
| \(\mathrm{ru}^{f,\mathrm{up}}\) | Link_ramp_limit_start_up over \(\Xi \times \mathcal{L}\), neutral where the data has no row — most flow in the snapshot a link starts, per unit of nominal power; no value means no limit |
| \(\mathrm{rd}^{f,\mathrm{dn}}\) | Link_ramp_limit_shut_down over \(\Xi \times \mathcal{L}\), neutral where the data has no row — most flow in the snapshot before a link stops, per unit of nominal power; no value means no limit |
| \(\mathrm{UT}^{f}\) | Link_min_up_time over \(\Xi \times \mathcal{L}\) — least snapshots a link stays on once started |
| \(\mathrm{u}^{f,0}\) | 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 |
| \(\mathrm{f}^{0}\) | Link_p_init over \(\Xi \times \mathcal{L}\), neutral where the data has no row — the flow a link brought into the horizon — PyPSA's p_init, read only where the link came in running; no value means it is unknown, so the link carries no ramp row at the first snapshot |
| \(\mathrm{c}^{f,\mathrm{up}}\) | 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 \(\mathcal{L}\), neutral 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 \(\Xi \times \mathcal{L}\), neutral 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 |
| \(\mathrm{z}^{\mathrm{nom}}\) | 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 |
| \(\mathrm{ru}^{z}\) | Process_ramp_limit_up over \(\Xi \times \mathcal{T} \times \mathcal{J}\), neutral where the data has no row — most a process may raise its internal power between snapshots, per unit of nominal power; no value means no limit — read at the later of the two snapshots, so the limit may change over time |
| \(\mathrm{rd}^{z}\) | Process_ramp_limit_down over \(\Xi \times \mathcal{T} \times \mathcal{J}\), neutral where the data has no row — most a process may lower its internal power between snapshots, per unit of nominal power; no value means no limit — read at the later of the two snapshots, so the limit may change over time |
| \(\mathrm{com}^{z}\) | Process_committable over \(\mathcal{J}\) — whether internal power is gated by an on/off status decision |
| \(\mathrm{ru}^{z,\mathrm{up}}\) | Process_ramp_limit_start_up over \(\Xi \times \mathcal{J}\), neutral where the data has no row — most internal power in the snapshot a process starts, per unit of nominal power; no value means no limit |
| \(\mathrm{rd}^{z,\mathrm{dn}}\) | Process_ramp_limit_shut_down over \(\Xi \times \mathcal{J}\), neutral where the data has no row — most internal power in the snapshot before a process stops, per unit of nominal power; no value means no limit |
| \(\mathrm{UT}^{z}\) | Process_min_up_time over \(\Xi \times \mathcal{J}\) — least snapshots a process stays on once started |
| \(\mathrm{u}^{z,0}\) | 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 |
| \(\mathrm{z}^{0}\) | Process_p_init over \(\Xi \times \mathcal{J}\), neutral where the data has no row — the internal power a process brought into the horizon — PyPSA's p_init, read only where the process came in running; no value means it is unknown, so the process carries no ramp row at the first snapshot |
| \(\mathrm{c}^{z,\mathrm{up}}\) | 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 \(\mathcal{J}\), neutral 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 |
| \(\mathrm{load}\) | 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 |
| \(\mathrm{act}^{f}\) | 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) |
| \(\mathrm{W}^{f}\) | Link_capital_weight over \(\mathcal{L}\) — the sum of period weights a link stands in — PyPSA's active * period_weighting, summed, 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 |
|---|---|
| \(\mathrm{Link\_com\_ext}\) | 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 |
| \(\mathrm{Link\_committed}\) | Link_committed over \(\mathcal{L} \times \mathcal{T}\) — a committable link that stands in the snapshot's period — every unit-commitment row's set |
| \(\mathrm{Link\_ramps\_from\_previous}\) | Link_ramps_from_previous over \(\mathcal{L} \times \Xi \times \mathcal{T}\) — a snapshot whose ramp reads a previous output — any snapshot but its period's first, and the horizon's first where the link comes in off or carries an initial output |
| \(\mathrm{Process\_committed}\) | Process_committed over \(\mathcal{J} \times \mathcal{T}\) — a committable process that stands in the snapshot's period — every unit-commitment row's set |
| \(\mathrm{Process\_ramps\_from\_previous}\) | Process_ramps_from_previous over \(\mathcal{J} \times \Xi \times \mathcal{T}\) — a snapshot whose ramp reads a previous output — any snapshot but its period's first, and the horizon's first where the process comes in off or carries an initial output |
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 |
| \(u^{f}\) | Link_status over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-status — how much of a committable link is on, a share in [0, 1] rather than an integer: the relaxation the keyword solves (variables.py:86-87) |
| \(\mathit{up}^{f}\) | Link_start_up over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-start_up — how much of a committable link turns on this snapshot, a share in [0, 1] (variables.py:137-138) |
| \(\mathit{dn}^{f}\) | Link_shut_down over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-shut_down — how much of a committable link turns off this snapshot, a share in [0, 1] (variables.py:188-189) |
| \(u^{z}\) | Process_status over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — Process-status — how much of a committable process is on, a share in [0, 1] rather than an integer: the relaxation the keyword solves (variables.py:86-87) |
| \(\mathit{up}^{z}\) | Process_start_up over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — Process-start_up — how much of a committable process turns on this snapshot, a share in [0, 1] (variables.py:137-138) |
| \(\mathit{dn}^{z}\) | Process_shut_down over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — Process-shut_down — how much of a committable process turns off this snapshot, a share in [0, 1] (variables.py:188-189) |
| \(F\) | 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 |
|---|---|
| \(\mathit{Link\_p\_nom\_effective}\) | Link_p_nom_effective over \(\Xi \times \mathcal{L}\) — the build a link's limits are taken against — the chosen one where it is extendable, the given one otherwise |
| \(\mathit{Link\_previous\_status}\) | 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 |
| \(\mathit{Link\_previous\_p}\) | Link_previous_p over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — the flow a link carries into a snapshot — at the first, the p_init it brought in where it came in running and nothing where it came in off; the previous snapshot's after that |
| \(\mathrm{Link\_ramp\_up\_rate}\) | Link_ramp_up_rate over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — the ramp limit a link's up row reads — PyPSA's ramp_limit_up, or the full build where it has none, since a start-up ramp alone builds the row |
| \(\mathrm{Link\_ramp\_down\_rate}\) | Link_ramp_down_rate over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — the ramp limit a link's down row reads — PyPSA's ramp_limit_down, or the full build where it has none, since a shut-down ramp alone builds the row |
| \(\mathrm{Link\_start\_up\_rate}\) | Link_start_up_rate over \(\Xi \times \mathcal{L}\) — the start-up ramp a link's up row reads — PyPSA's ramp_limit_start_up, or the full build where it has none |
| \(\mathrm{Link\_shut\_down\_rate}\) | Link_shut_down_rate over \(\Xi \times \mathcal{L}\) — the shut-down ramp a link's down row reads — PyPSA's ramp_limit_shut_down, or the full build where it has none |
| \(\mathrm{Link\_p\_nom\_committed}\) | Link_p_nom_committed over \(\Xi \times \mathcal{L}\) — the build a committed link's ramp rows are taken against — one module where the build is extendable and modular, the given build otherwise |
| \(\mathit{Link\_ramp\_up\_allowance}\) | Link_ramp_up_allowance over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — how far a link may raise flow between two snapshots — its ramp limit of the build while it stays on, plus its start-up ramp in the snapshot it turns on |
| \(\mathit{Link\_ramp\_down\_allowance}\) | Link_ramp_down_allowance over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — how far a link may lower flow between two snapshots — its ramp limit of the build while it stays on, plus its shut-down ramp in the snapshot it turns off |
| \(\mathit{Process\_p\_nom\_effective}\) | Process_p_nom_effective over \(\Xi \times \mathcal{J}\) — the build a process's limits are taken against — the chosen one where it is extendable, the given one otherwise |
| \(\mathit{Process\_previous\_status}\) | 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 |
| \(\mathit{Process\_previous\_p}\) | Process_previous_p over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — the internal power a process carries into a snapshot — at the first, the p_init it brought in where it came in running and nothing where it came in off; the previous snapshot's after that |
| \(\mathrm{Process\_ramp\_up\_rate}\) | Process_ramp_up_rate over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — the ramp limit a process's up row reads — PyPSA's ramp_limit_up, or the full build where it has none, since a start-up ramp alone builds the row |
| \(\mathrm{Process\_ramp\_down\_rate}\) | Process_ramp_down_rate over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — the ramp limit a process's down row reads — PyPSA's ramp_limit_down, or the full build where it has none, since a shut-down ramp alone builds the row |
| \(\mathrm{Process\_start\_up\_rate}\) | Process_start_up_rate over \(\Xi \times \mathcal{J}\) — the start-up ramp a process's up row reads — PyPSA's ramp_limit_start_up, or the full build where it has none |
| \(\mathrm{Process\_shut\_down\_rate}\) | Process_shut_down_rate over \(\Xi \times \mathcal{J}\) — the shut-down ramp a process's down row reads — PyPSA's ramp_limit_shut_down, or the full build where it has none |
| \(\mathrm{Process\_p\_nom\_committed}\) | Process_p_nom_committed over \(\Xi \times \mathcal{J}\) — the build a committed process's ramp rows are taken against — one module where the build is extendable and modular, the given build otherwise |
| \(\mathit{Process\_ramp\_up\_allowance}\) | Process_ramp_up_allowance over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — how far a process may raise internal power between two snapshots — its ramp limit of the build while it stays on, plus its start-up ramp in the snapshot it turns on |
| \(\mathit{Process\_ramp\_down\_allowance}\) | Process_ramp_down_allowance over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — how far a process may lower internal power between two snapshots — its ramp limit of the build while it stays on, plus its shut-down ramp in the snapshot it turns off |
| \(\mathit{Link\_output\_arrival}\) | 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 \(\Xi\) |
| \(\mathit{Link\_opex}\) | 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) |
| \(\mathit{Link\_capex}\) | Link_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 |
| \(t \ominus^{\mathrm{relation}(t)} k\) | within=relation[...] — \(t-k\) inside the group of \(t\) |
| \(\mathrm{pos}(t)\) | position() — the position of \(t\), counted from \(0\); \(t\) is the label |
| \(\mathrm{pos}_{\mathrm{relation}(t)}(t)\) | position(within=relation[...]) — the position of \(t\) inside its group |
Conditions¶
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_committed
\[
\mathrm{Link\_committed}_{l,t} \iff \mathrm{com}^{f}_{l} \wedge \mathrm{on}^{f}_{t,l} \qquad \forall\, l \in \mathcal{L},\ t \in \mathcal{T}
\]
Link_ramps_from_previous
\[
\mathrm{Link\_ramps\_from\_previous}_{l,\xi,t} \iff \mathrm{pos}_{\mathrm{snapshot\_period}(t)}(t) > 0 \vee \mathrm{pos}(t) = 0 \wedge \left( \mathrm{u}^{f,0}_{\xi,l} = 0 \vee \mathrm{f}^{0}_{\xi,l} \text{ is defined} \right) \qquad \forall\, l \in \mathcal{L},\ \xi \in \Xi,\ t \in \mathcal{T}
\]
Process_committed
\[
\mathrm{Process\_committed}_{j,t} \iff \mathrm{com}^{z}_{j} \wedge \mathrm{on}^{z}_{t,j} \qquad \forall\, j \in \mathcal{J},\ t \in \mathcal{T}
\]
Process_ramps_from_previous
\[
\mathrm{Process\_ramps\_from\_previous}_{j,\xi,t} \iff \mathrm{pos}_{\mathrm{snapshot\_period}(t)}(t) > 0 \vee \mathrm{pos}(t) = 0 \wedge \left( \mathrm{u}^{z,0}_{\xi,j} = 0 \vee \mathrm{z}^{0}_{\xi,j} \text{ is defined} \right) \qquad \forall\, j \in \mathcal{J},\ \xi \in \Xi,\ t \in \mathcal{T}
\]
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
\[
z_{\xi,t,j} \in \mathbb{R} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{on}^{z}_{t,j}
\]
Link_status
\[
0 \le u^{f}_{\xi,t,l} \le 1 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t}
\]
Link_start_up
\[
0 \le \mathit{up}^{f}_{\xi,t,l} \le 1 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t}
\]
Link_shut_down
\[
0 \le \mathit{dn}^{f}_{\xi,t,l} \le 1 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t}
\]
Process_status
\[
0 \le u^{z}_{\xi,t,j} \le 1 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t}
\]
Process_start_up
\[
0 \le \mathit{up}^{z}_{\xi,t,j} \le 1 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t}
\]
Process_shut_down
\[
0 \le \mathit{dn}^{z}_{\xi,t,j} \le 1 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t}
\]
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¶
Link_p_nom_effective
\[
\mathit{Link\_p\_nom\_effective}_{\xi,l} = \begin{cases} F_{l} & \text{if } \mathrm{ext}^{f}_{l} \\ \mathrm{f}^{\mathrm{nom}}_{\xi,l} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ l \in \mathcal{L}
\]
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
\[
\mathit{Link\_status\_carried\_over}_{\xi,t,l} = \begin{cases} \mathrm{u}^{f,0}_{\xi,l} & \text{if } \mathrm{pos}(t) = 0 \\ u^{f}_{\xi,t - 1,l} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L}
\]
Link_previous_p
\[
\mathit{Link\_previous\_p}_{\xi,t,l} = \begin{cases} \mathrm{u}^{f,0}_{\xi,l} \cdot \mathrm{f}^{0}_{\xi,l} & \text{if } \mathrm{pos}(t) = 0 \\ f_{\xi,t - 1,l} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L}
\]
Link_ramp_up_rate
\[
\mathrm{Link\_ramp\_up\_rate}_{\xi,t,l} = \begin{cases} \mathrm{ru}^{f}_{\xi,t,l} & \text{if } \mathrm{ru}^{f}_{\xi,t,l} \text{ is defined} \\ 1 & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L}
\]
Link_ramp_down_rate
\[
\mathrm{Link\_ramp\_down\_rate}_{\xi,t,l} = \begin{cases} \mathrm{rd}^{f}_{\xi,t,l} & \text{if } \mathrm{rd}^{f}_{\xi,t,l} \text{ is defined} \\ 1 & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L}
\]
Link_start_up_rate
\[
\mathrm{Link\_start\_up\_rate}_{\xi,l} = \begin{cases} \mathrm{ru}^{f,\mathrm{up}}_{\xi,l} & \text{if } \mathrm{ru}^{f,\mathrm{up}}_{\xi,l} \text{ is defined} \\ 1 & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ l \in \mathcal{L}
\]
Link_shut_down_rate
\[
\mathrm{Link\_shut\_down\_rate}_{\xi,l} = \begin{cases} \mathrm{rd}^{f,\mathrm{dn}}_{\xi,l} & \text{if } \mathrm{rd}^{f,\mathrm{dn}}_{\xi,l} \text{ is defined} \\ 1 & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ l \in \mathcal{L}
\]
Link_p_nom_committed
\[
\mathrm{Link\_p\_nom\_committed}_{\xi,l} = \begin{cases} \mathrm{f}^{\mathrm{mod}}_{l} & \text{if } \mathrm{ext}^{f}_{l} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \\ \mathrm{f}^{\mathrm{nom}}_{\xi,l} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ l \in \mathcal{L}
\]
Link_ramp_up_allowance
\[
\mathit{Link\_ramp\_up\_allowance}_{\xi,t,l} = \begin{cases} \mathrm{Link\_ramp\_up\_rate}_{\xi,t,l} \cdot \mathrm{Link\_p\_nom\_committed}_{\xi,l} \cdot \mathit{Link\_previous\_status}_{\xi,t,l} + \mathrm{Link\_start\_up\_rate}_{\xi,l} \cdot \mathrm{Link\_p\_nom\_committed}_{\xi,l} \cdot \left( u^{f}_{\xi,t,l} - \mathit{Link\_previous\_status}_{\xi,t,l} \right) & \text{if } \mathrm{com}^{f}_{l} \\ \mathrm{Link\_ramp\_up\_rate}_{\xi,t,l} \cdot \mathit{Link\_p\_nom\_effective}_{\xi,l} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L}
\]
Link_ramp_down_allowance
\[
\mathit{Link\_ramp\_down\_allowance}_{\xi,t,l} = \begin{cases} \mathrm{Link\_ramp\_down\_rate}_{\xi,t,l} \cdot \mathrm{Link\_p\_nom\_committed}_{\xi,l} \cdot u^{f}_{\xi,t,l} + \mathrm{Link\_shut\_down\_rate}_{\xi,l} \cdot \mathrm{Link\_p\_nom\_committed}_{\xi,l} \cdot \left( \mathit{Link\_previous\_status}_{\xi,t,l} - u^{f}_{\xi,t,l} \right) & \text{if } \mathrm{com}^{f}_{l} \\ \mathrm{Link\_ramp\_down\_rate}_{\xi,t,l} \cdot \mathit{Link\_p\_nom\_effective}_{\xi,l} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L}
\]
Process_p_nom_effective
\[
\mathit{Process\_p\_nom\_effective}_{\xi,j} = \begin{cases} Z_{j} & \text{if } \mathrm{ext}^{z}_{j} \\ \mathrm{z}^{\mathrm{nom}}_{\xi,j} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ j \in \mathcal{J}
\]
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
\[
\mathit{Process\_status\_carried\_over}_{\xi,t,j} = \begin{cases} \mathrm{u}^{z,0}_{\xi,j} & \text{if } \mathrm{pos}(t) = 0 \\ u^{z}_{\xi,t - 1,j} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J}
\]
Process_previous_p
\[
\mathit{Process\_previous\_p}_{\xi,t,j} = \begin{cases} \mathrm{u}^{z,0}_{\xi,j} \cdot \mathrm{z}^{0}_{\xi,j} & \text{if } \mathrm{pos}(t) = 0 \\ z_{\xi,t - 1,j} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J}
\]
Process_ramp_up_rate
\[
\mathrm{Process\_ramp\_up\_rate}_{\xi,t,j} = \begin{cases} \mathrm{ru}^{z}_{\xi,t,j} & \text{if } \mathrm{ru}^{z}_{\xi,t,j} \text{ is defined} \\ 1 & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J}
\]
Process_ramp_down_rate
\[
\mathrm{Process\_ramp\_down\_rate}_{\xi,t,j} = \begin{cases} \mathrm{rd}^{z}_{\xi,t,j} & \text{if } \mathrm{rd}^{z}_{\xi,t,j} \text{ is defined} \\ 1 & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J}
\]
Process_start_up_rate
\[
\mathrm{Process\_start\_up\_rate}_{\xi,j} = \begin{cases} \mathrm{ru}^{z,\mathrm{up}}_{\xi,j} & \text{if } \mathrm{ru}^{z,\mathrm{up}}_{\xi,j} \text{ is defined} \\ 1 & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ j \in \mathcal{J}
\]
Process_shut_down_rate
\[
\mathrm{Process\_shut\_down\_rate}_{\xi,j} = \begin{cases} \mathrm{rd}^{z,\mathrm{dn}}_{\xi,j} & \text{if } \mathrm{rd}^{z,\mathrm{dn}}_{\xi,j} \text{ is defined} \\ 1 & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ j \in \mathcal{J}
\]
Process_p_nom_committed
\[
\mathrm{Process\_p\_nom\_committed}_{\xi,j} = \begin{cases} \mathrm{z}^{\mathrm{mod}}_{j} & \text{if } \mathrm{ext}^{z}_{j} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \\ \mathrm{z}^{\mathrm{nom}}_{\xi,j} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ j \in \mathcal{J}
\]
Process_ramp_up_allowance
\[
\mathit{Process\_ramp\_up\_allowance}_{\xi,t,j} = \begin{cases} \mathrm{Process\_ramp\_up\_rate}_{\xi,t,j} \cdot \mathrm{Process\_p\_nom\_committed}_{\xi,j} \cdot \mathit{Process\_previous\_status}_{\xi,t,j} + \mathrm{Process\_start\_up\_rate}_{\xi,j} \cdot \mathrm{Process\_p\_nom\_committed}_{\xi,j} \cdot \left( u^{z}_{\xi,t,j} - \mathit{Process\_previous\_status}_{\xi,t,j} \right) & \text{if } \mathrm{com}^{z}_{j} \\ \mathrm{Process\_ramp\_up\_rate}_{\xi,t,j} \cdot \mathit{Process\_p\_nom\_effective}_{\xi,j} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J}
\]
Process_ramp_down_allowance
\[
\mathit{Process\_ramp\_down\_allowance}_{\xi,t,j} = \begin{cases} \mathrm{Process\_ramp\_down\_rate}_{\xi,t,j} \cdot \mathrm{Process\_p\_nom\_committed}_{\xi,j} \cdot u^{z}_{\xi,t,j} + \mathrm{Process\_shut\_down\_rate}_{\xi,j} \cdot \mathrm{Process\_p\_nom\_committed}_{\xi,j} \cdot \left( \mathit{Process\_previous\_status}_{\xi,t,j} - u^{z}_{\xi,t,j} \right) & \text{if } \mathrm{com}^{z}_{j} \\ \mathrm{Process\_ramp\_down\_rate}_{\xi,t,j} \cdot \mathit{Process\_p\_nom\_effective}_{\xi,j} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J}
\]
Link_output_arrival
\[
\mathit{Link\_output\_arrival}_{\xi,t,o} = \begin{cases} f_{\xi,t \ominus^{\mathrm{snapshot\_period}(t)} \mathrm{d}^{f},\mathrm{Link\_output\_link}(o)} \cdot \eta_{\xi,t,o} & \text{if } \mathrm{cyc}^{f}_{o} \\ f_{\xi,t \boxminus_{0}^{\mathrm{snapshot\_period}(t)} \mathrm{d}^{f},\mathrm{Link\_output\_link}(o)} \cdot \eta_{\xi,t,o} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ o \in \mathcal{O}
\]
Process_output_arrival
\[
\mathit{Process\_output\_arrival}_{\xi,t,r} = \begin{cases} z_{\xi,t \ominus^{\mathrm{snapshot\_period}(t)} \mathrm{d}^{z},\mathrm{Process\_output\_process}(r)} \cdot \alpha_{\xi,t,r} & \text{if } \mathrm{cyc}^{z}_{r} \\ z_{\xi,t \boxminus_{0}^{\mathrm{snapshot\_period}(t)} \mathrm{d}^{z},\mathrm{Process\_output\_process}(r)} \cdot \alpha_{\xi,t,r} & \text{otherwise} \end{cases} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ r \in \mathcal{R}
\]
Generator_opex
\[
\mathit{Generator\_opex}_{\xi} = \sum_{t \in \mathcal{T}} \sum_{g \in \mathcal{G}} p_{\xi,t,g} \cdot \mathrm{c}_{\xi,t,g} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{snapshot\_period}(t)} + \sum_{t \in \mathcal{T}} \sum_{g \in \mathcal{G}} p_{\xi,t,g} \cdot p_{\xi,t,g} \cdot \mathrm{c}^{(2)}_{\xi,t,g} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{snapshot\_period}(t)} \qquad \forall\, \xi \in \Xi
\]
Link_opex
\[
\mathit{Link\_opex}_{\xi} = \sum_{t \in \mathcal{T}} \sum_{l \in \mathcal{L}} f_{\xi,t,l} \cdot \mathrm{c}^{f}_{\xi,t,l} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{snapshot\_period}(t)} + \sum_{t \in \mathcal{T}} \sum_{l \in \mathcal{L}} f_{\xi,t,l} \cdot f_{\xi,t,l} \cdot \mathrm{c}^{f,(2)}_{\xi,t,l} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{snapshot\_period}(t)} \qquad \forall\, \xi \in \Xi
\]
Link_commitment_opex
\[
\mathit{Link\_commitment\_opex}_{\xi} = \sum_{t \in \mathcal{T}} \sum_{l \in \mathcal{L}} u^{f}_{\xi,t,l} \cdot \mathrm{c}^{f,\mathrm{on}}_{\xi,t,l} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{snapshot\_period}(t)} + \sum_{t \in \mathcal{T}} \sum_{l \in \mathcal{L}} \mathit{up}^{f}_{\xi,t,l} \cdot \mathrm{c}^{f,\mathrm{up}}_{\xi,t,l} + \sum_{t \in \mathcal{T}} \sum_{l \in \mathcal{L}} \mathit{dn}^{f}_{\xi,t,l} \cdot \mathrm{c}^{f,\mathrm{dn}}_{\xi,t,l} \qquad \forall\, \xi \in \Xi
\]
Process_opex
\[
\mathit{Process\_opex}_{\xi} = \sum_{t \in \mathcal{T}} \sum_{j \in \mathcal{J}} z_{\xi,t,j} \cdot \mathrm{c}^{z}_{\xi,t,j} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{snapshot\_period}(t)} + \sum_{t \in \mathcal{T}} \sum_{j \in \mathcal{J}} z_{\xi,t,j} \cdot z_{\xi,t,j} \cdot \mathrm{c}^{z,(2)}_{\xi,t,j} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{snapshot\_period}(t)} \qquad \forall\, \xi \in \Xi
\]
Process_commitment_opex
\[
\mathit{Process\_commitment\_opex}_{\xi} = \sum_{t \in \mathcal{T}} \sum_{j \in \mathcal{J}} u^{z}_{\xi,t,j} \cdot \mathrm{c}^{z,\mathrm{on}}_{\xi,t,j} \cdot \mathrm{w}_{t} \cdot \mathrm{w}^{y}_{\mathrm{snapshot\_period}(t)} + \sum_{t \in \mathcal{T}} \sum_{j \in \mathcal{J}} \mathit{up}^{z}_{\xi,t,j} \cdot \mathrm{c}^{z,\mathrm{up}}_{\xi,t,j} + \sum_{t \in \mathcal{T}} \sum_{j \in \mathcal{J}} \mathit{dn}^{z}_{\xi,t,j} \cdot \mathrm{c}^{z,\mathrm{dn}}_{\xi,t,j} \qquad \forall\, \xi \in \Xi
\]
scenario_opex
\[
\mathit{scenario\_opex}_{\xi} = \mathit{Generator\_opex}_{\xi} + \mathit{Link\_opex}_{\xi} + \mathit{Link\_commitment\_opex}_{\xi} + \mathit{Process\_opex}_{\xi} + \mathit{Process\_commitment\_opex}_{\xi} \qquad \forall\, \xi \in \Xi
\]
Link_capex
\[
\mathit{Link\_capex} = \sum_{\xi \in \Xi,\ l \in \mathcal{L}} \pi_{\xi} \cdot F_{l} \cdot \mathrm{c}^{\mathrm{cap},f}_{\xi,l} \cdot \mathrm{W}^{f}_{l}
\]
risk_weighted_opex
\[
\mathit{risk\_weighted\_opex} = \sum_{\xi \in \Xi} \pi_{\xi} \cdot \mathit{scenario\_opex}_{\xi}
\]
total_cost
\[
\mathit{total\_cost} = \mathit{Link\_capex} + \mathit{risk\_weighted\_opex}
\]
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
\[
\mathit{Generator\_injection}_{n,\xi,t} = \sum_{g \in \mathcal{G} \,:\, \mathrm{Generator\_bus}(g) = n} \mathrm{sgn}_{g} \cdot p_{\xi,t,g} \qquad \forall\, n \in \mathcal{N},\ \xi \in \Xi,\ t \in \mathcal{T}
\]
Link_injection
\[
\mathit{Link\_injection}_{n,\xi,t} = -\left( \sum_{l \in \mathcal{L} \,:\, \mathrm{Link\_bus0}(l) = n} f_{\xi,t,l} \right) + \sum_{o \in \mathcal{O} \,:\, \mathrm{Link\_output\_bus}(o) = n} \mathit{Link\_output\_arrival}_{\xi,t,o} \qquad \forall\, n \in \mathcal{N},\ \xi \in \Xi,\ t \in \mathcal{T}
\]
Load_injection
\[
\mathrm{Load\_injection}_{n,\xi,t} = \sum_{d \in \mathcal{D} \,:\, \mathrm{Load\_bus}(d) = n} \mathrm{Load\_demand}_{\xi,t,d} \qquad \forall\, n \in \mathcal{N},\ \xi \in \Xi,\ t \in \mathcal{T}
\]
Process_injection
\[
\mathit{Process\_injection}_{n,\xi,t} = \sum_{r \in \mathcal{R} \,:\, \mathrm{Process\_output\_bus}(r) = n} \mathit{Process\_output\_arrival}_{\xi,t,r} \qquad \forall\, n \in \mathcal{N},\ \xi \in \Xi,\ t \in \mathcal{T}
\]
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
\[
p_{\xi,t,g} \ge \underline{\mathrm{p}}_{\xi,t,g} \cdot \mathrm{p}^{\mathrm{nom}}_{\xi,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \neg \mathrm{ext}_{g} \wedge \neg \mathrm{com}_{g} \wedge \mathrm{on}_{t,g}
\]
Generator_fix_p_upper
\[
p_{\xi,t,g} \le \overline{\mathrm{p}}_{\xi,t,g} \cdot \mathrm{p}^{\mathrm{nom}}_{\xi,g} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ g \in \mathcal{G} \,:\, \neg \mathrm{ext}_{g} \wedge \neg \mathrm{com}_{g} \wedge \mathrm{on}_{t,g}
\]
Link_fix_p_lower
\[
f_{\xi,t,l} \ge \underline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \neg \mathrm{ext}^{f}_{l} \wedge \neg \mathrm{com}^{f}_{l} \wedge \mathrm{on}^{f}_{t,l}
\]
Link_fix_p_upper
\[
f_{\xi,t,l} \le \overline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \neg \mathrm{ext}^{f}_{l} \wedge \neg \mathrm{com}^{f}_{l} \wedge \mathrm{on}^{f}_{t,l}
\]
Link_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
\[
F_{l} \le \overline{\mathrm{f}}^{\mathrm{nom}}_{\xi,l} \qquad \forall\, \xi \in \Xi,\ l \in \mathcal{L} \,:\, \mathrm{ext}^{f}_{l} \wedge \mathrm{act}^{f}_{l} \wedge \overline{\mathrm{f}}^{\mathrm{nom}}_{\xi,l} \text{ is defined}
\]
Link_com_p_lower
\[
f_{\xi,t,l} \ge \underline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \cdot u^{f}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \neg \mathrm{ext}^{f}_{l} \wedge \neg \left( \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right)
\]
Link_com_p_upper
\[
f_{\xi,t,l} \le \overline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \cdot u^{f}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \neg \mathrm{ext}^{f}_{l} \wedge \neg \left( \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right)
\]
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_com_up_time
\[
\sum_{t' \in \mathcal{T} \,:\, 0 \le t - t' < \mathrm{UT}^{f}} \mathit{up}^{f}_{\xi,t',l} \le u^{f}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \mathrm{UT}^{f}_{\xi,l} > 0 \wedge \mathrm{pos}(t) > 0
\]
Link_com_ext_p_upper_cap
\[
f_{\xi,t,l} \le \overline{\mathrm{f}}_{\xi,t,l} \cdot F_{l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_com\_ext}_{l,t}
\]
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
\[
f_{\xi,t,l} \ge \underline{\mathrm{f}}_{\xi,t,l} \cdot F_{l} + \mathrm{M}^{f}_{\xi,l} \cdot u^{f}_{\xi,t,l} - \mathrm{M}^{f}_{\xi,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_com\_ext}_{l,t}
\]
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_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
\[
\mathit{dn}^{f}_{\xi,t,l} \le \mathrm{N}^{f,\mathrm{fix}}_{\xi,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{Link\_committed}_{l,t} \wedge \neg \left( \mathrm{ext}^{f}_{l} \wedge \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right)
\]
Process_com_p_lower
\[
z_{\xi,t,j} \ge \underline{\mathrm{z}}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \cdot u^{z}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \neg \mathrm{ext}^{z}_{j} \wedge \neg \left( \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right)
\]
Process_com_p_upper
\[
z_{\xi,t,j} \le \overline{\mathrm{z}}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \cdot u^{z}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \neg \mathrm{ext}^{z}_{j} \wedge \neg \left( \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right)
\]
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_com_up_time
\[
\sum_{t' \in \mathcal{T} \,:\, 0 \le t - t' < \mathrm{UT}^{z}} \mathit{up}^{z}_{\xi,t',j} \le u^{z}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \mathrm{UT}^{z}_{\xi,j} > 0 \wedge \mathrm{pos}(t) > 0
\]
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
\[
\mathit{dn}^{z}_{\xi,t,j} \le \mathrm{N}^{z,\mathrm{fix}}_{\xi,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{Process\_committed}_{j,t} \wedge \neg \left( \mathrm{ext}^{z}_{j} \wedge \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right)
\]
Link_p_ramp_limit_up
\[
f_{\xi,t,l} - \mathit{Link\_previous\_p}_{\xi,t,l} \le \mathit{Link\_ramp\_up\_allowance}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \left( \mathrm{ru}^{f}_{\xi,t,l} \text{ is defined} \vee \mathrm{ru}^{f,\mathrm{up}}_{\xi,l} \text{ is defined} \right) \wedge \neg \left( \mathrm{com}^{f}_{l} \wedge \mathrm{ext}^{f}_{l} \wedge \neg \left( \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right) \right) \wedge \mathrm{Link\_ramps\_from\_previous}_{l,\xi,t} \wedge \mathrm{on}^{f}_{t,l}
\]
Link_p_ramp_limit_down
\[
\mathit{Link\_previous\_p}_{\xi,t,l} - f_{\xi,t,l} \le \mathit{Link\_ramp\_down\_allowance}_{\xi,t,l} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \left( \mathrm{rd}^{f}_{\xi,t,l} \text{ is defined} \vee \mathrm{rd}^{f,\mathrm{dn}}_{\xi,l} \text{ is defined} \right) \wedge \neg \left( \mathrm{com}^{f}_{l} \wedge \mathrm{ext}^{f}_{l} \wedge \neg \left( \mathrm{f}^{\mathrm{mod}}_{l} > 0 \right) \right) \wedge \mathrm{Link\_ramps\_from\_previous}_{l,\xi,t} \wedge \mathrm{on}^{f}_{t,l}
\]
Process_p_ramp_limit_up
\[
z_{\xi,t,j} - \mathit{Process\_previous\_p}_{\xi,t,j} \le \mathit{Process\_ramp\_up\_allowance}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \left( \mathrm{ru}^{z}_{\xi,t,j} \text{ is defined} \vee \mathrm{ru}^{z,\mathrm{up}}_{\xi,j} \text{ is defined} \right) \wedge \neg \left( \mathrm{com}^{z}_{j} \wedge \mathrm{ext}^{z}_{j} \wedge \neg \left( \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right) \right) \wedge \mathrm{Process\_ramps\_from\_previous}_{j,\xi,t} \wedge \mathrm{on}^{z}_{t,j}
\]
Process_p_ramp_limit_down
\[
\mathit{Process\_previous\_p}_{\xi,t,j} - z_{\xi,t,j} \le \mathit{Process\_ramp\_down\_allowance}_{\xi,t,j} \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \left( \mathrm{rd}^{z}_{\xi,t,j} \text{ is defined} \vee \mathrm{rd}^{z,\mathrm{dn}}_{\xi,j} \text{ is defined} \right) \wedge \neg \left( \mathrm{com}^{z}_{j} \wedge \mathrm{ext}^{z}_{j} \wedge \neg \left( \mathrm{z}^{\mathrm{mod}}_{j} > 0 \right) \right) \wedge \mathrm{Process\_ramps\_from\_previous}_{j,\xi,t} \wedge \mathrm{on}^{z}_{t,j}
\]
Bus_nodal_balance
\[
\mathit{Bus\_injection}_{\xi,t,n} = 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ n \in \mathcal{N}
\]
Link_com_p_before
\[
f_{\xi,t - 1,l} - \mathrm{Link\_shut\_down\_rate}_{\xi,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \cdot u^{f}_{\xi,t - 1,l} - \left( \overline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} - \mathrm{Link\_shut\_down\_rate}_{\xi,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \right) \cdot \left( u^{f}_{\xi,t,l} - \mathit{up}^{f}_{\xi,t,l} \right) \le 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{com}^{f}_{l} \wedge \neg \mathrm{ext}^{f}_{l} \wedge \lvert \{ \xi' \in \Xi \,:\, \lvert \{ t' \in \mathcal{T} \,:\, \mathrm{c}^{f,\mathrm{up}}_{\xi',t',l} \neq \mathrm{c}^{f,\mathrm{dn}}_{\xi',t',l} \} \rvert > 0 \} \rvert = 0 \wedge \mathrm{on}^{f}_{t,l}
\]
Link_com_p_current
\[
f_{\xi,t,l} - \overline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \cdot u^{f}_{\xi,t,l} + \left( \overline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} - \mathrm{Link\_start\_up\_rate}_{\xi,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \right) \cdot \mathit{up}^{f}_{\xi,t,l} \le 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{com}^{f}_{l} \wedge \neg \mathrm{ext}^{f}_{l} \wedge \lvert \{ \xi' \in \Xi \,:\, \lvert \{ t' \in \mathcal{T} \,:\, \mathrm{c}^{f,\mathrm{up}}_{\xi',t',l} \neq \mathrm{c}^{f,\mathrm{dn}}_{\xi',t',l} \} \rvert > 0 \} \rvert = 0 \wedge \mathrm{pos}(t) > 0 \wedge \mathrm{on}^{f}_{t,l}
\]
Link_com_partly_start_up
\[
f_{\xi,t,l} - f_{\xi,t - 1,l} - \left( \underline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} + \mathrm{Link\_ramp\_up\_rate}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \right) \cdot u^{f}_{\xi,t,l} + \underline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \cdot u^{f}_{\xi,t - 1,l} + \left( \underline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} + \mathrm{Link\_ramp\_up\_rate}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} - \mathrm{Link\_start\_up\_rate}_{\xi,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \right) \cdot \mathit{up}^{f}_{\xi,t,l} \le 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{com}^{f}_{l} \wedge \neg \mathrm{ext}^{f}_{l} \wedge \lvert \{ \xi' \in \Xi \,:\, \lvert \{ t' \in \mathcal{T} \,:\, \mathrm{c}^{f,\mathrm{up}}_{\xi',t',l} \neq \mathrm{c}^{f,\mathrm{dn}}_{\xi',t',l} \} \rvert > 0 \} \rvert = 0 \wedge \mathrm{on}^{f}_{t,l}
\]
Link_com_partly_shut_down
\[
f_{\xi,t - 1,l} - f_{\xi,t,l} - \mathrm{Link\_shut\_down\_rate}_{\xi,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \cdot u^{f}_{\xi,t - 1,l} + \left( \mathrm{Link\_shut\_down\_rate}_{\xi,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} - \mathrm{Link\_ramp\_down\_rate}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \right) \cdot u^{f}_{\xi,t,l} - \left( \underline{\mathrm{f}}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} + \mathrm{Link\_ramp\_down\_rate}_{\xi,t,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} - \mathrm{Link\_shut\_down\_rate}_{\xi,l} \cdot \mathrm{f}^{\mathrm{nom}}_{\xi,l} \right) \cdot \mathit{up}^{f}_{\xi,t,l} \le 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ l \in \mathcal{L} \,:\, \mathrm{com}^{f}_{l} \wedge \neg \mathrm{ext}^{f}_{l} \wedge \lvert \{ \xi' \in \Xi \,:\, \lvert \{ t' \in \mathcal{T} \,:\, \mathrm{c}^{f,\mathrm{up}}_{\xi',t',l} \neq \mathrm{c}^{f,\mathrm{dn}}_{\xi',t',l} \} \rvert > 0 \} \rvert = 0 \wedge \mathrm{on}^{f}_{t,l}
\]
Process_com_p_before
\[
z_{\xi,t - 1,j} - \mathrm{Process\_shut\_down\_rate}_{\xi,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \cdot u^{z}_{\xi,t - 1,j} - \left( \overline{\mathrm{z}}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} - \mathrm{Process\_shut\_down\_rate}_{\xi,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \right) \cdot \left( u^{z}_{\xi,t,j} - \mathit{up}^{z}_{\xi,t,j} \right) \le 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{com}^{z}_{j} \wedge \neg \mathrm{ext}^{z}_{j} \wedge \lvert \{ \xi' \in \Xi \,:\, \lvert \{ t' \in \mathcal{T} \,:\, \mathrm{c}^{z,\mathrm{up}}_{\xi',t',j} \neq \mathrm{c}^{z,\mathrm{dn}}_{\xi',t',j} \} \rvert > 0 \} \rvert = 0 \wedge \mathrm{on}^{z}_{t,j}
\]
Process_com_p_current
\[
z_{\xi,t,j} - \overline{\mathrm{z}}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \cdot u^{z}_{\xi,t,j} + \left( \overline{\mathrm{z}}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} - \mathrm{Process\_start\_up\_rate}_{\xi,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \right) \cdot \mathit{up}^{z}_{\xi,t,j} \le 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{com}^{z}_{j} \wedge \neg \mathrm{ext}^{z}_{j} \wedge \lvert \{ \xi' \in \Xi \,:\, \lvert \{ t' \in \mathcal{T} \,:\, \mathrm{c}^{z,\mathrm{up}}_{\xi',t',j} \neq \mathrm{c}^{z,\mathrm{dn}}_{\xi',t',j} \} \rvert > 0 \} \rvert = 0 \wedge \mathrm{pos}(t) > 0 \wedge \mathrm{on}^{z}_{t,j}
\]
Process_com_partly_start_up
\[
z_{\xi,t,j} - z_{\xi,t - 1,j} - \left( \underline{\mathrm{z}}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} + \mathrm{Process\_ramp\_up\_rate}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \right) \cdot u^{z}_{\xi,t,j} + \underline{\mathrm{z}}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \cdot u^{z}_{\xi,t - 1,j} + \left( \underline{\mathrm{z}}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} + \mathrm{Process\_ramp\_up\_rate}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} - \mathrm{Process\_start\_up\_rate}_{\xi,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \right) \cdot \mathit{up}^{z}_{\xi,t,j} \le 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{com}^{z}_{j} \wedge \neg \mathrm{ext}^{z}_{j} \wedge \lvert \{ \xi' \in \Xi \,:\, \lvert \{ t' \in \mathcal{T} \,:\, \mathrm{c}^{z,\mathrm{up}}_{\xi',t',j} \neq \mathrm{c}^{z,\mathrm{dn}}_{\xi',t',j} \} \rvert > 0 \} \rvert = 0 \wedge \mathrm{on}^{z}_{t,j}
\]
Process_com_partly_shut_down
\[
z_{\xi,t - 1,j} - z_{\xi,t,j} - \mathrm{Process\_shut\_down\_rate}_{\xi,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \cdot u^{z}_{\xi,t - 1,j} + \left( \mathrm{Process\_shut\_down\_rate}_{\xi,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} - \mathrm{Process\_ramp\_down\_rate}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \right) \cdot u^{z}_{\xi,t,j} - \left( \underline{\mathrm{z}}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} + \mathrm{Process\_ramp\_down\_rate}_{\xi,t,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} - \mathrm{Process\_shut\_down\_rate}_{\xi,j} \cdot \mathrm{z}^{\mathrm{nom}}_{\xi,j} \right) \cdot \mathit{up}^{z}_{\xi,t,j} \le 0 \qquad \forall\, \xi \in \Xi,\ t \in \mathcal{T},\ j \in \mathcal{J} \,:\, \mathrm{com}^{z}_{j} \wedge \neg \mathrm{ext}^{z}_{j} \wedge \lvert \{ \xi' \in \Xi \,:\, \lvert \{ t' \in \mathcal{T} \,:\, \mathrm{c}^{z,\mathrm{up}}_{\xi',t',j} \neq \mathrm{c}^{z,\mathrm{dn}}_{\xi',t',j} \} \rvert > 0 \} \rvert = 0 \wedge \mathrm{on}^{z}_{t,j}
\]
The spec, differential/pypsa/rungs/rung_67_linearized_link_process.yaml — the file projected onto what this rung builds:
version: 0
description: '`n.optimize(linearized_unit_commitment=True)`, as a patch over `examples/pypsa.yaml`. The
status, its starts and its stops of a committable generator, link and process are shares in [0, 1] rather
than integers, and four rows PyPSA adds only under the keyword tighten the relaxation of a unit with
a fixed build whose start and stop cost the same in every snapshot and every scenario (`constraints.py:599-699`).
A modular committable unit is refused, as PyPSA refuses it. Every other row is the integer run''s.'
dimensions:
scenario: {dtype: str, description: 'the futures dispatch is chosen in, each with a weight'}
snapshot: {dtype: datetime, ordered: true, description: dispatch periods}
bus: {dtype: str, description: network nodes}
generator: {dtype: str, description: 'generating units, each on one bus'}
link: {dtype: str, description: 'controllable connections, each from one bus to the buses it delivers
to'}
link_output: {dtype: str, 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: {dtype: str, description: 'generalized multi-port converters, each with an internal power that
every port draws or delivers at its own rate'}
process_output: {dtype: str, 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: {dtype: str, description: 'demands, each on one bus'}
period: {dtype: int, ordered: true, description: investment periods — PyPSA's `investment_periods`}
relations:
snapshot_period: {key: snapshot, values: period, description: the investment period a snapshot falls
in}
Generator_bus: {key: generator, values: bus, description: the bus a generator sits on}
Link_bus0: {key: link, values: bus, description: the bus a link leaves}
Link_output_link: {key: link_output, values: link, description: the link an output port belongs to}
Link_output_bus: {key: link_output, values: bus, description: 'the bus an output port delivers to —
PyPSA''s `bus1`, `bus2`, … columns. A link of three output ports is three labels here rather than
a third relation, so the file states any number of them'}
Process_output_process: {key: process_output, values: process, description: the process a port belongs
to}
Process_output_bus: {key: process_output, values: bus, description: 'the bus a port draws from or delivers
to — PyPSA''s `bus0`, `bus1`, … columns. A process of three ports is three labels here rather than
a third relation, so the file states any number of them'}
Load_bus: {key: load, values: bus, description: the bus a load sits on}
parameters:
snapshot_weightings_objective:
dims: [snapshot]
dtype: float
description: PyPSA's `snapshot_weightings.objective` — hours a snapshot stands for in the cost
Generator_p_nom:
dims: [scenario, generator]
dtype: float
description: nominal power
Generator_p_nom_extendable:
dims: [generator]
dtype: bool
description: whether the nominal power is a decision
Generator_p_min_pu:
dims: [scenario, snapshot, generator]
dtype: float
description: least output, per unit of nominal power
Generator_p_max_pu:
dims: [scenario, snapshot, generator]
dtype: float
description: most output, per unit of nominal power — an availability profile
Generator_marginal_cost:
dims: [scenario, snapshot, generator]
dtype: float
description: cost of one unit of output
Generator_marginal_cost_quadratic:
dims: [scenario, snapshot, generator]
dtype: float
description: cost of the square of one unit of output
Generator_sign:
dims: [generator]
dtype: float
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`)
Generator_committable:
dims: [generator]
dtype: bool
description: whether output is gated by an on/off status decision
Link_ramp_limit_up:
dims: [scenario, snapshot, link]
dtype: float
missing: neutral
description: most a link may raise its flow between snapshots, per unit of nominal power; no value
means no limit — read at the later of the two snapshots, so the limit may change over time
Link_ramp_limit_down:
dims: [scenario, snapshot, link]
dtype: float
missing: neutral
description: most a link may lower its flow between snapshots, per unit of nominal power; no value
means no limit — read at the later of the two snapshots, so the limit may change over time
Link_p_nom:
dims: [scenario, link]
dtype: float
description: nominal power
Link_p_nom_extendable:
dims: [link]
dtype: bool
description: whether the nominal power is a decision
Link_p_min_pu:
dims: [scenario, snapshot, link]
dtype: float
description: least flow, per unit of nominal power — negative for a link that carries both ways
Link_p_max_pu:
dims: [scenario, snapshot, link]
dtype: float
description: most flow, per unit of nominal power
Link_efficiency:
dims: [scenario, snapshot, link_output]
dtype: float
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`)
Link_output_delay:
dims: [link_output]
dtype: int
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`)
Link_output_cyclic_delay:
dims: [link_output]
dtype: bool
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
Link_marginal_cost:
dims: [scenario, snapshot, link]
dtype: float
description: cost of one unit of flow
Link_marginal_cost_quadratic:
dims: [scenario, snapshot, link]
dtype: float
description: cost of the square of one unit of flow
Link_committable:
dims: [link]
dtype: bool
description: whether flow is gated by an on/off status decision
Link_ramp_limit_start_up:
dims: [scenario, link]
dtype: float
missing: neutral
description: most flow in the snapshot a link starts, per unit of nominal power; no value means no
limit
Link_ramp_limit_shut_down:
dims: [scenario, link]
dtype: float
missing: neutral
description: most flow in the snapshot before a link stops, per unit of nominal power; no value means
no limit
Link_min_up_time:
dims: [scenario, link]
dtype: int
description: least snapshots a link stays on once started
Link_status_initial:
dims: [scenario, link]
dtype: int
description: one where the link was on before the first snapshot, zero where off — PyPSA's `up_time_before
> 0`, data prep
Link_p_init:
dims: [scenario, link]
dtype: float
missing: neutral
description: the flow a link brought into the horizon — PyPSA's `p_init`, read only where the link
came in running; no value means it is unknown, so the link carries no ramp row at the first snapshot
Link_start_up_cost:
dims: [scenario, snapshot, link]
dtype: float
description: cost of one start in this snapshot
Link_shut_down_cost:
dims: [scenario, snapshot, link]
dtype: float
description: cost of one stop in this snapshot
Link_stand_by_cost:
dims: [scenario, snapshot, link]
dtype: float
description: cost of one snapshot spent on
Link_p_nom_mod:
dims: [link]
dtype: float
missing: neutral
description: the module size a build comes in whole numbers of; no value means the build is continuous
Link_modules_installed:
dims: [scenario, link]
dtype: float
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'
Link_big_m:
dims: [scenario, link]
dtype: float
missing: neutral
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
Link_p_min_pu_nonneg:
dims: [link]
dtype: bool
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
Process_p_nom:
dims: [scenario, process]
dtype: float
description: nominal internal power
Process_p_nom_extendable:
dims: [process]
dtype: bool
description: whether the nominal internal power is a decision
Process_p_min_pu:
dims: [scenario, snapshot, process]
dtype: float
description: least internal power, per unit of nominal power — negative for a process that runs both
ways
Process_p_max_pu:
dims: [scenario, snapshot, process]
dtype: float
description: most internal power, per unit of nominal power
Process_rate:
dims: [scenario, snapshot, process_output]
dtype: float
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`)
Process_output_delay:
dims: [process_output]
dtype: int
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
Process_output_cyclic_delay:
dims: [process_output]
dtype: bool
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
Process_marginal_cost:
dims: [scenario, snapshot, process]
dtype: float
description: cost of one unit of internal power
Process_marginal_cost_quadratic:
dims: [scenario, snapshot, process]
dtype: float
description: cost of the square of one unit of internal power
Process_ramp_limit_up:
dims: [scenario, snapshot, process]
dtype: float
missing: neutral
description: most a process may raise its internal power between snapshots, per unit of nominal power;
no value means no limit — read at the later of the two snapshots, so the limit may change over time
Process_ramp_limit_down:
dims: [scenario, snapshot, process]
dtype: float
missing: neutral
description: most a process may lower its internal power between snapshots, per unit of nominal power;
no value means no limit — read at the later of the two snapshots, so the limit may change over time
Process_committable:
dims: [process]
dtype: bool
description: whether internal power is gated by an on/off status decision
Process_ramp_limit_start_up:
dims: [scenario, process]
dtype: float
missing: neutral
description: most internal power in the snapshot a process starts, per unit of nominal power; no value
means no limit
Process_ramp_limit_shut_down:
dims: [scenario, process]
dtype: float
missing: neutral
description: most internal power in the snapshot before a process stops, per unit of nominal power;
no value means no limit
Process_min_up_time:
dims: [scenario, process]
dtype: int
description: least snapshots a process stays on once started
Process_status_initial:
dims: [scenario, process]
dtype: int
description: one where the process was on before the first snapshot, zero where off — PyPSA's `up_time_before
> 0`, data prep
Process_p_init:
dims: [scenario, process]
dtype: float
missing: neutral
description: the internal power a process brought into the horizon — PyPSA's `p_init`, read only where
the process came in running; no value means it is unknown, so the process carries no ramp row at
the first snapshot
Process_start_up_cost:
dims: [scenario, snapshot, process]
dtype: float
description: cost of one start in this snapshot
Process_shut_down_cost:
dims: [scenario, snapshot, process]
dtype: float
description: cost of one stop in this snapshot
Process_stand_by_cost:
dims: [scenario, snapshot, process]
dtype: float
description: cost of one snapshot spent on
Process_p_nom_mod:
dims: [process]
dtype: float
missing: neutral
description: the module size a build comes in whole numbers of; no value means the build is continuous
Process_modules_installed:
dims: [scenario, process]
dtype: float
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'
Load_p_set:
dims: [scenario, snapshot, load]
dtype: float
description: demand
Load_sign:
dims: [load]
dtype: float
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`)
Load_active:
dims: [load]
dtype: bool
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`)
scenario_weight:
dims: [scenario]
dtype: float
description: PyPSA's `scenario_weightings.weight` — the probability of a future
period_weight_objective:
dims: [period]
dtype: float
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`)
Generator_active:
dims: [snapshot, generator]
dtype: bool
description: whether a generator stands in a snapshot's period — PyPSA's `active`, from build year
and lifetime, data prep
Link_active:
dims: [snapshot, link]
dtype: bool
description: whether a link stands in a snapshot's period — PyPSA's `active`, data prep
Process_active:
dims: [snapshot, process]
dtype: bool
description: whether a process stands in a snapshot's period — PyPSA's `active`, data prep
Link_active_asset:
dims: [link]
dtype: bool
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`)
Process_active_asset:
dims: [process]
dtype: bool
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`)
Link_capital_weight:
dims: [link]
dtype: float
description: the sum of period weights a link stands in — PyPSA's `active * period_weighting`, summed,
data prep
Link_p_nom_min:
dims: [scenario, link]
dtype: float
description: least nominal power an extendable link may be built at
Link_p_nom_max:
dims: [scenario, link]
dtype: float
description: most nominal power an extendable link may be built at
Link_capital_cost:
dims: [scenario, link]
dtype: float
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'
variables:
Generator_p:
dims: [scenario, snapshot, generator]
where: Generator_active
domain: continuous
missing: absent
description: '`Generator-p` — output of a generator in a snapshot'
Link_p:
dims: [scenario, snapshot, link]
where: Link_active
domain: continuous
missing: absent
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'
Process_p:
dims: [scenario, snapshot, process]
where: Process_active
domain: continuous
missing: absent
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'
Link_status:
dims: [scenario, snapshot, link]
where: Link_committed
bounds: {lower: 0.0, upper: 1.0}
domain: continuous
missing: absent
description: '`Link-status` — how much of a committable link is on, a share in [0, 1] rather than
an integer: the relaxation the keyword solves (`variables.py:86-87`)'
Link_start_up:
dims: [scenario, snapshot, link]
where: Link_committed
bounds: {lower: 0.0, upper: 1.0}
domain: continuous
missing: absent
description: '`Link-start_up` — how much of a committable link turns on this snapshot, a share in
[0, 1] (`variables.py:137-138`)'
Link_shut_down:
dims: [scenario, snapshot, link]
where: Link_committed
bounds: {lower: 0.0, upper: 1.0}
domain: continuous
missing: absent
description: '`Link-shut_down` — how much of a committable link turns off this snapshot, a share in
[0, 1] (`variables.py:188-189`)'
Process_status:
dims: [scenario, snapshot, process]
where: Process_committed
bounds: {lower: 0.0, upper: 1.0}
domain: continuous
missing: absent
description: '`Process-status` — how much of a committable process is on, a share in [0, 1] rather
than an integer: the relaxation the keyword solves (`variables.py:86-87`)'
Process_start_up:
dims: [scenario, snapshot, process]
where: Process_committed
bounds: {lower: 0.0, upper: 1.0}
domain: continuous
missing: absent
description: '`Process-start_up` — how much of a committable process turns on this snapshot, a share
in [0, 1] (`variables.py:137-138`)'
Process_shut_down:
dims: [scenario, snapshot, process]
where: Process_committed
bounds: {lower: 0.0, upper: 1.0}
domain: continuous
missing: absent
description: '`Process-shut_down` — how much of a committable process turns off this snapshot, a share
in [0, 1] (`variables.py:188-189`)'
Link_p_nom_ext:
dims: [link]
where: Link_p_nom_extendable AND Link_active_asset
domain: continuous
missing: absent
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'
Process_p_nom_ext:
dims: [process]
where: Process_p_nom_extendable AND Process_active_asset
domain: continuous
missing: absent
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'
constraints:
Generator_fix_p_lower:
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
description: '`Generator-fix-p-lower` — a fixed generator outputs at least its minimum'
Generator_fix_p_upper:
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
description: '`Generator-fix-p-upper` — a fixed generator outputs at most what is available'
Link_fix_p_lower:
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
description: '`Link-fix-p-lower` — a fixed link carries at least its minimum, negative for the other
way'
Link_fix_p_upper:
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
description: '`Link-fix-p-upper` — a fixed link carries at most its nominal power'
Link_ext_p_nom_lower:
dims: [scenario, link]
where: Link_p_nom_extendable AND Link_active_asset
expression: Link_p_nom_ext >= Link_p_nom_min
description: '`Link-ext-p_nom-lower` — the chosen build is at least its floor in every scenario'
Link_ext_p_nom_upper:
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
description: '`Link-ext-p_nom-upper` — the chosen build is at most its cap in every scenario; a cap
of infinity is no row'
Link_com_p_lower:
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
description: '`Link-com-p-lower` — a committed link flows at least its minimum; off, at least nothing'
Link_com_p_upper:
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
description: '`Link-com-p-upper` — a committed link flows at most what is available; off, at most
nothing'
Link_com_transition_start_up:
dims: [scenario, snapshot, link]
where: Link_committed
expression: Link_start_up >= Link_status - Link_previous_status
description: '`Link-com-transition-start-up` — turning on is a start, counted against the state the
link carried into the snapshot'
Link_com_transition_shut_down:
dims: [scenario, snapshot, link]
where: Link_committed
expression: Link_shut_down >= Link_previous_status - Link_status
description: '`Link-com-transition-shut-down` — turning off is a stop, counted against the state the
link carried into the snapshot'
Link_com_up_time:
dims: [scenario, snapshot, link]
where: Link_committed AND Link_min_up_time > 0 AND position(snapshot) > 0
expression: sum_back(Link_start_up, along=snapshot, window=Link_min_up_time) <= Link_status
description: '`Link-com-up-time` — a link started within its own minimum up time is still on. The
first snapshot''s share of the window is the brought-in up time''s, which the must-stay-up mask
carries'
Link_com_ext_p_upper_cap:
dims: [scenario, snapshot, link]
where: Link_com_ext
expression: Link_p <= Link_p_max_pu * Link_p_nom_ext
description: '`Link-com-ext-p-upper-cap` — a committed extendable link flows at most what is available
of the chosen build, whatever its status'
Link_com_ext_p_upper_big_m:
dims: [scenario, snapshot, link]
where: Link_com_ext
expression: Link_p <= Link_big_m * Link_status
description: '`Link-com-ext-p-upper-bigM` — off, a link flows nothing; on, the big M is no bound'
Link_com_ext_p_lower:
dims: [scenario, snapshot, link]
where: Link_com_ext
expression: Link_p >= ((Link_p_min_pu * Link_p_nom_ext) + (Link_big_m * Link_status)) - Link_big_m
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'
Link_com_ext_p_lower_nonneg:
dims: [scenario, snapshot, link]
where: Link_com_ext AND Link_p_min_pu_nonneg
expression: Link_p >= 0
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'
Link_status_p_fixed_upper:
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
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'
Link_start_up_p_fixed_upper:
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
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'
Link_shut_down_p_fixed_upper:
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
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'
Process_com_p_lower:
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
description: '`Process-com-p-lower` — a committed process runs at least its minimum; off, at least
nothing'
Process_com_p_upper:
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
description: '`Process-com-p-upper` — a committed process runs at most what is available; off, at
most nothing'
Process_com_transition_start_up:
dims: [scenario, snapshot, process]
where: Process_committed
expression: Process_start_up >= Process_status - Process_previous_status
description: '`Process-com-transition-start-up` — turning on is a start, counted against the state
the process carried into the snapshot'
Process_com_transition_shut_down:
dims: [scenario, snapshot, process]
where: Process_committed
expression: Process_shut_down >= Process_previous_status - Process_status
description: '`Process-com-transition-shut-down` — turning off is a stop, counted against the state
the process carried into the snapshot'
Process_com_up_time:
dims: [scenario, snapshot, process]
where: Process_committed AND Process_min_up_time > 0 AND position(snapshot) > 0
expression: sum_back(Process_start_up, along=snapshot, window=Process_min_up_time) <= Process_status
description: '`Process-com-up-time` — a process started within its own minimum up time is still on.
The first snapshot''s share of the window is the brought-in up time''s, which the must-stay-up mask
carries'
Process_status_p_fixed_upper:
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
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'
Process_start_up_p_fixed_upper:
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
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'
Process_shut_down_p_fixed_upper:
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
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'
Link_p_ramp_limit_up:
dims: [scenario, snapshot, link]
where: (Link_ramp_limit_up OR Link_ramp_limit_start_up) AND NOT (Link_committable AND Link_p_nom_extendable
AND NOT (Link_p_nom_mod > 0)) AND Link_ramps_from_previous AND Link_active
expression: Link_p - Link_previous_p <= Link_ramp_up_allowance
description: '`Link-p-ramp_limit_up` — a link raises flow no faster than its ramp limit of the build,
and a committed one no further than its start-up ramp in the snapshot it turns on. A link that came
into the horizon running carries a row at the first snapshot only where its `p_init` gives the flow
it brought in, and no link carries one at the start of a later investment period — nor does any
link a big M releases instead'
Link_p_ramp_limit_down:
dims: [scenario, snapshot, link]
where: (Link_ramp_limit_down OR Link_ramp_limit_shut_down) AND NOT (Link_committable AND Link_p_nom_extendable
AND NOT (Link_p_nom_mod > 0)) AND Link_ramps_from_previous AND Link_active
expression: Link_previous_p - Link_p <= Link_ramp_down_allowance
description: '`Link-p-ramp_limit_down` — a link lowers flow no faster than its ramp limit of the build,
and a committed one no further than its shut-down ramp in the snapshot it turns off. A link that
came into the horizon running carries a row at the first snapshot only where its `p_init` gives
the flow it brought in, and no link carries one at the start of a later investment period — nor
does any link a big M releases instead'
Process_p_ramp_limit_up:
dims: [scenario, snapshot, process]
where: (Process_ramp_limit_up OR Process_ramp_limit_start_up) AND NOT (Process_committable AND Process_p_nom_extendable
AND NOT (Process_p_nom_mod > 0)) AND Process_ramps_from_previous AND Process_active
expression: Process_p - Process_previous_p <= Process_ramp_up_allowance
description: '`Process-p-ramp_limit_up` — a process raises internal power no faster than its ramp
limit of the build, and a committed one no further than its start-up ramp in the snapshot it turns
on. A process that came into the horizon running carries a row at the first snapshot only where
its `p_init` gives the internal power it brought in, and no process carries one at the start of
a later investment period — nor does any process a big M releases instead'
Process_p_ramp_limit_down:
dims: [scenario, snapshot, process]
where: (Process_ramp_limit_down OR Process_ramp_limit_shut_down) AND NOT (Process_committable AND
Process_p_nom_extendable AND NOT (Process_p_nom_mod > 0)) AND Process_ramps_from_previous AND Process_active
expression: Process_previous_p - Process_p <= Process_ramp_down_allowance
description: '`Process-p-ramp_limit_down` — a process lowers internal power no faster than its ramp
limit of the build, and a committed one no further than its shut-down ramp in the snapshot it turns
off. A process that came into the horizon running carries a row at the first snapshot only where
its `p_init` gives the internal power it brought in, and no process carries one at the start of
a later investment period — nor does any process a big M releases instead'
Bus_nodal_balance:
dims: [scenario, snapshot, bus]
expression: Bus_injection == 0
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.'
Link_com_p_before:
dims: [scenario, snapshot, link]
where: Link_committable AND NOT Link_p_nom_extendable AND count(count(Link_start_up_cost != Link_shut_down_cost,
over=snapshot) > 0, over=scenario) == 0 AND Link_active
expression: shift(Link_p, along=snapshot, offset=1) - Link_shut_down_rate * Link_p_nom * shift(Link_status,
along=snapshot, offset=1) - (Link_p_max_pu * Link_p_nom - Link_shut_down_rate * Link_p_nom) * (Link_status
- Link_start_up) <= 0
description: '`Link-com-p-before` — the output a link had entering this snapshot fits the share of
it still on, less the share it is shutting down at the shut-down ramp (`constraints.py:635-649`).
The translated terms vacate the first snapshot, as PyPSA''s `sns[1:]` does'
Link_com_p_current:
dims: [scenario, snapshot, link]
where: Link_committable AND NOT Link_p_nom_extendable AND count(count(Link_start_up_cost != Link_shut_down_cost,
over=snapshot) > 0, over=scenario) == 0 AND position(snapshot) > 0 AND Link_active
expression: Link_p - Link_p_max_pu * Link_p_nom * Link_status + (Link_p_max_pu * Link_p_nom - Link_start_up_rate
* Link_p_nom) * Link_start_up <= 0
description: '`Link-com-p-current` — output fits the share on, and the share starting up only up to
the start-up ramp (`constraints.py:652-665`)'
Link_com_partly_start_up:
dims: [scenario, snapshot, link]
where: Link_committable AND NOT Link_p_nom_extendable AND count(count(Link_start_up_cost != Link_shut_down_cost,
over=snapshot) > 0, over=scenario) == 0 AND Link_active
expression: Link_p - shift(Link_p, along=snapshot, offset=1) - (Link_p_min_pu * Link_p_nom + Link_ramp_up_rate
* Link_p_nom) * Link_status + Link_p_min_pu * Link_p_nom * shift(Link_status, along=snapshot, offset=1)
+ (Link_p_min_pu * Link_p_nom + Link_ramp_up_rate * Link_p_nom - Link_start_up_rate * Link_p_nom)
* Link_start_up <= 0
description: '`Link-com-partly-start-up` — raising output while a share is starting up is bounded
by the ramp of the share on and the start-up ramp of the share coming on (`constraints.py:667-682`)'
Link_com_partly_shut_down:
dims: [scenario, snapshot, link]
where: Link_committable AND NOT Link_p_nom_extendable AND count(count(Link_start_up_cost != Link_shut_down_cost,
over=snapshot) > 0, over=scenario) == 0 AND Link_active
expression: shift(Link_p, along=snapshot, offset=1) - Link_p - Link_shut_down_rate * Link_p_nom *
shift(Link_status, along=snapshot, offset=1) + (Link_shut_down_rate * Link_p_nom - Link_ramp_down_rate
* Link_p_nom) * Link_status - (Link_p_min_pu * Link_p_nom + Link_ramp_down_rate * Link_p_nom - Link_shut_down_rate
* Link_p_nom) * Link_start_up <= 0
description: '`Link-com-partly-shut-down` — lowering output while a share is shutting down is bounded
likewise, by the shut-down ramp (`constraints.py:684-699`)'
Process_com_p_before:
dims: [scenario, snapshot, process]
where: Process_committable AND NOT Process_p_nom_extendable AND count(count(Process_start_up_cost
!= Process_shut_down_cost, over=snapshot) > 0, over=scenario) == 0 AND Process_active
expression: shift(Process_p, along=snapshot, offset=1) - Process_shut_down_rate * Process_p_nom *
shift(Process_status, along=snapshot, offset=1) - (Process_p_max_pu * Process_p_nom - Process_shut_down_rate
* Process_p_nom) * (Process_status - Process_start_up) <= 0
description: '`Process-com-p-before` — the output a process had entering this snapshot fits the share
of it still on, less the share it is shutting down at the shut-down ramp (`constraints.py:635-649`).
The translated terms vacate the first snapshot, as PyPSA''s `sns[1:]` does'
Process_com_p_current:
dims: [scenario, snapshot, process]
where: Process_committable AND NOT Process_p_nom_extendable AND count(count(Process_start_up_cost
!= Process_shut_down_cost, over=snapshot) > 0, over=scenario) == 0 AND position(snapshot) > 0 AND
Process_active
expression: Process_p - Process_p_max_pu * Process_p_nom * Process_status + (Process_p_max_pu * Process_p_nom
- Process_start_up_rate * Process_p_nom) * Process_start_up <= 0
description: '`Process-com-p-current` — output fits the share on, and the share starting up only up
to the start-up ramp (`constraints.py:652-665`)'
Process_com_partly_start_up:
dims: [scenario, snapshot, process]
where: Process_committable AND NOT Process_p_nom_extendable AND count(count(Process_start_up_cost
!= Process_shut_down_cost, over=snapshot) > 0, over=scenario) == 0 AND Process_active
expression: Process_p - shift(Process_p, along=snapshot, offset=1) - (Process_p_min_pu * Process_p_nom
+ Process_ramp_up_rate * Process_p_nom) * Process_status + Process_p_min_pu * Process_p_nom * shift(Process_status,
along=snapshot, offset=1) + (Process_p_min_pu * Process_p_nom + Process_ramp_up_rate * Process_p_nom
- Process_start_up_rate * Process_p_nom) * Process_start_up <= 0
description: '`Process-com-partly-start-up` — raising output while a share is starting up is bounded
by the ramp of the share on and the start-up ramp of the share coming on (`constraints.py:667-682`)'
Process_com_partly_shut_down:
dims: [scenario, snapshot, process]
where: Process_committable AND NOT Process_p_nom_extendable AND count(count(Process_start_up_cost
!= Process_shut_down_cost, over=snapshot) > 0, over=scenario) == 0 AND Process_active
expression: shift(Process_p, along=snapshot, offset=1) - Process_p - Process_shut_down_rate * Process_p_nom
* shift(Process_status, along=snapshot, offset=1) + (Process_shut_down_rate * Process_p_nom - Process_ramp_down_rate
* Process_p_nom) * Process_status - (Process_p_min_pu * Process_p_nom + Process_ramp_down_rate *
Process_p_nom - Process_shut_down_rate * Process_p_nom) * Process_start_up <= 0
description: '`Process-com-partly-shut-down` — lowering output while a share is shutting down is bounded
likewise, by the shut-down ramp (`constraints.py:684-699`)'
expressions:
Link_p_nom_effective:
dims: [scenario, link]
description: the build a link's limits are taken against — the chosen one where it is extendable,
the given one otherwise
cases:
extendable: {when: Link_p_nom_extendable, expression: Link_p_nom_ext}
otherwise: Link_p_nom
Link_previous_status:
dims: [scenario, snapshot, link]
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
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:
dims: [scenario, snapshot, link]
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
cases:
opening: {when: position(snapshot) == 0, expression: Link_status_initial}
otherwise: shift(Link_status, along=snapshot, offset=1)
Link_previous_p:
dims: [scenario, snapshot, link]
description: the flow a link carries into a snapshot — at the first, the `p_init` it brought in where
it came in running and nothing where it came in off; the previous snapshot's after that
cases:
opening: {when: position(snapshot) == 0, expression: Link_status_initial * Link_p_init}
otherwise: shift(Link_p, along=snapshot, offset=1)
Link_ramp_up_rate:
dims: [scenario, snapshot, link]
description: the ramp limit a link's up row reads — PyPSA's `ramp_limit_up`, or the full build where
it has none, since a start-up ramp alone builds the row
cases:
given: {when: Link_ramp_limit_up, expression: Link_ramp_limit_up}
otherwise: '1'
Link_ramp_down_rate:
dims: [scenario, snapshot, link]
description: the ramp limit a link's down row reads — PyPSA's `ramp_limit_down`, or the full build
where it has none, since a shut-down ramp alone builds the row
cases:
given: {when: Link_ramp_limit_down, expression: Link_ramp_limit_down}
otherwise: '1'
Link_start_up_rate:
dims: [scenario, link]
description: the start-up ramp a link's up row reads — PyPSA's `ramp_limit_start_up`, or the full
build where it has none
cases:
given: {when: Link_ramp_limit_start_up, expression: Link_ramp_limit_start_up}
otherwise: '1'
Link_shut_down_rate:
dims: [scenario, link]
description: the shut-down ramp a link's down row reads — PyPSA's `ramp_limit_shut_down`, or the full
build where it has none
cases:
given: {when: Link_ramp_limit_shut_down, expression: Link_ramp_limit_shut_down}
otherwise: '1'
Link_p_nom_committed:
dims: [scenario, link]
description: the build a committed link's ramp rows are taken against — one module where the build
is extendable and modular, the given build otherwise
cases:
modular_build: {when: Link_p_nom_extendable AND Link_p_nom_mod > 0, expression: Link_p_nom_mod}
otherwise: Link_p_nom
Link_ramp_up_allowance:
dims: [scenario, snapshot, link]
description: how far a link may raise flow between two snapshots — its ramp limit of the build while
it stays on, plus its start-up ramp in the snapshot it turns on
cases:
committed: {when: Link_committable, expression: Link_ramp_up_rate * Link_p_nom_committed * Link_previous_status
+ Link_start_up_rate * Link_p_nom_committed * (Link_status - Link_previous_status)}
otherwise: Link_ramp_up_rate * Link_p_nom_effective
Link_ramp_down_allowance:
dims: [scenario, snapshot, link]
description: how far a link may lower flow between two snapshots — its ramp limit of the build while
it stays on, plus its shut-down ramp in the snapshot it turns off
cases:
committed: {when: Link_committable, expression: Link_ramp_down_rate * Link_p_nom_committed * Link_status
+ Link_shut_down_rate * Link_p_nom_committed * (Link_previous_status - Link_status)}
otherwise: Link_ramp_down_rate * Link_p_nom_effective
Process_p_nom_effective:
dims: [scenario, process]
description: the build a process's limits are taken against — the chosen one where it is extendable,
the given one otherwise
cases:
extendable: {when: Process_p_nom_extendable, expression: Process_p_nom_ext}
otherwise: Process_p_nom
Process_previous_status:
dims: [scenario, snapshot, process]
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
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:
dims: [scenario, snapshot, process]
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
cases:
opening: {when: position(snapshot) == 0, expression: Process_status_initial}
otherwise: shift(Process_status, along=snapshot, offset=1)
Process_previous_p:
dims: [scenario, snapshot, process]
description: the internal power a process carries into a snapshot — at the first, the `p_init` it
brought in where it came in running and nothing where it came in off; the previous snapshot's after
that
cases:
opening: {when: position(snapshot) == 0, expression: Process_status_initial * Process_p_init}
otherwise: shift(Process_p, along=snapshot, offset=1)
Process_ramp_up_rate:
dims: [scenario, snapshot, process]
description: the ramp limit a process's up row reads — PyPSA's `ramp_limit_up`, or the full build
where it has none, since a start-up ramp alone builds the row
cases:
given: {when: Process_ramp_limit_up, expression: Process_ramp_limit_up}
otherwise: '1'
Process_ramp_down_rate:
dims: [scenario, snapshot, process]
description: the ramp limit a process's down row reads — PyPSA's `ramp_limit_down`, or the full build
where it has none, since a shut-down ramp alone builds the row
cases:
given: {when: Process_ramp_limit_down, expression: Process_ramp_limit_down}
otherwise: '1'
Process_start_up_rate:
dims: [scenario, process]
description: the start-up ramp a process's up row reads — PyPSA's `ramp_limit_start_up`, or the full
build where it has none
cases:
given: {when: Process_ramp_limit_start_up, expression: Process_ramp_limit_start_up}
otherwise: '1'
Process_shut_down_rate:
dims: [scenario, process]
description: the shut-down ramp a process's down row reads — PyPSA's `ramp_limit_shut_down`, or the
full build where it has none
cases:
given: {when: Process_ramp_limit_shut_down, expression: Process_ramp_limit_shut_down}
otherwise: '1'
Process_p_nom_committed:
dims: [scenario, process]
description: the build a committed process's ramp rows are taken against — one module where the build
is extendable and modular, the given build otherwise
cases:
modular_build: {when: Process_p_nom_extendable AND Process_p_nom_mod > 0, expression: Process_p_nom_mod}
otherwise: Process_p_nom
Process_ramp_up_allowance:
dims: [scenario, snapshot, process]
description: how far a process may raise internal power between two snapshots — its ramp limit of
the build while it stays on, plus its start-up ramp in the snapshot it turns on
cases:
committed: {when: Process_committable, expression: Process_ramp_up_rate * Process_p_nom_committed
* Process_previous_status + Process_start_up_rate * Process_p_nom_committed * (Process_status
- Process_previous_status)}
otherwise: Process_ramp_up_rate * Process_p_nom_effective
Process_ramp_down_allowance:
dims: [scenario, snapshot, process]
description: how far a process may lower internal power between two snapshots — its ramp limit of
the build while it stays on, plus its shut-down ramp in the snapshot it turns off
cases:
committed: {when: Process_committable, expression: Process_ramp_down_rate * Process_p_nom_committed
* Process_status + Process_shut_down_rate * Process_p_nom_committed * (Process_previous_status
- Process_status)}
otherwise: Process_ramp_down_rate * Process_p_nom_effective
Link_output_arrival:
dims: [scenario, snapshot, link_output]
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
cases:
wrapping: {when: Link_output_cyclic_delay, expression: 'shift(at(Link_p, by=Link_output_link[link]),
along=snapshot, offset=Link_output_delay, edge=''wrap'', within=snapshot_period[period]) * Link_efficiency'}
otherwise: shift(at(Link_p, by=Link_output_link[link]), along=snapshot, offset=Link_output_delay,
edge=0, within=snapshot_period[period]) * Link_efficiency
Process_output_arrival:
dims: [scenario, snapshot, process_output]
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
cases:
wrapping: {when: Process_output_cyclic_delay, expression: 'shift(at(Process_p, by=Process_output_process[process]),
along=snapshot, offset=Process_output_delay, edge=''wrap'', within=snapshot_period[period])
* Process_rate'}
otherwise: shift(at(Process_p, by=Process_output_process[process]), along=snapshot, offset=Process_output_delay,
edge=0, within=snapshot_period[period]) * Process_rate
Generator_opex: {expression: 'sum(sum(((Generator_p * Generator_marginal_cost) * snapshot_weightings_objective)
* at(period_weight_objective, by=snapshot_period[period]), over=generator), over=snapshot) + sum(sum((((Generator_p
* Generator_p) * Generator_marginal_cost_quadratic) * snapshot_weightings_objective) * at(period_weight_objective,
by=snapshot_period[period]), over=generator), over=snapshot)'}
Link_opex: {expression: 'sum(sum(((Link_p * Link_marginal_cost) * snapshot_weightings_objective) * at(period_weight_objective,
by=snapshot_period[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[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[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[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[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[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 + 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`)
Link_capex: {expression: sum(scenario_weight * Link_p_nom_ext * Link_capital_cost * Link_capital_weight)}
risk_weighted_opex: {expression: 'sum(scenario_weight * scenario_opex, over=scenario)'}
total_cost:
dims: []
expression: Link_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:
dims: [scenario, snapshot, load]
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`)
cases:
active: {when: Load_active, expression: Load_sign * Load_p_set}
otherwise: '0'
Generator_injection: {expression: 'sum(Generator_sign * Generator_p, over=generator, by=Generator_bus[bus])'}
Link_injection: {expression: '-sum(Link_p, over=link, by=Link_bus0[bus]) + sum(Link_output_arrival,
over=link_output, by=Link_output_bus[bus])'}
Load_injection: {expression: 'sum(Load_demand, over=load, by=Load_bus[bus])'}
Process_injection: {expression: 'sum(Process_output_arrival, over=process_output, by=Process_output_bus[bus])'}
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:
Link_com_ext: {condition: Link_committable AND Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0) AND
Link_active, 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'}
Link_committed: {condition: Link_committable AND Link_active, description: a committable link that stands
in the snapshot's period — every unit-commitment row's set}
Link_ramps_from_previous: {condition: 'position(snapshot, within=snapshot_period[period]) > 0 OR (position(snapshot)
== 0 AND (Link_status_initial == 0 OR Link_p_init))', description: 'a snapshot whose ramp reads
a previous output — any snapshot but its period''s first, and the horizon''s first where the link
comes in off or carries an initial output'}
Process_committed: {condition: Process_committable AND Process_active, description: a committable process
that stands in the snapshot's period — every unit-commitment row's set}
Process_ramps_from_previous: {condition: 'position(snapshot, within=snapshot_period[period]) > 0 OR
(position(snapshot) == 0 AND (Process_status_initial == 0 OR Process_p_init))', description: 'a
snapshot whose ramp reads a previous output — any snapshot but its period''s first, and the horizon''s
first where the process comes in off or carries an initial output'}
objective: {sense: minimize, expression: total_cost}
The prep — every table the spec declares, from the network — and the solve:
from differential.pypsa.prep import relation, static, varying, weighting
n = build() # the network from the PyPSA tab
sources = {
'snapshot': pl.Series('snapshot', list(timesteps(n)), dtype=pl.Datetime('us')),
'bus': pl.Series('bus', list(names(n.buses.index).astype(str)), dtype=pl.String),
**{
dim: pl.Series(dim, list(names(n.static(component).index).astype(str)), dtype=pl.String)
for component, dim in DIM.items()
},
**scenarios(n),
**periods(n, multi),
**carriers(n, multi),
'Generator_bus': relation(n, 'Generator', 'bus'),
'Link_bus0': relation(n, 'Link', 'bus0'),
'Load_bus': relation(n, 'Load', 'bus'),
'snapshot_weightings_objective': weighting(n, 'objective'),
'Generator_sign': per_component('Generator', first_scenario(n.generators['sign'])),
'Load_p_set': varying(n, 'Load', 'p_set'),
'Load_sign': per_component('Load', first_scenario(loads['sign'])),
'Load_active': per_component('Load', first_scenario(loads['active']), bool),
}
with sps.solve('differential/pypsa/rungs/rung_67_linearized_link_process.yaml', sources) as solution:
solution.objective # 47777.333333
The network, rung_67_linearized_link_process.py in the corpus — the spine plus what this rung adds:
# SPDX-FileCopyrightText: mathspec Contributors
#
# SPDX-License-Identifier: MIT
"""Rung 67: linearized commitment of a link and a process — both tightened where start and stop cost the same, and an extendable link the tightening skips."""
from __future__ import annotations
import spine
PATCH = 'variants/pypsa_linearized_uc.yaml'
OPTIMIZE = {'linearized_unit_commitment': True}
def build():
"""The spine plus an east bus that committable links and a process serve from the north, and a dear backup there."""
n = spine.build()
n.add('Bus', 'east')
n.add(
'Link',
'tie67',
bus0='north',
bus1='east',
committable=True,
p_nom=60,
p_min_pu=0.3,
marginal_cost=4,
min_up_time=2,
up_time_before=0,
ramp_limit_up=0.4,
ramp_limit_down=0.4,
ramp_limit_start_up=0.5,
ramp_limit_shut_down=0.5,
start_up_cost=30,
shut_down_cost=30,
)
n.add(
'Process',
'conv67',
bus0='north',
bus1='east',
rate0=-1.25,
committable=True,
p_nom=50,
p_min_pu=0.3,
marginal_cost=3,
min_up_time=2,
up_time_before=0,
ramp_limit_up=0.4,
ramp_limit_down=0.4,
ramp_limit_start_up=0.5,
ramp_limit_shut_down=0.5,
start_up_cost=20,
shut_down_cost=20,
)
n.add(
'Link',
'ext67',
bus0='north',
bus1='east',
committable=True,
p_nom_extendable=True,
p_nom_max=30,
capital_cost=5,
p_min_pu=0.2,
marginal_cost=2,
up_time_before=0,
start_up_cost=10,
shut_down_cost=10,
)
n.add('Generator', 'backup67', bus='east', p_nom=200, marginal_cost=400)
n.add('Load', 'east_load', bus='east', p_set=[10, 110, 120, 20])
return n
The data¶
The tables this rung is the first to declare (45), as the prep produced them:
Link_active_asset.csv
Link_big_m.csv
Link_capital_cost.csv
Link_capital_weight.csv
Link_min_up_time.csv
Link_modules_installed.csv
Link_p_init.csv
Link_p_min_pu_nonneg.csv
Link_p_nom_max.csv
Link_p_nom_min.csv
Link_ramp_limit_down.csv
scenario,snapshot,link,value
base,2015-01-01T00:00:00.000000,tie67,0.4
base,2015-01-01T01:00:00.000000,tie67,0.4
base,2015-01-01T02:00:00.000000,tie67,0.4
base,2015-01-01T03:00:00.000000,tie67,0.4
Link_ramp_limit_shut_down.csv
Link_ramp_limit_start_up.csv
Link_ramp_limit_up.csv
scenario,snapshot,link,value
base,2015-01-01T00:00:00.000000,tie67,0.4
base,2015-01-01T01:00:00.000000,tie67,0.4
base,2015-01-01T02:00:00.000000,tie67,0.4
base,2015-01-01T03:00:00.000000,tie67,0.4
Link_shut_down_cost.csv
scenario,snapshot,link,value
base,2015-01-01T00:00:00.000000,ext67,10.0
base,2015-01-01T00:00:00.000000,tie67,30.0
base,2015-01-01T00:00:00.000000,wire,0.0
base,2015-01-01T01:00:00.000000,ext67,10.0
base,2015-01-01T01:00:00.000000,tie67,30.0
base,2015-01-01T01:00:00.000000,wire,0.0
base,2015-01-01T02:00:00.000000,ext67,10.0
base,2015-01-01T02:00:00.000000,tie67,30.0
base,2015-01-01T02:00:00.000000,wire,0.0
base,2015-01-01T03:00:00.000000,ext67,10.0
base,2015-01-01T03:00:00.000000,tie67,30.0
base,2015-01-01T03:00:00.000000,wire,0.0
Link_stand_by_cost.csv
scenario,snapshot,link,value
base,2015-01-01T00:00:00.000000,ext67,0.0
base,2015-01-01T00:00:00.000000,tie67,0.0
base,2015-01-01T00:00:00.000000,wire,0.0
base,2015-01-01T01:00:00.000000,ext67,0.0
base,2015-01-01T01:00:00.000000,tie67,0.0
base,2015-01-01T01:00:00.000000,wire,0.0
base,2015-01-01T02:00:00.000000,ext67,0.0
base,2015-01-01T02:00:00.000000,tie67,0.0
base,2015-01-01T02:00:00.000000,wire,0.0
base,2015-01-01T03:00:00.000000,ext67,0.0
base,2015-01-01T03:00:00.000000,tie67,0.0
base,2015-01-01T03:00:00.000000,wire,0.0
Link_start_up_cost.csv
scenario,snapshot,link,value
base,2015-01-01T00:00:00.000000,ext67,10.0
base,2015-01-01T00:00:00.000000,tie67,30.0
base,2015-01-01T00:00:00.000000,wire,0.0
base,2015-01-01T01:00:00.000000,ext67,10.0
base,2015-01-01T01:00:00.000000,tie67,30.0
base,2015-01-01T01:00:00.000000,wire,0.0
base,2015-01-01T02:00:00.000000,ext67,10.0
base,2015-01-01T02:00:00.000000,tie67,30.0
base,2015-01-01T02:00:00.000000,wire,0.0
base,2015-01-01T03:00:00.000000,ext67,10.0
base,2015-01-01T03:00:00.000000,tie67,30.0
base,2015-01-01T03:00:00.000000,wire,0.0
Link_status_initial.csv
Process_active.csv
snapshot,process,value
2015-01-01T00:00:00.000000,conv67,true
2015-01-01T01:00:00.000000,conv67,true
2015-01-01T02:00:00.000000,conv67,true
2015-01-01T03:00:00.000000,conv67,true
Process_active_asset.csv
Process_committable.csv
Process_marginal_cost.csv
scenario,snapshot,process,value
base,2015-01-01T00:00:00.000000,conv67,3.0
base,2015-01-01T01:00:00.000000,conv67,3.0
base,2015-01-01T02:00:00.000000,conv67,3.0
base,2015-01-01T03:00:00.000000,conv67,3.0
Process_marginal_cost_quadratic.csv
scenario,snapshot,process,value
base,2015-01-01T00:00:00.000000,conv67,0.0
base,2015-01-01T01:00:00.000000,conv67,0.0
base,2015-01-01T02:00:00.000000,conv67,0.0
base,2015-01-01T03:00:00.000000,conv67,0.0
Process_min_up_time.csv
Process_modules_installed.csv
Process_output_bus.csv
Process_output_cyclic_delay.csv
Process_output_delay.csv
Process_output_process.csv
Process_p_init.csv
Process_p_max_pu.csv
scenario,snapshot,process,value
base,2015-01-01T00:00:00.000000,conv67,1.0
base,2015-01-01T01:00:00.000000,conv67,1.0
base,2015-01-01T02:00:00.000000,conv67,1.0
base,2015-01-01T03:00:00.000000,conv67,1.0
Process_p_min_pu.csv
scenario,snapshot,process,value
base,2015-01-01T00:00:00.000000,conv67,0.3
base,2015-01-01T01:00:00.000000,conv67,0.3
base,2015-01-01T02:00:00.000000,conv67,0.3
base,2015-01-01T03:00:00.000000,conv67,0.3
Process_p_nom.csv
Process_p_nom_extendable.csv
Process_ramp_limit_down.csv
scenario,snapshot,process,value
base,2015-01-01T00:00:00.000000,conv67,0.4
base,2015-01-01T01:00:00.000000,conv67,0.4
base,2015-01-01T02:00:00.000000,conv67,0.4
base,2015-01-01T03:00:00.000000,conv67,0.4
Process_ramp_limit_shut_down.csv
Process_ramp_limit_start_up.csv
Process_ramp_limit_up.csv
scenario,snapshot,process,value
base,2015-01-01T00:00:00.000000,conv67,0.4
base,2015-01-01T01:00:00.000000,conv67,0.4
base,2015-01-01T02:00:00.000000,conv67,0.4
base,2015-01-01T03:00:00.000000,conv67,0.4
Process_rate.csv
scenario,snapshot,process_output,value
base,2015-01-01T00:00:00.000000,conv67_bus0,-1.25
base,2015-01-01T00:00:00.000000,conv67_bus1,1.0
base,2015-01-01T01:00:00.000000,conv67_bus0,-1.25
base,2015-01-01T01:00:00.000000,conv67_bus1,1.0
base,2015-01-01T02:00:00.000000,conv67_bus0,-1.25
base,2015-01-01T02:00:00.000000,conv67_bus1,1.0
base,2015-01-01T03:00:00.000000,conv67_bus0,-1.25
base,2015-01-01T03:00:00.000000,conv67_bus1,1.0
Process_shut_down_cost.csv
scenario,snapshot,process,value
base,2015-01-01T00:00:00.000000,conv67,20.0
base,2015-01-01T01:00:00.000000,conv67,20.0
base,2015-01-01T02:00:00.000000,conv67,20.0
base,2015-01-01T03:00:00.000000,conv67,20.0
Process_stand_by_cost.csv
scenario,snapshot,process,value
base,2015-01-01T00:00:00.000000,conv67,0.0
base,2015-01-01T01:00:00.000000,conv67,0.0
base,2015-01-01T02:00:00.000000,conv67,0.0
base,2015-01-01T03:00:00.000000,conv67,0.0
Process_start_up_cost.csv
scenario,snapshot,process,value
base,2015-01-01T00:00:00.000000,conv67,20.0
base,2015-01-01T01:00:00.000000,conv67,20.0
base,2015-01-01T02:00:00.000000,conv67,20.0
base,2015-01-01T03:00:00.000000,conv67,20.0
Process_status_initial.csv
process.csv
process_output.csv